A prototype computer program (referred to as SC11) has been developed that uses a thermodynamic ...... B.3 1979 April 14: Bruce Unit 1 P13 Fuel Damage on Refuelling . ...... The molar heat capacity is often represented by an equation of the form. ( ). 2,0,1, .... plane2 = Plot3D[{z=2-2y},{x,0,1},{y,0,1}, BoxRatios->Automatic,.
Implementation of a Thermodynamic Solver within a Computer Program for Calculating Fission-Product Release Fractions Mise en application d’un algorithme thermodynamique dans un code de calcul d’émissions des produits de fission A thesis submitted to the Division of Graduate Studies of the Royal Military College of Canada By
Duncan Henry Barber
In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy (Nuclear Science and Engineering) 2013 March
©This thesis may be used within the Department of National Defence, but copyright for open publication remains the property of the author.
THE ROYAL MILITARY COLLEGE OF CANADA
In acknowledgement for industry support, this thesis may be used within Atomic Energy of Canada Limited, Bruce Power, CANDU Owners Group, Hydro-Québec, New Brunswick Power, Ontario Power Generation, and Societatea Nationala Nuclearelectrica provided a suitable reference is provided. © Duncan Henry Barber, 2013
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This work is dedicated to the memory of family members who served King and Country during the world wars and other conflicts: Ernest Armitage (killed in France, WWI); John Williams, R.N.V.R., R.N.D., M.C. (WWI); Tom Williams (Civil Defence WWII); Frances Williams (Civil Defence, WWII); and David Barber, (WWII and India 1945-1948). We will remember them.
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ACKNOWLEDGMENTS I greatly appreciate the support, guidance, and encouragement of my Ph.D. supervisors Dr. Brent J. Lewis and Dr. Paul Chan during my studies at the Royal Military College of Canada. The guidance from Dr. William T. Thompson and Dr. Emily C. Corcoran is also appreciated. The interactions with other graduate students, particularly Markus H.A. Piro, Ali El-Jaby, Gino Bruni, Monika Kleczek and Adam Blackier added greatly to the experience. The RMC model of the thermodynamics of irradiated uranium dioxide has been an ongoing project at the Royal Military College of Canada for about 20 years. This work has benefitted immensely from the commitment of Dr. B.J. Lewis, Dr W.T. Thompson, Dr. E.C. Corcoran and many graduate students, including, most recently, Dr. M.H.A. Piro. Support for the UNENE Chair in Nuclear Fuel Modelling from the nuclear industry, Natural Sciences and Engineering Research Council and the RMC Foundation is appreciated. The support of Karen Barber and Joan Barber is gratefully acknowledged. Atomic Energy of Canada Limited, Chalk River Laboratories, supported this work, through the Research and Development program, and through access to computer facilities; compilers; and computer programs, including ORIGEN-ARP and ORIGEN-S from the SCALE 5.1 and SCALE 6.0 suites. Approvals and encouragement from Thambiayah Nitheanandan, Branch Manager of the Fuel and Fuel Channel Safety Branch, and Joanne Ball, Director of Reactor Safety Division, are appreciated. The CANDU® schematics in this thesis are copyright AECL, and were obtained from the CANTEACH website where they are available for educational and academic purposes. https://canteach.candu.org/Pages/ImageLibrary.aspx Collaboration with A.I. Popescu, Code Custodian for SOURCE IST 2.0, continues to be a pleasure. The CANDU Owners Group supported part of this work through the Industry Standard Toolset program and through its funding agreement with the Radiation Shielding Information Computational Center at Oak Ridge National Laboratories through which the SCALE 6.0 suite was obtained. Ontario Power Generation Incorporated and Atomic Energy of Canada Limited provided access to the computer program SOURCE IST 2.0P11, its documentation and validation cases. Comments from AECL and nuclear industry reviewers are appreciated. Assistance from Dr L. Lebel, Dr. C. Thiriet and Dr. A. Trottier with translations is appreciated.
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The authors of validation documents relevant to SOURCE IST 2.0P11 included (alphabetically by last name): M. Audette-Stuart, D.H. Barber, L.W. Dickson, R.S. Dickson, F. Doria, R.J. Lemire, C. McLean, W.C. Muir, A.I. Popescu, B. Szpunar, M. Vujic, and S. Yatabe. Use of material generated by these authors is acknowledged. These proprietary documents are not individually referenced. The assistance of librarians at the Ontario Hydro Research Division Library, the Ontario Hydro Head Office Library, the Ontario Hydro Public Reference Centre, the Ontario Power Generation Library, and Atomic Energy of Canada Limited’s Chalk River Library throughout my career is greatly appreciated.
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ABSTRACT Barber, Duncan Henry, Ph.D. (Nuclear Science and Engineering) Royal Military College of Canada, 2013 January, Implementation of a Thermodynamic Solver into a Computer Program for Calculating Fission-Product Release Fractions, Supervised by Professors B.J. Lewis and P.K. Chan. During some postulated accidents at nuclear power stations, fuel cooling may be impaired. In such cases, the fuel heats up and the subsequent increased fission-gas release from the fuel to the gap may result in fuel sheath failure. After fuel sheath failure, the barrier between the coolant and the fuel pellets is lost or impaired, gases and vapours from the fuel-to-sheath gap and other open voids in the fuel pellets can be vented. Gases and steam from the coolant can enter the broken fuel sheath and interact with the fuel pellet surfaces and the fission-product inclusion on the fuel surface (including material at the surface of the fuel matrix). The chemistry of this interaction is an important mechanism to model in order to assess fission-product releases from fuel. Starting in 1995, the computer program SOURCE 2.0 was developed by the Canadian nuclear industry to model fission-product release from fuel during such accidents. SOURCE 2.0 has employed an early thermochemical model of irradiated uranium dioxide fuel developed at the Royal Military College of Canada. To overcome the limitations of computers of that time, the implementation of the RMC model employed lookup tables to pre-calculated equilibrium conditions. In the intervening years, the RMC model has been improved, the power of computers has increased significantly, and thermodynamic subroutine libraries have become available. This thesis is the result of extensive work based on these three factors. A prototype computer program (referred to as SC11) has been developed that uses a thermodynamic subroutine library to calculate thermodynamic equilibria using Gibbs energy minimization. The Gibbs energy minimization requires the system temperature (T) and pressure (P), and the inventory of chemical elements (n) in the system. In order to calculate the inventory of chemical elements in the fuel, the list of nuclides and nuclear isomers modelled in SC11 had to be expanded from the list used by SOURCE 2.0. A benchmark calculation demonstrates the improvement in agreement of the total inventory of those chemical elements included in the RMC fuel model to an ORIGEN-S calculation. ORIGEN-S is the Oak Ridge isotope generation and depletion computer program. The Gibbs energy minimizer requires a chemical database containing coefficients from which the Gibbs energy of pure compounds, gas and liquid mixtures, and solid solutions can be calculated. The RMC model of irradiated uranium dioxide fuel has been converted into the required format.
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The Gibbs energy minimizer has been incorporated into a new model of fissionproduct vaporization from the fuel surface. Calculated release fractions using the new code have been compared to results calculated with SOURCE IST 2.0P11 and to results of tests used in the validation of SOURCE 2.0. The new code shows improvements in agreement with experimental releases for a number of nuclides. Of particular significance is the better agreement between experimental and calculated release fractions for 140La. The improved agreement reflects the inclusion in the RMC model of the solubility of lanthanum (III) oxide (La2O3) in the fuel matrix. Calculated lanthanide release fractions from earlier computer programs were a challenge to environmental qualification analysis of equipment for some accident scenarios. The new prototype computer program would alleviate this concern.
Keywords: Nuclear Engineering; Material Science; Thermodynamics; Radioactive Material, Gibbs Energy Minimization, Actinide Generation and Depletion, FissionProduct Generation and Depletion. viii
RÉSUMÉ Barber, Duncan Henry, doctorat (génie nucléaire) Collège Militaire Royal du Canada, janvier 2013. Mise en application d’un algorithme thermodynamique dans un code de calcul d’émissions des produits de fission, sous la direction des Professeurs B.J. Lewis et P.K. Chan. Lors de certains accidents postulés de centrales nucléaires, le refroidissement du combustible peut être compromis. Ainsi, la température du combustible augmente et le relâchement des gaz de fission quittant le combustible pour atteindre le jeu combustible-gaine s’accroit, ce qui peut induire une rupture de la gaine du combustible. Après une telle rupture, la barrière physique séparant le caloporteur du combustible est rompue totalement ou partiellement permettant la sortie des gaz et des vapeurs depuis le jeu combustible-gaine et depuis les pores ouvertes des pastilles-combustible dans le circuit primaire. A l’inverse gaz et caloporteur sous forme gazeuse peuvent entrer par la rupture de la gaine et interagir avec les pastilles-combustible et les produits de fission à leur surface. La chimie de ces interactions est un important mécanisme à modéliser pour estimer la quantité de produits de fission sortis du combustible. A partir de 1995, le code de calcul, SOURCE 2.0, a été développé par l'industrie nucléaire canadienne pour modéliser la sortie de produits de fission du combustible lors de telles conditions accidentelles. A l’origine, SOURCE 2.0 a utilisé un modèle thermochimique du combustible de dioxyde d'uranium irradié développé au Collège Militaire Royal du Canada. Pour mettre en œuvre ce modèle, malgré la capacité limitée de calculs des ordinateurs, des tables de conditions d’équilibre préalablement calculées ont été utilisées. Par la suite, ce modèle a été amélioré, la capacité de calcul des ordinateurs a augmenté de manière significative et les bibliothèques de données thermodynamiques sont devenues disponibles. Cette thèse est le résultat de travaux complets fondés sur ces trois facteurs. Un code de calcul prototype appelé SC11, qui utilise une bibliothèque de sousprogrammes thermodynamiques pour calculer l’équilibre thermodynamique par minimisation de l’énergie de Gibbs, a été développé. La méthode de minimisation de l'énergie de Gibbs requière la température (T) et la pression (P) du système, et l'inventaire des éléments chimiques (n) présents dans le système. Afin de calculer l'inventaire des éléments chimiques contenus dans le combustible, la liste de nucléides et des isomères modélisés dans SC11 a dû être augmentée à partir de la liste utilisée par SOURCE 2.0. Un calcul de référence a montré l’amélioration des résultats lorsque l’inventaire complet des éléments chimiques était utilisé comme dans le modèle de combustible de CMR comparé à celui d’ORIGEN-S utilisant un nombre plus limité d’éléments chimiques. ORIGEN-S est le code de calcul de production et de disparition d’isotopes développé { Oak Ridge National Laboratory. ix
La méthode de minimisation de l’énergie de Gibbs requière une bibliothèque chimique contenant les coefficients { partir desquels l’énergie de Gibbs des composés purs, sous forme de mélange gazeux et liquide, ainsi que l’énergie de Gibbs de solutions solides peuvent être calculées. Le modèle de CMR du combustible de dioxyde d'uranium irradié a été converti dans le format requis. La méthode de minimisation de l’énergie de Gibbs a été incorporée dans un nouveau modèle de vaporisation des produits de fission depuis la surface du combustible. Les taux d’émission calculés utilisant ce nouveau code ont été comparés aux résultats calculés utilisant SOURCE IST 2.0P11, ainsi qu’{ ceux des tests utilisés pour la validation de SOURCE 2.0. Le nouveau code montre un meilleur accord avec les émissions expérimentales pour un certain nombre de nucléides. En particulier, l'accord entre la quantité de 140La émis calculée et celle expérimentale est significativement amélioré. Cette amélioration est probablement due à la prise en compte dans le modèle de CMR de la solubilité du sesquioxyde de lanthane (La2O3) dans la matrice-combustible. Jusqu’{ présent, le calcul d’émissions de lanthanide, a causé des problèmes dans les analyses de qualification environnementale. Le nouveau code prototype pourrait atténuer ce problème.
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TABLE OF CONTENTS Acknowledgments.............................................................................................................v Abstract .............................................................................................................................. vii Résumé ................................................................................................................................ ix Table of Contents ............................................................................................................. xi List of Tables ..................................................................................................................xvii List of Figures.................................................................................................................. xix 1
Introduction ................................................................................................................ 1 1.1 1.2 1.3
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A Brief History of Nuclear Power in Canada ............................................................... 2 CANDU® Pressurized Heavy Water Reactors ...........................................................12 Nuclear Safety Analysis .....................................................................................................16
Literature Review ...................................................................................................19 2.1 Nuclear Safety Analysis Computer Programs ...........................................................19 2.1.1 VICTORIA.....................................................................................................................19 2.1.2 ELSA ..............................................................................................................................20 2.1.3 FASTGRASS .................................................................................................................20 2.1.4 MFPR .............................................................................................................................21 2.1.5 TRANSURANUS .........................................................................................................21 2.1.6 ELESTRES and ELOCA ............................................................................................22 2.1.7 SOURCE 2.0 .................................................................................................................22 2.2 Thermodynamics .................................................................................................................23 2.2.1 Chemical Equilibrium from Gibbs Energy Minimization ..........................23 2.3 The RMC Thermochemical Model of Uranium-Dioxide Fuel ..............................25 2.3.1 Chemical Elements Modelled ..............................................................................26 2.3.2 Pure Substances ........................................................................................................27 2.3.3 Solution Phases .........................................................................................................28
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Goals of Research ....................................................................................................29 3.1 3.2
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Outline of Thesis Work ......................................................................................................30 Rationale for these Activities ..........................................................................................31
Background Theory ...............................................................................................35 4.1 Chemical Thermodynamics .............................................................................................35 4.1.1 Computation of Molar Gibbs Energy ................................................................35 4.1.2 Absolute Enthalpy and Standard Enthalpy of Formation at 298.15 K ..................................................................................................................36 4.1.3 Absolute Entropy and Standard Entropy at 298.15 K ...............................37 4.1.4 Representations of Molar Heat Capacity.........................................................38 4.1.5 Derivation of Molar Enthalpy, Molar Entropy and Molar Gibbs Energy from Molar Heat Capacity......................................................................39 4.1.6 Entropy of Mixing in Ideal Solutions ................................................................41 xi
4.1.7 Partial Molar Gibbs Energy of Mixing .............................................................. 43 4.1.8 Gibbs’ Phase Rule..................................................................................................... 46 4.1.9 An Example of Gibbs Energy Minimization ................................................... 48 4.1.10 Gibbs Energy Minimization and Equilibrium Constants .......................... 53 4.2 Fission Yield and Fission-Product Inventories........................................................ 58
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Inventory Benchmarking Exercises ............................................................... 63 5.1 Nuclide Benchmarking...................................................................................................... 64 5.1.1 SCALE 6.0 ORIGEN-S Input File.......................................................................... 66 5.1.2 SOURCE IST 2.0P11 Input Values ...................................................................... 69 5.1.3 Output Comparisons .............................................................................................. 72 5.2 Benchmarking Molar Inventory of Chemical Elements ....................................... 92 5.2.1 SOURCE IST 2.0P11 ................................................................................................ 92 5.2.2 Revised Nuclide Set ................................................................................................ 94 5.3 Benchmarking Revised Code and Library ................................................................. 96
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Model Development and Code Implementation ....................................... 99 6.1 Incremental Software Requirements .......................................................................... 99 6.2 Model Description ............................................................................................................100 6.2.1 Physics Data .............................................................................................................100 6.2.2 Chemical Analogues..............................................................................................101 6.2.3 Initialization ............................................................................................................103 6.2.4 Equilibrium at the Fuel Surface and Releases to the Gap ......................103 6.2.5 Fission-Product Release from the Gap ..........................................................106 6.3 Existing SOURCE 2.0 Structure ....................................................................................107 6.4 Revised Initialization .......................................................................................................109 6.4.1 MODULE ChemElem .............................................................................................109 6.4.2 MODULE CAData ....................................................................................................109 6.4.3 SUBROUTINE InitChemApp ..............................................................................110 6.4.4 SUBROUTINE CAbort ...........................................................................................110 6.4.5 SUBROUTINE SetChemAppUnits.....................................................................110 6.4.6 Deletions and Incidental Changes ...................................................................111 6.5 Implementation of Revised Model for Fission-Product Vaporization from the Fuel Surface ......................................................................................................111 6.5.1 SUBROUTINE FSFPVap .......................................................................................112 6.5.2 SUBROUTINE ChemCalc .....................................................................................113 6.6 Limitations...........................................................................................................................118 6.6.1 Use of Analogues ....................................................................................................118 6.6.2 Vaporization of Tin (126Sn) ................................................................................119 6.6.3 Behaviour of Grain-Boundary Bubbles .........................................................119 6.6.4 Boundary Condition for Fission-Product Diffusion from Grains ........120
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Benchmarking of Fractional Releases ........................................................ 123 7.1 7.2 7.3 7.4
Summary of Results .........................................................................................................124 Benchmarking 140La .........................................................................................................127 Benchmarking 134Cs and 137Cs .....................................................................................129 Benchmarking 85Kr...........................................................................................................131 xii
7.5 7.6 7.7 7.8 7.9 7.10 7.11
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Discussion ............................................................................................................... 145 8.1 8.2 8.3
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Benchmarking 95Zr and 95Nb........................................................................................ 132 Benchmarking 103Ru and 106Ru.................................................................................... 134 Benchmarking 131I ............................................................................................................ 137 Benchmarking 133Xe and 135Xe .................................................................................... 138 Benchmarking 140Ba ........................................................................................................ 139 Benchmarking 144Ce ........................................................................................................ 140 Benchmarking 125Sb and 154Eu and Assessment of Chemical Analogues ............................................................................................................................ 142 Discussion of Benchmarking of SOURCE IST 2.0P11 Nuclide Inventories .......................................................................................................................... 145 Discussion of Benchmarking of Total Inventories of Chemical Elements............................................................................................................................... 148 Discussion of Benchmarking of Fission-Product Release Fractions ............. 149
Conclusions ............................................................................................................ 155
10 Recommendations............................................................................................... 157 10.1 Verification of Chemical Data....................................................................................... 157 10.2 Additions to the Chemical Database.......................................................................... 157 10.2.1 Neptunium Vapour Species ............................................................................... 158 10.2.2 Incorporation of Neptunium and Plutonium into the NonStoichiometric Fluorite Model ......................................................................... 158 10.3 Proposed Deletion from the Chemical Database .................................................. 159 10.3.1 Caesium Trizirconate ........................................................................................... 159 10.4 Proposed Revisions to the Database ......................................................................... 159 10.4.1 Enthalpy of Formation of Cs2MoO4 ................................................................ 159 10.5 Verification of Physics Data .......................................................................................... 160 10.6 Nuclide Inventory Benchmarking .............................................................................. 161 10.7 Revised Model of Releases Due to Grain-Boundary Bubble Interlinkage ......................................................................................................................... 161 10.8 Boundary Condition for Fission-Product Diffusion within Fuel Grains ...... 162 10.9 Oxygen Transport ............................................................................................................. 163
