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Fully Automated 3-D Parallel Simulation and Optimization of a Full Scale Pressurized Water Reactor Fuel Assembly with Bu...

Permanent Link: http://ufdc.ufl.edu/UFE0022844/00001

Material Information

Title: Fully Automated 3-D Parallel Simulation and Optimization of a Full Scale Pressurized Water Reactor Fuel Assembly with Burnup Corrected Cross Sections
Physical Description: 1 online resource (150 p.)
Language: english
Creator: Plower, Thomas
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: burnup, depletion, deterministic, nuclear, transport
Nuclear and Radiological Engineering -- Dissertations, Academic -- UF
Genre: Nuclear Engineering Sciences thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Computational nuclear fuel burnup analysis is an essential field within the Nuclear Engineering discipline, since it plays important functions in core reactivity management, criticality safety, Special Nuclear Materials management, and fuel assembly reload design of commercial power and research reactors. Three dimensional (3-D) deterministic transport methods provides unique advantages in the fuel burnup analysis field and the intention of this thesis is to demonstrate the author's contributions to the development of a novel 3-D deterministic fuel burnup package called the PENTRAN /PENBURN (Parallel Environment Neutral particle Transport/Parallel Environment Burnup) suite. Specifically, cross section generation procedures will be presented including discussions on development of a coupled cross section interpolator code called INTERP-XS. Additionally, detailed fuel burnup analysis of a 17x17 PWR assembly will be presented. Finally, the development of an automated sequence driver called BURNDRIVER will be shown. Major conclusions include: excellent agreement between INTERP-XS generated cross sections and those generated by SCALE, demonstration of 3-D burnup effects captured by PENTRAN/PENBURN through PWR assembly analysis, and successful creation of a user-friendly burnup sequence driver.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Thomas Plower.
Thesis: Thesis (M.S.)--University of Florida, 2008.
Local: Adviser: Sjoden, Glenn E.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022844:00001

Permanent Link: http://ufdc.ufl.edu/UFE0022844/00001

Material Information

Title: Fully Automated 3-D Parallel Simulation and Optimization of a Full Scale Pressurized Water Reactor Fuel Assembly with Burnup Corrected Cross Sections
Physical Description: 1 online resource (150 p.)
Language: english
Creator: Plower, Thomas
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: burnup, depletion, deterministic, nuclear, transport
Nuclear and Radiological Engineering -- Dissertations, Academic -- UF
Genre: Nuclear Engineering Sciences thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Computational nuclear fuel burnup analysis is an essential field within the Nuclear Engineering discipline, since it plays important functions in core reactivity management, criticality safety, Special Nuclear Materials management, and fuel assembly reload design of commercial power and research reactors. Three dimensional (3-D) deterministic transport methods provides unique advantages in the fuel burnup analysis field and the intention of this thesis is to demonstrate the author's contributions to the development of a novel 3-D deterministic fuel burnup package called the PENTRAN /PENBURN (Parallel Environment Neutral particle Transport/Parallel Environment Burnup) suite. Specifically, cross section generation procedures will be presented including discussions on development of a coupled cross section interpolator code called INTERP-XS. Additionally, detailed fuel burnup analysis of a 17x17 PWR assembly will be presented. Finally, the development of an automated sequence driver called BURNDRIVER will be shown. Major conclusions include: excellent agreement between INTERP-XS generated cross sections and those generated by SCALE, demonstration of 3-D burnup effects captured by PENTRAN/PENBURN through PWR assembly analysis, and successful creation of a user-friendly burnup sequence driver.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Thomas Plower.
Thesis: Thesis (M.S.)--University of Florida, 2008.
Local: Adviser: Sjoden, Glenn E.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022844:00001


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1 FULLY AUTOMATED 3-D PARALLEL SIMULATI ON AND OPTIMIZATION OF A FULL SCALE PRESSURIZED WATER REACTOR FUEL ASSEMBLY WITH BURNUP CORRECTED CROSS SECTIONS By THOMAS JOSEPH PLOWER A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2008

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2 2008 Thomas Joseph Plower

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3 To Kathy and the rest of my family: my parents, Tom and Marcia; and my sister, Emily.

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4 ACKNOWLEDGMENTS First and forem ost, I would like to thank Dr. Glenn Sjoden for his advisement and support over the past year and a half. His dedication to students is unparalleled. I also would like to express gratitude to three of my fellow burnup team members: Tr avis Mock, Kevin Manalo, and Mireille Rowe. Each colleague has either sign ificantly contributed or supported me in the development of the PENTRAN/PENBURN burnup package. Additionally, many thanks go to Dr. Mark DeHart from Oak Ridge National Labor atory, who made significant modifications to the SCALE code driver. Finall y, Id like to thank Dr. Tanguy Courau and Dr. Jack Ohanian for their participation in my thesis committee.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ............................................................................................................... 4LIST OF TABLES ...........................................................................................................................8LIST OF FIGURES .......................................................................................................................13LIST OF ABBREVIATIONS ........................................................................................................ 16ABSTRACT ...................................................................................................................... .............17CHAPTER 1 INTRODUCTION TO NUCLEAR FU EL BURNUP DISCIPLINE ..................................... 181.1Introduction .................................................................................................................. 181.2Status of PENTRAN/PENBURN Code System (June 2007) ...................................... 191.3Burnup Package Contributions ....................................................................................202 OVERVIEW OF CURRENT BURNUP PACKAGES .......................................................... 222.1Transport Methods ....................................................................................................... 22 2.1.1Boltzmann Transport Equation .......................................................................... 22 2.1.2Diffusion theory .................................................................................................24 2.1.3Monte Carlo method .......................................................................................... 262.2Burnup Methodology ...................................................................................................26 2.2.1Forward-Euler Quasi-Static Burnup Approach .............................................. 27 2.2.2Predictor-Corrector Quasi Static Burnup Approach ......................................282.3Current Burnup Code Packages ...................................................................................29 2.3.1The SCALE5.1 Code System ............................................................................292.3.1.1The T-DEPL control sequence .................................................................. 292.3.1.2The T5-DEPL control sequence ................................................................292.3.1.3The T6-DEPL control sequence ................................................................30 2.3.2The MCNPX Code System ................................................................................30 2.3.3The CASMO-4 Code System............................................................................. 302.4The PENTRAN/PENBURN Burnup Package ............................................................. 31 2.4.1The PENTRAN Transport Solver ......................................................................31 2.4.2The PENPOW Reaction Rate Solver .................................................................32 2.4.3The PENBURN Bateman Solver .......................................................................32

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6 3 BURNUP DEPENDENT MULTIGROUP CROSS SECTION GENERATION .................. 353.1Cross Section Phenomena ............................................................................................ 35 3.1.1Resonance Self Shielding .................................................................................. 35 3.1.2Spatial Self Shielding .........................................................................................36 3.1.3Doppler Broadening ...........................................................................................373.2Cross Section Extraction Procedure using SCALE ..................................................... 37 3.2.1The SCALE Procedure ......................................................................................373.2.1.1Self-shielding modules .............................................................................. 393.2.1.2Transport solver ......................................................................................... 403.2.1.3Burnup modules ......................................................................................... 403.2.1.4Important T-DEPL settings and special executables ................................. 403.2.1.5Important T-NEWT settings ...................................................................... 423.2.1.6Shell module .............................................................................................. 433.2.1.7The ANISN Library Production Option (ALPO) ...................................... 433.2.1.8The SCALE Format code (SCALFORM) ................................................. 44 3.2.2Cross-Section Generation Us ing T-DEPL and T-NEWT .................................. 44 3.2.3The PWR cross section library development ..................................................... 453.3The PWR Library Optimization Study ........................................................................ 483.4The NJOY Procedure ................................................................................................... 523.5The INTERP-XS Code ................................................................................................54 3.5.1Code Development............................................................................................. 55 3.5.2Cross Section Library Linking ........................................................................... 57 3.5.3Comparison of INTERP-XS w ith SCALE/NJOY Procedure ............................ 584 THE 3-D PENTRAN/PENBURN BURNUP ANALYSIS OF 17X17 PWR ASSEMBLY ...................................................................................................................... .....854.1Assembly Specifications .............................................................................................. 854.2Unit Cell Analysis ........................................................................................................ 86 4.2.1Eigenvalue Study ............................................................................................... 86 4.2.2Burnup Study .....................................................................................................87 4.2.3Fuel Pin Homogenization ..................................................................................924.3Assembly Analysis....................................................................................................... 93 4.3.1Memory Optimization ........................................................................................ 94 4.3.2Assembly Convergence Analysis ...................................................................... 95 4.3.33-D Assembly Burnup Results...........................................................................98 4.3.4Comparing PENBURN and ORIGEN-ARP ....................................................101 4.3.5Methodology differences between PENBURN and ORIGEN-ARP ............... 101

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7 5 AUTOMATION OF PENT RAN/PENBURN BURNUP PROCEDURE ............................ 1205.1Overview of BURNDRIVER .................................................................................... 120 5.1.1Summary of Inputs ...........................................................................................1215.1.1.1Description of burnset.inp ....................................................................... 1225.1.1.2Running BURNDRIVER ........................................................................1255.2Xenon Irradiation Step Size Study .............................................................................1266 CONCLUSIONS AND FU TURE WORK ........................................................................... 1346.1Conclusions ................................................................................................................1346.2Future Work ...............................................................................................................135APPENDIX A T-DEPL INPUT ....................................................................................................................137B T-NEWT INPUT .................................................................................................................. 140C ALPO INPUT .......................................................................................................................142D XSLIST.TXT INPUT ...........................................................................................................143E BURNSET.INP INPUT ........................................................................................................145LIST OF REFERENCES .............................................................................................................146BIOGRAPHICAL SKETCH .......................................................................................................150

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8 LIST OF TABLES Table page 3-1 Summary of PWR operating paramete rs used for library generation ................................ 633-2 Summary of burnup data poi nts for each library study ...................................................... 633-3 LibID TempID and BrnupID for PWR cross section library ........................................... 643-4 Percent difference between U-235s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a branch calculation with Tfuel=950 K and Tmod=550 K ........................................................................................................................643-5 Percent differences between U-238s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a branch calculation with Tfuel=950 K and Tmod=550 K ........................................................................................................................643-6 Percent difference between Pu-239s total cr oss section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a branch calculation with Tfuel=950 K and Tmod=550 K ........................................................................................................................643-7 Percent difference between Pu-240s total cr oss section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a branch calculation with Tfuel=950 K and Tmod=550 K ........................................................................................................................653-8 Percent difference between Xe-135s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a branch calculation with Tfuel=950 K and Tmod=550 K ........................................................................................................................653-9 Percent difference between Sm -149s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a branch calculation with Tfuel=950 K and Tmod=550 K ........................................................................................................................653-10 Percent difference between H-1s total cross section ( t) generated by INTERP-XS and the SCALE/NJOY procedure for a branch calculation with Tfuel=950 K and Tmod=550 K ........................................................................................................................653-11 Percent difference between O-16s total cross section ( t) generated by INTERP-XS and the SCALE/NJOY procedure for a branch calculation with Tfuel=950 K and Tmod=550 K ........................................................................................................................653-12 Percent difference between U-235s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a branch calculation with Tfuel=1050 K and Tmod=600 K ........................................................................................................................66

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9 3-13 Percent difference between U-238s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a branch calculation with Tfuel=1050 K and Tmod=600 K ........................................................................................................................663-14 Percent difference between Pu-239s total cr oss section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a branch calculation with Tfuel=1050 K and Tmod=600 K ........................................................................................................................663-15 Percent difference between Pu-240s total cr oss section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a branch calculation with Tfuel=1050 K and Tmod=600 K ........................................................................................................................663-16 Percent difference between Xe-135s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a branch calculation with Tfuel=950 K and Tmod=600 K ........................................................................................................................663-17 Percent difference between Sm -149s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a branch calculation with Tfuel=1050 K and Tmod=600 K ........................................................................................................................673-18 Percent difference between H-1s total cross section ( t) generated by INTERP-XS and the SCALE/NJOY procedure for a branch calculation with Tfuel=1050 K and Tmod=600 K ........................................................................................................................673-19 Percent difference between O-16s total cross section ( t) generated by INTERP-XS and the SCALE/NJOY procedure for a branch calculation with Tfuel=1050 K and Tmod=600 K ........................................................................................................................673-20 Percent difference between U-235s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=950 K and Tmod=550 K .................................................................................................................673-21 Percent differences between U-238s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=950 K and Tmod=550 K .................................................................................................................683-22 Percent difference between Pu-239s total cr oss section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=950 K and Tmod=550 K .................................................................................................................683-23 Percent difference between Pu-240s total cr oss section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=950 K and Tmod=550 K .................................................................................................................683-24 Percent difference between Xe-135s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=950 K and Tmod=550 K .................................................................................................................68

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10 3-25 Percent difference between Sm -149s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=950 K and Tmod=550 K .................................................................................................................683-26 Percent difference between H-1s total cross section ( t) generated by INTERP-XS and the SCALE/NJOY procedure for a reference calculation with Tfuel=950 K and Tmod=550 K ........................................................................................................................693-27 Percent difference between O-16s total cross section ( t) generated by INTERP-XS and the SCALE/NJOY procedure for a reference calculation with Tfuel=950 K and Tmod=550 K ........................................................................................................................693-28 Percent difference between U-235s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=1050 K and Tmod=600 K .................................................................................................................693-29 Percent difference between U-238s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=1050 K and Tmod=600 K .................................................................................................................693-30 Percent difference between Pu-239s total cr oss section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=1050 K and Tmod=600 K .................................................................................................................693-31 Percent difference between Pu-240s total cr oss section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=1050 K and Tmod=600 K .................................................................................................................703-32 Percent difference between Xe-135s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=950 K and Tmod=600 K .................................................................................................................703-33 Percent difference between Sm -149s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=1050 K and Tmod=600 K .................................................................................................................703-34 Percent difference between H-1s total cross section ( t) generated by INTERP-XS and the SCALE/NJOY procedure for a reference calculation with Tfuel=1050 K and Tmod=600 K ........................................................................................................................703-35 Percent difference between O-16s total cross section ( t) generated by INTERP-XS and the SCALE/NJOY procedure for a reference calculation with Tfuel=1050 K and Tmod=600 K ........................................................................................................................704-1 Westinghouse 17x17 OFA specificationa ........................................................................1034-2 Fresh fuel concentrations for 3 wt% enriched UO2 fuel pellets .......................................103

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11 4-3 Heterogeneous unit cell keff results from NEWT and PENTRAN ...................................1034-4 Percent differences between average scal ar flux values in fuel, gap, clad, and moderator regions for NEWT and PENTRAN ................................................................ 1034-5 Comparison of PENBURN and SCALE burnup results for selected isotopes ................ 1044-6 Comparison of PENTRAN/PENBURN and SCALE5.1 keff results over 541 day burn sequence ...........................................................................................................................1054-7 Fuel composition comparison of hete rogeneous and homogenized fuel zones ............... 1054-8 PENTRAN mass balance analys is for fissile material (UO2) in 2-D model comparison .................................................................................................................... ...1064-9 Homogenized (fuel+gap+clad) unit cell keff results from SCALE5.1 and PENTRAN ...1064-10 Maximum normalized flux error and corresponding coarse mesh for groups 1-3 .......... 1064-11 Actinide results (atom/barn/cm) for fuel rod 1 [x-y center at (0.6716, 0.6716 cm)] for 10.9 GWd/MTHM of assembly burnup ........................................................................... 1064-12 Actinide results (atom/barn/cm) for fuel rod 68 [x-y center at (5.7108, 5.7108 cm)] for 10.9 GWd/MTHM of assembly burnup ..................................................................... 1074-13 Actinide results (atom/barn/cm) for fu el rod 132 [x-y center at (9.4902 10.75 cm)] for 10.9 GWd/MTHM of assembly burnup ..................................................................... 1074-14 Percent differences between PENBUR N and ORIGEN-ARP at various burnup set points ................................................................................................................................1075-1 Comparison of Xe-135 concentrations for reference burnup case of 1 day irradiation steps versus 2, 3, 4 and 12 day irradiation st eps totaling to 14 days of irradiation .........1295-2 Comparison of keff for reference burnup case of 1 day irradiation steps versus 2, 3, 4 and 12 day irradiation steps totali ng to 14 days of irradiation. ........................................1295-3 Comparison of Xe-135 concentrations for reference burnup case of 3 day irradiation steps versus 30 day irradiation steps to taling to 36 days of irradiation ........................... 1305-4 Comparison of keff for reference burnup case of 3 day irradiation steps versus 30 day irradiation steps totaling to 36 days of irradiation ........................................................... 1305-5 Comparison of Xe-135 concentrations for reference burnup case of 6 day irradiation steps versus 60 day irradiation steps to taling to 66 days of irradiation ........................... 1305-6 Comparison of keff for reference burnup case of 6 day irradiation steps versus 60 day irradiation steps totaling to 66 days of irradiation ........................................................... 131

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12 5-7 Comparison of Xe-135 concentrations for reference burnup case of 12 day irradiation steps versus 120 day irradiation steps to taling to 132 days of irradiation ....................... 1315-8 Comparison of keff for reference irradiation case of 12 day irradiation steps versus 120 day irradiation steps totaling to 132 days of irradiation ........................................... 131

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13 LIST OF FIGURES Figure page 2-1 Explicit Forward-Euler burnup methodology .................................................................... 342-2 Predictor-corrector burnup methodology with exte nded step depletion. ...........................343-1 Pointwise absorption cross sect ion data for U-238 (KAERI, 2000) .................................. 713-2 Temperature comparison of Pu-240 (n,gamma) cross section ........................................... 713-3 Generalized SCALE5.1 cross section generation procedure ............................................. 723-4 The T-DEPL (left) and T-NE WT (right) control sequences .............................................. 723-5 Burnup dependency of U-235 absorpti on cross-section for reference case (E1upper=20 MeV, E2upper=1.01 MeV, E3upper=0.625 eV) .......................................................................733-6 Burnup dependency of Pu-240 absorption cross-section for reference case (E1upper=20 MeV, E2upper=1.01 MeV, E3upper=0.625 eV) .......................................................................733-7 Burnup dependency of Xe-135 thermal absorption cross-section for reference case (E1upper=20 MeV, E2upper=1.01 MeV, E3upper=0.625 eV) ....................................................743-8 Burnup dependency of Sm-149 thermal ab sorption cross-section for reference case (E1upper=20 MeV, E2upper=1.01 MeV, E3upper=0.625 eV) ....................................................743-9 Percent difference in actinide concentr ations (atom/barn/cm) after 64.6 GWd/MTHM between reference 46 library burnup run a nd 2, 3, 5, 7, 8 and 23 library burnup runs ...... 753-10 Percent difference in Xe-135 concentra tions (atom/barn/cm) after 64.6 GWd/MTHM between reference 46 library burnup run a nd 2, 3, 5, 7, 8 and 23 library burnup runs ...... 753-11 Difference in computed pcm for keff between reference 46 library burnup run and 2, 3, 5, 7, 8 and 23 library burnup runs .................................................................................. 763-12 Difference in computed pcm for keff between reference 46 library burnup run an 5, 7, and 8 library burnup runs ...................................................................................................763-13 The U-235 absorption cross section burnup and temperature dependencies ..................... 773-14 The Pu-239 absorption cross secti on burnup and temperature dependencies .................... 783-15 The Pu-240 absorption cross secti on burnup and temperature dependencies .................... 793-16 The Xe-135 absorption cross secti on burnup and temperature dependencies ................... 803-17 The Sm-149 absorption cross sectio n burnup and temperature dependencies ..................81

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14 3-19 Pointwise absorption cross sect ion data for Pu-239 (KAERI, 2000)................................. 833-20 The NJOY/TRANSX procedure ........................................................................................ 833-21 The INTERP-XS flowchart................................................................................................844-1 Plan view of Westinghouse 17x17 OFA assembly w/ fuel pin numbering ..................... 1084-2 Westinghouse fuel unit cell model (OD=1.2598 cm) ...................................................... 1084-3 Comparison of keff for PENBURN and SCALE .............................................................. 1094-4 Relative percent difference in concentration between SCALE and PENBURN with and without use of INTERP-XS for select Plutonium isotopes ...................................... 1094-5 Comparison of keff between PENTRAN/PENBURN a nd SCALE using INTERP-XS ...1104-6 Cycle length estimat e based on reactivity ........................................................................1114-7 Overview of two dimensional mesh scheme .................................................................. 1124-8 Group 1 (1.01 < E 20.0 MeV) normalized flux error for initial PENTRAN transport analysis .............................................................................................................1124-9 Group 2 (6.25x10-7 < E 1.01 MeV) normalized flux error for initial PENTRAN transport analysis .............................................................................................................1134-10 Group 3 (E < 6.25x10-7 MeV) normalized flux error for initial PENTRAN transport analysis ...................................................................................................................... .......1134-11 Relative axial neutron flux distribution at x-y center of Westinghouse fuel assembly based on initial fuel concentrations ..................................................................................1144-12 Relative neutron flux distribu tion for Westinghouse assembly ....................................... 1154-13 Three-dimensional overview of assembly neutron flux distribution ...............................1164-14 Expanded 3-D view of relative neutron flux distribution at z=182 cm for E<0.625 eV 1174-15 Material layout for assembly analysis ..............................................................................1184-16 Variation of the total axial flux distribution for cumulative burn times of 0, 20, 80, 140, and 220 days ............................................................................................................1194-17 Concentrations of Pu-239 as a functi on of burnup for depletion zones 132, 396, and 660 in fuel rod 132 ...........................................................................................................119

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15 5-1 Overview of BURNDRIVER script ................................................................................. 1325-2 Fission product decay chain involving Xe-135. .............................................................. 133

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16 LIST OF ABBREVIATIONS ALPO ANISN library production option BONAMI Bondarenko AMPX interpolator CENTRM Continuous energy transport module GMIX Generalized cross section mixer MCNP Monte Carlo neutral particle transport code NEWT New extended step characteristic-based transport code OPUS ORIGEN-S post proc essing utility for SCALE ORIGEN-S Oak Ridge isotope generation SCALE PENBURN Parallel environment burnup PENTRAN Parallel environment neutral particle transport PMC Produce multigroup cross sections SCALE Standardized computer an alysis for licensing evaluation T-DEPL TRITON depletion control sequence which uses NEWT, a 2-D deterministic transport solver T-DEPL5 TRITON depletion control seque nce which uses KE NO Va, a 3-D Monte Carlo transport solver T-DEPL6 TRITON depletion control seque nce which uses KENO VI, a 3-D Monte Carlo transport solver TRITON Transport rigor implemented with quasi-static time dependent operation for neutronic depletion

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17 Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science FULLY AUTOMATED 3-D PARALLEL SIMULATI ON AND OPTIMIZATION OF A FULL SCALE PRESSURIZED WATER REACTOR FUEL ASSEMBLY WITH BURNUP CORRECTED CROSS SECTIONS By Thomas Joseph Plower December 2008 Chair: Glenn Sjoden Major: Nuclear Engineering Sciences Computational nuclear fuel burnup analysis is an essential field within the Nuclear Engineering discipline, since it plays important functions in core reactivity management, criticality safety, Special Nuclear Materials management, and fuel assembly reload design of commercial power and research reactors. Thre e dimensional (3-D) deterministic transport methods provides unique advantages in the fuel burnup analysis fi eld and the intention of this thesis is to demonstrate the authors cont ributions to the development of a novel 3-D deterministic fuel burnup package called th e PENTRAN /PENBURN (Parallel Environment Neutral particle Transport/Parallel Environmen t Burnup) suite. Specifically, cross section generation procedures will be presented including discussions on development of a coupled cross section interpolator code called INTERP-XS. A dditionally, detailed fuel burnup analysis of a 17x17 PWR assembly will be presented. Finally, the development of an automated sequence driver called BURNDRIVER will be shown. Major conclusions include: excellent agreement between INTERP-XS generated cross sections a nd those generated by SCALE, demonstration of 3-D burnup effects captured by PENTRAN/PENB URN through PWR assembly analysis, and successful creation of a user-f riendly burnup sequence driver.

