sensitivity analyses for spent fuel pool criticality— revision 1 · 2018. 4. 6. · epri project...

2017 TECHNICAL REPORT

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Sensitivity Analyses for Spent Fuel Pool Criticality—Revision 1

EPRI Project Manager H. Akkurt

3420 Hillview Avenue Palo Alto, CA 94304-1338 USA PO Box 10412 Palo Alto, CA 94303-0813 USA 800.313.3774 650.855.2121

[email protected] 3002008197 www.epri.com Final Report, November 2017

Sensitivity Analyses for Spent Fuel Pool Criticality–

Revision 1

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v

Abstract

The Nuclear Energy Institute (NEI) has issued a report entitled “Guidance for Performing Criticality Analyses of Fuel Storage at Light Water Reactor Power Plants” referred to as NEI 12-16, and submitted to the Nuclear Regulatory Commission (NRC) for review and endorsement in 2013. As part of the review process, four NRC/NEI public meetings with industry and EPRI participation were conducted between September 2013 and February 2014 to identify and reach a consensus on issues that are important for criticality safety analysis and that should be included in the guidance document.

The guidance document also identifies a number of parameters that may have negligible impact on reactivity and can therefore be excluded from future criticality analyses. Subsequently, these low worth items were discussed in order to reach a consensus and to provide technical justification for elimination in future applications by performing sensitivity analyses and documenting the results. For this purpose, a series of computations were performed to demonstrate the effect of many parameters such as manufacturing tolerances, the amount of boron margin needed to offset a number of uncertainties in tolerances, recommended modeling approaches for consistency purposes, and the impact of other parameters such as eccentric positioning, concrete composition, and pool temperature. The analyses were performed for representative rack geometries, fuel types, and varying burnup and enrichment values to cover wide ranges. The computations were performed using SCALE 6.1.2 with ENDF/B-VII libraries. This report describes the range of parameters investigated as well as results of the sensitivity analyses performed in support of NEI 12-16 Criticality Guidance document.

Keywords Burnup credit NEI 12-16 Spent fuel pool criticality Used fuel

EXECUTIVE SUMMARY

vii

Deliverable Number: 3002008197 Product Type: Technical Report

Product Title: Sensitivity Analyses for Spent Fuel Pool Criticality—Revision 1

PRIMARY AUDIENCE: Nuclear criticality safety analysts at nuclear power plants and regulators SECONDARY AUDIENCE: Nuclear criticality safety analysts at research organizations and vendors

KEY RESEARCH QUESTION

The Nuclear Energy Institute (NEI), with EPRI and industry participation, prepared a report titled “Guidance for Performing Criticality Analyses of Fuel Storage at Light-Water Reactor Power Plants,” referred as NEI 12-16. The objectives of the criticality guidance document are to 1) define the methods and approaches to be used in criticality analysis; 2) describe the simplifying assumptions and associated justifications; and 3) provide guidance for spent fuel pool (SFP) criticality safety analysis for improved consistency, clarity, and completeness. The key question for this study was to identify, evaluate, and demonstrate whether or not the impact of certain parameters on criticality analysis are negligible and therefore can be ignored in future analyses.

RESEARCH OVERVIEW

The criticality guidance document was submitted to the U.S. Nuclear Regulatory Commission (NRC) in 2013, and four NRC/NEI public meetings with industry and EPRI participation were conducted between September 2013 and February 2014. The culmination of discussions at these meetings led to the identification of a set of items requiring further analysis. In support of the guidance document, sensitivity analyses were performed to determine the impact of certain parameters on the criticality analysis and to provide technical justification on low worth items that have a negligible impact on reactivity, and therefore, do not require analysis in future applications. The analyses were performed using Westinghouse 17x17 fuel, two representative rack geometries, three neutron absorber areal density values, and varying enrichment and burnups. The goal was to ensure that results are applicable for a wide range of problems and analyses. For a subset of these parameters, computations were repeated using Combustion Engineering 16x16 fuel to demonstrate that the results and conclusions are independent of fuel type. Subsequently, more than 1000 calculations were performed to clarify or provide technical justification for a number of assumptions and to avoid repetition of analyses for low worth items with each application. The computations were performed using SCALE 6.1.2 with the ENDF/B-VII cross section libraries.

KEY FINDINGS • Modeling the in-core measurement thimbles produces a small, but non-negligible effect on reactivity.

Therefore, in-core measurement thimbles should be modeled in the analysis instead of using margin to compensate for this effect.

• Manufacturing tolerances on the guide tube and instrument tubes have negligible impact on the reactivity values; hence, no further analysis is required. Similarly, manufacturing tolerances for the cladding inner diameter (or thickness) have a negligible effect on the computed reactivity and can be neglected in future analysis.

EXECUTIVE SUMMARY

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• In order to reduce calculations for the borated portion of the criticality analysis, analysts may reserve50 ppm soluble boron margin to offset the change in the uncertainties from the unborated analyses aswell as the worth of the fuel spacer grids. This amount can be added to the required soluble boronconcentration for accident cases.

• The reactivity effect of the manufacturing tolerances on neutron absorber panel sheathing is negligiblefor Region 2 racks that credit absorber panels and no further analysis is required.

• A separation of 25 cm is sufficient for neutronic decoupling of assemblies. Based on the computationalresults, it is concluded that PWR racks having an empty row of cells between regions do not requireinterface analysis.

• Based on the previous studies and computations provided in this report, it is concluded that ignoringgadolinium in the criticality safety analysis is conservative.

WHY THIS MATTERS

The generic conclusions provided in this report are used in criticality guidance document. This allows avoidance of repeating the same analysis on a specific plant basis and impacts analyst’s and reviewer’s time.

HOW TO APPLY RESULTS

Some of the conclusions reached in this report provide the technical justification in individual analysis to demonstrate that the impact of certain parameters on criticality analysis are negligible and therefore can be ignored in future analyses.

LEARNING AND ENGAGEMENT OPPORTUNITIES • This report, along with NEI 12-16, Guidance for Performing Criticality Analyses of Fuel Storage at Light-

Water Reactor Power Plants, provides additional resources for complete spent fuel criticality analysis.

EPRI CONTACTS: Hatice Akkurt: Senior Project Manager, Used Fuel and HLW Management Program, [email protected].

PROGRAM: Used Fuel and HLW Management Program, Program 41.03.01

IMPLEMENTATION CATEGORY: Reference

ix

Table of Contents

Section 1: Introduction ........................................ 1-1

Section 2: Description of Models and Reference Cases ................................................. 2-1

2.1 Description of Fuel Assembly ................................. 2-1 2.2 Description of Rack Geometries ............................. 2-2 2.3 Computer Code, Nuclear Data, and Models ........... 2-5

2.3.1 Depletion Model .......................................... 2-5 2.3.2 Rack Models ............................................... 2-9

2.4 Description of the Reference Cases ...................... 2-10

Section 3: Impact of In-Core Detector Measurement Thimble on Depletion Reactivity ........................................... 3-1

Section 4: Reactivity Effect of Fuel Manufacturing Tolerances .......................................... 4-1

4.1 Guide Tube Manufacturing Tolerance ..................... 4-2 4.2 Fuel Cladding Inner Diameter Manufacturing Tolerance .................................................................. 4-5

Section 5: Considerations When Crediting Soluble Boron ................................................. 5-1

5.1 Impact of Modeling the Grid Spacer ...................... 5-1 5.2 Changes in Uncertainties with Soluble Boron Content ................................................................... 5-10

5.2.1 Validation, Burnup Record, and Depletion Uncertainties ...................................................... 5-10 5.2.2 Changes in Uncertainties Due to Fuel Tolerances ......................................................... 5-13 5.2.3 Changes in Uncertainties Due to Rack Tolerances ......................................................... 5-18 5.2.4 Statistical Combination of Uncertainties From Manufacturing Tolerances .................................... 5-21

5.3 Recommendation for Soluble Boron Margin .......... 5-23

x

Section 6: Reactivity Effect of the Neutron Absorber Sheathing Tolerance ............ 6-1

Section 7: Distance Required for Neutronic Decoupling of Assemblies ................... 7-1

Section 8: Impact of Finite Versus Infinite Array Modeling on Reactivity ....................... 8-1

Section 9: Impact of Eccentric Positioning of Fuel in the Rack Cells on Reactivity ............. 9-1

9.1 Analysis of Racks with Full Eccentric Positioning ....... 9-1 9.2 Modeling Partial Eccentric Loading ........................ 9-6 9.3 Recommendation for Eccentricity Reactivity ............. 9-8

Section 10: Impact of Concrete Composition on Reactivity ........................................ 10-1

Section 11: Impact of Pool Temperature on Reactivity ........................................ 11-1

Section 12: Impact of Gadolinium Burnable Absorbers on Spent Fuel Reactivity .. 12-1

Section 13: Summary and Conclusions .............. 13-1

Section 14: References ...................................... 14-1

Appendix A: Electronic Data ............................... A-1

xi

List of Figures

Figure 2-1 Cross section of a typical PWR Region 1 rack ..... 2-3

Figure 2-2 Cross section of a typical PWR Region 2 rack ..... 2-4

Figure 2-3 Diagram of a WABA rod in a guide tube ........... 2-8

Figure 2-4 Region 1, flux trap, KENO Model with W 17x17 Fuel .......................................................................... 2-9

Figure 2-5 Region 2 KENO model with CE 16x16 Fuel ..... 2-10

Figure 3-1 The difference in reactivity (Δk) due to modeling the measurement thimble ............................................. 3-5

Figure 5-1 Reactivity effect of spacer grid as a function of soluble boron concentration (Region 2, 0.015 g 10B/cm2) ................................................................... 5-6

Figure 7-1 Reference model for the separation analysis ........ 7-2

Figure 7-2 Model for the separation analysis with a 10 cm gap .......................................................................... 7-2

Figure 7-3 Model for the infinite separation (vacuum boundary conditions) .................................................. 7-3

Figure 7-4 Neutron multiplication factor as a function of the distance between sets of assemblies ............................. 7-4

Figure 8-1 Model for three assemblies in an empty Region 1 ................................................................... 8-5

Figure 8-2 Model for five assemblies in an empty Region 1 ................................................................... 8-5

Figure 8-3 Model for eight assemblies in an empty Region 1 ................................................................... 8-6

Figure 8-4 Ratio of finite model multiplication factor to infinite array multiplication factor for 5% enrichment and zero burnup values ..................................................... 8-6