11 References .............................................................................................................. 165 Appendix A ..................................................................................................................... 185 A Postulated Accidents in Nuclear Safety Analysis ....................................................... 185 A.1 Large-Break Loss Of Coolant Accident (LOCA) ..................................................... 185 A.2 Small-Break Loss Of Coolant Accident (LOCA) ..................................................... 186 A.2.1 Out-of-Core Failures............................................................................................. 186 A.2.2 In-Core Break .......................................................................................................... 189 A.3 Loss of Coolant Accident with Loss of Emergency Core Cooling ................... 190 A.4 Secondary-Side Breaks ................................................................................................... 191 A.5 Loss of Flow ........................................................................................................................ 191 A.6 Fuel Handling Accident .................................................................................................. 192 A.7 Loss of Regulation ............................................................................................................ 193 xiii
A.8
Auxiliary System Failures ..............................................................................................193
Appendix B..................................................................................................................... 195 B Actual Nuclear Generating Station Incidents in Canada ..........................................195 B.1 1962 December: Nuclear Power Demonstration (NPD) Fuelling Machine O-Ring Seal Leak .............................................................................................197 B.2 1967 April: Douglas Point Calandria Tube Fretting ............................................198 B.3 1979 April 14: Bruce Unit 1 P13 Fuel Damage on Refuelling ..........................199 B.4 1983 August 01: Pickering Unit 2 G16 Pressure Tube Failure .......................199 B.5 1986 March 28: Bruce Unit 2 N06 Pressure and Calandria Tube Failure ...................................................................................................................................201 B.6 1988 November: Pickering NGS-A Unit 1 Overpower Transient ...................203 B.7 1989 March 13: Gentilly Unit 2 Loss of Class IV Power .....................................204 B.8 1990 January 23: Bruce Unit 4 Channel C08 Fuelling Machine Event .........204 B.9 1990 September 25-27: Pickering Unit 2 Flux Tilt ..............................................205 B.10 1990 November 30: Darlington Unit 2 N12 Fuel Damage ................................207 B.11 1991 June 07: Pickering Unit 3 Boiler Inlet Valve Leak .....................................208 B.12 1994 December 10: Pickering Unit 2 Bleed Condenser Relief Line Failure ...................................................................................................................................208 B.13 2003 August 14: Ontario Multi-Unit Loss of Class IV Power ...........................209 B.14 2008 April 09: Pickering B Unit 7 Calandria Tube A13 Crack .........................211
Appendix C ..................................................................................................................... 213 C Fuel Channel Maps .................................................................................................................213 C.1 NPD Nuclear Generating Station Channel Map .....................................................213 C.2 Douglas Point NGS Channel Map.................................................................................214 C.3 Pickering NGS-A Channel Map .....................................................................................215 C.4 CANDU-6®/Pickering NGS-B Channel Map.............................................................216 C.5 Bruce/Darlington NGS-A Channel Map ....................................................................217
Appendix D .................................................................................................................... 219 D Fission-Product Release Code SOURCE 2.0 ..................................................................219 D.1 SOURCE 2.0 in the Safety Analysis Sequence .........................................................219 D.1.1 Overview Description of SOURCE 2.0 ............................................................221 D.2 Modelling Aspects in SOURCE 2.0 ..............................................................................223 D.2.1 Inventory Bins ........................................................................................................223 D.2.2 Actinides ...................................................................................................................224 D.2.3 Fission Products.....................................................................................................227 D.2.4 Sheath and Fuel-to-Sheath Gap ........................................................................229 D.2.5 Fuel Geometry.........................................................................................................230 D.3 Domain of Application ....................................................................................................230 D.4 Phenomena and Models .................................................................................................231 D.4.1 Grain-Level Phenomena......................................................................................233 D.4.2 Annulus-Level Phenomena ................................................................................240 D.4.3 Pin-Level Phenomena ..........................................................................................242 D.4.4 Nuclide Transformations and Nuclear Data................................................246
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Appendix E ..................................................................................................................... 249 E Sample SC11 User Input Files and Output Files ......................................................... 249 E.1 Case Geometry Data File ................................................................................................ 250 E.2 Reference Geometry File ............................................................................................... 253 E.3 Fresh Fuel File.................................................................................................................... 255 E.4 Time-Dependent Input Data (Transient_In) .......................................................... 255 E.5 File of File Names.............................................................................................................. 259 E.6 Sample Batch File for Running a Case ...................................................................... 260 E.7 SC11 Timings for Test Cases ........................................................................................ 261 E.8 Release Fraction Table from Summary Output File ............................................ 262 E.9 Extracts from Screen Output File ............................................................................... 267
Appendix F ..................................................................................................................... 275 F RMC Thermochemical Database for Uranium Dioxide, its Activation and Fission Products ................................................................................................................ 275 F.1 Formatting........................................................................................................................... 275 F.2 DATReader .......................................................................................................................... 275 F.3 Compound Data ................................................................................................................. 276 F.3.1 Sorting Order by Compound Name ................................................................ 276 F.3.2 Sorting Order of Phases ...................................................................................... 276 F.3.3 Temperature Ranges ........................................................................................... 277 F.3.4 H(298.15) and S(298.15)................................................................................... 277 F.3.5 Powers of Temperature in the Isobaric Heat Capacity (Cp) Expressions ............................................................................................................. 277 F.4 Solution Models ................................................................................................................. 401 F.4.1 Gas/Vapour Phase ................................................................................................ 402 F.4.2 Uranium-Dioxide Host Phases ......................................................................... 404 F.4.3 Uranium Dioxide Fluorite Solid Solution (FCC) ........................................ 404 F.4.4 Liquid Uranium-Dioxide Phase ........................................................................ 404 F.4.5 Noble Metals............................................................................................................ 405 F.4.6 Double Oxides ......................................................................................................... 408 F.4.7 Uranium Noble-Metal Phase ............................................................................. 410 F.4.8 Rhombohedral Rare-Earth Uranium Oxides .............................................. 410 F.4.9 Liquid Uranium Molybdenum Oxide ............................................................. 411 F.5 Mixing Parameters ........................................................................................................... 411
Appendix G ..................................................................................................................... 417 G Discrepancies in Thermochemical Data ........................................................................ 417 G.1 Discrepancies Observed in Examining Output of Calculated Equilibria ............................................................................................................................. 417 G.1.1 Rhodium Dioxide Gas .......................................................................................... 417 G.1.2 Plutonium Gas ........................................................................................................ 418 G.1.3 Neptunium Metal................................................................................................... 419 G.2 Discrepancies Detected in Calculating Thermodynamic Quantities ............. 419 G.2.1 Lanthanum Gas ...................................................................................................... 420 G.2.2 Molybdenum Gas ................................................................................................... 420
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G.2.3 G.2.4
Technetium Dioxide Gas .....................................................................................422 Fictive Compounds ...............................................................................................423
Appendix H .................................................................................................................... 425 H Nuclide List and Utility Program arplibreader ...........................................................425 H.1 SC11 Nuclide List ..............................................................................................................425 H.2 Utility Program arplibreader........................................................................................426 H.2.1 Relevant ORIGEN-S Library Records .............................................................426 H.2.2 Overview of arplibreader ...................................................................................428
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LIST OF TABLES Table 1 Table 2 Table 3 Table 4 Table 5 Table 6 Table 7 Table 8 Table 9 Table 10 Table 11 Table 12 Table 13 Table 14
Table 15 Table 16 Table 17 Table 18 Table 19 Table 20 Table 21 Table 22 Table 23 Table 24 Table 25 Table 26
Chronology of In-Service Nuclear Power Units in Canada..................................................................................................... 9 Nuclear Safety Accident Categories ...............................................17 Actual Reactor Events in Canada ....................................................18 ORIGEN-S CANDU® 37-element Sub-libraries ..........................63 ORIGEN-S Irradiation Conditions ...................................................65 SOURCE 2.0P11 Irradiation Conditions .......................................65 ORIGEN-S (SCALE 6.0) Input............................................................67 Fuel Bundle Description .....................................................................70 Nominal Fuel Data.................................................................................71 Fuel Power Data .....................................................................................72 Nuclides with Signed Difference from Mean Lower Than Lower Limit ...................................................................74 Nuclides with Signed Difference from Mean above the Upper Limit .........................................................................76 Nuclides with Signed Difference from Mean within the Limits....................................................................................77 SOURCE IST 2.0P11 Inventory of a Chemical Element in the RMC Thermochemical Model as a Fraction of the ORIGEN-S Inventory for That Chemical Element ..................................................................................93 Inventory of a Chemical Element from Revised Code and Revised Physics Data Library as a Fraction of ORIGEN-S Chemical Inventory .................................97 Chemical Analogues in SOURCE 2.0 and SC11 ....................... 102 Call Tree of Major SOURCE Routines ......................................... 107 SOURCE IST 2.0 Validation Cases ................................................ 123 Paired Statistics Comparing Individual Nuclides ................. 125 Domain of Application of SOURCE 2.0 ....................................... 230 SOURCE 2.0 Phenomena.................................................................. 231 SC11 Timings for Test Cases.......................................................... 261 Consistency Check of Uranium/Noble-Metal Phase ........................................................................................................ 271 The RMC Fuel Chemistry Database Compounds and Components ................................................................................. 278 List of Solution Models ..................................................................... 401 Ideal Gas Phase Constituents ........................................................ 403 xvii
Table 27 Table 28 Table 29 Table 30
Constituents of Liquid Uranium-Dioxide Phase ................... 405 Excess Mixing Parameters ............................................................. 412 Nuclides Modelled in SC11 ............................................................ 425 Capture Cross-Section for 234U (n, γ) 235U ............................... 429
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LIST OF FIGURES Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19
In-Service Nuclear Power Reactors in Canada .........................11 CANDU-6® Reactor Assembly (Coutesy of AECL and CANTEACH) ....................................................................................13 CANDU-6® Primary Heat Transport System (Coutesy of AECL and CANTEACH) ...............................................14 Calandria Cross-Section (Coutesy of AECL and CANTEACH) .............................................................................................16 Mathematica 8 Notebook to Plot Relationship among Three Species ...........................................................................49 Plot of Stoichiometric Constraints .................................................50 System Gibbs Energy in Joules vs. Moles of Hydrogen Molecules.............................................................................51 Details Close to the Minimum of System Gibbs Energy ........................................................................................................51 Mathematica 8 Command to Minimize Gibbs Energy for This System .......................................................................52 Mathematica 8 Results ........................................................................52 FactSage Output in FACT Format for the Equilibrium ..............................................................................................52 Fission Product Inventory for Natural Uranium at Two Burnups as a Function of Fission Product Mass Number .........................................................................59 Fission-Product Inventory in Natural Uranium at 10 and 100 MW·h·kg-1 ....................................................................61 Plutonium Isotopes 239Pu, 240Pu and 241Pu in Modelled Bundle from SOURCE IST 2.0P11 and ORIGEN-S 6.0 Analysis ........................................................................88 Comparison of SOURCE and ORIGEN-S Inventories for Plutonium-239 .......................................................89 Comparison of SOURCE and ORIGEN-S Inventories for Plutonium-240 .......................................................89 Comparison of SOURCE and ORIGEN-S Inventories for Plutonium-241 .......................................................90 Comparison of SOURCE and ORIGEN-S Inventories of 238Pu and 242Pu ..........................................................90 Comparison of SOURCE and ORIGEN-S Inventories for 242Pu ............................................................................91 xix
Figure 20 Figure 21 Figure 22 Figure 23 Figure 24 Figure 25 Figure 26 Figure 27 Figure 28 Figure 29 Figure 30 Figure 31 Figure 32 Figure 33 Figure 34 Figure 35 Figure 36 Figure 37 Figure 38 Figure 39 Figure 40 Figure 41 Figure 42 Figure 43 Figure 44 Figure 45 Figure 46 Figure 47 Figure 48 Figure 49 Figure 50 Figure 51 Figure 52 Figure 53 Figure 54 Figure 55
Schematic of the Equilibrium System (not to scale) ....................................................................................................... 104 Calculated Vs. Experimental Releases for 140La .................... 127 Calculated Vs. Experimental Releases for 134Cs .................... 129 Calculated Vs. Experimental Releases for 137Cs .................... 130 Calculated Vs. Experimental Releases for 85Kr ...................... 131 Calculated Vs. Experimental Releases for 95Zr ...................... 133 Calculated Vs. Experimental Releases for 95Nb ..................... 134 Calculated Vs. Experimental Releases for 103Ru ................... 135 Calculated Vs. Experimental Releases for 106Ru ................... 136 Calculated Vs. Experimental Releases for 131I........................ 137 Calculated Vs. Experimental Releases for 133Xe .................... 138 Calculated Vs. Experimental Releases for 135Xe .................... 139 Calculated Vs. Experimental Releases for 140Ba .................... 140 Calculated Vs. Experimental Releases for 144Ce .................... 141 Calculated Vs. Experimental Releases for 125Sb .................... 142 Calculated Vs. Experimental Releases for 154Eu.................... 143 NPD NGS Channel Map .................................................................... 213 Douglas Point NGS Channel Map ................................................. 214 Pickering NGS-A Channel Map ..................................................... 215 CANDU-6®/Pickering NGS-B Channel Map............................. 216 Bruce/Darlington NGS-A Channel Map .................................... 218 Example Case Geometry File ......................................................... 252 Example Geometry Reference Data File ................................... 254 Example Fresh Fuel File .................................................................. 255 Example Transient Input File ....................................................... 256 Example File of File Names ............................................................ 260 Batch File to Run Sample Case ..................................................... 260 Fractional Release Table ................................................................. 263 SC11 Text Output Header ............................................................... 267 ChemCalc Header before Calling the Gibbs Energy Minimizer .............................................................................. 267 Input to Gibbs Energy Minimizer ................................................ 268 Calculated Gas Composition .......................................................... 269 Calculated Fluorite Phase Composition ................................... 270 Other Calculated Solution Phases ............................................... 270 Predicted Pure Substances ............................................................ 272 Output from DATReader for Lanthanum Gas ........................ 421
xx
1 Introduction In 2012, nuclear power stations supplied 56.4% of the electricity demand in Ontario [IESO 2013]. Part of the work to support nuclear power generation is the ongoing analysis of nuclear events and emerging issues. Some existing safety analysis has been performed with bounding assumptions.
The “true” consequences of a
postulated event are expected to be less than those of the bounding analysis. There is also a move to analyse more-extreme events that had previously been deemed to be too unlikely to happen. In some cases, new initiating events have been identified that had not previously been considered. In other cases, analysts are looking at “How bad can it get?”, rather than “How likely is it to get that bad?” The purpose of this thesis is to demonstrate the incorporation of a thermodynamic solver into the Canadian nuclear industry fission-product release computer program SOURCE 2.0 [Brito 1995] [Barber 1999] [Barber 2001] [Barber 2005]. The solver uses Gibbs energy minimization. Gibbs energy is named after J. Willard Gibbs, who documented the criteria for chemical equilibria, first in a footnote [Gibbs 1873] and later in a lengthy paper [Gibbs 1876].
This thesis includes a description of
accompanying work that was required to create a prototype version of a nuclear safety analysis computer program containing such a solver. The details of such a solver have recently been described [Piro 2008] [Piro 2011]. The solver uses a version of the RMC thermochemical model for irradiated uranium dioxide fuel most recently documented by Corcoran [Corcoran 2009] and Piro [Piro 2011]. Before
1
2 discussing thermodynamics and nuclear safety analysis, a brief history of nuclear power in Canada will be presented.
1.1 A Brief History of Nuclear Power in Canada The history of nuclear power in Canada is built on the foundations of academic research starting with the appointment of a New Zealander, Prof. Ernest Rutherford, as the MacDonald Professor of Physics at McGill University in Montreal in 1898 [Rutherford 1905] [Brooks 1993] [Brown 2009].
Rutherford had been a
graduate student of J.J. Thomson at the Cavendish Institute, University of Cambridge (England).
In 1904, Rutherford published the first edition of his book,
Radio-activity. The turn of that century was a time of such rapid progress that the second edition came out the following year [Rutherford 1905]. Rutherford moved back to England and was at The University of Manchester from 1907-1919. Then, he served as director of the Cavendish Institute at Cambridge from 1919 until his death in 1937. One of Rutherford’s students at the Cavendish Institute was George C. Laurence. Laurence, a Canadian, returned to Canada in 1930 to join the National Research Council of Canada. The Council was interested in radium and X-rays in the 1930s due to their use in medicine. Canadian production of radium was from the Eldorado Gold Mines Limited mine at Port Radium on Great Bear Lake, North-West Territories [Arsenault 2005]. The uranium separated from radium ore was treated as a waste by-product. During 1941 and 1942, Laurence worked on a sub-critical assembly made with coke (carbon) and black uranium oxide [Laurence 1980].
