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Final Report 3002008197, Sensitivity Analyses for Spent Fuel Pool Criticality - Revision 1.
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Sensitivity Analyses for Spent Fuel Pool Criticality Revision 1 2017 TECHNICAL REPORT

Sensitivity Analyses for Spent Fuel Pool Criticality-Revision 1 All or a portion of the requirements of the EPRI Nuclear Quality Assurance Program apply to this product.

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 askepri@epri.com 3002008197 www.epri.com Final Report, November 2017

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Acknowledgments The following organization, under contract to the Electric Power Research Institute (EPRI), prepared this report:

NuclearConsultants.com 695 Vine Court Ann Arbor, MI 48103 Principal Investigator D. Lancaster This report describes research sponsored by EPRI.

This publication is a corporate document that should be cited in the literature in the following manner:

Sensitivity Analyses for Spent Fuel Pool Criticality-Revision 1.

EPRI, Palo Alto, CA: 2017.

3002008197.

iii

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 v

EXECUTIVE

SUMMARY

Deliverable Number: 3002008197 Product Type: Technical Report Product

Title:

Sensitivity Analyses for Spent Fuel Pool CriticalityRevision 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.

vii

EXECUTIVE

SUMMARY

In order to reduce calculations for the borated portion of the criticality analysis, analysts may reserve 50 ppm soluble boron margin to offset the change in the uncertainties from the unborated analyses as well as the worth of the fuel spacer grids. This amount can be added to the required soluble boron concentration for accident cases.

The reactivity effect of the manufacturing tolerances on neutron absorber panel sheathing is negligible for 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 computational results, it is concluded that PWR racks having an empty row of cells between regions do not require interface analysis.

Based on the previous studies and computations provided in this report, it is concluded that ignoring gadolinium 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 analysts and reviewers 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, hakkurt@epri.com.

PROGRAM: Used Fuel and HLW Management Program, Program 41.03.01 IMPLEMENTATION CATEGORY: Reference Together...Shaping the Future of Electricity Electric Power Research Institute 3420 Hillview Avenue, Palo Alto, California 94304-1338

PO Box 10412, Palo Alto, California 94303-0813 USA 800.313.3774

650.855.2121

askepri@epri.com

www.epri.com

© 2017 Electric Power Research Institute (EPRI), Inc. All rights reserved. Electric Power Research Institute, EPRI, and TOGETHER...SHAPING THE FUTURE OF ELECTRICITY are registered service marks of the Electric Power Research Institute, Inc.

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 ix

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 x

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 (k) 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 10 B/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 xi

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 12-3 Non-fission product 155Gd content as a function of burnup ................................................................ 12-4 Figure 12-4 Non-fission produced 156Gd content as a function of burnup .................................................... 12-5 Figure 12-5 Non-fission product 157Gd content as a function of burnup ................................................................ 12-5 xii

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 xiii

Table 5-2 Reactivity effect of spacer grid at 2000 ppm for Region 2 ................................................................... 5-3 Table 5-3 Reactivity effect of spacer grid at 1700 ppm for Region 1 ................................................................... 5-4 Table 5-4 Reactivity effect of spacer grid at 1700 ppm for Region 2 ................................................................... 5-5 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 xiv

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 xv

Table 12-1 Fuel assembly data for M1-M4 assembly designs ................................................................... 12-2 Table 12-2 Volume-averaged enrichments for Siemens fuel . 12-2 xvi

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 1-1

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.

1-2

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 2-1

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.

2-2

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

Detail A Gap Figure 2-2 Cross section of a typical PWR Region 2 rack 2-4

Table 2-2 Absorber plate compositions 0.015 g 10B/cm2 0.030 g 10B/cm2 Areal Density Areal Density Atoms/barn-cm wt.% Atoms/barn-cm wt.%

10 B 0.00710218 0.0445612 0.0142044 0.0891223 11 B 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 SCALEs 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 hours0.00116 days 0.0278 hours 1.653439e-4 weeks 3.805e-5 months , 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 hours0.00116 days 0.0278 hours 1.653439e-4 weeks 3.805e-5 months 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.

2-5

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.

2-6

Table 2-4 Depletion assumptions W 17x17 CE 16x16 Parameter Depletion 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.

2-7

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 10 B (atoms/barn-cm) 0.0029903 IFBA Coating Thickness 0.001 IFBA Coating Atom Densities Zr (atoms/barn-cm) 0.0322187 10 B (atoms/barn-cm) 0.0215913 Figure 2-3 Diagram of a WABA rod in a guide tube 2-8

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.

2-9

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 (k).

2-10

Table 2-6 Computed multiplication factors, k, for Region 1 reference cases Areal Density Enrichment Burnup W 17x17 CE 16x16 (g 10 B/cm )

2 (wt% 235 U) (GWd/MTU) k 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 2-11

Table 2-7 Computed multiplication factors, k, for Region 2 reference cases Areal Density Enrichment Burnup W 17x17 CE 16x16 (g 10 B/cm )

2 (wt% 235U) (GWd/MTU) k 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 5 0 1.01846 0.94346 (0 areal density) 2-12

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 (k) for voided versus unvoided tubes are illustrated in Figure 3-1.

3-1

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 k From Areal Density Enrichment Burnup Voided IT Unvoided (g 10 B/cm2) (wt% 235U) (GWd/MTU) Depletion k 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 k From Areal Density Enrichment Burnup Voided IT Unvoided (g 10 B/cm2) (wt% 235U) (GWd/MTU) Depletion k Depletion 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 3-2

Table 3-3 Voided instrument tube depletion results for Region 2 with W 17x17 fuel k From Areal Density Enrichment Burnup Voided IT Unvoided (g 10 B/cm2) (wt% 235U) (GWd/MTU) Depletion k Depletion 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 3-3

Table 3-4 Voided instrument tube depletion results for Region 2 with CE 16x16 fuel k From Areal Density Enrichment Burnup Voided IT Unvoided (g 10 B/cm2) (wt% 235 U) (GWd/MTU) Depletion k Depletion 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 3-4

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

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 k. If there is a manufacturing tolerance uncertainty of 0.0005 in k, 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 4-1

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 k 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 k 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.

4-2

Table 4-1 Reactivity effect due to guide tube tolerance for Region 1 W 17x17 Burnup CE 16x16 Areal Density Enrichment Guide Tube (GWd/ Guide Tube (g 10 B/cm2) (wt% 235U) Tolerance MTU) Tolerance (k)

(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 4-3

Table 4-2 Reactivity effect due to guide tube tolerance for Region 2 Areal Burnup W 17x17 Guide CE 16x16 Enrichment Density (GWd/ Tube Tolerance Guide Tube (wt% 235U)

(g 10 B/cm2) MTU) (k) 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 4-4

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 (k) 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.

4-5

Table 4-3 Reactivity effect of cladding inner diameter tolerance for Region 1 W 17x17 CE 16x16 Areal Density Enrichment Burnup Cladding ID Cladding ID (g 10 B/cm2) (wt% 235U) (GWd/MTU) Tolerance Tolerance (k) (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 4-6

Table 4-4 Reactivity effect of cladding inner diameter tolerance for Region 2 W 17x17 CE 16x16 Areal Density Enrichment Burnup Cladding ID Cladding ID (g 10 B/cm2) (wt% 235U) (GWd/MTU) Tolerance Tolerance (k) (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 4-7

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 5-1

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 (k) 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 W 17x17 CE 16x16 Areal Density Enrichment Burnup Grid Worth Grid Worth (g 10B/cm2) (wt% 235U) (GWd/MTU)

(k) (k) 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 5-2

Table 5-2 Reactivity effect of spacer grid at 2000 ppm for Region 2 CE 16x16 Areal Density Enrichment Burnup W 17x17 Grid Worth (g B/cm )

10 2 (wt% 235 U) (GWd/MTU) Grid Worth (k)

(k) 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 5-3

Table 5-3 Reactivity effect of spacer grid at 1700 ppm for Region 1 W 17x17 Areal Density Enrichment Burnup Grid (g 10 B/cm2) (wt% 235 U) (GWd/MTU)

Worth (k) 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 5-4

Table 5-4 Reactivity effect of spacer grid at 1700 ppm for Region 2 Areal Density Enrichment Burnup W 17x17 (g 10 B/cm )2 (wt% 235U) (GWd/MTU) Grid Worth (k) 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 5-5

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).

5-6

Table 5-5 Reactivity effect of soluble boron concentration at 2000 ppm in Region 1 W 17x17 CE 16x16 Areal Density Enrichment Burnup Boron Boron (g 10 B/cm2) (wt% 235U) (GWd/MTU) Worth Worth (pcm/ppm) (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 5-7

Table 5-6 Reactivity effect of soluble boron concentration and grid worth (ppm) at 2000 ppm for W 17x17 fuel in Region 2 W 17x17 W 17x17 Soluble Areal Density Enrichment Burnup Boron Boron to (g 10B/cm2) (wt% 235U) (GWd/MTU) Worth Offset Grid (pcm/ppm)

(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 5-8

Table 5-7 Reactivity effect of soluble boron concentration and grid worth (ppm) at 2000 ppm for CE 16x16 fuel in Region 2 CE 16x16 CE 16x16 Soluble Areal Density Enrichment Burnup Boron Boron to (g 10 B/cm )2 (wt% 235 U) (GWd/MTU) Worth Offset Grid (pcm/ppm)

(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 5-9

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 ks at various burnups with zero ppm and Tables 5-5 through 5-7 present the calculated ks 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 (k/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.