Figure 9-1 Impact of eccentric loading on reactivity as a function of the number of eccentrically loaded assemblies................................................................. 9-7

xii

Figure 10-1 SCALE model for the concrete analysis ........... 10-2

Figure 11-1 Change in reactivity with temperature for Region 1 and Region 2 racks without neutron absorbers ................................................................ 11-2

Figure 11-2 Change in reactivity with temperature for under-moderated racks containing neutron absorbers ............ 11-3

Figure 12-1 Reactivity effect of Gadolinium ...................... 12-3

Figure 12-2 Non-fission product 154Gd content as a function of burnup ................................................................ 12-4


Figure 12-4 Non-fission produced 156Gd content as a function of burnup .................................................... 12-5


xiii

List of Tables

Table 2-1 Fuel Dimensions (cm) ......................................... 2-1

Table 2-2 Absorber plate compositions .............................. 2-5

Table 2-3 Isotope set followed after shutdown ..................... 2-6

Table 2-4 Depletion assumptions ....................................... 2-7

Table 2-5 Burnable absorber description (dimensions in cm) 2-8

Table 2-6 Computed multiplication factors, k, for Region 1 reference cases ........................................................ 2-11

Table 2-7 Computed multiplication factors, k, for Region 2 reference cases ........................................................ 2-12

Table 3-1 Voided instrument tube depletion results for Region 1 with W 17x17 fuel ....................................... 3-2

Table 3-2 Voided instrument tube depletion results for Region 1 with CE 16x16 fuel ...................................... 3-2

Table 3-3 Voided instrument tube depletion results for Region 2 with W 17x17 fuel ....................................... 3-3

Table 3-4 Voided instrument tube depletion results for Region 2 with CE 16x16 fuel ...................................... 3-4

Table 4-1 Reactivity effect due to guide tube tolerance for Region 1 ................................................................... 4-3

Table 4-2 Reactivity effect due to guide tube tolerance for Region 2 ................................................................... 4-4

Table 4-3 Reactivity effect of cladding inner diameter tolerance for Region 1 ................................................ 4-6

Table 4-4 Reactivity effect of cladding inner diameter tolerance for Region 2 ................................................ 4-7

Table 5-1 Reactivity effect of spacer grid at 2000 ppm for Region 1 ................................................................... 5-2

xiv




Table 5-5 Reactivity effect of soluble boron concentration at 2000 ppm in Region 1 ............................................... 5-7

Table 5-6 Reactivity effect of soluble boron concentration and grid worth (ppm) at 2000 ppm for W 17x17 fuel in Region 2 ................................................................... 5-8

Table 5-7 Reactivity effect of soluble boron concentration and grid worth (ppm) at 2000 ppm for CE 16x16 fuel in Region 2 ............................................................... 5-9

Table 5-8 Change in reactivity with burnup at 0 and 2000 ppm soluble boron rack conditions for W 17x17 fuel .. 5-11

Table 5-9 Change in reactivity with burnup at 0 and 2000 ppm soluble boron rack conditions for CE 16x16 fuel .. 5-12

Table 5-10 Change in reactivity due to increase of fuel pellet diameter to its tolerance limit ............................ 5-14

Table 5-11 Change in reactivity due to increased enrichment of fuel to its tolerance limit ........................ 5-15

Table 5-12 Change in reactivity due to reduction of cladding outer diameter to its tolerance limit ............... 5-16

Table 5-13 Change in reactivity due to increased fuel pin pitch ....................................................................... 5-17

Table 5-14 Change in reactivity due to decreased cell pitch to its tolerance limit .................................................. 5-19

Table 5-15 Change in reactivity due to decreased cell wall thickness to its tolerance limit ..................................... 5-20

Table 5-16 Statistically combined manufacturing tolerance reactivities ............................................................... 5-22

Table 5-17 Summary of the potential bias due to using unborated uncertainties and ignoring the grid for high soluble boron cases (2000 ppm) ............................... 5-24

Table 6-1 Reactivity effect of sheathing tolerance for Region 1 configurations ......................................................... 6-2

xv

Table 6-2 Reactivity effect of sheathing tolerance for Region 2 configurations ......................................................... 6-3

Table 7-1 Computed neutron multiplication factor as a function of separation for selected cases ....................... 7-4

Table 7-2 Ratio of the neutron multiplication factor at a distance to the infinite separation neutron multiplication factor for each case ................................................... 7-5

Table 8-1 Ratio of neutron multiplication factor for a finite number of assemblies to an infinite model in Region 1 (vacuum boundary condition) ...................................... 8-3

Table 8-2 Ratio of neutron multiplication factor for a finite number of assemblies to an infinite model in Region 2 (vacuum boundary condition) ...................................... 8-4

Table 8-3 Ratio of neutron multiplication factor of a small set of assemblies to an infinite set (water reflected) ............. 8-7

Table 9-1 Reactivity effect due to eccentric loading using a 20x20 model for Region 1 .......................................... 9-2

Table 9-2 Reactivity effect due to eccentric loading using a 20x20 model for Region 2 .......................................... 9-3

Table 9-3 Reactivity effect due to eccentric loading as a function of model size for Region 1 .............................. 9-5

Table 9-4 Reactivity effect due to eccentric loading as a function of model size for Region 2 .............................. 9-6

Table 10-1 Elemental compositions of the SCALE supplied concretes ................................................................ 10-1

Table 10-2 Reactivity effect of increasing water gap between the rack and the SFP wall (Rocky Flats Concrete) ................................................................ 10-3

Table 10-3 Reactivity effect of different concrete compositions ........................................................... 10-3

Table 10-4 Comparison of Concrete Made of Single Elements ................................................................. 10-4

Table 10-5 Elemental compositions of the conservative concrete .................................................................. 10-5

Table 11-1 Water density at 2 atm .................................. 11-2

xvi

Table 12-1 Fuel assembly data for M1–M4 assembly designs ................................................................... 12-2

Table 12-2 Volume-averaged enrichments for Siemens fuel . 12-2

1-1

Section 1: Introduction In 2013, the Nuclear Energy Institute (NEI) issued “Guidance for Performing Criticality Analyses of Fuel Storage at Light-Water Reactor Power Plants,” which is referred as NEI 12-16 [1]. The primary objectives of the NEI 12-16 criticality guidance document are to:

1. Define the methods and approaches to be used in criticality analysis

2. Describe the simplifying assumptions and associated justifications

3. Provide improved clarity, completeness, and consistency for spent fuel pool (SFP) criticality safety analysis.

For this purpose, four NRC/NEI public meetings with industry and EPRI participation were conducted between September 2013 and February 2014 to identify important and negligible parameters. One objective of these meetings was to identify and reach a consensus on low worth parameters that have negligible impact on criticality analyses. The ultimate goal was to provide technical justification for these low worth parameters and subsequently eliminate the need to repeat analysis for every application by referring to this document.

The first meeting focused on the fuel assembly, while the second meeting focused on issues around the storage rack and neutron absorbers. During the third meeting, the emphasis was on criticality code benchmarking. The focus of the last meeting was burnup credit and depletion uncertainty. Summaries of each of these meeting can be found in references [2-5] and presentation materials from each meeting can be found in references [6-9].

During these meetings, a series of items were identified for further sensitivity analyses to provide technical justification for simplifying assumptions in order to demonstrate that certain parameters have negligible impact on reactivity and therefore require no further analysis.

The purpose of this report is to provide technical justification for items that were discussed and identified as requiring further analysis to reach generic conclusions. This report presents the results of sensitivity analyses by providing computational results and analyses for clarification and justification purposes. Subsequently, the report aims to reach a generic resolution for demonstration of negligible items and identification of non-negligible items in criticality analyses.

This report is organized as follows: Section 2 presents a description of the problem parameters, including fuel, rack geometry, the simulation code and cross

1-2

sections used in the analysis, and the computed reactivity values for the reference cases. The impact of measurement thimbles on the computed reactivity values is discussed in Section 3. Computational results demonstrating the negligible impact of manufacturing tolerances for guide tube and cladding inner diameter on SFP reactivity are presented in Section 4. Section 5 provides computational results and analysis to address biases and uncertainties under borated conditions. The impact of neutron absorber panel sheathing uncertainties is presented in Section 6. Section 7 provides computational results to address the question of how much space is needed between assemblies to fully neutronically decouple them. Section 8 investigates the sensitivity to geometric modeling by analyzing the number of assemblies needed to produce a reactivity equivalent to an infinite array. The impact of eccentric positioning, compared to centered positioning is discussed in Section 9. The effects of concrete composition and pool temperature on reactivity are discussed in Sections 10 and 11, respectively. Section 12 provides a discussion on the impact of Gadolinium burnable absorbers on spent fuel reactivity. The summary and conclusions of this study are presented in Section 13.

2-1

Section 2: Description of Models and Reference Cases

This section presents descriptions of modeling parameters, including fuel, rack geometry, simulation codes, and nuclear data used for these analyses. The computed neutron multiplication factors, k, for the reference cases are presented at the end of this section.

2.1 Description of Fuel Assembly

The reference fuel for this analysis is one of the Westinghouse 17x17 fuel assembly designs, referred to as W 17x17 from this point forward. For sensitivity analyses, this fuel is selected as the base fuel since it is the most commonly used pressurized water reactor (PWR) fuel. Currently, it is used in 34 of the 65 PWRs in the United States. It is also the fuel used for the depletion reactivity benchmarks produced by EPRI [10]. In order to demonstrate that results presented in this report are not fuel type dependent, a subset of analyses were also performed using Combustion Engineering 16x16 fuel assembly, referred as CE 16x16 from this point forward. The dimensions for the W 17x17 [10] and CE 16x16 [11] fuels are presented in Table 2-1.

Table 2-1 Fuel Dimensions (cm)

W 17x17 CE 16x16

Assembly Pitch 21.5036 20.7772

Fuel Pin Pitch 1.2598 1.28524

Pellet OD 0.8192 0.82550

Cladding ID 0.836 0.84328

Cladding OD 0.950 0.97028

Guide Tube ID 1.122 2.286

Guide Tube OD 1.224 2.4892

2-2

2.2 Description of Rack Geometries

Many spent fuel pools are divided into two regions: 1) a flux trap region, often called Region 1, and 2) a tightly spaced region, referred to as Region 2. These racks are generally designed with neutron absorber panels with a 10B areal density varying from 0.01 to 0.03 g 10B/cm2. Figure 2-1 shows a cross section of a typical PWR Region 1 fuel rack, used for high reactivity, fresh (unirradiated) fuel. This design provides for two plates of absorber between each cell separated by a water gap. The cross section of a typical Region 2 rack is illustrated in Figure 2-2. This region is used to store fuel with lower reactivity. In this design, there is only one absorber plate between fuel assemblies. All of the materials, except the neutron absorber panels, are made of stainless steel.