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18 CHAPTER 1 INTRODUCTION TO NUCLEAR FUEL BURNUP DISCIPLINE 1.1 Introduction The United States (US) is in an energ y cris is, given the rising elec tricity demand from an ever-growing population, increasing energy demands and cost due to a significant dependence on foreign oil, and growing concern over greenhouse gas emissions contributed by coal fired power plants. Even critics agree that nuclear energy will play a critical role in filling the energy gap, since it is one of the cleanest, safest, and eco nomical base load solutions. Recent trends have suggested that the US is on the ve rge of a nuclear renaissance given utility intere st in license extensions, power upgrades of cu rrent plants, and construction of new plants (Tompkins, 2008). The nuclear renaissance has also prompted the US Department of Energy (DOE) to create the Global Nuclear Energy Partnershi p (GNEP), a project calling fo r new reactors specifically designed to be fueled with the stockpile of spent nuclear assemb lies currently stored at on-site pools and storage casks (Michal, 2008). These spent assemblies are extremely valuable, since they contain recoverable fissile material (princip ally uranium and plutonium). The nuclear fuel burnup engineer is responsible fo r tracking concentrations of uranium, plutonium, and other transuranics and fission products with in these spent fuel assemblies. Computational nuclear fuel burnup analysis is an essential field within the Nuclear Engineering discipline, since it plays important functions in core reactivity management, criticality safety, burnup credit, and fuel asse mbly reload design of commercial power and research reactors. In addition, fu el burnup analysis serves as a vita l tool in national security and non-proliferation applications by providing the ability to track the content of Special Nuclear Materials (SNM) within reactor fuel.

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19 Current reactor analysis tools employed in i ndustry are lacking the ability to accurately track three dimensional (3-D) burnup detail s based on high resoluti on transport theory calculations. Common burnup analysis tools like Standardized Co mputer Analysis for Licensing and Evaluation version 5.1s (SCALE5.1s) T-DE PL control sequence or the HELIOS code system are based on two dimensional (2-D) deterministic models which do not account for the 3D variation of the neutron flux distribution (Dehart, 2006b; Wemple et al, 2008). Disregarding 3-D dependencies will often introduce significant errors in burnup re sults, in particular towards the axial periphery of reactor assemblies where the neutron flux is ch anging most rapidly (DeHart, 2008). Recent attempts at 3-D burnup simulations employ Monte Carlo based methods for transport, such as MCNPX (Fensin, 2008) MONTEBURNS (Poston and Trellue, 1999), SWAT2 (Mochizuki et al., 2003), and ALEP H (Haeck, 2007). This methodology can be troublesome due to inherent characteristics of the method (i.e. statisti cal uncertainty, fission source convergence issues, and high dominance ratios) (LAbbate, 2007). Additionally, coupling Monte Carlo based transport w ith a depletion solver also brings uncertainties on how to incorporate statistical error with isotopic concentrations. Ideally, the best method of capturing 3-D detail of reactor systems is to perform transport by directly solving the Linear Boltzmann E quation (LBE) in 3-D. The PENTRAN/PENBURN suite (Parallel Environment Neutral particle Transport/ Parallel Environment Burnup) is a University of Florida (UF) developed fuel transport/depletion solver which has the ability to perform deterministic burnup by solving the LBE in 3-D via the Sn method. 1.2 Status of PENTRAN/PENBURN Code System (June 2007) Since the summer of 2007, PENBURN, the fuel depletion module coupled to the PENTRAN transport solver, had been under developm ent for approximately one year at UF. PENBURNs production and batch Bateman subroutin es had been fully tested and benchmarked

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20 with the Mathematica code package for the Ur anium/Plutonium series (Manalo, 2008). Fission product modeling was not fully incorporated. Microscopic cross sections independent of burnup (i.e. based solely on fresh fuel concentrati ons) derived from SCALE were being used to formulate macroscopic cross sections with the general Group cross-sectio n Mixer (GMIX) code. Gaps existed in microscopic cross section data for several actinides and fission products. Additionally, the reference test case for the PENTRAN/PENBURN suite was a simple Uranium fuel pin of arbitrary design and specification. Mo reover, the development of cross-sections and data exchange between PENTRAN and PENPOW /PENBURN was manually driven, creating a cumbersome and inefficient system for practic al applications of 3-D burnup analysis. It was apparent that a clea r procedure for development of burnup dependent microscopic cross-sections using SCALE was needed. A dditionally, PENTRAN/PENBURN needed to be put to the test, beyond a simple uranium fuel pi n, with a current power reactor fuel assembly design that could demonstrate th e capabilities and unique feat ures of the PENTRAN/PENBURN suite. Finally, an automated burnup sequence drive r than can create directories and files, execute programs, and summarize output was need ed in order to simplify and streamline the PENTRAN/PENBURN burnup procedure. The follo wing section will detail the authors contributions to the development and impr ovement of the PENTRAN/PENBURN burnup suite. 1.3 Burnup Package Contributions Contributions to the PENTRAN/PENBURN bur nup suite can be separated into three topics: Prim ary developer of Interpolate-Cross Sec tion code (INTERP-XS) which performs linear interpolation on burnup and temperature dependent microscopic cross section database for PWR, Magnox, and Clinch River Breeder Reactor designs. Cross sections are derived from SCALE5.1 and in some cases NJOY.

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21 3-D PENTRAN/PENBURN burnup analysis of a 17x17 Westinghouse Optimized Fuel Assembly (OFA) containing 792 depletion zones. Primary developer of Burnup Driver (BURNDRI VER) script for para llel processor based computation which automates and stream lines the entire PENTRAN/PENBURN burnup procedure by creating directory folders, creat ing and moving files, executing codes in the proper sequence, and summarizing output data. Chapter 2 discusses current transpor t methods, burnup methodologies, and burnup packages offered by US national labs. Chapter 3discusses cross section generation procedures employed including details on the in terpolator code, INTERP-XS. Ch apter 4 contains detailed 3D PENTRAN/PENBURN results of the Westinghouse PWR assembly analysis. Chapter 5 provides insight for the automated BURNDRIVER script. Finally, Chapter 6 highlights major conclusions and future work.

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22 CHAPTER 2 OVERVIEW OF CURRENT BURNUP PACKAGES In order to perform fuel burnup analysis on a reactor core, there are several computational tools necessary. These include: neutron cross se ction processing modules, neutron flux solver, reaction rate module, fuel depletion solver, and an automated burnup sequence driver. Beyond these tools, there is also an enormous amount of nuclear data required in order to capture the correct problem dependent interaction physics. The range of data types include neutron microscopic cross sections (absorption, fission, scattering, and total), fission neutron energy spectrum ( ), number of neutrons released per fission ( ), energy release per fission (occasionally coupled with the fission cross section to define a power cross section), fission yield data, and radioactive decay constants, ( ) The following section will begin with a discussion of transport methods, followed by commentary on general bur nup methodologies, and finally an overview of current burnup packages including de tails on the PENTRAN/PENBURN suite. 2.1 Transport Methods 2.1.1 Boltzmann Transport Equation The neutron flux distribution in a reactor system can be exactly derived by balancing the production and loss mechanisms for a system. Th e steady state multigroup form of the Linear Boltzmann Transport Equation (LBE) for a multiplyi ng system is given in Equation 2-1. The left side includes loss by leakage and collision; scat ter, fission, and independe nt sources are on the right hand side (Lewis and Miller, 1993). ) ,()() ,( rrrgg g ) ,() ,()(' )' ,() ,(' 1' 4 1' 4 rqrrd k r rdgind G g ggf o g g g g ggs (2-1)

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23 Approximations of the transport equation via deterministic discrete ordinates invoke a discretization of the energy, angle, and space variables. Discretiz ation of energy is performed by spectrally averaging over energy groups (g=1, G) spanning from high to low energies, resulting in the multigroup form seen in Equation 2-1. The scattering term is generally expanded using a truncated set of spherical (surface) harmonics by Legendre polynomials. In 3-D Cartesian form, the vector is generally expressed using directional cosines projected on the x, y, and z axis, respectively. Additi onally, the streaming term ( ) in Equation 2-1 can be decomposed (Equation 2-2) in 3-D Cartesian form. zyx (2-2) Provided with the previous treatments, the Legendre expanded multigroup form of the transport equation in 3-D Cartesian geometries is expressed in Equation 2-3. ),,,,(),,(),,,,() (zyxzyx zyx zyxg g g G g L l l k k l lgl lggsP kl kl zyxPzyx l1 '01 ,' ,',)( )!( )!( 2),,()(){,,()12( G g g gf o g k lgS k lgCzyxzyx k kzyx kzyx1' 0,' ,' ,' ),,(),,( )]}sin(),,()cos(),,([ (2-3) where = x direction cosine fo r angular ordinate = y direction cosine for angular ordinate = z direction cosine for angular ordinate g = group g angular particle flux (for groups g=1,G ) = azimuthal angle constructed from )/arctan( with proper phase shift g = total group macros copic cross section l= Legendre expansion index (Ll ,0 ), L =0 or odd truncation lgsg ,' = th lLegendre moment of the macrosc opic differential scattering cross section from groupgg ) ( lP= th lLegendre polynomial lg ,' = th lLegendre scalar fl ux moment for group g

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24 )(k lP = th l, th k Associated Legendre polynomial k lgC ,' = th l, th kCosine Associated Legendre scalar flux moment for group g k lgS ,' = th l, th kSine Associated Legendre sc alar flux moment for group g g = group fission distribution constant (neutrons) ok = criticality eigenvalue (neutrons) g f = group fission production (neutrons) The flux moments, lg ,' k lgC ,' and k lgS ,' are defined in terms of and as: 1 1 2 0 ,')',',,,( 2 )'( 2 ),,( zyx d P d zyxg l lg (2-4) 1 1 2 0 ,')',',,,()'cos( 2 )'( 2 ),,( zyxk d P d zyxg k l lg k C (2-5) 1 1 2 0 ,')',',,,()'sin( 2 )'( 2 ),,( zyxk d P d zyxg k l lg k S (2-6) Note that this form of the LBE is solved within the PENTRAN code package over distinct angular directions; this method is called the discrete ordinates or Sn method (Carlson and Lathrop, 1964). A large system of algebrai c equations representing the components of the discretized flux is needed, requi ring large amounts of computer power in order to obtain a solution in a reasonable time. The neutron diffusion equation, an approximation to the LBE, is commonly chosen for 3-D reactor analysis over the full steady state form LBE mainly because of the immense undertaking required to solve the stea dy state form of the LBE with six independent variables (spatial (3), energy (1), and angul ar direction (2)). 2.1.2 Diffusion theory In neutron diffusion theory, the goal is to simplify the Linear Boltzmann Equation by attempting to integrate simplified angular dependenci es of the flux and arrive at an equation that contains solely scalar flux terms, ( r,E,t ) with appropriate assumptions. In order to arrive at the diffusion equation from the LBE, the zeroth and first angular moments of the LBE are formulated to derive two equations with two unknowns, ( r,E,t ) and J ( r,E,t ). One key

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25 assumption, however, is that the angular flux is weakly dependent on angle, i.e. (Duderstadt and Hamilton, 1976): ) ,,( 3),( 4 1 ) ,,( ErJEr Er (2-7) Where, ( r,E,t ) is the scalar flux. J( r,E,t ) is the neutron current density. It is also routine to consider the neutron source te rm is isotropic. Additionally it is assumed that the rate of time variation of the current density is much smaller than the interaction frequency, described in Equation 2-8. Typical valu es for interaction frequency are around 105 s-1, thus, only extremely large time thus only extremely larg e variations in current would falsify this assumption (Duderstadt and Hamilton, 1976). tt J J 1 (2-8) Where, v is the neutron velocity. t is the total cross section. As with any assumption or approximation to an exact solution, instances may arise where applications of the diffusion equation can cause difficulties. In general, diffusion theory is troublesome when radiation syst ems are characterized by: strong angular flux dependencies model heterogeneity localized sources and/or absorbers Additionally, diffusion theory is invalid near vacuum boundaries, where a linearly anisotropic flux assumption fails. To adjust for these issues, transpor t-correction factors are often introduced to enable limited physics modeling to match experimental observation (Yamamoto, 1986).

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26 2.1.3 Monte Carlo method The Monte Carlo method avoids having to di rectly handle the LBE by using probability laws representing basic physical processes (i.e. neutron scatter, captu re, fission) and random numbers in order to obtain the average value of a random vari able through random sampling. Associated with the average value (i.e. flux tally, reaction rate, ei genvalue) is a variance/standard deviation and a confidence level representing the deviation of the sample average from the true mean. Monte Carlo codes have become increasingly popular for reactor tran sport analysis with the growth of parallel computing. While achieving a criticality eigenvalue is relatively straight forward, run times for large models requiri ng converged fission sources for proper burnup computation quickly becomes very time consuming. This long convergence time often times correlated to a systems dominan ce ratio (Nease et al, 2008). Th e dominance ratio is defined as DR = k1/ ko, where ko is the eigenvalue of th e fundamental mode and k1 is the eigenvalue for the first higher mode. The domi nance ratio is an important parameter which indicates the convergence rate for numerically iterative pro cedures, such as the case when determining keff and power distributions using Monte Carlo based methods. If the dominance ratio is near 1, solution convergence is slow and users must be wary of false convergence. If the dominance ratio is low (DR<0.9), the solution should c onverge quickly. Know ledge of the systems dominance ratio coupled with cycle-to-cycle keff and Shannon entropy are diagnostics for helping determine fission source convergence. 2.2 Burnup Methodology Provided with a transport solution either calculated deterministically by solving the full form LBE or stochastically via Monte Carlo me thod, fuel burnup analysis can be performed to model the transmutation process that nuclear fu el undergoes through irradiation and radioactive

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27 decay. The in-growth of new actinides and fissi on products can be explicitly modeled through a set of coupled first order di fferential equations known as Bateman equations. The Bateman equations can be decomposed into two component s; one component related to flux and the other related to radioactive decay. The equation requires the use of fluxes, number densities, crosssections, and radioactive decay constants in orde r to determine nuclide inventory. Examining the multigroup nuclide consumption equation without ra dioactive decay (Equation 2-9), recall that the solution to this first order differential equation is simply of the exponential form (Equation 210). G g gi g i irtrtrN dt trdN1 ,)(),(),( ),.( (2-9) Where, ( r,t ) is neutron flux at position r in t and t+dt. Ni( r,t ) is the atom density of isotope i. i(r) is the absorption cr oss section of isotope i at position r. G g t t dttrr gi rNtrNi i1 2 1 ),()( exp)0,(),( (2-10) Note how the atom density ( Ni) is dependent on the time-inte grated flux, however the flux is also dependent on the atom density. This ma kes for a non-linear equation. To account for this, a quasi-static approach is taken, and it is assume d the flux is time independe nt over an irradiation step/period and an average flux over the step ( avg) replaces the integral and integrand. 2.2.1 Forward-Euler Quasi-Static Burnup Approach If irradiation periods are short enough, the fl ux calculated at the beginning of a burn step may suffice, and can be substituted for avg for the entire step. This procedure is commonly referred to as a Forward-Euler approach to burnup simulation, sinc e explicit information calculation at the beginning of the interv al is used over th e entire burn step. Figure 2-1 shows a four irradiation burn step sequence. It is worthy to note that the Forward Euler app roach does

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28 possess numerical instabilities when time steps ar e selected too big, however has reasonable stability so long the so-called Courant-Friedr ichs-Lewy condition is fulfilled (Strickwerda, 2004). 2.2.2 Predictor-Corrector Quasi Static Burnup Approach A more conservative methodology, which attemp ts to account for the time dependence of the flux over an irradiation pe riod, is called the Predictor -Corrector quasi-static burnup approach. In this methodology, the flux solution at the beginning of an irradiation period is used to perform depletion to the midpoint of the peri od. The isotope inventories and microscopic cross sections are updated at the midpoint of the time step and a transport calculation is performed again. The midpoint flux solution and midpoint microscopic cross sections are then used to perform depletion from the beginning of the step to the end of the step. In general, with current burnup code packages such as SCALE and MCNPX, the depletion is exte nded past the end of the step to the midpoint of the following irradiati on period. A visual aid of the same four step irradiation burn sequence discussed with Forward-Euler appro ach is supplied in Figure 2-2 For exam ple, a burnup sequence would start wi th cross sections (XS01p), an initial transport solution (T01p) for an initial burnup of B01p (which is effectively 0 GWd/MTHM). Depletion would be performed to the midpoint of the initial step ( to 0. 5) and cross sections would be updated (XS02p) and transport would be re-performed (T02p). The transport solution and microscopic cross sections from step02p (i.e. T02p and XS02p, respectively) would then be used to perform burnup over the entire burn step, spanning from 0 to 1.0. Burnup is then extended through the midpoint of the next step with updated cross sec tions (XS0n), however, power rescaling may be in order if the speci fic power differs from the initial burn step.

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29 2.3 Current Burnup Code Packages Two of the most popular fuel burnup solvers in the US are SCALE5.1 and MCNPX. Oak Ridge National Lab (ORNL) is responsible fo r developing and mainta ining SCALE, under contract with the DOE and the NRC. Los Alamos National Lab (LANL) is responsible for developing and maintaining MCNP5/MCNPX. Additionally, one popul ar industry burnup simulation package is CASMO4, developed by Studsvik. 2.3.1 The SCALE5.1 Code System SCALE performs reactor physics, criticality safe ty, radiation shielding, and spent fuel characterization for nuclear facili ties and transportation/storage package designs. There are three control sequences within the transport rigor implemented with quasi-static time-dependent operation for neutronic depletion (TRITON) cont rol module which are dedicated to performing fuel depletion analysis: T-DEPL, T5 -DEPL, and T6-DEPL (DeHart, 2006b). 2.3.1.1 The T-DEPL control sequence The T-DEPL control sequence is SCALEs two dimensional (2-D) deterministic approach towards fuel burnup analysis. The sequence uses ei ght modules in order to properly handle cross section processing, transport so lving, and fuel depletion an alysis. These modules include: Bondarenko AMPX Interpolator (BONAMI), Worker (WORKER), Continuous Energy Transport Module (CENTRM), Pr oduce Multigroup Cross sections (PMC), New Extended Step Characteristic-based Transport code (N EWT), Couple (COUPLE), Oak Ridge Isotope Generation SCALE (ORIGEN-S), a nd ORIGEN-S Post Processing Utility for SCALE (OPUS) Chapter 3 contains a full section de dicated to each of these modules. 2.3.1.2 The T5-DEPL control sequence The T5-DEPL control sequence is functiona lly identical to the T-DEPL sequence, however, the 3-D NEWT deterministic transport so lver in T-DEPL is replaced KENO version 5a

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30 (KENO VA), a three dimensional (3-D) Monte Carl o based transport solver (Hollenbach et al, 2006). 2.3.1.3 The T6-DEPL control sequence Likewise, the T6-DEPL control sequence is functionally identical to the T-DEPL and T5DEPL sequences, however, the transport solver is replaced with KENO version 6 (KENO VI), an extension of KENO VA that contains a more elaborate geometry package using quadratic equations to create surfaces (Hollenbach et al, 2006). 2.3.2 The MCNPX Code System Similar to SCALEs KENO Va and 6, MCNP X performs radiation transport analysis based on Monte Carlo methods. One of the most notab le features of the X version relative to version 5 of the MCNP code is the capability of performing bu rnup/depletion. MCNPX performs a steady state eigenvalue calculati on in order to evaluate the sy stems eigenvalue, 63 group flux spectra, energy-integrated reacti on rates, fission multiplicity (), and recoverable energy per fission (Q) (Hendricks et al, 2008). This data is then passed to CINDER90, a coupled fuel depletion module. In order to solve for the time dependent nuclide inventory, CINDER90 employs the Markov linear chain technique. CI NDER90 has the ability to track 3400 nuclides, 1325 fission products, and has fission yield da ta for around 30 actinides (Fensin, 2008). CINDER90 has also integrated into another code system called MONTEBURNS, which links MCNP with either CINDER90 or ORIGEN2 depletion module from Oak Ridge National Lab. 2.3.3 The CASMO-4 Code System CASMO-4 is a multigroup two dimensional tran sport code developed by Studsvik. The code solves the two dimensional transport equation for exact heterogeneous geometries. CASMO-4 has data for over 300 nuclides, using th e new ENDF VII libraries. Users have the capability of performing burnup calculations on BWR and PWR assemblies and fuel pins. The

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31 code has the ability of handling cy lindrical fuel rods with varying enrichments arranged in square pitches. CASMO-4 also has the ability to inco rporate Gadolinium rods, burnable poisons, and cluster control rods. The code can also li nk with Studsviks nodal core model called SIMULATE-4 (Edenius et al, 1995). 2.4 The PENTRAN/PENB URN Burnup Package Beyond possessing a qualified cro ss section library a nd good power history, a key tool for performing 3-D deterministic burnu p analysis is having an accurate, robust, and computationally efficient 3-D transport solver. PENTRAN serves the transport role for PENBURN. PENTRAN code development started in 1995 by Glenn Sjoden and Alireza Haghighat at Penn State University, and has continued to mature over the past 13 years. It has been experimentally well benchmarked by the Venus-3 Reactor owned by SCK in Belgium and rigorously tested with such computational tools as MCNP, TWOTRAN-II, THREEDANT, DORT, and TORT (Sjoden and Haghighat, 1997; Sjoden and Haghighat, 2008). PENBURN is the coupled fuel depletion so lver developed by Kevin Manalo for his Masters Thesis project betw een 2006 and 2008 (Manalo, 2008). When provided with zonebased reaction rates from a reaction rate solver called Parallel Environment Power (PENPOW), another module written by Manalo, PENBURN computes time-dependent isotope concentrations. PENBURN utilizes the direct Bateman-solver chain solution technique in order to compute isotope concentrations for a specified power history. 2.4.1 The PENTRAN Transport Solver PENTRAN iteratively solves the 3-D multigroup form of the LBE in Cartesian geometries with anisotropic scattering using Pl Legendre moments and level-symmetric Sn angular quadratures. The code has several essential util ity packages which generate the 3-D Cartesian mesh, mix macroscopic cross-sect ions, and pull together parallel data. PENTRAN has a parallel

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32 memory structure and is parallelized for me ssage passing using the standardized Message Passing Interface (MPI) library for po rtability to almost any distributed memory parallel machine design. PENTRAN provides the ability for large transport problems to be decomposed into angle, energy, and space. Some of PENTRANs unique features include: Adaptive differencing scheme strategyPENTRAN can select different differencing schemes (i.e. Linear Diamond, Directional Theta Weighted, Exponential Directio nal Iterative, etc) based on problem physics for each coarse mesh within a transport problem. Variable 3-D meshing with Ta ylor Projection Mesh CouplingPENTRAN has the ability to vary the mesh along the x y and z directions between different coarse meshes containing heterogeneous zones. Additionally, mesh inter polation between adjacent coarse meshes (with potentially different fine mesh) is accomplis hed using Taylor Proj ection Mesh Coupling. 2.4.2 The PENPOW Reaction Rate Solver Prior to burnup/depletion anal ysis, PENBURN must be supplie d with reaction rates (given irradiation is occurring within the cycle) PENTRAN obviously provides the neutron flux, however a module is required to co uple the multigroup cross sections ( f, a) with the corresponding flux. This task is performed by PENPOW. These reaction ra tes are written to a file and passed to PENBURN (Manalo, 2008). 2.4.3 The PENBURN Bateman Solver When provided with zone-based reaction rates from PENPOW, PENBURN computes time-dependent isotope concentrations using the direct Bateman solution for a set of approximately 150 actinides and fission products PENBURN models the transmutation of actinides and fission products (occurring indepe ndently or by combination of neutron fission, neutron capture, decay, decay, or isomeric transition) via enumeration of linear chains from a path matrix (Manalo, 2008). Th e matrix identifies how actinid es and/or fission products are

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33 linked to each other in order to form the lin ear chains. Once enumerated, PENBURN uses the direct Bateman batch equation (Equation 2-11) to solve for nuclide concentrations of isotope i in a linear chain. t i t jeN e NtNo i i l i j i jk lk jk ill o l i 1 11 11... )( (2-11) where, Nl is the number of atoms of precursor nuclide l at time t=0 l is the chain-linking pr ecursor rate constant i is the effective decay constant for nuclide i accounting for G g gg 1 and Ni(t) is the number of atoms of nuclide i at time t Ni 0(t) is the number of atoms of nuclide i at time t=0

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34 Figure 2-1. Explicit Fo rward-Euler burnup methodology Figure 2-2. Predictor-corrector burnup methodology with extended step depletion. Step suffixes with a 1p or 2p indicate points where transport calc ulations are being performed. Step suffixes with a n indicate points where depletion is extended to the midpoint of the next irradiation step

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35 CHAPTER 3 BURNUP DEPENDENT MULTIGROUP CROSS SECTION GENERATION Cross-sectio n generation is a vital process, since improper treatment will produce issues not only in transport solution (i.e flux and eigenvalue) but also reaction rates, which in turn affect burnup/depletion results. Unlike Monte Carlo based met hods like MCNP, which simply use high-resolution point-wise cross section databases in order to establish interaction probabilities, deterministic transport solvers re quire multigroup cross sections averaged in an energy bin appropriate to the mode ling effort with proper resonan ce self-shielding, spatial selfshielding, and Doppler broadening treatment in order to capture the correct physics. This requires significant up-front effort prior to the full model transport and burnup analysis, which is one reason why Monte Carlo is so often a popular approach to burnup. The following sections will summarize the various cross-section effects that require consideration in order captur e proper physics, discuss the procedure in SCALE (and where required NJOY99.0 ) used to apply these treatments, and the INTERP-XS code that was created in order to generate problem dependent cro ss section sets based on SCALE generated data. 3.1 Cross Section Phenomena 3.1.1 Resonance Self Shielding Fission neutrons are born at relatively high en ergies, with average fission neutron energies around 2 MeV. These fast neutrons escape the fu el and interact with the surrounding moderator and structure. As they interact and slow down, neutrons must pass through the resonance energy range, typically from below 1 MeV to epither mal energies,, where neutrons have a large probability of being captured (as depicted by the sharp peaks of the absorption cross section in Figure 3-1 ). This range can be further broken down in to resolved and unresolved energy ranges. In the resolv ed range, cross section spikes are distinct and separable, while in the unresolved

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36 range the cross section behavior is much more co mplicated and more difficult to distinguish. As a result of the large absorpti on probability, flux depressions are created around resonances, an effect commonly referred to as resonance or energy self-shielding (Duderstadt and Hamilton, 1976). Resonance absorption is an extremely impor tant phenomenon, considering it has large impacts on reactor criticality, neutron flux distribution, multigroup cross-section collapsing, breeding ratios, and burnup. In a burnup calculation, it is impe rative that the impact of resonance self shielding is acc ounted for, since irradiation of fuel generates significant concentrations of resonance absorbers (i.e. Pu-239, Pu-240, Pu-241). Studies have suggested, however, that resonance absorbers can be ignor ed and treated as infinitely dilute when concentrations reach levels below 1x10-3 atom/barn/cm (DeHart, 2007). 3.1.2 Spatial Self Shielding Spatial self-shielding can be most easily explai ned by a brief discussion of the rim effect. The rim effect is a phenomenon where fissile and fertile material on the edge of a fuel pin preferentially absorb incoming slow moving neut rons, creating a thermal flux depression towards the center of the fuel pin. Additionally, fu el pins observe higher burnup rates toward the periphery of the pin relative to the interior of the pin, creating higher concentrations of resonance absorber material in these regions. Both the thermal flux dependence on distance from fuel pin center and increased resonance absorber material in the rod periphery could have significant impact on the multigroup cross-section collapse. This same concept could also be carried over to a more macroscopic level with a fuel assembly. Fuel pins located near water holes or strong absorbers, such as control rods, may be exposed to higher thermal fluxes, thus shielding or shadowing nearby fuel pins. This spatial dependency and shadowing is often times accounted for with Dancoff factors (Duderstadt and Hamilton, 1976).