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Table 5-8 Change in reactivity with burnup at 0 and 2000 ppm soluble boron rack conditions for W 17x17 fuel k/GWd/MTU k/GWd/MTU Final at at Areal Density Enrichment Burnup 0 ppm 2000 ppm (g 10 B/cm2) (wt% 235U) (GWd/

Rack Rack MTU)

Conditions 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 5-11

Table 5-9 Change in reactivity with burnup at 0 and 2000 ppm soluble boron rack conditions for CE 16x16 fuel k/GWd/MT k/GWd/MT Burnup U at U at Areal Density Enrichment (GWd/ 0 ppm 2000 ppm (g 10 B/cm2) (wt% 235U)

MTU) Rack Rack Conditions 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 5-12

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 k 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.

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Table 5-10 Change in reactivity due to increase of fuel pellet diameter to its tolerance limit Enrich- Tolerance Areal Burnup Tolerance Change in ment Reactivity Region Density (GWd/ Reactivity Tolerance (wt% at 2000 (g 10B/cm2) MTU) at 0 ppm Reactivity 235 U) ppm 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 5-14

Table 5-11 Change in reactivity due to increased enrichment of fuel to its tolerance limit Tolerance Areal Burnup Tolerance Change in Enrichment Reactivity Region Density (GWd/ Reactivity Tolerance (wt% 235U) at 2000 (g 10B/cm2) MTU) at 0 ppm Reactivity ppm Westinghouse 17x17 Fuel 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 5-15

Table 5-12 Change in reactivity due to reduction of cladding outer diameter to its tolerance limit Enrich- Tolerance Areal Burnup Tolerance Change in ment Reactivity Region Density (GWd/ Reactivity Tolerance (wt% at 2000 (g 10B/cm2) MTU) at 0 ppm Reactivity 235 U) ppm Westinghouse 17x17 Fuel 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 5-16

Table 5-13 Change in reactivity due to increased fuel pin pitch Enrich-Areal Burnup Tolerance Tolerance Change in ment Region Density (GWd/ Reactivity Reactivity at Tolerance (wt%

(g 10B/cm2) 235 MTU) at 0 ppm 2000 ppm Reactivity U)

Westinghouse 17x17 Fuel 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 5-17

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 investigatedcell pitch and cell wall thicknessare 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 k. 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.

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Table 5-14 Change in reactivity due to decreased cell pitch to its tolerance limit Tolerance Areal Enrich- Burnup Tolerance Change in Reactivity Region Density ment (GWd/ Reactivity Tolerance at 2000 (g 10B/cm2) (wt% 235U) MTU) at 0 ppm Reactivity ppm Westinghouse 17x17 Fuel 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 0.0011 2 0.03 3.5 30 0.0014 0.0024 0.0011 2 0.03 5 60 0.0009 0.0021 0.0012 1 0 2 0 0.0109 0.0089 -0.0020 1 0 5 40 0.0110 0.0099 -0.0012 1 0.015 5 10 0.0102 0.0085 -0.0017 1 0.03 5 0 0.0101 0.0081 -0.0020 5-19

Table 5-15 Change in reactivity due to decreased cell wall thickness to its tolerance limit Areal Enrich- Burnup Tolerance Tolerance Change in Region Density ment (GWd/ Reactivity Reactivity at Tolerance (g B/cm )

10 2 (wt% 235 U) MTU) at 0 ppm 2000 ppm Reactivity Westinghouse 17x17 Fuel 2 0 2 0 0.0032 0.0007 -0.0025 2 0 3.5 30 0.0022 0.0006 -0.0016 2 0 5 0 0.0029 0.0004 -0.0025 2 0 5 30 0.0023 0.0006 -0.0018 2 0 5 60 0.0023 0.0005 -0.0018 2 0.015 3.5 30 -0.0003 -0.0005 0.0002 2 0.03 3.5 30 -0.0004 -0.0005 0.0001 2 0.03 5 0 -0.0003 -0.0007 0.0004 2 0.03 5 30 -0.0005 -0.0005 0.0000 2 0.03 5 60 -0.0004 -0.0003 -0.0001 1 0 2 0 0.0041 -0.0001 -0.0040 1 0 3.5 40 0.0037 0.0000 -0.0037 1 0 5 0 0.0045 -0.0001 -0.0044 1 0 5 40 0.0039 0.0001 -0.0038 1 0.015 5 0 -0.0019 -0.0018 -0.0001 1 0.03 5 0 -0.0023 -0.0020 -0.0003 CB 0 5 0 0.0027 0.0002 -0.0025 CE 16x16 Fuel 2 0 2 0 0.0032 0.0003 -0.0030 2 0 3.5 30 0.0028 0.0000 -0.0027 2 0 5 0 0.0032 0.0001 -0.0030 2 0 5 60 0.0025 0.0001 -0.0024 2 0.015 5 60 -0.0003 -0.0005 0.0003 2 0.03 3.5 30 -0.0005 -0.0005 0.0000 2 0.03 5 60 -0.0003 -0.0004 0.0001 1 0 2 0 0.0038 -0.0003 -0.0035 1 0 5 40 0.0034 -0.0004 -0.0030 1 0.015 5 10 -0.0019 -0.0016 -0.0003 1 0.03 5 0 -0.0021 -0.0018 -0.0003 5-20

5.2.4 Statistical Combination of Uncertainties From Manufacturing Tolerances As is evident from the computational results presented in the previous sections, some results showed an increase in reactivity with increased soluble boron concentration, while others showed a decrease. Therefore, the total impact of the soluble boron concentration on the reactivity effect of manufacturing tolerances must be determined by statistically combining all of the results.

Table 5-16 presents the results after the impact of individual manufacturing tolerances on reactivity have been statistically combined. In most cases, the statistically-combined uncertainty due to fuel and rack manufacturing tolerances decreases with the addition of soluble boron. However, fresh 5 wt% fuel in a Region 2 rack with no absorber panels has a significantly larger uncertainty due to large positive impact associated with cell pitch. In reality, this case is unrealistic since fresh fuel with 5 wt% enrichment would not meet the regulatory acceptance criteria for an unborated Region 2 rack and will not be placed in this region. However, this case will be used to conservatively bound the projected additional boron needed if zero soluble boron calculations are applied in the analysis.

5-21

Table 5-16 Statistically combined manufacturing tolerance reactivities Total Total Change in Areal Enrich- Burnup Tolerance Tolerance Total Region Density ment (GWd/ Reactivity Reactivity Tolerance (g 10 B/cm2) (wt% 235U) MTU) at 2000 at 0 ppm Reactivity ppm Westinghouse 17x17 Fuel 2 0 2 0 0.0093 0.0079 -0.0015 2 0 3.5 30 0.0054 0.0058 0.0004 2 0 5 0 0.0051 0.0085 0.0035 2 0 5 30 0.0047 0.0055 0.0008 2 0 5 60 0.0043 0.0048 0.0005 2 0.015 3.5 30 0.0052 0.0052 0.0000 2 0.03 3.5 30 0.0048 0.0050 0.0002 2 0.03 5 0 0.0053 0.0059 0.0005 2 0.03 5 30 0.0053 0.0047 -0.0006 2 0.03 5 60 0.0044 0.0038 -0.0006 1 0 2 0 0.0156 0.0122 -0.0034 1 0 3.5 40 0.0124 0.0106 -0.0019 1 0 5 0 0.0165 0.0156 -0.0008 1 0 5 40 0.0132 0.0121 -0.0011 1 0.015 5 0 0.0125 0.0116 -0.0009 1 0.03 5 0 0.0123 0.0109 -0.0014 CB 0 5 0 0.0071 0.0064 -0.0007 CE 16x16 Fuel 2 0 2 0 0.0129 0.0115 -0.0014 2 0 3.5 30 0.0096 0.0110 0.0014 2 0 5 0 0.0116 0.0147 0.0031 2 0 5 60 0.0083 0.0098 0.0015 2 0.015 5 60 0.0093 0.0071 -0.0021 2 0.03 3.5 30 0.0091 0.0074 -0.0017 2 0.03 5 60 0.0083 0.0063 -0.0020 1 0 2 0 0.0175 0.0123 -0.0052 1 0 5 40 0.0171 0.0131 -0.0041 1 0.015 5 10 0.0135 0.0110 -0.0025 1 0.03 5 0 0.0133 0.0110 -0.0022 5-22

5.3 Recommendation for Soluble Boron Margin Since conditions that credit soluble boron generally have a significant margin above the requirements to meet the criticality safety criteria, it is proposed that a conservative soluble boron addition be applied such that the large number of calculations for demonstrating the reactivity effect of tolerances with borated water can be avoided. The boron concentration needed to offset the reactivity impact caused by ignoring the grid modeling was presented earlier in Table 5-6 and Table 5-7 for W 17x17 and CE 16x16 fuel, respectively. Table 5-17 presents the reactivity effect of tolerances converted to an equivalent boron ppm, using the boron worth values from Table 5-5, Table 5-6, and Table 5-7. In Table 5-17, the grid worth and the reactivity effect of the tolerances are added.

For fuel in a flux trap rack or a close packed rack with neutron absorber panels, it is conservative to use the model without a grid and apply the unborated uncertainties. However, for Region 2 racks without neutron absorber panels, the grids and manufacturing tolerances can have a greater impact than in the unborated condition.