The Region 2 rack design has locations for fuel inside and between stainless steel tubes. The spaces between the tubes are called resultant cells. Since Region 2 racks are not symmetric around a single cell, a 2x2 model is required. In order to create a model that allows the assembly to be placed anywhere in the cell (or resultant cell) periodic boundary conditions rather than reflective boundary conditions are required.

Seven rack configurations were used in the analysis. For both the Region 1 and Region 2 racks, areal densities of 0.0, 0.015, and 0.03 g 10B/cm2 were used. In addition to these six configurations, the Region 2 rack design with zero areal density was configured in a checkerboard design of fresh fuel and empty storage cells.

The absorber material is modeled as a homogeneous mixture of Al and B4C. The amount of B4C is established by the 10B areal density. The zero areal density case uses pure Al with a density of 2.65 g/cm3 for the absorber plates. Table 2-2 provides the atom densities and weight percentages (wt%) for the plates with 0.015 and 0.030 g 10B/cm2 areal densities, assuming 19.9 atom percent 10B abundance.

2-3

Detail A

Figure 2-1 Cross section of a typical PWR Region 1 rack

2-4

Detail A

Figure 2-2 Cross section of a typical PWR Region 2 rack

Gap

2-5

Table 2-2 Absorber plate compositions

0.015 g 10B/cm2

Areal Density 0.030 g 10B/cm2

Areal Density

Atoms/barn-cm wt.% Atoms/barn-cm wt.% 10B 0.00710218 0.0445612 0.0142044 0.0891223 11B 0.0285872 0.197212 0.0571743 0.394425

C 0.00892234 0.0671506 0.0178447 0.134301

Al 0.0408748 0.691076 0.0226030 0.382151

2.3 Computer Code, Nuclear Data, and Models

Computations were performed using SCALE 6.1.2 with the 238-group ENDF/B-VII cross section library [12]. Analyses consist of two steps: depletion analysis and criticality calculation.

2.3.1 Depletion Model

The depletion model uses SCALE’s TRITON t5-depl sequence. This TRITON sequence begins with treating the cross sections for unresolved and resolved resonances with BONAMI and CENTRM. This is followed by use of KENO-V.a for the flux calculation used to collapse the cross sections to one energy group. The one-group cross sections are then used in ORIGEN to predict the isotopic content as a function of burnup. The depletion model is a two-dimensional analysis of an assembly in the core (includes the inter assembly gap).

TRITON allows the user to select the number of isotopes to carry through the depletion via the “addnux” parameter. For this analysis, the addnux parameter was set to 4, which means the maximum number of isotopes, 388, is used. The assumed cooling time after the assembly depletion is 100 hours, which is selected to be representative of the maximum reactivity. Since SCALE 6.1 does not output isotopic data for burnups after cooling for less than the maximum specified burnup, a short program was used to correct the isotopic inventory due to radioactive decay for 100 hours at the desired burnups. Many of the 388 isotopes in the addnux=4 set are for structural materials rather than fission products. Of the 388 isotopes, only 185 have any significant impact on keff. These 185 isotopes are collected from the SCALE/TRITON output using the OPUS module. The 185 isotopes are listed in Table 2-3. All of the radioactive isotopes in the 185 isotope set were decayed. Isotopes with atom densities less than 1E-12 atoms per barn cm are not included in the analysis since the impact would be negligible. Finally, Sm-149 is in equilibrium with Pm-149. The Pm-149 atom density is cut in half before decaying to Sm-149 to represent 50% power operation at the end of life.

2-6

Table 2-3 Isotope set followed after shutdown

Isotope Isotope Isotope Isotope Isotope Isotope Isotope

Ag-109 Cm-243 Gd-160 Nd-145 Rb-85 Sm-153 Te-130

Ag-110m Cm-244 Ge-73 Nd-146 Rb-86 Sm-154 Te-132

Ag-111 Cm-245 Ge-76 Nd-147 Rb-87 Sn-115 U-234

Am-241 Cm-246 Ho-165 Nd-148 Rh-103 Sn-116 U-235

Am-242m Cs-133 I-127 Nd-150 Rh-105 Sn-117 U-236

Am-243 Cs-134 I-129 Np-237 Ru-100 Sn-118 U-237

As-75 Cs-135 I-131 Np-238 Ru-101 Sn-119 U-238

Ba-134 Cs-136 I-135 Np-239 Ru-102 Sn-120 Xe-128

Ba-135 Cs-137 In-115 O-16 Ru-103 Sn-122 Xe-129

Ba-136 Dy-160 Kr-82 Pd-104 Ru-104 Sn-123 Xe-130

Ba-137 Dy-161 Kr-83 Pd-105 Ru-105 Sn-124 Xe-131

Ba-138 Dy-162 Kr-84 Pd-106 Ru-106 Sn-125 Xe-132

Ba-140 Dy-163 Kr-85 Pd-107 Ru-99 Sn-126 Xe-133

Br-81 Dy-164 Kr-86 Pd-108 Sb-121 Sr-86 Xe-134

Cd-110 Er-166 La-138 Pd-110 Sb-123 Sr-88 Xe-135

Cd-111 Eu-151 La-139 Pm-147 Sb-124 Sr-89 Xe-136

Cd-112 Eu-152 La-140 Pm-148 Sb-125 Sr-90 Y-89

Cd-113 Eu-153 Mo-100 Pm-148m Se-76 Tb-159 Y-90

Cd-114 Eu-154 Mo-95 Pm-149 Se-77 Tb-160 Y-91

Cd-115m Eu-155 Mo-96 Pm-151 Se-80 Tc-99 Zr-91

Cd-116 Eu-156 Mo-97 Pr-141 Se-82 Te-122 Zr-93

Ce-140 Gd-152 Mo-98 Pr-143 Sm-147 Te-124 Zr-95

Ce-141 Gd-154 Mo-99 Pu-238 Sm-148 Te-125 Zr-96

Ce-142 Gd-155 Nb-95 Pu-239 Sm-149 Te-126

Ce-143 Gd-156 Nd-142 Pu-240 Sm-150 Te-127m

Ce-144 Gd-157 Nd-143 Pu-241 Sm-151 Te-128

Cm-242 Gd-158 Nd-144 Pu-242 Sm-152 Te-129m

The depletion analysis requires a number of assumptions about the conditions in the power reactor. Traditionally, conservative or bounding assumptions are used. For this analysis typical assumptions are made. Table 2-4 lists the depletion assumptions.

2-7

Table 2-4 Depletion assumptions

Parameter W 17x17 Depletion

CE 16x16 Depletion

Specific Power (W/g of heavy metal) 38.1 38.1

Pellet Density (g/cm3) 10.34 10.34

Fuel Temperature (K) 1050 1050

Moderator Temperature(K) 616 616

Moderator Density (g/cm3) 0.60208 0.60208

Soluble Boron (ppm) 900 1200

Removable Burnable Absorber 20 finger WABA None

Fixed Burnable Absorber 104 IFBA rods None

As a common practice in criticality analysis, no credit is given for residual burnable absorbers; consequently, they are not included in the modeling after the fuel assembly is depleted. Many criticality analysts credit integral fuel burnable absorbers (IFBAs) in fresh fuel; however, these cases are not included in this analysis. Instead, burnable absorbers are used in the depletion analysis. The long cycles now used in PWRs require burnable absorbers to ensure a negative moderator temperature coefficient and to reduce the power peaking at low burnups. The depletion analysis used for this report assumes that the W 17x17 fuel was depleted with a 20-fingered wet annular burnable absorber (WABA) and 104 IFBA rods. The depletion model is the same as Case 7 of the depletion reactivity benchmarks [10]. Table 2-5 provides the physical description of the burnable absorbers, and Figure 2-3 provides the geometry of the WABA. The radial positioning of the 104 IFBA rods in the assembly can be found in Figure 2-4. To date, a wide range of integral burnable absorbers have been employed in CE fuel: Gd, Er, and Boron coatings. For this analysis, the CE 16x16 fuel was depleted without burnable absorbers.

The flux used to collapse the cross sections is averaged over user-specified materials. Since the flux spectrum is harder in IFBA rods, for W 17x17 fuel, two different material compositions are used for the average fluxes, IFBA rods and non-IFBA rods. These two material compositions then result in two different atom density sets in the rack model. The impact of using a single depletion zone or two was determined to have a negligible reactivity effect. For CE fuel, all of the fuel rods were assumed to be the same enrichment and were averaged together.

2-8

Table 2-5 Burnable absorber description (dimensions in cm) [10]

Parameter

WABA Inner Cladding Inner Radius 0.286

WABA Inner Cladding Outer Radius 0.339

WABA Pellet Inner Radius 0.353

WABA Pellet Outer Radius 0.404

WABA Outer Cladding Inner Radius 0.418

WABA Outer Cladding Outer Radius 0.484

WABA Pellet Atom Densities

C (atoms/barn-cm) 0.00140923

O (atoms/barn-cm) 0.0623784

Al (atoms/barn-cm) 0.0415904 10B (atoms/barn-cm) 0.0029903

IFBA Coating Thickness 0.001

IFBA Coating Atom Densities

Zr (atoms/barn-cm) 0.0322187 10B (atoms/barn-cm) 0.0215913

Figure 2-3 Diagram of a WABA rod in a guide tube

2-9

2.3.2 Rack Models

For the rack models, the SCALE sequence CSAS5 was used. This sequence calls upon BONAMI and CENTRM for the cross section processing followed by KENO V.a for the criticality calculation. For all of the analysis, 2000 generations and 8000 neutrons per generation were used. This produces a Monte Carlo one sigma uncertainty of about 0.0002.

For Region 1 rack analysis, a single cell with periodic boundary conditions was modeled. Figure 2-4 shows this model with burned W 17x17 fuel. The light blue and red circles on Figure 2-4 represent fuel rods without or with IFBA coatings, respectively. The guide tubes are empty since the WABAs used in the depletion analysis are removed for the rack analysis.

