ML18088B397

Final Report 3002010613, Benchmarks for Quantifying Fuel Reactivity Depletion Uncertainty - Revision 1.

ML18088B397
Person / Time
Site:	Nuclear Energy Institute
Issue date:	10/31/2017
From:	Electric Power Research Institute
To:	Office of Nuclear Reactor Regulation
Shared Package
ML18088B394	List: ML18088B392 ML18088B395 ML18088B397 ML18088B398 ML18088B399 ML18088B400
References
Download: ML18088B397 (144)

Text

Benchmarks for Quantifying Fuel Reactivity Depletion UncertaintyRevision 1 2017 TECHNICAL REPORT

Benchmarks for Quantifying Fuel Reactivity Depletion UncertaintyRevision 1 All or a portion of the requirements of the EPRI Nuclear Quality Assurance Program apply to this product.

EPRI Project Manager A. Hakkurt 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 3002010613 www.epri.com Final Report, October 2017

DISCLAIMER OF WARRANTIES AND LIMITATION OF LIABILITIES THIS DOCUMENT WAS PREPARED BY THE ORGANIZATION(S) NAMED BELOW AS AN ACCOUNT OF WORK SPONSORED OR COSPONSORED BY THE ELECTRIC POWER RESEARCH INSTITUTE, INC. (EPRI).

NEITHER EPRI, ANY MEMBER OF EPRI, ANY COSPONSOR, THE ORGANIZATION(S) BELOW, NOR ANY PERSON ACTING ON BEHALF OF ANY OF THEM:

(A) MAKES ANY WARRANTY OR REPRESENTATION WHATSOEVER, EXPRESS OR IMPLIED, (I) WITH RESPECT TO THE USE OF ANY INFORMATION, APPARATUS, METHOD, PROCESS, OR SIMILAR ITEM DISCLOSED IN THIS DOCUMENT, INCLUDING MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, OR (II) THAT SUCH USE DOES NOT INFRINGE ON OR INTERFERE WITH PRIVATELY OWNED RIGHTS, INCLUDING ANY PARTY'S INTELLECTUAL PROPERTY, OR (III) THAT THIS DOCUMENT IS SUITABLE TO ANY PARTICULAR USER'S CIRCUMSTANCE; OR (B) ASSUMES RESPONSIBILITY FOR ANY DAMAGES OR OTHER LIABILITY WHATSOEVER (INCLUDING ANY CONSEQUENTIAL DAMAGES, EVEN IF EPRI OR ANY EPRI REPRESENTATIVE HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES) RESULTING FROM YOUR SELECTION OR USE OF THIS DOCUMENT OR ANY INFORMATION, APPARATUS, METHOD, PROCESS, OR SIMILAR ITEM DISCLOSED IN THIS DOCUMENT.

REFERENCE HEREIN TO ANY SPECIFIC COMMERCIAL PRODUCT, PROCESS, OR SERVICE BY ITS TRADE NAME, TRADEMARK, MANUFACTURER, OR OTHERWISE, DOES NOT NECESSARILY CONSTITUTE OR IMPLY ITS ENDORSEMENT, RECOMMENDATION, OR FAVORING BY EPRI.

THE FOLLOWING ORGANIZATIONS, UNDER CONTRACT TO EPRI, PREPARED THIS REPORT:

Massachusetts Institute of Technology (MIT)

Studsvik Scandpower, Inc.

THE TECHNICAL CONTENTS OF THIS PRODUCT WERE NOT PREPARED IN ACCORDANCE WITH THE EPRI QUALITY PROGRAM MANUAL THAT FULFILLS THE REQUIREMENTS OF 10 CFR 50, APPENDIX B. THIS PRODUCT IS NOT SUBJECT TO THE REQUIREMENTS OF 10 CFR PART 21.

NOTE For further information about EPRI, call the EPRI Customer Assistance Center at 800.313.3774 or e-mail askepri@epri.com.

Electric Power Research Institute, EPRI, and TOGETHERSHAPING THE FUTURE OF ELECTRICITY are registered service marks of the Electric Power Research Institute, Inc.

Copyright © 2017 Electric Power Research Institute, Inc. All rights reserved.

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

Massachusetts Institute of Technology (MIT) 77 Massachusetts Ave.24-221 Cambridge, MA 02139 Principal Investigator K. Smith Studsvik Scandpower, Inc.

309 Waverley Oaks Road Suite 406 Waltham, MA 02452 Principal Investigators S. Tarves T. Bahadir R. Ferrer This report describes research sponsored by EPRI.

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

Benchmarks for Quantifying Fuel Reactivity Depletion Uncertainty Revision 1.

EPRI, Palo Alto, CA: 2017.

3002010613.

iii

Abstract Analytical methods, described in this report, are used to systematically determine experimental fuel assembly sub-batch reactivity as a function of burnup. Fuel sub-batch reactivities are inferred using more than 600 in-core pressurized water reactor (PWR) flux maps taken during 44 cycles of operation at the Catawba and McGuire nuclear power plants.

The analytical methods systematically search for fuel sub-batch reactivities that minimize differences between measured and computed fission rates, using Studsvik Scandpowers CASMO-5 and SIMULATE-3 reactor analysis tools. More than eight million SIMULATE-3 core calculations are used to reduce one million measured fission rate signals to a set of ~3000 experimental fuel sub-batch reactivities over the range of 0 to 55 gigawatt-days per metric ton (GWd/T) burnup.

Experimental biases derived for the CASMO-5 lattice physics code were used to develop a series of experimental benchmarks that can be used to quantify fuel assembly reactivity decrement biases and uncertainties of other code systems used in spent-fuel pool (SFP) and cask criticality analyses. Specification of eleven experimental lattice benchmarks, covering a range of enrichments, burnable absorber loading, boron concentration, and lattice types are documented in this report.

This report provides a basis for quantification of combined nuclide inventory and cross-section uncertainties in computed reactivity burnup decrements. Final 95/95 tolerance limits for the measured reactivity decrements are shown to be less than 3.05% of the fuel assembly depletion reactivity.

Results support reactivity decrement tolerance limits that are smaller than the 5% assumption that has historically been applied in SFP criticality analysis, and this assumption has now been demonstrated to be both valid and conservative for CASMO-5 based fuel depletion analyses.

Keywords Cask criticality Depletion uncertainty Experimental benchmarks Nuclear criticality Reactivity depletion Spent fuel pool criticality v

EXECUTIVE

SUMMARY

Deliverable Number: 3002010613 Product Type: Technical Report Product

Title:

Benchmarks for Quantifying Fuel Reactivity Depletion Uncertainty Revision 1 PRIMARY AUDIENCE: Nuclear criticality safety analysts at nuclear power plants and regulators SECONDARY AUDIENCE: Nuclear criticality safety analysts at research organizations and vendors KEY RESEARCH QUESTION What are the magnitudes of the bias and uncertainty in analytical computations of depleted fuel reactivity for burnup credit analysis that arises from depletion during nuclear plant operation? By using the eleven benchmark lattices presented in this report, applicants can provide the technical justification for the biases and uncertainties in depleted fuel reactivity needed in spent fuel criticality licensing applications.

RESEARCH OVERVIEW Experimentally measured flux map data from forty-four cycles of operation of the Duke Energy Catawba and McGuire plants has been used to infer the hot full power (HFP) bias and uncertainty of CASMO-5 computed lattice depletion reactivity decrements. TSUNAMI module of the SCALE code system has been used to extend the HFP uncertainties to cold spent fuel pool (SFP) rack conditions. The measured depletion reactivity decrements for eleven pressurized water reactor (PWR) benchmark lattices are tabulated and provided to spent fuel criticality analysts so that they can quantify the biases and uncertainties of their specific lattice depletion and criticality analysis computational tools.

KEY FINDINGS

• CASMO-5 HFP reactivity burnup decrement biases are less than 200 pcm over the burnup range from 10 to 60 GWd/T.

• Cold reactivity burnup decrement uncertainties are approximately 350 pcm at 10 GWd/T and 900 pcm at 60 GWd/T.

• Reactivity decrement tolerance limits are smaller than the 5% historical assumption (Kopp Memo) traditionally applied in SFP criticality analysis.

• The 95/95 tolerance limits for the measured reactivity decrements are shown to be less than 3.05% of fuel assembly depletion reactivities.

WHY THIS MATTERS Use of the eleven benchmark lattices provided in this report provides a more straightforward path to determining the biases and uncertainties in spent fuel depletion analysis. Furthermore, quantification of reactivity decrement biases and uncertainties for spent fuel analysis tools provides technical justification for the validity of the historical Kopp Memo 5% criterion, as this analysis demonstrated that historical Kopp memo recommendation is conservative.

vii

EXECUTIVE

SUMMARY

HOW TO APPLY RESULTS Spent fuel criticality analysts can compute the eleven experimental benchmarks provided in this report and deduce biases and uncertainties for their specific nuclide depletion and criticality analysis codes. These biases and uncertainties can be combined with other uncertainties to establish 95/95 tolerance limits on computed spent fuel criticality eigenvalues for depleted fuel assemblies in their licensing submittals.

LEARNING AND ENGAGEMENT OPPORTUNITIES

• This report, along with companion report (3002010614, Utilization of the EPRI Depletion Benchmarks for Burnup Credit Validation - Revision 1) has been developed for criticality analysts working on burnup credit.

• In addition to these two reports, 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.

Acronyms BOC Beginning of Cycle CMS Core Management System EFPD Effective Full Power Days EOC End of Cycle EFPD Effective Full Power Days EOFP End of Full Power EPRI Electric Power Research Institute HFP Hot Full Power HZP Hot Zero Power IFBA Integral Fuel Burnable Absorbers LPB Lumped Burnable Poisons NEI Nuclear Energy Institute NRC Nuclear Regulatory Commission OFA Optimized Fuel Assembly OLS Ordinary Least Square ORNL Oak Ridge National Laboratory PWR Pressurized Water Reactor RAI Request for Additional Information RFA Robust Fuel Assembly SFP Spent Fuel Pool WABA Wet Absorber Burnable Poisons WLS Weighted Least Square ix

Table of Contents Abstract ................................................................. V Executive Summary .............................................. VII Section 1: Product Description ............................. 1-1 1.1 Analytical Methods .................................................... 1-2 1.2 Summary of Results .................................................... 1-3 1.3 Experimental Benchmarks ........................................... 1-3 1.4 Summary of Conclusions ............................................ 1-4 1.5 Significant Changes from Previous (Rev 0)

Document ....................................................................... 1-4 Section 2: Introduction ........................................ 2-1 2.1 Background .............................................................. 2-1 2.2 Historical Approaches................................................ 2-2 2.3 Project Outline .......................................................... 2-3 Section 3: Summary of Analysis Approach .......... 3-1 3.1 Overview ................................................................. 3-1 3.2 Flux Map Measurements ............................................ 3-1 3.3 Relationship of Flux Map Errors to Fuel Reactivity .......... 3-1 3.4 Flux Map Perturbation Calculations ............................. 3-2 3.5 Measured Sub-batch Reactivity Errors .......................... 3-4 3.6 Simultaneous Determination of All Sub-batches Reactivities ..................................................................... 3-5 Section 4: Analysis Codes: Studsvik CMS ............. 4-1 4.1 Code System Overview .............................................. 4-1 Section 5: Duke Energys Reactor Models ............ 5-1 5.1 Overview ................................................................. 5-1 5.2 Fuel Types ................................................................ 5-3 5.3 CMS Code Versions .................................................. 5-4 5.4 Core Follow Summary Results ..................................... 5-4 5.5 Flux Map Summary Results ......................................... 5-8 5.6 Reactor Model Summary ............................................ 5-8 Section 6: Details of Analysis Implementation ..... 6-1 xi

6.1 Super-batch Definitions............................................... 6-1 6.2 3D Versus 2D Searches.............................................. 6-1 6.3 Sub-batch Sensitivities ................................................ 6-5 6.4 Iteration Implementation ............................................. 6-6 Section 7: Measured HFP Reactivity Bias and Uncertainty......................................... 7-1 7.1 Interpretation of Data ................................................. 7-1 7.2 Sub-batch Sensitivities ................................................ 7-4 7.3 Sensitivities to Reactor Unit ......................................... 7-5 7.4 Sub-batch Enrichment Sensitivities................................ 7-7 7.5 Burnup Reactivity Decrement Biases and Prediction Intervals.......................................................................... 7-7 7.6 Further Refinements of Burnup Reactivity Decrement Biases and Prediction Intervals ........................................ 7-14 7.7 Boron and Cycle Burnup Sensitivities ......................... 7-21 7.8 Sensitivity to Lattice and Nodal Codes ....................... 7-21 Section 8: Measured Cold Reactivity Bias and Uncertainty......................................... 8-1 8.1 Overview ................................................................. 8-1 8.2 Fuel Temperature Uncertainties.................................... 8-1 8.3 Cold Uncertainty Change From Cross-Section Uncertainties ................................................................... 8-3 8.4 TSUNAMI Uncertainty Analysis ................................... 8-4 8.5 TSUNAMI Analysis Results .......................................... 8-5 8.6 HFP to Cold Reactivity Decrement Uncertainty ............. 8-14 8.7 Cold Reactivity Decrement Bias and Tolerance Limit ............................................................................. 8-16 Section 9: Experimental Reactivity Decrement Benchmarks ....................................... 9-1 9.1 Experimental Benchmark Methodology ........................ 9-1 9.2 Experimental Benchmark Specification ......................... 9-1 9.3 Experimental Reactivity Decrement Tables .................... 9-3 9.4 End-Users Application of Experimental Reactivity Decrements ..................................................................... 9-3 Section 10:Summary of Conclusions ................... 10-1 10.1 Bias and Tolerance Limits in Percent of Depletion Reactivity Decrement ...................................................... 10-1 10.2 General Conclusions.............................................. 10-2 10.3 CASMO-5 Specific Conclusions .............................. 10-2 10.4 Related Conclusions............................................... 10-3 10.5 Experimental Benchmarks ....................................... 10-3 xii

Section 11:References ........................................ 11-1 Appendix A: Studsvik CMS Analysis Codes ....... A-1 A.1 Code System Overview.............................................. A-1 A.2 INTERPIN-4 .............................................................. A-2 A.3 INTERPIN-4 Thermal Conductivities ............................. A-2 A.4 INTERPIN-4 Solid Pellet Swelling and Gap Conductance .................................................................. A-3 A.5 INTERPIN-4 Fuel Temperature Edits for SIMULATE-3 ...... A-3 A.6 CASMO-4 Lattice Physics Code .................................. A-4 A.7 CASMO-4 Cross Section Library ................................. A-4 A.8 CASMO-4 Isotopic Depletion Model ........................... A-7 A.9 CASMO-5 Lattice Physics Code .................................. A-7 A.10 CASMO-5 Baffle/Reflector Models ........................... A-7 A.11 CMSLINK - CASMO-to-SIMULATE Linking Code ......... A-8 A.12 CMSLINK Multi-dimensional Data Tabulation.............. A-8 A.13 SIMULATE-3 Nodal Code Overview .......................... A-9 A.14 SIMULATE-3 PWR Thermal Hydraulics Model ........... A-10 A.15 SIMULATE-3 Nuclear Data Interpolation................... A-11 A.16 SIMULATE-3 Two-group Nodal Diffusion Model ........ A-11 A.17 SIMULATE-3 Macroscopic Depletion Model.............. A-13 A.18 SIMULATE-3 Detector Fission Rate Computation ........ A-14 Appendix B: Reactivity Benchmark Specifications...................................... B-1 B.1 Nominal Fuel Assembly .............................................. B-3 B.2 CASE 1: 3.25% Enriched - No Burnable Absorbers ....... B-4 B.3 CASE 2: 5.00% Enriched - No Burnable Absorbers ....... B-5 B.4 CASE 3: 4.25% Enriched - No Burnable Absorbers ....... B-6 B.5 CASE 4: Small Fuel Pin .............................................. B-7 B.6 CASE 5: 20 Lumped Burnable Poison (WABA) Pins ....... B-8 B.7 CASE 6: 104 Integral Fuel Burnable Absorbers (IFBA)

Pins................................................................................ B-9 B.8 CASE 7: 104 IFBA and 20 WABA Pins ..................... B-10 B.9 CASE 8: High Boron Depletion ................................. B-11 B.10 CASE 9: Nominal Case Branched to SFP Hot Isothermal Temperatures = 150F .................................... B-12 B.11 CASE 10: Nominal Case Branched to SFP High Rack Boron Concentration = 1500 ppm .................................. B-13 B.12 CASE 11: High Power (150% of Nominal)

Depletion .............................................................................

................................................................................... B-14 Appendix C: Reactivity Benchmark Specifications...................................... C-1 xiii

C.1 Burnup Reactivity Decrements: Cold, No Cooling ......... C-2 C.2 Burnup Reactivity Decrements: Cold, 100-hour Cooling . C-3 C.3 Burnup Reactivity Decrements: Cold, 5-Year Cooling ..... C-3 C.4 Burnup Reactivity Decrements: Cold, 15-Year Cooling ... C-4 xiv

List of Figures Figure 1-1 Reactivity Decrement Example ........................... 1-1 Figure 1-2 CASMO-5 HFP Reactivity Decrement Bias vs.

Sub-Batch Burnup ....................................................... 1-2 Figure 2-1 CASMO-5 Reactivity Decrement ........................ 2-2 Figure 3-1 Computed Fission Rate Errors With 3 Sub-batch Burnup Multipliers Applied to One Sub-batch (yellow boxes) ...................................................................... 3-3 Figure 3-2 Change in r.ms. Fission Rate Error vs. Sub-batch Multiplier .................................................................. 3-5 Figure 3-3 Determination of Sub-batch Burnup Multiplier as a Function of Burnup .................................................. 3-5 Figure 3-4 Nodal (3D) r.m.s. Differences for One Sub-batch . 3-6 Figure 3-5 Radial (2D) r.m.s. Differences for One Sub-batch . 3-7 Figure 5-1 Comparison of SIMULATE and Measured Boron .. 5-5 Figure 6-1 Cycle 12 - Nodal r.m.s. Fission Rates ................ 6-2 Figure 6-2 Cycle 12 - Radial r.m.s. Fission Rates ................ 6-3 Figure 6-3 Cycle 19 - Nodal r.m.s. Fission Rates ................ 6-4 Figure 6-4 Cycle 19 - Radial r.m.s. Fission Rates ................ 6-4 Figure 6-5 Multi-cycle Sub-batch Minimization .................... 6-5 Figure 6-6 Multi-cycle Sub-batch Minimization, Split Batch ... 6-6 Figure 6-7 Effective Multi-cycle Sub-batch Minimization........ 6-8 Figure 7-1 Casmo-5 Bias in Reactivity ................................ 7-2 Figure 7-2 Reactivity Decrement Bias vs. Sub-batch Sensitivity .................................................................. 7-4 Figure 7-3 Bias in Reactivity Decrement - McGuire-1 ........... 7-5 Figure 7-4 Bias in Reactivity Decrement - McGuire-2 ........... 7-6 xv

Figure 7-5 Bias in Reactivity Decrement - Catawba-1 .......... 7-6 Figure 7-6 Bias in Reactivity Decrement - Catawba-2 .......... 7-7 Figure 7-7 CASMO-5 Decrement Bias Fit - Quadratic Regression................................................................. 7-8 Figure 7-8 Decrement Bias Prediction Interval vs. Sub-batch Burnup ...................................................................... 7-9 Figure 7-9 Decrement Bias Variance Shape vs. Sub-batch Burnup .................................................................... 7-10 Figure 7-10 Decrement Bias WLS Linear Regression vs.

Burnup .................................................................... 7-11 Figure 7-11 Decrement Bias WLS Quadratic Regression vs. Burnup ............................................................... 7-11 Figure 7-12 Decrement Bias Standard Deviation vs. Sub-batch Sensitivity ....................................................... 7-12 Figure 7-13 Decrement Bias Variance Shape vs. Sub-batch Sensitivity ................................................................ 7-13 Figure 7-14 Decrement Bias WLS Quadratic Regression vs.

Burnup .................................................................... 7-14 Figure 7-15 Correction for Sub-Batch Burnup Distributions .. 7-15 Figure 7-16 Intra-batch Reactivity Decrement Bias Addition vs. Sub-batch Burnup ................................................ 7-16 Figure 7-17 Cycle-collapsed Reactivity Decrement Data ..... 7-17 Figure 7-18 Reactivity Decrement Quadratic WLS Regression for Cycle-collapsed Data ........................... 7-18 Figure 7-19 Reactivity Decrement Linear WLS Regression For Cycle-collapsed Data ................................................ 7-19 Figure 7-20 Normality Tests of Cycle-Collapsed WLS Regression Residuals ................................................ 7-20 Figure 8-1 Typical INTERPIN-4 Fuel Temperature Change With Burnup .............................................................. 8-2 Figure 8-2 Hot-to-Cold Additional Uncertainty vs. Burnup ... 8-15 Figure A-1 UO2 Conductivity as a Function of Burnup and Temperature .............................................................. A-3 Figure A-2 Typical INTERPIN-4 Fuel Temperature Change with Burnup ............................................................... A-4 Figure A-3 Computational Flow Diagram of CASMO-4 ........ A-6 xvi

Figure A-4 CASMO-5 Baffle/Reflector Geometry ................ A-8 Figure A-5 SIMULATE-3 Flowchart ................................... A-10 xvii

List of Tables Table 1-1 Measured CASMO-5 HFP Reactivity Decrement Biases and Tolerance Limits ......................................... 1-3 Table 1-2 Measured CASMO-5 Cold Reactivity Decrement Biases and Tolerance Limits ......................................... 1-3 Table 5-1 Reactor and Fuel Data ....................................... 5-2 Table 5-2 Feed Fuel Characteristics ................................... 5-3 Table 5-3 McGuire Unit-1 Boron Comparisons .................... 5-6 Table 5-4 McGuire Unit-2 Boron Comparisons .................... 5-6 Table 5-5 Catawba Unit-1 Boron Comparisons ................... 5-7 Table 5-6 Catawba Unit-2 Boron Comparisons ................... 5-7 Table 5-7 Comparison of SIMULATE-3 and Measured Fission Rates .............................................................. 5-8 Table 7-1 Measured CASMO-5 HFP Reactivity Decrement Bias and Prediction Interval Half-Width ....................... 7-19 Table 7-2 Measured CASMO-5 HFP Reactivity Decrement Bias and Tolerance Limit ........................................... 7-21 Table 7-3 Measured CASMO-5 BOC to EOC Reactivity Decrements ............................................................. 7-21 Table 7-4 Inferred CASMO-5 Fuel Batch Reactivity Biases .. 7-23 Table 8-1 Fuel Temperature Effect on Hot and Cold Lattice Reactivity .................................................................. 8-3 Table 8-2 Multiplication Factor Uncertainty (2-sigma) as Function of Burnup ..................................................... 8-5 Table 8-3 HFP to Cold Reactivity Uncertainty (2-sigma) as Function of Burnup ..................................................... 8-6 Table 8-4 Correlation Coefficients, ck, Between Reactor Conditions by Lattice and Burnup ................................. 8-8 xix

Table 8-5 Correlation Coefficients, ck, Between Lattice Types (Relative to 0 GWd/T) .............................................. 8-10 Table 8-6 Correlation Coefficients, ck, Between Lattice Types (By Individual Burnup State)....................................... 8-11 Table 8-7 HFP to Cold Uncertainty Matrix (2-sigma) at Cold Conditions............................................................... 8-12 Table 8-8 HFP to Cold Uncertainty Matrix (2-sigma) in Rack Geometry ................................................................ 8-13 Table 8-9 HFP to Cold Additional Uncertainty Matrix (2-sigma in pcm) at Cold Conditions .............................. 8-14 Table 8-10 HFP to Cold Additional Uncertainty Matrix (2-sigma in pcm) at Cold Conditions .............................. 8-15 Table 8-11 HFP to Cold Additional Uncertainty (2-sigma) vs.