The highest potential bias from using unborated uncertainties and ignoring the grid shown on Table 5-17 is 40 ppm. In order to preserve some margin, it is recommended to ignore the grid in the modeling, use unborated uncertainties, and reserve an additional 50 ppm in soluble boron concentration margin to offset these effects.

In summary, instead of performing a large number of calculations on a routine basis for borated conditions, it would be reasonable to use some of the available margin. Since the reactivity effect of the spacer grids and the change in the total uncertainties are expected to never exceed 40 ppm, reserving 50 ppm soluble boron concentration margin to offset these reactivity effects is conservative. This reserved margin should be added to the required soluble boron concentration for accident cases compared to the technical specifications or to the minimum boron concentration following a boron dilution accident.

5-23

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

Change in Areal Enrich- Burnup Total Grid Sum Region Density ment (GWd/ Tolerance Worth (ppm)

(g 10B/cm2) (wt% 235U) MTU) Reactivity (ppm)

(ppm)

Westinghouse 17x17 Fuel 2 0 2 0 -11 18 6 2 0 3.5 30 4 12 16 2 0 5 0 29 11 40 2 0 5 30 8 5 13 2 0 5 60 6 4 10 2 0.015 3.5 30 1 -11 -10 2 0.03 3.5 30 3 -7 -4 2 0.03 5 0 6 -13 -7 2 0.03 5 30 -9 -23 -32 2 0.03 5 60 -10 -24 -34 1 0 2 0 -31 5 -26 1 0 3.5 40 -23 -13 -36 1 0 5 0 -8 -10 -18 1 0 5 40 -13 -19 -32 1 0.015 5 0 -12 -38 -50 1 0.03 5 0 -21 -52 -73 CB 0 5 0 -9 -33 -42 CE 16x16 Fuel 2 0 2 0 -11 15 5 2 0 3.5 30 14 9 23 2 0 5 0 25 7 31 2 0 5 60 17 5 22 2 0.015 5 60 -33 -11 -44 2 0.03 3.5 30 -23 -7 -30 2 0.03 5 60 -33 -19 -52 1 0 2 0 -50 0 -50 1 0 5 40 -49 -10 -59 1 0.015 5 10 -38 -40 -78 1 0.03 5 0 -32 -41 -73 5-24

Section 6: Reactivity Effect of the Neutron Absorber Sheathing Tolerance Most of the manufacturing tolerances for rack dimensions have a sufficiently large reactivity effect that their impact needs to be calculated for each application.

However, one manufacturing tolerance is small enough that it would be possible to demonstrate its negligible impact. Most racks use a thin stainless steel sheet to hold the absorber panel in place. Due to the small volume of this sheathing, the reactivity effect of the manufacturing tolerance of sheathing may be negligible.

This section presents computational results demonstrating the reactivity effect of manufacturing tolerances on sheathing for Region 1 and Region 2 racks.

The standard neutron absorber panel sheathing is between 0.02 in (0.0508 cm) and 0.035 in (0.0889 cm) thick. The standard tolerance on stainless steel sheet of this thickness is given by the ASTM standard A480 [16]. For stainless steel sheet of thickness 0.02 in (0.051 cm) to 0.035 in (0.089 cm), the standard tolerance on the thickness is 0.002 in (0.0051 cm). The reactivity effect of the sheathing tolerance for Region 1 and Region 2 configurations is presented in Table 6-1 and Table 6-2, respectively. It should be noted that the sign associated with the reactivity change is not important as the sign will change depending on how the manufacturing tolerance is applied, either as an increase or decrease from the original dimensions. This was confirmed by repeating the computation for the most limiting case with a reduction in thickness. The results were the same within Monte Carlo uncertainties with a simple sign change.

As can be seen from Table 6-1 and Table 6-2, the reactivity effect of the sheathing tolerance is small. However, for Region 1 configurations the reactivity difference is generally greater than 50 pcm. For Region 1 configurations, thicker sheathing decreases the flux trap water, which causes decreased thermalization and absorption. Subsequently, when there are no neutron absorber panels, the presence of the steel is more important since there is no strong absorber of thermal neutrons. While this effect causes the reactivity effect of sheathing tolerance to become non-negligible (larger than 50 pcm), it is still small (less than ~100 pcm). Based on the computational results, the reactivity effect of the sheathing tolerance is negligible for Region 2 racks with neutron absorber panels and no further analysis is required in the future.

6-1

Table 6-1 Reactivity effect of sheathing tolerance for Region 1 configurations W 17x17 CE 16x16 Sheathing Sheathing Areal Density Enrichment Burnup Tolerance Tolerance (g 10 B/cm2) (wt% 235U) (GWd/MTU) Reactivity Reactivity Effect Effect (k)

(k) 0 2 0 -0.0012 -0.0011 0 3.5 0 -0.0009 -0.0012 0 3.5 20 -0.0012 -0.0010 0 3.5 40 -0.0012 -0.0004 0 5 0 -0.0012 -0.0012 0 5 20 -0.0008 -0.0008 0 5 40 -0.0007 -0.0007 0.015 3.5 0 0.0003 0.0002 0.015 3.5 10 0.0003 0.0002 0.015 5 0 -0.0001 0.0005 0.015 5 10 0.0000 0.0001 0.03 5 0 0.0006 0.0010 6-2

Table 6-2 Reactivity effect of sheathing tolerance for Region 2 configurations W 17x17 CE 16x16 Areal Burnup Enrichment Reactivity Effect Reactivity Effect Density (GWd/

(wt% 235U) of the Sheathing of the Sheathing (g 10B/cm2 ) MTU)

Tolerance (k) Tolerance (k) 0 2 0 -0.0012 -0.0012 0 3.5 0 -0.0009 -0.0006 0 3.5 20 -0.0005 -0.0007 0 3.5 30 -0.0004 -0.0009 0 3.5 40 -0.0005 -0.0003 0 5 0 -0.0004 -0.0010 0 5 30 -0.0007 -0.0010 0 5 40 -0.0004 -0.0007 0 5 60 -0.0009 -0.0010 0.015 2 0 0.0001 -0.0002 0.015 3.5 0 0.0003 -0.0003 0.015 3.5 10 -0.0001 0.0002 0.015 3.5 20 0.0001 0.0002 0.015 3.5 30 0.0002 0.0000 0.015 3.5 40 -0.0002 0.0003 0.015 5 0 0.0002 0.0003 0.015 5 20 0.0002 -0.0001 0.015 5 30 -0.0002 -0.0003 0.015 5 40 -0.0001 0.0004 0.015 5 60 0.0001 0.0002 0.03 2 0 0.0003 0.0003 0.03 3.5 0 0.0001 0.0003 0.03 3.5 10 0.0005 -0.0002 0.03 3.5 20 -0.0002 0.0002 0.03 3.5 30 0.0001 0.0002 0.03 3.5 40 0.0003 0.0004 0.03 5 0 -0.0002 0.0001 0.03 5 20 -0.0001 0.0002 0.03 5 30 0.0004 0.0000 0.03 5 40 0.0001 0.0001 0.03 5 60 0.0003 0.0001 Checkerbrd 5 0 -0.0004 Not calculated 6-3

Section 7: Distance Required for Neutronic Decoupling of Assemblies This section presents the computational results for determining the required distance in unborated water between assemblies for neutronic decoupling to occur. To determine how much separation is needed for assemblies to be considered neutronically decoupled, a model with 16 assemblies in a Region 2 configuration was developed. This model, shown in Figure 7-1, was used as the reference case. The analysis was performed using vacuum boundary conditions.

The assemblies were eccentrically located toward the center of the model. A cruciform water gap was then added to the center of the model. The size of the cruciform water gap was increased, in one-centimeter steps, until it reached to 30 cm (11.8 in). Beyond 30 cm (11.8 in), larger steps were applied. As an example, the KENO model with a 10 cm (~3.94 in) gap is presented in Figure 7-2.

In order to determine when the separation of the sets of assemblies represents almost complete neutronic decoupling a model was created with one set of assemblies modeled in a corner. Figure 7-3 shows this model. By using the k from the four assemblies alone model, it is possible to determine if nearly complete neutronic decoupling is achieved.

7-1

Figure 7-1 Reference model for the separation analysis 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)

The cases with a separation between assemblies were simulated using W 17x17 fuel with seven different Region 2 rack configurations. For the case with areal density of 0.015 g 10B/cm2, 3.5 wt% 235U enrichment, and zero burnup the separation was increased in 1.0 cm (~0.394 in) steps. The computed neutron multiplication factor as a function of separation distance for this configuration is presented in Figure 7-4. For the other configurations, analysis was performed only for a subset of areal density, enrichment, and burnup values. The computed neutron multiplication factor as a function of distance for the selected configurations is presented in Table 7-1. For easier comparisons, the ratio of the multiplication factor with a given distance to the infinite separation multiplication factor for each case is presented in Table 7-2. Neutron multiplication factor as a function of distance between assemblies is illustrated in Figure 7-4.

As is evident from the data presented in both tables and Figure 7-4, a gap of 25 cm (~9.84 in) of unborated water is sufficient for assemblies to effectively decouple neutronically from each other. If there are neutron absorber panels, as in cases 5 to 7 in Table 7-2; then, the decoupling of assemblies is achieved with less separation. This is due to the absorption of neutrons in neutron absorber panels after full thermalization in the water gap. However, as seen on Table 7-2, the rate of decoupling is fairly independent of the enrichment or burnup of the fuel.