Figure 2-4 Region 1, flux trap, KENO Model with W 17x17 Fuel

For Region 2 modeling, a 2x2 representation with periodic boundary conditions is used. In this model, a rack tube with its absorber plates is placed in the lower left of the model and the rest of the model is built upon it. As shown in Figure 2-5, Region 2 model requires slicing through the cell wall for the edges of the model.

2-10

Figure 2-5 Region 2 KENO model with CE 16x16 Fuel

2.4 Description of the Reference Cases

Computations were performed for two rack geometry models, specifically Region 1 and 2, as discussed in Section 2.3. For each rack design, analyses were performed for a set of neutron absorber 10B areal densities, fuel enrichments, and burnup selected to capture and represent the variation in these values. Furthermore, they were used to determine if any areal density, enrichment, or burnup dependent trends exist.

Table 2-6 shows parameters for the 12 Region 1 cases as well as the calculated multiplication factors, k, for these reference cases. Similarly, Table 2-7 shows the parameters for the 32 Region 2 reference cases and corresponding calculated multiplications factors, k. The last case is a checkerboard of fresh fuel assemblies and empty storage cells, where the assemblies in the resultant cells were removed.

The remainder of this report presents the difference in reactivity between the individual case and the reference case (Δk).

2-11

Table 2-6 Computed multiplication factors, k, for Region 1 reference cases

Areal Density (g 10B/cm2)

Enrichment (wt% 235U)

Burnup (GWd/MTU)

W 17x17 k

CE 16x16 k

0 2 0 1.01342 0.96109

0 3.5 0 1.16627 1.10426

0 3.5 20 1.01987 0.95572

0 3.5 40 0.91530 0.85059

0 5 0 1.24480 1.18118

0 5 20 1.10157 1.04043

0 5 40 0.99702 0.93511

0.015 3.5 0 0.90060 0.87646

0.015 3.5 10 0.83603 0.80670

0.015 5 0 0.96671 0.93918

0.015 5 10 0.90007 0.87265

0.03 5 0 0.94097 0.91764

2-12

Table 2-7 Computed multiplication factors, k, for Region 2 reference cases



Burnup (GWd/MTU)

W 17x17 k

CE 16x16 k

0 2 0 1.20915 1.16744

0 3.5 0 1.37180 1.33119

0 3.5 20 1.18714 1.14562

0 3.5 30 1.11926 1.07674

0 3.5 40 1.06171 1.01773

0 5 0 1.45144 1.41305

0 5 30 1.20877 1.17501

0 5 40 1.14886 1.11367

0 5 60 1.04731 1.00760

0.015 2 0 0.99275 0.95765

0.015 3.5 0 1.15132 1.10982

0.015 3.5 10 1.06985 1.02256

0.015 3.5 20 1.00407 0.95575

0.015 3.5 30 0.94720 0.89814

0.015 3.5 40 0.89886 0.84913

0.015 5 0 1.23502 1.18991

0.015 5 20 1.08816 1.04365

0.015 5 30 1.03219 0.98715

0.015 5 40 0.98075 0.93424

0.015 5 60 0.89289 0.84447

0.03 2 0 0.96239 0.92995

0.03 3.5 0 1.11593 1.07776

0.03 3.5 10 1.03650 0.99307

0.03 3.5 20 0.97370 0.92810

0.03 3.5 30 0.91849 0.87224

0.03 3.5 40 0.87138 0.82435

0.03 5 0 1.19740 1.15575

0.03 5 20 1.05539 1.01298

0.03 5 30 1.00053 0.95819

0.03 5 40 0.95081 0.90727

0.03 5 60 0.86566 0.82019

Checkerboard (0 areal density)

5 0 1.01846 0.94346

3-1

Section 3: Impact of In-Core Detector Measurement Thimble on Depletion Reactivity

In PWRs, the in-core 235U fission rate distribution is measured to confirm peak power is less than the established safety limits. To monitor peak power, about a third of the assemblies have a measurement thimble placed in the instrument tube at the center of the assembly. In most Westinghouse plants, fission detectors are moved within the thimbles, but the thimbles are fixed during the operating cycle. The measurement thimbles are filled primarily with gas.

The measurement thimbles are part of the reactor system and are not in the assembly when transferred to the pool. The measurement thimbles are about 0.8 cm (~0.315 in) in diameter [13] and there is only one per assembly. However, the measurement thimbles displace water, which causes spectrum hardening during depletion. Consequently, the fuel surrounding the thimble cell becomes more reactive for a given burnup. Traditionally, these thimbles have been ignored while performing the criticality safety analysis since it was assumed that their impact on reactivity would be negligible. This section documents an investigation of the validity of this assumption.

In order to determine the reactivity effect of these thimbles, depletion analyses were performed using W 17x17 and CE 16x16 fuels with and without a measurement thimble. In the case of the Westinghouse fuel, it was assumed that the entire instrument tube was voided to simulate the presence of a measurement thimble. This is conservative since the instrument tube ID is 1.143 cm (~0.450 in), and the measurement thimble is about 0.8 cm (~0.315 in) (about 60% of the volume). Further, only about a third of the assemblies have measurement thimbles. The CE 16x16 depletion assumed a 1.016 cm (~0.400 in) diameter void in the center of the central guide tube.

The computed reactivity values for the voided instrument tube depletion and the difference between voided and unvoided tubes for Region 1 racks with W 17x17 and CE 16x16 fuels are presented in Table 3-1 and Table 3-2, respectively. The same results for Region 2 with W 17x17 and CE 16x16 fuels are listed in Table 3-3 and Table 3-4, respectively. The Monte Carlo uncertainty for each case is less than 0.0002. The differences in reactivity between the two KENO calculations (Δk) for voided versus unvoided tubes are illustrated in Figure 3-1.

3-2

As shown in the figure and tables, the change in reactivity increases with increasing burnup. Although the reactivity is small, non-negligible reactivities (greater than 50 pcm for some cases) have been found for a subset of the cases. Therefore, it is recommended that measurement thimbles should be included in future analysis and modeled as a void in the calculations

Table 3-1 Voided instrument tube depletion results for Region 1 with W 17x17 fuel



Burnup (GWd/MTU)

Voided IT Depletion k

Δk From Unvoided Depletion

0 3.5 20 1.01987 0.0000

0 3.5 40 0.91612 0.0008

0 5 20 1.10200 0.0004

0 5 40 0.99725 0.0002

0.015 3.5 10 0.83613 0.0001

0.015 5 10 0.90039 0.0003

Table 3-2 Voided instrument tube depletion results for Region 1 with CE 16x16 fuel



Burnup (GWd/MTU)



0 3.5 20 0.95606 0.0003

0 3.5 40 0.85161 0.0010

0 5 20 1.04079 0.0004

0 5 40 0.93599 0.0009

0.015 3.5 10 0.80671 0.0000

0.015 5 10 0.87288 0.0002

3-3

Table 3-3 Voided instrument tube depletion results for Region 2 with W 17x17 fuel



Burnup (GWd/MTU)



0 3.5 20 1.18749 0.0003

0 3.5 30 1.12004 0.0008

0 3.5 40 1.06253 0.0008

0 5 30 1.20883 0.0001

0 5 40 1.14934 0.0005

0 5 60 1.04826 0.0010

0.015 3.5 10 1.06978 -0.0001

0.015 3.5 20 1.00474 0.0007

0.015 3.5 30 0.94791 0.0007

0.015 3.5 40 0.89943 0.0006

0.015 5 20 1.08836 0.0002

0.015 5 30 1.03232 0.0001

0.015 5 40 0.98109 0.0003

0.015 5 60 0.89344 0.0006

0.03 3.5 10 1.03698 0.0005

0.03 3.5 20 0.97389 0.0002

0.03 3.5 30 0.91937 0.0009

0.03 3.5 40 0.87200 0.0006

0.03 5 20 1.05557 0.0002

0.03 5 30 1.00102 0.0005

0.03 5 40 0.95144 0.0006

0.03 5 60 0.86690 0.0012

3-4

Table 3-4 Voided instrument tube depletion results for Region 2 with CE 16x16 fuel



Burnup (GWd/MTU)



0 3.5 20 1.14645 0.0008

0 3.5 30 1.07734 0.0006

0 3.5 40 1.01873 0.0010

0 5 30 1.17519 0.0002

0 5 40 1.11441 0.0007

0 5 60 1.00850 0.0009

0.015 3.5 10 1.02267 0.0001

0.015 3.5 20 0.95594 0.0002

0.015 3.5 30 0.89877 0.0006

0.015 3.5 40 0.84980 0.0007

0.015 5 20 1.04375 0.0001

0.015 5 30 0.98723 0.0001

0.015 5 40 0.93485 0.0006

0.015 5 60 0.84559 0.0011

0.03 3.5 10 0.99267 -0.0004

0.03 3.5 20 0.92829 0.0002

0.03 3.5 30 0.87271 0.0005

0.03 3.5 40 0.82529 0.0009

0.03 5 20 1.01332 0.0003

0.03 5 30 0.95833 0.0001

0.03 5 40 0.90802 0.0008

0.03 5 60 0.82101 0.0008

3-5

Figure 3-1 The difference in reactivity (Δk) due to modeling the measurement thimble

4-1

Section 4: Reactivity Effect of Fuel Manufacturing Tolerances

Criticality analysis includes a determination of the reactivity effect of manufacturing tolerances. This reactivity effect is applied as an uncertainty in the calculation of the maximum keff values. The manufacturing tolerances for fuel are:

1. Enrichment

2. Pellet density

3. Pellet outer diameter

4. Cladding inner diameter (or thickness)

5. Cladding outer diameter

6. Guide tube thickness (and instrument tube thickness)

Because tolerances on the fuel dimensions are small, the reactivity effect due to fuel manufacturing tolerances is generally small. However, two of these tolerances, the cladding inner diameter (or thickness) and the guide tube thickness, have a much smaller reactivity effect such that calculations should not be required. This section provides justification for eliminating future calculations.

Before presenting computational results, it is necessary to define a threshold value such that any uncertainty less than this threshold value is deemed negligible. An individual uncertainty that affects the total uncertainty by less than 0.5% is negligible. When independent uncertainties are statistically combined, an uncertainty that is 10% of the total uncertainty contributes less than 0.5% of the total uncertainty. For example, assume the uncertainty from fresh fuel validation is 0.005 in Δk. If there is a manufacturing tolerance uncertainty of 0.0005 in Δk, the statistically combined uncertainty is:

Combined Uncertainty = (0.0052 + 0.00052)0.5 = 0.005025

It should be noted that in this example only one large and one small uncertainty are used. If there are other large uncertainties, the effect of small uncertainties becomes even less significant.