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37 3.1.3 Doppler Broadening The resonance energy range is an important region of the ne utron spectrum where special treatment must be given to thermal motion of target nuclei, specifically heavy nuclides. The width of these resonances is quite narrow (E < 1 eV), thus modest speeds of thermal nuclear motion can shift the energy dependence of th e cross section within the neighborhood of a resonance, and this is referred to as Doppler Broadening. As exaggerated in Figure 3-2 as tem perature increases, the resonance broadens and its maximum magn itude decreases (although the integral reaction rate over a span of energies is conserve d), reducing energy self-shielding and the associated flux depression. As a resu lt, an increase in resonance absorption is experienced (Duderstadt and Hamilton, 1976). 3.2 Cross Section Extraction Procedure using SCALE Burnup dependent cross sections used by the PENTRAN/PENBURN suite were generated primarily using the SCALE5.1 code package, and more specifically the T-DEPL control sequence in SCALE5.1. Of the 150 isotopes that are tracked in PE NBURN, cross sections for 14 isotopes could not be extracted from SCALEs 238 group master library (based on ENDF VI pointwise data). These isotopes could not be cr eated, because they simply were not included on the library. In order to fill this cross s ection void, NJOY 99.0 was employed. NJOY is a comprehensive computer package capable of producing multi-group cross section data from ENDF formatted data files. The following subs ections will detail the procedure used within SCALE5.1 in order to extract cross-sections. 3.2.1 The SCALE Procedure The idea behind SCALEs cross-section generati on procedure is to begin with a fine group problem independent master data set, like the ENDF VI based 238 group library used for PENTRAN/PENBURN, and transform the library into a 238 group problem dependent library

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38 that has been properly self-shielded. This 238 group library can then be collapsed by applying flux weighting overall all groups, according to Equation 3-1. In SCALE5.1, the collapsed microscopic cross sections for each isotope com posing the model materials are written to file called ft30f001 g g g gE E E E gdEEr dEErEr r1 1),( ),(),( )( (3-1) The problem dependent cross section set can then be used to perform reactor analysis, such as a standalone eigenvalue calcula tion or a burnup analysis. If re quested, burnup is performed in order to obtain updated isotopic concentrations. Another self-s hielding treatment is performed based on the new isotopic concentrations, and this process is repeated for all burn steps. Figure 3-3 depicts the generalized concept. Pursuing the pathway terminating with only 2-D deterministic transport analysis with NEWT is called the T-NEWT procedure in SCA LE5.1. The alternative to this pathway is to continue on with burnup. This control sequence is referred to as T-DEPL, T5-DEPL, and T6DEPL depending on the transport solver used. T-DEPL utilizes the 2-D deterministic transport code called NEWT, while T5-DEPL and T6-DEPL use 3-D Monte Carlo based transport solvers KENO-VA and KENO VI, respective ly. All three sequences us e ORIGEN-S for depletion. The T-DEPL sequence was chosen to gene rate burnup dependent microscopic cross section libraries for PENTRAN/PENBURN, thus the self-shielding modules, transport solver, and burnup module used for this sequence will be discussed in the following sections. An overview of the T-DEPL and T-NEWT sequences is shown in Figure 3-4 Note that both sequences begin with the user choosing a problem independent m aster library. For

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39 PENTRAN/PENBURN calculations, the 238 group ENDF VI library was selected. The selfshielding models are then execute d, based on initial fuel concentr ations and problem geometries. Once cross sections are properly treated, transpor t is performed using the NEWT module. At this point, a cross section collapse can be perf ormed based on the flux solution from NEWT. The collapsed cross sections are written to either savcolNN (where NN is the step number in hexadecimal format for T-DEPL) or ft30f001 files (for T-NEWT). Note that the self-shielding modules apply not only to T-DEPL, but al so to T5-DEPL, T6-DEPL and T-NEWT. 3.2.1.1 Self-shielding modules Bondarenko AMPX Interpolator (BONAMI) retr ieves AMPX master data set containing Bondarenko factors, performs a resonance self-shielding calculation based on the Bondarenko method, and produces problem depende nt master cross section sets for the unresolved resonance ener gy range (Greene, 2006). Worker (WORKER) reads cross section librari es formatted as AMPX master or working libraries and reformat as a new library in working library format (Hollenbach and Petrie, 2006). Continuous Energy Transport Modu le (CENTRM) calculates continuous-energy neutron spectra using deterministic approximations to the Linear Boltzmann Transport Equation (LBE) in one-dimensional geometries or in finite medium. Problem specific flux solution used as a weighting function to perform res onance self-shielding for multigroup data in the resolved resonance energy range (Asgari et al, 2006). Produce Multigroup Cross sections (PMC) uses weighting function generated by CENTRM in order to produce problem dependent, resonanc e self-shielded, multigroup cross sections in the resolved resonance energy ra nge (Hollenbach and Williams, 2006).

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40 3.2.1.2 Transport solver New Extended Step Characteristic (ESC)-based Transport code (NEWT) 2-D discrete ordinates transport code based on the Extended Step Characteristic (ESC) approach solving the LBE for spatial discretization on an ar bitrary geometry choice (DeHart, 2006a). 3.2.1.3 Burnup modules Couple (COUPLE) couples problem dependent cr oss sections with flux weighting factors in order to produce libraries needed for is otopic depletion (Gauld and Hermann, 2006). Oak Ridge Isotope Generation SCALE (O RIGEN-S) calculates time dependent concentrations and radiati on source terms for a large number of isotopes which are generated/depleted through fission, transmutati on, or radioactive decay based on the Matrix Exponential Method (Gauld et al, 2006b). ORIGEN-S Post Processing Util ity for SCALE (OPUS) produces an output file, which can be used to create plots of output data from ORIGEN-S (Gauld and Horwedel, 2006). 3.2.1.4 Important T-DEPL settings and special executables There are several special flags that need to be activated wi thin a T-DEPL input (Appendix A) in order to override sequence defaults and extract a complete set of microscopic cross sections for PENTRAN/PENBURN. The following s ection should be consid ered a reference for future PENTRAN/PENBURN users interested in cross section development. Note that microscopic cross-sections can only be extracted for those isotopes that compose materials (fuel, gap, clad, moderator) within a model. By default in a T-DEPL sequence, TRITON initially adds to all depletion materials trace quantities (1x10-20 atom/barn/cm) of isotopes considered to be impor tant to burnup, however, not a ll of the isotopes on the master cross section library are added. In order for the us er to increase the number of isotopes added in

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41 trace quantities (and effectively increase the collapsed cross section database), a special keyword, parm=addnux= N is required at the beginni ng of the input (DeHart, 2006b). If N equals 0, no additional nuclides are added. If N equals 1, a set of 16 actinides is added in trace quantities. If N equals 2, a set of 66 nuclides is added in trace quantities; 16 actinides from setting N equal to 1 and additional 50 nuclides. If N equals 3, another set of 166 nuclides is added, totaling to 232 nuclides added in trace quantities. A set of tables identifying the nuclides added in trace quantities can be found within the TRITON section of the SCALE5.1 manual. Fo r PENTRAN/PENBURN library calculations, parm=addnux=3 was selected in order to maxi mize the amount of nuclides that can be added with minimal user effort. SCALE users have th e ability to add even more nuclides from the master library not covered with addnux= by manua lly incorporating nuclid es of interest (in trace quantities) to the material composition of the depletion zone s. This information is input by the user within the READ composition sectio n of the input, along with the general material composition information for the model. Note if th e nuclide is not in the master library, then the cross sections cannot be extracted. There are several additional modifications ne eded to the T-DEPL sequence to create and save collapsed cross section sets from the master 238 groups to i user selected energy groups. First and foremost, the SCALE5.1 version released from ORNL does not save collapsed crosssection data sets following each NEWT transport calculation in T-DEPL. The released version only saves 238 group working libraries. There ar e also memory allocation issues in the PMC module using the 238 group ENDF VI library in combination w ith parm=addnux=3, primarily

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42 related to compiler dependent prob lems. In order to circumvent th ese issues, interacting with the SCALE5.1 developers, the author obtained modified versions of the TRITON and PMC executables from ORNL. Therefore, users inte rested in developing a dditional burnup dependent cross sections should contact St eve Bowman or Mark DeHart from the SCALE5.1 development team ( scalehelp@ornl.gov ) to obtain the updated executables. Given the user has the modified executab les, the collapse=yes keyword m ust be activated within the READ model section of the T-DEPL i nput to perform a collapse. Following this, a READ collapse section must be inserted which specifies the users collapsed cross section group structure. Additionally, in order to prevent the T-DEPL sequence from overwriting the collapsed cross section set created for each bu rn step, the parm=savlib keyword must be activated in similar fashion to parm=addnux= N (DeHart, 2006b). To be clear and avoid confusion, in order to add the maximu m set of trace quantitie s and save collapsed cross section sets afte r each burn step (as done for PENTRA N/PENBURN), the user must have the keyword parm=(savlib, addnux=3) present. After each burn step, a collapsed cross section set entitled savcolNN will be saved within the temporary directory SCALE creates on the users computer. The NN suffix refers to the burn step number, in hexadecimal format. Note that the savcol NN file is really a copy of the ft30f001 cross section dump file, which is overwritten after every burn step by NEWT. 3.2.1.5 Important T-NEWT settings Recall with the T-NEWT sequence, SCALE user s are able to perform 3-D deterministic transport analysis with NEWT. The sequence pr ovides many of the same functionality of TDEPL, without the burnup. In fact if one compares the T-NEWT input (Appendix B) with the TDEPL input (Appendix A), they are almost id entical with the one addition of a READ burndata block in the T-DEPL input.

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43 The T-NEWT sequence provides the user with the ability to create a single, problem dependent microscopic cross-section for isotopes of interest within the material composition data. Like with T-DEPL, the addnux keyword can be used with the T-NEWT input in order to have the capability of augmenti ng the collapsed cross section database. A dditionally, instead of the user being concerned with savcolNN files generated for each burn step, the user must only be concerned with a single ft30f001 file that contains all of the cross section data. 3.2.1.6 Shell module When any SCALE control sequence terminates (given the input is executed by dragging and dropping the input onto the SCALE icon), th e temporary directory where all the working files are stored is automatically deleted. To save files from the temporary directory, the user must add to the end of the T-DEPL input: =shell copy savcol00 "%RTNDIR%\filename1" copy savcol01 "%RTNDIR%\ filename2" copy savcol02 "%RTNDIR%\ filename3" end This set of commands will copy and save the co llapsed files of interest from the temporary directory to the working director y where the users input is curre ntly. The user may also access the temporary directory as SCALE5.1 is executing in order to copy/save fi les that have already been produced. This may be necessary if post processing modules (such as OPUS) are running extended periods of time with no apparent end in sight. 3.2.1.7 The ANISN Library Production Option (ALPO) The ALPO module in SCALE is used to conve rt AMPX working cros s section libraries (such as savcol NN or ft30f001 files) into ANISN format libraries (Greene and Dunn, 2006) which are format friendly with cross s ection processing codes utilized by the

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44 PENTRAN/PENBURN suite. In order to create a PENTRAN/PENBURN compatible data set, the ALPO module must be us ed to convert all savcol NN and ft30f001 files. A sample ALPO input can be found in Appendix C. 3.2.1.8 The SCALE Format code (SCALFORM) One final module called SCALEFORM is needed in order to post process microscopic cross section files generated from ALPO. SCALEFORM is a PENTRAN/PENBURN utility code that converts FIDO input commands present within files written by ALPO into a standard input format that is readable by GMIX, the genera lized macroscopic cross section mixer used by PENTRAN/PENBURN. 3.2.2 Cross-Section Generation Using T-DEPL and T-NEWT A combination of the T-DEPL and T-NEWT co ntrol sequences was used to generate a fully optimized, burnup and temperature (fuel/moderator) dependent micros copic cross section library for a 3 wt % enriched UO2 fuel pin from at 17x17 Westinghouse OFA fuel assembly. The cross section procedure for PENTRAN/PENBURN can be broken down into three steps: Reference Step: Perform a detailed T-DEPL burnup cal culation (with cross section collapse and file save settings activated) for a unit cell representation of the system of interest, assuming an average system power, typical fu el and moderator opera ting temperatures, and maximum potential discharge burnup. The user should be cautious in burn step size (i.e. number of irradiation days per bur n step) since this run will be used to evaluate cross section variation as a function of burnup. Fuel isotopic gram results or weight percents should be saved from each step for future branch calculations. Optimization Step: Given the reference T-DEPL calculat ion used a conservative approach with regards to number of steps selected to model burnup out to maximum potential discharge, the user has created an excess of libraries needed to capture cross section burnup

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45 dependencies. As a result, the number of librari es can be reduced to make the library more efficient and manageable. Library op timization is achieved by performing a PENTRAN/PENBURN burnup study on the system unit cell using the conservative burnup library, followed by repeated st udies using fewer library burn up points. Percent differences are then examined comparing burnup runs usin g the conservative library versus runs using the streamlined libraries. Branch Step: Once optimized, a branch calculation is performed using the T-NEWT sequence at each of the reduced burnup set points in order to capture potential variation in system operating temperature effects. For clarity, the Reference Step is used to establish the typical burnup profile assuming average system power and operati ng conditions. T-NEWT calcula tions are then performed (at each of the remaining potential system opera ting temperatures) for each of the optimized reference burnup set points. Isotopic concentr ations from the reference T-DEPL sequence (considered based depletion) are used as the fuel material composition for each respective TNEWT calculation. Output microscopic cross section files from T-DE PL and T-NEWT are always post-processed with ALPO and SC ALFORM in order to prepare use with PENTRAN/PENBURN The next subsection will detail the work performed in order to generate the cross-section library for the 3 wt % enriched UO2 fuel pin unit cell model. 3.2.3 The PWR cross section library development Three reactor systems were proposed in attemp t to capture the spectrum of reactor systems for the PENTRAN/PENBURN cr oss-section library: PWR: Westinghouse OFA 17x17 lattice, UO2 fuel, water cooled.

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46 Magnox: Graphite Moderated, Natural metal uranium, CO2 cooled. Clinch River: Breeder reactor, MOX fuel, sodium cooled. The author was responsible for fully optimizing and analyzing the PWR cr oss section database. The reference burnup sequence for the Magnox a nd Clinch River reactors has also been performed, with a detailed analysis perf ormed for the PWR library presented here. The PWR burnup dependent cross section library series was generated based on a unit cell model of a 3 wt % enriched UO2 fuel pin from at 17x17 West inghouse OFA using SCALEs TDEPL and T-NEWT sequences. A single fuel depletion region was considered for analysis. Furthermore, several different operating condition s for the PWR system were needed in order to capture the variation of operating conditions (i.e. burnup, fuel and moderator temperature, moderator density, etc.). Table 3-1 summ arizes the conditions assumed for generating the PWR library, based on thermal channel an alysis and literature reviews. The 238 group ENDF VI library was selected as the master cross-section library for which the PENTRAN/PENBURN PWR library would be generated from. The library contains 330 nuclides with 17 moderators treated with the S( ) scattering treatment. The 238 group library was collapsed from pointwise ENDF VI data based on the following weighting function (Bowman et al, 2008): Maxwellian spectrum from 1x10-5 to 0.125 eV. 1/E spectrum from 0.125 to 67.4 keV. Fission spectrum from 67.4 keV to 10 MeV. 1/E spectrum from 10 to 20 MeV. The 238 group working library was colla psed from 238 groups to 3 groups (E1upper=20 MeV, E2upper=1.01 MeV, E3upper=0.625 eV) using the 2-D transpor t solution provided by NEWT.

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47 Although a two group library is selected for light water reactor analysis, a three group structure was selected to closely match the collapsed reaction rate arrangement used by SCALEs ORIGEN-S depl etion module. Following the procedure outlined, the referen ce burnup analysis was initially performed, given the operation parameters in Table 3-1 Maxim um potential burnup was extended out to 67.15 GWd/MTHM. The burnup was conservatively distributed over 45 burn steps, using SCALEs Predictor Corrector methodology discussed in Chapter 1. Figures 3-5 through 3-8 depict the variation of iso tope cross sections as a function of burnup for the reference conditions. Figures 3-5 through 3-8 have focused on a since this cross section tended to reflect the trends observed by other tran sport constants such as f, t and scattering matrix. Comparing actinide plots in Figures 3-5 and 3-6 it is clear that cross sect ion burnup trending is dependent not only on isotope, but also by energy group. Cross section deviation for Pu-240 was more apparent in group 2 relative to groups 1 and 3, however, the U-235 variation was m ore evident in group 3, relative to groups 1 and 2. The intensity of cross section burnup dependence was also much stronger with Pu-240 rela tive to U-235. The absorption cross section for Pu-240 starting from initial fuel concentration (no burnup) to di scharge varies approximately 250 barns. On the other hand, U-235 varied only 7 barns. Furthermore, the shape of the cross section trend (where apparent in energy group) is di fferent between Pu-240 and U-235. Th e Pu-240 trend is to start at higher cross section barn values and progress to lower barn va lues. The U-235 trend is the opposite starting lower and progressing to higher cross sec tion barn values. In general, examination of keynote fission products (Cs-137, Kr-85, Zr-95, etc) did not show a large dependency as a function of burnup, however two important poisons which have a large impact on reactivity management due vary strongly: Xe135 and Sm-149. From Figures 3-

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48 7 and 3-8 it is apparent that both fission products have very la rge therm al absorption cross sections (~1.4x106 barns for Xe-135 and 4.8x104 barns for Sm-149). Both fission products have very interesting trends within the first 3 GWd/MTHM of burnup. Note how the absorption cross section has a sharp drop with in the first 500 MWd/MTHM (a ~ 20,000 barns for Xe-135 and a ~ 500 barns for Sm-149). Following 500 MWd/MTHM, the absorption cross section increases ~ 85,000 barns for Xe-135 and ~1600 barn for Sm-149 in a in a sinusoidal manner. These kinds of observations along with the tr ends seen with U-235 and Pu-240 were very important in the following optimization step which streamlined th e PWR library from a rather bulky 46 library burnup points. 3.3 The PWR Library Optimization Study To perform the optimization study, a PENT RAN/PENBURN parametr ic burnup study was performed on the 3 wt % enriched Westinghouse OFA fuel pin unit cell model mimicking SCALE. Recall that library optimization is achieved by performing a burnup study on the system unit cell using the conservative burnup libra ry (i.e. 46 burnup library set points), followed by repeated studies using fewer library burnup poin ts. The actual procedure detailing how the burnup dependent cross sections are implemented within th e PENTRAN/PENBURN sequence has yet to be fully revealed, but this will be highl ighted shortly. At this time, it is important to note that throughout the burnup process, microscopic cross sections are updated following each burnup step utilizing the 3-group collapsed cross sections genera ted using SCALE5.1. The burnup scheme used for all studies was a 25 burn step sequence totaling to 1900 days of irradiation, or 64.6 GWd/MT HM burnup, assuming a power density of 34 MW/MTHM. Six reduced library data sets were compared rela tive to the reference burnup study set utilizing 46 burnup points. Table 3-2 describes the various data sets.

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49 An optimization criterion was developed in order to determine which reduced library set was the most efficient, yet still captured th e correct burnup dependency within a reasonable accuracy target. The optimization criterion was based on two factors. Firstly, the percent difference in discharge concentration (atom/ba rn/cm) for several major actinides and fission products was determined by comparing burnup runs using the 46 lib rary case and the N library case, where N ranged between 2, 3, 5, 7, 8, and 23. Base d on observation from the reference run, it appeared that Pu-240 and Xe -135 isotopes possessed the strongest cross section dependencies on burnup, therefore these nuclides were considered to be the most influential in the decision process. Secondly, percent mil (pcm) diffe rences were calculated for each PENTRAN eigenvalue calculation performed in the sequence, comparing keff for the reference 46 library burnup run with the N library burnup runs. Results for each optimization criterion are in Figures 3-9 through 3-12. Based on the percent dif ference criterion, it is clear from Figure 3-9 th at just two libraries are insufficient in capturing the proper burnup dependency for the actinides. As expected, Pu240 had the largest percent difference (-21.96%) be tween the reference 46 library run and the two library run. This is due to Pu-240s larg e dependence of cross-s ection as a function of burnup, mentioned in previous disc ussions. Note how the Uranium series, however, did not show substantial differences between using two libraries or 23 libraries (< 1%). This is a result of the series relatively flat trend in cross-section variation for uranium is otopes as a function of burnup. Surprisingly, despite the significant burnup dependence exhi bited by Xe-135, the percent difference in concentration between the 46 library run and two library run at discharge varied only by -2.72 %, as shown in Figure 3-10 Overall, it appears that shrinking the PWR library from 46 burnup points to 23 burnup points stil l leaves a library that is very conservative.