Considering that the cell pitch in PWR racks varies from 20 cm (~7.874 in) to 25 cm (~9.843 in), it can be concluded that an empty row between two cells decouples them from adjacent areas of the rack. Therefore, analysis to determine if increased reactivity occurs at an interface is not needed when there is 25 cm of water between racks or an empty row of cells.

7-3

Figure 7-4 Neutron multiplication factor as a function of the distance between sets of assemblies Table 7-1 Computed neutron multiplication factor as a function of separation for selected cases Case 1 2 3 4 5 6 7 Areal Density 0 0 0 0 0.015 0.030 0.030 Enrichment 2 3.5 5 5 3.5 5 5 Burnup GWd/ 0 0 0 60 0 0 60 MTU Gap Computed neutron multiplication factors (cm) 2 1.1145 1.2687 1.3460 0.9745 1.0684 1.1161 0.8088 4 1.0759 1.2279 1.3040 0.9470 1.0393 1.0883 0.7899 7 1.0268 1.1712 1.2442 0.9025 1.0049 1.0544 0.7652 10 1.0013 1.1417 1.2122 0.8773 0.9892 1.0384 0.7527 15 0.9850 1.1221 1.1916 0.8612 0.9815 1.0304 0.7464 20 0.9795 1.1163 1.1852 0.8564 0.9804 1.0296 0.7459 25 0.9786 1.1152 1.1834 0.8550 0.9802 1.0292 0.7459 Infinite 0.9787 1.1151 1.1835 0.8547 0.9798 1.0292 0.7458 7-4

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

Gap 1 2 3 4 5 6 7 (cm) 2 1.139 1.138 1.137 1.140 1.090 1.084 1.085 4 1.099 1.101 1.102 1.108 1.061 1.057 1.059 7 1.049 1.050 1.051 1.056 1.026 1.025 1.026 10 1.023 1.024 1.024 1.027 1.010 1.009 1.009 15 1.006 1.006 1.007 1.008 1.002 1.001 1.001 20 1.001 1.001 1.001 1.002 1.001 1.000 1.000 25 1.000 1.000 1.000 1.000 1.000 1.000 1.000 7-5

Section 8: Impact of Finite Versus Infinite Array Modeling on Reactivity It has been a common concern that a few assemblies with abnormal characteristics can cause a local criticality event. Because of this concern, there is an interest in determining how the reactivity of a limited number of assemblies compares to the reactivity of an infinite array. In this section, the neutron multiplication factor of a finite number of assemblies are compared to the neutron multiplication factor from an infinite array in order to determine how large a model needs to be to simulate an infinite model.

The first set of calculations consisted of square arrays of fuel assemblies with vacuum boundary conditions on all sides. In these arrays, the fuel was placed eccentrically so that all of the fuel was as close to the center of the array as possible. The first set of calculations was performed for the 43 configurations (checkerboard was excluded) described and used in the previous sections. The W 17x17 fuel was used for all of these cases. The ratio of the calculated reactivity for all of these cases to the reference case reactivity was computed. The reference case refers to the one that was modeled using 20x20 assemblies that are eccentrically located in the storage cells. For the reference case, periodic boundary conditions were used. It is assumed that this model represents an infinite array.

The ratio of the neutron multiplication factor from the finite model to the infinite array model for Region 1 and Region 2 are presented in Table 8-1 and Table 8-2, respectively. As can be seen from the results listed in Table 8-1 and Table 8-2, the fuel characteristics, burnup, and enrichment do not have significant impact on the ratio of the infinite array multiplication factor to the finite model multiplication factor. The computational results also indicate that the rack design and areal density of the absorber panels only have an impact on the ratio for smaller numbers of assemblies. As is evident from the computational results, the 144-assembly case (12x12) produces results that are very close to the infinite case for all areal densities and rack designs.

Although this preliminary study was useful, in reality, in spent fuel pools, reflection by water or other assemblies needs to be taken into account. Therefore, the analysis was extended to water-reflected cases. For this purpose, initially, a large (20x20) Region 2 rack with no fuel assemblies was modeled. Fuel assemblies were then added to the model in incremental steps. For all of the Region 2 (except checkerboard) cases, 1, 2, 3, 4, 5, 6, 8, 12, and 16 assemblies 8-1

were eccentrically located and the resultant reactivity values were computed. The arrangement of fuel assemblies for three-, five-, and eight-assembly configurations are shown in Figure 8-1, Figure 8-2, and Figure 8-3, respectively.

For all of the other cases, the rectangular form produced the highest reactivity value. For the five-assembly case, a cruciform arrangement was expected to be most limiting case. However, with eccentric positioning in a cruciform only three assemblies can be adjacent to each other compared to four assemblies in a square. Therefore, the eccentric locations of fuel in the cell made the cruciform arrangement less limiting than the square plus one arrangement.

Figure 8-4 illustrates the ratio of the computed neutron multiplication factors for a finite model compared to an infinite array as a function of the number of assemblies in the group. Table 8-3 presents the ratio of computed neutron multiplication factors for a finite number of assemblies compared to the infinite array. In this table, the ratios are presented for arrays of 4, 6, 8, and 16 assemblies. For the other arrays, the reader is referred to the electronic data described in the appendix.

Based on the computational results presented in these figures and tables, for the four assemblies to cause a local criticality event, these assemblies must be significantly more reactive than allowed limits in the storage racks. The highest value of k2x2/kinf for the four assemblies in any of the configurations is 0.90. If the storage rack were designed for a neutron multiplication factor of 1.0, the four assemblies would need to have a neutron multiplication of 1.0/0.9 or 1.1 to create a local isolated criticality event. Therefore, an error in the manufacturing tolerances or end effects is not a large enough margin for a four-assembly set to cause a local criticality event. In Region 2, even eight assemblies in a group would need a large error in order to cause a local criticality concern. In Region 2, approximately 16 assemblies are needed to reach 95% of the infinite assembly neutron multiplication factor.

8-2

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

Areal Burnup Enrichment 2x2 4x4 8x8 12x12 Density (GWd/

(wt% 235 U) k2x2/kinf k4x4/kinf k8x8/kinf k12x12/kinf (g 10B/cm2) MTU) 0 2 0 0.865 0.964 0.993 0.998 0 3.5 0 0.867 0.964 0.993 0.998 0 3.5 20 0.865 0.964 0.993 0.999 0 3.5 40 0.864 0.963 0.993 0.998 0 5 0 0.867 0.965 0.993 0.998 0 5 20 0.866 0.965 0.993 0.998 0 5 40 0.865 0.964 0.993 0.998 0.015 3.5 0 0.900 0.968 0.992 0.996 0.015 3.5 10 0.899 0.967 0.992 0.997 0.015 5 0 0.901 0.969 0.993 0.998 0.015 5 10 0.899 0.968 0.992 0.997 0.03 5 0 0.906 0.970 0.993 0.998 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)

Areal Burnup Enrichment 2x2 4x4 8x8 12x12 Density (GWd/

(wt% 235U) k2x2/kinf k4x4/kinf k8x8/kinf k12x12/kinf (g 10 B/cm2) MTU) 0 2 0 0.781 0.934 0.984 0.994 0 3.5 0 0.781 0.933 0.983 0.993 0 3.5 20 0.777 0.930 0.981 0.992 0 3.5 30 0.776 0.930 0.981 0.992 0 3.5 40 0.776 0.930 0.981 0.992 0 5 0 0.782 0.933 0.983 0.993 0 5 30 0.777 0.930 0.981 0.991 0 5 40 0.776 0.929 0.980 0.991 0 5 60 0.775 0.929 0.981 0.991 0.015 2 0 0.817 0.946 0.987 0.995 0.015 3.5 0 0.818 0.947 0.988 0.996 0.015 3.5 10 0.817 0.946 0.988 0.995 0.015 3.5 20 0.816 0.945 0.987 0.995 0.015 3.5 30 0.816 0.945 0.987 0.995 0.015 3.5 40 0.817 0.945 0.988 0.996 0.015 5 0 0.819 0.947 0.988 0.996 0.015 5 20 0.817 0.946 0.988 0.995 0.015 5 30 0.817 0.946 0.987 0.995 0.015 5 40 0.817 0.946 0.988 0.995 0.015 5 60 0.817 0.945 0.988 0.995 0.03 2 0 0.822 0.946 0.987 0.995 0.03 3.5 0 0.823 0.947 0.988 0.995 0.03 3.5 10 0.822 0.947 0.988 0.996 0.03 3.5 20 0.821 0.946 0.988 0.995 0.03 3.5 30 0.822 0.947 0.988 0.996 0.03 3.5 40 0.821 0.947 0.988 0.995 0.03 5 0 0.824 0.948 0.989 0.996 0.03 5 20 0.823 0.947 0.988 0.995 0.03 5 30 0.822 0.947 0.988 0.996 0.03 5 40 0.822 0.947 0.988 0.995 0.03 5 60 0.822 0.947 0.987 0.995 8-4

Figure 8-1 Model for three assemblies in an empty Region 1 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 Figure 8-4 Ratio of finite model multiplication factor to infinite array multiplication factor for 5% enrichment and zero burnup values 8-6

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

Areal Burnup 4 6 8 16 Enrichment Density (GWd/ Assem Assem Assem Assem (wt% 235U)

(g B/cm )