The uncertainty in reactivity derived from code validation against UO2 critical experiments is generally above 0.005. The reactor burnup record uncertainty is also generally above 0.005 for burnups of interest. Assuming that one of these

4-2

uncertainties is above 0.005, an uncertainty of 0.0005 would be negligible when statistically combined. Each criticality analyst should know the largest uncertainty and would then be able to determine a negligible uncertainty. For this generic work, any uncertainty of 0.0005 or less in Δk is considered negligible.

In order to evaluate the reactivity of many of the manufacturing tolerances, the dimensional changes used in the models were some factor larger than the tolerance that would have come from the manufacturing drawings. The calculated reactivity was then divided by this factor. This assumption of linearity was confirmed for the cases with the highest reactivity difference.

4.1 Guide Tube Manufacturing Tolerance

The total volume of all zirconium in the guide tubes is small compared to the volume of the zirconium in the fuel clad. Since the tolerance on the guide tube dimensions and the fuel clad are similar, the impact of the guide tube manufacturing tolerance on reactivity is relatively small. A typical tolerance for the W 17x17 guide tube thickness, inner diameter, or outer diameter is 0.002 in (~0.051 mm) [14]. Since the guide tubes for CE fuel are larger, a tolerance of 0.003 is used [15].

Calculations were performed for the 44 configurations previously described. The guide tube outside diameter and therefore the thickness was increased as part of the analysis. The guide tube outside diameter was increased by the tolerance multiplied by a factor of 4.1 for W 17x17 fuel and a factor of 2.3 for CE 16x16 fuel. This was done to clearly identify the reactivity effect associated with the manufacturing tolerance and to distinguish it from the Monte Carlo uncertainty.

The reactivity effect due to the guide tube tolerance for W 17x17 and CE 16x16 fuels for Region 1 and Region 2 are presented in Table 4-1 and Table 4-2, respectively. In reality, the computed Δk values resulted in a decrease in reactivity compared to the reference cases because water is removed from the assembly. However, in Table 4-1 and Table 4-2, the differences are reported as positive values since the diameter could have been decreased by the same amount. To confirm this, the most limiting W 17x17 case (Region 1, 0.015 areal density, 5 wt% enrichment, zero burnup) was re-analyzed by reducing the thickness, instead of increasing the thickness. The reactivity effect was confirmed to be positive and was the same magnitude within the Monte Carlo uncertainty.

As demonstrated in Table 4-1 and Table 4-2, the difference in reactivity due to guide tube tolerance is less than 0.0005. There is no obvious significant trend as a function of rack design, areal density, enrichment or burnup.

As discussed previously, any uncertainties of 0.0005 or less is considered negligible when statistically combined with the other tolerances. Based on the wide range of configurations, the reactivity due to guide tube (and instrument tube) manufacturing tolerances is not significant and can be neglected in future analysis.

4-3

Table 4-1 Reactivity effect due to guide tube tolerance for Region 1



Burnup (GWd/ MTU)

W 17x17 Guide Tube Tolerance

(∆k)

CE 16x16 Guide Tube

Tolerance (∆k)

0 2 0 0.0002 0.0001

0 3.5 0 0.0002 0.0002

0 3.5 20 0.0003 0.0001

0 3.5 40 0.0002 0.0001

0 5 0 0.0002 0.0002

0 5 20 0.0002 0.0000

0 5 40 0.0002 0.0000

0.015 3.5 0 0.0003 0.0004

0.015 3.5 10 0.0003 0.0003

0.015 5 0 0.0004 0.0000

0.015 5 10 0.0004 0.0003

0.03 5 0 0.0004 0.0002

4-4

Table 4-2 Reactivity effect due to guide tube tolerance for Region 2

Areal Density

(g 10B/cm2)


Burnup (GWd/ MTU)

W 17x17 Guide Tube Tolerance

(∆k)

CE 16x16 Guide Tube

Tolerance (∆k)

0 2 0 0.0001 0.0002

0 3.5 0 0.0002 -0.0001

0 3.5 20 0.0002 0.0001

0 3.5 30 0.0001 0.0000

0 3.5 40 0.0001 0.0000

0 5 0 0.0002 0.0000

0 5 30 0.0001 0.0002

0 5 40 0.0001 0.0001

0 5 60 0.0002 0.0002

0.015 2 0 0.0001 0.0002

0.015 3.5 0 0.0002 0.0001

0.015 3.5 10 0.0004 0.0001

0.015 3.5 20 0.0002 0.0001

0.015 3.5 30 0.0003 0.0001

0.015 3.5 40 0.0002 0.0002

0.015 5 0 0.0002 0.0001

0.015 5 20 0.0002 0.0004

0.015 5 30 0.0003 0.0003

0.015 5 40 0.0003 0.0000

0.015 5 60 0.0003 0.0002

0.03 2 0 0.0002 0.0001

0.03 3.5 0 0.0003 0.0001

0.03 3.5 10 0.0002 0.0003

0.03 3.5 20 0.0003 0.0001

0.03 3.5 30 0.0003 0.0000

0.03 3.5 40 0.0002 0.0000

0.03 5 0 0.0004 0.0002

0.03 5 20 0.0004 0.0001

0.03 5 30 0.0002 0.0001

0.03 5 40 0.0003 0.0002

0.03 5 60 0.0002 0.0002

4-5

4.2 Fuel Cladding Inner Diameter Manufacturing Tolerance

Zirconium is commonly used as cladding material due to its low absorption cross section. The reactivity effect due to the tolerances on the fuel rod cladding inner diameter was analyzed by exchanging zirconium volume with void.

A typical manufacturing tolerance on the cladding inner diameter of W 17x17 fuel is 0.0015 in (~0.0038 cm) [14]. Since the CE fuel pin diameter is slightly larger, for CE 16x16 fuel a tolerance of 0.002 in (~0.0051 cm) is used. The analysis used an increased inner diameter of 0.05 cm (0.02 in) for the W 17x17 fuel and an increase of 0.1 cm (0.04 in) for the CE 16x16 fuel. A test case was performed with the CE 16x16 fuel to determine if it is a reasonable approximation to assume that the effect is proportional to the change in inner diameter. This test case reduced the tolerance from 0.1 cm (0.04 in) to 0.02 cm and observed that the reactivity change was one fifth of the 0.1 cm case, confirming the linearity assumption.

The reactivity effect of the 0.0015 in (~0.0038 cm) tolerance for the W 17x17 fuel and the 0.002 in (~0.0051 cm) tolerance for the CE 16x16 fuel are presented in Table 4-3 and Table 4-4, respectively. As evident from the tables, there are no reactivity changes (Δk) higher than 0.0005. The maximum change in reactivity is for the cases with zero areal density and low enrichment. For these cases, the absorption rate is significantly lower; consequently, the small absorption in the zirconium can cause small reactivity changes. However, even for these cases, the reactivity is still within the Monte Carlo uncertainties.

Based on the computational results, the reactivity associated with the manufacturing tolerance on the cladding inner diameter (or thickness) is negligible and no further calculations are needed. These results are based on cladding inner diameter tolerances of 0.0015 in (~0.0038 cm) and 0.002 in (~0.0051 cm) for W 17x17 and CE 16x16 fuel, respectively.

4-6

Table 4-3 Reactivity effect of cladding inner diameter tolerance for Region 1



Burnup (GWd/MTU)

W 17x17 Cladding ID Tolerance

(∆k)

CE 16x16 Cladding ID Tolerance

(∆k)

0 2 0 0.0003 0.0003

0 3.5 0 0.0002 0.0003

0 3.5 20 0.0002 0.0002

0 3.5 40 0.0002 0.0002

0 5 0 0.0002 0.0002

0 5 20 0.0002 0.0002

0 5 40 0.0002 0.0002

0.015 3.5 0 -0.0001 -0.0001

0.015 3.5 10 0.0000 -0.0001

0.015 5 0 -0.0001 -0.0001

0.015 5 10 0.0000 -0.0001

0.03 5 0 -0.0001 -0.0002

4-7

Table 4-4 Reactivity effect of cladding inner diameter tolerance for Region 2



Burnup (GWd/MTU)

W 17x17 Cladding ID Tolerance

(∆k)

CE 16x16 Cladding ID Tolerance

(∆k) 0 2 0 0.0004 0.0005 0 3.5 0 0.0004 0.0005 0 3.5 20 0.0003 0.0004 0 3.5 30 0.0003 0.0004 0 3.5 40 0.0003 0.0004 0 5 0 0.0003 0.0004 0 5 30 0.0003 0.0004 0 5 40 0.0003 0.0004 0 5 60 0.0003 0.0004

0.015 2 0 0.0003 0.0003 0.015 3.5 0 0.0003 0.0003 0.015 3.5 10 0.0002 0.0003 0.015 3.5 20 0.0003 0.0003 0.015 3.5 30 0.0002 0.0003 0.015 3.5 40 0.0002 0.0003 0.015 5 0 0.0002 0.0003 0.015 5 20 0.0002 0.0003 0.015 5 30 0.0002 0.0003 0.015 5 40 0.0002 0.0003 0.015 5 60 0.0002 0.0003 0.03 2 0 0.0003 0.0003 0.03 3.5 0 0.0002 0.0003 0.03 3.5 10 0.0002 0.0003 0.03 3.5 20 0.0002 0.0003 0.03 3.5 30 0.0002 0.0002 0.03 3.5 40 0.0002 0.0003 0.03 5 0 0.0002 0.0003 0.03 5 20 0.0002 0.0002 0.03 5 30 0.0002 0.0003 0.03 5 40 0.0002 0.0002 0.03 5 60 0.0002 0.0002

5-1

Section 5: Considerations When Crediting Soluble Boron

The limiting conditions for criticality analysis are contained in the Code of Federal Regulations 10CFR 50.68 (b) (4):

If no credit for soluble boron is taken, the keff of the spent fuel storage racks loaded with fuel of the maximum assembly reactivity must not exceed 0.95, at a 95% probability, 95% confidence level, if flooded with un-borated water.

If credit is taken for soluble boron, two conditions are to be analyzed:

- The keff of the spent fuel storage racks loaded with fuel of the maximum fuel assembly reactivity must not exceed 0.95, at a 95% probability, 95% confidence level, if flooded with borated water, and;

- The keff must remain below 1.0 (subcritical), at a 95% probability, 95% confidence level, if flooded with un-borated water.