3 Laurence was able to borrow 450 kg of this uranium “waste” from Eldorado Gold Mines Limited. Before the fall of France in May 1940, a team in France had been working with heavy water and uranium. The French had acquired the stockpile of heavy water from the Norsk (Norwegian) Hydro heavy-water plant at Vemork, Norway1, before the German invasion of Norway in April 1940. This heavy water and many of the scientists from the French laboratory were evacuated to the Cavendish Institute in Cambridge, England. In the interests of keeping the project safe from German bombing of Britain, and to foster collaboration with the United States’ Manhattan Project, the nuclear heavy-water laboratory was moved to Montréal, Québec. The Canadian laboratories had responsibility for researching a heavy-water plutonium production reactor and the separation of 239Pu from low-burnup2 uranium fuel and 233U
1
2
from thorium fuel.
After failed attempts by British forces, the British Special Operations Executive (SOE) sent British-trained Norwegian nationals to destroy the Norwegian heavy-water plant. On the night of 1943 February 27/28, the plant was put out action [Gallagher 2002]. The author has performed calculations using ORIGEN-S from SCALE 5.1 [Gauld 2006a] for CANDU® fuel at a total thermal power of 488 kW per bundle. The upper limit on burnup to produce weapons-grade plutonium ({Hydrogen, Oxygen, Steam}, BoxRatios->Automatic, PlotStyle->Yellow, PlotRange->{0,1}, ClippingStyle->None] plane2 = Plot3D[{z=2-2y},{x,0,1},{y,0,1}, BoxRatios->Automatic, PlotStyle->Directive[Purple,Opacity[0.5]], PlotRange->{0,1}, ClippingStyle->None] Intersect = ParametricPlot3D[{1-z=(2 – z)/2,z},{z,0,1}, PlotStyle-> {Thick,Green}] Show[{plane1,plane2,Intersection}]
Figure 5
Mathematica 8 Notebook to Plot Relationship among Three Species
The molar Gibbs energy values at standard pressure were calculated using FactSage 6.1 and the RMC thermochemical database for nuclear fuel [Piro 2011]. The Gibbs energy of the system is plotted in Figure 7 and Figure 8. The first graph, Figure 7, shows the variation along the entire intersection of the planes. The second graph, Figure 8, shows the area around the minimum in Gibbs energy.
The
50 independent variable was selected to be moles of hydrogen as the number of moles of steam and of oxygen are close to 1.0 and 0.5 and the relative difference in the values plotted on the x-axis would be more difficult to see had either of those parameters been selected. The lack of smoothness in Figure 7 and more obviously in Figure 8 is a result of round-off in dealing with very small quantities of hydrogen.
Figure 6
Plot of Stoichiometric Constraints
51
-350,000
System Gibbs Energy (J)
-400,000
-450,000
-500,000
-550,000
-600,000 0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
Moles of Hydrogen Molecules
Figure 7
System Gibbs Energy in Joules vs. Moles of Hydrogen Molecules
-566782.66884600
System Gibbs Energy (J)
-566782.66884602
-566782.66884604
-566782.66884606
-566782.66884608
-566782.66884610 1.10E-10
1.30E-10
1.50E-10
1.70E-10
1.90E-10
Moles of Hydrogen Molecules
Figure 8
Details Close to the Minimum of System Gibbs Energy
52 A Mathematica 8 [Wolfram 2010] command to minimize the system Gibbs energy was written as shown in Figure 9 and evaluates to the results in Figure 10. NMinimize[{-145427.1 mH – 220764.1 mO – 448462.2 mW + 8314.472 (mH Log[mH/mT] + mO LOG[mO/mT] +mW Log [mW/mT]), m ≥0, mO≥0, mH≥0, mH
m
1., mO
0.5m
1.,
mT == mH + mO +mW},{mH,mW,mO,mT}]
Figure 9
Mathematica 8 Command to Minimize Gibbs Energy for This System 566782.6688460815, *mH 1.49850427711447 10 m 0.9999999998501495, mO 0.500000000074925, mT 1.500000000074925+ Figure 10
,
Mathematica 8 Results
The corresponding output from the commercial thermochemistry package FactSage 6.1 [Bale 2002] is presented in Figure 11. H2 +
O2 =
1.5000 mol gas_ideal (34.015 gram, 1.5000 mol, 123.09 litre, 2.7635E-04 g/ml) (1000.00 K, 1 atm, a=1.0000) ( 0.66667 H2O + 0.33333 O2 + 9.9899E-11 H2) The cutoff concentration has been specified to 1.0000E-75 ***************************************************************** H G V S Cp (J) (J) (litre) (J/K) (J/K) ***************************************************************** -2.04483E+05 -5.66783E+05 1.23087E+02 3.62300E+02 5.86896E+01 Total mass/gram = 34.015
Figure 11
FactSage Output in FACT Format for the Equilibrium
Once the mole fractions in the FactSage output are multiplied by the 1.5000 moles in the phase, the results are identical within the printed precision.
53 The consistency of the two solutions to the numerical problem can be determined by checking that the concentrations calculated satisfy the equilibrium constant. That is ( )
(
( ) ) ( )
(
( )
)
(4-43)
( ) is evaluated using the FactSage/Piro data [Piro 2011]
where, previously used,
( )
448462.2
( )
( 145427.1)
( )
1 2
1 2 ( 220764.1)
( )
192653.05
(4-44)
1.11558 10.
(4-45)
and 192653.05 (8.314472
1000.0)
The quotient of partial pressures is
(
( ) ) ( )
. .
1.11559 10.
.
(4-46)
These values agree to the accuracy of the FactSage output. 4.1.10 Gibbs Energy Minimization and Equilibrium Constants For the sample problem, and recognizing that ln
ln
,
(4-47)
54 the system Gibbs energy can be written as ln
.
(4-48)
From the stoichiometric balance constraints, (4-49)
and 1 2
1 2
.
(4-50)
Hence,
1,
(4-51)
1 2
(4-52)
1.
(4-53)
and, obviously,
The total number of moles of gas is ,
hence,
(4-54)
55 1
1 2
1
1 2.
(4-55)
Taking the derivative of the system Gibbs energy with respect to
1 2
ln
.
(4-56)
However, the first three terms (in brace brackets “*+”) on the right-hand side represent the Gibbs energy for the reaction creating one mole of hydrogen and can be represented by
,
. The second part of the subscript indicates that the
Gibbs energy change is per mole of the indicated compound formed. The whole equation can be divided through by
. The term
(4-57)
can be rewritten as
.
(4-58)
To find the minimum of system Gibbs energy, the first derivative is zero, hence,
0
,
ln
.
(4-59)
56 The summation can be separated into two sums. The first sum evaluates to zero, since
1 2
1
1
1 2
1
1 1 2
1 2 0.
(4-60)
In the second sum, the substitution ln( )
ln
(4-61)
can be made. Hence,
ln( )
ln
1 2 ln
ln
ln
ln
,
.(4-62)
Finally,
0
,
ln
which, treating all components as ideal gases, leads to
,
,
(4-63)
57
exp
The
,
.
,
(4-64)
is the heat of reaction for
.
(4-65)
The derivations with respect to the other molar quantities yield similar results
exp
(4-66)
,
where the reaction to produce 1 mole of oxygen is 2
2
when the derivative is taken with respects to exp
(4-67)
, and (4-68)
,
where the reaction to produce one mole of steam is .
(4-69)
Clearly the heats of reaction for the different forms of the chemical equilibrium are related by
,
,
,
.
(4-70)
58 The zero derivatives occur at the same values of the molar quantities of each substance (molecular hydrogen, molecular oxygen and steam).
Thus, the
minimization of Gibbs energy with respect to each reactant leads to the expression for the equilibrium constant for the reaction in terms of the Gibbs energy change for the reaction.
4.2 Fission Yield and Fission-Product Inventories In this section, an example is provided of the fission-product inventories at constant power for CANDU® fuel at burnup values of 10 MW·h·kg-1and 100 MW·h·kg-1. Given that typical exit burnup of CANDU® fuel in Ontario Power Generation reactors was 200 MW·h·kg-1 [Tait 2000], the first burnup is relatively fresh fuel, while the second is close to the average in-core burnup. In nuclear fission, a nucleus is broken into two other nuclei and excess neutrons. The bulk of the fission products from thermal fission of 235U tend to fall within two well-defined mass regions 80 to 110 atomic mass units and 125 to 155 atomic mass units. Occasionally, there are three nuclei created, in a process called ternary fission, with the third nucleus having a mass of up to 14 atomic mass units. The light ternary fission products are not modelled. The distribution of fission-product yields is often plotted as a function of mass number in sets of curves for each target and neutron energy. These graphs show the instantaneous fission yield of all nuclides and nuclear isomers having the same mass number plotted as the dependent variable with mass number as the independent variable.
59 Decay and transmutation of fission products will alter the makeup of the fuel with time and further irradiation.
For the computation of chemical equilibria in
irradiated fuel, it is the inventories at the time of the calculation rather than the amount that has been created and may have decayed or been transmuted that matters. A sample calculation was performed (using ORIGEN-S from SCALE 5.1) for the irradiation of 19.25 kg of uranium at a constant power of 488 kW. The results at 10 and 100 MW·h·kg-1 are shown in Figure 12 and in Figure 13.
1.00E+00
1.00E-01
Relative Molar Abundance
1.00E-02
1.00E-03
1.00E-04
1.00E-05
1.00E-06
1.00E-07
1.00E-08 70
90
110
130
150
170
Mass Number 10 MW.h/kgU 100 MW.h/kgU
Figure 12
Fission-Product Inventory for Natural Uranium at Two Burnups as a Function of Fission Product Mass Number
60 The results are plotted at 10 MW·h·kg-1 to show fission products primarily from 235U fission. The results at 100 MW·h·kg-1show a difference as more of the fission is occurring in
239Pu.
The offset of the line corresponding to 100 MW·h·kg-1 to the
right of the line corresponding to 10 MW·h·kg-1 is the result of an increase in fissionproduct mass from the fission of the heavier target. Figure 12 is similar to the yield curves, but has a few noticeable valleys and peaks. The valleys represent the depletion of that mass number by neutron absorption in 93Zr, 113Cd, 115Cd, 135Xe, 149Sm, 151Sm, 155Gd
and 157Gd. The peaks at one higher mass
unit represent the products of radiative neutron capture and their decay products. Figure 13, plotted by atomic number (but labelled by the symbol of the corresponding chemical element), has a saw tooth pattern superimposed that reflects the greater stability of nuclides with an even atomic number rather than an odd atomic number.
61
1.00E+00
Fraction of Total Fission Products
1.00E-01
1.00E-02
1.00E-03
1.00E-04
1.00E-05
Ge As Se Br Kr Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe Cs Ba La Ce Pr Nd Pm Sm Eu Gd Tb Dy
1.00E-06
10 MW.h/kgU
Figure 13
100 MW.h/kgU
Fission-Product Inventory in Natural Uranium at 10 and 100 MW·h·kg-1
62
63
5 Inventory Benchmarking Exercises Within the context of SOURCE IST 2.0, the calculations of radionuclide inventories are used internally to calculate the fractional releases of radiologically significant nuclides. The release fractions are to be combined with inventories determined by a computer program for calculating radionuclide inventories. One such program is ORIGEN-S in SCALE 6.0.
A library for CANDU® 37-element fuel bundles is
distributed with ORIGEN-S [Gauld 1995] [Gauld 2009a]. The library has 8 sublibraries of cross-sections for different burnups. While these are referred to as burnup-dependent libraries, the dependence is actually on the neutron energy spectrum. The neutron energy spectrum changes as absorbing nuclides build up in the fuel as a function of burnup and initial fuel composition. The range of burnups and midpoint burnup of each sub-library are given in Table 4. Table 4
Library Section 1 2 3 4 5 6 7 8 Sum
Starting Burnup MW·d·t-1 0 480 960 1920 3840 5760 7680 9600
ORIGEN-S CANDU® 37-element Sub-libraries Midpoint Burnup MW·d·t-1 240 720 1440 2880 4800 6720 8640 10560
Incremental Burnup MW·d·t-1 480 480 960 1920 1920 1920 1920 1920 11520
Ending Burnup MW·d·t-1 480 960 1920 3840 5760 7680 9600 11520
Ending Burnup MW·h·kg-1 11.52 23.04 46.08 92.16 138.24 184.32 230.4 276.48
Burnup Increment MW·h·kg-1 11.52 11.52 23.04 46.08 46.08 46.08 46.08 46.08 276.48
64 Since ORIGEN-S is developed in the United States, the burnups are stated in MW·d·t-1. Conversions to MW·h·kg-1 are provided in the last two columns. In Section 5.1, benchmarking of individual nuclide inventories as a function of burnup allows an assessment of systematic issues with the nuclear data used in SOURCE IST 2.0P11. With the addition of thermochemical calculations to a prototype version of SOURCE 2, the calculated inventories of chemical elements will be used directly to calculate the chemical speciation of the fuel. Thus, benchmarking of the elemental composition against ORIGEN-S is an important development step.
The
benchmarking has two goals, to determine the agreement of radiologicallysignificant nuclides as calculated by SOURCE 2.0 and ORIGEN-S, and to determine the agreement of elemental inventories between SOURCE 2.0 and ORIGEN-S.
5.1 Nuclide Benchmarking The test case modelled irradiation of 19.25 kg of uranium at a constant power of 462 kW (~26 kW/m) to a burnup of 200 MW·h·kg-1. The mass of uranium is within the range for production lots of CANDU® 37-element fuel.
The test case was
designed so that the fuel bundle accumulates burnup at the rate of 1.0 MW·d·t-1 per hour. Thus, the fuel reaches the final burnup of the last sub-library in 480 days. The power is slightly higher than the value used by Tait [Tait 2000] as an average value for Ontario CANDU® stations. The conditions of the ORIGEN-S representation of the irradiation cases are provided in Table 5. No decay periods are modelled.
65 Table 5
ORIGEN-S Case 1 2 3 4 5 6 7 8 Total
Case Duration (Days) 20 20 40 80 80 80 80 80 480
ORIGEN-S Irradiation Conditions
End Time (Days) 20 40 80 160 240 320 400 480
Intervals in ORIGEN-S Case 10 10 10 8 8 8 8 8 70
Ending Burnup MW·d·t-1 480 960 1920 3840 5760 7680 9600 11520
End Burnup MW·h·kg-1 11.52 23.04 46.08 92.16 138.24 184.32 230.4 276.48
Corresponding bundle conditions for SOURCE IST 2.0P11 are given in Table 6. Table 6
ORIGEN-S Case 1 2 3 4 5 6 7 8 Total
Case Duration (Days) 20 20 40 80 80 80 80 80 480
SOURCE 2.0P11 Irradiation Conditions
End Burnup (MW·h·kg-1) 11.52 23.04 46.08 92.16 138.24 184.32 230.40 276.48
Case Burnup (MW·h·kg-1) 11.52 11.52 23.04 46.08 46.08 46.08 46.08 46.08 276.48
Number of SOURCE Time Intervals In ORIGEN-S Case 1 1 2 4 4 4 4 4 24
SOURCE Time per Interval (seconds) 1728000 1728000 1728000 1728000 1728000 1728000 1728000 1728000 41472000
The ORIGEN-S irradiation case is performed as a point calculation. That is, all the fuel is modelled as being at a single power. To correspond to this condition, the SOURCE IST 2.0P11 calculation was run with the element power of all four rings of
66 the fuel bundle at the 1/37 of the bundle power. While this power distribution is non-physical, it does mean that both codes are modelling the same (admittedly nonphysical) conditions (or the same idealization, depending on one’s viewpoint). The SOURCE 2.0 simulation was performed with ten annuli in each fuel element. The power distribution within each fuel element is flat, with no account for flux depression, to match the ORIGEN-S approximation. The half-life data in SOURCE IST 2.0 were primarily taken from ICRP-38 [ICRP 1983]. The SOURCE IST 2.0 cross-section data were taken primarily from thermal cross-sections in the 14th edition of the chart of the nuclides [Walker 1989]. The ORIGEN-S CANDU® 37-element data file [Gauld 1995] distributed with ORIGEN-S 6.0 [Gauld 2009a] was created in 1995. The ORIGEN-S cross-sections are weighted for neutron energy spectrum, and each sub-library has weighted crosssections corresponding to the spectrum for the midpoint of the irradiation interval. Because the SOURCE 2.0 calculation uses one constant cross-section per reaction and ORIGEN-S uses differently-weighted cross-sections in each of eight burnup intervals, differences in the calculated results should be expected. These differences cannot be entirely eliminated by altering the constant cross-sections in SOURCE 2.0. 5.1.1
SCALE 6.0 ORIGEN-S Input File
The SCALE 6.0 input file to run the ORIGEN-S simulation is given in Table 7.