10 2 MTU) k4/kinf k6/kinf k8/kinf k16/kinf 0 2 0 0.823 0.862 0.886 0.943 0 3.5 0 0.823 0.863 0.886 0.942 0 3.5 20 0.819 0.859 0.883 0.939 0 3.5 30 0.819 0.859 0.883 0.938 0 3.5 40 0.819 0.859 0.883 0.939 0 5 0 0.823 0.863 0.886 0.941 0 5 30 0.820 0.859 0.883 0.939 0 5 40 0.819 0.859 0.882 0.938 0 5 60 0.818 0.858 0.882 0.938 0.015 2 0 0.843 0.878 0.898 0.951 0.015 3.5 0 0.843 0.879 0.906 0.951 0.015 3.5 10 0.842 0.877 0.898 0.951 0.015 3.5 20 0.842 0.877 0.897 0.951 0.015 3.5 30 0.841 0.877 0.897 0.950 0.015 3.5 40 0.842 0.877 0.897 0.951 0.015 5 0 0.844 0.879 0.899 0.952 0.015 5 20 0.842 0.877 0.898 0.951 0.015 5 30 0.842 0.877 0.898 0.951 0.015 5 40 0.842 0.877 0.898 0.951 0.015 5 60 0.842 0.877 0.897 0.951 0.03 2 0 0.847 0.881 0.900 0.951 0.03 3.5 0 0.847 0.881 0.900 0.952 0.03 3.5 10 0.846 0.880 0.900 0.952 0.03 3.5 20 0.846 0.880 0.900 0.951 0.03 3.5 30 0.846 0.880 0.900 0.952 0.03 3.5 40 0.846 0.880 0.900 0.951 0.03 5 0 0.848 0.882 0.902 0.953 0.03 5 20 0.847 0.880 0.900 0.952 0.03 5 30 0.846 0.880 0.900 0.952 0.03 5 40 0.846 0.880 0.900 0.952 0.03 5 60 0.846 0.880 0.900 0.951 8-7

Section 9: Impact of Eccentric Positioning of Fuel in the Rack Cells on Reactivity The storage cells in an SFP rack are designed to be slightly larger than the fuel assemblies. Although criticality analysis generally assumes that the fuel assembly is placed in the center of the cell, it is possible for the fuel assembly to be located anywhere within the cell. Eccentric positioning of the assemblies in the cell can increase or decrease reactivity.

In order to assess the impact of eccentric positioning on reactivity, several cases were analyzed. First, it was investigated whether the center positioning of the fuel assembly, in storage racks with neutron absorber panels, results in the highest reactivity. Second, analysis was performed to determine the size of the model needed to accurately reflect the reactivity impact of eccentric positioning.

9.1 Analysis of Racks with Full Eccentric Positioning Computations were performed using a 20x20 model with fuel eccentrically located in the cells so that the fuel was closest to the center of the model. The analyses were performed for all 43 reference cases, excluding the Region 2 checkerboard configuration. The difference in reactivity (k) between the eccentric positioning configuration and the centrically loaded configuration taken from the infinite model are presented in Table 9-1 and Table 9-2 for Region 1 and Region 2, respectively.

Results show that the impact of eccentric positioning on reactivity is more significant for CE 16x16 fuel, compared to W 17x17 fuel. This is primarily due to the fact that CE 16x16 fuel assembly has a smaller cross sectional area and the same rack design was used for both fuel designs. It would be likely that a rack designed for CE 16x16 fuel would have a smaller cell size but it was desirable for this effort to use a design that would allow a large movement in the cell. For W 17x17 fuel, the assembly positioning can change up to 0.47 cm (~0.185 in) before reaching to the cell wall. However, CE 16x16 fuel can move up to 0.89 cm

(~0.350 in). Even though there is a large range of reactivity effects from eccentric positioning, the computational results show that when neutron absorber panels are present, the reactivity effect from eccentric positioning is zero or negative for every case in Region 1 and Region 2.

9-1

Therefore, no further analysis or calculations are needed in order to determine the impact of eccentric positioning on reactivity when neutron absorber panels are present in storage racks.

Table 9-1 Reactivity effect due to eccentric loading using a 20x20 model for Region 1 Areal Enrichment Burnup W 17x17 CE 16x16 Density (wt% 235U) (GWd/MTU) k k (g 10 B/cm2) 0 2 0 0.0048 0.0150 0 3.5 0 0.0069 0.0219 0 3.5 20 0.0053 0.0171 0 3.5 40 0.0052 0.0153 0 5 0 0.0079 0.0228 0 5 20 0.0065 0.0194 0 5 40 0.0055 0.0170 0.015 3.5 0 -0.0008 -0.0037 0.015 3.5 10 -0.0002 -0.0034 0.015 5 0 -0.0012 -0.0015 0.015 5 10 0.0000 -0.0018 0.03 5 0 -0.0005 -0.0029 9-2

Table 9-2 Reactivity effect due to eccentric loading using a 20x20 model for Region 2 Areal Density Enrichment Burnup W 17x17 CE 16x16 (g 10 B/cm ) 2 (wt% 235U) (GWd/MTU) k k 0 2 0 0.0018 0.0066 0 3.5 0 0.0021 0.0094 0 3.5 20 0.0027 0.0052 0 3.5 30 0.0023 0.0045 0 3.5 40 0.0017 0.0045 0 5 0 0.0025 0.0093 0 5 30 0.0022 0.0050 0 5 40 0.0026 0.0046 0 5 60 0.0017 0.0040 0.015 2 0 -0.0037 -0.0071 0.015 3.5 0 -0.0032 -0.0055 0.015 3.5 10 -0.0025 -0.0042 0.015 3.5 20 -0.0014 -0.0037 0.015 3.5 30 -0.0014 -0.0035 0.015 3.5 40 -0.0018 -0.0035 0.015 5 0 -0.0020 -0.0033 0.015 5 20 -0.0011 -0.0030 0.015 5 30 -0.0013 -0.0034 0.015 5 40 -0.0014 -0.0023 0.015 5 60 -0.0012 -0.0026 0.03 2 0 -0.0032 -0.0075 0.03 3.5 0 -0.0027 -0.0065 0.03 3.5 10 -0.0018 -0.0048 0.03 3.5 20 -0.0013 -0.0036 0.03 3.5 30 -0.0016 -0.0036 0.03 3.5 40 -0.0013 -0.0032 0.03 5 0 -0.0023 -0.0041 0.03 5 20 -0.0012 -0.0027 0.03 5 30 -0.0007 -0.0027 0.03 5 40 -0.0008 -0.0028 0.03 5 60 -0.0005 -0.0025 9-3

For storage racks that do not have neutron absorber panels on all sides of the cell, the reactivity effect due to eccentric loading needs to be determined.

Historically, 2x2 calculations have been performed to determine the impact of eccentric positioning on reactivity; however, this is insufficient to determine the maximum possible effect.

The reactivity effect due to eccentric loading derived from smaller models for Region 1 configurations without neutron absorber panels is presented in Table 9-3. For CE 16x16 fuel assembly computations, only the 2x2 case was performed since the trend was established with W17x17 fuel assembly. The reactivity effect due to eccentric loading for small versus large array models for Region 2 racks are presented in Table 9-4. Although Table 9-3 suggests that an 8x8 model may be sufficient, it is clear from the results presented in Table 9-4, an 8x8 array model is still not sufficient for finding the maximum reactivity effect due to eccentric loading.

The key observation from Table 9-3 and Table 9-4 is that the size of the model used in simulations to capture the impact of eccentric loading is important. As evident from the values shown in both tables, a 2x2 model is not sufficient to capture the full effect of the reactivity impact due to eccentric fuel loading. While a 2x2 model may produce no positive reactivity, a larger model can yield positive reactivity, as shown in Table 9-4. The next subsection investigates the change in reactivity with the number of collocated eccentric assemblies.

9-4

Table 9-3 Reactivity effect due to eccentric loading as a function of model size for Region 1 Areal 2x2 4x4 8x8 20x20 Enrichment Burnup Density Model Model Model Model (wt% 235U) (GWd/MTU)

(g 10B/cm2) k k k k W 17x17 fuel 0 2 0 0.0033 0.0047 0.0049 0.0048 0 3.5 0 0.0046 0.0060 0.0066 0.0069 0 3.5 20 0.0040 0.0049 0.0052 0.0053 0 3.5 40 0.0031 0.0044 0.0048 0.0052 0 5 0 0.0048 0.0067 0.0076 0.0079 0 5 20 0.0043 0.0062 0.0067 0.0065 0 5 40 0.0035 0.0050 0.0057 0.0055 CE 16x16 fuel 0 2 0 0.0116 - - 0.0150 0 3.5 0 0.0171 - - 0.0219 0 3.5 20 0.0126 - - 0.0171 0 3.5 40 0.0115 - - 0.0153 0 5 0 0.0168 - - 0.0228 0 5 20 0.0146 - - 0.0194 0 5 40 0.0129 - - 0.0170 9-5

Table 9-4 Reactivity effect due to eccentric loading as a function of model size for Region 2 Areal 2x2 4x4 8x8 20x20 Enrichment Burnup Model Model Model Density Model (wt% 235 U) (GWd/MTU)