Burnup .................................................................... 8-15 Table 8-12 Measured CASMO-5 Cold Reactivity Decrement Biases and Tolerance Limits ....................................... 8-16 Table 9-1 Benchmark Lattice Cases .................................... 9-2 Table 10-1 Measured Cold Reactivity Decrements (in pcm) for Nominal Benchmark Lattices ................................. 10-1 Table 10-2 Measured CASMO-5 Cold Reactivity Decrement Biases and Tolerance Limits Expressed as Percentage of Absolute Value of Depletion Reactivity Decrement ........ 10-2 Table B-1 Benchmark Lattice Cases .................................... B-2 Table C-1 Reactivity Decrement 95/95 Tolerance Limits (in k) ........................................................................... C-2 Table C-2 Measured Reactivity Decrement - No Cooling (in k) ........................................................................... C-2 Table C-3 Measured Reactivity Decrement - 100-Hour Cooling (in k) .......................................................... C-3 Table C-4 Measured Reactivity Decrement Year Cooling (in k) ....................................................................... C-3 Table C-5 Measured Reactivity Decrement Year Cooling (in k) .......................................................... C-4 xx

Section 1: Product Description Methods for treating burnup credit in spent fuel pool criticality analysis commonly made use of the Nuclear Regulatory Commission (NRC) 1998 Kopp Memo [1], which allows analysts to use 5% of the computed fuel depletion k to compensate for reactivity decrement uncertainties (see Figure 1-1) which might arise from uncertainties in computed nuclide number densities and/or neutron cross sections.

Figure 1-1 Reactivity Decrement Example The guidance in the Kopp Memo provided regulatory clarity and stability for many years. Starting in 2005, regulatory staff positions on acceptable criticality analysis methods evolved through interactions with licensees, and the basis for the guidance in the Kopp Memo was portrayed as being insufficient in light of operational/licensing changes being sought by utilities. In 2010, the NRC requested that applicants supply quantification and/or justification for the 5%

reactivity decrement uncertainty assumption.

This report provides experimental quantification of pressurized water reactor (PWR) fuel reactivity burnup decrement biases and uncertainties obtained through extensive analysis of in-core flux map data from operating power 1-1

reactors. Analytical methods, described in this report, are used to systematically determine experimental fuel sub-batch reactivities that best match measured fission rate distributions and to evaluate biases and uncertainties of computed lattice physics fuel reactivities.

1.1 Analytical Methods Forty-four 18-month cycles of flux map data from Duke Energys Catawba (Units 1 and 2) and McGuire (Units 1 and 2) plants have been analyzed with Studsvik Scandpowers CASMO-5 [2] and SIMULATE-3 [3] reactor analysis codes. By systematically searching for fuel sub-batch reactivities that best match measured fission rate distributions, biases and uncertainties of computed reactivity decrements are experimentally determined. These analyses employ more than 8 million SIMULATE-3 nodal core calculations to extract approxi-mately 3000 measured sub-batch reactivities from flux map data. The individual estimates of the reactivity decrement bias (measured minus calculated reactivity decrement) form a large data set plotted here as a function of sub-batch burnup in Figure 1-2.

Note: positive reactivity decrement bias implies that the calculated reactivity decrement (a negative quantity) is too negative, and the calculated lattice eigenvalue change with depletion is being non-conservatively over-predicted.

Figure 1-2 CASMO-5 HFP Reactivity Decrement Bias vs. Sub-Batch Burnup 1-2

1.2 Summary of Results Differences between predicted and measured assembly reactivities, illustrated in the preceding figure, are caused by a number of factors: fission rate measurement uncertainties, modeling approximations in the nodal core simulator, uncertainties in fuel burnups, and uncertainties in assembly reactivities as a function of burnup.

The objective of this report is to quantify the latter component of uncertainty -

even though scatter in the data is dominated by other components. Regression analysis is used to determine best-estimate biases and tolerance limits of CASMO-5s computed HFP reactivity decrements, and it is shown that biases are less than 200 pcm and uncertainties are approximately 800 pcm at 60 GWd/T, as summarized in Table 1-1.

Table 1-1 Measured CASMO-5 HFP Reactivity Decrement Biases and Tolerance Limits Burnup (GWd/T) 10.0 20.0 30.0 40.0 50.0 60.0 CASMO-5 Bias (pcm) 66 101 106 80 22 -64 95/95 Tolerance Limit (pcm) 207 386 537 655 745 803 Analysis demonstrates that the bias and uncertainties are independent (within experimental uncertainties) of fuel assembly design, core boron concentration, and cycle burnup.

Analysis with TSUNAMI module of SCALE code system [4], developed by Oak Ridge National Laboratory (ORNL), is used to extend HFP results to cold conditions. It is shown that extremely high correlation of reactivities between hot and cold conditions results in additional uncertainties from HFP to cold conditions, and final biases and tolerance limits are summarized in Table 1-2 in units of pcm and percentage of depletion reactivity.

Table 1-2 Measured CASMO-5 Cold Reactivity Decrement Biases and Tolerance Limits Burnup (GWd/T) 10.0 20.0 30.0 40.0 50.0 60.0 CASMO-5 Bias (pcm) 66 101 106 80 22 -64 95/95 Tolerance Limit (pcm) 348 537 654 752 831 888 CASMO-5 Bias (% of depletion reactivity) 0.58 0.50 0.38 0.23 0.05 -0.13 95/95 Tolerance Limit (% of depletion reactivity) 3.05 2.66 2.33 2.12 1.95 1.81 1.3 Experimental Benchmarks The experimental biases derived for the CASMO-5 lattice reactivities are used to develop a series of experimental benchmarks that can be used to quantify reactivity decrement biases and uncertainties for other code systems used in lattice depletion and criticality analysis. Specification of eleven experimental 1-3

lattice benchmarks, covering a range of enrichments, burnable absorber loading, boron concentration, and lattice types are documented in this report.

Results demonstrate that experimental benchmarks are not sensitive to the cross-section library or code version used to reduce the experimental data.

Interested parties can use these experimental benchmarks and their analysis tools to generate reactivity decrement biases and tolerance limits that are specific to those tools.

1.4 Summary of Conclusions Results presented in this report provide quantification of combined nuclide inventory and cross-section uncertainties in reactivity burnup decrement which support a smaller reactivity decrement uncertainty than the 5% criterion often used in historical SFP analysis. The data presented in this report demonstrate that the 95/95 tolerance limit on CASMO-5 depletion reactivity decrements is less than 3.05% of depletion reactivity.

Experimental reactivity decrement biases derived from flux map data are also shown to be similar to those derived from changes in biases of reactor soluble boron concentration from beginning (BOC) to end of cycle (EOC).

1.5 Significant Changes from Previous (Rev 0) Document This report contains many significant changes from the initial EPRI report [5]

published in 2011. The previous analysis was also published in Reference [6].

Changes address issues raised in both NRC request for additional information (RAIs) and face-to-face meetings, and the most significant changes are:

Using weighted least square (WLS) regression models with weights to treat the reactivity decrement heteroscedasticity in both burnup and measurement sensitivity.

Collapsing burnup decrement bias data to one point per sub-batch/cycle, to eliminate the correlation effects between successive flux map data points within each cycle of operation.

Eliminating all post-minimization screening of sensitivity and cycle burnup data points that had been previously used to eliminate some low sensitivity data.

Determining 95/95 tolerance limits of measured reactivity decrements by using statistical methods to replace the perturbed library engineering approach that was previously used.

Using 1-sided 95/95 tolerance limits (and normality testing) to replace the 2-sigma uncertainties of the original report.

Replacing burnup-independent uncertainties with burnup-dependent tolerance limits, to more appropriately model the increasing uncertainty of measured burnup decrements with sub-batch burnups.

1-4

Section 2: Introduction

2.1 Background

Criticality analysis of spent fuel pools and casks is performed using large-scale Monte Carlo or multi-group transport eigenvalue calculations for various load-ings of spent fuel racks. These calculations have two fundamental sources of uncertainty: the nuclide inventory of the fuel assemblies, and neutron cross-section data. For racks loaded with fresh fuel, these uncertainties can be quanti-fied directly by making extensive comparisons of calculations with the many cold critical measurements that have been performed in rack geometries. Such analyses provide quantification of calculational uncertainties as a function of fuel assembly design, fuel pin enrichments, rack geometries, coolant temperature, coolant boron concentration, etc. Such uncertainties include contributions from:

the nuclide inventory of the fuel assemblies, basic neutron cross-section data, and analytical methods.

Since experimental criticals do not exist for depleted fuel assemblies, storage rack criticals provide no quantification of uncertainties arising from changes in nuclide concentrations and/or uncertainties in cross-section data for nuclides produced by depletion (for example, production of transuranic nuclides and fission products).

The difficulty and expense of performing depleted fuel criticals makes it clear that such data will not be available in the near future - so direct quantification of depletion uncertainties is not easily achieved.

The application of burnup credit in spent fuel pool and cask criticality analysis involves defining a large sequence of conservative calculations that cover all anticipated loadings and uncertainties in those analyses. Conservative assump-tions and/or uncertainties are applied to compensate for lack of complete know-ledge, for quantities such as: maximum fuel temperature, maximum moderator temperature, uncertainty in soluble boron concentration, maximum burnable absorber usage, most limiting axial burnup distribution, maximum error in the declared burnup. This report provides data that can be used for validation of lattice physics code predictions of commercial spent nuclear fuel nuclide concentrations and assembly burnup reactivities that include the uncertainties of fundamental nuclear cross sections.

2-1

2.2 Historical Approaches In order to compensate for the lack of depleted criticals, current methods for treating burnup credit in spent fuel pool criticality analysis often made use of the NRC 1998 Kopp Memo [1], which allowed analysts to use 5% of the fuel depletion k (computed using criticality tools) to compensate for reactivity decrement uncertainties which might arise from uncertainties in computed nuclide number densities and/or neutron cross sections. The guidance in the Kopp Memo provided regulatory clarity and stability for many years. Starting in 2005, regulatory staff positions on acceptable criticality analysis methods evolved through interactions with licensees, and the basis for the guidance in the Kopp Memo was portrayed as being insufficient in light of operational/licensing changes being sought by utilities. In 2010, the NRC requested applicants to supply quantification and/or justification for the historical 5% uncertainty assumption.

Figure 2-1 displays a CASMO-5 k-infinity curve versus burnup computed for a typical 17x17 fuel assembly without burnable absorbers. By comparing the computed k-infinity at any burnup with k-infinity at zero burnup, the computed reactivity decrement can be evaluated. In this figure, at a burnup of about 48 GWd/T, the reactivity decrement is about -40% delta-k. The Kopp Memo instructs one to assume that the reactivity decrement is only 95% of the com-puted reactivity decrement, which in this example, is equivalent to assuming that the fuel is approximately 2% k more reactive than computed.

Figure 2-1 CASMO-5 Reactivity Decrement 2-2

For cask criticality analysis, chemical assays have been used to validate the isotopic content, and MOX and UO2 critical experiments have been used to vali-date actinide worths. Various approaches have been used for validating fission product worths. The approach presented in this report simplifies the current approach for burnup credit by simultaneously addressing nuclide inventory and nuclide reactivity biases.

2.3 Project Outline The remainder of this document details a direct approach to quantifying fuel depletion uncertainties by using operational reactor data and corresponding reactor analysis tools. Comparisons of computed fuel depletion effects and measured core depletion effects are available from every operating reactor on a near continuous basis. One way of viewing reactor data is that they provide a great many instances of the depleted fuel criticals that we desire. These power reactor configurations include:

many assembly lattice types many burnable absorber types a spectrum of assembly burnups impacts of numerous minor fuel depletion effects, including:

- fuel stack elongation

- fuel pellet cracking

- fuel pellet swelling

- cladding corrosion/crud buildup

- fuel rod bowing Challenges in using measured reactor data and computed reactor models to quantify the uncertainty in reactivity decrements arise because of the need to:

Extract uncertainties for each fuel assembly enrichment/absorber type in cores containing many different fuel types.

Determine the burnup dependence of assembly reactivity decrement biases and uncertainties.

Account for differences in assembly reactivity uncertainties at hot operating conditions (~900K fuel temperature, ~550K coolant temperature) and the cold conditions that normally exist in spent fuel pools and casks.

The next section of this report provides an overview of the procedure used to experimentally quantify fuel reactivity decrement uncertainties. Subsequent sections provide:

Specific details of the implementation of this procedure.

An application of this analysis procedure to 44 cycles of measured reactor data from four Duke Energy PWRs.

2-3

Documentation of derived biases and tolerance limits in CASMO-5 reactivity burnup decrements.

A set of experimental benchmarks that can be used to quantify reactivity burnup decrement biases and uncertainties for any lattice physics code/criticality analysis tool.

2-4

Section 3: Summary of Analysis Approach 3.1 Overview In-core flux maps taken as a routine part of PWR operation (usually every 30 days) provide measured data that can be used to quantify the accuracy of computed assembly power distributions. This data are routinely used to determine 95/95 confidence intervals on predicted assembly and pin power distributions needed for NRC licensing of core designs.

The analytical methods employed in this project use the same measured flux map data and core analysis tools to deduce errors in assembly reactivities at each flux map and to determine the assembly depletion decrement bias and uncertainty. In order to use power reactor data to develop depletion decrement biases and uncer-tainties for each type of fuel assembly (for example, lattice pitch, fuel enrichment, burnable absorber type), one needs to separate the reactivity contributions of each fuel type in the core. Section 3 of this report outlines the analytical procedures used to determine depletion decrement biases and uncertainties, and Section 6 provides in-depth details of the procedure - as it has been implemented.

3.2 Flux Map Measurements At each flux map measurement, several (usually 5 or 6) traversing 235U fission chambers are passed axially through instrumentation tubes at the center of approximately 50 instrumented fuel assemblies. By collecting detector signals from all fission chambers as they are passed through a common instrument tube, an inter-calibration of the detector signals is performed and all 50 measured signals are re-normalized to provide a measured 3D spatial distribution of fission rates throughout the reactor core. The fission rates are typically integrated axially into 61 discrete intervals (~6 cm), which are later collapsed to correspond to the 24 axial nodes (~15 cm) that are typically used in reactor analysis models. This type of measurement is performed routinely, and measured fission rate distributions are used to monitor technical specification compliance of core power distributions.

3.3 Relationship of Flux Map Errors to Fuel Reactivity The concept of using flux maps to deduce errors in sub-batch fuel reactivities is motivated by the fact that the distribution of fission rates errors is sensitive to errors in the burnup dependence of computed fuel reactivity. If analysis models have errors in fuel reactivity that are independent of the fuel depletion, the spatial 3-1

shape of flux map errors would not be sensitive to errors in fuel reactivity. Such space-independent errors would be similar to those observed when the boron concentration is altered in a computational model - the reactivity change is nearly the same at all core locations, and differences between computed and measured fission rates are very insensitive to errors in boron concentration.

However, errors in fuel reactivity arising from imperfect predictions of nuclide concentrations or errors in neutron cross-section data will necessarily change (usually increase) with assembly burnup. Since reactors are loaded with fuel having a large range of burnups, any depletion-induced errors in fuel reactivity will necessarily have a spatial dependence across the reactor core. Consequently, the accuracy of computed fission rate distributions is sensitive to the spatial distribution of these reactivity errors. This core characteristic makes it possible to deduce the magnitude of errors in reactivity of each fuel sub-batch by determin-ing the spatial distribution of fuel reactivities that produces the best agreement with measured fission rate distributions.

3.4 Flux Map Perturbation Calculations The analysis technique employed here uses the SIMULATE-3 reactor analysis nodal code to perform a series of exact perturbation calculations to minimize the global root-mean-square deviation between measured and computed detector signals for each fuel sub-batch (assembly type, enrichment, and burnable absorber configuration, and burnup batch) in the reactor core. In this approach, sub-batch reactivity is altered by re-evaluating all nuclear lattice parameters (cross sections, discontinuity factors, detector response functions, etc.) at a new sub-batch nodal burnup. The computed sub-batch nodal burnup, which is used as the interpolant in the nuclear data library, is systematically altered by a factor, MB. The spatial distribution of fission rates is very sensitive to the fuel sub-batch reactivity, as is depicted in Figure 3-1 for three values of the sub-batch burnup multiplier (0.90, 1.0 and 1.10) applied to the highlighted assemblies. From this figure, it can be seen that the root mean square (r.m.s.) difference between calculated and measured radial fission rates (at the instrumented locations) are 4.2, 1.2, and 3.3%, for these cases. Individual assembly fission rates are more sensitive, with differences as large as 8.4% being observed for MB =0.9.

3-2

R P N M L K J H G F E D C B A

-0.005 -0.023 1 0.008 0.000 0.020 0.022

-0.046 -0.045 0.012 2 -0.020 -0.006 0.004 0.006 0.032 -0.003 0.032 -0.017 -0.042 -0.039 3 0.020 0.012 0.012 -0.012 0.007 0.039 0.064 0.013

-0.056 -0.051 0.061 4 -0.017 0.003 -0.008 0.020 0.055 -0.062 0.032 0.069 0.027 -0.042 5 0.010 -0.001 0.005 0.007

-0.010 -0.066 -0.015 0.055

-0.013 -0.018 0.038 6 0.004 0.011 -0.001 0.026 0.038 -0.040 0.039 0.031 0.064 -0.011 7 0.011 -0.011 0.011 -0.004

-0.014 -0.053 -0.039 0.002

-0.008 0.025 0.080 0.042 0.057 0.029 0.009 8 -0.003 0.013 0.008 0.002 -0.002 0.017 0.001 0.001 0.001 -0.059 -0.037 -0.056 0.005 -0.007

-0.009 0.048 0.084 -0.017 9 0.007 0.006 0.014 -0.004 0.022 -0.036 -0.051 0.009

-0.005 10 -0.002 0.001

-0.039 0.005 0.092 0.026 -0.036 11 -0.018 -0.017 0.020 0.004 -0.015 0.003 -0.037 -0.047 -0.016 0.005

-0.015 0.037 -0.048 12 -0.012 0.009 -0.003

-0.009 -0.016 0.040

-0.057 -0.068 0.025 -0.041 13 0.000 -0.018 0.013 -0.014 0.054 0.029 0.001 0.011

-0.052 0.002 -0.036 -0.070 14 -0.026 0.018 0.003 -0.031 0.000 0.033 0.041 0.006

-0.033 -0.005 r.m.s. diff 15 -0.012 -0.001 MB=0.9 4.2%

0.008 0.003 MB=1.0 1.2%

MB=1.1 3.3%

Figure 3-1 Computed Fission Rate Errors With 3 Sub-batch Burnup Multipliers Applied to One Sub-batch (yellow boxes) 3-3

The reason for choosing a sub-batch burnup multiplier is that if there are errors in reactivity predictions of the lattice depletion code, the errors would be seen by all assemblies in the sub-batch. For example, if fission rates predicted in all assemblies of a sub-batch were either consistently low or consistently high, this would be a strong indication of lattice code depletion errors (e.g., nuclide con-centration errors, cross-section data errors, resonance modeling approximations, approximations in solving neutron transport equations, approximations in solving the nuclide depletion equations, approximations in modeling of boron history, etc.) The data often show, however, that fission rate differences vary in both sign and magnitude within a sub-batch. This indicates that most of the differences in fission rates are due to factors not directly related to errors in reactivity predictions with burnup.

3.5 Measured Sub-batch Reactivity Errors If the sub-batch burnup multiplier MB is driven through a range of values, one can determine the value of MB that minimizes the r.m.s. deviation between measured and computed detector signals, as depicted in Figure 3-2. One can see that the set of MB values creates a smooth function, the minimum of which is the burnup multiplier (Mmin) that leads to the most accurate prediction of radial fission rates for this flux map. In this example, the MB value of ~1.01 produces the most accurate prediction of fission rates. SIMULATE-3 edits of batch k-infinities for each value of MB are then used to construct an estimate of the reactivity error [defined as k-infinity (MB=Mmin) minus k-infinity (MB=1.0)] for this fuel sub-batch at its sub-batch burnup.

By applying this procedure to many cycles of flux maps, one can estimate the reactivity error for each sub-batch as a function of burnup. Figure 3-3 displays plots of the r.m.s. differences between measured and computed fission rates (on the left axis) vs. computed batch burnup x MB, for one sub-batch of fuel as it progresses through three successive cycles of reactor operation. The values of Mmin are also plotted as symbols (on the right axis). By measuring sub-batch reactivity errors for every flux map in every reactor cycle, one can construct estimates of the error in sub-batch reactivity and the corresponding shapes of sub-batch reactivity error vs. sub-batch burnup. Note that the burnup multiplier has been plotted against the computed sub-batch-averaged burnup (not including the multiplier), so the minimum points for the two sets of data are slightly misaligned.

3-4

Figure 3-2 Change in r.ms. Fission Rate Error vs. Sub-batch Multiplier Figure 3-3 Determination of Sub-batch Burnup Multiplier as a Function of Burnup 3.6 Simultaneous Determination of All Sub-batches Reactivities At any one time, the reactor core contains many sub-batches of fuel (typically 10 to 15), and it is important that Mmin be determined simultaneously for all sub-batches such that the global r.m.s. differences between computed and measured fission rates are minimized. This is achieved by performing a local search in a succession of passes over all sub-batches to determine the local minimum. The plots in Figure 3-4 show the minimized r.m.s fission rate differences and optimal values of Mmin for one sub-batch between the zero pass (upper plot) and final iterative pass (lower plot). Several things can be observed from these plots:

1. for high sensitivity cases (e.g., end of cycle 16 and all of cycle 17), the iterative results are not very sensitive to the iteration,

2. for cases with low sensitivities to the sub-batch burnup multiplier, the zero pass results (independent perturbations of each sub-batch in the core) can be far from the converged results, and 3-5

3. the iteratively converged results display more consistent burnup trends than zero pass results. Thus, the iterative approach is preferable to the non-iterative approach.

Figure 3-4 Nodal (3D) r.m.s. Differences for One Sub-batch Note that if sub-batch multipliers could reduce the r.m.s. to zero, then it could be argued that each sub-batch assembly is experiencing the same discrepancy, which would be indicative of depletion errors. The data, however, shows that although r.m.s. differences are reduced with sub-batch multipliers, the reduction is a small fraction of the total deviation, and therefore, residual deviations must be caused by factors other than sub-batch reactivity (and hence are not indicative of depletion errors).