67 Table 7 Description Shell Command Case 1
Case 2
Case 3
Case 4
ORIGEN-S (SCALE 6.0) Input
ORIGEN-S (SCALE 6.0) Input =shell copy C:\scale6\data\arplibs\candu37e ft33f001 end =origens 0$$ a4 33 e t candu37 3$$ 33 a3 1 0 a16 2 a33 0 e t 35$$ 0 t 56$$ 10 10 a6 3 a10 0 a13 3 a15 3 a18 1 e 57** 0 a3 0 0.04166667 e t Case 1 0.01925 MTU 58** 0.462 0.462 0.462 0.462 0.462 0.462 0.462 0.462 0.462 0.462 60** 2 4 6 8 10 12 14 16 18 20 66$$ a5 1 a9 1 e 73$$ 922340 922350 922380 74** 1.0395 136.8868 19112.07 75$$ 2 2 2 t candu37 3$$ 33 a3 2 0 a33 0 e t 35$$ 0 t 56$$ 10 10 a6 3 a10 10 a15 3 a18 1 e 57** 20 a3 0 0.04166667 e t Case 2 0.01925 MTU 58** 0.462 0.462 0.462 0.462 0.462 0.462 0.462 0.462 0.462 0.462 60** 22 24 26 28 30 32 34 36 38 40 66$$ a5 1 a9 1 e t candu37 3$$ 33 a3 3 0 a33 0 e t 35$$ 0 t 56$$ 10 10 a6 3 a10 10 a15 3 a18 1 e 57** 40 a3 0 0.08333333 e t Case 3 0.01925 MTU 58** 0.462 0.462 0.462 0.462 0.462 0.462 0.462 0.462 0.462 0.462 60** 44 48 52 56 60 64 68 72 76 80 66$$ a5 1 a9 1 e t candu37 3$$ 33 a3 4 0 a33 0 e t 35$$ 0 t 56$$ 8 8 a6 3 a10 10 a15 3 a18 1 e 57** 80 a3 0 0.1666667 e t Case 4 0.01925 MTU 58** 0.462 0.462 0.462 0.462 0.462 0.462 0.462 0.462 60** 90 100 110 120 130 140 150 160 66$$ a5 1 a9 1 e t
68 Table 7 Description Case 5
Case 6
Case 7
Case 8
(Continued)
ORIGEN-S (SCALE 6.0) Input candu37 3$$ 33 a3 5 0 a33 0 e t 35$$ 0 t 56$$ 8 8 a6 3 a10 8 a15 3 a18 1 e 57** 160 a3 0 0.1666667 e t Case 5 0.01925 MTU 58** 0.462 0.462 0.462 0.462 0.462 0.462 60** 170 180 190 200 210 220 230 240 66$$ a5 1 a9 1 e t candu37 3$$ 33 a3 6 0 a33 0 e t 35$$ 0 t 56$$ 8 8 a6 3 a10 8 a15 3 a18 1 e 57** 240 a3 0 0.1666667 e t Case 6 0.01925 MTU 58** 0.462 0.462 0.462 0.462 0.462 0.462 60** 250 260 270 280 290 300 310 320 66$$ a5 1 a9 1 e t candu37 3$$ 33 a3 7 0 a33 0 e t 35$$ 0 t 56$$ 8 8 a6 3 a10 8 a15 3 a18 1 e 57** 320 a3 0 0.1666667 e t Case 7 0.01925 MTU 58** 0.462 0.462 0.462 0.462 0.462 0.462 60** 330 340 350 360 370 380 390 400 66$$ a5 1 a9 1 e t candu37 3$$ 33 a3 8 0 a33 0 e t 35$$ 0 t 56$$ 8 8 a10 8 a15 3 a18 1 e 57** 400 a3 0 0.1666667 e t Case 8 0.01925 MTU 58** 0.462 0.462 0.462 0.462 0.462 0.462 60** 410 420 430 440 450 460 470 480 66$$ a5 1 a9 1 e t 56$$ f0 t end
0.462 0.462
0.462 0.462
0.462 0.462
0.462 0.462
The file was created with ORIGEN-ARP [Gauld 2009b] and edited to add the shell commands (first three lines), to delete ORIGEN-ARP specific commands and to change an octathorpe (“#”) with an equals sign. Readers interested in the details of the input are referred to the ORIGEN-S documentation [Gauld 2009a]. The selection of 8 intervals in the 80-day cases, rather than 10 as in the shorter cases, ensures that
69 output data are produced to compare to each SOURCE IST 2.0P11 output time at 20 day intervals. The SOURCE time interval of 20 days corresponds to a burnup increment of 11.52 MW·h·kg-1. This burnup increment is within the 10 to 12 MW·h·kg-1 range recommended for ELESTRES-IST, and recommended for the normal operating conditions (NOC) part of SOURCE 2.0 validation exercises with CANDU® fuel. 5.1.2
SOURCE IST 2.0P11 Input Values
SOURCE IST 2.0P11 has four user-supplied data files to provide input to the code. Three files provide geometric data, bounds on the geometric data, and fuel composition. The fuel bundle details and fuel composition are presented in Table 8. The values given in brackets in Table 8 are implied by other input or coding assumptions. They do not appear explicitly in the input file. The SOURCE IST 2.0P11 case-specific input consists of 1726 lines. Given this length, rather than provide the entire input file the nominal data that should have no effect on inventories are presented in Table 9 and the powers used are provided in Table 10. The values in that table are selected to be within the valid range and such that additional models are not activated to the extent achievable.
70 Table 8 Parameter Number of Channel Groups Number of Channels per Group Number of Bundles per Channel Number of Fuel Element Groups per Bundle Number of Fuel Elements per Group Ring Number of Fuel Element Groups Fuel Element Rings per Bundle Number of Fuel Elements per Bundle Mass of Uranium per Fuel Element (kg) 234U Isotopic (Atomic or molar fraction) 235U Isotopic (Atomic or molar fraction) 235U Isotopic (Atomic or molar fraction) Number of Axial Segments per Fuel Element Stack Length Number of Annuli per Fuel Element Annulus Geometry
Equal Radius
Pellet Radius Dishes and chamfers
0.006075 (None)
9
Value 1
Fuel Bundle Description Rationale A single bundle case requires 1 channel
1
A single bundle requires 1 channel
1
Only 1 bundle in this case
4
All fuel elements in one ring are in the same group. One representative fuel element is modelled per group. Modelled from outer ring to central pin. This order is user-specified. Ring number of fuel element groups modelled from outer ring to central pin. Number of fuel element rings per bundle including central pin. Implied from other inputs
18, 12, 6, 1 1, 2, 3, 4 4 (37) 0.52027027
19.25 kg per bundle / 37 fuel elements
0.000055
Natural uranium
0.007200
Natural uranium
(Balance)
Natural uranium (calculated internally by difference) No axial subdivision. Matches ORIGEN-S idealization.
1 0.47429 10
Cold stack length in metres 5 and 10 are typical values for SOURCE analyses of fuel elements Preferred value to match initial ELESTRES and ELOCA nodalization Cold radius in metres Not modelled in SOURCE IST 2.0
The stack length is used by SOURCE 2.0 only to allocate fuel mass between axial segments. With only one axial segment, there is no re-allocation required. This value was taken from the BTF104 validation exercise and is slightly shorter than production 37-element CANDU® fuel (0.480 to 0.4802 m).
71
Table 9
Nominal Fuel Data
Parameter Sheath Failure Time
Value 1.0D+300 s
Fuel Rewet Time
1.0D+300 s
Caesium to Steam Ratio Coolant Temperature Coolant Pressure Coolant flow of hydrogen water inert gas steam Nature of Inert Gas in Coolant Fuel Temperature
1.0D-5 538 K 10 MPa 0 mol/s 0 mol/s 0 mol/s 0 mol/s None 1000 K
Gap Pressure
10 MPa
Hydrostatic Stress Temperature Gradient
-10 MPa 0 K/m
Fuel Stoichiometric Deviation
0.00
Mass Fraction of Molten UO2 Mass Fraction of in Liquid Phase from UO2 Interaction with Zircaloy Mass Fraction of UO2 Dissolved in Molten Zircaloy Mass Fraction of UO2 Vaporized Mass Fraction of UO2 Leached by Coolant
0.00 0.00 0.00
Rationale Recognizable large value indicating no sheath failure. Recognizable large value indicating no rewet.
Not used unless there is sheath failure.
Uniform temperature (non-physical). Temperature-driven models are not being tested. Nominal value approximating coolant pressure. Compressive stress from gap pressure. Uniform temperature (non-physical). Temperature-driven models are not being tested. Nominal value, oxidation is not being modelled.
Nominal value, phase changes are not being modelled.
0.00 0.00
In this idealized case, with no flux depression modelled within the bundle or within the fuel element, the annular powers (which are related solely to the volume of the annuli) do not change with fuel ring, or as the fuel composition changes with burnup.
72 Table 10 Annulus 1 2 3 4 5 6 7 8 9 10 Total
5.1.3
Fuel Power Data
Power (kW) 0.124864865D+00 0.374594595D+00 0.624324324D+00 0.874054054D+00 1.123783784D+00 1.373513514D+00 1.623243243D+00 1.872972973D+00 2.122702703D+00 2.372432432D+00 12.486486487D+00
Rationale Volume 1/100 of Cylinder Volume 3/100 of Cylinder Volume 5/100 of Cylinder Volume 7/100 of Cylinder Volume 9/100 of Cylinder Volume 11/100 of Cylinder Volume 13/100 of Cylinder Volume 15/100 of Cylinder Volume 17/100 of Cylinder Volume 19/100 of Cylinder 462 kW /37 fuel elements
Output Comparisons
The SOURCE output consists of data for 150 nuclides at 24 values of time, excluding the initial time. The ORIGEN-S input conditions have been prepared to provide comparison data at each of these time values. Prior to irradiation, only the three uranium isotopes (234U,
235U, 238U)
are present. SOURCE 2.0 does not currently
model the oxygen isotopes in the fuel. Thus, the total number of pairs of data for comparisons is 3603. 5.1.3.1 A Symmetrical Measure of Difference Given two calculated values with one being a more-trusted “reference” value, xref, one might use a relative difference, (xnew - xref)/xref, as a measure of difference of the “new” value xnew from the reference value. This relative difference is bounded by
73 -1.00 and +infinity10. The +infinity value looks alarmingly large compared to an apparently innocent -1.00, but both indicate that the two values are almost completely different. In the former case, x1 is very much smaller than x0, whereas in the latter case, x1 is very much larger than x0. A more symmetrical measure is obtained, by dividing the difference by the average value of the two values 11, (x1-x0)/((x1+x0)/2). This quantity can be called the signed difference from the mean (SDM). When the numbers are close together, this measure is close to the relative difference between them. When they differ largely in value, this measure is symmetrically bounded by -2.00 and +2.00.
For non-negative numbers, this
measure has the added benefit of being undefined only if both numbers are equal to zero. In this case, the calculation can be replaced by zero since the values are the same. 5.1.3.2 Summary of Results The range of signed differences from the mean that represent a relative difference in the SOURCE value of ±20% of the ORIGEN-S value is -0.222 to +0.182.
The
agreement is assessed based on the largest magnitude of the 24 comparisons for a given nuclide with no initial inventory, or 25 comparisons for the three initial nuclides in the fuel, 234U, 235U and 238U. Of the 150 nuclide modelled by SOURCE IST
10
11
There is an implicit assumption that the relative difference is calculated as (x 1-x0)/x0, where x0 is the preferred (or “more-trusted”) value. Thus, a negative relative difference indicates that the “new” or “less-trusted” value x1 is less than x0. Similarly, a positive relative difference indicates that the “new” or “less-trusted” value x1 is greater than x0. This sign convention makes intuitive sense. Mathematically, (x1-x0)/((x1+x0)/2) = 2 (x1-x0)/(x1+x0). With this sign convention, a negative difference indicates that x1 is smaller than x0. A positive difference indicates that x1 is larger than x0.
74 2.0P11, 27 nuclides fall below -0.222 for at least one time (see Table 11), 21 nuclides are above +0.182 for at least one time (see Table 12), and the remaining 102 nuclides are between these limits (see Table 13). Table 11 Rank 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Nuclides with Signed Difference from Mean Lower Than Lower Limit Nuclide
238Pu 106Rh 109Pd 153Sm 82Br 153Eu 156Eu 128Sb 241Am 240Np 241Pu 242Pu 112Ag 157Eu 112Pd 122Sb 113Ag 129Te 113mCd 129Sb 124Sb 129I 105Tc 105Ru 111Ag 86Rb 135Cs
Minimum SDM -2.00 -1.38 -1.24 -1.08 -1.01 -0.974 -0.919 -0.875 -0.846 -0.834 -0.817 -0.681 -0.580 -0.563 -0.546 -0.539 -0.407 -0.401 -0.396 -0.379 -0.358 -0.310 -0.282 -0.281 -0.268 -0.247 -0.223
Maximum SDM -1.60 -0.168 -0.244 -0.133 -0.611 -0.035 -0.347 -0.3263 -0.766 -0.779 -0.243 -0.0468 -0.0606 -0.289 -0.0508 -0.391 0.0659 -0.0773 -0.278 -0.0632 -0.110 -0.139 0.0503 0.0480 -0.0121 -0.171 -0.157
Average SDM -1.87 -0.406 -0.338 -0.719 -0.694 -0.578 -0.660 -0.428 -0.790 -0.812 -0.467 -0.315 -0.129 -0.372 -0.117 -0.512 -0.00373 -0.159 -0.305 -0.146 -0.285 -0.193 4.73E-5 -9.29E-4 -0.0410 -0.2215 -0.178
Assessment All Low Low Average All Low Low Average All Low Low Average All Low All Low All Low All Low All Low Low Average Low All Low Low All Low Low Low All Low Low Low Average Low Low Low Low Low Low
In Table 11, the minimum signed difference from the mean is the largest magnitude when the list contains only negative values.
There are nuclides with positive
differences that are smaller in magnitude than the largest magnitude negative difference from the mean.
The nuclides are ranked by the largest magnitude
75 (negative) difference from the mean. In this ranking, a rank of 1 represents the nuclide with the worst agreement between SOURCE and ORIGEN-S for which SOURCE calculates a smaller inventory than ORIGEN-S.
Since neither the
radiological importance nor the total inventory has been factored into the ranking, it is not necessarily the order in which SOURCE IST 2.0P11 nuclear data for nuclides should be investigated. Of the 27 nuclides listed in Table 11, 11 nuclides have all three of minimum, average and maximum differences below the target value; hence, the SOURCE inventories that were compared at all 24 times are more than 20% below the ORIGEN-S inventory. These nuclides are assessed as “All Low”. An additional 5 nuclides have an average difference (and minimum (most negative) difference) of more than 20% below the ORIGEN-S values.
The nuclides are rated as “Low Average”.
The
remaining 11 nuclides have at least one time for which the SOURCE-calculated inventory is more than 20% below the ORIGEN-S value (as reflected by the maximum, least negative difference). These are rated as “Low”. The “All Low” category also meets the criterion for “Low Average” and “Low”, but only the worst rating is listed similarly the “Low Average” would also meet the criterion for “Low”. Notably,
105Tc
is listed as low despite the average SDM being positive, but not high
enough for it to be more than 20% higher than ORIGEN-S. Nuclides with higher inventories calculated by SOURCE IST 2.0P11 than by ORIGEN-S are listed in Table 12.
76 Table 12 Rank 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Nuclides with Signed Difference from Mean above the Upper Limit
Nuclide 240mNp 126Sb 110mAg 148mPm 242mAm 155Eu 115mCd 154Eu 93Y 236U 130I 83Kr 125Sb 130Sb 148Pm 127mTe 130Xe 133mTe 131Xe 105Rh 132Sb
Minimum SDM 2.00 1.76 1.79 0.715 0.0937 0.336 0.741 0.417 0.385 0.348 0.0155 0.0115 0.0764 0.243 0.123 0.109 0.082 0.187 0.0124 -0.0422 0.168
Maximum SDM 2.00 1.92 1.88 1.70 1.60 0.949 0.766 0.702 0.438 0.357 0.341 0.300 0.289 0.283 0.262 0.254 0.241 0.226 0.210 0.208 0.187
Average SDM 2.00 1.80 1.80 1.54 1.08 0.817 0.757 0.584 0.402 0.351 0.265 0.150 0.109 0.270 0.231 0.139 0.175 0.198 0.108 0.165 0.174
Assessment All High All High All High All High High Average All High All High All High All High All High High Average High High All High High Average High High High Average High High High*
Note: The assessment of “High*” indicates that the SOURCE value is assessed as “High” based on a relative difference from ORIGEN-S, but the SDM is less than 0.20, but greater than 0.181818. A value of 2.00 for 240mNp indicates that the numbers for the SOURCE and ORIGEN-S inventories are completely different. The rank is based on the maximum signed difference from the mean, since the larger magnitude value for each nuclide is positive. Of the 21 nuclides listed in Table 12, 10 have all three of minimum, maximum and average SDM above the target value; these nuclides are assessed as “All High”. Four nuclides have both average and maximum above the target value; these nuclides are rated “High Average”. Those with only the maximum difference above the target value are rated as “High”.