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50 Still, using a library with between 5 and 8 bur nup points seemed most appropriate; however, the second criterion (examination of PCM diffe rences) still needed examination. Examining plots of pcm difference in keff at each of the PENTRAN transport calculation points between the reference 46 library run and a lternative library runs reemphasized the idea that two libraries simply do not track cross se ction burnup dependencies pr operly. Differences in keff for the 2 and 3 library runs spanned betw een exact agreement early on in the burnup sequence, to pcm values ranging between 400 a nd 1000 pcm. Runs using 5, 7 and 8 libraries were typically within 200-250 pcm or less. As with the concentration crit erion, it appeared using a library between 5 and 8 burnup points was most appropriate in balancing development effort, computational efficiency, and accuracy. Based on the analysis, however, it does not appear that the PWR library is gaining higher accuracy in te rms of concentration differences or lower pcm differences in keff by using 7 or 8 libraries, t hus the 8 library case was el iminated as a candidate. When comparing the 5 and 7 library runs, actinide percen tage differences were of the same order of magnitude. Xe-135 concentration differences were slightly improved between models, thus toward to lean towards conservatism, the 7 libr ary run was selected yielding an optimum number of burnup points necessary to capture burnup dependencies usi ng points at 0, 0.459, 17.85, 26.35, 39.95, 51.85, and 67.15 GWd/MTHM. To generate the required libraries, four T-NE WT branch calculations were performed at each of the seven reference burnup points. This procedure created 28 cross section libraries, in addition to the seven libraries from the reference calculation, totaling to 35 libraries. Figures 313 through 3-18 shows the variations in isotope cross sections as a function of burnup and tem perature for all conditions modeled fo r selected actinides and fission products.

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51 Note from Figure 3-13 how increases in fuel tem per ature for U-235 shrink the group 3 (thermal) absorption probability. Also, in Figure 3-15, Pu-240 displayed the sam e trend for group 2, however, there was not as strong of a de pendency on temperature, decreasing ~ 50 barns between 700 K and 2500 K. Variations in thermal absorption cro ss-section of U-235 ( Figure 313) were in excess of 100 barns over the librarys range of temperature, while Pu-239s therm al absorption cross section ( Figure 3-14 ) shifted nearly 200 barns. The group 3 (therm al group) cross-section trends for Pu-239 we re different from the other ac tinides presented, however, since absorption probabilities grew as fuel temperatures increased. This can be correlated to the strong resonance absorption peak observed at ~ 0.270 eV, shown in Figure 3-19 Investigation of Pu-239s absorption cross-section for group 2, however, did show that Pu-239 followed the same tem perature trend as Pu-240 for group 2, where cross sections values dropped with increasing fuel temperatur e. Xe-135s abso rption probability ( Figure 3-16 ) dem onstrated a very strong dependence on te mperature, decreasing by over 500,000 barns from 700 K to 2500 K, while Sm-149s cross section ( Figure 3-17 ) varied nearly 8000 barns. Conversely, Kr-85 ( Figure 3-18 ) showed very little dependenc e varying only 0.3 barns over the wide tem perature range. The PWR library contains 240 isotopes deri ved from the T-DEPL/T-NEWT procedure, however there still remained 14 isotopes (A m-244, Ag-110m, Np-235, Np-236, Pu-243, As-77, Br-82, Gd-159, I-133, Mo-98, Mo-100, Pm-145, Pm146, Pm-150) that could not be extracted from SCALE. As mentioned prev iously, SCALE users are only able to extract cross sections which are present within the master library, and 14 of the isotopes were missing. In order to fill the cross section void, NJOY99.0 was used. The fo llowing section will discuss the NJOY code package.

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52 3.4 The NJOY Procedure NJOY99.0 is a comprehensive computer code package that produces multigroup transport cross sections from evaluated nuclear data which is in the ENDF format. NJOY consists of a set of 24 modules, each designed to perform a sp ecific task. The following seven NJOY modules were used to generate the missing SCALE cr oss section data for the PENTRAN/PENBURN suite: RECONRReads an ENDF tape and produces a co mmon energy grid for all reactions such that all cross sections can be obtained to within a specified tolerance by linear interpolation. Creates point wise cross-sections which are written onto a point-ENDF (PENDF) tape for future use. BROADRReads a PENDF tape and Doppler-broad ens the data using the accurate pointkernel method. After broadening and thinning, the summation cross sections (total, inelastic) are written to a new PENDF tape for future use. UNRESRProduces effective self-s hielded pointwise cross s ections, versus energy and background cross-section in the unresolved ra nge. This is done for each temperature produced by BROADR, using aver age resonance parameters fr om the ENDF evaluation. Results are once again added to the PENDF tape. THERMRProduces pointwise cross sections in the thermal range. Energy to energy incoherent inelastic scattering matrices can be computed for free-ga s scattering or for bound scattering using a pre-co mputed scattering law S( ) in ENDF format.. GROUPRProcesses the pointwise cr oss sections modified by the modules described above into multigroup form, based on a specific group structure and weighting function. NJOY has

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53 the option of using a built-in or custom wei ghting function for cross section group collapsing. Resulting file referred to as a GENDF tape. PLOTR/VIEWRCreates a postscript file for a vi sual validation that a proper group collapse has been performed relative to the pointwise data. MATXSRFormats multi-group data from GEND F file and converts GENDF to MATXS format which is suitable for separate code called TRANSX which is capable of producing the desired ANISN library format for PENTRAN/PENBURN. As hinted by the last module description, a final code called TR ANSX, a reformatting code, was used to post-process NJOY data and produce ANISN readable libraries. The entire procedure is shown in Figure 3-20 As com pared to the SCALE procedure, the NJOY procedure devised for PENTRAN/PENBURN cross section generation is a less rigorous approach for cross section treatment. This is mainly due to the following reasons: Collapsing procedure: With T-DEPL/T-NEWT control sequences, the SCALE master library is collapsed from pointwise data to a 238 group library based on a weighting function for thermal, epithermal resonance, and fission en ergies (Maxwellian; 1/ E; fission spectrum). A problem dependent, collapsed working library is then generated from the 238 group master library, based on the fuel pin unit cell flux solution from the NEWT transport code. Alternatively, the NJOY procedure collapses directly from pointwise data to the same SCALE collapsed group structure using a light water reactor weighting function. Several options were available (constant, 1/E, fast sp ectrum, etc) however this weighting function was selected because this closely matches the spectrum observed in a PWR system. As a

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54 result, cross section treatment is more generi c for a light water reactor system relative to SCALEs problem specific treatment. Self-shielding treatment: The UNRESR unresolved resonance self-shielding module of NJOY is based on the B0 approximation, where for large homogeneous systems and narrow resonances, the weighting flux is assumed to follow the form (MacFarlane and Kidman, 1977): i to tEC E EC E )( )( )( ) ( (3-2) The weighting function, C ( E ), is assumed to be a sl owly varying function of E and t( E ) is the total macroscopic cross section for the system. Note that t( E ) can be further decomposed such that the effect of other isotopes within a system is represented by o, referred to as a background cross section and t i( E ) is the total cross section for the isotope of interest. Based on the formulation, note how the background cross section can effectively control the flux depression around a resonance. If o << t(E), the weighting flux shows a dip and a strong self-shielding effect is experienced here. If o >>t(E), the weighting flux is pr oportional to C(E) and no selfshielding effect is experienced. This treatment is referred to as infinite dilution (MacFarlane and Muir, 2000). Considering the 14 isotopes proc essed are generally of low concentration with relatively weak unresolved resonance peaks, the infinite dilution treatment was applied. SCALEs T-DEPL procedure handles unresolve d resonance processi ng internally through BONAMI. SCALE can handle both homogeneous and heterogeneous effects related to resonance self-shielding processing through BONAMI. 3.5 The INTERP-XS Code Although a user could rerun the entire SCALE/NJOY procedure for a specific temperature/burnup case not covere d by reference or branch calcula tions, one could try to avoid

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55 this situation since this procedure can be very time c onsuming. Hence, provided with a problem dependent cross section library/database from SCALE and NJOY procedures, an interpolator code was needed in order to generate cross-section files seamlessly with the PENTRAN/PENBURN suite. The INTERP-XS code was created to handle this task. INTERP-XS works with library files generate d with the SCALE and NJOY procedures in order to generate burnup and temperature (fuel/m oderator) dependent cross section files based on user supplied interpolation points. The followi ng subsections will detail code development, library linking with INTER P-XS, and validation. 3.5.1 Code Development The underlying idea for the INTERP-XS code wa s to consider each cr oss section library file, representing a specific burnup a nd fuel/moderator temperature, as a state point. One could then interpolate between two files (or state points) in order to gene rate a desired system condition. Provided with a suffi cient number of burnup/temper ature points (as discussed in previous sections), a simple linear interpolation should suffi ce to capture dependencies in between state points. The INTERP-XS code provides two di fferent interpolation options: Interpolate based on user supplied system burnup at a pre-computed fuel/moderator temperature for a specific reactor library. Interpolate based on user supplied system burnup and fuel/moderator temperatures for a specific reactor library. The only inputs required by the user are: interpolation choice (1 or 2), system burnup (GWd/MTHM), fuel temperature (K), moderator temperature (K), and library identifier (i.e. PWR library, Magnox library, etc). By comparing the user supplied information with a library

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56 descriptor file ( xslist.txt) which details the burnup and te mperature points available for the library, INTERP-XS extracts the necessary files from the library database and performs burnup and temperature interpolation. A code overview is supplied in Figure 3-21 Boxes in blue are library files for fuel isotope interpolation, while boxes in red are library files for m oderator isotope interpolation. Fi les that are coupled together for ei ther burnup or temperature dependent interpolation are connected by a bracket. Files with an int in the file name are intermediate files that contain interpolated results for the next calculation in line. The final output interpolated cross section file is in purple. Note how option 2 requires twice as many files and an extra interpolation step as compared to option 1 sin ce interpolation is based on burnup and temperature as opposed to solely burnup. As mentioned previously, a lin ear interpolation subroutine was implemented to generate cross sections based upon two st ate point files. For example, assume the user chooses INTERPXS option 1, where burnup interpolation is strictly performed. Cross sections are generated using the following formulation: 1, 1 12 1,2, *)(i ii iBB BB (3-3) Where, B1 refers to burnup state point of cross section file 1 (GWd/MHTM). i,1 refers to corresponding cross section for isotope i at state point B1 (barn). B2 refers to burnup state point of cross section file 2 (GWd/MHTM). i,2 refers to corresponding cross section for isotope i at state point B2 (barn). B* refers to user supplied burnup stat e point of interest (GWd/MHTM). i refers to corresponding interpol ated cross section for isotope i at state point B*(barn). B1< B*< B2 If temperature based interpola tion was being performed, the same formulation in Equation 3-3 would be used except burnup set points would be replaced with temperature set points.

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57 3.5.2 Cross Section Library Linking For INTERP-XS to extract the correct library fi les based on user input, a library descriptor file was needed to contain information for each r eactor system detailing the library file structure for archiving cross section data in addition to the burnup and fuel/moderator state points. This responsibility was given to the xslist.txt file (Appendix D). This file contains the following library format information for each reactor system: lib rary prefix identifier (up to 3 characters in length), library descriptor commen t (up to 30 characters in length) number of isotopes in library, number of collapsed cross-section groups, Legendre order, and cross section table length. An xslist.txt input of particular importance to the us er is the library prefix identifier. The library prefix identifier is a character ID whic h is used by all file names making up a particular reactor system library. In general, library cr oss section file names are formatted as follows: LibID _TempID _BrnupID .xsc The LibID is effectively the library prefix identifier. For example, the PWR library uses a library prefix of t for all of its cross section files. (The TempID and BrnupID will be discussed in the next paragrap h.) Recall that the library identifier is one of five user inputs required ( Figure 3-21 ), s ince the user is responsible for selecting the reactor system from which the interpolation is based upon. As a result, a new user should examine the xslist.txt file to determine which library character prefix to select. Additional library descriptor information within the xslist.txt file includes: average system neutron energy (MeV), fuel and moderator te mperature set points (K), burnup set points (GWd/MTHM), and SCALE material IDs identifyi ng fuel and moderator isotopes. Note that coupled with each fuel/moderator temperature and burnup set point is an associated integer ID, corresponding to the previously mentioned TempID and BrnupID For example, assume for the PWR library (library prefix id entifier of t) that a fuel/m oderator temperature of 1000/600 K corresponds to a TempID integer of 4 and a burnup of 2.5 GWd/MTHM corresponds to a

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58 BrnupID integer of 10. The cross section file na me corresponding to this state point is t_4_10.xsc. With this file name arrangement, the user can easily identify the state point each library file corresponds to ba se purely on the file name. Table 3-3 describes the LibID, TempID and BrnupID for the PW R library. Given the xslist.txt file, INTERP-XS iteratively compar es the user supplied fuel/moderator temperatures and burnup set points with the library s reference set points and determines which library files are needed to pe rform interpolation. Error messa ges are supplied to the users console if requested temperature or burnup set po ints exceed the boundaries of the library. A log file ( run.log ) is also supplied, indicating reactor library selected, in terpolation option, interpolation values, and files that were used for interpolation 3.5.3 Comparison of INTERP-XS with SCALE/NJOY Procedure To examine the accuracy of interpolated cross sections generated from the PWR library of INTERP-XS, two different comparat ive studies were performed: Cross sections generated at two ne w branch fuel/moderator temperatures (based upon the original reference depletion run of Tfuel=1000 K and Tmod=600 K) using the SCALE/NJOY PWR model were compared to cross sections generated from INTERP-XS with the PWR library data set. Cross sections generated using two new reference cases with the SCALE/NJOY PWR model were compared to cross sections generated from INTERP-XS with the PWR library which, recall, used the original reference case of Tfuel=1000 K and Tmod=600K. NOTE: Both comparative studies used the same fuel/moderator temperature combinations: Tfuel=950K/Tmod=550K & Tfuel=1050K/Tmod=600K

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59 As a reminder, a reference calculation is the ba se depletion calculation under which typical operating parameters such as power density, initial fuel enrichment, fuel temperature, and moderator temperature are assume d. Branch calculations spawn from the reference case, since isotopic compositions from each optimized burn step of the reference calculation are saved and used for the branch calculation. The branch calc ulation is a standalone eigenvalue calculation which performs transport analysis on the syst em of interest at new branch fuel/moderator temperatures. The purpose of the first study was to demons trate how well cross sections generated from INTERP-XS using a new specified burnup/temperature combination (provided that the original reference case of Tfuel=1000 K and Tmod=600 K still applies) comp are with cross sections generated using the same burnup/temperature co mbination in SCALE/NJOY. The second study, on the other hand, was performed to show how well cross sections generated from a new SCALE/NJOY reference case (Tfuel=950K/Tmod=550K & Tfuel=1050K/Tmod=600K ) compare with cross sections generate d from INTERP-XS PWR, which use a different reference case Tfuel=1000K/Tmod=600K. Although percent differences have been calculated betwee n INTERP-XS and SCALE/NJOY procedures for all isotopes, transport cross-section probabilities ( t, a, f, scattering matrix), and neutron energy groups, a summary of results repr esenting general cross section trends is presented in the following tables. Tables 3-4 through 3-11 display percent differences between IN TERP-XS and for one of the two new SCALE/NJOY branch calculations (Tfuel=950K/Tmod=550K) for several isotope cross sect ions at various stages of burnup. Tables 312 through 3-19 display percent differences betw een INTERP-XS and the final SCALE/NJOY

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60 branch calculations (Tfuel=1050K/Tmod=600K) for several isotope cross sections at various stages of burnup. INTERP-XS performed very well for actinides, fission products, and moderator isotopes in the first branch calculation. For example, maximum percent differences for U-235 and U-238 over the range of burnup were -0.5 % and -0.08 %, respectively at 67.15 GWd/MTHM for group 2. Percent differences for Pu-240, Xe-135, and Sm -149 were generally larger (maximum percent difference of 2.7 %) as compared to other isotopes presented; how ever this is expected since previous analysis showed how they are strongl y dependent on burnup. Moderator cross sections generated by INTERP-XS performed extremely we ll, with maximum percent differences around -0.1 % for H-1 and 0.02% for O-16 at 67.15 GWd/MT HM. Overall, the ge neral trend for all isotopes cross sections was that differences tended to increase w ith burnup, and were found to be a maximum at the end library burnup point (67.15 GWd/MTHM). Results from the second branch calculat ion comparison with INTERP-XS showed good agreement overall for actinides, fission produc ts, and moderator isot opes, however, percent differences were relatively higher than in th e first comparison. For example, the maximum percent difference for U-235 was around -8.9 % as compared to -0.5%. Percent differences for Pu-240, Xe-135, and Sm-149 were also relatively larg er as compared to other isotopes presented; with maximum percent differe nces around 12 %. Moderator cross sections generated by INTERP-XS performed very well, with maximum pe rcent differences less than 1 % for H-1 and O-16 at 67.15 GWd/MTHM. The larger percent differences relative to the first branch comparison experienced by some actinides and fission products are more than likely attributed to INTERP-XS interpolating between a two cross section libraries that have rela tively larger spread in temperature difference.

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61 In this interpolation situation, one library used a fuel temper ature of 1000 K, while the second cross section library used a fuel temperature of 2500 K. There is a large spread between the two library temperature set points, (T=1500 K) when compared to other library set points of (700 K, 800 K, 900 K) which have differences of only 100 K. There may be a temperature dependence between 1000 K and 2500 K that is not being captured with two libraries. Tables 3-20 through 3-27 display percent differences be tween INTERPXS and for one of the two new SCALE/NJOY reference calculations (Tfuel=950K/Tmod=550K) for several isotope cross sections at vari ous stages of burnup. Tables 3-28 through 3-35 display percent differences between IN TERP-XS and the final SCALE/NJOY reference calculation (Tfuel=1050K/Tmod=600K) for several isotope cross sect ions at various stages of burnup. Based on the first reference calculation co mparison, INTERP-XS performed extremely well for actinides, fission products, and moderato r isotopes. For exam ple, maximum percent differences for U-235 and U-238 over the range of burnups were -1.7 % and -0.2 %, respectively at 67.15 GWd/MTHM for group 3. Percent diffe rences for Pu-240, Xe-135, and Sm-149 were generally larger as compared to other isotopes pres ented; however this is expected since previous analysis showed how they are strongly de pendent on burnup. Moderator cross sections generated by INTERP-XS performed very well, w ith maximum percent differences less than 1 % for H-1 and O-16 at 67.15 GWd/MTHM. INTERP-XS also performed we ll for actinides, fission produc ts, and moderator isotopes, however percent differences were higher in this case relative to the first SCALE/NJOY reference calculation. For example, the maximum percen t difference for U-235 was around -9.2 %, as compared to -1.7% at 67.15 GWd/MTHM for group 3. Percent differences for Pu-240, Xe-135, and Sm-149 were also relatively larger as compar ed to other isotopes presented; with maximum

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62 percent differences around 11.5 %. As with the branch calculation at Tfuel=1050K, this is caused by a result of INTERP-XS inter polating between two cr oss section libraries that have larger deviations in fuel temperature. Moderator cr oss sections generated by INTERP-XS performed very well, with maximum percent differences less than 1 % for H-1 and O-16 at 67.15 GWd/MTHM. A key point related to th e INTERP-XS comparison with the SCALE/NJOY reference calculation (Tfuel=950K,1050 K) cross sections is that th e INTERP-XS PWR libraries were built with a reference depletion run of Tfuel=1000 K. Although the referen ce depletion runs differed by 50 K from SCALEs depletion runs, the INTERP -XS cross section libra ries still performed well, with maximum percent differences ar ound 10 % at later bur nup library points.

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63 Table 3-1. Summary of PWR operating para meters used for library generation Parameter Reference Branch 1 Branch 2 Branch 3 Branch 4 Power Density (MW/MTHM) 34.0 Fuel Temperature (K) 1000 700 800 900 2500 Moderator Temperature (K) 600 300 400 500 600 Moderator Density (g/cm3) 0.66118 1.0034 0.94513 0.84279 0.66118 Table 3-2. Summary of burnup data points for each library study Library Count 46 (Ref) 23 8 7 5 3 2 0 0 0 0 0 0 0 0 1 0.051 0.459 0.4590.4590.45933.1567.152 0.17 1.02 9.35 17.8517.8567.15 3 0.459 2.38 17.8526.3539.95 4 1.02 4.25 26.3539.9567.15 5 1.7 7.65 39.9551.85 6 2.38 11.05 51.8567.15 7 3.06 14.45 67.15 8 4.25 17.85 9 5.95 21.25 10 7.65 24.65 11 9.35 28.05 12 11.05 31.45 13 12.75 34.85 14 14.45 38.25 15 16.15 41.65 16 17.85 45.05 17 19.55 48.45 18 21.25 51.85 19 22.95 55.25 20 24.65 58.65 21 26.35 62.05 22 28.05 67.15 23 29.75 24 31.45 25 33.15 45 67.15 *** Burnup library points following number 26 increment in steps of 1.7 GWd/MTHM.

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64 Table 3-3. LibID TempID and BrnupID for PWR cross section library LibID Library Description TempID Fuel Temperature (K) Moderator Temperature (K) BrnupID Burnup (GWd/MTHM) t PWR, 3 wt % enriched UO2 1 700 300 0 0 2 800 400 3 0.0459 3 900 500 16 17.85 4 1000 600 21 26.35 5 2500 600 29 39.95 36 51.85 45 67.15 Table 3-4. Percent difference betw een U-235s total cross section ( t) generated by INTERP-XS and the SCALE/NJOY procedure for a branch calculation with Tfuel=950 K and Tmod=550 K Table 3-5. Percent differences betw een U-238s total cross section (t) generated by INTERP-XS and the SCALE/NJOY procedure for a branch calculation with Tfuel=950 K and Tmod=550 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 -0.008 -0.004 -0.004 -0.004 -0.004 -0.005 -0.005 2 -0.175 -0.151 -0.127 -0.111 -0.111 -0.095 -0.079 3 0 -0.009 -0.009 -0.009 -0.018 -0.028 -0.037 Table 3-6. Percent difference betwee n Pu-239s total cross section ( t) generated by INTERP-XS and the SCALE/NJOY procedure for a branch calculation with Tfuel=950 K and Tmod=550 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 -0.008 -0.004 -0.004 -0.004 -0.003 -0.003 -0.005 2 -0.249 -0.239 -0.3 -0.335 -0.403 -0.467 -0.542 3 0.271 0.302 0.2 0.219 0.266 0.302 0.347 t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 -0.01 -0.004 -0.004 -0.004 -0.004 -0.004 -0.004 2 -0.281 -0.251 -0.291 -0.325 -0.389 -0.453 -0.526 3 -0.046 -0.069 -0.054 -0.051 -0.062 -0.103 -0.162

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65 Table 3-7. Percent difference betwee n Pu-240s total cross section ( t) generated by INTERP-XS and the SCALE/NJOY procedure for a branch calculation with Tfuel=950 K and Tmod=550 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 -0.007 0.005 0.004 0.004 0.004 0.005 0.005 2 -0.799 0.762 1.201 1.64 2.169 2.45 2.754 3 0.129 0.129 0.163 0.163 0.152 0.136 0.121 Table 3-8. Percent difference betwee n Xe-135s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure fo r a branch calculation with Tfuel=950 K and Tmod=550 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 0.026 0.002 -0.003 -0.005 -0.007 -0.007 -0.009 2 -0.812 -0.802 -1.303 -1.56 -1.938 -2.217 -2.522 3 -0.385 -0.41 -0.385 -0.376 -0.403 -0.462 -0.547 Table 3-9. Percent difference betwee n Sm-149s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure fo r a branch calculation with Tfuel=950 K and Tmod=550 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 0.027 0.003 -0.002 -0.005 -0.006 -0.008 -0.006 2 -0.575 -0.549 -0.838 -0.995 -1.219 -1.4 -1.6 3 -0.59 -0.598 -0.589 -0.585 -0.61 -0.658 -0.734 Table 3-10. Percent difference betw een H-1s total cross section ( t) generated by INTERP-XS and the SCALE/NJOY procedure for a branch calculation with Tfuel=950 K and Tmod=550 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 0.064 0.014 0.007 0.004 0 0 0 2 -0.081 -0.034 -0.04 -0.054 -0.067 -0.088 -0.101 3 -0.099 -0.113 -0.105 -0.099 -0.11 -0.131 -0.16 Table 3-11. Percent difference betw een O-16s total cross section (t) generated by INTERP-XS and the SCALE/NJOY procedure for a branch calculation with Tfuel=950 K and Tmod=550 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 0.066 0.024 0.019 0.014 0.019 0.019 0.024 2 -0.01 0.003 0.008 0.01 0.013 0.013 0.015 3 -0.015 -0.015 -0.018 -0.015 -0.015 -0.018 -0.02