One normally considers the core radial fission distribution to be more sensitive to batch reactivities than the axial shape, which would lead one to conclude it might be preferable to minimize the radial (2D) r.m.s deviations rather than the nodal (3D) r.m.s deviation. Figure 3-5 displays plots of the radial r.m.s.

deviations (both searches were performed to minimize the 3D differences), and one can observe that there is little difference between the minimum points of the 2D r.m.s. values and the 3D r.m.s. values of Figure 3-4. However, 2D r.m.s differences are more sensitive (i.e., display bigger changes) to the burnup multipliers.

3-6

Figure 3-5 Radial (2D) r.m.s. Differences for One Sub-batch Section 5 provides a detailed description of the final algorithm implemented to solve the many sub-batch minimizations. It should be noted that this method of determining errors in computed assembly reactivities from flux map data has one unique characteristic - this analytical method is completely independent of errors in core-wide reactivity predictions (for example, k-eff, critical boron, etc.). Thus, the proposed analysis method is completely complementary to reactivity-based methods normally used for quantifying errors in computational models (for example, critical assembly analysis, reactor startup criticals, shutdown margin measurements, and boron letdown comparisons).

3-7

Section 4: Analysis Codes: Studsvik CMS The Studsvik Core Management System (CMS) is routinely used to perform the neutronic and thermal-hydraulic analysis needed for design, optimization, and safety analysis of nuclear reactor cores. While the CMS suite of codes is capable of performing steady-state and transient (dynamic) analysis of reactor cores, the methods described in this document are restricted to the CMS codes needed to perform steady-state and pseudo steady-state core analysis.

4.1 Code System Overview The CMS code system consists of five separate codes that are used as a package to perform reactor core analysis. The five codes are:

INTERPIN-4 [7] for analyzing the 1-D fuel temperatures for an individual fuel pin, as a function of:

Fuel pin design (e.g., enrichment, gas pressurization, etc.)

Linear heat loading Fuel burnup CASMO-5 [2, 8] for analyzing the 2-D neutronic behavior of an individual fuel assembly, as a function of:

Lattice design (e.g., pin enrichment layout, burnable absorber design, etc.)

Local conditions (e.g., fuel temperature, coolant density, boron content, etc.)

Fuel burnup Control rod insertion CMSLINK [9] for generating a library of tabularized CASMO-5 data for a collection of fuel assemblies and reflector types, as a function of:

Fuel burnup Thermal hydraulic conditions Control rod insertion Fuel history effects SIMULATE-3 [3, 10-19] for analyzing the detailed 3-D reactor core neutronic and thermal hydraulic behavior over the reactor core lifetime, as a function of:

Reactor power 4-1

Coolant flow rate and inlet temperature Fuel burnup Control bank insertion INTERPIN-4 and CMSLINK are often considered as auxiliary codes in the CMS suite. On the other hand, CASMO-5 and SIMULATE-3 are very large (many hundreds of thousands of lines of FORTRAN) codes that perform the bulk of the physics modeling in CMS. Appendix A details the physics models and methods of these codes that are important for understanding how CASMO-5 and SIMULATE-3 are used for this project.

4-2

Section 5: Duke Energys Reactor Models 5.1 Overview Data from four of Duke Energys PWR units [20] have been used to determine measured fuel burnup reactivity decrement biases and uncertainties. All units are 4-loop Westinghouse reactors containing 17x17 fuel assemblies. Duke Energy provided complete specifications for the reactor, the fuel, and operational data so that CASMO-5/SIMULATE models could be independently constructed for this project. Detailed flux map data for all cycles of operation were included in the data package, thus enabling application of the previously outlined reactivity decrement methodology. Reactor cycle parameters are summarized in Table 5-1.

5-1

Table 5-1 Reactor and Fuel Data HZP Maximum Maximum Maximum Cycle Length Enrichment Unit Cycles Boron LBP IFBA WABA+IFBA (EFPD) Range (%)

(ppm) # # #

McGuire-1 10 to 21 363-514 3.40-4.95 1576-2000 24 128 24 + 128 McGuire-2 10 to 20 429-518 3.64-4.90 1690-2037 24 128 24 + 128 Catawba-1 9 to 19 407-522 3.45-4.75 1501-2104 24 128 16 + 128 Catawba-2 8 to 17 451-527 3.50-4.90 1819-2109 24 128 20 + 128 5-2

5.2 Fuel Types The fuel assemblies loaded into the Duke reactors for these cycles were of two distinct mechanical types: Arevas MarkBW with lumped burnable poisons (LBPs) and Westinghouses robust fuel assembly (RFA) fuel with wet annular burnable absorbers (WABAs) and/or integral fuel burnable absorbers (IFBAs).

The MarkBW fuels used a range of LBP enrichment spanning from 1% to 4% by weight B4C. As the reactors moved to 18-month cycles, the core loadings became more complex with the introduction of split enrichment feeds and many different burnable poison combinations. As evident from the fuel descriptions presented in Table 5-2, each cycle contains feed fuel divided into 5 to 12 sub-batches (for example, different combinations of enrichment and/or burnable absorbers). The number of fuel assembly types exceeds 100 for the analyzed cycles of each of the four units.

Table 5-2 Feed Fuel Characteristics Enrichment # of sub Enrichment # of sub Cycle Cycle

(%) batches (%) batches McGuire-1 McGuire-2 10 3.40 4 10 3.85 / 3.95 7 11 3.40 / 3.55 9 11 3.90 / 4.15 7 12 3.67 9 12 3.78 6 13 3.92 8 13 4.09 / 4.39 11 14 4.14 / 4.50 7 14 3.77 / 4.33 7 15 4.40 / 4.75 6 15 4.16 / 4.56 12 16 3.92 / 4.35 7 16 4.37 / 4.67 8 17 4.45 / 4.74 9 17 4.35 / 4.75 8 18 4.01 / 4.64 5 18 4.05 / 4.70 6 19 4.00 / 4.68 7 19 3.90 / 4.80 8 20 4.00 / 4.85 9 20 3.65 / 4.90 9 21 3.60 / 4.95 10 Catawba-1 Catawba-2 9 3.86 8 8 3.98 6 10 3.65 - 3.92 6 9 4.32 / 4.42 9 11 4.02 6 10 4.54 5 12 4.50 6 11 3.90 / 4.20 6 13 3.81 / 4.31 6 12 4.35 / 4.66 8 14 4.19 / 4.46 9 13 4.00 / 4.75 8 15 4.18 / 4.53 10 14 4.45 /4.75 8 16 4.42 / 4.67 10 15 3.80 / 4.73 11 17 3.88 / 4.51 9 16 4.38 / 4.90 8 18 4.05 / 4.51 8 17 3.80 / 4.82 9 19 3.96 / 4.75 7 5-3

CASMO-5 lattice calculations were performed for each unique axial layer (for example, burnable poison zone, cutback burnable poison zone, axial blanket, etc.)

of each fuel type. Complete CASMO-5 PWR case matrices of data were generated spanning the full range of hot to cold reactor conditions with burnups up to 80 GWd/T. Depletion histories were performed for boron, moderator temperature, and fuel temperature so that the effects from variable reactor boron concentrations and local power density could be modeled directly in SIMULATE-3.

CASMO-5 reflector cases (for lower, upper, radial with baffle, and radial with both baffle and barrel) were executed to generate equivalent reflector data as a function of moderator temperature and boron concentration for use in SIMULATE-3 reflector nodes.

5.3 CMS Code Versions The analysis in this project used the following QA production code versions for all cycle depletion analysis:

INTERPIN-4 Version 4.01 CASMO-5 Version 2.00.00 CMSLINK Version 1.27.00 SIMULATE-3 Version 6.09.22_PWR_1 A special branch version of SIMULATE-3 was created to perform the automated perturbation cases described in Section 6. That version is designated:

SIMULATE-3 Version 6.09.22_EPRI 5.4 Core Follow Summary Results SIMULATE-3 core follow calculations were performed for each reactor cycle, using the core loading patterns and the operational reactor history. The as-measured core power, core coolant flow, coolant inlet temperature, and control rod positions were used as boundary conditions for the SIMULATE-3 calcula-tions, and a boron search to critical was performed at each depletion step. The SIMULATE-3 model used a four-node-per-assembly radial nodalization, 24 axial nodes over the active fuel height (356.76 cm), and one homogenized reflector node at the top and at the bottom of the fuel stack. Each cycle was divided into fine depletion steps (30-100 depletion points per cycle) so fluctuations in reactor conditions faithfully followed the history of reactor operations.

The accuracy of SIMULATE-3 depletion calculations was checked by comparing computed and measured boron concentrations at points where measured plant chemistry boron data and measured 10B isotopic data were available. A typical comparison between plant boron data (corrected to natural 10 B /11B ratio) and computed SIMULATE-3 critical boron concentrations are displayed in Figure 5-1. From the data in this figure, it can be observed that the 5-4

gross core reactivity is well predicted, including the early-cycle burnout of the strongly self-shielded burnable poisons.

Comparisons of calculated and measured hot zero power (HZP) critical boron concentrations, as well as beginning of cycle (BOC) ~25 effective full power days (EFPD) and end of cycle (EOC), extrapolated to zero ppm boron concentrations, are summarized for all four units in Tables 5-3 to 5-6. Of particular interest are any trends from BOC to EOC in the mean differences of calculated and measured boron, which can be seen to be less than 26 ppm for all four units.

Figure 5-1 Comparison of SIMULATE and Measured Boron 5-5

Table 5-3 McGuire Unit-1 Boron Comparisons Calculated -

Cycle Length Measured Boron Measured Boron at end of (ppm)

Cycle (ppm)

HFP, HZP HFP HZP HFP 0 ppm = EOC BOC BOC EOFP BOC BOC EOC 10 383.4 --- 1142 86 --- 12 -28 11 363.2 1746 1107 45 27 8 -22 12 380.0 1803 1150 154 28 5 -24 13 442.5 2000 1328 50 19 -6 -26 14 465.5 1955 1252 59 5 4 -36 15 492.7 1576 906 49 9 -9 -24 16 501.9 1920 1299 91 10 -4 -22 17 514.0 1975 1337 135 -3 -10 -37 18 505.0 1973 1331 109 -4 -7 -28 19 487.5 1899 1279 149 -2 -25 -35 20 478.2 1942 1267 93 8 -6 -52 21 --- 1840 1161 --- 12 -7 ---

Average 10 -4 -30 Table 5-4 McGuire Unit-2 Boron Comparisons Calculated -

Cycle Length Measured Boron Measured Boron at end of (ppm)

Cycle (ppm)

HFP, HZP HFP HZP HFP 0 ppm = EOC BOC BOC EOFP BOC BOC EOC 10 431.8 1839 1177 13 20 -2 -41 11 429.0 1906 1248 106 13 -17 -17 12 423.9 2037 1359 41 26 3 -11 13 446.2 1896 1189 15 -10 -30 -35 14 486.4 1691 1090 141 18 -13 -35 15 517.8 1919 1301 25 13 -1 -38 16 502.6 1887 1241 26 -13 -19 -33 17 511.9 1908 1238 114 2 -14 -34 18 494.8 1818 1146 158 26 6 -44 19 475.8 1817 1117 4 23 2 -30 20 --- 1713 1035 --- 5 -23 ---

Average 11 -10 -32 5-6

Table 5-5 Catawba Unit-1 Boron Comparisons Calculated -

Cycle Length Measured Boron Measured Boron at end of (ppm)

Cycle (ppm)

HFP, HZP HFP HZP HFP 0 ppm = EOC BOC BOC EOFP BOC BOC EOC 9 421.1 1876 1214 43 27 -1 2 10 407.6 1840 1173 82 37 14 -8 11 445.4 1983 1267 116 44 18 0 12 486.8 2012 1275 28 32 3 -3 13 491.2 1501 871 17 35 7 8 14 515.7 1899 1285 82 44 17 15 15 500.9 1888 1246 157 18 12 9 16 521.8 2104 1371 112 21 9 4 17 505.7 2097 1402 131 51 34 12 18 482.6 2011 1341 10 45 25 8 19 --- 1920 1241 --- 24 2 ---

Average 34 13 5 Table 5-6 Catawba Unit-2 Boron Comparisons Calculated -

Cycle Length Measured Boron Measured Boron at end of (ppm)

Cycle (ppm)

HFP, HZP HFP HZP HFP 0 ppm = EOC BOC BOC EOFP BOC BOC EOC 8 451.5 1869 1186 69 46 35 12 9 472.0 2082 1352 49 38 30 9 10 490.9 1906 1164 222 64 37 4 11 495.6 1797 1153 15 44 32 20 12 483.1 1781 1153 49 51 27 16 13 527.3 1889 1256 30 32 18 22 14 501.2 1871 1195 103 30 20 16 15 498.5 1967 1253 58 52 43 16 16 464.4 1828 1106 42 37 27 15 17 499.0 1750 1054 --- 35 25 9 Average 43 30 14 5-7

5.5 Flux Map Summary Results Measured flux map data for each unit was taken at intervals of about 30 EFPD throughout the cycles. Each flux map has been analyzed with SIMULATE-3, and a summary of comparisons with measured data is displayed in Table 5-7. It can be seen that the SIMULATE-3 radial fission rate distributions (axial integrals over each of the detector positions) are predicted with a mean difference slightly above 1 percent. 3D node-by-node (24 axial nodes) fission rates are predicted with a mean difference of less than 3 percent.

Accurate predictions of fission rate distributions are very important as a starting point for subsequent application of the burnup reactivity decrement methodology because the analytical tools must be capable of accurately predicting fission rate distributions when provided accurate fuel assembly reactivities.

Table 5-7 Comparison of SIMULATE-3 and Measured Fission Rates Mean Mean Axial Mean Nodal (3D)

Radial (2D)

1. of Flux r.m.s. r.m.s.

Reactor r.m.s.

Maps Difference Difference Difference

(%) (%)

(%)

McGuire-1 161 1.15 1.64 2.64 McGuire-2 171 1.20 1.70 2.67 Catawba-1 179 1.22 1.46 2.50 Catawba-2 169 1.24 1.82 2.82 Un-weighted Average 1.20 1.66 2.66 The flux map measurement errors from reproducibility tests and symmetry measurements are generally observed to be about 0.5% for any individual radial flux map position (thimble). Since the observed deviation between computed and measured fission rates in Table 5-7 has an average r.m.s. difference of 1.2%, the 0.5% uncertainty from the measurement is so small that it does not affect the results of this study.

5.6 Reactor Model Summary The CMS models for the Duke reactors have been developed by applying a production model to all reactor and fuel data supplied by Duke Energy. All four units employ consistent modeling techniques, which is important for combining cross-units results needed for the cumulative statistics in this project.

The agreement of the SIMULATE-3 core follow model with plant measured data demonstrates that both core reactivity and spatial distributions of fission rates are well-predicted throughout the cycles and across all units. Consequently, these models and measured reactor data form a well-qualified basis for the analysis presented in this report.

5-8

Section 6: Details of Analysis Implementation For every reactor condition at which a flux map is available, a sequence of SIMULATE-3 calculations is performed to evaluate the error in sub-batch reactivity for all the sub-batches in the reactor core. Section 3 provided a brief overview of the analysis procedure used to quantify the computed reactivity decrement bias and uncertainty. However, in the overall iterative sequence described in Section 3, there are a number of details that are needed for practical implementation.

6.1 Super-batch Definitions Since there are many sub-batches (e.g., 4-12) introduced in each cycle (as displayed in Table 5-2), it is important that there are enough assemblies in the core to make a search for the sub-batch reactivity meaningful. For instance, when there are eight or fewer assemblies in a sub-batch, the sub-batch would only occupy a single core location in an octant-symmetrically-loaded core. In such a case, the sensitivity of the r.m.s. differences in computed and measured fission rates would be very sensitive to measurement errors at that core location. In order to alleviate such sensitivities, we have chosen to lump any sub-batches having fewer than 12 assemblies into a super-batch with all corresponding enrichment sub-batches also having fewer than 12 assemblies. Consequently, this super-batch actually represents a number of different burnable poison configurations. All sub-batches with more than 12 assemblies are treated explicitly as their own sub-batch, since the sub-batch will occupy at least 2 different locations in an octant of the reactor core.

6.2 3D Versus 2D Searches As was pointed out in Section 3, it is not obvious if the search to minimize differences between computed and measured fission rates should be performed with the radial (2D) or nodal (3D) fission rates. We have examined a large number of searches using both the radial and nodal differences to drive the search. In general, little difference has been observed between the results of either type of search, but individual cases can be found in which one or the other seems more effective. Since the nodal search is intuitively more general, we have chosen to base the searches in this report on minimizing the r.m.s. differences in the nodal (3D) fission rates.

6-1

In all cases, this search for optimal sub-batch burnup multipliers is guaranteed to reduce the deviation between computed and measured fission rates. Typical reductions in nodal r.m.s. values and corresponding radial r.m.s. values are dis-played in Figures 6-1 and 6-2. In such cases, one observes that even though the search minimizes the nodal r.m.s. differences, the radial r.m.s. differences are also all reduced. In fact, it is not uncommon for the magnitude of the reduction in radial r.m.s. differences to exceed that of the nodal r.m.s. differences.

Figure 6-1 Cycle 12 - Nodal r.m.s. Fission Rates 6-2

Figure 6-2 Cycle 12 - Radial r.m.s. Fission Rates However, there is nothing inherent in the search process to guarantee that the radial r.m.s. differences will actually be reduced. By examining a great number of cycles of data, some instances have been found in which iterative reduction of the nodal r.m.s differences actually increases the radial r.m.s differences, as displayed in Figures 6-3 (consistent improvement in core-wide 3D r.m.s.) and 6-4 (inconsistent improvement in core-wide 2D r.m.s.). This behavior has only been observed when initial radial r.m.s. differences are very small (less than 1%), and the increases in the iterative r.m.s. differences are also very small.

6-3

Figure 6-3 Cycle 19 - Nodal r.m.s. Fission Rates Figure 6-4 Cycle 19 - Radial r.m.s. Fission Rates 6-4

6.3 Sub-batch Sensitivities In order for the search to determine the sub-batch burnup multipliers that minimize r.m.s. differences between the calculation and the measurement, it is important that the sub-batch actually display a significant sensitivity to the sub-batch reactivity multiplier. There are several instances in which this sensitivity does not exist. One such case occurs when a sub-batch is located in core positions of little reactivity worth relative to the locations of in-core detectors - such as when it is placed in extreme peripheral core locations for the sub-batchs last cycle in the core (for example, very low-leakage core loading patterns). When a search for the sub-batch multiplier is performed, one observes a very flat r.m.s.

difference as the sub-batch multiplier is changed - as depicted in Figure 6-5 for the Cycle 18 cases. In such cases, the sub-batch multipliers are very sensitive to the iteration, and converged sub-batch multipliers often display large fluctuations at successive flux maps - which is clearly unphysical.

Figure 6-5 Multi-cycle Sub-batch Minimization Another instance of very low sensitivity can be observed in Figure 6-6 for the data from the first half of Cycle 18. In these cases, the large amount of burnable absorbers makes the k-infinity curve versus burnup almost flat. As a result, there is little sensitivity to the sub-batch burnup - until the burnable absorber is significantly depleted (e.g., 10-15 GWd/T).

6-5

Another situation that can lead to small sensitivities occurs when only a few assemblies from a sub-batch are used in a cycle. This often occurs when fuel is inserted into the core for its fourth cycle, as depicted in Figure 6-6. Here for Cycle 21, only a few assemblies of the sub-batch are re-used and there is very little sensitivity to this sub-batch - as evidenced by the flat r.m.s. differences, as the sub-batch multiplier is changed. Note also that the initial and iterative results for this case (the large blue dots) are dramatically different and very uncertain for such low sensitivity cases.

Figure 6-6 Multi-cycle Sub-batch Minimization, Split Batch Cases that have such low sensitivities are easy to eliminate from the overall search space by simply performing the calculation and monitoring the sensitivity. All such low sensitivity cases are eliminated from the search space - as is explained in the following section.

6.4 Iteration Implementation The final computational sequence implemented for the analysis in this report can be broken down into a number of discrete steps. For each reactor state at which flux map data is available, the following sequence of steps is performed:

1. Perform standard flux map analysis and compute the initial r.m.s deviation between computed and measured 3D fission rates 6-6

2. Start loop over all sub-batches in the core and over all values of the sub-batch burnup multipliers, Mb, from 0.85 to 1.15

a. For each sub-batch, determine the sub-batch sensitivity, defined as the minimum of the 2D r.m.s with 0.85 and 1.15 multipliers minus the minimum 2D r.m.s.

3. End loop over sub-batches

4. Set all active sub-batch burnup multipliers, Mbuse=1.0

5. Start iterative loop for 8 sequential passes

6. Start loop over all sub-batches in the core from maximum to minimum sub-batch sensitivity and over all values of sub-batch burnup multipliers from 0.85 to 1.15

a. update the active value of Mbuse with the value of Mb corresponding to the minimum 3D r.m.s. (subject to the constraint that Mbuse not change by more than +/- an input value (0.02) in any single pass)

b. If the current sub-batch sensitivity is less than an input value (0.3%) or if the number of assemblies in the sub-batch is less than an input value (12) set the active value of the sub-batch multiplier Mbuse to 1.0

7. End loop over sub-batches

8. End iterative loop over sequential passes

9. For all sub-batches (not subject to the constraint of step 6b), compute the SIMULATE-3 reactivity error as the difference of sub-batch reactivities for Mb= Mbuse and Mb=1.0 This iterative procedure constrains the change in sub-batch multipliers to be less than 0.02 at each pass so that small changes in sub-batch multipliers are made for all sub-batches before any sub-batch multiplier is changed by a large amount.

The rationale for this choice is that the r.m.s differences are often sensitive to all sub-batch multipliers, and it is undesirable to complete a search for one sub-batch before examining the impacts of the other sub-batches in the core. In any case, it should be recognized that this search solves a local minimization problem and is not guaranteed to find the global minimum (which is nearly impossible to determine).

This analytical procedure is also performed for a fixed number of iterations rather than monitoring directly the convergence of results. The reason for this choice is that since sub-batch multipliers are changed in finite steps of 0.01, there are rare cases in which some sub-batches produce multipliers that oscillate by 0.01 in successive passes. This level of oscillation is certainly not important for deter-mining the error in sub-batch reactivity (as explained in the following section),

and it is far more straightforward to accept such oscillations as an additional uncertainty - rather than switching to a continuous variable search to find the true local minimum.

6-7

Figure 6-7 displays sub-batch multipliers for one sub-batch in Cycles 16 to 18, and it can be seen that the iteration produces values that are more consistent from cycle to cycle than the pass zero results. This is not only more physical (i.e.,

reactivity discrepancies should be smooth functions of sub-batch burnup across cycles), but also provides indirect indication that the simultaneous search across all sub-batches is effectively implemented in SIMULATE-3.

Figure 6-7 Effective Multi-cycle Sub-batch Minimization For each flux map, this analytical procedure requires approximately 4000 SIMULATE-3 calculations (11 total passes x 31 sub-batch multipliers/sub-batch x ~12 sub-batches in the core). Consequently, analysis of the 44 Duke reactor cycles (680 flux maps) requires a total of approximately 2.7 million SIMULATE-3 cases to be executed. Coding changes have been made in SIMULATE-3 (Version 6.09.22_EPRI) so that this procedure is automatically invoked without need for human intervention, and search results are recorded in a special file that is post-processed to make plots and spreadsheets of results.