When soluble boron credit is taken, the second criterion (keff less than 1.0) is the more limiting. Generally the soluble boron concentration available for accident conditions or after a boron dilution event exceeds the requirements. The intent of this section is to determine a conservative amount of this soluble boron concentration margin that can cover differences between borated and un-borated conditions in lieu of performing a large number of calculations for borated cases, especially for uncertainties associated with manufacturing tolerances. Specifically, it is conservative to ignore the grid for cases not crediting boron, but this assumption may not apply at the high soluble boron conditions credited for accident conditions. In general, the reactivity effect of the manufacturing tolerances changes with the addition of soluble boron; however, estimates of this change are needed to determine the magnitude of the additional soluble boron concentration needed to offset the impact of uncertainties due to manufacturing tolerances. Calculations in Section 5.2 will provide a basis for estimating a conservative reactivity.

5.1 Impact of Modeling the Grid Spacer

Computations are performed to determine a conservative estimate of the reactivity effect of spacer grids at 2000 ppm. For the purposes of this analysis, the grids are modeled as void. This is a conservative approach, but the conservatism is minimal since the neutron absorption cross section for the

5-2

zirconium grid material is small. The selected grid volume is 2% of the volume of the water in the area defined by the number pins per row times the pin pitch over the active fuel length. In reality, the grid volume is less than this volume. Grid designs have changed over the years, and many details are proprietary. Two percent covers past and anticipated future designs for PWR fuels. However, this grid volume assumption can be checked against proprietary data available to the licensees, and if not bounded by the 2% assumption, the impact of the grid can be increased in proportion to the difference in the volume fraction.

The reactivity effects of the spacer grid at 2000 ppm soluble boron concentration for both fuel types in Region 1 and Region 2 are presented in Table 5-1 and Table 5-2, respectively. As can be seen from the results in these tables, the reactivity effect of including the grid in the criticality model is still negative even at 2000 ppm for all cases with the exception of low enrichment in Region 1 and for Region 2 when there are no neutron absorber panels. Furthermore, neutron absorber panels in the SFP reduce the magnitude of the reactivity effect of the spacer grid. The maximum reactivity effect (Δk) of the spacer grid is only 0.0023.

The soluble boron requirements are generally less than 2000 ppm. The grid worth from 2000 ppm should be conservative for the actual ppm requirements. To confirm this, the reactivity effect of the grid spacer was calculated for the W 17x17 fuel at an intermediate soluble boron level of 1700 ppm. The results are presented in Table 5-3 for Region 1 and Table 5-4 for Region 2, respectively. When the results tabulated in Table 5-1 are compared to results in Table 5-3 and the results in Table 5-2 are compared against results presented in Table 5-4, it is confirmed that the reactivity effect due to the spacer grid increases with increasing soluble boron concentration. However, it also shows that the change in reactivity of 300 ppm (that is, 1700 ppm to 2000 ppm) is small.

Table 5-1 Reactivity effect of spacer grid at 2000 ppm for Region 1



Burnup (GWd/MTU)

W 17x17 Grid Worth

(Δk)

CE 16x16 Grid Worth

(Δk) 0 2 0 0.0006 0.0000 0 3.5 0 -0.0005 -0.0009 0 3.5 20 -0.0013 -0.0012 0 3.5 40 -0.0011 -0.0008 0 5 0 -0.0011 -0.0013 0 5 20 -0.0011 -0.0014 0 5 40 -0.0016 -0.0009

0.015 3.5 0 -0.0019 -0.0025 0.015 3.5 10 -0.0025 -0.0021 0.015 5 0 -0.0027 -0.0027 0.015 5 10 -0.0029 -0.0026 0.03 5 0 -0.0035 -0.0029

5-3




Burnup (GWd/MTU)

W 17x17 Grid Worth (Δk)

CE 16x16 Grid Worth

(Δk) 0 2 0 0.0023 0.0020

0 3.5 0 0.0020 0.0015

0 3.5 20 0.0007 0.0006

0 3.5 30 0.0011 0.0009

0 3.5 40 0.0008 0.0005

0 5 0 0.0013 0.0008

0 5 30 0.0004 0.0004

0 5 40 0.0002 0.0005

0 5 60 0.0003 0.0004

0.015 2 0 0.0004 0.0004

0.015 3.5 0 0.0001 -0.0004

0.015 3.5 10 -0.0004 -0.0002

0.015 3.5 20 -0.0008 -0.0005

0.015 3.5 30 -0.0008 -0.0002

0.015 3.5 40 -0.0005 -0.0008

0.015 5 0 -0.0006 -0.0006

0.015 5 20 -0.0011 -0.0011

0.015 5 30 -0.0015 -0.0011

0.015 5 40 -0.0009 -0.0011

0.015 5 60 -0.0008 -0.0007

0.03 2 0 0.0002 0.0001

0.03 3.5 0 -0.0006 -0.0010

0.03 3.5 10 -0.0006 -0.0008

0.03 3.5 20 -0.0012 -0.0007

0.03 3.5 30 -0.0005 -0.0005

0.03 3.5 40 -0.0007 -0.0006

0.03 5 0 -0.0011 -0.0010

0.03 5 20 -0.0017 -0.0011

0.03 5 30 -0.0015 -0.0014

0.03 5 40 -0.0011 -0.0016

0.03 5 60 -0.0015 -0.0012

Checkerbrd 5 0 -0.0028 Not calculated

5-4




Burnup (GWd/MTU)

W 17x17 Grid

Worth (Δk) 0 2 0 0.0001

0 3.5 0 -0.0014

0 3.5 20 -0.0014

0 3.5 40 -0.0008

0 5 0 -0.0010

0 5 20 -0.0014

0 5 40 -0.0012

0.015 3.5 0 -0.0023

0.015 3.5 10 -0.0029

0.015 5 0 -0.0034

0.015 5 10 -0.0037

0.03 5 0 -0.0034

5-5




Burnup (GWd/MTU)

W 17x17 Grid Worth (Δk)

0 2 0 0.0021

0 3.5 0 0.0015

0 3.5 20 0.0007

0 3.5 30 0.0006

0 3.5 40 -0.0002

0 5 0 0.0011

0 5 30 0.0002

0 5 40 0.0002

0 5 60 0.0002

0.015 2 0 0.0004

0.015 3.5 0 -0.0003

0.015 3.5 10 -0.0008

0.015 3.5 20 -0.0010

0.015 3.5 30 -0.0009

0.015 3.5 40 -0.0007

0.015 5 0 -0.0014

0.015 5 20 -0.0011

0.015 5 30 -0.0018

0.015 5 40 -0.0009

0.015 5 60 -0.0017

0.03 2 0 0.0000

0.03 3.5 0 -0.0007

0.03 3.5 10 -0.0014

0.03 3.5 20 -0.0012

0.03 3.5 30 -0.0013

0.03 3.5 40 -0.0012

0.03 5 0 -0.0014

0.03 5 20 -0.0016

0.03 5 30 -0.0017

0.03 5 40 -0.0013

0.03 5 60 -0.0018

5-6

For additional confirmation, the reactivity effect due to the spacer grid was computed at zero ppm and 1000 ppm for the Region 2 rack with 5 wt% enriched fuel and an areal density of 0.015 g 10B/cm2. The reactivity effect of the spacer grid as a function of soluble boron for this case is illustrated in Figure 5-1.

Figure 5-1 Reactivity effect of spacer grid as a function of soluble boron concentration (Region 2, 0.015 g 10B/cm2)

The next step in determining a conservative soluble boron concentration for borated cases is to calculate the corresponding reactivity effect of the soluble boron. For each case, calculations were performed at 1700 and 2000 ppm. From the difference in reactivity, the reactivity effect of boron is determined in pcm/ppm. With this data, it is possible to establish the amount of soluble boron that is equivalent to the reactivity effect of the spacer grid. The reactivity effect of the soluble boron concentration for borated cases for Region 1 is presented in Table 5-5. In this case, the reactivity effect of the spacer grid in ppm is not included since there is only one non-limiting case in Region 1 showing an increase in reactivity due to inclusion of the spacer grid at high soluble boron levels. The reactivity of soluble boron concentration and the amount of soluble boron needed to offset the reactivity effect of the spacer grid in pcm/ppm and ppm for the W 17x17 and CE 16x16 fuels in Region 2 are presented in Table 5-6 and Table 5-7, respectively.

Based on the computational results, the maximum soluble boron needed to offset the reactivity effect of the spacer grids is 18 ppm (W17x17 fuel in Region 2 with no absorber panels, 2 wt% 235U, and no burnup).

5-7

Table 5-5 Reactivity effect of soluble boron concentration at 2000 ppm in Region 1



Burnup (GWd/MTU)

W 17x17 Boron Worth

(pcm/ppm)

CE 16x16 Boron Worth

(pcm/ppm)

0 2 0 11.1 10.5

0 3.5 0 11.4 10.8

0 3.5 20 9.3 8.9

0 3.5 40 8.1 7.9

0 5 0 10.7 10.6

0 5 20 9.4 9.3

0 5 40 8.2 8.3

0.015 3.5 0 7.6 7.5

0.015 3.5 10 6.5 6.7

0.015 5 0 7.1 7.1

0.015 5 10 6.4 6.6

0.03 5 0 6.7 7.0

5-8

Table 5-6 Reactivity effect of soluble boron concentration and grid worth (ppm) at 2000 ppm for W 17x17 fuel in Region 2



Burnup (GWd/MTU)

W 17x17 Boron Worth

(pcm/ppm)

W 17x17 Soluble Boron to

Offset Grid (ppm)

0 2 0 13.0 18 0 3.5 0 12.6 16 0 3.5 20 10.1 7 0 3.5 30 9.4 12 0 3.5 40 9.1 9 0 5 0 11.8 11 0 5 30 9.3 5 0 5 40 8.8 2 0 5 60 8.1 4

0.015 2 0 10.0 4 0.015 3.5 0 9.7 1 0.015 3.5 10 8.2 -4 0.015 3.5 20 7.6 -10 0.015 3.5 30 7.2 -11 0.015 3.5 40 6.7 -7 0.015 5 0 9.0 -6 0.015 5 20 7.4 -15 0.015 5 30 7.1 -21 0.015 5 40 6.7 -14 0.015 5 60 6.3 -12 0.03 2 0 9.5 3 0.03 3.5 0 9.3 -6 0.03 3.5 10 8.0 -7 0.03 3.5 20 7.4 -16 0.03 3.5 30 7.0 -7 0.03 3.5 40 6.6 -11 0.03 5 0 8.7 -13 0.03 5 20 7.0 -25 0.03 5 30 6.8 -23 0.03 5 40 6.5 -17 0.03 5 60 6.0 -24