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66 Table 3-12. Percent difference betw een U-235s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure fo r a branch calculation with Tfuel=1050 K and Tmod=600 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 -0.066 -0.057 -0.055 -0.055 -0.055 -0.057 -0.059 2 -1.842 -1.783 -1.873 -1.93 -2.039 -2.153 -2.314 3 -8.205 -8.245 -8.536 -8.603 -8.71 -8.816 -8.941 Table 3-13. Percent difference betw een U-238s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure fo r a branch calculation with Tfuel=1050 K and Tmod=600 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 -0.05 -0.044 -0.043 -0.043 -0.043 -0.045 -0.046 2 -0.895 -0.84 -0.79 -0.773 -0.748 -0.731 -0.715 3 -1.12 -1.121 -1.155 -1.172 -1.198 -1.207 -1.225 Table 3-14. Percent difference between Pu-239s total cross section (t) generated by INTERPXS and the SCALE/NJOY procedure fo r a branch calculation with Tfuel=1050 K and Tmod=600 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 -0.055 -0.048 -0.047 -0.047 -0.048 -0.048 -0.049 2 -1.585 -1.552 -1.815 -1.91 -2.064 -2.195 -2.378 3 7.514 7.494 6.006 5.874 5.851 5.89 5.938 Table 3-15. Percent difference between Pu-240s total cross section (t) generated by INTERPXS and the SCALE/NJOY procedure for a branch calculation with Tfuel=1050 K and Tmod=600 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 -0.043 -0.039 -0.039 -0.039 -0.041 -0.041 -0.043 2 -5.025 -4.972 -8.917 10.056 11.289 11.974 12.708 3 -3.585 -3.515 -3.335 -3.358 -3.42 -3.469 -3.501 Table 3-16. Percent difference between Xe-135s total cross section (t) generated by INTERPXS and the SCALE/NJOY procedure fo r a branch calculation with Tfuel=950 K and Tmod=600 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 0.181 0.132 0.127 0.123 0.12 0.12 0.123 2 -4.744 -4.73 -6.87 -7.649 -8.721 -9.498 -10.339 3 -11.263 -11.404 -11.196 -11.148 -11.154 -11.235 -11.386

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67 Table 3-17. Percent difference between Sm-149s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure fo r a branch calculation with Tfuel=1050 K and Tmod=600 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 0.179 0.132 0.127 0.122 0.121 0.121 0.122 2 -3.512 -3.504 -4.759 -5.214 -5.819 -6.27 -6.78 3 -8.349 -8.453 -8.152 -8.071 -8.028 -8.074 -8.195 Table 3-18. Percent difference betw een H-1s total cross section ( t) generated by INTERP-XS and the SCALE/NJOY procedure for a branch calculation with Tfuel=1050 K and Tmod=600 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 0 0 0 0 0 0 0 2 0.04 0.04 0.04 0.04 0.04 0.04 0.047 3 0.061 0.061 0.063 0.066 0.068 0.068 0.068 Table 3-19. Percent difference betw een O-16s total cross section (t) generated by INTERP-XS and the SCALE/NJOY procedure for a branch calculation with Tfuel=1050 K and Tmod=600 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 0 0 0 0 0 0 0 2 0 0 -0.003 0 -0.003 0 -0.003 3 0.005 0.005 0.003 0.005 0.005 0.005 0.005 Table 3-20. Percent difference betw een U-235s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=950 K and Tmod=550 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 -0.008 -0.012 -0.012 -0.014 -0.015 -0.014 -0.014 2 -0.289 -0.326 -0.512 -0.546 -0.58 -0.573 -0.533 3 -0.054 -0.098 -0.755 -1.052 -1.416 -1.604 -1.705

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68 Table 3-21. Percent differences betw een U-238s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=950 K and Tmod=550 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 -0.008 -0.01 -0.01 -0.011 -0.011 -0.011 -0.011 2 -0.024 -0.056 -0.064 -0.071 -0.087 -0.103 -0.118 3 0 -0.009 -0.092 -0.138 -0.193 -0.22 -0.229 Table 3-22. Percent difference between Pu-239s total cross section (t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=950 K and Tmod=550 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 -0.007 -0.011 -0.011 -0.011 -0.011 -0.011 -0.012 2 -0.259 -0.279 -0.547 -0.618 -0.71 -0.758 -0.772 3 0.271 0.27 0.052 0.035 -0.009 -0.062 -0.142 Table 3-23. Percent difference between Pu-240s total cross section (t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=950 K and Tmod=550 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 -0.007 -0.008 -0.007 -0.008 -0.008 -0.009 -0.009 2 -0.872 -0.969 -4.39 -4.041 -3.935 -4.365 -5.139 3 0.129 0.129 0.092 0.056 0.005 -0.01 0 Table 3-24. Percent difference between Xe-135s total cross section (t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=950 K and Tmod=550 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 0.022 0.048 0.045 0.048 0.051 0.053 0.048 2 -0.886 -0.928 -1.756 -1.807 -1.874 -1.964 -2.089 3 -0.385 -0.474 -1.324 -1.694 -2.16 -2.39 -2.519 Table 3-25. Percent difference between Sm-149s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=950 K and Tmod=550 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 0.024 0.047 0.045 0.047 0.048 0.048 0.048 2 -0.636 -0.691 -1.264 -1.318 -1.365 -1.42 -1.482 3 -0.592 -0.692 -1.42 -1.739 -2.132 -2.332 -2.454

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69 Table 3-26. Percent difference betw een H-1s total cross section ( t) generated by INTERP-XS and the SCALE/NJOY procedure for a reference calculation with Tfuel=950 K and Tmod=550 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 0.057 0.111 0.104 0.107 0.115 0.115 0.108 2 -0.074 -0.128 -0.168 -0.175 -0.175 -0.175 -0.169 3 -0.105 -0.129 -0.431 -0.566 -0.744 -0.844 -0.899 Table 3-27. Percent difference betw een O-16s total cross section (t) generated by INTERP-XS and the SCALE/NJOY procedure for a reference calculation with Tfuel=950 K and Tmod=550 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 0.061 0.094 0.09 0.09 0.094 0.094 0.085 2 -0.013 -0.025 -0.028 -0.028 -0.028 -0.03 -0.033 3 -0.015 -0.015 -0.038 -0.045 -0.058 -0.065 -0.068 Table 3-28. Percent difference betw een U-235s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=1050 K and Tmod=600 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 -0.041 -0.041 -0.041 -0.043 -0.043 -0.044 -0.044 2 -1.186 -1.193 -1.436 -1.493 -1.559 -1.595 -1.626 3 -7.155 -7.184 -8.068 -8.408 -8.827 -9.054 -9.195 Table 3-29. Percent difference betw een U-238s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=1050 K and Tmod=600 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 -0.033 -0.031 -0.031 -0.033 -0.033 -0.034 -0.034 2 -0.493 -0.485 -0.476 -0.475 -0.474 -0.481 -0.488 3 -0.965 -0.966 -1.082 -1.136 -1.207 -1.243 -1.261 Table 3-30. Percent difference between Pu-239s total cross section (t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=1050 K and Tmod=600 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 -0.034 -0.034 -0.034 -0.036 -0.037 -0.037 -0.037 2 -1.025 -1.026 -1.374 -1.474 -1.616 -1.712 -1.808 3 6.491 6.39 5.302 5.231 5.183 5.144 5.085

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70 Table 3-31. Percent difference between Pu-240s total cross section (t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=1050 K and Tmod=600 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 -0.028 -0.027 -0.028 -0.028 -0.03 -0.03 -0.031 2 -3.153 -3.22 -9.497 -9.653 -9.957 -10.562 -11.52 3 -3.31 -3.24 -3.233 -3.314 -3.435 -3.483 -3.491 Table 3-32. Percent difference between Xe-135s total cross section (t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=950 K and Tmod=600 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 0.113 0.115 0.113 0.115 0.117 0.117 0.115 2 -2.837 -2.875 -4.935 -5.365 -5.938 -6.388 -6.908 3 -9.683 -9.799 -10.404 -10.702 -11.093 -11.316 -11.484 Table 3-33. Percent difference between Sm-149s total cross section ( t) generated by INTERPXS and the SCALE/NJOY procedure for a reference calculation with Tfuel=1050 K and Tmod=600 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 0.113 0.113 0.111 0.111 0.115 0.115 0.113 2 -2.17 -2.225 -3.516 -3.781 -4.114 -4.366 -4.656 3 -6.913 -7.019 -7.407 -7.615 -7.901 -8.078 -8.223 Table 3-34. Percent difference betw een H-1s total cross section ( t) generated by INTERP-XS and the SCALE/NJOY procedure for a reference calculation with Tfuel=1050 K and Tmod=600 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 -0.171 -0.068 -0.061 -0.054 -0.043 -0.047 -0.054 2 0.249 0.148 0.121 0.135 0.155 0.175 0.209 3 0.759 0.767 0.466 0.33 0.166 0.097 0.084 Table 3-35. Percent difference betw een O-16s total cross section (t) generated by INTERP-XS and the SCALE/NJOY procedure for a reference calculation with Tfuel=1050 K and Tmod=600 K t Burnup (GWd/MTHM) Group 0 0.459 17.85 26.35 39.95 51.85 67.15 1 -0.165 -0.089 -0.085 -0.08 -0.08 -0.085 -0.094 2 0.025 0 -0.01 -0.01 -0.015 -0.015 -0.02 3 0.05 0.05 0.03 0.023 0.013 0.008 0.008

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71 Figure 3-1. Pointwise absorption cross section data for U-238 (KAERI, 2000) Figure 3-2. Temperature comparison of Pu-240 (n,gamma) cross section

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72 Figure 3-3. Generalized SCALE5.1 cr oss section generation procedure Figure 3-4. The T-DEPL (left) and T-NEWT (right) control sequences

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73 Figure 3-5. Burnup dependency of U-235 absorp tion cross-section for reference case (E1upper=20 MeV, E2upper=1.01 MeV, E3upper=0.625 eV) Figure 3-6. Burnup dependency of Pu-240 absorp tion cross-section for reference case (E1upper=20 MeV, E2upper=1.01 MeV, E3upper=0.625 eV)

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74 Figure 3-7. Burnup dependency of Xe-135 thermal absorption cross-section for reference case (E1upper=20 MeV, E2upper=1.01 MeV, E3upper=0.625 eV) Figure 3-8. Burnup dependency of Sm-149 thermal absorption cross-section for reference case (E1upper=20 MeV, E2upper=1.01 MeV, E3upper=0.625 eV)

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75 Figure 3-9. Percent difference in actinide concentra tions (atom/barn/cm) after 64.6 GWd/MTHM between reference 46 library burnup run and 2, 3, 5, 7, 8 and 23 library burnup runs Figure 3-10. Percent difference in Xe-135 concentrations (ato m/barn/cm) after 64.6 GWd/MTHM between reference 46 library burnup run and 2, 3, 5, 7, 8 and 23 library burnup runs

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76 Figure 3-11. Difference in computed pcm for keff between reference 46 library burnup run and 2, 3, 5, 7, 8 and 23 library burnup runs Figure 3-12. Difference in computed pcm for keff between reference 46 library burnup run an 5, 7, and 8 library burnup runs

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77 A B Figure 3-13. The U-235 absorption cross sec tion burnup and temperat ure dependencies A) Contour lines B) 3-D representation

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78 A B Figure 3-14. The Pu-239 absorption cross sec tion burnup and temperature dependencies A) Contour lines B) 3-D representation

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79 A B Figure 3-15. The Pu-240 absorption cross sec tion burnup and temperature dependencies A) Contour lines B) 3-D representation

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80 A B Figure 3-16. The Xe-135 absorption cross sec tion burnup and temperature dependencies A) Contour lines B) 3-D representation

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81 A B Figure 3-17. The Sm-149 absorption cross se ction burnup and temperature dependencies A) Contour lines B) 3-D representation

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82 A B Figure 3-18. The Kr-85 absorption cross sec tion burnup and temperat ure dependencies A) Contour lines B) 3-D representation

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83 Figure 3-19. Pointwise absorption cross section data for Pu-239 (KAERI, 2000) Figure 3-20. The NJOY/TRANSX procedure

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84 Figure 3-21. The INTERP-XS flowchart

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85 CHAPTER 4 THE 3-D PENTRAN/PENBURN BURNUP ANALYSIS OF 17X17 PWR ASSEMBLY Beginning in June 2007, PENTRAN/PENBURN testing had been lim ited to simple uranium fuel pin fuel depletion studies since the burnup package was still in the developmental stages. A larger PENTRAN model containing seve ral hundred depletion zone s, such as what is required for detailed analysis of a full size co mmercial reactor fuel assembly, was needed to demonstrate 3-D burnup effects captured by PENBURN. A Westinghouse 17x17 PWR fuel assembly was selected as the candidate design. Initially, studies were performed on a fuel pin unit cell model. Naturally, the unit cell model was then expanded to full assembly analysis. The following sections will detail the entire de velopment of the PENT RAN/PENBURN modeling, highlighting cross section procedures use d, PENTRAN mesh development and transport analysis, and finally ending with burnup results. 4.1 Assembly Specifications The Westinghouse OFA design ( Figure 4-1 ) has several different fu el enrichm ent options, spanning from 2.0 wt% up to 5.0 wt % U-235 enrichment. The 3 wt% enriched UO2 fuel design was selected for burnup analysis. Research on other PWR computationa l burnup studies showed that typical operating temperatur es selected for fuel, clad, and moderator are 1000 K, 620 K, and 600 K, respectively (Wagner, 2001). Given that typical PWRs operate at around ~2250 psi, coupling the pressure and temperature with NIST fluid property tables determined the water moderator density to be 0.66118 g/cm3. Soluble boron concentrations were not considered for this analysis, nor were control rods, guide tubes, or any other type of instrumentation. Note by opting to simplify the PENTRAN transport model through omission of guid e tubes in water hole locations, the moderator ratio has been arti ficially increased in these regions. Tables 4-1 and 4-2 provide assembly specifications along with fuel com position selected for analysis.

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86 For an 800 MWe PWR plant with a thermal efficiency between 0.25-0.30, the thermal power output required from the reactor core is around 3000 MWth. Provided that reactors typically have around 200 assemb lies with 264 fuel rods per a ssembly, given they are of Westinghouse OFA design, this equates to 86.5 MT of uranium metal fuel. With this information, an average specific power was sel ected to be 34 MW/MTHM. This compares well with specific powers pr ovided in literature. 4.2 Unit Cell Analysis The fundamental element composing a nuclear assembly is the fuel pin surrounded by moderator ( Figure 4-2 ). Commonly as an initial step in reactor assem bly analysis, a unit cell model representing an infinite lattice of fuel pins is analyzed. Cross-sections for a heterogeneous, 3 wt % enriched fuel pin un it cell model were genera ted using SCALE5.1s TNEWT control procedure, discussed in Chapte r 2. As a reminder, the T-NEWT procedure generates a cross section set based on the initial fuel c oncentrations, specified in Table 4-2 The 238 group ENDF/B-VI based AMPX library was select ed as the m aster library from which to collapse a three group structure in order to generate cross sections with a P1 Legendre order. A three group neutron energy structure (E1 upper limit=20 MeV, E2 upper limit=1.01 MeV, E3 upper limit=0.625eV) was chosen to match the structure used by SCALE5.1 in the ORIGEN-S depletion module; this was performed to enable future comparisons of burnup with PENBURN. For the NEWT 2-D deterministic transport solution which will collapse the 238 group working library to 3 groups, an S8 quadrature was selected along with specu lar reflective boundary conditions on all model external boundaries. 4.2.1 Eigenvalue Study Once cross-sections were formulated, a comparative eigenvalue study was performed between PENTRAN and SCALE in order to estimate how well the collapsed cross section set

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87 performed within the PENTRAN model. Whenever possible, transport model settings in PENTRAN were modified in order to match NEWTs transport model as close as possible. This included using specular reflective boundary conditions on all external PENTRAN model boundaries, including z boundaries, and matching S8 quadrature. This allowed the PENTRAN 3-D model to effectively become 2-D. One tr ansport difference which cannot be avoided is differencing scheme methodologies. NEWT solves the 2-D form of the LBE using the Extended Step Characteristic approach while PENTRAN solves the 3-D form of the LBE via Sn method with an adaptive differencing strategy. Resu lts from the comparison study performed on the heterogeneous models are found in Table 4-3 V ery good agreement in keff was observed, with 180 pcm difference between PENTRAN and NEWT. Average scalar flux values for fuel, gap, clad, and moderator regions we re also analyzed in order to determine percent differences betwee n NEWT and PENTRAN. Results summarized in Table 4-4 show good agreem ent in fuel gap and clad regions, with a maximum percent differences of -1.253 % in group 1 (1.01 MeV < E 20 MeV) for the fuel pellet region. The moderator region showed the largest differen ces between NEWT and PENTRAN, with group 3 having a percent difference 2.442 %. 4.2.2 Burnup Study Provided with confidence from the ei genvalue comparative study, burnup study was performed with the PENTRAN/PENBURN suite with the Westinghouse fuel pin model. Whenever possible, transport settings in NEWT and PENTRAN were chosen to be identical, including flux and eigenvalue conve rgence criteria being set to 5x10-5 and S8 quadrature. The same boundary conditions used for the eigenvalue calculation were also used for the burnup study. Since the PENTRAN/PENBURN suite had not incorporated INTERP-XS within the burnup procedure at the time of analysis, micros copic cross sections developed from the T-

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88 NEWT procedure were used throughout the bu rnup analysis. Although it is well known that energy per fission is isotope de pendent, at the time of analysis PENBURN had assumed a constant energy release per fissi on of 200 MeV/fission when scaling flux to system power, thus to account for this in SCALE, the parm=orgnflux option was chosen in the T-DEPL sequence to match flux scaling as close as possible with PE NBURN. The latest release of PENBURN has been modified in order to account for isotopic dependent fission energy. Finally, a 22 step burn sequence (cumulative burn times of 1, 2, 3, 4, 5, 6, 7, 10, 13, 16, 21, 26, 31, 51, 71, 91, 141, 191, 241, 341, 441, 541 days) with a constant specif ic power of 34 MW/MTHM was assumed. Three metrics were used to vali date PENBURN results with SCALE: Relative percent difference between PENBURN a nd SCALE results after the final burn step (t=541 d or 18.4 GWd/MTHM). Mean of relative percent differences between PENBURN and SCALE over the entire burnup sequence, ie: 100 11 S i SCALE ji PENBURN ji PENBURN ji jN N N S P (4-1) Where, S is the number of burn steps. Nij is the atom/barn/cm result of step i, nuclide j Examination of keff after each burn step. Table 4-5 summarizes the relative percent difference and average relative difference for Comparing burnup results at 541 days (column 2 of Table 4-5 ) showed good agreem ent between PENBURN and SCALE for the uraniu m series, Pu-239, Np-237, and Np-239. For Pu240 through Pu-242, differences were larger. PE NBURN results for fission products without decay precursors produced predominately from fi ssion (and not from the decay or absorption of

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89 another isotope) were within 10% or le ss of values reported by SCALE5.1. From Table 4-5 these nuclides include Kr-85, Zr-95, and Cs-137. Note how the absolute percent difference fo r selected isotopes (i e. U-235, U-237, Np-237) can be quite different from the average absolu te percent difference. This is caused by the variation of absolute percent difference as a function of burn step. Com paring PENBURN results with SCALE, a larger difference is experienced initially at early time steps, with better agreement later with increased burnup. After 18.4 GWd/MTHM of burnup, 52 % of nucli des (71 of 137) tracked in PENBURN were within + 30% of SCALE5.1s results, while 47% of nuclides (64 of 137) were within + 20% of SCALE5.1s results. In general, PENBURN is in good agreement when comparing uranium series with SCALE, however tended to overestimate the burn-in of the plutonium series compared with SCALE5.1. Of the nuclides outside the + 50% range of SCALE5.1, PENBURN appears to overestimate quantities of fission products that ha ve relatively large capture cross sections in thermal and resonance regions. The overestimate of these poison nuclides is also apparent when comparing PENTRAN/PENBURN keff results with SCALE5.1 at later time steps ( Table 4-6 ). Note how the keff values in Table 4-6 are at different tim e st eps. In SCALEs T-DEPL control sequence, a predictor-corrector approa ch is used where transport calculations are performed on anticipated concentrations at the mid-point of a given burnup step. Depletion is then performed in ORIGEN-S ove r the entire step based on the mid-way point transport solution and cross-sections. At the time of analysis the PENTRAN/PENBURN sequence did not have this methodology incorporated a nd a quasi-static burn forward Euler process was employed, where fluxes calculated at the beginning of the burn step remain constant throughout. This is the

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90 reason output keff results for SCALE are at the mi dway point of burn steps, while PENTRAN/PENBURN keff results are at the beginning of each burn step. It appears the PENTRAN/PENBURN sequence is tracking keff fairly well relative to SCALE, considering resonance changes in microscopic cross sections are currently not accoun ted for in PENBURN at the time of analysis. A comparison plot of keff for PENTRAN/PENBURN and SCALE can be found in Figure 4-3 It is im portant to take note of the large difference in co mputation time between the SCALE and PENTRAN/PENBURN burn sequences. The 22 burn step sequence for PENTRAN required approximately 35 minutes on 8 processors, while the same sequence for SCALE took approximately 776 minutes on one machine. In each burn step, the PENTRAN calculation was performed in parallel over eight processors (4 GB/processor) on the PENBURN team s BOHR cluster (24 processors, 4 GB per processor). Since SCALE5.1 cannot be executed in parallel, th e T-DEPL control sequence was performed on a single machine. Without paralle l capabilities in SCALEs transport, another reason for increased computation time comes from the computation of resonance and spatial selfshielding treatments on the microscopic cross-sec tions for each burn step. It is apparent from work presented in Chapter 2 that microscopic cro ss sections are sensitive to the differences in nuclide number densities that occur during the deplet ion of fuel with similar compositions. Note, however that DeHart recently demonstrated th at only when nuclide number densities approach 1.E-03, the infinite dilution model (used for PENBURN in this study) breaks down, and notable effects warranting res onance self shielding on micros copic cross sections require consideration for accurate nuclide concentrations (DeHart, 2007).

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91 Following the completion of INTERP-XS interpol ator code and PWR cross section library based on the 3 wt% enriched Westinghouse fuel pin, the PENTRAN/PENBURN study was performed again to determine whether any improvement would be observed using burnup dependent cross sections w ith the INTERP-XS sequence. Based on the results, the largest improvement was experienced with the Plutonium series, with percent differences re ducing as much as 29 % ( Figure 4-4 ). Recall from discussions in Chapter 2 that Pu-240 cross sections had a st rong dependency on burnup, even as early as 10 GWd/MTHM. Considering, Pu-240, Pu-241, and Pu-242 are linked within PENBURNs mapping matrix through neutron captur e, it is clear why such a dramatic improvement in results is experienced. Comparing plots of keff shown in Figures 4-3 and 4-5 note that the cr ossover of SCALE and PENTR AN keff plots experienced previously no longe r exists when bur nup dependent cross sections are used in PENTRAN. The keff results appear more stable and the relative difference of keff appears relatively constant. Prior studi es have attributed the difference in keff to numerical transport sweep (Manalo, 2008). Note if burnup corrected cross sections are not implemen ted, the fuel cycle length (determined by keff dropping below 1.0) is over estim ated by 2500 MWd/MTHM relative to when cross section dependencies are implemented ( Figure 4-6 ). This corresponds to nearly a 10% overestim ate of a typical fuel cycle by simply not accounting for burnup dependencies. Although broad group cross-sections with the same energy bin stru cture as ORIGEN-S were derived from SCALEs TNEWT control sequence, there still are several differences between the PENTRAN/PENBURN and T-DEPL control sequence. They include:

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92 Fission Yield Data SCALE5.1: Considers one neutron induced fission ener gy for fissionable isotopes. Example: U235 (thermal), U-238 (fast) PENBURN: Considers three neutron induced fission energies (thermal/epithermal/fast) for all fissionable isotopes. Transport Differencing Scheme SCALE5.1: NEWT uses the extended step-character istic approach to solve the 2-D LBE on polygon geometry. PENTRAN: PENTRAN uses an adaptive differencing strategy to solve the LBE in a 3-D blockadaptive Cartesian (hexahedral) geometry. Depletion Methodology SCALE5.1: Uses a predictor-corrector approach to fo recast cross-sections and flux values at a mid-point in burn step. The antici pated cross-sections and fluxes are then used for depletion. PENBURN: At the time of calculation, used a quasi-st atic forward Euler approach, where flux calculated at the beginni ng of the burn step remains constant over the step. Solution to Nuclide Chain Equations SCALE5.1: Uses matrix-exponential method. PENBURN: Uses the linear chain method. 4.2.3 Fuel Pin Homogenization In order to save on computational memory for the full assembly analysis which would model all 264 fuel rods, the heterogeneous fuel pi n (fuel/gap/clad) needed to be collapsed to one homogeneous region. By collapsing, each fuel pin could be modeled with a coarser mesh setting without having to be concerned with maintain ing gap and clad zones in transport modeling. Although common practice is to collapse a unit cell model into one homogeneous region with fuel, gap, clad, and moderator intermixed, it wa s desired to maintain model heterogeneity between pin and moderator regions.