6-8

Section 7: Measured HFP Reactivity Bias and Uncertainty The SIMULATE-3 flux map analysis procedure described in Section 6 was performed for all flux maps in the 44 cycles of Catawba Units 1 and 2 and McGuire Units 1 and 2 for which reactor power was above 95%. This analysis produces HFP measured reactivity errors for each sub-batch at each flux map.

This section describes how the data from this analysis are used to infer biases in CASMO-5 sub-batch reactivities, and how these biases are translated into measured reactivity decrements and corresponding uncertainties.

7.1 Interpretation of Data If one plots the estimated sub-batch reactivity biases (k in pcm) versus sub-batch burnup, the data appear as displayed in Figure 7-1. These 2856 measured sub-batch reactivities represent those points from the complete set of approxi-mately 8000 data points (680 maps x ~12 sub-batches per map) that satisfied the two screening criteria of having 12 or more assemblies in a sub-batch and having a detector r.m.s. difference sensitivity greater than 0.3% - as fission rate differences were iteratively minimized.

The 0.3% minimum sensitivity criteria used in the iterative minimization of r.m.s. differences was necessary so that sub-batches with sensitivities that approach zero would not be interpreted as requiring near-infinite changes in assembly reactivity to minimize fission rate r.m.s. differences. An alternate interpretation of such sub-batches is that the variances of inferred reactivity biases approach infinity for sub-batches with near-zero sensitivity. Treatment of sub-batch sensitivities and variances of the retained 2856 measured sub-batch reactivities are explicitly addressed (in Section 7.2) where the use of WLS regressions is detailed.

7-1

Figure 7-1 Casmo-5 Bias in Reactivity For comparison purposes, the +/-5% reactivity decrement curves (as computed for a 4.75% enriched, no burnable poison Westinghouse RFA fuel lattice at 900 ppm boron) are plotted in this figure with the two black lines. These curves do not correspond directly to the most appropriate 5% reactivity decrement since reactivities in this plot are computed at HFP conditions with CASMO not at cold conditions with SFP criticality tools. Nonetheless, the curves provide useful insight to help interpret the scatter in individual data points.

There are a number of things that can be observed from this data. First, there are very few data points at less than 10 GWd/T burnup. This is a result of the fact that almost all sub-batches have large amounts of burnable absorber - which makes the k-infinity curve very flat in burnup, as observed from the boron letdown curve in Figure 5-1. Consequently, no attempt will be made to quantify the reactivity decrement biases or uncertainties for burnups less than 10 GWd/T. One should note that since reactivity decrement biases and uncer-tainties at zero burnup are by definition zero, it should be easy to estimate reactivity decrement biases and uncertainties in this range. Normally, interest focuses on much higher burnups for spent fuel criticality analyses.

One also observes that the data form distinct lines, particularly at high burnup.

This is a direct result of two facts: 1) the slopes of fuel reactivity vs. burnup are very similar for all fuel types (after burnable absorbers are depleted), and 2) the 7-2

search for sub-batch burnup multipliers was performed with a discrete 0.01 mul-tiplier resolution. Consequently, the data behavior is expected, and one should simply interpret each data point as each having an intrinsic added measurement uncertainty proportional to burnup and having a magnitude of approximately

+/-100 pcm at 50 GWd/T. Because there are so many data points in the com-posite set of data, this uncertainty has almost no impact on results deduced from the data.

At first glance, the data appear to be nearly equally distributed around 0 pcm decrement error, with a large spread in individual points. It is important to understand what influences this spread in data. Items known to contribute to the spread in the individual data points of Figure 7-1 include:

Fission rate measurement errors or uncertainties Differences in sub-batch spectra vs. CASMO-5 lattice assumption (zero leakage)

Differences in intra-assembly spatial flux distributions vs. lattice assumption Influences from super-batch lumping of multiple burnable poison loadings Imperfect knowledge of core configuration (fuel bowing, fuel elongation, crud)

Errors in computed sub-batch burnups (used as the plot ordinate)

Errors in SIMULATE-3 nodal and detector physics models Errors in SIMULATE-3 cross-section data fitting models Errors in CASMO-5 computed nuclide inventory vs. fuel burnup Errors in fundamental neutron cross-section data Imperfect knowledge of reactor operating power level The items in this list have been divided into two sets, indicated by bullet type.

The simple bulleted terms have two distinct characteristics: 1) because both measured and computed fission rates are normalized distributions, these effects are expected to be randomly distributed with little bias, and 2) these effects either do not enter into SFP/cask criticality analysis or are treated with their own uncertainties. For instance, errors in SIMULATE-3 models or lattice spectral assumptions are not relevant for SFP analysis because such analysis is performed directly by Monte Carlo in rack geometry.

The first two of the check-mark bulleted items in this list are the two terms we seek to measure in this project, and it is clear that the effects in this sub-list will not be random in nature - as one expects these errors to change systematically (in an as-yet unknown manner) as fuel assemblies are burned.

In the iterative analysis method, all categories of errors are treated as if they are errors in CASMO-5 sub-batch reactivities - which is the reason we expect the 7-3

spread in individual data points to be much larger than the actual CASMO-5 sub-batch reactivity errors. What remains to be shown is that one can use this set of data, with its inherent spread, to correctly deduce the errors in CASMO-5 lattice reactivities.

7.2 Sub-batch Sensitivities The measured reactivity decrement bias data was plotted vs. sub-batch sensitivity, and a quadratic regression was performed to determine the 95% prediction interval for the reactivity decrement bias versus sub-batch sensitivity, as displayed in Figure 7-2. The 95% prediction interval was used to compute the normalized shape of 2-sigma variation versus sensitivity. The data was fitted only up to a sensitivity of 4.0%, as the data becomes exceedingly sparse at the higher sensitivity end of the data. The plus signs in this figure are variance points as determined using the MATLAB [21] VAR function for eight separate sub-batch sensitivity bins - to verify that the quadratic fit was reasonable.

The data in Figure 7-2 demonstrate that many sub-batches with low sensitivities have the largest measured reactivity decrement biases. This is not unexpected, because sub-batches that have very little influence on the computed fission rate distributions require a very large change in computed sub-batch reactivity (k-infinity) to change the computed fission rate distribution and minimize deviations from the measured fission rate distributions. The correlation between sub-batch sensitivity and reactivity decrement bias will become important later when regression analysis of the data is used to infer biases and uncertainties for the reactivity decrement biases as a function of sub-batch burnup.

Figure 7-2 Reactivity Decrement Bias vs. Sub-batch Sensitivity 7-4

7.3 Sensitivities to Reactor Unit If the data are examined separately for each of the four reactor units, the plots displayed in Figures 7-3 to 7-6 are obtained. The data in each plot show that there is very little difference between burnup reactivity decrement biases measured in one unit or another. Since all four units have fuels of similar range of enrichments and burnable absorbers, the lack of sensitivity to the reactor unit is not surprising. Consequently, for the analysis that follows in this report, data for all four units are treated as a single large data set in which measured sub-batch reactivity decrement biases do not depend on the reactor unit in which each fuel sub-batch was depleted.

Figure 7-3 Bias in Reactivity Decrement - McGuire-1 7-5

Figure 7-4 Bias in Reactivity Decrement - McGuire-2 Figure 7-5 Bias in Reactivity Decrement - Catawba-1 7-6

Figure 7-6 Bias in Reactivity Decrement - Catawba-2 Because the data for each of the four units are so similar, all data will be lumped together for the remainder of this report so that more data points are available to improve the statistics of measured reactivity decrements biases and uncertainties.

7.4 Sub-batch Enrichment Sensitivities The fuel sub-batches for the Duke reactors span the range of enrichments from 3.4% to 4.9% enrichment in 235U. The measured reactivity decrement biases plotted in Figures 7-1 and 7-2 to 7-6 are displayed in blue for the enrichment range of 3.4% to 4.35% and in red for the range from 4.35% to 4.90%.

There is no significant trend of the reactivity decrement bias with burnup, so all of the data will be treated as a single set without regard to sub-batch enrichment, so we can look more precisely at the burnup dependence of the reactivity decrement bias.

7.5 Burnup Reactivity Decrement Biases and Prediction Intervals With all units, enrichments, and sub-batches lumped into one data set we can perform regression analysis of the data to determine the burnup dependence of CASMO-5 bias and uncertainty of reactivity decrements. Figure 7-7 displays results of MATLABs ordinary least squares (OLS) quadratic regression 7-7

constrained to zero bias at zero burnup (i.e., since burnup reactivity decrement is 0.0 at zero burnup by definition, then the bias must also be 0.0 at zero burnup).

Figure 7-7 CASMO-5 Decrement Bias Fit - Quadratic Regression From this plot it can be seen that the regression fit to the bias has a shape that grows from 0.0 to about 200 pcm at 50 GWd/T burnup. The prediction interval width has the same shape in burnup as the bias, with a half-width of about 900 pcm. In order for the prediction intervals derived from the OLS regression analysis to be strictly applicable, the data should satisfy certain criteria:

The ordinate values must be known exactly (the sub-batch burnups)

The variance of each data point must be independent of the ordinate Every data point must be independent from all other points The residuals (differences between the individual points and the regression fit at that ordinate) must have normal distributions for all ordinate values Unfortunately, none of these points are satisfied by the regression data in Figure 7-7:

1. the ordinates are not known exactly - since they are computed not measured burnups,

2. the data is heteroscedastic, as the variance grows with burnup and this variation cannot be known precisely,

3. the data at successive flux maps are correlated - since core power distributions evolve slowly, results from one flux map and the next are highly correlated,

4. the residuals here are clearly not normally distributed.

7-8

The fact that the sub-batch burnups are not known exactly (burnups are a SIMULATE-3 computed parameter) is not a very important limitation for the regression, because uncertainty in the sub-batch burnup merely affects the abscissa positioning (horizontal) of data and not the data ordinate (vertical) value.

Consequently, it is easy to surmise that the impact on the regression fit from misplacing of sub-batch burnups will be very small. However, the OLS assumption that the variance is independent of burnup is clearly not valid. This is, in fact, the reason that bounds were historically expressed in terms of a percentage of burnup reactivity decrement, so the bounds would grow with burnup.

We can plot the absolute value of decrement bias data vs. sub-batch burnup and use a quadratic regression to determine the 95% prediction interval for the reactivity decrement bias versus sub-batch burnup, as displayed in Figure 7-8.

The fitted 95% prediction interval was used to compute the shape of 2-sigma data variation versus burnup, and the square of this variation (the variance) was fit to a quadratic polynomial and renormalized as displayed in Figure 7-9. This figure also contains variance points, as determined using the MATLAB VAR function for fifteen separate sub-batch burnup bins - to verify that the quadratic fit was reasonable.

Figure 7-8 Decrement Bias Prediction Interval vs. Sub-batch Burnup 7-9

Figure 7-9 Decrement Bias Variance Shape vs. Sub-batch Burnup Having an estimate of the burnup dependence of the variance for the heteroscedastic data, we can now perform weighted least square (WLS) regression and derive non-constant prediction intervals for the regression data.

Regression fits versus burnup were performed using the MATLAB nlinfit function with the weight option to use the individual data weights, computed as described above. Confidence intervals corresponding to each data point were computed using the MATLAB nlpredci function with Covar, and weight options. Confidence interval curves as a function of burnup were computed using MATLAB polyfit function to fit individual confidence interval data to 6-th order polynomials (since the confidence interval has more shape than the quadratic regression). Prediction intervals corresponding to each data point were computed using the MATLAB nlpredci function with Covar, predopt observation, and weight options. Prediction interval curves as a function of burnup were computed using MATLAB nlinfit function to fit individual prediction interval data to quadratic polynomials - constrained to a value of 0.0 at 0.0 GWd/T burnup.

Applying linear and quadratic WLS regressions to the decrement bias data using a weight function for sub-batch i as a function of sub-batch burnup, the regression results displayed in Figure 7-10 and 7-11 are obtained.

7-10

Figure 7-10 Decrement Bias WLS Linear Regression vs. Burnup Figure 7-11 Decrement Bias WLS Quadratic Regression vs. Burnup 7-11

These prediction intervals now accurately capture the heteroscedastic nature of the data variances, and these prediction intervals follow the traditional bounding shape. The differences between the linear and the quadratic regressions are not very large, but the quadratic regression prediction interval is narrower than the linear regression. The quadratic reactivity decrement bias at large burnup is considerably flatter at high burnup, and this shape is closer to that might be expected from the physics of lattice depletions - where any bias introduced in computational models from the misprediction of higher actinide effects might be expected to saturate at high burnup. Regression performed in subsequent analysis of this report use quadratic regressions, so the fits can become flatter at high burnup - if the data support such a shape.

The reactivity decrement data are heteroscedastic in not only sub-batch burnup, but also in sub-batch sensitivity. This dependence was displayed in Figure 7-2, which is repeated here as Figure 7-12. The 95% prediction interval width was used to compute the normalized shape of 2-sigma variation versus sensitivity.

The square of this variation (the variance) was fit to a quadratic polynomial and normalized as displayed in Figure 7-13. The 2856 data points were fit only up to a sensitivity of 4.0%, as the data become exceedingly sparse at the higher sensitivity end of the data. The plus signs in this figure are variance points as determined using the MATLAB VAR function for eight separate sub-batch sensitivity bins - to verify that the quadratic fit was reasonable.

Figure 7-12 Decrement Bias Standard Deviation vs. Sub-batch Sensitivity 7-12

Figure 7-13 Decrement Bias Variance Shape vs. Sub-batch Sensitivity MATLAB WLS quadratic regressions to the decrement bias data were performed using weight functions for sub-batch i, incorporating both sub-batch burnup and sub-batch sensitivity using two different variants of the weight

function, There was little difference between regression fits and prediction intervals computed using these two variance estimation procedures. However, the product formulation was selected for all subsequent regression analysis based on the fact that it correctly produces zero weight should either the sensitivity or burnup variances go to infinity, and the additive formulation does not have this property.

The quadratic regression fits and prediction intervals obtained using both heteroscedastic terms (sub-batch burnup and sensitivity) are displayed in Figure 7-14. The prediction interval width is narrower than that previously displayed in Figure 7-11 where heteroscedastic sensitivities were not treated.

The narrower prediction interval fits with ones intuition from observing the strong correlation between reactivity decrement bias and sensitivity, as shown in Figure 7-12. All subsequent results in this report treat the heteroscedastic nature of both the sub-batch sensitivity and sub-batch burnup.

7-13

Figure 7-14 Decrement Bias WLS Quadratic Regression vs. Burnup 7.6 Further Refinements of Burnup Reactivity Decrement Biases and Prediction Intervals There are a few additional refinements of the regression analysis that are required to account for other small deficiencies of the experimental measured reactivity decrement bias data.

The first of these refinements arises from the fact that the sub-batch decrement burnup multipliers that were used to compute sub-batch reactivity bias (in pcm) made the assumption that all fuel within a sub-batch could be represented by a single sub-batch-average burnup. A conservative correction for computing reactivity decrement biases from batch-averaged burnups can be implemented by:

1. evaluating the maximum value of the second derivative of reactivity within each sub-batch/cycle burnup range,

2. multiplying this second derivative by the maximum difference of any assembly burnup from the sub-batch average burnup, and

3. multiplying this result by the sub-batch average burnup change (EM -

Eave) determined in the 235U fission distribution r.m.s. minimization.

7-14

The sub-batch bias and sub-batch bias additions are depicted schematically in Figure 7-15 for a hypothetical sub-batch of three assemblies having burnup E1, E2, and E3.

Figure 7-15 Correction for Sub-Batch Burnup Distributions These reactivity decrement bias additions for all data points are displayed in Figure 7-16. The magnitude of these corrections is very small for most data points because either the slope of reactivity is nearly constant within the range of batch burnup within a cycle, or because the range of intra-batch burnup is very small. (Note that if the derivative of k-infinity were independent of burnup, the intra-sub-batch burnup distribution would require no additional correction to the bias.) When considering all sub-batch data points, the average of the maximum deviation of intra-batch burnup from the sub-batch average burnup is 2.0 GWd/T in absolute units and 6.6% in relative terms - not very large. The implementation of this correction includes three additional conservatisms:

1. The second derivative of reactivity is evaluated at its maximum anywhere in the sub-batch/cycle.

2. The intra-batch burnup difference is taken as the maximum value within the sub-batch - even when it corresponds to only a single assembly of all the assemblies within the sub-batch.

3. The intra-batch burnup distribution correction is explicitly added to each sub-batchs measured reactivity decrement bias, and the sign of the addition 7-15

is selected to maximize the absolute value of reactivity decrement bias (for example, positive biases are increased and negative biases are decreased).

Figure 7-16 Intra-batch Reactivity Decrement Bias Addition vs. Sub-batch Burnup Another limitation of the experimentally measured burnup reactivity decrement bias data mentioned previously in Section 7.5 was that every data point must be independent from every other point. We know that the data at successive flux maps are highly correlated - since core power distributions evolve slowly, results from one flux map and the next are very highly correlated. Rather than treating this correlation directly, we have chosen to make the approximation that all data for one sub-batch within each reactor cycle are fully correlated. We can then collapse all data within individual sub-batch/cycles to one average value per cycle by statistically combining individual reactivity decrement biases and burnups with their respective weights (i.e., the reciprocal variance product). This is the assumption of 100% correlation of data within each sub-batch/cycle which is necessary so regression fit confidence intervals can be applied correctly (given that we do not know the precise intra-cycle correlation of data that would be needed to use individual data point regressions). When collapsed over each cycle, there are 270 sub-batch/cycle reactivity decrement bias points available for the subsequent analysis.

Two different methods for collapsing the sub-batch/cycle decrement bias data were examined:

7-16

1. un-weighted collapsing and

2. collapsing with individual data weights.

Figure 7-17 displays un-collapsed and collapsed reactivity decrement bias data for nine typical sub-batch/cycles. In this figure:

The diamond symbols represent burnup points of un-collapsed data, the square symbols represent un-weighted collapsed points, and the circle symbols represent the weighted collapsed points.

By examining data for separate colors (i.e., sub-batches) it can be seen that weighted and un-weighed collapsed data differ very little in reactivity decrement bias and only slightly more in collapsed burnup. As might be expected, regression analysis was shown to be extremely insensitive to the collapsing method employed, so the more intuitive weighted collapse was selected for all subsequent regression analysis.

A WLS quadratic regression fit of the sub-batch/cycle-collapsed data is displayed in Figure 7-18. Note that the data tend to separate into three clusters that represent the fresh, once-burned, and twice-burned fuel sub-batches. Note the prediction intervals are still narrower than those obtained in the previous un-collapsed WLS regression of the 2856 individual data points, as displayed in Figure 7-14.

Figure 7-17 Cycle-collapsed Reactivity Decrement Data 7-17

Figure 7-18 Reactivity Decrement Quadratic WLS Regression for Cycle-collapsed Data The shape of the prediction interval bounds in Figure 7-18 appears to deviate from the cone shape of previous figures because of the parabolic shape of the regression fit, but the prediction interval width remains similar. This is clearer in Figure 7-19, where linear WLS regression results are displayed, and the prediction interval appears more conical. Note in the linear regression, the confidence interval is narrower than that of the quadratic regression of Figure 7-

18. However, we still chose to use quadratic regressions because it is important to allow for a regression shape that could have an asymptotic value at large burnups

- where isotopic inventories of the fuel assemblies become more constant (e.g.,

235 U is nearly depleted and 239 Pu becomes nearly constant).

7-18

Figure 7-19 Reactivity Decrement Linear WLS Regression For Cycle-collapsed Data The measured CASMO-5 biases in HFP reactivity decrement bias and 95%

prediction interval half-width as a function of sub-batch burnup are presented in Table 7-1.

Table 7-1 Measured CASMO-5 HFP Reactivity Decrement Bias and Prediction Interval Half-Width Burnup (GWd/T) 10.0 20.0 30.0 40.0 50.0 60.0 CASMO-5 Bias (pcm) 66 101 106 80 22 -64 Prediction Interval (pcm) 226 420 585 713 812 875 In order for the prediction interval data to be confidently used to construct a formal tolerance limit for the measured reactivity decrement biases, the regression residuals displayed in Figure 7-18 must be normally distributed. In order to test for normality, the standardized residuals (differences between the data points and the quadratic regression fit divided by the square root of the variance of each data point) were used in a Shapiro-Wilk test (using the StatPlus as add-on to Excel) to determine if the data pass the normality test. As can be seen from the results in Figure 7-20, the residuals pass the Shapiro-Wilk normality test, as well as the Kolmogorov-Smirnov/Lilliefor and DAgostino normality tests.

7-19

Figure 7-20 Normality Tests of Cycle-Collapsed WLS Regression Residuals The important point to recall here is that because the sub-batch/cycle data points having been compressed to a single value, there are no correlation effects between successive flux map measurement points to be considered. Consequently, the regression prediction interval widths can be justifiably used - since the residuals correspond to a normal distribution, a condition that is needed for inferring the 95% prediction intervals for the regression fits.

The prediction interval is not the final quantity used to determine the HFP uncertainty of the measured reactivity decrement bias. Rather, we seek a 95/95 tolerance limit on the measured biases, and a tolerance limit factor must be applied to the prediction interval half-widths. With 270 data points in the regression fit, the 2-sided 95/95 tolerance limit factor is 1.074 (e.g. k2=2.114) for a 95% Students t-value of 1.969. However, for our intended application, it is more appropriate to use a 1-sided 95/95 tolerance limit because one need not be concerned with data outside the 95/95 band in the conservative direction. The 1-sided 95/95 tolerance limit factor for 270 data points is 0.918 (e.g. k1=1.807).

Table 7-2 displays the final HFP reactivity decrement bias tolerance limits which are ~8% less than the prediction interval half-widths.

7-20

Table 7-2 Measured CASMO-5 HFP Reactivity Decrement Bias and Tolerance Limit Burnup (GWd/T) 10.0 20.0 30.0 40.0 50.0 60.0 CASMO-5 Bias (pcm) 66 101 106 80 22 -64 Prediction Interval two-sided 226 420 585 713 812 875 (pcm) 95/95 Tolerance Limit one-207 386 537 655 745 803 sided (pcm) 7.7 Boron and Cycle Burnup Sensitivities Another cross check of the accuracy of the decrement biases deduced from flux map data is to compare the BOC to EOC trends from the flux map data with the mean changes in measured boron bias from BOC to EOC. Such a comparison is presented in Table 7-3 for each of the four Duke Energy Plants -

assuming a core-average burnup of 10 GWd/T at BOC and 30 GWd/T at EOC and a conversion from boron error to pcm using an assumed value of 9.0 pcm/ppm. These data show that the mean flux map reactivity decrements agree within 194 pcm (i.e., 234 pcm - 40 pcm) of the measured boron bias changes for each of the four reactors.

Table 7-3 Measured CASMO-5 BOC to EOC Reactivity Decrements Reactor Boron Bias Flux Map Decrement Bias (pcm @ 9 pcm/ppm) (pcm)

Unit BOC EOC BOC-EOC 10 30 30-10 (ppm) (ppm) (pcm) GWd/T GWd/T GWd/T McGuire 1 -4 -30 234 66 106 40 McGuire 2 -10 -32 198 66 106 40 Catawba 1 13 5 72 66 106 40 Catawba 2 30 14 144 66 106 40 Mean 162 All differences between measured boron reactivity decrement changes and measured flux map measured reactivity decrement changes are well within HFP reactivity decrement bias tolerance limits of Table 7-2.