Checkerbrd 5 0 8.4 -33

5-9

Table 5-7 Reactivity effect of soluble boron concentration and grid worth (ppm) at 2000 ppm for CE 16x16 fuel in Region 2



Burnup (GWd/MTU)

CE 16x16 Boron Worth

(pcm/ppm)

CE 16x16 Soluble Boron to

Offset Grid (ppm)

0 2 0 13.0 15 0 3.5 0 13.0 12 0 3.5 20 10.8 6 0 3.5 30 10.0 9 0 3.5 40 9.3 5 0 5 0 12.5 7 0 5 30 10.2 4 0 5 40 9.7 5 0 5 60 8.8 5

0.015 2 0 9.9 4 0.015 3.5 0 9.8 -4 0.015 3.5 10 8.7 -3 0.015 3.5 20 8.0 -6 0.015 3.5 30 7.5 -2 0.015 3.5 40 6.9 -11 0.015 5 0 9.3 -7 0.015 5 20 7.8 -13 0.015 5 30 7.5 -15 0.015 5 40 7.1 -15 0.015 5 60 6.4 -11 0.03 2 0 9.5 1 0.03 3.5 0 9.5 -11 0.03 3.5 10 8.3 -9 0.03 3.5 20 7.6 -9 0.03 3.5 30 7.2 -7 0.03 3.5 40 6.7 -8 0.03 5 0 8.9 -11 0.03 5 20 7.6 -15 0.03 5 30 7.1 -20 0.03 5 40 6.8 -24 0.03 5 60 6.1 -19

5-10

5.2 Changes in Uncertainties with Soluble Boron Content

The largest uncertainties in most criticality analyses are the depletion uncertainty, the burnup (reactor record) uncertainty, and the validation uncertainty. These will be discussed in the next section followed by a discussion on uncertainty due to fuel and rack manufacturing tolerances.

5.2.1 Validation, Burnup Record, and Depletion Uncertainties

The three largest uncertainties in SFP criticality analysis remain the same or decrease with increasing soluble boron.

The validation uncertainty generally does not depend on the soluble boron level. In most validation suites, soluble boron cases are included. The soluble boron worth has been well predicted when using ENDF/B-V to ENDF/B-VII. When critical experiments are grouped into separate sets with and without soluble boron, the validation uncertainty of the two sets are essentially the same (i.e., there is no significant trend associated with soluble boron content).

The impact of burnup (reactor record) uncertainty on reactivity increases as a function of burnup. Tables 2.6 and 2.7 provide the calculated k’s at various burnups with zero ppm and Tables 5-5 through 5-7 present the calculated k’s at the same burnups at 2000 ppm of boron. These data allow the change in reactivity to be determined as a function of burnup at zero and 2000 ppm in the SFP. Table 5-8 and Table 5-9 illustrate how the change in reactivity with burnup (Δk/GWd/MTU) differs between 0 and 2000 ppm rack conditions. As evident from the data presented in both tables, the burnup record uncertainty decreases with increasing soluble boron concentration in the rack.

The depletion reactivity uncertainty should also decrease with increasing soluble boron in the SFP for the same reason that the burnup (reactor record) uncertainty decreases. When using the chemical assay direct difference approach, the appropriate rack model for the 2000 ppm case would reduce the differences that would be observed using a 0 ppm rack model. However, when using the EPRI depletion benchmarks [10], the uncertainty in the experimental data controls the size of the uncertainty rather than the rack conditions.

5-11

Table 5-8 Change in reactivity with burnup at 0 and 2000 ppm soluble boron rack conditions for W 17x17 fuel



Final Burnup (GWd/ MTU)

Δk/GWd/MTU at

0 ppm Rack

Conditions

Δk/GWd/MTU at

2000 ppm Rack

Conditions Region 1

0 3.5 20 -0.0073 -0.0043

0 3.5 40 -0.0052 -0.0037

0 5.0 20 -0.0072 -0.0049

0 5.0 40 -0.0052 -0.0041

0.015 3.5 10 -0.0065 -0.0036

0.015 5 10 -0.0067 -0.0047 Region 2

0 3.5 20 -0.0092 -0.0058

0 3.5 30 -0.0068 -0.0052

0 3.5 40 -0.0058 -0.0044

0 5 30 -0.0081 -0.0061

0 5 40 -0.0060 -0.0050

0 5 60 -0.0051 -0.0042

0.015 3.5 10 -0.0081 -0.0046

0.015 3.5 20 -0.0066 -0.0049

0.015 3.5 30 -0.0057 -0.0045

0.015 3.5 40 -0.0048 -0.0038

0.015 5 20 -0.0073 -0.0055

0.015 5 30 -0.0056 -0.0047

0.015 5 40 -0.0051 -0.0045

0.015 5 60 -0.0044 -0.0037

0.03 3.5 10 -0.0079 -0.0045

0.03 3.5 20 -0.0063 -0.0047

0.03 3.5 30 -0.0055 -0.0044

0.03 3.5 40 -0.0047 -0.0037

0.03 5 20 -0.0071 -0.0053

0.03 5 30 -0.0055 -0.0046

0.03 5 40 -0.0050 -0.0043

0.03 5 60 -0.0043 -0.0036

5-12

Table 5-9 Change in reactivity with burnup at 0 and 2000 ppm soluble boron rack conditions for CE 16x16 fuel



Burnup (GWd/ MTU)

Δk/GWd/MTU at

0 ppm Rack

Conditions

Δk/GWd/MTU at

2000 ppm Rack

Conditions Region 1

0 3.5 20 -0.0074 -0.0048

0 3.5 40 -0.0053 -0.0036

0 5.0 20 -0.0070 -0.0050

0 5.0 40 -0.0053 -0.0040

0.015 3.5 10 -0.0070 -0.0046

0.015 5 10 -0.0067 -0.0050 Region 2

0 3.5 20 -0.0093 -0.0061

0 3.5 30 -0.0069 -0.0050

0 3.5 40 -0.0059 -0.0042

0 5 30 -0.0079 -0.0060

0 5 40 -0.0061 -0.0049

0 5 60 -0.0053 -0.0042

0.015 3.5 10 -0.0087 -0.0058

0.015 3.5 20 -0.0067 -0.0050

0.015 3.5 30 -0.0058 -0.0044

0.015 3.5 40 -0.0049 -0.0037

0.015 5 20 -0.0073 -0.0057

0.015 5 30 -0.0057 -0.0047

0.015 5 40 -0.0053 -0.0044

0.015 5 60 -0.0045 -0.0037

0.03 3.5 10 -0.0085 -0.0056

0.03 3.5 20 -0.0065 -0.0048

0.03 3.5 30 -0.0056 -0.0043

0.03 3.5 40 -0.0048 -0.0036

0.03 5 20 -0.0071 -0.0056

0.03 5 30 -0.0055 -0.0046

0.03 5 40 -0.0051 -0.0043

0.03 5 60 -0.0044 -0.0036

5-13

5.2.2 Changes in Uncertainties Due to Fuel Tolerances

This section presents changes in reactivity with soluble boron content due to increased fuel pellet diameter, fuel enrichment, reduced cladding outer diameter, and increased fuel pin pitch.

The manufacturing tolerance on the fuel pellet diameter is small, about 0.0013 cm (assumed for this analysis). The change in reactivity due to this tolerance for a subset of the rack and fuel cases is presented in Table 5-10. The results presented in Table 5-10 show that the reactivity effect due the fuel pellet diameter tolerance increases with the addition of soluble boron. However, since the reactivity effect of the tolerance is small, there is little impact on the overall reactivity of the system.

The standard fuel enrichment tolerance is 0.05 wt% 235U. For a subset of rack and fuel conditions, enrichment is increased by 0.05 wt%, and the resultant reactivity values were computed for zero and 2000 ppm soluble boron concentrations. Change in reactivity with soluble boron due to increased fuel enrichment is presented in Table 5-11. The difference in the reactivity due to increased enrichment between zero and 2000 ppm is small. The largest difference is for 5 wt% 235U enriched fuel, but the maximum difference is only 0.0013 in Δk for the borated tolerance.

Reducing the cladding outer diameter increases the amount of water around fuel and thus increases reactivity. However, when the soluble boron level is high, it can actually decrease reactivity. To demonstrate this effect, calculations were performed using an assumed tolerance of 0.004 cm for cladding outer diameter for both fuel types. The computational results for this case are presented in Table 5-12. As shown in the table, even though there is a sign change, the reactivity with unborated water is always higher. In the borated condition, the maximum positive reactivity often comes from increasing the cladding diameter. However, since reactivity is nearly linear with change in pin diameter, the absolute value of the calculated reactivity provides the maximum reactivity.

Finally, the fuel pin pitch can be increased to its limits. For these calculations, the increased pitch was determined by taking the reactor core assembly pitch (see Table 2-1) divided by the number of fuel pins in a row. The fuel pin pitch tolerance for W 17x17 fuel is 0.00512 cm. The fuel pin pitch tolerance for the CE 16x16 fuel is 0.01334 cm. If the pin pitch were larger than this value, the fuel assembly would not fit in the core. Table 5-13 shows the reactivity effect of the tolerance for increased fuel pin pitch size at zero and 2000 ppm soluble boron in the rack as well as the differences in reactivity values. The differences between the W 17x17 and the CE 16x16 results are due to the difference in the size of the tolerance. The reactivity effect is smaller in the borated cases.