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93 Homogenization was performed based on pin geometry ( Table 4-7 ), m eaning initial fuel, gap, and clad concentrations were weighted by each respective regi ons volume. A more rigorous homogenization procedure would be to weight concentrations by maintaining equal reaction rates between heterogeneous and homogeneous models; however for the purposes of this analysis, the simpler volume weighting was selected. By transforming the unit cell model from a he terogeneous to homoge neous fuel pin, x-y meshing for the model was reduced from 22x22 to 12x12. Fissile mass balance analysis performed with PENMSH-XP, a utility code wh ich generates PENTRAN inputs, demonstrated that target and model masses matc hed extremely well, as shown in Table 4-8 A final eigenvalue com parative study was pe rformed on the homogeneous unit cell model, similar to what was performed on the heterogeneous model. The same transport settings used for PENTRAN and SCALE in the hete rogeneous models, were also applied to the homogeneous cases. Eigenvalue results in Table 4-9 show reas onable agreement between SCALE and PENTRAN with differences more than likely at tributed to differencing schemes, however a significant drop in keff (~ 740 pcm) was shown between heterogeneous and homogeneous models. This is primarily caused by spreading the fuel and zirconium clad over a larger area through homogenization, allowing U238 capture resonances to have a larger impact while neutrons are slowing down. 4.3 Assembly Analysis With unit cell analysis complete, the next step was to expand the homogeneous fuel pin unit cell model into a 17x17 fuel assembly. The following subsections detail PENTRAN memory optimization analysis, pre-burnup st udy PENTRAN convergence analysis, and finally ending with 3-D burnup results.

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94 4.3.1 Memory Optimization Before PENTRAN/PENBURN analysis could begin a memory optimization study was needed in order to determine the optimum sc heme of building the PENTRAN geometry. For readers unfamiliar with PENTRAN, problem geomet ries are constructed in PENTRAN within a coarse mesh. Three dimensional Cartesian arrays of coarse meshes are formed and problem geometry is constructed within each coarse mesh. A fine mesh discretizing the problem geometry is then selected for each coarse mesh. As a result, there are endless ways of representing a problem geometry. For instan ce, the Westinghouse assemblys 17x17 fuel pin lattice structure could be grouped into one large coarse mesh (i .e, 1x1 x-y coarse mesh), a 17x17 coarse mesh array structure, or even something even finer like a 34x34 mesh where a quarter of a fuel pin is represented in each coarse mesh. PENTRAN users must keep in mind, however, that the number of fine meshes within a coarse mesh should be on the order of ~ 10,000 to 20,000, since significantly larger values can place an ov erload of message passing buffer requirements for a typical Beowulf cl uster architecture on a part icular coarse mesh; however, this is machine dependent, and too small values will lead to parallel inefficiency. Past experiences with PENTRAN transport modeling of large reactor sy stems placed single fuel pins within a very tight coarse mesh (Mock, 2006) where the side s of the coarse mesh boundary matched the diameter of the fuel pins ( Figure 4-7a ). This a llows the user to easily control meshing within the fuel and moderator regions. This methodology in addition to a pin grouping scheme, where an array of heterogeneously repres ented pins is grouped within a coarse mesh for transport computation ( Figure 4-7b ), were selected for testing. For PENTRAN m emory testing purposes, th e Westinghouse assembly was reduced to a quarter model since the purpose of analysis is to understand memory requirements based on meshing style. Parallel settings were identical in each test, such that coarse meshes in each

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95 problem were split over 4 proce ssors (PENTRAN parallel decom position vector of <-1,-1,-4>), with 4 GB/processor. The total number of fine mesh required to spatially discretize the problem was held to ~62,000. Results from PENTRAN processor log files sh owed that the conservative coarse mesh methodology approach required 478.5 MB per pr ocessor while the 3x3 pin grouping approach required 260.3 MB per processor. This is near ly around a factor of ~1.8 in memory savings by simply choosing coarse mesh scheme (B) over coarse mesh scheme A), in Figure 4-7 As a result, optimum PENTRAN parallel efficiency is achieved when more computational work (ie. problem fine mesh to be processed through di fferencing routines) is assigned per parallel process. Grouping a single pin per coarse mesh is a very inefficient way of splitting the problem, since it requires over 20 times the number of coarse mesh. 4.3.2 Assembly Convergence Analysis The full length 3-D PENTRAN model of the 17x17 Westinghouse assembly (using homogenized fuel pins) was developed usi ng the pin grouping methodology previously discussed. Although the model could have been reduced in computational size because of geometric symmetry, one goal was to demonstr ate the computational aptitudes of PENTRAN and PENBURN, thus the full length model wa s used for analysis. The PENTRAN model required 1472 coarse mesh (8x8x23) and 4,504,780 total fine meshes with a maximum fine mesh per coarse mesh setting of 6,480, and yielded a hy per-fine representation of each fuel pin in the assembly in 3-D. The same cross section set derived from the previous unit cell analysis was used for the fuel assembly. Recall these micros copic cross sections were derived from SCALEs T-NEWT procedure based on initial fuel concentrations for a specular-re flected unit cell model with a single continuous fuel zone. Although a more rigorou s cross section methodology could be used, where microscopic cross sections for specific fuel zone types could be derived, the

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96 purpose of the study is to demonstrate 3-D burnup effects captured by the PENTRAN/PENBURN suite; not to compare isot opic results with, say, Post Irradiation Examination (PIE) data from an actual spent fuel assembly (Manalo, 2008). Initially, PENTRAN global flux and eigenvalu e convergence criteria were set to 5x10-5 with maximum outer iteration cutoff of 100. An S8 quadrature was selected for analysis, creating 10 directions per octant in a unit sphere, and 80 total directions. Specul ar reflective conditions were applied to the assembly x-y external bound aries, however vacuum boundaries were applied to z external boundaries. Considering PWR reac tors typically have an upper and lower plenum mixing region, a 2 cm region (~ 3.5 therma l mean free paths) of water was added above and below the assembly model. A flat flux di stribution was used as the initial guess flux distribution. The PENTRAN analysis was executed on the PE NBURN teams BOHR cluster, which has six nodes, four processors per node (4 GB of RAM each) totaling to 96 GB of RAM. The fuel assembly problem was executed in parallel over a ll 24 processors, with 4 pr ocessors dedicated to angle, 3 to energy, and 2 to space (4x3x2=24) The problem was given 7200 minutes of dedicated time on the BOHR cluste r, with fluxes converged to 3x10-3 on the axial periphery, with higher convergence for interior cells. Figures 4-8 through 4-10 show the norm alized flux convergence achieved for groups 1, 2, and 3 respectively, for all 1,472 coarse mesh within the problem geometry. Note coarse mesh 1 through 64 represent the bottom z-level (containing solely water) spanning axially from 0 to 2 cm while coarse mesh 1,409 through 1,472 represent the top z-level (also containing solely water) spanning axially from 367.76 cm to 369.76 cm. Coarse mesh numbers ranging between 65 and 1408 contain fuel and moderator regions. Its apparent from the previous figures that group 2 dominated group convergence, especially

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97 towards the axial periphery region of the assemb ly. This is logical since there is a strong gradient in the flux due to vacuum boundary conditions, making the adaptive differencing schemes work harder in these situations. From Figures 4-9 and 4-10, there are clear horizontal lines spanning 64 coarse mesh in le ngth, showing the relatively flat convergence within a z-level. Analysis of the axial neutron flux distribution ( Figure 4-11 ) showed the e xpected cosine trend with p eaking occurring at the axial midplane due to axial vacuum boundary conditions and problem symmetry. It is apparent that group 2 is the dominant neutron energy group, contributing to 59.5 % of the total flux at the axia l centerline, while grou ps 1 and 3 contribute 19.5% and 20.0 % respectively. Recall a uniform fuel and moderator temperature profile was assumed (Tf=1000 K; Tm=600K) for analysis. In a real reac tor, the temperature may shift from core inlet to exit as much as 50 to 60 Kelvi n, thus the smooth cosine may become slightly skewed. Figures 4-11 and 4-12 also provided confidence in the initial transport solution. Note how the peaks an d valleys of groups 1 and 3 correlate to fuel pin positions and water holes along the diagonal vector of the fuel assembly. The next figures ( Figure 4-13 and 4-14) provide a 3-D rendering of the neut ron flux distribution. Figure 4-13 shows the strong axial gradient in neutron flux for the assembly, with over an order of magnitude in flux change for group 2. In addition, water holes cr eated by the absence of control rod fingerlings also have an important im pact on neutron thermalization of the system, as seen with the bright red representation in Figure 4-14a Neutrons born in the surrounding fuel pins are heavily m oderated in these regions and it is clear that thes e thermal neutrons are migrating back to the fuel Note that fuel pins within the water hole zone (outlined in orange in Figure 4-13b ) experience about 20% higher therm al flux th an pins outside this region near the

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98 assembly x-y periphery. Overa ll, initial PENTRAN analysis ha s clearly demonstrated that neutron flux profiling requires 3-D detail. In order to perform the burnup study in a reas onable fashion, convergence criteria had to be loosened. Based on a goal of achieving at least 1x10-4 convergence on keff, PENTRAN log processor files were examined to determine the first outer iteration where this convergence was achieved. This occurred at iteration 48, with a keff convergence of 8.67x10-5. Table 4-10 summarizes the corresponding m axi mum normalized flux errors afte r 48 outer iterations. Note that coarse mesh 1 through 64 and 1408 through 1472 make up the top and bottom water regions, while coarse mesh 65 through 1407 make up the fuel regions. Note that theses three coarse mesh all reside in the top and bottom z-levels, where surrounding water regions are adjunct to the vacuum boundary condition. These problematic regions were not of particular interest since they are in the axial water buffer region and will not have a significant impact on the fuel regions where burnup is most important. In order to account for these convergence issues, a spatially dependent convergence criterion was applied to the PENTRAN assembly model. The upper and lo wer periphery water re gions (coarse mesh 164 and 1408-1472) had a flux convergence criterion of 7x10-3. The inner fuel/moderator regions used a convergence of 1x10-3 and a eigenvalue convergence of 1x10-4 was selected. 4.3.3 3-D Assembly Burnup Results With optimized convergence criterion, a seven step burn sequence (cumulative burn times of 3, 7, 20, 40, 80, 140, 220, and 320 days) with a constant specific power of 34 MW/MTHM was selected for analysis. In order to enhance computational speed up, PENTRAN preconditioned flux files generated from the from the n-1 burn step transport solution were used as the initial guess solution for the nth transport calculation. These files were created by REPRO, a utility code written by the author. REPRO reads the zero and first flux moments for each

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99 group and fine mesh stored on PE NTRAN flux files and rewrites them onto new output files in PENTRAN precondition format. If preconditioned files are present with the PENTRAN input at execution time, PENTRAN will read the flux moments for each group and fine mesh from the files and use them as the initial flux guess. Considering the n-1 burn steps solution should be a reasonable guess for step ns flux profile, computation time wa s expected to decrease as compared to starting each new burn step transport calculation with a flat spatially weighted flux distribution. A clever depletion zone numb ering procedure was used in order to easily know the correlation between depletion zone and fuel pin nu mber. The assembly was partitioned into three axial depletion regions ( Figure 4-15b ). W ithin a depletion region, each fuel pin segment was assigned a depletion zone number. For example, depletion region I (purple) spanned from 105260.76 cm in the axial direction, and contains de pletion zone numbers 1-264. Depletion region II (yellow) spanned from 35-105 cm and 260.76-330.76 cm, and contains depletion zone numbers 265-528. Finally, depletion region III (green) spanned from 0-35 cm and 330.76-365.76 cm, and contains depletion zone numbers 529-792. Fuel pin numbering within a specific depletion region, ( Figure 4-15a), increm ents in x direction most freque ntly, followed by the y direction. To be clear, if one is interested in burnup results of fuel pi n 1 (southwest corner pin of Figure 4-13b ), one would need to exam ine results for deple tion zone number 1 (region I), 265 (region II), and 529 (region III). By simply adding 264 and 528 to the fuel pin number, one can easily identify the depletion zones that make up a fuel pin. Tables 4-11 through 4-13 display actinide results for fuel rods 1, 68, and 132 (highlighted with a star in Figure 4-14a) at the assem bly discharge point of 10.9 GWd/MTHM. Although results are available for all 264 fuel rods, these th ree rods were selected in order to represent

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100 average results within different depletion regions of the assembly that are subject to varying fluxes due to water holes. Finally, Figures 4-16 shows the variation of the spatial flux distribution at vari ous burnup positions. The 3-D variation of the neutron flux distribution is clearly ref lected in the burnup results ( Tables 4-11 through 4-13). For example, within fuel rod 132, U-235 atom /barn/cm concentrations in depletion region II and III are about 28 % and 92 % percent higher relative to region I, respectively. The axial burnout of U-235 shown in the prev ious tables is clearly shown in Figure 4-16 which shows the power/flux sh ifting from the inner to outer periphery of the assembly throughout irradiation. Also of interest for fuel rod 132 is the ax ial variation of Pu-239. Note how depletion region II has slightly larger concentrations of Pu -239 relative to region I after 10.9 GWd/MTHM. This was not the case throughout earlier time steps, as shown in Figure 4-17. It app ears from the figure that Pu-239 concen trations are beginning to reach equilibrium in depletion region I (DZ-132), while Pu-239 concen trations in regions II (DZ-396) and III (DZ660) are continuing to grow. Besides burnup results, there was also a not eworthy decrease in computation time for PENTRAN calculations at each transport calculat ion step, related primarily to the use of preconditioned flux files from REPRO. Recall, initial analysis showed that in order to achieve a maximum normalized flux error of 6.70x10-3 over all energy groups, this required around 4 days of dedicated cluster time. PENTRAN computat ion time per burn step was reduced to around 1 day of computation time with use of REPRO, e ffectively a factor of ~4 decrease in work required by PENTRAN. This demonstrates how flux moment preconditioning based on the previous burn step is an effective method of reducing total computation time required to complete a burnup sequence.

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101 4.3.4 Comparing PENBURN and ORIGEN-ARP A Westinghouse 17x17 OFA assembly with the sa me power history was also modeled in SCALE5.1s ORIGEN-ARP point depletion module for comparison purposes with PENBURN. ORIGEN-ARP performs point depletion calculations using ORIGEN-S code along with pregenerated cross sections for various assembly types (Gauld et. al., 2006a). Table 4-14 shows percent differences between PE NBURNs global results (summ ed over all depletion zones) and ORIGEN -ARPs point depletion results at different burnup stages. 4.3.5 Methodology differences between PENBURN and ORIGEN-ARP Early in burnup life, PENBURN and ORIGEN -ARP match reasonably well, however as time progresses major actinides begi n to diverge. This is also re flected in Cs-137 concentrations. A better burnup comparison could be made using SCALE5.1s T6-DEPL burnup control sequence, which performs a 3-D transport ca lculation with SCALEs KENOVa module. One limitation, however, is that the TRITON sequence is limited to 255 depletion zones (Dehart, 2006b). There are several reasons that most likely correlate to the differe nces between PENBURN and ORIGEN-ARP methodology. Like with th e unit cell analysis, differences between PENBURN and ORIGEN-ARP are most likely caused by: Fission yield data differences Burnup dependent cross section differences Bateman equation solution methodology differences In addition to these differences in sequence methodology, ORIGEN-ARP implements a less rigorous transport solution, using a simple point calculation based on system power level and a pre-generated set of cross section data from NEWT. This is one reason why the module

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102 runs much faster than going the T-DEPL pa thway within SCALE. PENTRAN analysis, on the other hand, solved the full form LBE in 3-D for heterogeneous depletion zones. Moreover, the PENTRAN model used homogenize d (based on volume weighting) fuel pins to represent the 17x17 lattice while ORIGEN-ARPs pre-calculated NEWT analys is represented fuel pins heterogeneously. Although presumed but not directly mentione d, the entire burnup procedure spanning from cross section blending to bur nup execution is automated thro ugh a Linux Bash script called burndriver.sh or BURNDRIVER. The next chapter will discuss script development, including utility codes that were created in or der to fulfill neces sary functionality.

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103 Table 4-1. Westinghouse 17x17 OFA specifications Fuel pin pitch 1.2598 cm Fuel pellet diameter 0.7844 cm Clad inner diameter 0.8004 cm Clad outer diameter 0.9144 cm Assembly pitch 21.5 cm Active fuel length 365.76 cm Array size 17x17 Number of fuel rods 264 Number of control rod guide tubes 24 Number of instrument tubes 1 Table 4-2. Fresh fuel concentrations for 3 wt% enriched UO2 fuel pellets Nuclide Wt. Percent O-16 11.8532 U-234 0.0224 U-235 2.6444 U-236 0.0122 U-238 85.4678 TOTAL 100.0 Table 4-3. Heterogeneous unit cell keff results from NEWT and PENTRAN Transport Code Meshing keff keff tolerance NEWT 22x22 1.30338 5x10-5 PENTRAN 22x22x5 1.30100 5x10-5 Table 4-4. Percent differences between average scalar flux values in fuel, gap, clad, and moderator regions for NEWT and PENTRAN NEWT g NEWT g PENTRAN g 100 % Region Grp 1 Grp 2 Grp 3 Fuel -1.253 0.484 -0.111 Gap -1.046 0.512 -0.571 Clad -1.013 0.539 -0.727 Water 1.539 0.127 -2.442

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104 Table 4-5. Comparison of PENBURN and SCALE bur nup results for selected isotopes Nuclide Relative Difference at t=541 d Mean of Relative Differences Over Entire burnup sequence U-238 0.44% 0.08% U-235 1.98% 0.20% U-236 1.78% 0.88% Mo-95 2.84% 2.31% Sr-90 4.07% 2.50% Xe-133 8.11% 2.61% Pu-239 2.89% 3.27% Zr-95 9.25% 3.58% Np-239 5.07% 3.65% Cs-137 8.24% 4.03% Kr-85 0.96% 4.33% Nd-147 11.85% 4.53% I-131 5.95% 7.06% Tc-99 9.60% 9.43% Xe-135 13.67% 9.55% Y90 9.26% 9.57% Xe-131 22.41% 13.50% Pu-240 27.11% 16.68% Pu-241 31.42% 22.97% Pu-242 25.74% 28.14% Np-237 0.27% 46.70% U-237 7.38% 47.90%

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105 Table 4-6. Comparison of PENTRAN/PENBURN and SCALE5.1 keff results over 541 day burn sequence PENTRAN/PENBURN SCALE Cumulative Burn Time (d) keff Cumulative Burn Time (d) keff 0 1.30141 0 1.30099 1 1.27100 0.5 1.27534 2 1.26627 1.5 1.25875 3 1.26524 2.5 1.25621 4 1.26464 3.5 1.25494 4 1.26424 4.5 1.25378 6 1.26392 5.5 1.25267 7 1.26347 6.5 1.25163 10 1.26239 8.5 1.24972 13 1.26125 11.5 1.24741 16 1.26005 14.5 1.24557 21 1.25803 18.5 1.24356 26 1.25584 23.5 1.24149 31 1.25372 28.5 1.23954 51 1.24508 41 1.23456 71 1.23472 61 1.22614 91 1.22333 81 1.21722 141 1.19675 116 1.20120 191 1.17059 166 1.17894 241 1.14627 216 1.15814 341 1.10211 291 1.12990 441 1.06494 391 1.09652 541 1.03689 491 1.06672 Table 4-7. Fuel composition comparison of heterogeneous and homogenized fuel zones Nuclide Heter. Wt. Percent Homog. Wt. Percent O-16 11.8532 9.9272 U-234 0.0224 0.0188 U-235 2.6444 2.2147 U-236 0.0122 0.0102 U-238 85.4678 71.5796 He-4 0.0242 Zr-nat. 16.2253 TOTAL 100.0 100.0

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106 Table 4-8. PENTRAN mass balance an alysis for fissile material (UO2) in 2-D model comparison Model Type Target Mass (g) Model Mass (g) Model/Target Ratio Heterogeneous 50.84 51.06 1.004 Homogeneous 50.84 51.19 1.007 Table 4-9. Homogenized (f uel+gap+clad) unit cell keff results from SCALE5.1 and PENTRAN Transport Code Meshing keff keff tolerance NEWT 12x12 1.28545 5x10-5 PENTRAN 12x12x5 1.29139 5x10-5 Table 4-10. Maximum normalized flux error and corresponding coarse mesh for groups 1-3 Energy Group Max Errnorm Coarse Mesh E < 6.25x10-7 MeV 2.92x10-3 11 6.25x10-7 < E 1.01 MeV 6.70 x10-3 1465 1.01 < E 20.0 MeV 9.49 x10-4 19 Table 4-11. Actinide results (atom/barn/cm) for fu el rod 1 [x-y center at (0.6716, 0.6716 cm)] for 10.9 GWd/MTHM of assembly burnup Nuclide Region I DZ*-1 Region II DZ*-265 Region III DZ*-529 U-235 2.357E-04 2.940E-04 4.265E-04 U-236 5.184E-05 4.253E-05 1.989E-05 U-237 1.398E-07 1.088E-07 2.303E-08 U-238 1.679E-02 1.674E-02 1.669E-02 Np-237 1.509E-06 1.124E-06 3.095E-07 Np-239 1.960E-06 1.819E-06 8.027E-07 Pu-239 4.673E-05 4.798E-05 3.933E-05 Pu-240 9.931E-06 8.766E-06 4.267E-06 *DZ-D epletion Z one

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107 Table 4-12. Actinide results (atom/barn/cm) for fuel rod 68 [x-y center at (5.7108, 5.7108 cm)] for 10.9 GWd/MTHM of assembly burnup Nuclide Region I DZ*-68 Region II DZ*-332 Region III DZ*-596 U-235 2.179E-04 2.778E-04 4.185E-04 U-236 5.412E-05 4.470E-05 2.103E-05 U-237 1.464E-07 1.149E-07 2.443E-08 U-238 1.680E-02 1.675E-02 1.670E-02 Np-237 1.580E-06 1.184E-06 3.220E-07 Np-239 2.019E-06 1.870E-06 8.219E-07 Pu-239 4.520E-05 4.657E-05 3.874E-05 Pu-240 1.071E-05 9.497E-06 4.661E-06 *DZ-D epletion Z one Table 4-13. Actinide results (atom/barn/cm) fo r fuel rod 132 [x-y center at (9.4902 10.75 cm)] for 10.9 GWd/MTHM of assembly burnup Nuclide Region I DZ*-132 Region II DZ*-396 Region III DZ*-660 U-235 2.174E-04 2.774E-04 4.184E-04 U-236 5.420E-05 4.475E-05 2.106E-05 U-237 1.467E-07 1.151E-07 2.449E-08 U-238 1.680E-02 1.675E-02 1.670E-02 Np-237 1.583E-06 1.186E-06 3.225E-07 Np-239 2.023E-06 1.873E-06 8.233E-07 Pu-239 4.516E-05 4.656E-05 3.876E-05 Pu-240 1.075E-05 9.518E-06 4.668E-06 *DZ-D epletion Z one Table 4-14. Percent differences between PENBURN and ORIG EN-ARP at various burnup set points Percent Difference [(PB-ARP)/ARP] Nuclide 3 days 4 days 20 days 140 days 220 days 320 days U-235 0.238% 0.111% -0.398% -5.762% -9.997% -15.806% U-236 3.99% 7.31% 13.34% 23.27% 24.23% 24.03% U-238 0.33% 0.40% 0.39% 0.73% 0.96% 1.27% Pu-239 18.55% -25.78% -13.74% -25.93% -28.23% -28.29% Pu-240 4.23% -30.89% -1.91% -23.26% -27.10% -27.50% Cs-137 22.63% -11.3% -5.6% -27.00% -32.65% -36.01%