7.8 Sensitivity to Lattice and Nodal Codes Additional tests have been performed to demonstrate that CASMO-5 and SIMULATE-3 do not contribute significantly to the measured reactivity decrements. First, one should be able to use any modern lattice code/cross section library and core analysis tool to produce high quality measured reactivity 7-21

decrement benchmarks that are expected to lie within the range of assigned uncertainties of the EPRI benchmarks. There are several additional studies that have been done to add quantification to this argument. In their respective M.S.

thesis, Gunow and Sykora [22-24] each used full-core multigroup neutron transport calculations to infer reactivity decrement biases for selected flux maps and sub-batches using the BEAVRS benchmark measured reactor data [25-26].

Both of these studies showed that the inferred reactivity decrements (see Table 6-2 in Reference 24, reproduced here as Table 7-4) were nearly the same when using SIMULATE-3 (two-group nodal diffusion calculations) and CASMO-5 (35-group, fine-mesh, transport calculations) to perform the core analysis. Thus, it is unlikely that any of the nodal model approximations have significantly influenced the inferred reactivity decrements of the original EPRI report [5].

These tests rule out any significant influence from core analysis approximations; such as lattice boundary conditions, two-group theory, assembly homogenization, macroscopic depletion, and pin power reconstruction.

Sykoras analysis [23] also showed that the burnup perturbation used to perform the k-infinity search in the EPRI methodology produced nearly identical reactivity decrements as using fuel temperature perturbations. This further substantiated the expectation that k-infinity itself dominates changes in core flux distribution, and the method by which the k-infinity perturbation is performed is not very important. Note from Table 7-4 results that the mean reactivity differences and 2-sigma deviations (for nodal diffusion vs. multi-group transport or burnup vs. temperature perturbation) are less than the tolerance limits assigned the measured reactivity decrements.

Another demonstration of the insensitivity of inferred reactivity decrement biases to the core analysis methods employed was obtained from studies done by R. D.

Harrison in the UK [27-28]. This analysis followed the EPRI methodology, but used the JEF2.2 rather than the ENDF-B/VII nuclear data library and the WIMS/PANTHER codes rather than the CASMO-5/SIMULATE-3 codes of the EPRI report. These studies produced reactivity decrement biases and uncertainties that are very similar to those of the Sykoras study [23, 24], further substantiating that the data library and nodal codes do not contribute significantly to the decrement biases and uncertainties.

The original version of this report [5] also contained direct comparisons of reactivity decrement biases inferred using the CASMO-4 lattice code [8]. The CASMO-4 cross section library uses a combination of ENDF-B/V and JEF 2.0 nuclear cross section data, and yet the measured reactivity decrements biases are very close to those inferred using CASMO-5 data, and they are also well within the assigned measurement uncertainties.

These tests have all demonstrated that CASMO-5 lattice approximations and the SIMULATE-3 nodal approximations do not directly contribute significantly to the measured reactivity decrements or its uncertainty.

7-22

Table 7-4 Inferred CASMO-5 Fuel Batch Reactivity Biases 7-23

Section 8: Measured Cold Reactivity Bias and Uncertainty The SIMULATE-3 flux map analysis procedure described in Sections 6 and 7 allowed quantification of the bias and uncertainty in CASMO-5 reactivity decrements at HFP conditions. However, for spent fuel pool and cask criticality analyses, biases and uncertainties are needed at cold conditions.

8.1 Overview The biases and uncertainties at HFP include errors associated with both the assembly isotopics and cross-section data uncertainties. At cold conditions (before cooling) the isotopics do not change, but there are additional uncertainties from the altered conditions. Two such sources of added uncertainty arise because of:

1) imprecise knowledge of exact physical properties (for example, fuel temperature, coolant temperature, boron concentration) during fuel irradiation, and

2) spectrum-induced reactivity changes from HFP to cold conditions from cross-section data uncertainties.

8.2 Fuel Temperature Uncertainties At SFP or cask conditions, coolant temperature, fuel temperature and boron concentrations are all well known. At HFP conditions coolant temperatures and boron concentrations are well known, and they do not depend in any direct way on sub-batch burnups. However, fuel temperatures are not as easy to compute accurately. Fuel conductivity decreases about 50% at high burnup, and pellet swelling and gap conductance changes cause fuel temperatures to change with pellet burnup. The net effect is that there is an added uncertainty in measured reactivity decrements because of imperfect knowledge of HFP fuel temperatures.

This situation is easiest to understand by assuming that one has a lattice code that computes HFP sub-batch reactivities with zero bias - for all burnups. If there are any errors in HFP fuel temperatures, the corresponding reactivity bias must be cancelled out by other biases in the lattice code reactivities at HFP conditions. Consequently, there are uncertainties in measured HFP reactivity decrements that arise from imperfect knowledge of fuel temperatures at operating 8-1

reactor conditions. In addition, even though SFP temperatures might be known exactly, the history (e.g., depletion) effects of fuel temperature errors also contribute additional uncertainties in lattice code reactivities at cold conditions.

There is no easy way to quantify precisely the fuel temperature reactivity decrement uncertainty change from HFP to cold conditions. The INTERPIN-4 plot of fuel temperature vs. burnup displayed in Figure 8-1 shows that predicted fuel temperatures decrease by about 50K as the pellet swells, the cladding creeps down, and as the pellet/cladding gap closes. At high burnup, the decrease in fuel conductivity overwhelms the gap conductance changes, and fuel temperatures increase significantly.

Figure 8-1 Typical INTERPIN-4 Fuel Temperature Change With Burnup One way to conservatively treat uncertainties in fuel temperatures on HFP and cold reactivities is to treat the entire reactivity effect as additional uncertainties.

By taking the highest and lowest fuel temperatures that occur anywhere in the nominal INTERPIN-4 predictions (4.75% enriched Westinghouse RFA fuel) and performing CASMO-5 calculations with these fixed temperatures, one obtains the table of reactivity differences presented in Table 8-1. These results show that at hot conditions, the instantaneous decrease in reactivity for the higher fuel temperature is partially compensated at high burnup by the production of additional plutonium, with the cumulative effect being almost zero at 55 GWd/T. However, in the branch cases to cold conditions, the higher HFP fuel temperature leads to a monotonic increase in lattice reactivity. These results show that the maximum difference reactivities are -150 pcm at HFP conditions and +206 pcm at cold conditions.

In the initial version of this EPRI report [5] a very conservative approach to the fuel temperature uncertainty was taken by statistically combining the maximum instantaneous fuel temperature difference (150 pcm) and the maximum historical 8-2

fuel temperature difference (206 pcm) to arrive at a combined fuel temperature uncertainty of 255 pcm - that was then applied independent of burnup. This approach leads to an extremely conservative uncertainty for low burnups, because the reactivity decrement uncertainty must physically go to 0.0 pcm at zero burnup. Consequently, it is more appropriate to statistically combine the two fuel temperature uncertainties at each burnup to obtain a more realistic uncertainty as a function of burnup. The right-most column of Table 8-1 displays the combined fuel temperature uncertainty as a function of burnup expressed in pcm.

At 10.0 GWd/T, the uncertainty is reduced to 146 pcm rather than the conservative 255 pcm previously used in the initial EPRI report [5].

Table 8-1 Fuel Temperature Effect on Hot and Cold Lattice Reactivity Branch to Cold ( Bor=0, Xen=0, Statistically Hot Depletion (HFP) 293K) Combined Burnup Uncertainty (GWd/T) k-infinity k-infinity Difference k-infinity k-infinity Difference (pcm) 946K-(946K) (897K) (946K) (897K) 946K-897K 897K 0.0 1.07712 1.07848 -0.00136 1.15285 1.15285 +0.00000 136 10.0 1.13346 1.13492 -0.00146 1.20192 1.20189 +0.00003 146 20.0 1.13467 1.13617 -0.00150 1.21248 1.21229 +0.00019 151 30.0 1.08533 1.08650 -0.00117 1.16481 1.16421 +0.00060 131 40.0 1.02515 1.02586 -0.00071 1.09975 1.09866 +0.00109 130 50.0 0.96862 0.96887 -0.00025 1.03605 1.03445 +0.00160 162 60.0 0.91905 0.91888 +0.00017 0.97875 0.97669 +0.00206 207 8.3 Cold Uncertainty Change From Cross-Section Uncertainties The TSUNAMI-3D sequence in ORNLs SCALE 6 [29] code system can be used in conjunction with CASMO-5 to characterize uncertainties in hot to cold reactivity changes due to cross-section uncertainty at various burnup points. The goal of the analysis is to establish the multiplication factor uncertainty between various fuel assemblies at different conditions in a quantifiable manner and to obtain a bound on the hot-to-cold reactivity uncertainty over the various assembly types and burnups - attributed to cross-section data uncertainties.

The TSUNAMI analysis sequences are capable of estimating the impact of cross-section uncertainties in a critical systems multiplication factor k by propagating uncertainties through the use of sensitivity coefficients and first-order perturba-tion theory. The sensitivity coefficients represent a change in the systems response due to a change in the input parameters. In particular, TSUNAMI approach uses explicit ( S k , x , g ) and implicit ( S x , g , i ) sensitivity coefficients, which are defined in the following manner.

,, =

8-3

, , = ,

where x, g is the macroscopic cross-section for reaction x and group g, and i is the nuclear data component of some isotope i. The implicit sensitivity coefficient is propagated to k or explicit sensitivity through the use of the chain rule for derivatives. The sensitivity coefficients are summed so that they account for the fact that changes in one cross section may affect another cross section via self-shielding perturbations. Finally, the response uncertainty is obtained by summing all the contributions to the system response from the uncertainties through the sensitivity coefficients and covariance data.

In addition to computing uncertainties in the multiplication factor, the SCALE 6 code system is capable of computing a correlation coefficient, which is representative of the similarity (in terms of uncertainty) between two critical systems. The computation of the correlation coefficient is performed by the TSUNAMI-IP sequence in SCALE 6, which uses the sensitivity data generated by TSUNAMI, along with nuclear covariance data to assess the similarity between the two systems.

8.4 TSUNAMI Uncertainty Analysis CASMO-5 was used to perform the lattice depletion and branch calculations for a variety of fuel assemblies. In order to obtain the burnup-dependent isotopic compositions in each fuel and burnable rod for the TSUNAMI-3D calculation, a script was developed which used the CASMO-5 lattice geometry, temperature, and region-wise isotopic composition to generate suitable SCALE 6 input files.

This process was applied to all lattice types and branch conditions for selected burnup points.

A 17 x 17 Westinghouse RFA fuel assembly with 5% enrichment, 104 IFBA, and 20 WABA was selected as a base case. A case matrix was constructed for different enrichments (3.5 % and 4.25 %), number of burnable absorbers (128 IFBA, 24 WABA), and fuel pin radius (smaller than nominal) for a total of five lattice cases. All five lattice cases were depleted with CASMO-5 to 60 GWd/T and branched from HFP to six other conditions (HFP No Xenon, Hot Zero Power, Cold 1000 ppm boron, Cold no boron, Cold no boron with 100-hour decay, and simplified rack geometry) at eight burnup points (0.0, 0.5, 10, 20, 30, 40, 50, and 60 GWd/T).

Since the covariance library in SCALE-6 is in multi-group format, the TSUNAMI-3D sequence uses the unresolved (BONAMIST) and resolved resonance self-shielding modules (NITAWLST or CENTRMST) to produce problem-specific multi-group cross-section and sensitivity libraries for the multi-group transport calculation. Cross-sections in each fuel pin region (with unique isotopic number densities) were self-shielded in the TSUNAMI calculation. In order to reduce the run-time, the NITAWLST module was used to perform the resolved resonance self-shielding calculation that necessitated the use of the 238-8-4

group ENDF/B-V library. Forward and adjoint multi-group transport calcu-lations in TSUNAMI-3D are performed by the KENO multi-group Monte Carlo code. Finally, the TSUNAMI-3D KENO-VI sequence was chosen to take advantage of the 1/4 assembly geometry symmetry. Once forward and adjoint transport computations were completed, the SAMS module was used to generate problem-specific uncertainty data and a sensitivity library to be used for post-processing. This library is read by TSUNAMI-IP to generate correlation coefficients. The specific versions of SCALE-6 that were used in this analysis were:

tsunami-3d_k6 6.0.34 p07_jan_2009 bonamist 6.0.21 p09_jan_2009 nitawlst 6.0.16 p30_dec_2008 kenovi 6.0.24 p07_jan_2009 sams6 6.0.29 p07_jan_2009 tsunami-ip 6.0.13 p30_dec_2008 8.5 TSUNAMI Analysis Results TSUNAMI can compute cross-section uncertainties for lattice multiplication factors as a function of various lattices, conditions, and burnups. The uncertainty results for the base lattice at HFP and cold conditions as a function of burnup are shown in Table 8-2.

Table 8-2 Multiplication Factor Uncertainty (2-sigma) as Function of Burnup Burnup (GWd/T) 0.5 10. 20. 30. 40. 50. 60.

k-infinity Hot 1.02068 1.08597 1.08298 1.03600 0.97772 0.92176 0.87200 Uncertainty (pcm) 1034 1104 1211 1265 1295 1311 1323 k-infinity Cold 1.16103 1.23579 1.25419 1.21057 1.14557 1.07995 1.01883 Uncertainty (pcm) 1015 1087 1209 1281 1326 1361 1388 The hot-to-cold reactivity uncertainties can be obtained from the data shown above and the correlation coefficient obtained from evaluation of the covariance matrix between the two states. The results from this analysis are shown in Table 8-3. The propagation of uncertainties as independent variables (without correlation) is also shown to illustrate the importance of the correlation between hot-to-cold conditions on the uncertainty.

8-5

Table 8-3 HFP to Cold Reactivity Uncertainty (2-sigma) as Function of Burnup Burnup (GWd/T) 0 0.5 10. 20. 30. 40. 50. 60.

Uncertainty (pcm) 347 427 459 508 527 530 521 509 Uncertainty (pcm)* 1479 1476 1580 1748 1840 1893 1926 1949

• Propagation of uncertainty such that the covariance (k-hot, k-cold)=0 The inclusion of the correlation reduces the uncertainty by about a factor of four.

The two states are expected to be highly correlated due to the fact that there is no burnup difference, and isotopic compositions remain the same.

For any lattice and depletion point, the similarity between different physical conditions can be quantified by the use of the correlation coefficient. A corre-lation coefficient of unity indicates perfect similarity (identical systems) while a correlation of zero indicates negligible similarity. In this analysis, the correlation factor shows the similarity between different states and lattice types at a fixed burnup step.

A summary of the correlation coefficients is shown in Table 8-4 for the five lattice types between nominal (HFP) and branch conditions. The first row in each lattice type is unity because HFP is the base case. All lattices show a very high degree of similarity between HFP and various cold conditions, at all burnup points - even though xenon, fuel temperature, coolant temperature, boron con-centration, and local rack conditions change dramatically. (For the rack case, a simplified uniform rack has been assumed with a pitch of 22.5 cm, a 0.1-cm thick stainless steel can, a 0.0625-cm thick borated aluminum poison sheet having a width of 19 cm, and a 10B areal density of 0.006 gm/cm2.)

A second comparison between different lattice types was performed at HFP, cold (no boron, 100-hour decay), and cold rack conditions, and results are presented in Tables 8-5 and 8-6. In Table 8-5, all correlation coefficients are computed relative to the base case at zero burnup. It can be seen that the similarity changes significantly with burnup as the isotopics of the fuel change from fresh uranium to the higher actinides and fission products. Table 8-6 displays the correlation coefficients for the same cases measured relative to the base case at each burnup state. These results indicate an extremely high degree of similarity exists between all lattice types - at each burnup point. This is important for this project, as biases in reactivity decrement as a function of burnup are derived directly from reactor measurements, and only the uncertainty of going from HFP reactor conditions to cold spent fuel pool/cask conditions is needed from the TSUNAMI analysis.

Finally, the quantities of direct interest in this study, reactivity and reactivity uncertainty between HFP and cold (no boron, 100-hour decay) are displayed in Table 8-7, for all lattice types. The data in Table 8-7 are not taken directly from TSUNAMI outputs, but rather they are based on the eigenvalue and uncertainty calculated by TSUNAMI at Hot Full Power (HFP) and cold conditions. The 8-6

state or condition eigenvalue and uncertainty are taken directly from the TSUNAMI output files. In order to obtain the 2-sigma uncertainties in Report Tables 8-7, the variance of the reactivity is obtained by computing the relative variance of the eigenvalue difference (see Eq. (41) paper in Reference [30]). The relative standard deviation of the hot-to-cold reactivity is obtained from the following equation, which is based on Eq. (41) of the referenced paper after some manipulations, 2 2 1 kh kc kh kc

= + 2Ch ,c ,

h c kh kc kh kc where k and k are the eigenvalue and standard deviation, respectively, Ch ,c is the correlation coefficient, and hc is the reactivity, defined as follows 1 1 h=

c kh kc Finally, the absolute two-sigma uncertainties are obtained by multiplying the relative standard deviation by the hot-to-cold reactivity and accounting for the fact that two standard deviations account for 95.45 % of values around a mean.

The maximum 2-sigma reactivity uncertainty (due to cross-section data uncertainties) over all lattice types and burnup points is 555 pcm. Table 8-8 displays the corresponding reactivity and reactivity uncertainty between HFP and cold simplified SFP rack conditions. The uncertainties displayed in Table 8-8 are uniformly lower than those in Table 8-7, indicating that the cross-section data uncertainties are less important in the SFP absorbing rack geometry. This is a reflection of the fact that the hardening of the spectrum caused by the SFP rack actually makes the spectrum closer to the lattice spectrum at HFP conditions than to the lattice spectrum at cold conditions. Consequently, the impacts of cross section uncertainties on the reactivity changes from HFP-to-cold conditions are very similar in operating reactor conditions and cold rack geometry.

8-7

Table 8-4 Correlation Coefficients, ck, Between Reactor Conditions by Lattice and Burnup Burnup (GWd/T) 0.0 0.5 10.0 20.0 30.0 40.0 50.0 60.0 HFP 1 1 1 1 1 1 1 1 HFP No Xe 1 0.9843 0.9817 0.9831 0.9854 0.9878 0.9898 0.9914 HZP 0.9992 0.9992 0.9992 0.9995 0.9994 0.9994 0.9995 0.9995 Base Cold 1000 ppm 0.9807 0.9609 0.9608 0.9646 0.9678 0.9702 0.9723 0.9734 Cold 0 ppm 0.9694 0.9506 0.9514 0.9560 0.9592 0.9611 0.9634 0.9640 Decay 100 hr 0.9705 0.9512 0.9519 0.9558 0.9591 0.9613 0.9633 0.9643 SNF Rack 0.9717 0.9543 0.9510 0.9543 0.9582 0.9605 0.9623 0.9641 HFP 1 1 1 1 1 1 1 1 HFP No Xe 1 0.9863 0.9829 0.9835 0.9856 0.9879 0.9899 0.9914 HZP 0.9993 0.9993 0.9992 0.9993 0.9994 0.9994 0.9995 0.9994 128 IFBA Cold 1000 ppm 0.9799 0.9638 0.9616 0.9648 0.9677 0.9703 0.9724 0.9734 24 WABA Cold 0 ppm 0.9708 0.9526 0.9525 0.9558 0.9587 0.9617 0.9638 0.9643 Decay 100 hr 0.9702 0.9548 0.9531 0.9559 0.9585 0.9614 0.9634 0.9641 SNF Rack 0.9725 0.9559 0.9518 0.9547 0.9572 0.9611 0.9630 0.9638 HFP 1 1 1 1 1 1 1 1 HFP No Xe 1 0.9851 0.9828 0.9853 0.9884 0.9907 0.9923 0.9934 HZP 0.9994 0.9992 0.9993 0.9984 0.9996 0.9995 0.9994 0.9995 3.5%

Cold 1000 ppm 0.9799 0.9617 0.9637 0.9675 0.9714 0.9726 0.9738 0.9744 Enrichment Cold 0 ppm 0.9670 0.9482 0.9521 0.9569 0.9603 0.9622 0.9631 0.9641 Decay 100 hr 0.9669 0.9482 0.9526 0.9566 0.9608 0.9622 0.9632 0.9639 SNF Rack 0.9734 0.9565 0.9538 0.9572 0.9612 0.9630 0.9641 0.9649 8-8

Table 8-4 (continued)

Correlation Coefficients, ck, Between Reactor Conditions by Lattice and Burnup Burnup (GWd/T) 0.0 0.5 10.0 20.0 30.0 40.0 50.0 60.0 HFP 1 1 1 1 1 1 1 1 HFP No Xe 1 0.9842 0.9818 0.9838 0.9867 0.9891 0.9910 0.9924 HZP 0.9994 0.9993 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 4.25%

Cold 1000 ppm 0.9808 0.9617 0.9618 0.9659 0.9698 0.9718 0.9734 0.9740 Enrichment Cold 0 ppm 0.9700 0.9504 0.9512 0.9558 0.9598 0.9625 0.9636 0.9641 Decay 100 hr 0.9696 0.9490 0.9524 0.9565 0.9602 0.9622 0.9636 0.9639 SNF Rack 0.9730 0.9547 0.9517 0.9560 0.9596 0.9624 0.9640 0.9645 HFP 1 1 1 1 1 1 1 1 HFP No Xe 1 0.9816 0.9781 0.9797 0.9827 0.9857 0.9882 0.9904 HZP 0.9992 0.9992 0.9994 0.9995 0.9995 0.9996 0.9996 0.9996 Small Cold 1000 ppm 0.9814 0.9608 0.9589 0.9618 0.9652 0.9690 0.9712 0.9728 Fuel Pin Cold 0 ppm 0.9709 0.9498 0.9488 0.9521 0.9556 0.9591 0.9616 0.9628 Decay 100 hr 0.9709 0.9510 0.9497 0.9530 0.9555 0.9596 0.9614 0.9630 SNF Rack 0.9743 0.9536 0.9486 0.9513 0.9548 0.9590 0.9615 0.9632 8-9

Table 8-5 Correlation Coefficients, ck, Between Lattice Types (Relative to 0 GWd/T)

Burnup (GWd/T) 0.0 0.5 10.0 20.0 30.0 40.0 50.0 60.0 Base 1 0.9837 0.8321 0.6849 0.5867 0.5149 0.4567 0.4100 128 I 24 W 0.9989 0.9838 0.8292 0.6827 0.5869 0.5147 0.4571 0.4115 HFP 3.5 % Enrich. 0.9927 0.9754 0.7323 0.5779 0.4879 0.4265 0.3817 0.3490 4.25 % Enrich. 0.9985 0.9812 0.7886 0.6346 0.5390 0.4705 0.4176 0.3777 Small Fuel Rad. 0.9976 0.9797 0.8280 0.6804 0.5827 0.5062 0.4461 0.3964 Base 1 0.9991 0.8569 0.7016 0.5857 0.4936 0.4177 0.3554 Cold 128 I 24 W 0.9988 0.9977 0.8509 0.6959 0.5823 0.4916 0.4168 0.3556 0 ppm 3.5 % Enrich. 0.9941 0.9920 0.7562 0.5798 0.4648 0.3805 0.3186 0.2738 Decay 100 hr 4.25 % Enrich. 0.9988 0.9974 0.8149 0.6468 0.5293 0.4386 0.3675 0.3123 Small Fuel Rad. 0.9979 0.9976 0.8661 0.7172 0.6015 0.5070 0.4266 0.3594 Base 1 0.9992 0.8505 0.6890 0.5716 0.4792 0.4032 0.3422 SNF 128 I 24 W 0.9988 0.9981 0.8446 0.6836 0.5675 0.4780 0.4034 0.3424 3.5 % Enrich. 0.9940 0.9920 0.7466 0.5643 0.4488 0.3650 0.3037 0.2599 Rack Geometry 4.25 % Enrich. 0.9988 0.9975 0.8065 0.6326 0.5138 0.4241 0.3534 0.2989 Small Fuel Rad. 0.9984 0.9976 0.8582 0.7022 0.5854 0.4906 0.4112 0.3444 8-10