77 Table 13 Nuclide 133Te 240Pu 84Kr 109Ag 135Xe 144Pr 235U 90Y 104Tc 137mBa 128mSb 132Xe 97mNb 84Br 234U 140La 135mXe 77As 140Ba 131Te 89Sr 99mTc 91Y 90Sr 79As 139Ba 137Cs 86Kr 95Zr 137Xe 144Ce 95Nb 134Xe 90Sr 238U 132Te 99Mo 141Ce 133I 133Cs 143Pr 142Ba 135I
Nuclides with Signed Difference from Mean within the Limits Minimum SDM -0.21847 -0.20765 -0.19728 -0.19032 -0.18075 -0.15882 -0.15015 -0.14834 -0.13988 -0.11851 -0.11607 -0.10841 -0.09056 -0.08897 -0.08599 -0.0673 -0.05076 -0.04458 -0.03875 -0.03753 -0.03744 -0.03348 -0.03234 -0.02623 -0.02618 -0.01667 -0.01581 -0.01566 -0.01323 -0.01237 -0.00673 -0.00502 -0.00212 -0.02623 -0.00036 -0.00585 0.005164 0.007708 0.003057 0.005277 -0.00038 -0.00795 0.007716
Maximum SDM -0.15636 -0.06145 -0.07463 -0.05558 -0.14063 -0.04058 -0.00026 -0.08128 0.031096 -0.01386 -0.00185 -0.0125 -0.05921 -0.00884 0.001481 -0.01594 0.016021 0.022464 -0.01285 0.005785 -0.02804 0.002155 -0.02331 -0.01938 0.005779 -0.00429 -0.01415 -0.00368 0.000834 0.003337 0.004178 0.003271 3.29E-05 -0.01938 -9.2E-05 0.007984 0.009767 0.01269 0.01275 0.013957 0.013977 0.014123 0.017293
Assessment Agree* Agree* Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree
78 Table 13 Nuclide 138Xe 238U 141Ba 141La 138Cs 131Sb 134I 132I 131I 142La 239U 101Tc 101Mo 102Mo 139Cs 143Ce 239Np 136Xe 91mY 239Pu 103mRh 147Pm 106Ru 91Sr 103Ru 102Tc 131mXe 83Br 89Rb 147Nd 134Te 130mSb 95Y 89Kr 88Rb 92Sr 85Rb 90mRb 92Y 88Kr 94Y 81Br 97Nb 133Xe
Minimum SDM 0.012566 -0.00036 0.006446 0.005578 0.005668 -0.00045 0.016306 -0.02002 0.001181 0.002993 -0.00242 0.007402 0.008676 -0.01717 0.015614 -0.00712 -0.00297 0.00023 -0.02131 0.001849 -0.0032 0.009461 0.016234 -0.02003 -0.00036 -0.01199 0.025016 -0.00192 -0.01546 0.018473 0.013657 0.005141 0.008106 -0.0243 -0.03106 -0.00876 0.037289 0.000203 -0.00346 -0.03223 0.001517 0.045375 0.040463 0.009317
(Continued) Maximum SDM 0.018663 -9.2E-05 0.01989 0.020331 0.020397 0.020629 0.021601 0.023911 0.02472 0.025065 0.025423 0.02586 0.025903 0.026052 0.026219 0.026582 0.026596 0.028081 0.028157 0.029551 0.030722 0.030963 0.031428 0.032404 0.032507 0.03266 0.033594 0.034156 0.034765 0.035078 0.036673 0.037025 0.037283 0.038443 0.03933 0.04911 0.051556 0.051631 0.051671 0.055081 0.055623 0.062121 0.069617 0.06978
Assessment Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree
79 Table 13 Nuclide 97Zr 87Kr 115Cd 121Sb 133mXe 134Cs 129mTe 85mKr 123Sb 127Sb 85Kr 127Te 242Am 131mTe 83Se 242Cm 136Cs
(Continued)
Minimum SDM 0.040082 0.003567 -0.02908 0.01853 -0.00356 -0.03071 -0.07661 0.044752 0.06965 0.087191 0.083082 0.049528 -0.03955 0.108169 0.051733 -0.03795 -0.02281
Maximum SDM 0.071824 0.07559 0.081429 0.088416 0.094248 0.096576 0.099834 0.103951 0.107945 0.111324 0.111464 0.121949 0.124144 0.130371 0.135282 0.139948 0.167244
Assessment Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree Agree
In Table 13, two nuclides are assessed as “Agree*” because the relative difference is within ±20%, even though the SDM is less than -0.20, but not less than -0.222222. Given that the maximum and minimum values are both within the target range; the average must also be with the target range. Hence, further classification of “Agree” is not required. 5.1.3.3 Detailed Comments on Selected Nuclides or Chains A value of the maximum signed difference from mean (SDM) of less than -1.0 indicates that at least one SOURCE value for a nuclide is less than one-third of the ORIGEN-S value for that nuclide at the same time value. Five nuclides fall into this category:
238Pu, 106Rh, 109Pd, 153Sm
and
82Br
(see Table 11).
A value of the
maximum signed difference from mean (SDM) greater than 1.0 indicates that at
80 least one SOURCE value for a nuclide is more than three times the ORIGEN-S value for that nuclide at the same time value. Five nuclides fall into this category: 126Sb, 110mAg, 148mPm
and
242mAm
(see Table 12).
240mNp,
These ten nuclides will be
discussed in sub-sections of this section. Then, the decay chain with mass number 129 (129Sb,
129mTe, 129Te,
and
129I)
will be discussed, because three nuclides from
this chain were listed as “Low”. Finally, uranium and plutonium nuclides will be discussed. Discussion of ORIGEN-S data in this section refers to the ORIGEN-S data library for CANDU® 37-element fuel bundles [Gauld 1995]. 5.1.3.3.1
238Pu
In the SOURCE 2.0 nuclear data, 238Pu is produced only by decay of 242Cm. seen as a terminator for the
242Cm
242Cm,
but was not of interest in and of
The ORIGEN-S data include production by
multiple neutron captures and decays from 237Np, 237Np
(n, γ) 238Np, and
238Np
was
decay chain. As such the calculated inventory
would accumulate the decay products of itself.
238Pu
236U:
β- decay to
239Pu
236U
238Pu.
(n, 2n) 238Pu and from
(n, γ) 237U,
237U
β- decay to
These additional pathways
(and the associated nuclear data) will be required before SOURCE-calculated inventories of 238Pu are likely to agree with ORIGEN-S calculations. It is noted that Tait [Tait 2000] found an inverse relationship between power and
238Pu
inventory
(at constant burnup), for reasons that were not explained. He also pointed out that 238Pu
had a small contribution to decay heat. It appears likely that the reason for the
inverse relationship is competition between β- decay of
238Np
to
238Pu
and
238Np
fission, 238Np (n, fission). At higher powers, the fission rate increases and the 238Np has less chance to decay to 238Pu.
81 5.1.3.3.2
106Rh
and 105Rh
The quantity of
105Rh
calculated by SOURCE is higher than that calculated by
ORIGEN-S; whereas the quantity of
106Rh
calculated by SOURCE is lower than that
calculated by ORIGEN-S. Furthermore, the quantity of 106Rh calculated by ORIGEN-S exceeds the quantity that would be in equilibrium with the decay of decay reaction 106Ru equilibrium with
106Rh
106Ru.
106Ru,
by the
β-. The quantity of 106Rh calculated by SOURCE is in
SOURCE IST 2.0P11 does not model
Accounting for this reaction would increase the quantity of power and decrease the amount of
105Rh.
105Rh
106Rh
(n, γ) 106Rh.
in the fuel on-
Addition of this reaction to the SOURCE
nuclide data file is recommended. Because 106Rh has a half-life of about 30 seconds, the increased inventory over that which is in equilibrium with
106Ru
would decay away in about the first three
minutes of (off-power) decay. In hot-cell experiments, gamma emission from 106Rh is used as a tracer for
106Ru,
which decays by beta decay without gamma emission.
Because ruthenium forms a volatile oxide (RuO4) on oxidation in air at high temperatures, the
106Ru
beta emission can be an important contributor to dose
under such conditions. The apparent discrepancy between the activities of these nuclides was investigated. It is concluded that for fuel that has been transported from a reactor at Chalk River (or from a power reactor) to the hot cells for fissionproduct release tests, the off-power decay period will be sufficiently long to reestablish radioactive equilibrium before the hot-cell experiment begins.
82 5.1.3.3.3
109Pd
This nuclide is a potential activation product of stable 108Pd
108Pd
by the reaction,
(n, γ) 109Pd. SOURCE IST 2.0P11 does not model this reaction. The impact of
an omitted activation reaction of a stable nuclide would be expected to increase with time. The value of signed difference from the mean for
109Pd
increases with
time and would not have been flagged as excessive at lower burnup.
108Pd
is not
currently modelled in SOURCE IST 2.0. 5.1.3.3.4
153Sm
This nuclide has a significant yield from the activation of 152Sm
152Sm
(n, γ) 153Sm which is not yet modelled in SOURCE 2.0.
152Sm
by the reaction is not currently
modelled in SOURCE 2.0. 5.1.3.3.5
82Br
Stable 81Br is modelled as a precursor for 82Br. The lower production of radioactive 82Br 81Br
in SOURCE IST 2.0P11 results from a smaller cross-section in SOURCE for (n, γ) 82Br than in the CANDU® 37-element bundle library ORIGEN-S.
5.1.3.3.6
240mNp
and 240Np
As indicated in Table 12, the SOURCE IST 2.0P11 value for
240mNp
is completely
different from that from ORIGEN-S in SCALE 6.0. Examination of the nuclear data provides the explanation. In the cross-section in SOURCE IST 2.0P11 (taken from [Walker 1989]), there is a partial cross-section for production of 240mNp from 239Np by radiative neutron capture. In the Chart of the Nuclides data used in SOURCE 2.0, the partial cross-sections for production of the ground state
240Np
and the excited
83 state 240mNp are equal. This fact suggests that the partial cross-section values were not measured, but are based on an assumption of an equal split between ground state (240Np) and first excited state (240mNp).
The cross-section for
240mNp
production is not present in the ORIGEN-S data library. The cross-section for 240Np production is larger in the ORIGEN-S data than in SOURCE. produces more
240Np
than SOURCE. Both the
240mNp
and
Thus, ORIGEN-S
240Np
inventories are
sufficiently small in the ORIGEN-S calculation as to be unimportant.
It is
recommended that 240mNp and 240Np be eliminated from the SOURCE IST 2.0 nuclide set. 5.1.3.3.7
126Sb
The over-estimate in SOURCE IST 2.0P11 is primarily due to the omission of the long-lived tin isotope
126Sn
(2.3E5 year half-life).
The yield for
126Sb
used in
SOURCE includes the yield that should be applied to 126Sn. The tin nuclide should be modelled as it represents a long-term source of
126Sb
production by decay, and
reduces the short-term inventory of 126Sb. 5.1.3.3.8
110mAg
and 109Ag
The lower inventory of stable
109Ag
and the higher inventory of
110mAg
in SOURCE
calculations than in ORIGEN-S calculations both result from a larger cross-section for
109Ag
(n, γ) 110mAg in the SOURCE data than in the ORIGEN-S data. The low
inventory of stable
109Ag
may also relate to the absence of
108Pd
in the SOURCE
nuclide set and the consequent absence of the radiative neutron capture reaction 108Pd
(n, γ) 109Pd.
109Pd
decays to 109Ag.
84 5.1.3.3.9
148mPm
and 148Pm
Both of these nuclides are activation products of 147Pm. Both have lower inventories in SOURCE calculations than in ORIGEN-S calculations. Review of the ORIGEN-S library indicates larger cross-sections for these reactions in ORIGEN-S than in SOURCE IST 2.0P11. 5.1.3.3.10 242mAm This nuclide is fissionable, but SOURCE 2.0 models neither that fission process nor the fission products produced from it. The ORIGEN-S CANDU® 37-element library [Gauld 1995] has cross-sections for 242mAm fission, but no fission yields. A number of choices are available. The most obvious is to follow the practice in the ORIGEN-S CANDU® 37-element library and model
242mAm
depletion by fission, but not the
accumulation of its fission products. Creation of a new ORIGEN-S CANDU® 37element library including 242mAm fission and accumulation of its fission products is another option. Given the small inventory of 242mAm at low burnup, the first option would be an appropriate first step.
Within the SOURCE decay computation
framework, there is no other modelling of the fission of an actinide that has no fission-product yields. 5.1.3.3.11 Isobar 129 The appearance of 129Sb, 129Te and 129I in the list of nuclides with lower inventories from SOURCE calculations than from ORIGEN-S resulted in a re-examination of yield data for this isobar. The chain yield for isobar 129 for
235U
fission in SOURCE IST
2.0P11 (taken from England and Rider [England 1994]) is about 0.54% while that
85 from ORIGEN-S is about 0.75%.
This difference represents about 25% of the
ORIGEN-S chain yield and is a likely cause for SOURCE-calculated inventories to be more than 20% lower than ORIGEN-S inventories. 5.1.3.3.12 Uranium Isotopes The initial isotopic fractions of uranium isotopes were specified in atomic (or molar) terms in SOURCE IST 2.0P11 (the only choice) and in mass terms for ORIGEN-S. Either basis can be used in ORIGEN-S. Mass was chosen as the basis for the ORIGEN-S calculation to ensure that the fuel mass was equal to the target value to within machine (computer floating-point) tolerances.
The differences in
inventories start off very small and remain smaller than 0.05 % for
238U.
agreement reflects the choice (in the late 1990s) of a cross-section for
238U
This that
reproduced earlier ORIGEN-S calculations of 238U depletion. The inventory of
234U
starts off with good agreement between SOURCE and
ORIGEN-S calculated inventories. The agreement drifts with time with SOURCE inventories being lower, ultimately by almost 9%. Further investigations revealed that the SOURCE cross-section for 234U (n, γ) 235U is larger than the ORIGEN-S values for all burnup intervals. The quantity of 234U in the fuel is sufficiently small that this inventory makes little difference to other calculations. The agreement between codes for 235U starts off being very good (reflecting similar initial conditions) and drifts apart until SOURCE has about 15% less
235U
than
ORIGEN-S at the end of the comparison irradiation case. In order to retain more 235U
at the same later time values, the total removal cross-section for 235U needs to
86 be decreased. There are two removal cross-sections modelled in SOURCE IST 2.0P11: fission and radiative neutron capture for
235U
(n, γ) 236U. The ORIGEN-S
cross-section for radiative neutron capture (~70 b 12) is smaller than the SOURCE IST 2.0P1 value (100 b). The fission cross-sections are similar, ~385 b in ORIGEN-S and 380 b in SOURCE IST 2.0P11. The minimum and maximum signed differences from the mean for 236U have about the same value. This constancy indicates that a constant multiplier could be applied. The reduction in the cross-section for
235U
(n, γ) 236U would reduce the fraction of
235U
consumed in radiative neutron capture. The original intention in modelling
236U
was that it would serve as a decay/activation chain terminator for
those nuclides created from
236U
236U
and
and its activation products and their decay
products. For future application to recycled uranium from light water reactors, SOURCE 2.0 should have the capability to model
236U
including its neutron capture
cross-section and the transmutation/decay chain to 238Pu. These data are available from the ORIGEN-S CANDU® 37-element data library [Gauld 1995]. Eight values for each cross-section are provided one for each burnup interval. The 236U
(n, γ) 237U decays in 6.75 days to
237Np.
237Np
radiative neutron capture (237Np (n, γ) 238Np) to get 238Np
12
237U
product of
is long-lived and undergoes 238Np
which decays to
238Pu.
is also fissile.
The barn (b) is 10-24 cm2 or 10-28 m2. It is the traditional unit for nuclear cross-sections.
87 The SOURCE-calculated inventories of the final uranium nuclide of interest, 239U, are within 3% of ORIGEN-S for each of the 24 burnup-values used for comparison. 5.1.3.3.13 Plutonium Isotopes The lightest plutonium isotope modelled by SOURCE 2.0,
238Pu,
was discussed in
Section 5.1.3.3.1. The agreement of 239Pu between the two codes reflects the careful calculation of the effective cross-section for 238U (n, γ) 239U and a reasonably accurate removal crosssection for 239Pu. Figure 14 shows comparison plots against time for inventories of 239Pu, 240Pu
and 241Pu. The inventory of 239Pu calculated by SOURCE IST 2.0P11 is in
good agreement with ORIGEN-S from SCALE 6.0 as seen also in Figure 15. There is a slightly larger inventory from SOURCE than from ORIGEN-S at intermediate times. The more distant spacing of the points in Figure 15 at low inventories than at high inventories indicates that rate of net growth of the
239Pu
is slowing at higher burn
up. From Figure 14, the SOURCE-calculated inventories of
240Pu
and
241Pu
are
smaller than those calculated by ORIGEN-S by about the same amount. However, the relative differences are more apparent in Figure 16 and Figure 17.
The
additional line for ideal agreement minus 20% shows that the agreement for 240Pu is clearly better than that for 241Pu.
88
1.4E+23
1.2E+23
Atoms of Nuclide per Fuel Bundle
1E+23
8E+22
6E+22
4E+22
2E+22
0 0
50
100
150
200
250
300
350
400
450
Time (Days)
Figure 14
SOURCE Pu-239
ORIGEN-S Pu-239
SOURCE Pu-240
ORIGEN-S Pu-240
SOURCE Pu-241
ORIGEN-S Pu-241
Plutonium Isotopes 239Pu, 240Pu and 241Pu in Modelled Bundle from SOURCE IST 2.0P11 and ORIGEN-S 6.0 Analysis
500
SOURCE IST 2.0P11 Calculated (atoms/bundle)
89
1.2E+23 1.0E+23 8.0E+22 6.0E+22 4.0E+22 2.0E+22 0.0E+00 0.00E+00 2.00E+22 4.00E+22 6.00E+22 8.00E+22 1.00E+23 1.20E+23 ORIGEN-S Calculated (atoms/bundle) Pu-239
SOURCE IST 2.0P11 Calculated (atoms/bundle)
Figure 15
Ideal Agreement
Comparison of SOURCE and ORIGEN-S Inventories for Plutonium-239
8E+22 7E+22 6E+22 5E+22 4E+22 3E+22 2E+22 1E+22 0 0.00E+00 1.00E+22 2.00E+22 3.00E+22 4.00E+22 5.00E+22 6.00E+22 7.00E+22 8.00E+22 ORIGEN-S Calculated (atoms/bundle) Pu-240
Figure 16
Ideal Agreement
Ideal - 20%
Comparison of SOURCE and ORIGEN-S Inventories for Plutonium-240
SOURCE IST 2.0P11 Calculated (atoms/bundle)
90
2E+22
1.6E+22
1.2E+22
8E+21
4E+21
0 0.00E+00
4.00E+21
8.00E+21
1.20E+22
1.60E+22
2.00E+22
ORIGEN-S Calculated (atoms/bundle) Pu-241
Figure 17
Ideal Agreement
"Ideal - 20%"
Comparison of SOURCE and ORIGEN-S Inventories for Plutonium-241
Atoms of Nuclide per Fuel Bundle
9E+21 8E+21 7E+21 6E+21 5E+21 4E+21 3E+21 2E+21 1E+21 0 0
50
100
150
200
250
300
350
400
450
Time (Days) SOURCE Pu-238
Figure 18
ORIGEN-S Pu-238
SOURCE Pu-242
ORIGEN-S Pu-242
Comparison of SOURCE and ORIGEN-S Inventories of 238Pu and 242Pu
500
91 From Figure 18, it is clear that the inventory of 238Pu is consistently small and does not follow the trend of the ORIGEN-S calculation. This observation is consistent with the finding in Section 5.1.3.3.1. Indeed, the inventory of
238Pu
is sufficiently
small that it might be neglected in SOURCE calculations. The agreement of 242Pu is somewhat better. The comparison plot of SOURCE inventory versus ORIGEN-S inventory for
242Pu
is provided in Figure 19. The agreement starts off poorer than
-20% but improves at higher burnup. Because
242Pu
is a small contributor to the
chemical inventory of plutonium, this poor agreement should have little impact on plutonium chemistry.