(g 10 B/cm2) k k k k W 17x17 fuel 0 2 0 -0.0100 -0.0031 0.0000 0.0018 0 3.5 0 -0.0120 -0.0040 -0.0002 0.0021 0 3.5 20 -0.0109 -0.0038 -0.0002 0.0027 0 3.5 30 -0.0104 -0.0034 -0.0007 0.0023 0 3.5 40 -0.0102 -0.0036 -0.0007 0.0017 0 5 0 -0.0130 -0.0047 -0.0001 0.0025 0 5 30 -0.0115 -0.0041 -0.0003 0.0022 0 5 40 -0.0108 -0.0039 -0.0006 0.0026 0 5 60 -0.0103 -0.0040 -0.0008 0.0017 CE 16x16 fuel 0 2 0 -0.0215 -0.0034 0.0050 0.0066 0 3.5 0 -0.0274 -0.0056 0.0047 0.0094 0 3.5 20 -0.0281 -0.0087 0.0012 0.0052 0 3.5 30 -0.0271 -0.0084 0.0002 0.0045 0 3.5 40 -0.0257 -0.0084 0.0003 0.0045 0 5 0 -0.0313 -0.0072 0.0039 0.0093 0 5 30 -0.0308 -0.0098 0.0002 0.0050 0 5 40 -0.0298 -0.0097 0.0000 0.0046 0 5 60 -0.0273 -0.0090 -0.0005 0.0040 9.2 Modeling Partial Eccentric Loading The loading of the fuel assembly in the cell can generally be considered random, despite efforts for central loading to maximize the distance from the cell walls in order to minimize the chances for damaging the fuel assembly. Having more than 100 eccentrically loaded assemblies in the same region is highly unlikely; however, having a few assemblies being clustered toward a common location cannot be eliminated as a possibility.

In order to address this issue, a 30x30 Region 1 model (comprised of 900 assemblies) was developed. In the initial state, all 900 assemblies were centrally located in the cells. Then, one by one, fuel in the storage cells were moved toward the center of the model. The analysis was performed using zero burnup, 5 wt% 235U enriched W 17x17 fuel in Region 1 with no absorber panels.

9-6

This case is selected for the current analysis since it is the one that yielded the highest reactivity effect from eccentric loading for W 17x17 fuel, based on the results presented in Table 9-1. Figure 9-1 shows the impact of eccentric loading on reactivity as a function of the number of fuel assemblies moved toward a central eccentric position for Region 1 racks with 5% enrichment, zero burnup, and no neutron absorber panels.

The reactivity effect from eccentric loading of four assemblies in this figure is much less than the magnitude of the effect determined by the 2x2 model in the previous section (0.00017 from Figure 9-1 versus 0.0048 from Table 9-3 ). This is primarily due to the fact that the 2x2 model used in the previous analysis assumes an infinite array of four assemblies propagated throughout the rack, not just four assemblies as in the analysis in this section. Additionally, the full reactivity impact of eccentric loading was 0.0082 in k for the 30x30 model. As can be seen from Figure 9-1, when 324 assemblies are eccentrically loaded, this full reactivity impact is met. The fluctuations in the plot are due to the Monte Carlo uncertainty of 0.0002.

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

9.3 Recommendation for Eccentricity Reactivity Based on the computational results presented in Subsection 9.1, no further analysis is needed in order to determine the impact of eccentric positioning on reactivity for racks with neutron absorber panels on all sides of each cell.

For racks without neutron absorber panels on all four sides, modeling several hundred assemblies to maximize the reactivity from eccentricity might be required. Recently, a statistical approach has been used to determine a maximum credible number of assemblies that could be eccentric about a point. This statistical approach is described in References 20-22.

9-8

Section 10: Impact of Concrete Composition on Reactivity This section presents the impact of concrete composition on the reactivity.

Concrete around the SFP can have a small effect on the criticality safety analysis.

For most SFP criticality safety calculations, an infinite model is used with reflective or periodic boundary conditions where concrete composition has no effect on reactivity. However, some SFP analyses allow reduced burnup requirements at the edge of the pool by taking credit for neutron leakage. In other cases, absorber panels are removed to take advantage of the boundary. In these cases, the concrete composition may have an effect on reactivity.

There is no standard composition for concrete and its elemental variation can vary significantly. Four built-in concrete compositions are included in the SCALE computer code [12]. Table 10-1 shows the elemental composition of these concretes.

Table 10-1 Elemental compositions of the SCALE supplied concretes Magnuson's Oak Ridge Regulatory Rocky Flats Element Concrete Concrete Concrete Concrete (wt%) (wt%) (wt%) (wt%)

Fe 0.5595 0.7784 1.4 1.01 H 0.3319 0.6187 1 0.75 C 10.5321 17.52 5.52 N 0.02 O 49.943 41.02 53.2 48.49 Na 0.1411 0.0271 2.9 0.63 Mg 9.42 3.265 1.25 Al 0.7859 1.083 3.4 2.17 Si 4.2101 3.448 33.7 15.5 S 0.2483 0.19 Cl 0.0523 K 0.9445 0.1138 1.37 Ca 22.6318 32.13 4.4 23 Ti 0.1488 0.1 Mn 0.0512 10-1

Initially, a 400-cell rack array surrounded by concrete was modeled. In the model, neutron absorber panels for the last two rows were removed. This large model showed that the impact of concrete composition on reactivity is negligible, as the variations were within the Monte Carlo uncertainties. In order to maximize the impact of the concrete composition and to be able to differentiate the reactivity effect associated with different concrete compositions, a 16-cell model was generated. The model is based on Region 2 with no neutron absorber and W 17x17 fuel with 2.0 wt% 235U enrichment and zero burnup. The SCALE model for this configuration is shown in Figure 10-1.

Figure 10-1 SCALE model for the concrete analysis A 1 cm water gap between the rack and concrete was selected to increase the effect of the concrete composition. Simulations were performed for a number of cases to confirm that the reactivity effect of concrete decreases with increased water gap. The reactivity effect due to increased water gap between storage rack and the concrete wall are presented in Table 10-2. As shown in Table 10-2, beyond 8 cm (~3.15inches) of water gap, the reactivity difference between water or concrete reflector becomes negligible. The 1 cm water gap is considerably smaller than the normal gap between the rack and the wall in a SFP. In order to 10-2

maximize the effect of composition of concrete on reactivity, the stainless steel liner was not modeled.

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

Water Gap (cm) Model k k from 1-cm gap 1 1.14055 -

2 1.13904 -0.0015 3 1.13795 -0.0026 4 1.13712 -0.0034 6 1.13585 -0.0047 8 1.13570 -0.0049 10 1.13532 -0.0052 30 1.13500 -0.0055 The reactivity effect associated with each of the four SCALE concrete compositions was computed using the 16 assembly model. The computed k for each type of concrete and the reactivity difference between each specific type and the reference case (Rocky Flats composition), are presented in Table 10-3. Based on the computational results, Magnuson concrete produces the most conservative reactivity.

Table 10-3 Reactivity effect of different concrete compositions Concrete Model k k from Rocky Flats Rocky Flats 1.14055 -

Magnusons 1.14374 0.0032 Regulatory 1.14051 0.0000 Oak Ridge 1.14211 0.0016 The next step was to keep the concrete density constant, but assume it is made of pure elements. The reactivity difference, compared to Rocky Flats concrete composition is listed in Table 10-4. As shown in Table 10-4, most of the components with smaller wt% in concrete produce a reduction in reactivity. If a conservative concrete is desired, hydrogen, nitrogen, sulfur, chlorine, potassium, titanium, manganese, and iron should be minimized. Calcium is often a key component in concrete but it should also be minimized in concrete to maximize reactivity. The components of concrete that yields a positive reactivity effect are silicon, carbon, oxygen, magnesium, sodium, and aluminum.

10-3

Table 10-4 Comparison of Concrete Made of Single Elements Concrete Element Model k k from Rocky Flats H 1.13274 -0.0078 C 1.15837 0.0178 N 1.13891 -0.0016 O 1.15534 0.0148 Na 1.14357 0.0030 Mg 1.14812 0.0076 Al 1.14066 0.0001 Si 1.14119 0.0006 S 1.13484 -0.0057 Cl 1.13503 -0.0055 K 1.13437 -0.0062 Ca 1.13657 -0.0040 Ti 1.13766 -0.0029 Mn 1.13623 -0.0043 Fe 1.13836 -0.0022 A conservative concrete would have the maximum content of those elements that produce a positive reactivity effect and the minimum content of those elements that produce a negative reactivity effect. The four SCALE concretes were used to determine the maximum and minimum amounts of each element as weight percents. Table 10-5 shows the normalized elemental composition of the conservative concrete. With time concrete dries out and loses some of its hydrogen. In order to avoid this concern, hydrogen has been removed from the dry conservative concrete. In order to keep the number densities constant compared to SCALE concretes, the density of the material is raised to 2.90 and 2.91 gm/cm3 for the dry and wet conservative concrete respectively.

10-4

Table 10-5 Elemental compositions of the conservative concrete Wet Dry Conservative Conservative Element Concrete Concrete (wt%) (wt%)

Fe 0.45 0.45 H 0.26 0.0 C 13.97 14.00 O 42.41 42.52 Na 2.31 2.32 Mg 7.51 7.53 Al 2.71 2.72 Si 26.87 26.94 Ca 3.51 3.52 Density (gm/cm3) 2.91 2.90 Table 10-6 provides the results of the analysis of the conservative concrete. The four conservative concretes preserve or remove the hydrogen and preserve the density or atom density. Preserving the atom density and removing the hydrogen causes the maximum reactivity effect and is selected for future work. The selected conservative concrete appears to have a large impact on reactivity (0.0087) in the small 4x4 model, but when used in a full pool with a normal water gap, and a stainless steel liner the impact would be smaller.