Table 8-6 Correlation Coefficients, ck, Between Lattice Types (By Individual Burnup State)

Burnup (GWd/T) 0.0 0.5 10.0 20.0 30.0 40.0 50.0 60.0 Base 1 1 1 1 1 1 1 1 128 I 24 W 0.9989 0.9990 0.9998 0.9999 0.9999 1 1 1 HFP 3.5 % Enrich. 0.9927 0.9931 0.9831 0.9870 0.9898 0.9919 0.9939 0.9958 4.25 % Enrich. 0.9985 0.9984 0.9963 0.9969 0.9976 0.9980 0.9984 0.9988 Small Fuel Rad. 0.9976 0.9975 0.9971 0.9977 0.9983 0.9979 0.9981 0.9982 Base 1 1 1 1 1 1 1 1 Cold 0 ppm 128 I 24 W 0.9988 0.9986 0.9997 0.9999 1 1 1 1 3.5 % Enrich. 0.9941 0.9939 0.9818 0.9836 0.9860 0.9885 0.9912 0.9937 Decay 100 hr 4.25 % Enrich. 0.9988 0.9987 0.9962 0.9963 0.9968 0.9972 0.9977 0.9983 Small Fuel Rad. 0.9979 0.9982 0.9978 0.9981 0.9982 0.9984 0.9984 0.9985 Base 1 1 1 1 1 1 1 1 SNF 128 I 24 W 0.9988 0.9992 0.9997 0.9999 1 1 1 1 3.5 % Enrich. 0.9940 0.9941 0.9817 0.9835 0.9860 0.9884 0.9910 0.9936 Rack Geometry 4.25 % Enrich. 0.9988 0.9988 0.9961 0.9963 0.9968 0.9972 0.9977 0.9982 Small Fuel Rad. 0.9984 0.9980 0.9977 0.9979 0.9982 0.9983 0.9986 0.9985 8-11

Table 8-7 HFP to Cold Uncertainty Matrix (2-sigma) at Cold Conditions Burnup (GWd/T) 0.0 0.5 10.0 20.0 30.0 40.0 50.0 60.0 Reactivity (pcm) 9867 11843 11425 12605 13919 14986 15891 16527 Base Uncertainty 347 427 459 508 527 530 521 509 128 IFBA Reactivity (pcm) 9977 11927 11367 12556 13916 15009 15888 16612 24 WABA Uncertainty 337 403 450 508 533 531 521 512 3.50% Reactivity (pcm) 12703 14810 13078 14402 15525 16266 16734 17034 Enrichment Uncertainty 365 437 498 555 550 537 518 500 4.25% Reactivity (pcm) 11069 13112 12209 13469 14747 15699 16415 16931 Enrichment Uncertainty 350 434 473 529 540 534 520 508 Reactivity (pcm) 10205 12262 11602 12658 13981 14991 15849 16473 Small Fuel Pin Uncertainty 322 402 442 497 524 518 509 492 8-12

Table 8-8 HFP to Cold Uncertainty Matrix (2-sigma) in Rack Geometry Burnup (GWd/T) 0.0 0.5 10.0 20.0 30.0 40.0 50.0 60.0 Base Reactivity (pcm) - - - - - - - -

10145 8018 6291 4658 4002 4097 4601 5344 Uncertainty 222 287 324 353 358 356 349 339 128 IFBA Reactivity (pcm) - - - - - - - -

24 WABA 10405 8323 6684 4858 4094 4130 4626 5347 Uncertainty 212 274 317 352 364 354 346 341 3.50% Reactivity (pcm) - - - - - - - -

Enrichment 12437 9905 7382 5715 5839 6687 7688 8688 Uncertainty 204 266 330 364 357 349 343 337 4.25% Reactivity (pcm) - - - - - - - -

Enrichment 11101 8772 6740 5028 4684 5123 5916 6873 Uncertainty 211 279 327 357 359 350 342 337 Small Fuel Pin Reactivity (pcm) - - - - - - - -

10594 8366 6705 5185 4676 5046 5851 7075 Uncertainty 201 274 315 348 356 345 336 327 8-13

8.6 HFP to Cold Reactivity Decrement Uncertainty Since the uncertainty changes in Table 8-8 may be dependent on the actual rack design, it is conservative to use the uncertainties computed directly at cold conditions - without taking any credit for reduction in uncertainty that would arise in SFP or cask geometry.

However, the uncertainty for fresh fuel in cold SFP or cask conditions will actually be determined for specific applications through evaluation of a large set of cold criticals, and there is no reason to include reactivity uncertainty due to fresh fuel cross-section uncertainties. Consequently, statistically subtracting the smallest fresh fuel uncertainty (the green cell) from the other uncertainties in Table 8-7, one obtains the hot-to-cold reactivity uncertainties (due to cross-section uncertainties) as a function of fuel depletion as displayed in Table 8-9.

Table 8-9 HFP to Cold Additional Uncertainty Matrix (2-sigma in pcm) at Cold Conditions Burnup (GWd/T) 0.0 0.5 10.0 20.0 30.0 40.0 50.0 60.0 Base 0 249 300 371 397 401 389 372 128 IFBA/24 WABA 0 221 298 380 413 410 397 385 3.50% Enrichment 0 240 339 418 411 394 368 342 4.25% Enrichment 0 257 318 397 411 403 385 368 Small Fuel Pin 0 241 303 379 413 406 394 372 The top blue curve in Figure 8-2 displays a plot of the 128 IFBA/24 WABA lattice additional uncertainties as a function of burnup when referenced to zero burnup. The large jump from 0.0 to 0.5 GWd/T burnup occurs in part because of the ~3000 pcm reactivity arising from Xe135 in the HFP depleted lattices.

Xenon must be present in both the hot and cold TSUNAMI cases to maintain consistency when computing Hot-to-Cold uncertainties. Note that the corresponding additional uncertainty curve does not approach 0.0 for low burnups as one expects from the definition of reactivity decrement.

An alternate interpretation of this data is to use the 0.5 GWd/T step as the reference for zero burnup, as displayed in the bottom red curve of Figure 8-2.

This curves shape trends towards 0.0 at zero burnup. With 0.5 GWd/T as the zero burnup reference, xenon is consistently represented in all data used to decompose the additional burnup uncertainty, as displayed in Table 8-10.

8-14

Figure 8-2 Hot-to-Cold Additional Uncertainty vs. Burnup Table 8-10 HFP to Cold Additional Uncertainty Matrix (2-sigma in pcm) at Cold Conditions Burnup (GWd/T) 0.0 0.5 10.0 20.0 30.0 40.0 50.0 60.0 Base - 0 168 275 309 314 299 277 128 IFBA/24 WABA - 0 200 309 349 346 330 316 3.50% Enrichment - 0 239 342 334 312 278 243 4.25% Enrichment - 0 188 302 321 311 286 264 Small Fuel Pin - 0 184 292 336 327 312 284 Consequently, we choose to use the maximum additional uncertainty from any of the five lattices of Table 8-10 (at each burnup step) as the appropriate hot-to-cold uncertainty versus burnup, as is displayed in the bottom row of Table 8-11.

Table 8-11 HFP to Cold Additional Uncertainty (2-sigma) vs. Burnup Burnup (GWd/T) 0.0 10.0 20.0 30.0 40.0 50.0 60.0 Uncertainty (pcm) 0 239 342 349 346 330 316 8-15

8.7 Cold Reactivity Decrement Bias and Tolerance Limit CASMO-5 does not have the ability to propagate nuclear cross section data uncertainties, so the SCALE 6 code system was used to perform such analyses.

Fortunately both CASMO-5 and SCALE 6 employ the nuclear ENDF-B/VII cross section, and the cross section covariance and uncertainties from SCALE 6 are equally applicable to CASMO-5. Consequently, it is appropriate to assume that HFP-to-cold uncertainty changes computed with SCALE6 data are equally applicable to CASMO-5. Hence, one can statistically combine the HFP one-sided tolerance limits (from Table 7-2), the fuel temperature 2-sigma uncertainties (from Table 8-1), and the HFP to cold additional uncertainties (from Table 8-11) to obtain a one-sided total 95/95 tolerance limit. Appending this data to the bias data of Table 7-2 one obtains the measured CASMO-5 cold reactivity decrement biases and tolerance limits, as displayed in Table 8-12.

The last row of data in Table 8-12 adds the cold tolerance limit for fuel depleted at 150% of nominal power density; by assuming the fuel temperature uncertainty is linear in fuel temperature. The later data are appropriate for fuel that might be depleted at 150% of nominal power density, where the fuel temperature uncertainties are larger than those for fuel depleted at nominal power densities.

Table 8-12 Measured CASMO-5 Cold Reactivity Decrement Biases and Tolerance Limits Burnup (GWd/T) 10.0 20.0 30.0 40.0 50.0 60.0 CASMO-5 Bias (pcm) 66 101 106 80 22 -64 Prediction Interval (pcm) 226 420 585 713 812 875 HFP Tolerance Limit (pcm) 207 386 537 655 745 803 Cold Tolerance Limit (pcm) 348 537 654 752 831 888 Cold Tolerance Limit (pcm)* 385 563 670 766 851 917

• Assuming 150% of nominal fuel temperature 8-16

Section 9: Experimental Reactivity Decrement Benchmarks 9.1 Experimental Benchmark Methodology The analysis presented in Section 7 has quantified the measured CASMO-5 reactivity burnup decrement errors and has further demonstrated that these errors are essentially independent of sub-batch enrichment, boron concentrations, etc.

Consequently, if one assumes the CASMO-5 biases in reactivity decrement are independent of fuel type (within the stated uncertainties), one can construct an experimental benchmark for HFP reactivity decrement by adding CASMO-5 biases to CASMO-5 computed reactivity decrements. In such a benchmark, the net effect is that lattice physics depletion uncertainties, including nuclide concentration and reactivity uncertainties, are experimentally determined.

Since nuclide inventories between HFP and cold (no cooling) conditions are identical, the only difference between HFP and cold arise from changes in fuel and coolant temperatures. The TSUNAMI analysis presented in Section 8 has demonstrated high similarity between all fuel types at HFP and cold conditions and has quantified the uncertainty changes from HFP-to-cold conditions. Thus, one obtains an experimental benchmark for cold reactivity decrement by adding the additional uncertainties that arise from HFP to cold conditions. Table 8-12 contains the CASMO-5 bias and tolerance limit data used to construct such experimental burnup reactivity decrement benchmarks.

9.2 Experimental Benchmark Specification Eleven cases have been selected for experimental benchmarks, based on the Westinghouse RFA assembly. CASMO-5 calculations have been performed for each case in Table 9-1, covering a range of:

enrichments burnable absorber loadings boron concentrations fuel and coolant temperatures decay times 9-1

Table 9-1 Benchmark Lattice Cases 1 3.25% Enrichment 2 5.00% Enrichment 3 4.25% Enrichment 4 Small Fuel Pin Depletion 5 20 WABA Depletion 6 104 IFBA Depletion 7 104 IFBA and 20 WABA Depletion 8 High Boron Depletion = 1500 ppm 9 Nominal Case Branch to SFP Hot Isothermal Temperatures = 150°F 10 Nominal Case Branched to SFP High Boron Concentration = 1500 ppm 11 High Power Depletion (power, coolant/fuel temp)

Case 3 with 4.25% enrichment and no burnable absorbers was chosen as the base case from which the lattice parameters were perturbed. For each case, the following calculations were performed:

CASMO-5 was depleted to 60 GWd/T at the specified power density, temperatures, and boron concentrations.

Cold cooling cases to 100 hours0.00116 days <br />0.0278 hours <br />1.653439e-4 weeks <br />3.805e-5 months <br />, 1 year, 5 years, and 15 years were performed for each branch case.

Branch cases to cold were performed as restarts from the cooling cases at burnups of 10, 20, 30, 40, 50, and 60 GWd/T.

Since the anticipated application of these experimental benchmarks is for analysts to measure biases for their SFP or cask analysis tools (usually Monte Carlo),

small simplifications of the standard CASMO-5 HFP depletion models were made to make subsequent analysis easier:

Thermal expansion of materials is ignored (cold dimensions are used)

Spacer grids are not modeled Water in guide tubes is modeled at the same temperature as the coolant Buckling search to critical is not used (since this is difficult for Monte Carlo methods)

None of these effects are important for the purposes of the experimental benchmark - it is only important that there be consistency between the CASMO-5 models and the models used with the SFP or cask tools.

The detailed descriptions of the eleven cases are contained in Appendix B.

9-2

9.3 Experimental Reactivity Decrement Tables The k-infinity from each computed CASMO-5 cold case was used to construct reactivity decrement tables, to which the CASMO-5 experimental biases (from Table 8-12 were added to obtain cold experimental reactivity decrements and uncertainties - displayed in the tables of Appendix C.

The reactivity decrement uncertainties in the Appendix C tables make the assumption that decrement uncertainties are independent of the cooling time.

This is a good approximation because the largest contributors to the change in reactivity decrement with cooling time are due to 135Xe decay, 241Pu decay (to 241 Am) and 155Eu decay (to 155Gd), and all these cross sections and decay constants have very small uncertainties.

9.4 End-Users Application of Experimental Reactivity Decrements Users applications of experimental reactivity decrements for each case are anticipated to follow these steps:

1. Lattice depletions are performed with the users lattice depletion tool to 60 GWd/T at the precise physical conditions specified in the Benchmarks.

2. Decay calculations for each cooling interval of interest (for example, 100-hour, 5-years, and 15-years) are performed with the users lattice depletion tool from each depletion branch (10, 20, 30, 40, 50, 60 GWd/T) of Step 1.

3. Fuel number densities at each depletion/cooling branch from Step 2 are transferred to the users criticality model (often Monte Carlo) of the lattice, and cold k-infinities are computed for each combination of lattice/burnup/cooling interval and lattice conditions.

Note: SFP/cask criticality analysis may make modeling approximations that involve averaging of fuel pin number densities. In such cases, the averaging must also be performed at this Step of the Benchmark analysis.

4. Step 3 k-infinities are used to construct reactivity decrement tables as a function of lattice type, burnup, and cooling interval (analogous to those in Appendix C).

5. Step 4 reactivity decrement tables are differenced from the experimental reactivity decrement tables of Appendix C to construct biases for the users methodology/tools as a function of lattice type, burnup, and cooling interval.

6. Reactivity decrement uncertainties are applied (Appendix C Table C-1) for each reactivity decrement of Step 5.

7. Biases from Step 5 and the uncertainties from Step 6 are combined with biases and uncertainties arising from other portions of the SFP/cask criticality analysis.

9-3

Section 10: Summary of Conclusions 10.1 Bias and Tolerance Limits in Percent of Depletion Reactivity Decrement The CASMO-5 reactivity decrement biases and 95/95 tolerance limits from Section 8 were expressed in terms of pcm. The ultimate application of the depletion benchmarks uncertainties for SFP analysis are much more convenient if they are applied in terms of the percentage of lattice depletion reactivity decrement. As demonstrated by the data presented in Tables 8-7 and 8-8, the depletion reactivity is much lower for lattices in rack conditions than in the nominal reactor conditions. Consequently, it is appropriate to use reactivity decrements for the in-reactor conditions to convert the CASMO-5 measured bias and uncertainties into percentage terms. Table 10-1 displays the same data as Appendix C, Table C-2, converted to pcm for the seven nominal benchmark lattices of the Section 9 benchmarks with 100-hour cooling. The last row of Table 10-1 (the minimum absolute value of reactivity decrement from any of the seven lattices) is used to convert the bias and tolerance limit pcm values into percentage of absolute value of depletion reactivities as displayed in Table 10-2.

The Table 10-2 data support the conclusion that reactivity bias tolerance limits are less than 3.05% of the depletion reactivity for all fuel burnups.

Table 10-1 Measured Cold Reactivity Decrements (in pcm) for Nominal Benchmark Lattices Lattice Sub-batch Burnup (GWd/T) 10 20 30 40 50 60 1 -13244 -23339 -32084 -39600 -45698 -50324 2 -11414 -20159 -28034 -35490 -42538 -48974 3 -12184 -21519 -29874 -37620 -44608 -50594 4 -12024 -21709 -30724 39350 -47308 -54154 5 -20404 -23299 -29954 -37210 43878 -49624 6 -17314 22099 -29654 -37300 -44338 -50394 7 -25194 -24129 -29784 -36900 -43588 -49404 Minimum Abs. Value 11414 20159 28034 35490 42538 48974 10-1

Table 10-2 Measured CASMO-5 Cold Reactivity Decrement Biases and Tolerance Limits Expressed as Percentage of Absolute Value of Depletion Reactivity Decrement Burnup (GWd/T) 10.0 20.0 30.0 40.0 50.0 60.0 CASMO-5 Bias (pcm) 66 101 106 80 22 -64 Cold Tolerance Limit (pcm) 348 537 654 752 831 888 CASMO-5 Bias (% of depletion) 0.58 0.50 0.38 0.23 0.05 -0.13 Cold Tolerance Limit (% of depletion) 3.05 2.66 2.33 2.12 1.95 1.81 10.2 General Conclusions The flux map analysis methods developed and demonstrated in this report are capable of providing experimental determination of fuel reactivity burnup decrement biases and tolerance limits. The large amount of flux map data utilized in the 44 cycles of Duke Energy reactor analysis provided sufficient experimental sub-batch reactivity estimates (approximately 3000 points) such that resulting tolerance limits in measured HFP sub-batch reactivity decrement errors are less than 2.22% of the depletion reactivity decrement for burnups between 10.0 and 60.0 GWd/T.

TSUNAMI analysis demonstrated such a high degree of correlation between PWR fuel assemblies that nuclear data uncertainties are nearly independent of assembly design and enrichment. TSUNAMI analysis has demonstrated that extremely high correlation of reactivities between hot-to-cold conditions results in additional uncertainties for extending HFP reactivity decrement measurements to cold conditions of less than 350 pcm over the range of burnups from 0 to 60 GWd/T.

The combined HFP tolerance limits and the additional Hot-to-Cold uncertainties result in final tolerance limits for measured cold reactivity decrements that are less than 3.05% of the depletion reactivity for burnups between 10.0 and 60.0 GWd/T.

10.3 CASMO-5 Specific Conclusions Reactivity decrement biases computed with CASMO-5 showed no enrichment dependence (within statistical uncertainties) over the range of 3.5 to 5.0% 235U enrichment.

Results demonstrate that the historical 5% reactivity decrement uncertainty assumption, often applied in SFP criticality analyses, is conservative for cold SFP assembly reactivities with burnups between 10.0 and 60.0 GWd/T when computed with the CASMO-5 code.

10-2

Results provide a basis for supporting a smaller reactivity burnup decrement uncertainty for the historical 5% criterion, as displayed in the CASMO-5 biases and uncertainties of Table 10-2.

10.4 Related Conclusions Reactivity decrement biases derived from flux map data have also been shown to be similar to those derived from the change in biases of reactor soluble boron concentrations from beginning of cycle (BOC) to end of cycle (EOC). This conclusion is based on the close agreement between changes in reactor boron biases and sub-batch reactivity decrement biases computed from flux map data with the CASMO-5 and SIMULATE-3 tools. These results add credibility to the more general assertion that changes in boron biases for other code systems should also be reliable indicators of fuel sub-batch reactivity decrement biases.

10.5 Experimental Benchmarks The experimental biases derived for the CASMO-5 lattice physics code have been used to develop a series of experimental benchmarks that can be used to quantify reactivity decrement biases and uncertainties for other code systems used in lattice depletion and SFP/cask criticality analysis.

Specification of eleven experimental lattice benchmarks, covering a range of enrichments, burnable absorber loading, boron concentration, and lattice types have been documented in this report.

Interested parties can use these experimental benchmarks and their specific analysis tools to generate reactivity decrement biases and uncertainties that are unique to those tools.

10-3

Section 11: References

1. L. Kopp, NRC memorandum from L. Kopp to T. Collins, Guidance on the Regulatory Requirements for Criticality Analysis of Fuel Storage at Light-Water Reactor Power Plants, dated August 19, 1998 (ADAMS Accession No. ML003728001).

2. J. Rhodes, et al., CASMO-5 Development and Applications, PHYSOR-2006, Vancouver, BC, Canada. September 10-14, (2006).

3. J. Cronin, et al., SIMULATE-3 Methodology Manual, STUDSVIK/SOA-95/18, Studsvik of America, Inc. (1995).

4. 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.

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

6. K. S. Smith, et al., Depletion Reactivity Benchmarks - Part 1: Experimental Benchmarks for Quantifying PWR Fuel Reactivity Depletion Uncertainty, Nuclear Technology, Vol. 187, pp. 39-56 (January 2014).

7. D. Hagrman, et al., INTERPIN-4 Model Improvements and Verification, SSP-07/445 Rev 0, Studsvik Scandpower, Inc. (2007).

8. D. Knott, et al., CASMO-4 Methodology Manual, STUDSVIK/SOA-95/02, Studsvik of America, Inc. (1995).

9. T. Bahadir, et al., CMSLINK Users Manual, STUDSVIK/SOA-97/04, Studsvik of America, Inc. (1997).

10. R. Lawrence, Progress in Nodal Methods for the Solutions of the Neutron Diffusion and Transport Equations, Prog. Nucl. Energy, Vol. 17, No. 3, Pergamon Press, (1986).

11. K. Smith, et al., QPANDA: An Advanced Nodal Method for LWR Analysis, Trans. Am. Nucl. Soc., Vol. 50, p 532, San Francisco, CA, (1985).

12. P. Esser and K. Smith, A Semi-Analytic Two-group Nodal Model for SIMULATE-3, Trans. Am. Nucl. Soc., Vol. 68, p 220, San Diego, CA, (1993).

11-1

13. K. Smith, Assembly Homogenization Techniques for Light Water Reactor Analysis, Prog. Nucl. Energy, Vol. 17, No. 3, Pergamon Press, (1986).

14. K. Smith and K. Rempe, Mixed-Oxide and BWR Pin Power Reconstruction in SIMULATE-3, PHYSOR 90, Vol. 2, p. VIII-11, Marseille, France, (1990).

15. K. Rempe, et al., SIMULATE-3 Pin Power Reconstruction: Methodology and Benchmarking, Proc. International Reactor Physics Conference, Vol.

III, p. 19, Jackson, WY, (1988).

16. K. Smith, MOX Analysis Methods in SIMULATE-3, Trans. Am. Nucl.

Soc., Vol. 76, p 181, Orlando FL, (1997).