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108 Figure 4-1. Plan view of Westinghouse 17x17 OFA assembly w/ fuel pin numbering Figure 4-2. Westinghouse fuel unit cell model (OD=1.2598 cm)

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109 Figure 4-3. Comparison of keff for PENBURN and SCALE Figure 4-4. Relative percent difference in c oncentration between SC ALE and PENBURN with and without use of INTERP-XS for select Plutonium isotopes

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110 Figure 4-5. Comparison of keff between PENTRAN/PENBURN and SCALE using INTERP-XS

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111 A B Figure 4-6. Cycle length estim ate based on reactivity. A) keff profile with and without the use of INTERP-XS. B) Expanded view of Figure 4-6a

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112 A B Figure 4-7. Overview of two dimensional mesh scheme. A) Single, high memory requirement coarse mesh methodology B) Pin grouping coarse mesh methodology Figure 4-8. Group 1 (1.01 < E 20.0 MeV) normalized flux error for initial PENTRAN transport analysis

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113 Figure 4-9. Group 2 (6.25x10-7 < E 1.01 MeV) normalized flux error for initial PENTRAN transport analysis Figure 4-10. Group 3 (E < 6.25x10-7 MeV) normalized flux error for initial PENTRAN transport analysis

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114 Figure 4-11. Relative axial neutron flux distributi on at x-y center of Westinghouse fuel assembly based on initial fuel concentrations

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115 A B Figure 4-12. Relative neutron flux distribution for Westinghous e assembly. A) Neutron flux distribution at axial center of Westinghouse fuel assembly spanning the vector from (0.0,0.0,182.0) to (21.5,21.5,182.0) based on initial fuel concentrations for all groups B) Like part A), however emphasis on groups 1 and 3

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116 A B C Figure 4-13. Three-dimensional overview of a ssembly neutron flux distribution A) E<0.625 eV, B) 0.625 eV < E< 1.01 MeV, and C) 1.01 MeV < E < 20 MeV

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117 A B Figure 4-14. Expanded 3-D view of relative neutron flux distribution at z=182 cm for E<0.625 eV A) With water moderator present B) Without water mode rator present. Note that a rescaling has been formed, relative to Figure 4-13

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118 A B Figure 4-15. Material layout for assembly analys is A) Depletion zone numbers for region I B) Axial depletion region layout

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119 Figure 4-16. Variation of the tota l axial flux distribution for cumulative burn times of 0, 20, 80, 140, and 220 days Figure 4-17. Concentrations of Pu-239 as a func tion of burnup for depletion zones 132, 396, and 660 in fuel rod 132

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120 CHAPTER 5 AUTOMATION OF PENTRAN/PENBURN BURNUP PROCEDURE In order for any code to be successful, it is im pe rative that it is user friendly as possible. Upon the authors arrival, it was clear to PENTRAN/PENBURN developers that the system required too much user responsibility, in terms of creation of inputs and di rectories, movement of files, execution of programs, and extraction of data. A driver script was needed which could manage the entire burnup procedure, spanning from cross section development to summarizing burnup output results. BURNDRIVER is a Linux Bash Shell script which automates the entire PENTRAN/PENBURN burnup procedur e. The script is aro und 3,000 lines in length and provides several user options for burnup methodology, microscopic cross section treatment, and sequence restart. The following chapter will detail the BURNDRIVER script development, including analysis on minimum irradiation st ep size in order to capture proper Xe-135 contributions. 5.1 Overview of BURNDRIVER The core of the BURNDRIVER script is ma de up of 6 executables. The programs, in order of execution, are: INTERP-XS, GMIX PENTRAN, REPRO, PENPOW, and PENBURN. INTERP-XS is the microscopic cross section inter polator code, which produces self-shielded and Doppler broadened cross section sets based upo n pre-generated SCALE/NJOY libraries. GMIX is the macroscopic cross section generator. PENTRAN is the 3-D deterministic flux solver. REPRO is the preconditioned flux file writer PENPOW calculates reaction rates based on PENTRAN flux and cross sections generated via SCALE/NJOY. Finally, PENBURN uses the PENPOW reaction rates and performs zone based fuel depletion. The burnup procedure can be found in Figure 5-1 In Figure 5-1 the dashed line delim its th e boundary where BURNDRIVER (or burndriver.sh) operates. Following along with the figure (assuming a Forward-Euler

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121 approach), a burnup sequence starts with cross section generation using INTERP-XS (optional) and GMIX. Fission neutron energy spectrum data created from the GMIX code is updated within the PENTRAN input in or der to account for variation in g as a function of burnup. Next, PENTRAN transport is performed in order to obtain model fluxes. If flagged, REPRO is executed to generate preconditione d flux files for the next burn steps PENTRAN calculation. With transport complete, reaction rates are form ulated with PENPOW and depletion is executed with PENBURN. Isotopic concentrations ar e updated based upon PENBURN results and the process is repeated for the next power history step. If decay is sele cted, transport is not performed and the procedure goes immediat ely to depletion for that step. The BURNDRIVER sequence is slightly di fferent when the Predictor-Corrector methodology is applied. This procedure is discus sed in detail in Chapter 1, however will be discussed here in terms of PENTRAN/PENBURN suite utilities. At sequence initiation, the BURNDRIVER uses GMIX cross section mixing and the PENTRAN transport solution as a predictor step. PENPOW r eaction rates are formulated and PENBURN burnup is executed to the midway of the burn step. Cross sections are updated at the midpoi nt and transport is performed again; this step is commonly referr ed to as the corrector step. The flux solution from the midpoint calculation is then used to perform burnup over the entire step. Burnup is commonly extended to the midpoint of the next step, and the predictorcorrector methodology is repeated. The approach attempts to correct for the variation of the flux within a burn step, due to the production of other transura nics and fissi on products. 5.1.1 Summary of Inputs From Figure 5-1 inputs f or the BURNDRIVER are listed in the left column. Filenames in green boxes are required inputs while filenames in orange boxes are optional inputs, based on

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122 user specifications in the burnset.inp file (Appendix E). The burnset.inp file is the linker between the script and burnup users. The input has several flags which can activate driver options related to burnup methodolog y, cross section treatment, or problem restart in addition to general irradiation/decay history. A brief summary of the remaining files is provided below. Minimum files required: 1. burnset.inp (BURNDRIVER input) 2. prbname.f90 (PENTRAN input) 3. prbname.gmx (GMIX input; initial fuel concentrations) 4. prbname.grp (GMIX group energy file) 5. penburn.path (PENBURN path matrix file) Optional files: A. prbname.xsc (microscopic cross section file) B. precflx#a# | precflx#b# (PENTRAN preconditioned flux files) C. prbname#.flx (precomputed PENTRAN flux files for initial burn step) D. prnbame.crs (mesh summary of precomput ed PENTRAN flux files) E. flx.log (flux log file for preco mputed PENTRAN flux files) F. prbanme.xrf (GMIX cross section index file) G. prbname.out (GMIX output/log file from precomputed transport run) H. prbname.xs (GMIX output macroscopic cross section file from precomputed transport run) 5.1.1.1 Description of burnset.inp The following subsection will further explain in detail the burnset.inp file structure, however there are a variety of references which can help explain each of the remaining files listed previously. Note: All comment lines are indicated by a / The format of the input is fixed, therefore no additional comment lines may be added to the in put. All line descriptions below are for active lines (i.e. those lines that do not begin with a /). Line 1, Input 1: Problem name. Line 1, Input 2: Burnup methodology option. / prob. name | PC flag ( 0=no,FE,1=PCA Std.,2=PCA HE)|memory save option(0=inact, 1=act) whpin 1 0 / # of processors for run|Step 0 flux files(0=no, 1=yes)|Restart flag(no<0; yes >0) 8 0 -1 / REPRO flag(1=active. REPRO,0=no precon flux files|precflx flag for initial run(0=no, 1=yes) 0 0 / INTERPXS flag (1=act,0=supply .xsc file)|INTERPXS option|Fuel,Mod Temp(K)|INTERPXS option data 1 1 1000 600 t

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123 If set to : Use Forward Euler approach If set to : Use Predictor Corrector appr oach, however do not extend PENTRAN transport solution past end of burn step. If set to : Use Predictor Corrector appr oach, extending PENTRAN transport solution to midpoint of next burn step. (RECOMMENDED) Line 1, Input 3: If set to, PENTRAN flux files are sa ved; if set to PENTRAN flux files are deleted. Line 2, Input 1: Number of processors dedicated fo r PENTRAN transport calculation, as specified in decomposition v ector of the PENTRAN input. Line 2, Input 2: Flag indicating whether flux files for in itial (step0) transport calculation have already been computed. These files (prbname#. flx) must be present along with flx.log, prbname.1, prbname.xs, prbname.out, prbname.xrf and prbname.crs in addition to the five mandatory files listed in previous section. Note that there should be as many flux files as energy groups. Line 2, Input 3: Flag indicating whether the user would like to restart from the last complete burn step. A value less than zero indicates that no restart is desired. A value greater than zero indicates a restart is desired. If a restart is desired, this input value should equal the suffix number of the last complete step folder. For exam ple in a 10 step sequence, if the last successful burn step was at folder step5 and failed at fold er step6, the user woul d enter 5 for the restart option. No other modifications to the burnset.inp file are necessary. Line 3, Input 1: Flag indicating if user would like to run REPRO which s upplies preconditioned flux files for next burn step. (0=no, 1=yes) Line3, Input 2: Flag indicating if user has precomputed preconditioned flux files for the first step. These files must be present along with fi ve mandatory files listed in previous section. Line 4, Input 1: Flag indicating if the user would lik e to use a precomputed, burnup-dependent microscopic cross section library with INTERP-XS program. (0=no, 1=yes) Line 4, Input 2: INTERP-XS interpolation option. OPTION 1: User would like to use pre-comput ed library at pre-computed system fuel temperature. OPTION 2: User would like to us e pre-computed library at an interpolated system fuel temperature. Line 4, Input 3,4 : System fuel temperature. System moderator temperature. IF OPTION 1 selected: User shoul d enter successively the fuel a nd moderator temperature that already exists for that library. IF OPTION 2 selected: User should enter successively the fuel and moderator temperature that is within the librarys temperature range. Line 4, Input 5: Library prefix descriptor (usually a single character).

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124 Line 5, Input 1: Flag indicating if the user would like to check PENTRAN run convergence after every transport calculati on (0=no, 1=yes). (Recommended) Line 6-8: Three line descriptor for PENPOW input. Line 9: Number of fuel depletion zones. Line 10: Range of fuel material numbers. The only re quirement is that the fuel material numbers are in sequential order. Order is ba sed on arrangement in PENTRAN input. Line 11-13: 3 line descriptor for PENBURN input. Line 14: Number of irradiation or cool steps Line 15-(15+bnsteps), Input 1: System power, expressed in either W/g (MW/MTHM) or Watts. (-) sign indicates W/g while (+) sign indicates total system power. If the INTERP-XS flag is on, the user must specify system power in W/g (or MW/MTHM). NOTE: The specific power option (W/g, heavy me tal) is the average specific power for the system. For example, if you are modeling a reacto r core that produces 1000 MWth and contains 30 MT heavy metal, the average specific power is 33.3 MW/MTHM (or 33.3 W/g). Some depletion zones may have highe r/lower specific power; howev er, the average for the entire system is 33.3 W/g. Line 15-(15+bnsteps), Input 2: Length of burn/cool step. Line 15-(15+bnsteps), Input 3: Time unit. Note that the time units should match between burn steps. Line 15-(15+bnsteps), Input 4: i=irradiation, c=cool/decay / PENTRAN Convergence STOP flag (0=no, 1=yes) 1 / Following 3 lines dedicated to PENPOW Problem Description SFCOMP Takahama PWR Pin Study xxx xxx / number of fuel materials 1 / range of fuel material number: eg. 1 10 1 1 / Following 3 lines dedicated to PENBURN Problem Description SFCOMP Takahama PWR Pin Study xxx xxx / # of irradiation/cool steps 2 / power, time, time unit, irrad (i)/cool(c),print step,print option,GMIX keyword -22.36 1 d i 1 2 s1 -22.36 1 d i 1 2 s2

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125 Line 15-(15+bnsteps), Input 5: Number of print steps per burn step. If larger than 1, burnup results will be available in each burnstep, howev er the data extraction script will not execute properly and burnsum.out file will not be presen t in working directory. Line 15-(15+bnsteps), Input 6: PENBURN output print option. If not set to 2, burnup results will be available in each step folder, however the data extracti on script will not execute properly and burnsum.out file will not be present in working directory. Line 15-(15+bnsteps), Input 7: GMIX suffix used to identify input file for next burn step. 5.1.1.2 Running BURNDRIVER The entire BURNDRIVER sequence is encapsulat ed within one folder entitled bd7. The folder contains several subfolders such as bin, codes, and demo. The bin folder contains the location of all executables for the sequence, including the burndriver.s h script. Prior to executing the driver, burndriver.sh must be modified in order to update th e path where the bin folder is located on the PC or cluster. This re quires the alteration of two lines which define the HOMEDIR and HOMDIRBIN variables. For example, if the bd7 folder was loaded on the users home folder (i.e. directory path is /home/user/bd7/), HOMEDIR should be equal to /home/user/bd7/ and HOMDIRBIN should equal /home/user/bd7/bin. To run the BURNDRIVER sequence, the us er needs to execute BURNDRIVER from inside the directory where the burnup sequence files described in the previous section are located. For example, if the above files are in a folder called demo in the users home directory (in a Linux environment) the user needs to type on th e command line from within the demo directory: /home/user/bd7/bin/burndriver.sh The first part entered on the command line (/home/user/bd7/bin/) is simply the path where the script burndriver.sh is located. This location will more than likely differ from machine to machine, depending on where the installation is performed.

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126 5.2 Xenon Irradiation Step Size Study Xe-135 has the largest absorp tion cross section of all nuc lides in a thermal reactor (T1/2=9.02 hr, abs=2.64x106 barns) and has a significant im pact on the neutron balance and reactor control. With a direct fission yield of only 0.32%, it is mainly produced from the fission product decay chain in Figure 5-2 (Benedict et al, 1981). The parent of the chain, Te-135, has a fi ssion yield of 6.09% and a half-life around 29 seconds. Since the half-life of Te-135 is so short, its buildup can be ignored and the chain is assum ed to start at I-135 (such th at fission yield of I-135 equals 6.09%) which has a half-life of 6.7 hours. In order to account for reactiv ity effects in thermal systems, a proper step size must be chosen for the first several days of irradiation to account for the buildup of Xe-135. The correct step size can vary from system to system, how ever the analysis with PENTRAN/PENBURN will focus on a specular reflected, single 3 wt% enriched UO2 fuel pin fuel pin from a 17x17 Westinghouse OFA. To begin, a very detailed 14 day burnup study of the Westinghouse fuel pin was performed (specific power set to 34 MW/MTHM) in order to define a reference case for comparison. Step sizes of one irradiation day were used for the reference case. Four additional test burnup cases totaling to 14 days of irradiation were repeat ed for the Westinghouse pin, however irradiation step sizes of 2, 3, 4, and 12 days were used for these cases. Burnup corrected microscopic cross sections were activated within the BURNDRIVER To determine the effectiveness of tracking Xe-135 in growth, two criterions were used: (1) Percent differen ces in Xe-135 concentrations between the reference and test burnup cases at each matching burnup point and (2) PCM difference between reference and test bur nup cases at each ma tching burnup point.

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127 Tables 5-1 and 5-2 display the results for the 14 day burnup study for the W estinghouse fuel pin. Note from th e far right column of Table 5-1 using a n initial irradiation step of 12 days showed less than 1 % difference in Xe-135 concen trations between the reference and test burnup case. In terms of PCM difference for the 12 day burn step case, maximum PCM differences were around 200 pcm at 13 days of irradiation, however PCM differences were less than 50 pcm at 12 and 14 days. These results motivated further investigation on considering irradiati on step sizes larger than 12 days. Three additional comparative burn up studies were performed out to 36, 66, and 132 days of irradiation with refe rence step sizes of 3, 6, and 12 days, respectively. One day irradiation step sizes were not used for the re ference case since this would require a excessive amount of burn steps to complete the reference case. The same two criterion used for the 14 day study were also used for the additional case studie s. Results for each case are summarized in Tables 5-3 through 5-8 Results from the 36 day irradiation case show that m aximum percent differences in Xe-135 concentration between the referenc e case of 3 day steps versus an initial irradiation step of 30 days were less than 2 %, with keff differences less than 50 pcm. The 66 and 132 day irradiation comparison results did degrade however, with Xe-135 concentration percent differences increasing to around 2.8 % and 4. 0 %, respectively with keff differences increasing to around 200 pcm. Based on the previous analysis, it appears that limiting the initial irradi ation step to around 14 days will track the in growth of Xe-135 concentrations to within 1 % of a very detailed irradiation history over that time frame. This recommendation also follows suit with advice from the SCALE code system, which indicates an initia l burn step of 10 to 15 days (Gauld, 2006a).

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128 An initial irradiation step of 30 days coul d be used, so long the PENTRAN/PENBURN user selects the Predictor-Corrector methodology option which performs burnup to the midpoint of an irradiation step. Thus, if the in itial irradiation step time was selected to be 28-30 days, burnup would initially be performed out to the first 14-15 days.

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129 Table 5-1. Comparison of Xe-135 concentrations for reference bur nup case of 1 day irradiation steps versus 2, 3, 4 and 12 day irradiation steps totaling to 14 days of irradiation REFERENCE 2-Day 3-Day 4-Day 12-Day Time (d) Atom/barn/cm Atom/barn/cm REF % Difference Atom/barn/cm REF % Difference Atom/barn/cm REF % Difference Atom/barn/cm REF % Difference 1 6.37E-09 2 7.20E-09 7.18E-09 -0.309 3 7.26E-09 7.24E-09 -0.310 4 7.27E-09 7.27E-09 -0.015 5 7.27E-09 6 7.28E-09 7.27E-09 -0.054 7.27E-09 -0.066 7.25E-09 -0.401 7 7.28E-09 8 7.29E-09 7.28E-09 -0.078 9 7.29E-09 7.28E-09 -0.139 10 7.30E-09 7.29E-09 -0.087 11 7.30E-09 12 7.31E-09 7.30E-09 -0.093 7.30E-09 -0.177 7.28E-09 -0.408 7.25E-09 -0.855 13 7.32E-09 7.32E-09 0.008 14 7.32E-09 7.32E-09 -0.091 7.32E-09 -0.014 Table 5-2. Comparison of keff for reference burnup case of 1 day irradiation steps versus 2, 3, 4 a nd 12 day irradiation steps totaling to 14 days of irradiation. REFERENCE 2-Day 3-Day 4-Day 12-Day Time (d) keff keff PCM REF Diff keff PCM REF Diff keff PCM REF Diff keff PCM REF Diff 0 1.30466 1.30466 0.00 1.30466 0.00 1.30466 0.00 1.30466 0.00 1 1.27186 2 1.26976 1.26994 14.18 3 1.26951 1.2664 -244.98 4 1.26904 1.26903 -0.79 5 1.26853 6 1.26505 1.26814 244.26 1.26521 12.65 1.26828 255.33 7 1.26748 8 1.26692 1.26706 11.05 9 1.26659 1.26604 -43.42 10 1.26575 1.26559 -12.64 11 1.26535 12 1.26496 1.265 3.16 1.26505 7.11 1.26524 22.14 1.26546 39.53 13 1.26488 1.26221 -211.09 14 1.26465 1.26424 -32.42 1.26469 3.16

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130 Table 5-3. Comparison of Xe-135 concentrations for reference burnup case of 3 day irradiation steps versus 30 day irradiation steps totaling to 36 days of irradiation Reference 30-Day Time (d) Atom/barn/cm Atom/barn/cm REF % Difference 3 7.24E-09 6 7.27E-09 9 7.28E-09 12 7.30E-09 15 7.32E-09 18 7.33E-09 21 7.34E-09 24 7.35E-09 27 7.36E-09 30 7.38E-09 7.25E-09 -1.7373 33 7.39E-09 7.38E-09 -0.1121 36 7.40E-09 7.39E-09 -0.1102 Table 5-4. Comparison of keff for reference burnup case of 3 da y irradiation steps versus 30 day irradiation steps totaling to 36 days of irradiation Reference 30-Day Time (d) keff keff PCM Ref Diff 0 1.30466 1.30466 3 1.2664 6 1.26521 9 1.26604 12 1.26505 15 1.26367 18 1.26049 21 1.262 24 1.262 27 1.26098 30 1.26013 1.26074 48.41 33 1.25610 1.25582 -22.29 36 1.25538 1.25558 15.93 Table 5-5. Comparison of Xe-135 concentrations for reference burnup case of 6 day irradiation steps versus 60 day irradiation steps totaling to 66 days of irradiation Reference 60-Day Time (d) Atom/barn/cm Atom/barn/cm REF % Difference 6 7.25E-09 12 7.28E-09 18 7.31E-09 24 7.34E-09 30 7.36E-09 36 7.39E-09 42 7.41E-09 48 7.42E-09 54 7.44E-09 60 7.46E-09 7.25E-09 -2.816 66 7.47E-09 7.45E-09 -0.275

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131 Table 5-6. Comparison of keff for reference burnup case of 6 da y irradiation steps versus 60 day irradiation steps totaling to 66 days of irradiation Reference 30-Day Time (d) keff keff PCM Ref Diff 0 1.30466 1.30466 0 6 1.26828 12 1.26524 18 1.26008 24 1.26213 30 1.26031 36 1.25551 42 1.25488 48 1.25302 54 1.25141 60 1.24809 1.24595 -171.46 66 1.24663 1.24593 -56.15 Table 5-7. Comparison of Xe-135 concentrations for reference burnup case of 12 day irradiation steps versus 120 day irradi ation steps totaling to 132 days of irradiation Reference 120-Day Time (d) Atom/barn/cm Atom/barn/cm REF % Difference 12 7.25E-09 24 7.31E-09 36 7.36E-09 48 7.40E-09 60 7.44E-09 72 7.47E-09 84 7.50E-09 96 7.52E-09 108 7.54E-09 120 7.55E-09 7.25E-09 -4.059 132 7.57E-09 7.50E-09 -0.837 Table 5-8. Comparison of keff for reference irradiation case of 12 day irradiation steps versus 120 day irradiation steps totaling to 132 days of irradiation Reference 120-Day Time (d) keff keff PCM Ref Diff 0 1.30466 1.30466 12 1.26546 24 1.26206 36 1.25534 48 1.25304 60 1.24812 72 1.24388 84 1.2385 96 1.23405 108 1.22822 120 1.22264 1.22241 -18.811752 132 1.21828 1.21577 -206.02817

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132 Figure 5-1. Overview of BURNDRIVER script

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133 Figure 5-2. Fission product d ecay chain involving Xe-135.

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134 CHAPTER 6 CONCLUSIONS AND FUTURE WORK Three-dim ensional burnup has a bright future in the nuclear fuel cycle analysis discipline, with room for future development. In order to extract accurate details of fuel isotopic concentrations, especially near fuel assembly axial peripheries, a transition in industry from 2-D to 3-D burnup codes is needed. A 3-D deterministi c approach for transport solving is especially attractive, considering the stochastic concerns pertaining to statistica l uncertainty and source convergence disappear. PE NTRAN is an ideal code system for 3-D deterministic transport analysis, since it is parallel code system with several unique f eatures like adaptive differencing scheme strategies, variable mesh options, and flux moment preconditioning (which is extremely helpful when performing burnup). With the mo re recent development of the coupled fuel depletion solver called PENBURN, the PE NTRAN/PENBURN suite is developing into a powerful burnup tool. 6.1 Conclusions One hurdle with deterministic transport met hods however is the requirement of multigroup cross sections that have the proper resonance energy self shielding and Doppler broadening treatments. A clear cross section generation procedure using SCALE and NJOY packages has been developed for the PENTRAN/PENBURN suite which can account for fuel/moderator temperature and burnup effects. A coupled interpolation progr am called INTERP-XS has also been created, which can generate problem dependent cross section sets for a PENTRAN/PENBURN burnup sequence based upon pre-generated SCALE/NJOY libraries. The PENTRAN/PENBURN suite has been rigoro usly tested with de tailed burnup analysis of a full length 17x17 Westinghouse PWR assembly. PENTRAN analysis demonstrated the str ong 3-D dependencies present in the flux distribution, with a strong gradient present in the axial direction.