5-14

Table 5-10 Change in reactivity due to increase of fuel pellet diameter to its tolerance limit

Region Areal

Density (g 10B/cm2)

Enrich-ment (wt% 235U)

Burnup (GWd/ MTU)

Tolerance Reactivity at 0 ppm

Tolerance Reactivity at 2000

ppm

Change in Tolerance Reactivity

Westinghouse 17x17 Fuel

2 0 2 0 0.0002 0.0007 0.0005

2 0 3.5 30 -0.0001 0.0004 0.0003

2 0 5 0 -0.0001 0.0006 0.0005

2 0 5 30 -0.0002 0.0003 0.0001

2 0 5 60 -0.0002 0.0003 0.0000

2 0.015 3.5 30 0.0001 0.0005 0.0004

2 0.03 3.5 30 0.0001 0.0005 0.0004

2 0.03 5 0 0.0002 0.0006 0.0004

2 0.03 5 30 0.0000 0.0004 0.0004

2 0.03 5 60 0.0000 0.0004 0.0004

1 0 2 0 0.0004 0.0007 0.0003

1 0 3.5 40 0.0001 0.0004 0.0003

1 0 5 0 0.0002 0.0006 0.0004

1 0 5 40 0.0000 0.0004 0.0004

1 0.015 5 0 0.0003 0.0006 0.0003

1 0.03 5 0 0.0003 0.0006 0.0003

CB 0 5 0 0.0003 0.0007 0.0004

CE 16x16 Fuel

2 0 2 0 0.0003 0.0008 0.0005

2 0 3.5 30 0.0000 0.0005 0.0005

2 0 5 0 0.0000 0.0006 0.0006

2 0 5 60 -0.0001 0.0004 0.0003

2 0.015 5 60 0.0001 0.0004 0.0003

2 0.03 3.5 30 0.0001 0.0005 0.0004

2 0.03 5 60 0.0001 0.0004 0.0003

1 0 2 0 0.0004 0.0007 0.0003

1 0 5 40 0.0001 0.0004 0.0003

1 0.015 5 10 0.0002 0.0005 0.0003

1 0.03 5 0 0.0003 0.0006 0.0003

5-15

Table 5-11 Change in reactivity due to increased enrichment of fuel to its tolerance limit

Region Areal

Density (g 10B/cm2)


Burnup (GWd/ MTU)



ppm



2 0 2 0 0.0080 0.0087 0.0007

2 0 3.5 30 0.0042 0.0035 -0.0007

2 0 5 0 0.0020 0.0032 0.0012

2 0 5 30 0.0027 0.0026 -0.0002

2 0 5 60 0.0022 0.0022 0.0000

2 0.015 3.5 30 0.0033 0.0034 0.0001

2 0.03 3.5 30 0.0031 0.0034 0.0003

2 0.03 5 0 0.0019 0.0028 0.0009

2 0.03 5 30 0.0029 0.0028 -0.0001

2 0.03 5 60 0.0023 0.0023 0.0001

1 0 2 0 0.0072 0.0076 0.0004

1 0 3.5 40 0.0029 0.0023 -0.0006

1 0 5 0 0.0020 0.0022 0.0002

1 0 5 40 0.0024 0.0020 -0.0004

1 0.015 5 0 0.0012 0.0025 0.0013

1 0.03 5 0 0.0018 0.0021 0.0003

CB 0 5 0 0.0017 0.0026 0.0010

CE 16x16 Fuel

2 0 2 0 0.0080 0.0084 0.0004

2 0 3.5 30 0.0040 0.0041 0.0001

2 0 5 0 0.0019 0.0030 0.0011

2 0 5 60 0.0024 0.0024 0.0000

2 0.015 5 60 0.0026 0.0023 -0.0003

2 0.03 3.5 30 0.0032 0.0037 0.0005

2 0.03 5 60 0.0020 0.0017 -0.0002

1 0 2 0 0.0070 0.0069 -0.0001

1 0 5 40 0.0025 0.0025 0.0000

1 0.015 5 10 0.0019 0.0024 0.0005

1 0.03 5 0 0.0016 0.0020 0.0004

5-16

Table 5-12 Change in reactivity due to reduction of cladding outer diameter to its tolerance limit

Region Areal

Density (g 10B/cm2)


Burnup (GWd/ MTU)



ppm



2 0 2 0 0.0006 0.0005 -0.0001

2 0 3.5 30 0.0008 0.0002 -0.0006

2 0 5 0 0.0009 0.0004 -0.0005

2 0 5 30 0.0010 0.0000 -0.0009

2 0 5 60 0.0010 0.0001 -0.0009

2 0.015 3.5 30 0.0013 -0.0002 -0.0011

2 0.03 3.5 30 0.0014 -0.0002 -0.0011

2 0.03 5 0 0.0018 -0.0004 -0.0013

2 0.03 5 30 0.0013 -0.0005 -0.0008

2 0.03 5 60 0.0013 -0.0003 -0.0009

1 0 2 0 0.0007 0.0002 -0.0005

1 0 3.5 40 0.0008 -0.0004 -0.0003

1 0 5 0 0.0009 -0.0005 -0.0004

1 0 5 40 0.0010 -0.0005 -0.0005

1 0.015 5 0 0.0024 -0.0010 -0.0015

1 0.03 5 0 0.0022 -0.0010 -0.0012

CB 0 5 0 0.0016 -0.0009 -0.0007

CE 16x16 Fuel

2 0 2 0 0.0005 0.0006 0.0000

2 0 3.5 30 0.0005 0.0004 -0.0002

2 0 5 0 0.0008 0.0004 -0.0004

2 0 5 60 0.0006 0.0002 -0.0005

2 0.015 5 60 0.0012 -0.0003 -0.0010

2 0.03 3.5 30 0.0013 -0.0002 -0.0010

2 0.03 5 60 0.0014 -0.0005 -0.0009

1 0 2 0 0.0008 -0.0002 -0.0007

1 0 5 40 0.0008 -0.0004 -0.0004

1 0.015 5 10 0.0019 -0.0009 -0.0010

1 0.03 5 0 0.0022 -0.0010 -0.0012

5-17

Table 5-13 Change in reactivity due to increased fuel pin pitch

Region Areal

Density (g 10B/cm2)


Burnup (GWd/ MTU)





2 0 2 0 0.0022 0.0012 -0.0010

2 0 3.5 30 0.0021 0.0018 -0.0003

2 0 5 0 0.0027 0.0028 0.0001

2 0 5 30 0.0022 0.0022 0.0000

2 0 5 60 0.0018 0.0019 0.0001

2 0.015 3.5 30 0.0033 0.0014 -0.0019

2 0.03 3.5 30 0.0031 0.0012 -0.0019

2 0.03 5 0 0.0040 0.0016 -0.0024

2 0.03 5 30 0.0038 0.0017 -0.0021

2 0.03 5 60 0.0033 0.0015 -0.0018

1 0 2 0 0.0045 0.0016 -0.0029

1 0 3.5 40 0.0048 0.0025 -0.0023

1 0 5 0 0.0065 0.0037 -0.0028

1 0 5 40 0.0055 0.0032 -0.0023

1 0.015 5 0 0.0033 0.0009 -0.0023

1 0.03 5 0 0.0031 0.0008 -0.0023

CB 0 5 0 0.0046 0.0020 -0.0026

CE 16x16 Fuel

2 0 2 0 0.0079 0.0051 -0.0028

2 0 3.5 30 0.0077 0.0073 -0.0004

2 0 5 0 0.0101 0.0102 0.0001

2 0 5 60 0.0070 0.0073 0.0002

2 0.015 5 60 0.0086 0.0046 -0.0040

2 0.03 3.5 30 0.0081 0.0038 -0.0043

2 0.03 5 60 0.0079 0.0042 -0.0037

1 0 2 0 0.0103 0.0034 -0.0068

1 0 5 40 0.0123 0.0071 -0.0052

1 0.015 5 10 0.0078 0.0031 -0.0047

1 0.03 5 0 0.0072 0.0023 -0.0048

5-18

5.2.3 Changes in Uncertainties Due to Rack Tolerances

This section investigates the reactivity effect of rack manufacturing tolerances when soluble boron is included. The two manufacturing tolerances investigated—cell pitch and cell wall thickness—are presented in this section.

For this analysis, the cell pitch for Region 1 racks is reduced by 0.254 cm (0.1 in). For Region 2 racks, the cell pitch is reduced to where the cell walls touch. The reactivity effects of tolerances on the cell pitch are presented in Table 5-14. Compared to the reactivity effect of all other tolerances, this tolerance has the largest positive difference between the zero ppm and the 2000 ppm cases. The biggest difference is for fresh 5 wt% fuel, where the maximum increase in the reactivity effect of manufacturing tolerance is 0.0041 in Δk. The effect dominates in Region 2, where placement of fresh fuel is generally prohibited except in a checkerboard pattern. The checkerboard pattern has a lower impact on reactivity with soluble boron.

Computational results are presented in Table 5-15 for the analysis determining the effect of soluble boron on the rack cell wall thickness tolerance reactivity. In this case, the cell wall thickness was reduced 0.02 cm (10% of the wall thickness). In general, when the SFP does not have absorber panels, the reduced rack cell wall thickness increases moderation. In the absence of neutron absorber panels, this increase in moderation causes a corresponding increase in reactivity. In racks with absorber panels, the additional moderation increases the effectiveness of the absorber panels; therefore, the reactivity decreases with decreasing rack cell wall thickness. Because the addition of soluble boron provides greater neutron absorption in the water, in most cases, the reactivity effect of the rack cell wall thickness tolerances decreases. Some small increases do occur in racks without neutron absorber panels.

5-19

Table 5-14 Change in reactivity due to decreased cell pitch to its tolerance limit

Region Areal

Density (g 10B/cm2)

Enrich-ment

(wt% 235U)

Burnup (GWd/ MTU)



ppm



2 0 2 0 0.0024 0.0049 0.0026

2 0 3.5 30 0.0013 0.0042 0.0029

2 0 5 0 0.0022 0.0064 0.0041

2 0 5 30 0.0010 0.0043 0.0033

2 0 5 60 0.0004 0.0037 0.0032

2 0.015 3.5 30 0.0018 0.0024 0.0007

2 0.03 3.5 30 0.0009 0.0020 0.0011

2 0.03 5 0 0.0019 0.0025 0.0006

2 0.03 5 30 0.0016 0.0022 0.0005

2 0.03 5 60 0.0012 0.0017 0.0004

1 0 2 0 0.0120 0.0104 -0.0016

1 0 3.5 40 0.0104 0.0098 -0.0006

1 0 5 0 0.0142 0.0143 0.0001

1 0 5 40 0.0110 0.0112 0.0002

1 0.015 5 0 0.0113 0.0102 -0.0012

1 0.03 5 0 0.0110 0.0094 -0.0016

CB 0 5 0 0.0035 0.0023 -0.0012

CE 16x16 Fuel

2 0 2 0 0.0044 0.0058 0.0014

2 0 3.5 30 0.0030 0.0059 0.0029

2 0 5 0 0.0043 0.0079 0.0036

2 0 5 60 0.0024 0.0052 0.0028

2 0.015 5 60 0.0017 0.0028

sensitivity analyses for spent fuel pool criticality— revision 1 · 2018. 4. 6. · epri project...

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