17. K. Smith and P. Esser, Nodal Transport Model for SIMULATE, Proc.

Spring Mtg., Kyoto, Japan, A49, Atomic Energy Society of Japan, (1993).

18. K. Smith, Practical and Efficient Iterative Method for LWR Fuel Assembly Homogenization, Trans. Am. Nucl. Soc., Vol. 71, p 238, Washington, DC, (1994).

19. K. Smith, Topical Report on Studsviks Core Management System (CMS),

SSP-09/477-C, Rev 0, Studsvik Scandpower, Inc. (2010).

20. J. L. Eller, Letter,

Reference:

Fuel, Core, and Operational Data to Support Core Physics Benchmark Analyses, DPC-1553.05.00.0222, Rev 0, March (2011).

21. Mathworks, MATLAB 7 Data Analysis, Version 7.11.0 (R2010b), The Mathworks, Inc. (2010).

22. G.A. Gunow, LWR Fuel Reactivity Depletion Verification Using 2D Full Core MOC and Flux Map Data, M.S. Thesis, MIT, https://dspace.mit.edu/handle/1721.1/97963, (2014).

23. E. Sykora, Testing the EPRI Reactivity Depletion Decrement Uncertainty Methods, M.S. Thesis, MIT, https://dspace.mit.edu/handle/1721.1/103653, (2015).

24. PWR Fuel Reactivity Depletion Uncertainty Quantification - Methods Validation Using BEAVRS Flux Map Data. EPRI, Palo Alto, CA: 2015.

3002006432.

25. N. Horelik, B. Herman, B. Forget, and K. Smith. Benchmark for Evaluation and Validation of Reactor Simulations (BEAVRS), v1.0.1, Proc.

Int. Conf. Mathematics and Computational Methods Applied to Nuc. Sci.

& Eng., Sun Valley, Idaho, (May 2013).

26. Benchmark for Evaluation and Validation of Reactor Simulations, Rev.

1.1.1, MIT Computational Reactor Physics Group (October 31, 2013).

Available at the MIT website: http://crpg.mit.edu/research/beavrs

27. R. D. Harrison, et al., Validation of WIMS/PANTHER PWR Fuel Reactivity Depletion Using the BEAVRS Benchmark Flux Map Data, PHYSOR 2016, Sun Valley, ID, May 1-5, (2016).

11-2

28. R. D. Harrison, et al., PANTHER Benchmarking of Nuclear Reactor Burnup Data, Undergraduate Thesis, University of Cambridge, Cambridge, UK, (2015).

29. M. L. Williams, B. T. Rearden, SCALE-6 Sensitivity/Uncertainty Methods and Covariance Data, Nuclear Data Sheets. 109. 2796-2800.

10.1016/j.nds.2008.11.012.

30. M. Williams, Sensitivity and Uncertainty Analysis for Eigenvalue-Difference Response, Nucl. Sci. Eng. 155, pp. 27 (2007).

31. R. MacFarlane, D. W. Muir, NJOY99 -Code System for Producing Pointwise and Multigroup Neutron and Photon Cross Sections from ENDF/B Data, Los Alamos National Laboratory, RSICC PSR-480, (2000).

32. TVA Watts Bar FSAR, Amendment 98, Available from:

pbadupws.nrc.gov/docs/ML1013/ML101370696.pdf

33. J. C. Wagner and C. V. Parks, Parametric Study of the Effect of Burnable Poison Rods for PWR Burnup Credit, NUREG/CR-6761 (ORNL/TM-2000/373), U.S. Nuclear Regulatory Commission, Oak Ridge National Laboratory, 2002.

34. R. Ellis, System Definition Document: Reactor Data Necessary for Modeling Plutonium Disposition in Catawba Nuclear Station Units 1 and 2, ORNL/TM-1999/255, Oak Ridge National Laboratory, 2000.

35. C. 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, 2002.

36. B. D. Murphy, Characteristics of Spent Fuel from Plutonium Disposition Reactors. Vol. 3: A Westinghouse Pressurized-Water Reactor Design, ORNL/TM-13170/V3, Oak Ridge National Laboratory, 1997.

37. Dissolution, Reactor, and Environmental Behavior of ZrO2-MgO Inert Fuel Matrix Neutronic Evaluation of MgO-ZrO2 Inert Fuels, Department of Nuclear Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel, February 2005. Available from:

http://aaa.nevada.edu/paper/trp19_03.pdf) 11-3

Studsvik CMS Analysis Codes The Studsvik Core Management System (CMS) is routinely used to perform the neutronic and thermal-hydraulic analysis needed for design, optimization, and safety analysis of nuclear reactor cores. While the CMS suite of codes is capable of performing steady-state and transient (dynamic) analysis of reactor cores, the methods described in this document are restricted to the CMS codes needed to perform steady-state and pseudo steady-state core analysis.

A.1 Code System Overview The CMS code system consists of five separate codes, which are used as a package to perform reactor core analysis. The five codes are:

INTERPIN-4 [7] for analyzing the 1-D fuel temperatures for an individual fuel pin, as a function of:

- Fuel pin design (e.g., enrichment, gas pressurization, etc.)

- Linear heat loading

- Fuel burnup CASMO-4 [8] or CASMO-5 [2] for analyzing the 2-D neutronic behavior of an individual fuel assembly, as a function of:

- Lattice design (e.g., pin enrichment layout, burnable absorber design, etc.)

- Local conditions (e.g., fuel temperature, coolant density, boron content, etc.)

- Fuel burnup

- Control rod insertion CMSLINK [9] for generating a library of tabularized CASMO-4 or CASMO-5 data for a collection of fuel assemblies and reflector types, as a function of:

- Fuel burnup

- Thermal hydraulic conditions

- Control rod insertion

- Fuel history effects SIMULATE-3 [3] for analyzing the detailed 3-D reactor core neutronic and thermal-hydraulic behavior over the reactor core lifetime, as a function of:

- Reactor power A-1

- Coolant flow rate and inlet temperature

- Fuel burnup

- Control bank insertion INTERPIN-4 and CMSLINK are often considered as auxiliary codes in the CMS suite, and they are described in this document only to the extent required to understand their interaction with CASMO-5 and SIMULATE-3. On the other hand, CASMO-5 and SIMULATE-3 are very large (many hundreds of thousands of lines of FORTRAN) codes that perform the bulk of the physics modeling in CMS.

This section details some of the more important physics models and methods that are important for understanding how CASMO-5 and SIMULATE-3 are used for this project.

A.2 INTERPIN-4 CASMO-5 and SIMULATE-3 need fuel temperature data as part of their respective physical models. CASMO-5 requires best-estimate average fuel pin temperature for each lattice type, and this temperature is typically assigned uniformly to all fuel pins in the lattice. Since the CASMO-5 case matrix includes lattice calculations (both branches and depletions) to off-nominal fuel temperatures, downstream SIMULATE-3 results are not very sensitive to the nominal CASMO-5 fuel temperatures. SIMULATE-3 results, however, are sensitive to the input fuel temperature tables - which provide the relationship between linear power density and the average fuel pin temperature. INTERPIN-4 is used to generate steady-state fuel temperature data that is provided to SIMULATE-3. INTERPIN-4 solves the 1-D radial heat conduction problem for an axial nodalized fuel pin, and temperatures are dependent on the physical models used to close the system of equations.

A.3 INTERPIN-4 Thermal Conductivities The cladding thermal conductivity in INTERPIN-4 is from MATPRO:

This oxide fuel conductivity model is taken from a recent NFI correlation that is plotted in Figure A-1 for UO2 fuel at 4 different burnups. It can be seen that the conductivity degradation from fresh to 60 GWd/T burnup is between 40 and 60 percent, and this degradation has a very significant effect on fuel temperatures as a function of burnup.

A-2

Figure A-1 UO2 Conductivity as a Function of Burnup and Temperature A.4 INTERPIN-4 Solid Pellet Swelling and Gap Conductance As fuel pellets are irradiated, solid pellet swelling occurs because of the production of embedded gaseous fission products. This pellet swelling is modeled in INTERPIN-4 as a simple function of fuel burnup, E, in GWd/T The fuel/clad gap conductance is modeled in INTERPIN-4 with two principal terms:

a gaseous conductance term and a solid contact conductance term. The benchmark parameters of the Kjaerheim-Roldstad gaseous gap conductance sub-model (that accounts for the effect of fuel pellet surface and clad inner surface roughness) and the minimum residual gap of the Ross Stoute solid contact conductance model have both been calibrated to match measured centerline temperatures from pin irradiations in the Halden Reactor Project.

A.5 INTERPIN-4 Fuel Temperature Edits for SIMULATE-3 When INTERPIN-4 is used to generate SIMULATE-3 fuel temperature data, several calculations are automatically performed at different power levels, and results (similar to those of Figure A-2) are used to derive functional fits of the difference between average fuel temperature and the bulk coolant temperature. These data tables are then used directly in SIMULATE-3, and the lifetime-averaged fuel temperature is used as input to CASMO-5.

A-3

Figure A-2 Typical INTERPIN-4 Fuel Temperature Change with Burnup A.6 CASMO-4 Lattice Physics Code CASMO-4 is a two-dimensional transport theory lattice physics code used to analyze PWR and BWR fuel assemblies. CASMO-4 computes multi-group, multi-dimensional neutron flux distributions by solving the neutron transport eigenvalue problem. The resulting neutron flux solutions are used to compute coupled nuclide depletion, gamma production, and gamma transport within a fuel assembly.

CASMO-4 can model fuel assemblies containing collections of cylindrical fuel rods, cylindrical burnable absorber rods, cluster control rods, and in-core instruments.

CASMO-4s two-dimensional heterogeneous geometrical capabilities permit modeling of both single-assembly and Cartesian collections of assemblies. CASMO-4 is used to generate assembly neutronic data for the SIMULATE-3 nodal reactor analysis code. A flow diagram of a typical CASMO-4 calculation is displayed in Figure A-3.

A.7 CASMO-4 Cross Section Library The CASMO-4 multi-group neutronic data library (N-Library) is the production neutronic data library used with CASMO-4, and it has been generated with the NJOY [31] data processing code that converts basic evaluated neutronic data (e.g.,

ENDF/B, JEF, etc.) from its continuous-energy form into multi-group neutronic data tablesas a function of material temperature and background cross sections. The CASMO-4 neutronic data library employs 70 neutron energy groups to cover the range from 0.0 to 10.0 MeV, consisting of 14 groups in the fast range (from 9.118 keV to 10.0 MeV), 13 groups in the resonance range (4.0 eV to 9.118 keV), and 43 groups in the thermal range (0.0 to 4.0 eV - with clustered groups around the 0.3 eV 235 Pu and 1.0 eV 240Pu resonances).

A-4

The N-Library contains absorption, fission, nu-fission, transport, and scattering cross sections for 108 nuclides and materials, including; 18 important heavy metal isotopes (234U to 246Cm), 30 explicit and 2 lumped fission products (1 saturating and 1 non-saturating), 5 common LWR moderators, numerous LWR structural materials, and many common LWR burnable absorber isotopes. In addition to cross-section data, the library contains fission neutron emission spectra, fission product yields, and delayed neutron yields for all fissionable isotopes and decay constants for all radioactive isotopes. The starting point for the N-library was data produced in 1985 with NJOY from the ENDF/B-IV evaluated nuclear data files. When additional isotopes were added to the initial library or when deficiencies with ENDF/B-IV data were discovered, more recently-evaluated data was used to generate additional/replacement data.

As a result, the N-library contains data from JEF-1 for:

Am-241 to Am-243 Cm-242 to Cm-246 Co-59, Ag-107, Ag-109, Cd-113, In-115 Natural Hf, Hf-176 to Hf-180 Pu-239 to Pu-242 from JEF-2.1 for:

Er-162 to Er-171 Tm-169 to Tm-171 Gd-154 to Gd-158 U-236 and from ENDF-B/VI, release 4 for:

Mg, Zr, Nb, Mo, Sn Eu-154 and Eu-155 A-5

Input Restart file Resonance calculation Data library Macroscopic cross sections Micro-group calculation Condense to macro-regions Macro-group calculation Condense to 2D groups 2-D characteristics transport calculation Fundamental mode calculation Few group constants Reaction rates Card image file Burnup corrector Zero Burnup Number densities Burnup predictor End Figure A-3 Computational Flow Diagram of CASMO-4 A-6

A.8 CASMO-4 Isotopic Depletion Model Once assembly flux distributions are known, reaction rates for each depletable nuclide are constructed so that the fuel depletion calculation can be performed. CASMO-4 makes the linearized chain approximation to decouple the depletion equations. The only approximation required in the linearized chain model is that backward transition rates (e.g., n2n, and alpha decay) in the middle of depletion chains be assumed constant over each time step.

When CASMO-4 detects the presence of gadolinia burnable absorbers in a lattice it automatically reduces burnup steps to 0.5 GWd/T until the gadolinia absorption is negligible, and then it reverts to large default depletion steps.

At each depletion step, CASMO-4 assumes that the power remains constant with depletion (rather than assuming that the flux remains constant). This is particularly important for accurate depletion, since the flux level and the average energy yield per fission change during a burnup step. The assumption necessitates a simple iterative calculation of the flux normalization so that the computed power at each depletion step remains constant.

A.9 CASMO-5 Lattice Physics Code CASMO-5 is a significantly upgraded version from CASMO-4. The principal differences from CASMO-4 are:

The N nuclear data library was replace with an ENDF/B-VII library The number of isotopes and materials in the library was increased from 108 to

~400 The use of lumped fission products was eliminated The library group structure was changed from 70 to 586 energy groups Resonance models were upgraded to improve the two-term rational approximation The number of energy groups in the 2D transport (MOC) was increased from 8 to 19 The ray spacing in the transport solver was reduced to 0.05 cm in all energy groups The polar angle quadrature was changed from Gauss-Legendre to the optimal T-Y quadrature The nuclide burnup model was changed from linearized chains to a partial matrix exponential A.10 CASMO-5 Baffle/Reflector Models PWR baffle and reflector data needed for SIMULATE-3 are generated directly with CASMO-5. CASMO-5 builds a 2-D transport model in which homogenous baffle and homogeneous reflector regions are appended to the side of the fuel assembly, as A-7

depicted in Figure A-4. This 2-D transport problem is solved with reflecting boundary conditions on three sides and a vacuum boundary condition on the outer reflector surface. CASMO-5 provides direct edits of the baffle/reflector cross sections and homogenization data that are used by SIMULATE-3 for its nodal model of PWR cores. Similar models are also built for the top and bottom reflectors based on the users specifications of the 1-D material representations above and below the fueled portion of the core.

Figure A-4 CASMO-5 Baffle/Reflector Geometry A.11 CMSLINK - CASMO-to-SIMULATE Linking Code CMSLINK is a utility processing code used in CMS to gather and format all CASMO data needed in SIMULATE-3. CMSLINK reads the CASMO data files, evaluates the depletion and branch cases that are available, determines the most appropriate multi-dimensional table representation, and creates a binary data library that can be read by SIMULATE-3.

A.12 CMSLINK Multi-dimensional Data Tabulation CMSLINK creates 1-D, 2-D and 3-D data tables for each of the assembly-averaged CASMO neutronic data, as a function of burnup (EXP), moderator temperature history (HTMO), boron history (HBOR), fuel temperature history (HTFU),

moderator temperature (density, TMO), shut down cooling (SDC), boron concentration (BOR), control rod presence (CRD), and fuel temperature (TFU). For PWR lattices, the data tables and their secondary and tertiary dependencies consist are:

Base 2-D table vs. (EXP, HTMO)

Delta HBOR, 2-D table vs. (EXP, HBOR)

Delta HTFU, 2-D table vs. (EXP, HTFU)

Delta TMO, 2-D table vs. (EXP, TMO)

Delta SDC, 2-D table vs. (EXP, SDC)

A-8

Delta BOR, 3-D table vs. (EXP, BOR, TMO)

Delta CRD, 3-D table vs. (EXP, CRD, TMO)

Delta TFU, 3-D table vs. (EXP, TFU, TMO)

Since pin power reconstruction and detector fission rate data are very large (e.g., pin power form functions), a simplified data representation is used for this data. For PWR lattices, the data tables consist of:

Base 1-D table vs. (EXP)

Delta TMO, 1-D table vs. (EXP)

Delta CRD, 2-D table vs. (EXP, CRD)

Delta HBOR, 1-D table vs. (EXP)

Delta SDC, 1-D table vs. (EXP)

Delta BOR, 1-D table vs. (EXP)

Delta TFU, 1-D table vs. (EXP)

CMSLINK creates a binary library containing data, for each CASMO lattice type, including the complete description of independent variables, table structure, and table values for every data table. In addition, QA file trail data (code version numbers, neutron library version numbers, executable creation dates, executing computers and run dates) are added to the library to provide a traceable data trail into SIMULATE-3.

A.13 SIMULATE-3 Nodal Code Overview SIMULATE-3 is the three-dimensional advanced nodal diffusion code used in the CMS system for analyzing the pseudo steady-state behavior of PWR and BWR cores.

SIMULATE-3 is a coupled nodal neutronics/thermal-hydraulic code capable of performing fuel depletion needed to model the reactor core throughout its lifetime.

The flow of a typical SIMULATE-3 computational sequence is depicted in the Figure A-5. It can be seen from this figure that for each depletion step, SIMULATE-3 performs a nested iteration to synchronize thermal-hydraulic conditions, nuclear data, neutronics power distributions, and fuel assembly depletion. When all nonlinear fields are converged, SIMULATE-3 then performs pin power reconstruction to recover individual pin power distributions and detector fission rates. The details of each of the major modules in SIMULATE-3 are described in the following sections of this report.

A-9

Specify Reactor Conditions Thermal Hydraulics Evaluation Nuclear Data Evaluation Nodal Power Computation Fuel Depletion Pin Power Reconstruction Detector Reaction Rate Calculation Figure A-5 SIMULATE-3 Flowchart A.14 SIMULATE-3 PWR Thermal Hydraulics Model The SIMULATE-3 PWR thermal hydraulics uses one characteristic hydraulic channel per fuel assembly (or four when using 4 node per assembly neutronics model) with the assumption of no radial cross-flow between assemblies. The axial nodalization of the thermal hydraulics is identical to that used in the neutronics, with 24 or more nodes in typical applications. Since SIMULATE-3 is a steady-state (not dynamic) code, these assumptions result in a thermal-hydraulic model that is basically a heat balance - with the following additional assumptions:

Assembly inlet flows are uniform (or distributed with a user-specified distribution).

Assembly inlet temperatures are uniform (or distributed with a user-specified distribution).

All fluid properties are evaluated at the primary system pressure (default is 2250 psi).

Direct energy deposition in coolant (neutron slowing down, gamma deposition, etc.) is a fixed fraction of the total power generated in a node (default is 2.5%).

Given these assumptions, the coolant enthalpy is computed by marching up each channel and adding the energy produced in each node to the enthalpy, and the coolant A-10

density is evaluated from the enthalpy using water properties from the ASME steam tables.

In SIMULATE-3, the node-averaged fuel temperature for node n is computed from the node-averaged coolant temperature, a tabulated function of linear power density of each node, Pn, and a constant quadratic term having the form:

TFU n = TMOn + TFU m ( EXP, P ) Pn + TFU mq Pn2 The linear tables are constructed for each fuel type, m, and are constructed as a function of nodal fuel burnup and power density, while the quadratic term is constant for each fuel type. The linear term is a user-input table for SIMULATE-3, and within the CMS suite of codes, INTERPIN-4 is used to generate the fuel temperature data tables.

The neutronic feedback in SIMULATE-3 is based on node-averaged conditions (the rod-by-rod variation in temperatures is ignored), and consequently node-averaged coolant density and fuel temperature are the only thermal-hydraulic parameters needed for steady-state SIMULATE-3 PWR calculations.

A.15 SIMULATE-3 Nuclear Data Interpolation Once thermal-hydraulic conditions are known (at each neutronic/hydraulic iteration),

nuclear data is evaluated for each node of the core model. Values for all instantaneous library parameters (BOR, DEN, TFU, SDC, and CRD) and each historical parameter (EXP, HTMO, HBOR, and HTFU) are constructed for each node. Linear interpolations in the 2-D and 3-D CMSLINK data tables are then performed to evaluate the required node-by-node parameters.

These data provide the non-linear link between the thermal hydraulics, fuel depletion, and neutronics models of SIMULATE, and multiple iterations are required to obtain a converged solution of core conditions.

A.16 SIMULATE-3 Two-group Nodal Diffusion Model Once the thermal-hydraulic conditions and cross sections are known for each node of the core model, a three-dimensional diffusion model for the core can be constructed, using standard notation, as 2 g Dg (r ) g (r ) + t , g (r=

) g ( r ) k g '=1 f , g ' (r ) + gg ' (r ) g ' (r )

eff .

A-11

Integrating this equation over the volume of each node in the core model, one obtains the nodal neutron balance equation 6 J gm, s m m 2 g m hs

+= t , g g f , g ' + mgg ' mg '

=s 1 = keff g' 1 ,

where J gm,s average net neutron current on surface, s, of node m 1

Vm mg g (r )dV is the average scalar neutron flux in node m and Vm volume of node m .

The nodal balance equation simply expresses the fact that the net neutron production in node m equals the rate at which neutrons leak out of the six surfaces of node m.

The nodal balance equation cannot be solved without additional relationships that relate the surface-averaged net currents to the node-averaged scalar fluxes.

SIMULATE-3 uses the well known transverse-integration method to derive these required coupling relationships. For instance, by integrating the nodal diffusion equation over the y and z directions, one obtains a 1-D coupling expression as a function of x d2 m 2 g D gm ( x) 2 dx m =

g ( x) + t , g ( x) m ( x) g k mf , g ' ( x) + mgg ' ( x) m ( x) + Lm, x ( x) g' g g '=1 eff where the transverse leakage for direction x in node m has been defined as 1 d2 d2 Dg ( x) dy 2 + dz 2 g (r ) dy dz m, x L ( x) g m

hy hz This transverse leakage expression is a rigorous expression for the x-dependence of the flux in node m. If one makes the assumption that the diffusion coefficient is independent of position within node m, an expression that relates the shape of the x-directed net current in node m to the transverse-integrated scalar flux can be written as d m J gm, x ( x) = D gm g ( x) dx A-12

The principal assumption in the transverse-integrated nodal methods is that the x-shape of the transverse leakage in node m can be represented accurately by a quadratic fit (preserving the node-averaged net leakages) to the average transverse leakage in three neighboring nodes m-1, m, and m+1. This approach permits one to construct 1-D coupling equations for each of the x, y, and z directions, and the transverse leakage terms depend only on the face-averaged net currents - which become known as the nodal balance equations are iteratively solved.

In order to fully close this system of equations, one must specify how the transverse-integrated fluxes are to be represented. SIMULATE-3 has two different approximations for the transverse-integrated flux shapes for direction u within each node:

2 m (u ) = m + 1,mu + 2,m (3u 2 1 ) + 3,m (u 3 u ) + 4,m (u 4 3u + 1 )

g g g g g g 4 4 10 80 or 1 u 3u 2 1 g (u ) = g + g u + g (3u ) + g (u ) + g (u m m 1, m 2, m 2 3, m 3 4, m 4

+ )

4 4 10 80 2

+ gc ,m cosh( g u ) sinh( g u ) + gs ,m sinh( g u )

g where g= mg / D gm For analysis of UO2 cores, SIMULATE-3 uses the polynomial expansion to represent the scalar flux shapes for both the fast and thermal groups. When cores containing MOX fuel assemblies are detected in SIMULATE-3, the thermal flux expansions are automatically changed to use the transcendental functions so that more accurate flux shapes are obtained at the interfaces between UO2 and MOX assemblies.