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135 The axial flux also showed significant burnup dependencies, with in itial distributions following a cosine shape, however at 10.9 GWd/MTHM, the flux began to flatten in the center and shift towards the periphery. This was a direct result of preferential burnup of fissile material in the center, relative to the axial exterior, as refl ected in U-235 isotopic concentrations. Finally, automation of the burnup sequence wa s a necessity for the PENTRAN/PENBURN system to be as user friendly as possible. Several options related to cr oss section treatment, burnup methodology, and sequence restart are supplied within the burnset.inp file. Xe-135 concentration studies pe rformed with the driver show ed that the optimum first irradiation step le ngth is around 14 days. The research performed over the past year has al so resulted in several publications (Plower et al, 2008a, 2008b, 2008c), in addition to conf erence presentations at the International Conference on Nuclear Engineering 16 (ICONE16) in Orlando, FL and PHYSOR 2008 in Interlaken, Switzerland. 6.2 Future Work The PWR library generated from the SCALE/NJOY procedure has been fully optimized and analyzed, however further work is needed on the Magnox library and sodium cooled mixed oxide (MOX) library. Effectively, the reference burnup run has been performed for these other systems, however the optimal number of burnup points needs to be examined for each case. Additionally, the libraries genera ted only consider one fuel regi on for cross section analysis. Further exploration is needed to understand the po tential spatial self-shi elding effects within a fuel pin. In addition, differe nt cross section treatments should be considered for different pin types within a fuel assembly. Investigations into other systems could be of interest, in particular CANDU systems.

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136 The PENTRAN/PENBURN analysis presen ted for the PWR assembly used burnup independent cross sections. Although this may be good enough at low burnup, further analysis should be performed in order to investigat e potential differences when cross section dependencies are accounted for. Additionally, a new assembly model should be selected from the Spent Fuel Isotopic Composition (SFCOMPO) database in order to perform a comparison with actual spent fuel data. For the BURNDRIVER, additional options co uld be added which reduce the amount of data output. For example, if a user is interested in actinide content for a few particular fuel pins, the user should have the ability to view only ac tinide concentrations for those pins. Additionally, output options which identify depletion zones wi th maximum Pu-239 content would be helpful.

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137 APPENDIX A T-DEPL INPUT SCALE T-Depl / Micro XS Build Used to create burnup dependent micro-xs ******************************************** T-DEPL ******************************************** 'Westinghouse PWR Fuel Pin Burnup 'Reference run for INTERP-XS Program 'start tdepl control sequence =t-depl parm=(savlib,addnux=3) 'title card Westinghouse Fuel Pin, from 17x17 OFA 'calling the 238 fine group ENDF-B6 library V6-238 'initiate composition read read comp 3 w/o enriched UO2 fuel-specifications taken for a 17x17 Westinghouse OFA from ORNL Benchmark WTPTfuel 1 10.5216 14 8016 11.8532 92234 2.238929E-2 92235 2.644404 92236 1.216426E-2 92238 85.467842 'Following nuclides are added in trace quantities in order to produce on output collapsed XS file 92237 1E-10 93238 1E-10 93239 1E-10 94236 1E-10 94244 1E-10 96245 1E-10 96246 1E-10 96247 1E-10 61601 1E-10 1 1000. end WTPTgap 2 0.07518 1 2004 100.0 1 650. end WTPTclad 3 6.40 1 40000 100.0 1 620. end WTPTmod 4 0.66118 2 1001 11.189 8016 88.811 1 600. end end comp 'read celldata initiation statement read celldata 'geometry type and boundary conditions 'note: we must def an approximation for a unit cell calculations within the xs section card latticecell squarepitch pitch 1.2598 4 fueld 0.7844 1 gapd 0.8001 2 cladd 0.9144 3 end 'end of celldata parameters' end celldata 45 burn steps (46 transport calculations) totaling 68 GWd/MTHM READ burndata p=34.0 b=3.0 d=0.0 end p=34.0 b=4.0 d=0.0 end p=34.0 b=13.0 d=0.0 end p=34.0 b=20.0 d=0.0 end p=34.0 b=20.0 d=0.0 end p=34.0 b=20.0 d=0.0 end p=34.0 b=20.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end

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138 p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end p=34.0 b=50.0 d=0.0 end END burndata READ depletion -1 END depletion READ model WH Pin READ param run=yes collapse=yes sn=8 epsilon=5e-5 echo=yes drawit=yes inners=10 prtmxsec=yes prtmxtab=yes prtxsec=yes prtbroad=yes END param READ collapse 22r1 177r2 39r3 END collapse READ materials 1 1 'uo2' end 2 1 'he' end 3 1 'zr' end 4 1 'h2o' end END materials READ geom global unit 1 com="Westinghouse Pin" 'geometry, geom#, radius' cylinder 10 0.39220 cylinder 20 0.40005 cylinder 30 0.45720 cuboid 40 0.62990 -0.6299 0.6299 -0.6299 'filling geometry with material "media 1" is fuel and resides within global unit 1 media 1 1 10 'media 2 inside global unit 1 inside cylinder 20 outside of cylinder 10' media 2 1 20 -10 media 3 1 30 -20 media 4 1 40 -30

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139 'boundary within geometry number 100, inside our cuboid, with meshing 10X10 (2 in x direction, 10 in y direction) boundary 40 36 36 END geom 'start reading bounds' READ bounds 'all boundaries are reflective boundary condition' -x=reflective +x=reflective -y=reflective +y=reflective END bounds END model 'end of tdepl sequence END Copy collapsed output cross sections after each burn step to working dir =shell copy savcol00 "%RTNDIR%\savcol00" copy savcol01 "%RTNDIR%\savcol01" copy savcol02 "%RTNDIR%\savcol02" copy savcol03 "%RTNDIR%\savcol03" copy savcol04 "%RTNDIR%\savcol04" copy savcol05 "%RTNDIR%\savcol05" copy savcol06 "%RTNDIR%\savcol06" copy savcol07 "%RTNDIR%\savcol07" copy savcol08 "%RTNDIR%\savcol08" copy savcol09 "%RTNDIR%\savcol09" copy savcol0A "%RTNDIR%\savcol0A" copy savcol0B "%RTNDIR%\savcol0B" copy savcol0C "%RTNDIR%\savcol0C" copy savcol0D "%RTNDIR%\savcol0D" copy savcol0E "%RTNDIR%\savcol0E" copy savcol0F "%RTNDIR%\savcol0F" copy savcol10 "%RTNDIR%\savcol10" copy savcol11 "%RTNDIR%\savcol11" copy savcol12 "%RTNDIR%\savcol12" copy savcol13 "%RTNDIR%\savcol13" copy savcol14 "%RTNDIR%\savcol14" copy savcol15 "%RTNDIR%\savcol15" copy savcol16 "%RTNDIR%\savcol16" copy savcol17 "%RTNDIR%\savcol17" copy savcol18 "%RTNDIR%\savcol18" copy savcol19 "%RTNDIR%\savcol19" copy savcol1A "%RTNDIR%\savcol1A" copy savcol1B "%RTNDIR%\savcol1B" copy savcol1C "%RTNDIR%\savcol1C" copy savcol1D "%RTNDIR%\savcol1D" copy savcol1E "%RTNDIR%\savcol1E" copy savcol1F "%RTNDIR%\savcol1F" copy savcol20 "%RTNDIR%\savcol20" copy savcol21 "%RTNDIR%\savcol21" copy savcol22 "%RTNDIR%\savcol22" copy savcol23 "%RTNDIR%\savcol23" copy savcol24 "%RTNDIR%\savcol24" copy savcol25 "%RTNDIR%\savcol25" copy savcol26 "%RTNDIR%\savcol26" copy savcol27 "%RTNDIR%\savcol27" copy savcol28 "%RTNDIR%\savcol28" copy savcol29 "%RTNDIR%\savcol29" copy savcol2A "%RTNDIR%\savcol2A" copy savcol2B "%RTNDIR%\savcol2B" copy savcol2C "%RTNDIR%\savcol2C" copy savcol2D "%RTNDIR%\savcol2D" end

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140 APPENDIX B T-NEWT INPUT =t-newt parm=(addnux=3) Westinghouse Fuel Pin, from 17x17 OFA V6-238 read comp WTPTfuel 1 10.5216 63 95241 3.80417E-17 95243 3.83591E-17 56138 7.23189E-28 58140 2.05064E-32 58142 3.17822E-29 58144 2.2728E-17 96242 3.82004E-17 96243 3.83591E-17 96244 3.85178E-17 96245 1.43791E-40 55133 2.09913E-17 55135 2.13086E-17 55137 2.1626E-17 63153 2.41474E-17 64155 2.44648E-17 57139 4.01752E-30 42095 1.49963E-17 42097 3.07243E-31 60143 2.25693E-17 60144 1.75001E-33 60145 2.28867E-17 60146 2.30454E-17 60148 2.33628E-17 8016 11.85772145 59141 8.49172E-36 94238 3.75656E-17 94239 3.77243E-17 94240 3.7883E-17 94241 3.80417E-17 94242 3.82004E-17 45103 1.6257E-17 44101 2.08414E-33 44102 1.266E-31 44104 4.33049E-29 62147 2.32041E-17 62149 2.35215E-17 62150 2.36802E-17 62151 2.38389E-17 62152 2.39887E-17 38090 8.42383E-27 43099 1.5631E-17 92234 0.02239302 92235 2.643963318 92236 0.012166287 92238 85.46375593 54131 2.06739E-17 54132 7.09436E-30 54134 1.80114E-27 54135 2.13086E-17 54136 3.80858E-25 40092 1.38854E-27 40093 1.61865E-29 40094 1.48376E-17 40095 1.53401E-26 40096 4.11626E-26 92237 1e-10 93238 1e-10 93239 1e-10 94236 1e-10 94244 1e-10 96246 1e-10 96247 1e-10 61601 1e-10 1 950 end WTPTgap 2 0.07518 1 2004 100.0 1 600 end WTPTclad 3 6.40 1 40000 100.0 1 570 end WTPTmod 4 0.76973 2 1001 11.189 8016 88.811 1 550 end end comp read celldata latticecell squarepitch pitch 1.2598 4 fueld 0.7844 1 gapd 0.8001 2 cladd 0.9144 3 end end celldata READ model WH Pin READ param run=yes collapse=yes sn=8 epsilon=5e-5 echo=yes drawit=yes inners=10 prtmxsec=yes prtmxtab=yes prtxsec=yes prtbroad=yes END param READ collapse 22r1 177r2 39r3 END collapse READ materials 1 1 'uo2' end 2 1 'he' end 3 1 'zr' end 4 1 'h2o' end END materials READ geom global unit 1 com="Westinghouse Pin" cylinder 10 0.39220 cylinder 20 0.40005 cylinder 30 0.45720 cuboid 40 0.62990 -0.6299 0.6299 -0.6299 media 1 1 10

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141 media 2 1 20 -10 media 3 1 30 -20 media 4 1 40 -30 boundary 40 36 36 END geom READ bounds -x=reflective +x=reflective -y=reflective +y=reflective END bounds END model END =alpo textoutp notused 0$$ 7 0 wrklibs iht ihs ihm Pnord PrtGA PrtScm NoCorr 1$$ 1 3 4 6 1 0 0 0 0 T wrklin# Accept 2$$ 30 0 T end =shell copy "_pun0000" "%RTNDIR%\t_5_0" end

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142 APPENDIX C ALPO INPUT =shell copy "C:\Users\tplower\Desktop\t-depl_1050_500\savcol0a" "%TMPDIR%\ft40f001" end =alpo textoutp notused 0$$ 7 0 wrklibs iht ihs ihm Pnord PrtGA PrtScm NoCorr 1$$ 1 3 4 6 1 0 0 0 0 T wrklin# Accept 2$$ 40 0 T end =shell copy "_pun0000" "%RTNDIR%\c_7_10" end

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143 APPENDIX D XSLIST.TXT INPUT Num. of lib energy setpoints | Energy setpoints (MeV), energy id, description 3 9.9471E-04 t WH PWR, 3 wt%, UO2 fuel pin 1.0000E-02 e Graphite mod, CO2 cooled, NatU 2.5410E-01 f CRBR, MOX fuel pin, Na cooled Number of isotopes per xs file (num_isot) for t lib 254 Number of comments per isotope (icmnt) for t lib 2 Number of energy groups (igrp) for t lib 3 Legendre order (ilord) for t lib 1 Cross-section table length (ihm) for t lib 6 Number of isotopes per xs file (num_isot) for e lib 279 Number of comments per isotope (icmnt) for e lib 2 Number of energy groups (igrp) for e lib 3 Legendre order (ilord) for e lib 1 Cross-section table length (ihm) for e lib 6 Number of isotopes per xs file (num_isot) for f lib 279 Number of comments per isotope (icmnt) for f lib 2 Number of energy groups (igrp) for f lib 3 Legendre order (ilord) for f lib 1 Cross-section table length (ihm) for f lib 6 Max. of lib. temp setpts | Temp setpts (K)|fuel id, mod id | fuel temp, mod temp, temp id 5 1 4 700 300 1 800 400 2 900 500 3 1000 600 4 2500 600 5 4 1 4 500 300 1 600 400 2 700 500 3 800 600 4 4 1 4 1200 300 1 1300 400 2 1400 500 3 1500 600 4 Max. of lib. burnup setpts | Burnup setpts (GWd/MTHM), burnup id | for each enrgy) 7 7 0 0 0.459 3 17.85 16 26.35 21 39.95 29 51.85 36 67.15 45 4 0 0

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144 5 1 10 2 15 3 4 0 0 5 1 10 2 15 3

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145 APPENDIX E BURNSET.INP INPUT /prob name | pred corr flag ( 0=no,1=PCA-S,2=PCA-HE) | memory save option (0=inactive, 1=active) whpin 2 0 /# of proc for PENTRAN|Step 0 flux files exist(0=no,1=yes)|Restart?( no-<0,>0-last complte step#) 8 0 -1 /REPRO(1=use precon flx files, 0=no precon flx files)|precflx flag for initial run (0=no,1=yes) 0 0 /INTERPXS flag(1=active,0=user supplied.xsc file)|INTERPXS opt|Fuel, Mod Temp(K) | INTERPXS libid 1 2 975.76 525.43 t / PENTRAN Convergence STOP flag [interrupt sequence based on PENTRAN convergence] (0=no, 1=yes) 1 /Following 3 lines dedicated to PENPOW Problem Description SFCOMP Takahama PWR Pin Study xxx xxx /number of fuel materials 3 /range of fuel material number: eg. 1 10 1 3 /Following 3 lines dedicated to PENBURN Problem Description SFCOMP Takahama PWR Pin Study xxx xxx /# of irradiation/cool steps 2 /power((-)Watts/g;(+) Watts),time,time unit,irrad(i)/cool(c),prt step, print opt, GMIX keywrd -25.36 3 d i 1 2 s1 -25.36 4 d i 1 2 s2

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146 LIST OF REFERENCES Abbate, A.L., Courau, T., Dum onteil, E., 2007. Monte Carlo Criticality Calculations: Source Convergence and Dominance Ratio in an Infinite Lattice Using MCNP and TRIPOLI4. First International C onference on Physics and Technology of Reactors and Applications, Morocco. Benedict, M., Pigford, T.H., Levi, H.W ., 1981. Nuclear Chemical Engineering, 2nd edition. McGraw-Hill Book Company, St. Louis, MO. Bowman, S.M., Dunn, M.E., Hollenbach, D.F ., Jordan, W.C., 2008. SCALE Cross Section Libraries, SCALE5.1 Manual. Oak Ridge National Laboratory, Oak Ridge, TN. DeHart, M. D., 2006a. NEWT: A New Transport Algorithm for Two-Dimensional Discrete Ordinates Analysis in Non-Orthogonal Geometries, SCALE5.1 Manual. Oak Ridge National Laboratory, Oak Ridge, TN. DeHart, M.D., 2006b. TRITION: A Two-Dimensi onal Transport and Depletion Module for Characterization of Spent Nuclear Fuel SCALE5.1 Manual. Oak Ridge National Laboratory, Oak Ridge, TN. DeHart, M.D., 2007. Simplification of Multigroup Cross Section Processing for Large Depletion Calculations in TRITON. Joint Interna tional Topical Meeti ng on Mathematics & Computation and Supercomputing in Nu clear Applications (M&C + SNA 2007) Monterey, CA. DeHart, M.D., 2008. Three-dimensional depletion analysis of the axial end of a Takahama fuel rod. International Conference on the Physics of Reactors Nuclear Power: A Sustainable Resource, Interlaken, Switzerland. Duderstadt, J.J, Hamilton, L.J, 1976. Nuclear Reactor Analysis. John Wiley & Sons, New York. Edenius M., Ekberg, K., Forssn, B., Knott, D., 1995. CASMO-4, A Fuel Assembly Burnup Program, Users Manual, STUDSVIK/SOA-95/1, Studsvik of America, Inc., Newton, MA. Fensin, M., Hendricks, J., Anghaie, S., 2008. MC NPX 2.6 depletion method enhancements and testing. International Conference on the Physics of Reactors Nuclear Power: A Sustainable Resource, Interlaken, Switzerland. Gauld, I.C., Bowman, S.M., Horwedel, J.E., 200 6a. ORIGEN-ARP: Automatic Rapid Processing for Spent Fuel Depletion, Decay and Sour ce Term Analysis, SCALE5.1 Manual. Oak Ridge National Laboratory, Oak Ridge, TN. Gauld, I.C., Hermann, O.W., 2006. COUPLE: SCALE System Module to Process ProblemDependent Cross Sections and Neutron Spectral Data for ORIGEN-S Analyses, SCALE5.1 Manual. Oak Ridge Nati onal Laboratory, Oak Ridge, TN.

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147 Gauld, I.C., Hermann, O.W., Westfall, R. M., 2006b. ORIGEN-S: SCALE System Module to Calculate Fuel Depletion, Actinide Transm utation, Fission Produc t Buildup and Decay, and Associated Radiation Source Terms, SCALE5.1 Manual. Oak Ridge National Laboratory, Oak Ridge, TN. Gauld, I.C., Horwedel, J.E., 2006. OPUS/PLOTO PUS: An ORIGEN-S Po st Processing Utility and Plotting Program for SCA LE, SCALE5.1 Manual. Oak Ridge National Laboratory, Oak Ridge, TN. Gauld, I.C, Murphy, B.D., Williams, M.L., 2006c. ORIGEN-S Data Libraries, SCALE5.1 Manual. Oak Ridge National Laboratory, Oak Ridge, TN. Greene, N.M., 2006. BONAMI: Resonance Self-Shielding by the Bondarenko Method, SCALE5.1 Manual. Oak Ridge Nati onal Laboratory, Oak Ridge, TN. Greene, N.M., Dunn, M.E., 2006. Users Guide for AMPX Utility Modules, SCALE5.1 Manual. Oak Ridge National Laboratory, Oak Ridge, TN. Haeck, W. and Verboomen, B., 2007, An optimal approach to Monte Carlo burn-up, Nucl. Sci.Eng., 156, 180-196. Hendricks, J.S., McKinney, G.W., Fensin, M.L., Ja mes, M.R., Johns, R.C., Durkee, J.W., Finch, J.P. Pelowitz, D.B., Waters, L.S., Johnson, M.W., 2008. MCNPX 2.6.0 Extensions. Los Alamos National Laboratory, Los Alamos, NM. Hollenbach, D.F., Petrie, L.M., 2006. WORKER : SCALE System Module for Creating and Modifying Working Format Libraries, SCALE5.1 Manual. Oak Ridge National Laboratory, Oak Ridge, TN. Korea Atomic Energy Research Institute (KAERI), 2000. Cross Section Plotter/Data Tool, http://atom.kaeri.re.kr .N uclear Data Evaluation Lab, KAERI, Seoul, South Korea. Lewis, E.E., Miller, W.F., 1993. Computationa l Methods of Neutron Transport. American Nuclear Society Publishing, LaGrange Park, IL. MacFarlane, R.E., Kidman, R.B., 1977. The B ackground Cross Section Approach to Generating Group Constants for Shielding Calculations. Fifth International Conference on Reactor Shielding, Knoxville, TN. MacFarlane, R.E., Muir, D.W., 2000. The NJOY Nu clear Data Processing System, Version91, Los Alamos National Laboratory, Los Alamos, NM. Manalo, K.L., 2008. Development, Optimization, and Testing of a 3-D Zone Based Burnup/Depletion Solver for Deterministic Transport, Masters Thesis. University of Florida, Gainesville, FL.

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148 Michal, R., 2008. Industry teams offer ideas for moving GNEP forward. Nuclear News, Vol. 51, No. 10, p. 29-34, American Nuclea r Society, LaGrange Park, IL. Mock, T., 2006. Tandem Use of Monte Carlo and De terministic Methods for Analysis of Large Scale Heterogeneous Radiation Systems, Ma sters Thesis. University of Florida, Gainesville, FL. Mochizuki, H., Suyama, K. and Okuno, H, 2003,SWAT2: the improved SWAT code system by incorporating the continuous energy monte carlo code MV P International Conference on Nuclear Criticality -ICNC' 2003, Tokaimura, Japan. Nease, B., Brown, F., Ueki, T., 2008. Dominance Ratio Calculations with MCNP. International Conference on the Physics of Reactors Nuc lear Power: A Sustainable Resource, Interlaken, Switzerland. Poston, D. L. and Trellue, H. R., 1999, User 'smanual, version 2.0 for MONTEBURNS version 1.0, LA-UR-99-4999, Los Alamos Nati onal Laboratory, Los Alamos, NM. Sjoden, G.E., Haghighat, A., 2007. The Exponentia l Directional Weighted (EDW) Differencing Scheme in 3-D Cartesian Geometry. Proceed ings of the Joint International Conference on Mathematics and Supercomputing for Nucl ear Applications, Saratoga Springs, New York, Vol II, pp.1267-1276. Sjoden, G.E., Haghighat, A., 2008. PENTRANTM Code System User Guide to Version 9.4X.1 Series. HSW Technologies, Gainesville, FL. Strikwerda, John C., 2004. Finite Difference Schemes and Partial Differential Equations. SIAM Publishing, Philadelphia, PA. Tompkins, Betsy, 2008. Maximizing the Assets. Nucl ear News, Vol. 51, No. 10, p. 20, American Nuclear Society, LaGrange Park, IL. Wagner, J.C., 2001. Computational Benchmark for Estimation of Reactivity Margin from Fission Products and Minor Actinides in PWR Burnup Credit, NUREG/CR, ORNL/TM 2000/306. Oak Ridge National La boratory, Oak Ridge, TN. Wemple, C.A., Gheorghiu, H-N.M., Stammler, R.J. J, Villarino, E.A., 2008. Recent Advances in the HELIOS-2 Lattice Physics Code. Internat ional Conference on the Physics of Reactors Nuclear Power: A Sustainable Re source, Interlaken, Switzerland. Williams, M.L., Asgari, M., Hollenbach, D.F ., 2006. CENTRM: A One-Dimensional Neutron Transport Code for Computing Pointwise Energy Spectra, SCALE5.1 Manual. Oak Ridge National Laboratory, Oak Ridge, TN.

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149 Williams, M.L., Hollenbach, D.F., 2006. PMC: A Program to Produce Multigroup Cross Sections Using Pointwise Energy Spectra from CENTRM, SCALE5.1 Manual. Oak Ridge National Laboratory, Oak Ridge, TN. Yamamoto, Toshihisa, 1986. Three dimensional tran sport correction in fast reactor core analysis. Journal of Nuclear Science and Technology, Vol. 23, pp. 849-858.

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150 BIOGRAPHICAL SKETCH Thom as graduated in May 2007 from the Univer sity of Florida with a B.S. in nuclear engineering. Upon graduation, Thomas was of fered a Graduate Research Assistant position under Dr. Glenn Sjoden and completed his M.S. in nuclear engineering in December 2008. After graduate school, Thomas plans on pursuing a career within the nuclear industry.