SOURCE IST 2.0P11 Calculated (atoms/bundle)
1E+22
8E+21
6E+21
4E+21
2E+21
0 0.00E+00
2.00E+21
4.00E+21
6.00E+21
8.00E+21
ORIGEN-S Calculated (atoms/bundle) Pu-242
Figure 19
Ideal Agreement
"Ideal - 20%"
Comparison of SOURCE and ORIGEN-S Inventories for 242Pu
1.00E+22
92
5.2 Benchmarking Molar Inventory of Chemical Elements Code versions up to SOURCE IST 2.0P11 were not intended to provide an inventory of major stable isotopes of each chemical element.
The nuclide list had been
selected to cover the nuclides of radiological significance. It was known that the coverage of the chemical inventory was incomplete. A benchmarking exercise was undertaken to assess the degree to which a SOURCE calculation of chemical inventories for its selected nuclides and nuclear isomers matches the inventory of chemical elements calculated by ORIGEN-S. 5.2.1
SOURCE IST 2.0P11
The test case was 19.25 kg of natural uranium (0.000055 atom fraction 234U, 0.0072 atom fraction 235U, and 0.992745 atom fraction 238U) irradiated at a constant power of 488 kW. In the SOURCE analysis, the irradiation temperature was set at an arbitrary temperature of 1000 K. The uncertainty in ORIGEN calculations has been estimated to be about 15%. The target for the SOURCE comparison is ± 20% for each chemical element. Failure to meet this criterion for an element included in the RMC thermochemical model is an indication that more isotopes of that element need to be modelled in the prototype computer program. The isotopes to add were extracted from the detailed ORIGEN-S nuclide calculations. There is no need to add isotopes for those elements that are not modelled in the RMC thermochemical model. The summary results of this benchmarking for chemical elements common to the RMC thermochemical model and to SOURCE IST 2.0P11 are provided in Table 14 at steps of 50 MW·h·kg-1from 50 MW·h·kg-1to 300 MW·h·kg-1.
93 Table 14 SOURCE IST 2.0P11 Inventory of a Chemical Element in the RMC Thermochemical Model as a Fraction of the ORIGEN-S Inventory for That Chemical Element Burnup for Constant Power of 488 kW for 19.25 kg Natural Uranium Element 50 100 150 200 250 300 Isotopes to Add 83m Krypton* 0.98 0.97 0.97 0.97 0.97 0.97 Kr** 87 Rubidium 0.29 0.29 0.29 0.29 0.29 0.29 Rb 88 Strontium 0.69 0.66 0.64 0.62 0.62 0.61 Sr 89 Yttrium 0.64 0.45 0.33 0.25 0.20 0.16 Y 91 Zirconium 0.15 0.11 0.08 0.06 0.05 0.04 Zr, 92Zr, 93Zr, 94Zr, 96Zr 95 Molybdenum 0.02 0.01 0.00 0.00 0.00 0.00 Mo, 97Mo, 98Mo, 100Mo 99 Technetium 0.00 0.00 0.00 0.00 0.00 0.00 Tc 100 Ruthenium 0.20 0.18 0.17 0.16 0.15 0.15 Ru, 101Ru, 102Ru, 104 Ru 103 Rhodium 0.04 0.02 0.01 0.01 0.01 0.01 Rh 104 Palladium 0.00 0.00 0.00 0.00 0.00 0.00 Pd, 105Pd, 106Pd, 107Pd, 108 Pd 128 Tellurium 0.15 0.09 0.07 0.05 0.04 0.04 Te, 130 Te 127 Iodine 0.79 0.75 0.73 0.72 0.71 0.71 I Xenon 1.00 1.01 1.01 1.01 1.01 1.01 Caesium 0.98 0.98 0.98 0.98 0.98 0.98 134 Barium 0.17 0.09 0.06 0.05 0.04 0.03 Ba, 137Ba, 138Ba 139 Lanthanum 0.03 0.02 0.01 0.01 0.01 0.01 La 140 Cerium 0.42 0.34 0.29 0.26 0.23 0.21 Ce, 142Ce 141 Praseodymium 0.30 0.13 0.08 0.06 0.04 0.04 Pr 143 Neodymium 0.03 0.01 0.01 0.01 0.01 0.00 Nd, 144Nd, 145Nd, 146 Nd, 148Nd, 150Nd Uranium 1.00 1.00 1.00 1.00 1.00 1.00 237 Neptunium 0.93 0.86 0.80 0.75 0.70 0.66 Np Plutonium 1.00 0.98 0.97 0.96 0.96 0.96 Notes * In the 2009 RMC model moles of krypton are added to moles of Xe. ** 83mKr is to be added not for inventory reasons, but because it is reported in many licensing submissions. Of particular concern is the representation of the metals in the “five-metal” noblemetal particles. The (modelled) radioactive ruthenium accounts for 15-20% of the chemical ruthenium, whereas the radioactive nuclides of the other four metals (molybdenum, technetium, rhodium and palladium) represent less than 5% (and
94 frequently less than 0.005%) of the chemical inventory of those elements.
If
thermochemical calculations were based on these inventories, the “five-metal” particles may not contain all five metals after some decay time and would be richer in ruthenium than would be the case if a more complete inventory calculation were used. 5.2.2
Revised Nuclide Set
This exercise has identified a minimum of 40 fission-product nuclides or nuclear isomers of 17 chemical elements to add to the nuclide library. The reason that this is a minimum is that long-lived parents of nuclides to be modelled may have a significant effect on the generation and depletion kinetics of a nuclide. For example, the long-lived tin nuclide 230,000 years.
126Sn
126Sn
decays to
126mSb
by β- decay with a half-life of
was added to the nuclides modelled in SC11 to account for the
delay in formation of
126Sb
due to the very slow decay of
126Sn13.
Without the
modelling of 126Sn, the inventory of 126Sb was larger than calculated with ORIGEN-S (see Table 12) because the entire cumulative yield of direct yield of
126Sb.
The inventory of
126Sb
126Sb
was re-assigned as the
would also decrease too quickly as it
would decay with its own half-life of 12.4 days rather than decay in secular
equilibrium with the 230,000 year half-life of its long-lived parent, 126Sn.
13
This work uses the half-life value of 230,000 years from ICRP-107 [ICRP 2008] rather than the ~100,000 years from earlier references, including ICRP-38 [ICRP 1983]. This value is consistent with the recent determination by Catlow et al. [Catlow 2003] and represents a change from the data used in the 1995 candu37e library [Gauld 1995] distributed with SCALE 5.1 [Gauld 2006a].
95 According to the decay data in ORIGEN-S [Gauld 2009a] and in ICRP-38 [ICRP 1983], 126Sn
decays to
126mSb
and not directly to the ground state.
decay 14% to the ground state (126Sb) and 86% to
126Te.
19.0 minutes. In the SC11 representation of this chain,
126mSb
has a branched
The half-life of
126Sn
126mSb
decays 14% to
is
126Sb
and 86% to 126Te. Three other fission products,
102mTc, 104Rh
and
144mPr,
were added to allow a good
representation of the decay and transmutation chain. The nuclear isomer 83mKr was added because it has been reported historically in safety analyses. The 40 fissionproduct nuclides in the last column of Table 14, as well as 144mPr
102mTc, 104Rh, 126Sn
and
were added to the fission-product list.
Three fission-product nuclides were identified to be deleted. The arsenic nuclides 77As
and
79As
have very small cumulative fission yields and short half-lives.
Combined, they represent a small fraction of the molar composition of fission products in reactor irradiated fuel. The final nuclide to be deleted is the nuclide 132Sb.
This nuclide has been deleted because the latest Nuclear Data Sheet for isobar
132 [Khazov 2005] indicates that the issue of which is the ground state,
132Sb,
and
which is the first isomeric state, 132mSb, is not satisfactorily resolved. With a lack of clarity, it is uncertain which fission yield and half-life is properly attributed to 132Sb and which to 132mSb. Neither 132Sb nor 132mSb as calculated by ORIGEN-S represent more than 1 part per million of the molar fission-product inventory. The revised library has 174 fission-product nuclide or nuclear isomers, compared to 133 in the SOURCE IST 2.0P11 library.
96 The modelling of
237Np
is needed to get a good representation of neptunium
isotopes, and requires the modelling of 237U (which is on the major production path for 237Np), and of 238Np (to which it is transmuted by radiative neutron capture and which decays to 238Np
238Pu
(already modelled). Thus, three actinides,
237U, 237Np
and
were added. The actinides 240mNp and 240Np represent a very small fraction of
the neptunium inventory in either the ORIGEN-S or SOURCE IST 2.0P11 calculations and were deleted. With the addition of 3 actinides and deletion of 2, the new library has 18 actinides nuclides or nuclear isomers compared to 17 in SOURCE IST 2.0P11. The revised data nuclide set includes 18 actinides and 174 fission-products and activated fission-product nuclides. The revised data file required minor revisions to the SOURCE IST 2.0P11 Fortran code that declares PARAMETER values related to dimensioning arrays and reading the physics data. The maximum length of a decay chain was increased to 11 from 10.
The maximum number of nuclides was
increased to 200 from 150. The maximum number of cross-sections per nuclide was increased from 2 to 3 to account for
239Pu,
which in the SC11 data file has three
cross-sections, those for 239Pu (n, 2n) 238Pu, 239Pu (n, γ) 240Pu and 239Pu (n, fission).
5.3 Benchmarking Revised Code and Library The benchmark was repeated using a prototype code version and the new data file. The new benchmarking results are shown in Table 15.
The results, shown in
Table 15, demonstrate that the results using the revised code and data have brought all 22 chemical elements within ±20% of the ORIGEN-S inventory and 18 out of 22 within ±5%.
The four elements with differences outside the range ±5% are
97 zirconium (+6%), iodine (-11% to -8%), neodymium (-12% to -2%) and neptunium (-18% to -5%). A difference of up to 5% can reasonably be attributed to the use in SOURCE of a single cross-section irrespective of actinide composition, while the ORIGEN-S library for CANDU® 37-element fuel bundles has multiple cross-sections for different burnups to represent the change in neutron spectrum as the actinide composition of the fuel changes with burnup. Table 15 Inventory of a Chemical Element from Revised Code and Revised Physics Data Library as a Fraction of ORIGEN-S Chemical Inventory
Element Krypton Rubidium Strontium Yttrium Zirconium Molybdenum Technetium Ruthenium Rhodium Palladium Tellurium Iodine Xenon Caesium Barium Lanthanum Cerium Praseodymium Neodymium Uranium Neptunium Plutonium
Burnup for Constant Power of 488 kW for 19.25 kg Natural Uranium 50 100 150 200 250 300 0.98 0.99 0.99 0.99 0.99 0.99 1.01 1.01 1.01 1.01 1.02 1.02 0.97 0.97 0.98 0.98 0.98 0.98 0.97 0.98 0.97 0.98 0.98 0.98 1.06 1.06 1.06 1.06 1.06 1.06 1.01 1.01 1.01 1.01 1.01 1.01 0.98 0.98 0.98 0.98 0.98 0.98 1.02 1.02 1.02 1.02 1.02 1.01 1.01 1.01 1.01 1.01 1.01 1.01 1.01 1.01 1.01 1.01 1.01 1.00 1.01 1.02 1.01 1.02 1.02 1.02 0.90 0.89 0.90 0.91 0.91 0.92 1.00 1.00 1.01 1.01 1.01 1.01 0.98 0.98 0.98 0.98 0.98 0.98 0.99 1.00 0.99 0.99 0.99 0.99 1.00 1.01 1.01 1.01 1.01 1.01 0.98 0.98 0.97 0.97 0.96 0.96 1.01 1.01 1.01 1.01 1.02 1.02 0.98 0.95 0.93 0.91 0.89 0.88 1.00 1.00 1.00 1.00 1.00 1.00 0.95 0.89 0.86 0.84 0.83 0.82 1.01 0.99 0.98 0.97 0.97 0.97
Range of Fractions Minimum Maximum 0.98 0.99 1.01 1.02 0.97 0.98 0.97 0.98 1.06 1.06 1.01 1.01 0.98 0.98 1.01 1.02 1.01 1.01 1.00 1.01 1.01 1.02 0.89 0.92 1.00 1.01 0.98 0.98 0.99 1.00 1.00 1.01 0.96 0.98 1.01 1.02 0.88 0.98 1.00 1.00 0.82 0.95 0.97 1.01
98 Additional cycles of benchmarking and updating of the physics data library may be necessary to create a verified tool for safety analysis.
The present results
demonstrate that the elemental inventories can be improved so that incorporation of an internal Gibbs energy minimization routine in a safety analysis code is feasible.
99
6 Model Development and Code Implementation The prototype computer program has been identified by mnemonic SC11. The components of the mnemonic are Source-term calculation, internal Gibbs energy minimization to determine equilibrium Chemistry, and recognition that the prototype is based on SOURCE IST 2.0P11.14 The problem solved by SC11, calculation of fission-product release fractions from irradiated uranium dioxide fuel, is unaltered from that solved by SOURCE IST 2.0.
6.1 Incremental Software Requirements The following software requirements are new to SC11: 1. Revise the handling of nuclear physics data to allow for the extra nuclides, the extra nuclear data, the longer decay-transmutation chains, and the greater branching incorporated into the SC11 nuclide model. 2. Remove analogues for chemical elements that are included in the revised RMC model of irradiated uranium dioxide fuel and provide analogues for the chemical elements that are no longer treated directly in the RMC model. 3. Perform initialization of the ChemApp software.
The ChemApp library
provides the subroutines to perform the required initialization, but the individual initialization tasks are called by an SC11 routine.
14
The underlining of characters indicates those are part of the mnemonic.
100 4. Replace the current model for fission-product release from the fuel surface with a model based on equilibrium among the chemical compositions at the fuel surface and in the gap. 5. The new model for fission-product release from the fuel surface shall incorporate the advective release model. This model ensures that if there is no stable condensed (solid or liquid) phase for a chemical element at the given conditions, then the entire fuel surface inventory of that element is released. The solid or liquid is deemed to have boiled to the gas phase. Two more general requirements affect implementation, rather than model development. 6. The number of changes to the code should be limited to maintain a path for SOURCE 2.0 development that could incorporate these changes. 7. The style and modular structure of the SOURCE 2.0 computer program are to be maintained.
6.2 Model Description The subsections of Section 6.2 address requirements 1 through 4 from Section 6.1. The model described in Section 6.2.4 meets both requirements number 4 and 5. 6.2.1
Physics Data
Incorporating the revised physics data does not require a change to the SOURCE 2.0 algorithm.
Fortran PARAMETER values were revised in the nuclide module.
MaxNNuc, the maximum number of nuclides, was increased to 200. MaxNiCh, the
101 maximum number of nuclides in a decay/transmutation chain was increased to 11. MaxNSig, the maximum of neutronic transmutation cross-sections for a nuclide was increased to 3. 6.2.2
Chemical Analogues
The second requirement relates to the use of chemical analogues. In SOURCE 2.0, some chemical elements were modelled using the most-volatile of two analogues. In SC11 only one analogue is used for any chemical element that is not modelled directly. Selenium is treated as iodine so that it transfers with its bromine decay product. Bromine is treated as iodine based on similarities of the chemistry of the halogens. Niobium is treated as zirconium because radio-niobium is created by zirconium decay and no element with a pentoxide is available as a better analogue. Silver and cadmium are treated as palladium because this element is the nearest modelled noble metal.
Antimony is treated as tellurium.
Promethium and
samarium are treated as neodymium as the nearest modelled primarily trivalent lanthanides.
Europium is treated as strontium because both strontium and
europium release under reducing conditions in which europium is probably released as the divalent europium (II) oxide species. The inventories of those chemical elements that are not modelled are not added to the inventory of their analogue prior to calculating the equilibrium; rather, the release fraction of the analogue is used as the release fraction for the unmodelled chemical element. A table of chemical elements in the range of atomic numbers modelled by SOURCE 2.0 and SC11 is provided in Table 16. It contains a list of chemical analogues where applicable.