A.17 SIMULATE-3 Macroscopic Depletion Model SIMULATE-3 performs fuel depletion throughout the life of the reactor core.

Explicit nuclide concentrations for 135I, 135Xe, 149Pm and 149Sm are tracked directly in SIMULATE-3 by solving the nuclide depletion chains and using CASMO-5 generated data for: 1) fission yields, 2) capture cross sections, and 3) decay constants.

All other isotopes are treated indirectly in SIMULATE-3 with a macroscopic depletion model. In SIMULATE-3s macroscopic depletion model, CASMO-5 data has been tabulated as a function of fuel burnup (EXP). Consequently, SIMULATE-3 needs only compute the fuel burnup - all other isotopic depletion effects are treated indirectly by interpolating in the CMSLINK data tables to the appropriate burnup point.

A-13

Actual fuel isotopic concentrations depend on the local conditions that the fuel assembly experiences during its lifetime. In order to approximate these history effects, SIMULATE-3 treats water density, fuel temperature, and boron concentration as history variables. For instance, nodes at the top of the core have been depleted with less coolant density that those nodes at the bottom of the core. The resulting harder spectrum leads to production of more plutonium (per GWd/T) at the top of the core.

SIMULATE-3 models this dependence on water density history by interpolating in the CMSLINK data tables with the historical density of coolant and interpolates in the CMSLINK history data tables. Each node in the core experiences a time-varying fuel temperature, coolant density, and boron, and consequently, historical variables must be integrated in time to yield appropriate history values. In SIMULATE-3 a weighted history model is used to accumulate the history variables. As an example, m m m when the burnup, in node m, advances from E to E + E the boron history in node m is accumulated as HBOR m ( E m ) + w BOR m ( E m )E m HBOR ( E + E )

m m m E m + w E m This weighted history formulation is motivated by the fact that when conditions change significantly, the most recent history tends to burn in more quickly than would be modeled by unity history weighting. The weighting parameter, w , is computed for each fuel type and history variable from the build-up rates in the CMSLINK library data. Typically the history weighting parameter is in the range of 2.0 to 2.5. This history treatment allows SIMULATE-3 to model depletion effect more accurately than if only fuel burnup was used.

SIMULATE-3 also treats the burnup shape within each core node. Homogenized cross-section terms are represented as functions of position in the radial direction. If the spatial shape of the cross section is known, it directly impacts the algebraic relationship for the nodal coupling parameters. The intra-nodal spatial shape of burnup in SIMULATE-3 is modeled by tracking the node surface-averaged burnups as well as the node-averaged burnup. A quadratic polynomial shape for the burnup is constructed for each direction using the two surface-averaged burnups for that direction and the node-averaged burnup. The quadratic burnup shape is then transformed into a quadratic cross-section shape and these shapes are used when solving for nodal coupling parameters. Treatment of the spatial variation of burnup within each node improves the accuracy of computed reactor core flux and power distributions.

A.18 SIMULATE-3 Detector Fission Rate Computation The SIMULATE-3 nodal method provides transverse-integrated flux shapes in each of the three directions. The nodal flux at each radial corner points of the assembly are evaluated by constructing a 2-D distribution from the x- and y-directed transverse-integrated fluxes and evaluating these distributions at each of the 4 corners as:

A-14

m ( x) m ( y) cp = g g g m g

cp Since each of the four nodes that meet at a corner can be used to approximate the corner point flux, one can combine the four homogeneous flux estimates, together with the four CASMO-5 corner point form functions (analogous to the surface discontinuity factors) to obtain a single estimate for the corner point flux:

cp ,CASMO cp ,CASMO cp ,CASMO cp ,CASMO cp g

+ cp g

+ cp g cp

+ g g ,i , j CASMO g ,i +1, j CASMO g ,i , j +1 CASMO g ,i +1, j +1 CASMO g 1 g 2 g 3 g 4 cp g =

4 .

Detector reaction rates for movable in-core detectors are computed directly in SIMULATE-3 from the two-group fluxes at the detector location (the heterogeneous corner point fluxes). The reaction rates for isotope i and interaction type are computed using detector cross sections from the CMSLINK library and reconstructed fluxes as:

RRi = 1CP i 1 + CP 2 2 i

A-15

Reactivity Benchmark Specifications Eleven experimental benchmarks, based on simplifications of publically available data for the Westinghouse RFA and OFA assemblies, are described here. They cover a range of enrichments, burnable absorber ladings, boron concentrations, fuel and coolant temperatures, and decay times.

For each case in Table B-1, a complete geometrical and material description follows, and the experimental reactivity decrement tables are presented in Appendix C.

The sources for non-proprietary are listed below:

RFA-like lattice and pin dimensions, taken from Reference [32].

OFA-like lattice/pin dimensions, taken from Reference [33].

WABA pin dimensions, taken from Reference [33].

IFBA and WABA burnable absorber loading patterns, taken from Reference [34].

IFBA 10B boron loading, taken from Reference [35].

WABA boron loading, taken from Reference [36].

IFBA modeling thickness and inert materials density, taken from Reference [37].

Note that all lattices are depleted with a power density of 104.5 W/cc (38.1 W/gm heavy metal) - except for case 11 that is depleted at 156.75 W/cc (150%

of nominal power density). All temperatures are in K and nuclide number densities are expressed in atoms/cc. For lattices that do not explicitly include the Structural Material Description and the Coolant Description, the nominal lattice values are applicable.

B-1

Table B-1 Benchmark Lattice Cases 1 3.25% Enrichment 2 5.00% Enrichment 3 4.25% Enrichment 4 Small Fuel Pin Depletion 5 20 WABA Depletion 6 104 IFBA Depletion 7 104 IFBA and 20 WABA Depletion 8 High Boron Depletion = 1500 ppm 9 Nominal Case Branch to SFP Hot Isothermal Temperatures = 150°F 10 Nominal Case Branched to SFP High Boron Concentration = 1500 ppm 11 High Power Depletion (power, coolant/fuel temp)

B-2

B.1 Nominal Fuel Assembly Physical Description Number of pins along side 17 Pin pitch 1.2598 cm Inter-assembly spacing 21.5036 cm Fuel pellet OR 0.4096 cm Clad IR 0.4180 cm Clad OR 0.4750 cm Guide/instrument tube IR 0.5610 cm Guide/instrument tube OR 0.6120 cm Structural Material Description Material (Zr-4)Density 6.55 (g/cm3)

Temp., unheated 580K Temp., heated 0.12*Tfuel+0.88*Tcoolant Fuel Rod Nuclide Number Density Instrument Tube Zr-4 4.32444E+22 Guide Tube Coolant Description, Depletion (Nominal) Coolant Description, Cold Boron Concentration 900 ppm Boron Concentration 0 ppm Temperature 580 K Temperature 293 K Nuclide Number Density Nuclide Number Density H 4.75756E+22 H 6.67431E+22 O 2.37894E+22 O 3.33738E+22 B 3.56773E+19 B-3

B.2 CASE 1: 3.25% Enriched - No Burnable Absorbers Fuel Material Description Material Density 10.340 (g/cm3)

Fuel Temperature 900 K Nuclide Number Density U-235 7.59010E+20 U-234 6.09917E+18 U-238 2.23037E+22 O 4.61377E+22 Fuel Rod Instrument Tube Guide Tube B-4

B.3 CASE 2: 5.00% Enriched - No Burnable Absorbers Fuel Material Description Material Density 10.340 (g/cm3)

Fuel Temperature 900 K Nuclide Number Density U-235 1.16768E+21 U-234 9.38308E+18 U-238 2.18964E+22 O 4.61469E+22 Fuel Rod Instrument Tube Guide Tube B-5

B.4 CASE 3: 4.25% Enriched - No Burnable Absorbers Fuel Material Description Material Density 10.340 (g/cm3)

Fuel Temperature 900 K Nuclide Number Density U-235 9.92536E+20 U-234 7.97571E+18 U-238 2.20709E+22 O 4.61429E+22 Fuel Rod Instrument Tube Guide Tube B-6

B.5 CASE 4: Small Fuel Pin Physical Description Number of pins along side 17 Pin pitch 1.2598 cm Inter-assembly spacing 21.5036 cm Fuel pellet OR 0.3922 cm Clad IR 0.4000 cm Clad OR 0.4572 cm Guide/instrument tube IR 0.5610 cm Guide/instrument tube OR 0.6120 cm Structural Material Description Material (Zr-4)Density 6.55 (g/cm3)

Temp., unheated 580K Temp., heated 0.12*Tfuel+0.88*Tcoolant Fuel Rod Nuclide Number Density Instrument Tube Zr-4 4.32444E+22 Guide Tube Fuel Material Description Material Density 10.340 (g/cm3)

Fuel Temperature 900 K Nuclide Number Density U-235 9.92536E+20 U-234 7.97571E+18 U-238 2.20709E+22 O 4.61429E+22 B-7

B.6 CASE 5: 20 Lumped Burnable Poison (WABA) Pins Fuel Material Description Material Density 10.340 (g/cm3)

Fuel Temperature 900 K Nuclide Number Density U-235 9.92536E+20 U-234 7.97571E+18 U-238 2.20709E+22 O 4.61429E+22 Lumped Burnable Poison (WABA)

Annular clad IR 0.2860 cm Annular clad OR 0.3390 cm Active region IR 0.3530 cm Active region OR 0.4040 cm Fuel Rod Inner clad IR 0.4180 cm Inner clad OR 0.4840 cm Instrument Tube Outer clad IR 0.5610 cm Guide Tube Outer clad OR 0.6120 cm Active Region LBP Material Density 3.65 (g/cm3)

Boron Loading 6.03 mg/cm B-10 Nuclide Number Density C 1.40923E+21 O 6.23784E+22 Al 4.15904E+22 B-10 2.99030E+21 B4C-Al2O3 Zr-4 Coolant Air B-8

B.7 CASE 6: 104 Integral Fuel Burnable Absorbers (IFBA) Pins Fuel Material Description Material Density 10.340 (g/cm3)

Fuel Temperature 900 K IFBA Description Material Density 6.100 (g/cm3)

Coating Density 0.925 mg/cm B-10 Coating Thickness 0.01 mm Nuclide Number Density U-235 9.92536E+20 U-234 7.97571E+18 U-238 2.20709E+22 O 4.61429E+22 Zr-4 3.22187E+22 B-10 2.15913E+22 Fuel Rod Instrument Tube Guide Tube IFBA Rod B-9

B.8 CASE 7: 104 IFBA and 20 WABA Pins Fuel Material Description Material Density 10.340 (g/cm3)

Fuel Temperature 900 K IFBA Description Material Density 6.100 (g/cm3)

Coating Density 0.925 mg/cm B-10 Coating Thickness 0.01 mm Nuclide Number Density U-235 9.92536E+20 U-234 7.97571E+18 U-238 2.20709E+22 O 4.61429E+22 Zr-4 3.22187E+22 B-10 2.15913E+22 Fuel Rod Lumped Burnable Poison (WABA)

Instrument Tube Material Density 3.65 (g/cm3)

Guide Tube Boron Loading 6.03 mg/cm B-10 IFBA Rod Nuclide Number Density C 1.40923E+21 LBP O 6.23784E+22 Al 4.15904E+22 B-10 2.99030E+21 B-10

B.9 CASE 8: High Boron Depletion Fuel Material Description Material Density 10.340 (g/cm3)

Fuel Temperature 900 K Nuclide Number Density U-235 9.92536E+20 U-234 7.97571E+18 U-238 2.20709E+22 O 4.61429E+22 Fuel Rod Instrument Tube Guide Tube Coolant Description, Depletion Boron Concentration 1500 ppm Temperature 580 K Nuclide Number Density H 4.75756E+22 O 2.37894E+22 B 5.94621E+19 B-11

B.10 CASE 9: Nominal Case Branched to SFP Hot Isothermal Temperatures = 150F Fuel Material Description Material Density 10.340 (g/cm3)

Fuel Temperature 900 K Nuclide Number Density U-235 9.92536E+20 U-234 7.97571E+18 U-238 2.20709E+22 O 4.61429E+22 Fuel Rod Instrument Tube Guide Tube Coolant Description, Cold Boron Concentration 0 ppm Temperature 338.7 K Nuclide Number Density H 6.55262E+22 O 3.27653E+22 B-12

B.11 CASE 10: Nominal Case Branched to SFP High Rack Boron Concentration = 1500 ppm Fuel Material Description Material Density 10.340 (g/cm3)

Fuel Temperature 900 K Nuclide Number Density U-235 9.92536E+20 U-234 7.97571E+18 U-238 2.20709E+22 O 4.61429E+22 Fuel Rod Instrument Tube Guide Tube Coolant Description, Cold Boron Concentration 1500 ppm Temperature 293 K Nuclide Number Density H 6.67431E+22 O 3.33738E+22 B 8.34184E+19 B-13

B.12 CASE 11: High Power (150% of Nominal) Depletion Fuel Material Description Material Density 10.340 (g/cm3)

Fuel Temperature 1072.5 K Nuclide Number Density U-235 9.92536E+20 U-234 7.97571E+18 U-238 2.20709E+22 O 4.61429E+22 Fuel Rod Instrument Tube Guide Tube Coolant Description, Depletion Boron Concentration 900 ppm Temperature 592.5 K Nuclide Number Density H 4.55525E+22 O 2.27778E+22 B 3.41601E+19 B-14

Reactivity Benchmark Specifications Tables of experimental reactivity decrements for the 11 cases of Appendix B are presented in the following set of tables. The four sets represent cooling intervals of 0 hours0 days <br />0 hours <br />0 weeks <br />0 months <br />, 100 hours0.00116 days <br />0.0278 hours <br />1.653439e-4 weeks <br />3.805e-5 months <br />, 5 years, and 15 years.

The definition of cold reactivity decrement as a function of lattice burnup, B, is defined as: kinf(B) - kref , where kref is taken as kinf(B=0) for lattices without burnable absorbers. Thus, kinf(B) for cases 5, 6, and 7 is computed with burnable absorbers still in the lattice, while kref is taken from case 3 without burnable absorbers. This definition is used so that high-burnup reactivity decrement does not depend directly on the initial burnable absorber loading. This definition is consistent with reactor data used to generate the measured decrement biases -

which include burnable absorbers. Since kref does not include burnable absorbers, the reported reactivity decrements include the combined reactivity change of both fuel and burnable absorbers. At high burnup, the reactivity of the burnable absorber approaches zero, and the reactivity decrement is dominated by the change in reactivity of the fuel.

The assigned uncertainties are independent of benchmark case (except for the high fuel temperature case), and uncertainties are displayed for each of the eleven Benchmark Cases in Table C-1.

The data used in this report are taken directly from a proprietary Studsvik report bearing the same title (report number, SSP-11/409-C Rev. 0) for which all work has been performed under the approved Studsvik QA Programs. If subsequent applications of data contained in this report require quality assurance, the proprietary QA version of this report can be obtained directly from Studsvik Scandpower, Inc.

C-1

Table C-1 Reactivity Decrement 95/95 Tolerance Limits (in k)

Sub-batch Burnup (GWd/T)

Case 10 20 30 40 50 60 1 0.00348 0.00537 0.00654 0.00752 0.00831 0.00888 2 0.00348 0.00537 0.00654 0.00752 0.00831 0.00888 3 0.00348 0.00537 0.00654 0.00752 0.00831 0.00888 4 0.00348 0.00537 0.00654 0.00752 0.00831 0.00888 5 0.00348 0.00537 0.00654 0.00752 0.00831 0.00888 6 0.00348 0.00537 0.00654 0.00752 0.00831 0.00888 7 0.00348 0.00537 0.00654 0.00752 0.00831 0.00888 8 0.00348 0.00537 0.00654 0.00752 0.00831 0.00888 9 0.00348 0.00537 0.00654 0.00752 0.00831 0.00888 10 0.00348 0.00537 0.00654 0.00752 0.00831 0.00888 11 0.00385 0.00563 0.00670 0.00766 0.00851 0.00917 Note that the WABA burnable absorbers are not removed in these calculations.

C.1 Burnup Reactivity Decrements: Cold, No Cooling Table C-2 Measured Reactivity Decrement - No Cooling (in k)

Sub-batch Burnup (GWd/T)

Case 10 20 30 40 50 60 1 -0.1774 -0.2749 -0.3586 -0.4306 -0.4889 -0.5330 2 -0.1601 -0.2452 -0.3215 -0.3935 -0.4613 -0.5230 3 -0.1678 -0.2584 -0.3390 -0.4134 -0.4804 -0.5377 4 -0.1672 -0.2610 -0.3477 -0.4304 -0.5066 -0.5720 5 -0.2457 -0.2752 -0.3397 -0.4095 -0.4735 -0.5285 6 -0.2160 -0.2638 -0.3368 -0.4104 -0.4778 -0.5358 7 -0.2906 -0.2829 -0.3380 -0.4065 -0.4707 -0.5263 8 -0.1679 -0.2564 -0.3340 -0.4048 -0.4681 -0.5221 9 -0.1693 -0.2597 -0.3395 -0.4129 -0.4788 -0.5350 10 -0.1284 -0.2077 -0.2800 -0.3470 -0.4069 -0.4573 11 -0.1745 -0.2626 -0.3389 -0.4082 -0.4698 -0.5224 C-2

C.2 Burnup Reactivity Decrements: Cold, 100-hour Cooling Table C-3 Measured Reactivity Decrement - 100-Hour Cooling (in k)

Sub-batch Burnup (GWd/T)

Case 10 20 30 40 50 60 1 -0.1324 -0.2334 -0.3208 -0.3960 -0.4570 -0.5032 2 -0.1141 -0.2016 -0.2803 -0.3549 -0.4254 -0.4897 3 -0.1218 -0.2152 -0.2987 -0.3762 -0.4461 -0.5059 4 -0.1202 -0.2171 -0.3072 -0.3935 -0.4731 -0.5415 5 -0.2040 -0.2330 -0.2995 -0.3721 -0.4388 -0.4962 6 -0.1731 -0.2210 -0.2965 -0.3730 -0.4434 -0.5039 7 -0.2519 -0.2413 -0.2978 -0.3690 -0.4359 -0.4940 8 -0.1211 -0.2124 -0.2929 -0.3666 -0.4326 -0.4890 9 -0.1232 -0.2166 -0.2995 -0.3760 -0.4448 -0.5035 10 -0.0962 -0.1779 -0.2527 -0.3221 -0.3842 -0.4365 11 -0.1230 -0.2144 -0.2942 -0.3668 -0.4315 -0.4868 C.3 Burnup Reactivity Decrements: Cold, 5-Year Cooling Table C-4 Measured Reactivity Decrement Year Cooling (in k)

Sub-batch Burnup (GWd/T)

Case 10 20 30 40 50 60 1 -0.1365 -0.2466 -0.3444 -0.4288 -0.4967 -0.5475 2 -0.1158 -0.2081 -0.2940 -0.3765 -0.4545 -0.5252 3 -0.1242 -0.2240 -0.3161 -0.4022 -0.4797 -0.5455 4 -0.1227 -0.2258 -0.3247 -0.4201 -0.5079 -0.5827 5 -0.2064 -0.2419 -0.3168 -0.3978 -0.4719 -0.5351 6 -0.1755 -0.2299 -0.3137 -0.3988 -0.4767 -0.5433 7 -0.2542 -0.2502 -0.3151 -0.3945 -0.4688 -0.5326 8 -0.1236 -0.2213 -0.3103 -0.3926 -0.4661 -0.5284 9 -0.1256 -0.2252 -0.3165 -0.4013 -0.4775 -0.5420 10 -0.0981 -0.1853 -0.2672 -0.3434 -0.4112 -0.4677 11 -0.1263 -0.2240 -0.3122 -0.3932 -0.4652 -0.5262 C-3

C.4 Burnup Reactivity Decrements: Cold, 15-Year Cooling Table C-5 Measured Reactivity Decrement Year Cooling (in k)

Sub-batch Burnup (GWd/T)

Case 10 20 30 40 50 60 1 -0.1417 -0.2650 -0.3765 -0.4724 -0.5487 -0.6051 2 -0.1179 -0.2179 -0.3137 -0.4062 -0.4934 -0.5720 3 -0.1272 -0.2367 -0.3402 -0.4373 -0.5242 -0.5972 4 -0.1255 -0.2380 -0.3485 -0.4555 -0.5532 -0.6355 5 -0.2097 -0.2550 -0.3412 -0.4329 -0.5161 -0.5863 6 -0.1787 -0.2427 -0.3379 -0.4338 -0.5210 -0.5947 7 -0.2576 -0.2634 -0.3395 -0.4295 -0.5127 -0.5836 8 -0.1268 -0.2343 -0.3348 -0.4280 -0.5108 -0.5803 9 -0.1286 -0.2379 -0.3405 -0.4361 -0.5214 -0.5930 10 -0.1009 -0.1966 -0.2882 -0.3733 -0.4484 -0.5104 11 -0.1295 -0.2372 -0.3370 -0.4288 -0.5100 -0.5782 C-4

Export Control Restrictions The Electric Power Research Institute, Inc. (EPRI, www.epri.com)

Access to and use of EPRI Intellectual Property is granted with the spe- conducts research and development relating to the generation, delivery cific understanding and requirement that responsibility for ensuring full and use of electricity for the benefit of the public. An independent, compliance with all applicable U.S. and foreign export laws and regu- nonprofit organization, EPRI brings together its scientists and engineers lations is being undertaken by you and your company. This includes as well as experts from academia and industry to help address an obligation to ensure that any individual receiving access hereunder challenges in electricity, including reliability, efficiency, affordability, who is not a U.S. citizen or permanent U.S. resident is permitted access health, safety and the environment. EPRI members represent 90% of the under applicable U.S. and foreign export laws and regulations. In the electric utility revenue in the United States with international participation event you are uncertain whether you or your company may lawfully in 35 countries. EPRIs principal offices and laboratories are located in obtain access to this EPRI Intellectual Property, you acknowledge that it Palo Alto, Calif.; Charlotte, N.C.; Knoxville, Tenn.; and Lenox, Mass.

is your obligation to consult with your companys legal counsel to deter-Together...Shaping the Future of Electricity mine whether this access is lawful. Although EPRI may make available on a case-by-case basis an informal assessment of the applicable U.S.

export classification for specific EPRI Intellectual Property, you and your company acknowledge that this assessment is solely for informational purposes and not for reliance purposes. You and your company ac-knowledge that it is still the obligation of you and your company to make your own assessment of the applicable U.S. export classification and ensure compliance accordingly. You and your company understand and acknowledge your obligations to make a prompt report to EPRI and the appropriate authorities regarding any access to or use of EPRI Intellec-tual Property hereunder that may be in violation of applicable U.S. or foreign export laws or regulations.

Program:

Used Fuel and High-Level Waste Management

© 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.

3002010613 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