Table 10-6 Reactivity effect of different concrete compositions Hydrogen Density k from Concrete Model k wt% (g/cm3) Rocky Flats Rocky Flats 1.01 2.32 1.1406 -

Conservative Concrete 0.26 2.32 1.1456 0.0050 Conservative Concrete 0.26 2.91 1.1455 0.0049 Conservative Concrete 0 2.32 1.1482 0.0076 Conservative Concrete 0 2.90 1.1493 0.0087 It is recommended that future criticality analyses of SFPs may use the dry conservative concrete specified on Table 10-5 with a density of 2.90 gm/cm3.

This conservative concrete can be used for all concretes and no further verification of the concrete conservatism is needed. This analysis did not address the optimum moderator condition for dry new fuel racks and the new fuel racks are much more sensitive to concrete composition.

10-5

Section 11: Impact of Pool Temperature on Reactivity To determine the impact of pool temperature on reactivity, one commonly used approach is to perform the analysis at expected minimum and maximum pool temperatures. This section presents the computational results for determining whether intermediate temperatures need to be analyzed in addition to minimum and maximum temperatures.

The analysis was performed using W 17x17 fuel for a subset of the standard configurations. It is assumed that the fuel and water were at the same temperature. The temperatures and densities used in the analysis are given in Table 11-1. Figure 11-1 shows the change in reactivity as a function of temperature for over-moderated racks for which cell separation is used to control reactivity (that is, Region 1 racks). Figure 11-2 shows the reactivity for under-moderated racks.

Region 1 racks without neutron absorber panels use separation for reactivity control. In these racks, the absorption in water is important; therefore, increasing the temperature reduces the water density and thus produces a positive reactivity effect. However, when the Region 1 racks have absorber plates, they too are under-moderated. It should be noted that a checkerboard arrangement of fuel in Region 2 with no neutron absorber uses separation to control reactivity; once again, increasing the temperature results in increases in reactivity.

The reactivity for Region 2 racks decreases with increasing temperature. The fuel is under-moderated by design in order to provide a negative power coefficient. It is important to note that the extra water in the racks is not sufficient to overwhelm this design feature. Absorbers in the racks increase this under-moderation, hence the separation in the lines on Figure 11-2.

For all of the cases analyzed, the highest reactivity is produced at the highest or lowest temperature. The Doppler feedback in the fuel is always negative. If the water reactivity change is positive, the two effects could cause a local minimum in reactivity. As evident from Figure 11-1, the behavior can deviate from monotonic increase. Hence, it is recommended to compute reactivity at highest, lowest, and intermediate temperatures to capture full behavior.

11-1

Table 11-1 Water density at 2 atm Temperature Temperature Water Density (K) (oF) (g/cm3) 277 39.2 1.00000 293 68 0.99825 303 86 0.99569 313 104 0.99226 323 122 0.98808 333 140 0.98324 343 158 0.97781 353 176 0.97184 363 194 0.96536 373 212 0.95840 383 230 0.95098 393 248 0.94311 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

Section 12: Impact of Gadolinium Burnable Absorbers on Spent Fuel Reactivity Burnable absorberswhich commonly take the form of 1) burnable poison rods (BPR) and 2) integral burnable absorbers (IBA)are used in PWRs to reduce the soluble boron level at the beginning of the cycle and to help control power distribution. Burnable poison rods contain neutron absorbing material inserted into the guide tubes of a PWR assembly during normal operation for reactivity control and enhanced fuel utilization. However, integral burnable absorbers are non-removable and are an integral part of the fuel assembly once it is manufactured. The four most commonly used IBA types in U.S. PWRs include

1) Westinghouse IFBA rod, 2) CE and Siemens assembly designs with UO2-Gd2O3 rods, 3) CE assembly designs with UO2-Er2O3 rods, and 4) CE assembly design Al2O3-B4C rods. Unlike the first three, the last one does not contain any fuel [17].

The impact of burnable absorbers on reactivity has also been studied by others

[17, 18]. Based on the previous work, it is concluded that ignoring Erbium in the analysis is conservative, and no future analysis is needed.

Similarly, for gadolinium extensive analysis is performed and documented [17].

The analysis documented in [17] compared reactivity with and without gadolinium while maintaining the reduced enrichment pins at the same location in the fuel assembly. When utilities compare their fuel assembly descriptions to their minimum burnup requirements, typically a volume-averaged enrichment is used. This study compares the reactivity of the gadolinium-bearing fuel assembly to the reactivity of the average enriched fuel assembly in order to ensure that possible non-conservative weighting of the enrichment does not overwhelm the residual gadolinium penalty.

The reactivity impact of gadolinium as a function of burnup for CE and Siemens (now AREVA) designs were previously analyzed in [17]. There is no reduction in enrichment for CE Gd-bearing fuel rods. The Siemens cases used lower 235U enrichments for the gadolinium bearing rods. Four Siemens designs were studied, designated M1, M2, M3, and M4. Fuel assembly data for the M1-M4 assembly designs were taken from [17] and listed in Table 12-1. Further 12-1

description of the fuel assembly, including the location of the gadolinium pins, can be found in [17].

Table 12-1 Fuel assembly data for M1-M4 assembly designs [17]

No. of UO2-UO2 Fuel Rod No. of UO2 Gd2O3/235U wt%

Configuration Gd2O3 rods Enrichment rods per for Designation per (wt% 235U) assembly UO2-Gd2O3 rods assembly 16 8.0/3.91 M1 4.25 236 12 4.0/4.08 16 8.0/3.91 M2 4.25 240 8 4.0/4.08 16 6.0/3.99 M3 4.25 244 4 2.0/4.16 M4 4.25 260 4 2.0/4.16 The computations were performed for these four cases using SCALE, and the results were compared against the same design with average enrichments. The volume-averaged enrichments for these four configurations are presented in Table 12-2. In the SCALE model, the gadolinium fuel pins were modeled using five equal volume concentric rings. The analysis was performed using the gadolinium assembly modeling guidance provided in the TRITON primer [19].

However, instead of using NEWT, flux calculations are performed using the KENO model. The modeling approach used in this work may not be adequate for the early depletion of gadolinium. More rings or additional neutron sampling may be required for the analysis of early depletion of gadolinium. However, because the residual worth of gadolinium is not sensitive to the early burnout rate, the presented approach is adequate for the purposes of this study.

Table 12-2 Volume-averaged enrichments for Siemens fuel Configuration Volume Averaged Enrichment Designation (wt% 235 U)

M1 4.223447 M2 4.225951 M3 4.233788 M4 4.248663 The computed reactivity values with and without gadolinium pins for these four configurations, using volume-averaged enrichment values, are presented in Figure 12-1. As shown in Figure 12-1, all of the k values decrease asymptotically towards zero and remain constant at this low k. The M4 configuration reaches equilibrium more rapidly since it has only 2 wt% Gd2O3 in 12-2

its fuel pins. In the inset of Figure 12-1, a closer look at lower values is included to clearly demonstrate the impact of gadolinium. The fluctuations at lower values are simply due to statistical uncertainties in Monte Carlo calculations. The reported one sigma uncertainty for these cases was about 0.0003 for each case.

Since the figure illustrates the difference between two Monte Carlo calculations, with and without gadolinium pins, the variation of about 0.001 would be expected. The average penalties due to the presence of gadolinium for the last 30 GWd/MTU for the M1, M2, M3, and M4 configurations are 0.0045, 0.0042, 0.0031, and 0.0003 respectively. These results track well with the amount of initial gadolinium in each configuration.

Figure 12-1 Reactivity effect of Gadolinium The reactivity effect due to gadolinium does not reach zero since 157Gd reaches equilibrium with 156Gd, and 155Gd reaches equilibrium with 154Gd. 154Gd and 156 Gd have low enough absorption cross sections such that they do not burn out.

The change in 154Gd content as a function of burnup is presented in Figure 12-2.

As can be seen from Figure 12-2, 154Gd content does not reach zero even at high burnup values. Since the 154Gd absorption cross section is sufficiently low, it does not burn out.

The change in 155Gd content as a function of burnup is illustrated in Figure 12-3.

In order to visualize the change in content for burnup values above 20 12-3

GWd/MTU, these values are re-plotted and shown in the Figure 12-3 inset. As can be seen from Figure 12-3, even at high burnup values, there is small amount of remaining 155Gd. Changes in 156Gd and 157Gd as a function of burnup are shown in Figure 12-4 and Figure 12-5, respectively.

Based on the previous studies [17, 18] and the computational results presented in this section, ignoring gadolinium in future analysis is conservative.

Figure 12-2 Non-fission product 154 Gd content as a function of burnup Figure 12-3 Non-fission product 155 Gd content as a function of burnup 12-4

Figure 12-4 Non-fission produced 156 Gd content as a function of burnup Figure 12-5 Non-fission product 157 Gd content as a function of burnup 12-5

Section 13: Summary and Conclusions The NEI 12-16 criticality guidance document was issued in 2013 and submitted to the NRC for review and endorsement. Once endorsed, it is anticipated that NEI 12-16 will supersede the previous guidance documents. As part of the review process, four NRC/NEI public meetings with industry and EPRI participation were conducted, and a series of items were identified for further analysis to provide technical justification for simplifying assumptions. The goal of the additional work was to demonstrate that the impact of certain parameters on criticality analysis are negligible and therefore can be ignored in future analyses.