102 Krypton is treated differently from other chemical elements that are not modelled directly. The molar inventory of krypton is added to the xenon inventory before the equilibrium calculation. Table 16 Chemical Element
Chemical Analogues in SOURCE 2.0 and SC11
Modelled Directly in SOURCE 2.0
SOURCE 2.0 Analogue(s)
Arsenic (As)
No
Sb
Selenium (Se)
No
Te
No
I
Bromine (Br)
No
I
No
I
Krypton (Kr)
N/A*
N/A
No
Xe
Rubidium (Rb)
No
Cs
Yes
N/A
Strontium (Sr)
Yes
N/A
Yes
N/A
Yttrium (Y)
Yes
N/A
Yes
N/A
Zirconium (Zr)
Yes
N/A
Yes
N/A
Niobium (Nb)
Yes
N/A
No
Zr
Molybdenum (Mo)
Yes
N/A
Yes
N/A
Technetium (Tc)
No
Mo
Yes
N/A
Ruthenium (Ru)
Yes
N/A
Yes
N/A
Rhodium (Rh)
Yes
N/A
Yes
N/A
Palladium (Pd)
No
Ru or Rh
Yes
N/A
Silver (Ag)
No
Ru or Rh
No
Pd
Cadmium (Cd)
No
Ru or Rh
No
Pd
Indium (In) Tin (Sn) Antimony (Sb) *
No indium nuclides modelled No tin nuclides modelled Yes
N/A signifies not applicable.
N/A
Modelled Directly in SC11
SC11 Analogue
No arsenic nuclides modelled
No indium nuclides modelled 126Sn
release not modelled
No
Te
103 Table 16 (Continued) Chemical Element
Modelled Directly in SOURCE 2.0
SOURCE 2.0 Analogue(s)
Modelled Directly in SC11
SC11 Analogue
Tellurium (Te)
Yes
N/A
Yes
N/A
Iodine (I)
Yes
N/A
Yes
N/A
Xenon (Xe)
N/A
N/A
Yes
N/A
Caesium (Cs)
Yes
N/A
Yes
N/A
Barium (Ba)
Yes
N/A
Yes
N/A
Lanthanum (La)
Yes
N/A
Yes
N/A
Cerium (Ce)
Yes
N/A
Yes
N/A
Praseodymium (Pr)
Yes
N/A
Yes
N/A
Neodymium (Nd)
Yes
N/A
Yes
N/A
Promethium (Pm)
No
Eu or Nd
No
Nd
Samarium (Sm)
No
Eu or Nd
No
Nd
Europium (Eu)
Yes
N/A
No
Sr
Uranium (U)
Yes
N/A
Yes
N/A
Neptunium (Np)
No
N/A
Yes
N/A
Plutonium (Pu)
Yes
N/A
Yes
N/A
6.2.3
Initialization
The initialization of the ChemApp software to satisfy requirement 3 does not require any model development. For efficiency (in terms of execution time), the chemical database should be read once and kept in memory. 6.2.4
Equilibrium at the Fuel Surface and Releases to the Gap
A schematic representation of the phases that participate in the equilibrium is presented in Figure 20. SOURCE 2.0 does not have models of either the fuel sheath
104 or the CANLUB layer, a graphite coating on the inside of the fuel sheath. It has been recommended that users do not use high gap flow rates until the fuel sheath is completely oxidized (as calculated by a sheath oxidation model in ELOCA [Sills 1979]). The zirconium in the sheath has a sufficiently high oxygen affinity that, under accident conditions, the fuel is protected from oxidation until the fuel sheath is fully oxidized.
Figure 20
Schematic of the Equilibrium System (not to scale)
The conditions for chemical equilibria outlined in section 2.2.1 are applied to a set of molar inventories of system components. As demonstrated in section F.4.1, the system components in the RMC model of irradiated uranium-dioxide fuel are the chemical elements, because each chemical element exists at least once in elemental form in at least one pure compound or solution phase. The equilibrium is calculated at the temperature of the fuel surface (if specified) or at the temperature of the centre of the outer annulus (if the fuel surface has not been specified), and at the system pressure provided in the user input.
105 6.2.4.1 Starting Inventories for Equilibrium Calculations The question of which inventories calculated by SOURCE 2.0 are participants in the equilibrium is based on equilibrium of co-existing phases at the fuel surface. The grain matrix has a zero concentration boundary-condition for all chemical elements except the actinides and oxygen; thus, of the material in the fuel grains, only the actinides modelled in the RMC model (uranium, neptunium and plutonium) and the associated oxygen exist in contact with the fuel surface. The oxygen content is calculated from the user-specified fuel stoichiometry. Material that is in the grain matrix, but which would diffuse out of the grains, is not part of the equilibrium system because it has not been transported to the appropriate place. The grainboundary inventory does not participate until it is released from grain-boundary bubbles to the fuel surface. As such the grain-boundary inventory is excluded from the equilibrium. The material in the gap is clearly in contact with the fuel surface and participates in the equilibrium. The molar inventory of each chemical element is calculated by adding the atomic inventories of all nuclides of that element in the gap and on the fuel surface and dividing by Avogadro’s number. Krypton is added to xenon because both elements are modelled as inert gases. The model for fission-product vaporization from the fuel surface is called only after sheath failure. For large sheath failures, the gap pressure and the system pressure should equalize. The gas phase in SOURCE 2.0 is specified as a molar flow rate of hydrogen (H 2), steam (H2O), inert gas (typically, He, N2 or Ar), and oxygen (O2). These flow rates
106 are the fraction of the bulk coolant flow rate that enters the gap and is in contact with the fuel surface. To obtain a molar quantity, the flow rates are multiplied by the duration of the time step. The hydrogen (H2) in the gas phase is added to the system as two moles of hydrogen atoms per mole of hydrogen (H2). The steam (H2O) is added as two moles of hydrogen atoms and one mole of oxygen atoms per mole of steam (H2O). The inert gas in the gas phase is added as one mole of xenon for each mole of inert gas molecules. For example one mole of nitrogen (N2) is modelled as one mole of xenon (Xe). Oxygen (O2) is added as two moles of oxygen atoms. 6.2.5
Fission-Product Release from the Gap
Once the equilibrium has been calculated, the fraction of each element in the gas phase is calculated. The gas phase fraction is equal to the quantity (in moles) of that element in the gas phase divided by the quantity of that element in the inventory for which the equilibrium was calculated. This fraction of the inventory of each nuclide participating in the equilibrium is transferred to the gap inventory. After sheath failure, the model for releases from the gap transfers the entire gap inventory to the released inventory. This action represents a venting of the gap to the surroundings. By ensuring that material which exists only in the vapour phase is transferred to the gap and venting the gap, the requirement to incorporate the behaviour of the advective release model of SOURCE 2.0 is met.
107
6.3 Existing SOURCE 2.0 Structure Before describing the implementation of changes, an annotated call tree for the existing SOURCE 2.0 prototype will be presented (Table 17). The starting version was a developmental prototype based on SOURCE IST 2.0P11 with changes due to work performed to couple ELOCA [Sills 1979] and SOURCE 2.0, and work on the updating of decay data in SOURCE 2.0. The subroutines FSFPVap, FSLimitT and their description are underlined. These models have been entirely replaced in the prototype computer program. The models in SOURCE IST 2.0P11 are described in Appendix D. Table 17
Call Tree of Major SOURCE Routines
Major Operations or Subroutines Called SOURCE_INIT
Loop on time steps SOURCE_STEP Geometry loops over all axial segments Loop over annuli FPREL
Description of Major Functionality Initialization; open error log file; open output files; write headers and time stamps to output files; open read and close input files; open, write and close data echo files Take a time step for all basis units Nested loops on channel groups, bundles, fuel element groups, and axial segments Calculate fission-product release to the fuel surface for each annulus
Rel_Phase_Change
Calculate releases due to phase changes
Leach
Calculate releases due to leaching
GGROW
Calculate grain and grain-boundary bubble growth
GSWEEP
Calculate grain-boundary sweeping
ACTINIDE
Calculate actinide generation and depletion
Redist
Redistribute fission product in fuel grains
108 Table 17 Major Operations or Subroutines Called DiffusionShell
(Continued) Description of Major Functionality Perform coupled fission-product generation, depletion and diffusion calculations in the fuel grains and generation and depletion on grain boundaries
NucProc
Perform fission-product generation and depletion calculations for the fuel surface, gap, and released inventories
Fuel surface to gap transport
Transfer noble gases to gap from fuel surface; condense other fission-products in the gap to the fuel surface
RETURN from FPREL End of loop on annuli IF sheath failed Radial_Transport
If the sheath has failed Accumulate all of the fuel surface inventories in the “fuel surface” of the outer annulus;
FSFPVap
Fission-product vaporization from the fuel surface
FSLimitT
Transfer elements from the fuel surface to the gap if there is no stable condensed phase calculated at these conditions
Rewet
If rewet occurs during this time step, a defined fraction for each chemical element is released from the fuel surface
ReleasesDueToSheathFailure
If the sheath has failed, release the gap inventory
END IF sheath failed End of loops over all axial segments End of loop on time steps SOURCE_END
Print final results and close output files
109
6.4 Revised Initialization 6.4.1
MODULE ChemElem
This new MODULE15 contains a list of chemical symbols from hydrogen (H) to fermium (Fm) in a Fortran array of CHARACTER PARAMETER values. The atomic numbers of hydrogen, oxygen, krypton, xenon, uranium, neptunium and plutonium are included as PARAMETER values. A subroutine to find the atomic number of a chemical element from its symbol and the defined PARAMETER values is contained in the MODULE. 6.4.2
MODULE CAData
This new MODULE holds chemical data used by the new model to print the composition of the calculated equilibrium state and to perform subsequent calculations. It also contains declarations for ALLOCATABLE arrays to receive data from queries to the chemical solver, and a SUBROUTINE SetIndSCInv which sets16 the elements of a vector to an index corresponding to each chemical element (system component) in the inventory from 1 (hydrogen) to 100 (fermium) to an index value. If the element is a system component, the index is set to the value that ChemApp has assigned to that chemical element. For elements modelled by a chemical analogue, the index is set equal to the ChemApp index of the analogue, but with a negative sign. The chemical analogues are “hard-coded” in SetIndSCInv. The
15
16
In discussing Fortran code, Fortran keywords are presented in upper case. Thus MODULE indicates that it the code is a Fortran MODULE, rather than a module, which usage implies a collection of related functions and subroutines. Underlined characters are part of the SUBROUTINE name SetIndCSInv.
110 index value is set to zero if the element is not modelled by ChemApp and not modelled by SC11 using an analogue. 6.4.3
SUBROUTINE InitChemApp
This subroutine performs initialization tasks of the ChemApp solver.
The
initialization promptly checks for a ChemApp security dongle and stops promptly after printing an error message to the log file if no dongle is present.
The
initialization is performed before any steps of the SOURCE_STEP are taken. A ChemApp copyright message and the ChemApp version number are printed. The ChemSage formatted data file containing the RMC thermochemical model for irradiated uranium dioxide fuel is opened and read. Integer values giving the number of system components, the number of possible phases, and the number of constituents in each phase are obtained. The number of pure phases is calculated. Data from the library that will not change are assigned to values in this MODULE. Other arrays in the MODULE are ALLOCATED to the required length for later use. These arrays have the SAVE attribute and will remain available for further use in the computer program. 6.4.4
SUBROUTINE CAbort
This subroutine replaces CAbort from the ChemApp sample with a routine that prints diagnostic messages in a format similar to that of SOURCE 2.0. 6.4.5
SUBROUTINE SetChemAppUnits
This subroutine sets the units for amount to moles, pressure to Pascal, temperature to Kelvin, and volume to cubic metres.
111 6.4.6
Deletions and Incidental Changes
The ratio of caesium to steam (CsStmRatio) that had been used to specify the relative quantities of fuel and fission-product material to coolant was an input specified by the user and is no longer required. The inventories of all required elements are now calculated directly from the nuclide inventories and from gas flow rates and time interval durations. The variable CsStmRatio is no longer read from input files. Unused functions and subroutines that managed the chemical lookup tables, and calculated mass-transfer limited transport and the advective releases have been deleted. Nine data files that contained chemical data in SOURCE 2.0 have been deleted and/or replaced by data MODULES that define the data in PARAMETER arrays or by the ChemSage formatted data used by ChemApp. The data file related to chemical analogues has been replaced by coding to perform this function. As with any major code development, there have been incidental changes to the coding that need not be described in this thesis, but are described in the (proprietary) COG model description document, the Fortran source code and the revision history.
6.5 Implementation of Revised Model for Fission-Product Vaporization from the Fuel Surface Given the modular structure of SOURCE 2.0, the replacement of the model for fission-product vaporization from the fuel surface required a minor change to the interface to SUBROUTINE FSFPVap, and replacement of FSFPVap and removal of
112 unused subordinates. The SUBROUTINE ChemCalc is called by FSFPVAp and is a generic wrapper for calls to ChemApp routines. 6.5.1
SUBROUTINE FSFPVap
SUBROUTINE FSFPVap models the Fuel Surface Fission-Product Vaporization process17. The inputs to SUBROUTINE FSFPVap are the duration of the time step for the calculation, the gas flow rates exposed to the fuel of hydrogen (H2), steam (H2O), inert gas (He, N2, Ar or none) and oxygen (O2) (all in moles·s-1); pressure (Pa), temperature (K), and fuel stoichiometric deviation (the dimensionless x in UO2+x). The atomic quantities of nuclides and nuclear isomers in the five inventory bins of the outer annulus are input values that are modified (INTENT (INOUT) in Fortran90 parlance). Apart from the fuel stoichiometry (which has been added), this is the same argument list as in SOURCE 2.0. The total atomic inventory in each of the grain matrix, the fuel surface and the gap is determined by calls to the existing SOURCE 2.0 routine GetChemInv. The inventory vectors for the gap and the fuel surface are added (stored by chemical element) and converted to moles. The molar inventory of krypton in the gap and fuel surface is added to that of xenon, and then the molar inventory of krypton is set to zero. Both xenon and krypton are modelled as inert gases and will only exist at equilibrium in the gas phase. The molar inventory of uranium, neptunium and plutonium in the grain matrix of the outer annulus is added to their molar inventories in the gap and
17
Underlined characters are part of the name FSFPVap.
113 the fuel surface. The quantities of hydrogen, steam, inert gas and oxygen are added to the inventory (following the rules in Section 6.2.4.1). At this point a call to the SC11 SUBROUTINE ChemCalc is made. The values returned from this call are fractions of elements in the gas phase, the fluorite phase, and all other phases combined. After returning from this call, a loop over all fissionproduct nuclides and nuclear isomers is started. Within this loop, the gas phase fraction of modelled elements (including those modelled by analogues) is transferred to the gap, and the remainder is left in the fuel surface. This transfer is performed on a nuclide-by-nuclide basis. 6.5.2
SUBROUTINE ChemCalc
The input values to SUBROUTINE ChemCalc are the molar inventories of all chemical elements listed in MODULE ChemElem that are part of the equilibrium system (in moles), the system pressure (Pa), and the fuel surface temperature (K). The output is an array over the system components (the chemical elements in the RMC model) of the fraction of that chemical element in the gas phase, the fluorite phase and any other phase. ChemCalc calls the ChemApp routine TQREMC18 (remove conditions) to remove the amounts, pressure and temperature from ChemApp data structures; and then calls SC11 SUBROUTINE SetChemAppUnits to ensure that units used by ChemApp are
18
The ChemApp subroutines used in this work all begin with “TQ” the rest of the name is mnemonic. A short description of the purpose is given in brackets at the first reference to each routine called.
114 moles for amount, Pascal for pressure, Kelvin for temperature, and cubic metres for volume.
Next, two calls to TQSETC (set conditions) set the pressure and
temperature to the input values thereof. The largest molar inventory among the input vector of molar inventories is found using the Fortran INTRINSIC FUNCTION MAXVAL. A temporary array of inventories is initialized to zero. At this point a loop over all elements is started. The index of the current element (in the ChemSage database) is retrieved from a prepopulated vector. If the element (i) is modelled by ChemApp, (ii) has an inventory that is less than or equal to one million moles, (iii) has an inventory that is greater than or equal to 1 atom, and (iv) has a molar inventory that is greater than 2-26 (~1.5E-8) times the largest molar inventory19, then this molar inventory is set in the temporary array, and is passed to the ChemApp data structure using the ChemApp SUBROUTINE TQSETC. Otherwise, the molar inventory is set to zero, the fraction in the gas phase is set to unity20, and the fractions in the fluorite phase and other phases are set to zero. The code prints appropriate messages for inventories greater than one million moles, for molar inventories less than zero, or for values that appear to be an indeterminate floatingpoint value. In any of these three cases, the program stops. In the absence of an error, once all the chemical elements have been processed, the loop on elements ends.
19
20
This quantity is explained further in Section 6.5.2.1.2. It is large enough to avoid nonconvergence and small enough to avoid ignoring trace elements, unless necessary to get convergence. This treatment, which will ultimately release these small inventories is intended as a conservative treatment of inventories that are probably too small to affect the final results.
115 Then, the program calls the ChemApp routine TQCE (calculate equilibrium). The ChemApp routine TQGETR (get results) is called to retrieve the quantity of a phase that is present in the calculated result. If the quantity of a phase is greater than zero, the name of the phase is printed21 and the quantity of each constituent of the phase is obtained using a second call to TQGETR. If the quantity present is greater than one molecule, a third call to TQGETR retrieves the partial molar Gibbs energy of the constituent. The name of the constituent, quantity present and partial molar Gibbs energy are printed. A series of calls to TQGETR retrieve the quantity of system components in each phase. The fractions of each element in the gas phase, the fluorite phase and in all other phases are calculated based on the quantities thus obtained and the saved quantities that were input to ChemApp. The sum of the fractions is checked to see if it is within 1E-8 of unity; if not, a diagnostic message is printed. The fractions of system components in the gas phase, the fluorite phase and in all other phases combined are returned to the calling routine, in this case FSFPVap. 6.5.2.1 Elimination Criterion for de minimus Inventories 6.5.2.1.1 Elemental Inventories of less than One Atom The prototype code writes22 the molar inventories of chemical elements, the temperature and pressure before calling the ChemApp [Eriksson 2008] subroutine TQCE. This output is intended to allow for debugging of the program and for
21 22
This output is typically redirected to a text file. During testing, this output was usually redirected to a text file.