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.

The sensitivity analyses were performed for representative fuel and rack geometries. The majority of the analyses were performed using Westinghouse 17x17 fuel; however, to demonstrate the validity of conclusions for other fuel types, the computations were repeated for Combustion Engineering 16x16 fuel for a subset of the parameters. The sensitivity analyses were performed for three neutron absorber areal densities, three different enrichments, and six burnups to ensure coverage of a wide range of parameters and scenarios. For this purpose, more than 1000 calculations were performed using SCALE 6.1.2 with 238 group ENDF/B-VII cross section libraries. Key conclusions based on the computational results are:

The impact of the in-core measurement thimbles on reactivity is small but not negligible (greater than 50 pcm for some cases). It is recommended that the measurement thimble be included in future analysis and modeled as a void in the calculations.

Manufacturing tolerances on the guide tubes, instrument tubes, and the fuel pin cladding inner diameter (or thickness), have negligible impact on computed reactivity and can therefore be ignored in future analyses.

Typically, the limiting condition in the criticality safety analysis is the unborated condition. Usually, excess soluble boron margin covers normal operation and accident conditions in PWR spent fuel pools. Therefore, instead of computing uncertainties due to manufacturing tolerances and bias due to the grid, analysts should reserve 50 ppm of soluble boron margin to offset these effects. This amount can be added to the required soluble boron concentration level for accident cases. The 50 ppm recommendation 13-1

conservatively covers the effects due to changes in manufacturing tolerances and grids not being modeled.

The reactivity impact of manufacturing tolerances on neutron absorber panel sheathing is negligible for Region 2 that credit absorber panels and it is recommended that further analysis is not required.

Computations demonstrated that a separation of 25 cm (~10 in) is sufficient for neutronic decoupling of assemblies. Therefore, interface analysis is not needed when a PWR rack has an empty row of cells between regions.

The number of assemblies that corresponds to an infinite model has been investigated. It has been shown that four assemblies (2x2 array) produce a reactivity that is 90% of an infinite model, while 16 assemblies (4x4 array) produce a reactivity value that is 97% and 95% of an infinite model for Region 1 and 2, respectively. It is concluded that small sets of assemblies require significant excess reactivity to cause a criticality concern.

For eccentric positioning of fuel assemblies in a storage rack with absorber panels on all sides of each cell there is a negligible impact on reactivity, compared to centric positioning. Consequently, no further analysis is needed when neutron absorber materials are present. However, when neutron absorber panels are not present, eccentric positioning of the assemblies can have an impact on the reactivity and this must be addressed using a large model in the SFP criticality analysis.

The impact of concrete composition on SFP reactivity was investigated. A concrete composition was established that is conservative for criticality analysis.

One of the approaches used in criticality safety analysis is to perform computations at minimum and maximum pool temperatures. To address concerns of any hidden local maximum at intermediate temperatures, computations were performed for intermediate values and no local maximum was found. However, it is recommended to perform computations at minimum, maximum, and intermediate temperatures.

Based on the previous studies and additional computations provided in this report, ignoring gadolinium burnable absorbers in a criticality safety analysis is conservative.

13-2

Section 14: References

1. NEI 12-16, Revision 1, Guidance for Performing Criticality Analyses of Fuel Storage at Light-Water reactor Power Plants, April 2014. NRC Adams access number ML14112A516.

http://pbadupws.nrc.gov/docs/ML1411/ML14112A516.pdf

2. Summary of September 24, 2013 Meeting on NEI 12-16, Guidance for performing criticality analyses of fuel storage at light-water reactor power plants, NRC Adams access number ML13268A115 http://pbadupws.nrc.gov/docs/ML1326/ML13268A115.pdf

3. Summary of October 31, 2013 Meeting on NEI 12-16, Guidance for performing criticality analyses of fuel storage at light-water reactor power plants, NRC Adams access number ML13309B558 https://www.nrc.gov/docs/ML1330/ML13309B558.pdf

4. Summary of January 17, 2014 Guidance for performing criticality analyses of fuel storage at light-water reactor power plants, NRC Adams access number ML14021A018 http://pbadupws.nrc.gov/docs/ML1402/ML14021A018.pdf

5. Summary of February 19, 2014 Guidance for performing criticality analyses of fuel storage at light-water reactor power plants, NRC Adams access number ML14051A252 http://pbadupws.nrc.gov/docs/ML1405/ML14051A252.pdf

6. Presentation material for NRC/NEI public meeting on NEI 12-16, September 24, 2013, NRC Adams access number ML13264A008 http://pbadupws.nrc.gov/docs/ML1326/ML13264A008.pdf

7. Presentation material for NRC/NEI public meeting on NEI 12-16, October 31, 2013, NRC Adams access number ML13308A015.

http://pbadupws.nrc.gov/docs/ML1330/ML13308A015.pdf

8. Presentation material for NRC/NEI public meeting on NEI 12-16, January 17, 2014, NRC Adams access number ML14021A016.

https://www.nrc.gov/docs/ML1402/ML14021A016.pdf.

9. Presentation material for NRC/NEI Public meeting on NEI 12-16, February 19, 2014, NRC Adams access number ML14050A10 http://pbadupws.nrc.gov/docs/ML1405/ML14050A010.pdf

10. Benchmarks for Quantifying Fuel Reactivity Depletion Uncertainty, EPRI, Palo Alto, CA: 1022909 (2011):

14-1

11. C.W. Gabel, PWR Reactor Physics Methodology Using Studsvik Design Codes, SCE-0901, Southern California Edison Company, San Clemente, CA, January 2009. NRC Adams access number ML090360738.

12. Scale: A Comprehensive Modeling and Simulation Suite for Nuclear Safety Analysis and Design, ORNL/TM-2005/39, Version 6.1, June 2011. Available from Radiation Safety Information Computational Center at Oak Ridge National Laboratory as CCC-785.

13. Chrome-plated Flux Thimbles, NS-ES-0042 (75370), Westinghouse Nuclear Services/Engineering Services, Pittsburgh, PA, January 2009.

14. Licensing Report For Beaver Valley Unit 2 Rerack, HI-2084175, Holtec International, New Jersey, October, 2010. (Table 4.5.2) NRC Adams access number ML102940458.

15. Licensing Report For Waterford Unit 3 Spent Fuel Pool Criticality Analysis, HI-2084014, Holtec International, New Jersey, July, 2008. (Page 13) NRC Adams access number ML082660649.

16. Standard Specification for General Requirements for Flat-Rolled Stainless and Heat-Resisting Steel Plate, Sheet, and Strip, ASTM A480/A480M-13b, ASTM International, West Conshohocken, PA, November 2013.

17. C.E. Sanders and J.C. Wagner, Study of the Effect of Integral Burnable Absorbers for PWR Burnup Credit, NUREG/CR-6760 (ORNL/TM-2000-321), U. S. Nuclear Regulatory Commission, Oak Ridge National Laboratory, March 2002.

18. J.R. Secker and J.A. Brown, Westinghouse PWR Burnable Absorber Evolution and Usage, Transactions- American Nuclear Society; 103; 733-734, American Nuclear Society, Winter Meeting, American Nuclear Society, 2010.

19. B.J. Ade, SCALE/TRITON Primer: A Primer for Light Water Reactor Lattice Physics Calculations, NUREG/CR-7041 (ORNL/TM-2011/21), U S.

Nuclear Regulatory Commission, Oak Ridge National Laboratory, November 2012.

20. Dominion Nuclear Connecticut, Inc., Millstone Power Station Unit 2 Response To Second Request For Additional Information Regarding Proposed Technical Specification Change For Spent Fuel Storage, July 21, 2015. NRC Adams access number ML15209A729.

21. Millstone Power Station, Unit No. 2 - Issuance Of Amendment Re:

Technical Specification Changes For Spent Fuel Storage Millstone Power Station, Unit No. 2 - Issuance Of Amendment Re: Technical Specification Changes For Spent Fuel Storage (Tac No. MF0435), June 23, 2016. NRC Adams access number ML16003A008.

22. Dale B. Lancaster, Bob Hall, and Charles T. Rombough, New Approach to Eccentric Positioning of Fuel Assemblies in a Spent Fuel Pool, Transactions of the American Nuclear Society, Vol. 114, New Orleans, Louisiana, June 12-16, 2016.

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Appendix A: Electronic Data In order to support confirmation of the analyses provided in this report, for verification and validation purposes, and facilitate future analysis of additional sensitivities for spent fuel pools, electronic data can be downloaded from the EPRI website. The electronic data includes all input files used in the analyses as well as a spreadsheet presenting all results. The spreadsheet is separated into separate sheets to cover the report topics.

A-1

The Electric Power Research Institute, Inc. (EPRI, www.epri.com) conducts research and development relating to the generation, delivery and use of electricity for the benefit of the public. An independent, nonprofit organization, EPRI brings together its scientists and engineers as well as experts from academia and industry to help address challenges in electricity, including reliability, efficiency, affordability, health, safety and the environment. EPRI members represent 90% of the electric utility revenue in the United States with international participation in 35 countries. EPRIs principal offices and laboratories are located in Palo Alto, Calif.; Charlotte, N.C.; Knoxville, Tenn.; and Lenox, Mass.

Together...Shaping the Future of Electricity Program:

Used Fuel and High-Level Waste Management

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