116 trouble-shooting. The input conditions could then be entered into the FactSage software [Bale 2010] to trouble-shoot the chemical equilibrium calculation outside of the overhead of a much-larger computer program for fission-product release. ChemApp uses the same algorithms as FactSage; hence, this approach corresponds to module testing of the computer program. In testing the SC11 prototypes, it was noted that there were cases in which the ChemApp subroutine failed to return in a reasonable amount of time. This condition is referred to by code developers as “hanging”23. By terminating these code runs from the command line, the file is closed and the input to the problematic calculation can be examined. The last set of input conditions for ChemApp would be the values for the case that had “hung”. In these cases, it was found that one or more chemical elements had an input inventory of less than one atom. The program was modified to set all inventories of less than one atom to zero. No further cases of the ChemApp subroutine “hanging” were encountered during testing. 6.5.2.1.2 Elimination of Small Fractional Inventories Having eliminated cases in which ChemApp did not return in a reasonable time, there were other cases in which the solver returned, but did not converge. The subroutine TQCE indicates non-convergence through a returned error flag that is checked by the SC11 SUBROUTINE ChemCalc. If the equilibrium calculation did not
23
For the purpose of this thesis, no distinction is made between the condition in which a subroutine has got into an infinite cycle and the condition in which convergence is very slow. Neither is acceptable in a production computer program.
117 converge, then SC11 would stop. These non-convergences occurred at the end of some cases as the fuel temperature was dropping.
In an attempt to obtain
convergence, the system temperature was increased slightly (for only the equilibrium calculation, not for the other calculations of fission-product release, e.g., fission-product diffusion, or grain growth). In some cases, this change resulted in convergence, but not in all cases. Again, the input conditions to the ChemApp subroutine were transferred to FactSage [Bale 2010] for further trouble-shooting. In all cases, at least one chemical element had an inventory much smaller than the largest inventory. The SC11 prototype was modified again so that inventories less than 2-26 (about 1.49E-8) of the largest inventory are set to zero24. 6.5.2.1.3 Inert Gas Inventory As an exception to the rules in sections 6.5.2.1.1 and 6.5.2.1.2 above, if the inert gas inventory (modelled as moles of xenon) is less than 1000 atoms, it is modelled as 1000 atoms. This exception is based on the observation that there are chemical equilibrium problems with no solution when the system pressure is fixed, the system temperature is low, a gas phase is permitted, and there is no inert gas. In such cases, the sum of partial pressures of vapours modelled in the system may be less than the imposed system pressure. One option is to redo the calculation with no gas/vapour phase permitted. In this case, the solid and liquid pure substances and solutions are calculated, but no gas/vapour phase. The option chosen in this
24
This value is the square root of the difference between 1.0 and the next largest floating-point number in IEEE-754 double-precision floating-point numbers [IEEE 1985] [Overton 2001]. Unlike 1.0E-8, it is represented exactly in IEEE-754 double-precision.
118 work is to add a small quantity of noble gas to the system. The partial pressure of the noble gas will be calculated to be the difference between the system pressure and the sum of the partial pressures of the other gases/vapours. This assumption allows vaporization of other fission products, even when the sum of their vapour pressures is less than the system pressure. Otherwise, no vaporization would occur. Neither SOURCE IST 2.0P11 nor SC11 models the helium fill gas originally in the fuel element, or 4He produced in the fuel by α–decay, by (n, α) reactions, or as a ternary fission product.
6.6 Limitations 6.6.1
Use of Analogues
There are chemical elements with nuclides modelled in SOURCE 2.0 (and/or SC11) that are not modelled in the RMC model of irradiated uranium dioxide fuel. These chemical elements are: arsenic (As), selenium (Se), bromine (Br), krypton (Kr), niobium (Nb), silver (Ag), cadmium (Cd), tin (Sn), antimony (Sb), samarium (Sm), europium (Eu), americium (Am) and curium (Cm). As already indicated in Section 6.2.4.1, krypton is treated as xenon and added on a molar basis to the xenon. In SC11,
77As
and
79As
have been deleted from the set of modelled nuclides. One
nuclide of tin (126Sn) is modelled in SC11, but not in SOURCE 2.0. This nuclide is considered in more detail in Section 6.6.2 below. The actinides (Am and Cm) are treated separately from the fission products and are released congruently with uranium. Their release behaviours are governed by models that depend on userspecified fractions of fuel that has (i) formed a liquid phase due to UO2/Zircaloy
119 interaction below the Zircaloy melting temperature, UO2 dissolution by molten Zircaloy or fuel melting, or (ii) formed a gas phase by fuel vaporization; or (iii) been dissolved or leached by water. The remaining fission products are released based on the calculated release fraction of a modelled chemical analogue. SOURCE 2.0 modelled niobium, antimony, and europium. These were eliminated from the more recent model. They represent a smaller molar inventory than technetium, palladium and rubidium, which were added. However, there is validation data for the fission-product release of 125Sb
95Nb,
and 154Eu. Thus, it is possible to benchmark these elements that are modelled
with analogues. The expanded version of ChemApp [Eriksson 2008] allows up to 48 system components so more elements could be added to the chemical model, provided acceptable thermodynamic data were available. 6.6.2
Vaporization of Tin (126Sn)
At present, there is no treatment of the thermochemistry of tin in the RMC model. The only tin nuclide that is included in the nuclide set for SC11 is 126Sn. Release of this nuclide is not calculated. 6.6.3
Behaviour of Grain-Boundary Bubbles
Within SOURCE 2.0, the behaviour of grain-boundary bubbles is assumed to be due to the quantities of krypton and xenon gas in the bubbles. No account is taken of the vapour pressure of other chemical species. Thus, if krypton and xenon were to be
120 fully released from a sample, no further release of other elements from the grainboundary bubbles to the fuel surface would be modelled until grain-boundary separation, fuel melting, matrix stripping or fuel leaching released more material from the grain or grain boundary to the fuel surface. Accounting for the vapour pressure of other fission-product compounds in grain-boundary bubbles would increase the pressure in the bubbles. Since bubble growth depends on bubble pressure, this increase in pressure could lead to earlier grain-boundary interconnection and earlier release of noble gases from the grain-boundary bubbles to the gap. This change has not been made in the prototype computer program. 6.6.4
Boundary Condition for Fission-Product Diffusion from Grains
In SOURCE 2.0, the boundary condition for diffusion of all fission-product nuclides from the grain matrix to the grain boundary is a perfect sink boundary condition. This assumption is valid (in the absence of resolution) for chemical elements that are not soluble in the grain matrix. As seen in section F.4.3, the fission-product elements Tc, Ru, Rh, Pd, I, and Xe have no compounds that are modelled as soluble in the grain matrix. Thus, this boundary condition is consistent for those chemical elements and for krypton (which is modelled as xenon). In the absence of a model of grain-boundary bubble behaviour that accounts for other gases/vapours in grainboundary bubbles (see Section 6.6.3), it is not recommended that a more physically based boundary condition be introduced at this time. By transferring material to the fuel surface without accounting for the chemistry of the grain-boundary bubbles, some material with limited volatility at normal
121 operating temperatures may be transferred earlier than in reality. The treatment of the current model in SC11 (and in SOURCE IST 2.0P11) would condense this material on the surface of the outer annulus rather than retain it where a moredetailed treatment of chemistry might predict it would be stable under those conditions.
122
123
7 Benchmarking of Fractional Releases A set of 18 validation test cases are used to compare new versions of SOURCE IST 2.0 against previous versions of the code and against experimental results. Table 18 contains a summary of the validation cases. Table 18
SOURCE IST 2.0 Validation Cases
Experiment and Test
Location
Sample Type
Environment
HCE2 BM04 HCE2 BM05 BTF104 BTF105B GBI3 DL5 PHEBUS FPT1 HCE2 H02 HCE3 H03 HCE4 J03 HCE1 M12 UCE12 T01 MCE2 T03 MCE1 T04 UCE12 T09 MCE2 T19 VERCORS 5
CRL CRL NRU NRU CRL Phebus Reactor CRL CRL CRL CRL CRL CRL CRL CRL CRL Grenoble, France Grenoble, France ORNL, USA
M M E E F B
VERCORS 4 ORNL VI-5
Pressure (MPa)
Burnup (MW·h ·kg-1)
Steam Steam Steam Steam Air Steam/H2
Maximum Test Temperature (K) 1803 1787 2173 2100 1313 2800
0.1 0.1 0.5 0.5 0.1 0.2
567 465 132 155 233 560
M M M M F F F M F M
Air Steam Steam Inert Steam Inert Air Inert Inert Steam/H2
2160 2110 1900 1872 1373 2105 2268 1671 2303 2570
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
233 233 208 457 441 457 338 370 457 812
M
Steam
2570
0.1
812
E
Hydrogen
2750
0.1
1008
Notes: Location: CRL – Chalk River Laboratories Hot Cells; NRU – National Research Universal at Chalk River; Grenoble – Centre d’Étude Nucléaire, Grenoble; Phebus – Cadarache, France; ORNL – Oak Ridge National Laboratory Fuel Sample Types are: B –Bundle, E –Element, F – Fragment and M – Mini-Element
124 Input files to run SOURCE IST 2.0 for each of these cases were provided on the distribution CD-ROM for SOURCE IST 2.0P11.
These cases were run with the
prototype code incorporating the thermochemical solver (SC11). For experiment HCE2 test BM05, a new transient input file was created for this work to model more closely the fuel burnup. This revised test case was executed with both computer programs, SOURCE IST 2.0P11 and SC11. There are fifteen radionuclides for which more than four experimental release fractions are available within the SOURCE validation base cases. These nuclides and statistical measures of the difference between the calculated release fraction and the experimental release fraction are presented in Table 19. Comparisons for individual nuclides are presented in Figure 21 through Figure 35 in Sections 7.2 through 7.11.
7.1 Summary of Results Two simple paired statistical measures have been calculated for each nuclide and each computer program. These are the mean difference and the root mean square difference. The pairing compares the calculated values for one computer program and one nuclide to the experimental value for the same nuclide.
Where the
computer program has calculated release fractions for nuclides that were not reported for that test, no comparison is performed. The columns labelled P11 contain differences between SOURCE IST 2.0P11 and reported experimental
125 results25.
The columns labelled SC11 contain from differences between the
prototype and reported experimental results. Table 19
Nuclide Type Noble Gas Volatile Fission Product Potentially Volatile Low-Volatile Fission Product Modelled with Analogue in SC11
Nuclide 85Kr 133Xe 135Xe 131I 134Cs 137Cs 103Ru 106Ru 140Ba 95Zr 140La 144Ce 95Nb 125Sb 154Eu
Paired Statistics Comparing Individual Nuclides
Points 11 4 5 10 17 18 10 11 9 9 8 10 9 8 8
Mean Signed Difference26 P11 SC11 0.006 0.006 -0.038 -0.038 -0.144 -0.144 -0.047 -0.048 -0.031 -0.084 -0.021 -0.047 0.326 0.083 0.111 -0.061 0.479 0.305 0.089 -0.057 0.695 0.068 0.037 -0.115 0.402 -0.121 0.212 -0.261 0.453 0.096
Root Mean Square Difference27 P11 SC11 0.203 0.203 0.184 0.184 0.256 0.256 0.182 0.183 0.272 0.302 0.241 0.231 0.523 0.307 0.312 0.157 0.654 0.481 0.308 0.137 0.770 0.149 0.228 0.197 0.579 0.239 0.408 0.407 0.617 0.322
The mean signed difference is a measure of bias. The root mean square difference is a measure of scatter. For the noble gases, the differences between the prototype results and the experimental results are the same as the differences between SOURCE IST 2.0P11
25
The proprietary data were obtained from a report for the CANDU Owners Group that cannot be referenced in the open literature.
26
, The mean signed difference is calculated as . The sign convention ensures that a negative difference indicates that a calculated value is less than the experimental value. The sum is over n pairs of experimental and calculated values for the same nuclide.
27
The root mean square difference is calculated as
()
,
()
()
sum is over n pairs of experimental and calculated values for the same nuclide.
()
. The
126 and the experimental results. This behaviour is expected for noble gases because the fission-product vaporization model has little effect on noble gases. For 131I, the results were the same except for one case with a 0.01 difference. The iodine is expected to react with an excess amount of caesium (on a molar basis) so that essentially all of the iodine forms caesium iodide. It is expected that all iodine on the fuel surface would vaporize using the models in either code. Thus, the result observed is expected. The results for caesium are very similar except for some large differences in release fractions related to the Cs2Zr3O7 discussed in Section 7.3. For 103Ru, 106Ru, 140Ba. 95Zr, 140La and 154Eu, the mean signed difference is smaller in magnitude and the smaller RMS difference indicates less scatter. For
144Ce,
the
negative bias is larger in magnitude, but the scatter is reduced. For 95Nb and 125Sb, the use of the chosen analogues has resulted in negative biases in place of the positive biases with SOURCE IST 2.0P11. In the next sub-sections, nuclides or groups of nuclides are discussed in more detail. The filled diamonds labelled P11 represent the present code, SOURCE IST 2.0P11. The open squares labelled SC11 represent the results from the prototype at the end of the test. In the case of xenon isotopes in in-reactor tests, the open triangles represent SOURCE IST 2.0P11 results at the end of the test. The filled diamonds were decay corrected to the start of test conditions. Thus for xenon isotopes, the open triangles should be compared to the open squares.
127
7.2 Benchmarking 140La A comparison of the calculated results for the prototype code and for the SOURCE IST 2.0P11 is shown in Figure 21 for the isotope represent the present code.
140La.
The points labelled P11
The open symbols labelled SC11 represent the
prototype. The results of the new model represent a significant improvement over the current production code.
1
Calculated Release Fraction
0.8
0.6
0.4
0.2
0 0
0.2
0.4
0.6
0.8
1
Experimental Release Fraction P11
Figure 21
SC11
Ideal
Calculated Vs. Experimental Releases for 140La
Lanthanide release fractions calculated by SOURCE IST 2.0P11 (and earlier fissionproduct release codes) are known to be higher than expected based on fissionproduct release experiments. In containment, lanthanides, being of low volatility
128 are expected to settle on surfaces. The deposition of radioactive lanthanides on equipment could lead to calculated radiation doses that would challenge the environmental qualification of equipment in containment. This revised model that calculates lower, but more realistic, release fractions could provide operators of nuclear generating stations with greater assurance that equipment will survive the analyzed accident scenario. The release fractions calculated with SC11 show improved agreement with experimental release fractions compared to those calculated with SOURCE IST 2.0P11. A summary of the mean (signed) difference and the root mean square difference based on paired statistics for SC11 and for SOURCE IST 2.0P11 is presented in Table 19. Both of these quantities are much lower for SC11 than for the earlier code version. In assessing
140La
releases, only eight cases with reported experimental releases
were compared. The longest half-life in the decay chain that produces 140La is that of
140Ba
(modelled as 12.74 days). The inventories of
140Ba
and
140La
small values within about two to four months after irradiation.
will drop to Calculated
inventories in these cases may be comparable to the numerical tolerances used in the solvers within SOURCE 2.0 and the calculated releases may be due entirely to the allowable numerical errors.
The inventories and release fractions are
essentially meaningless in such cases. Similar comments apply to other shorterlived nuclides, particularly for tests with no pre-test trace re-irradiation of the fuel samples.
129
7.3 Benchmarking 134Cs and 137Cs For
134Cs
(see Figure 22), all but two of the cases from SC11 had the same release
fraction (to two digits after the decimal place) as the earlier SOURCE IST 2.0P11 results. Since caesium is a volatile fission-product, it is expected that modelling its chemistry would not alter it release fraction.
1
Calculated Release Fraction
0.8
0.6
0.4
0.2
0 0
0.2
0.4
0.6
0.8
1
Experimental Release Fraction Cs-134
Figure 22
Cs-134
Ideal
Calculated Vs. Experimental Releases for 134Cs
In one case, the final release fraction for
134Cs
was significantly lower than in the
corresponding SOURCE IST 2.0P11. In the supplementary output from SC11, it was reported that the calculated equilibrium included Cs2Zr3O7 as a solid phase. This result was unexpected since caesium was observed to have released in this test and
130 tests under similar conditions. In the second case, 5% of the
134Cs
is calculated to
remain on the fuel surface by SOURCE IST 2.0P11. SC11 predicts no 134Cs remaining on the fuel surface. With SOURCE IST 2.0P11, one cannot determine the calculated speciation of the material on the fuel surface. The pattern for 137Cs is similar (see Figure 23). However, there is a small difference in one additional case. The mean difference has increased in magnitude with the SC11 prototype, but is still a small value and the root mean square difference is slightly smaller (see Table 19).
1
Calculated Release Fraction
0.8
0.6
0.4
0.2
0 0
0.2
0.4
0.6
0.8
Experimental Release Fraction P11
Figure 23
SC11
Ideal
Calculated Vs. Experimental Releases for 137Cs
1
131 In the same test case for both
134Cs
and
137Cs,
the calculated presence of Cs2Zr3O7
resulted in lower calculated release fractions with the prototype code SC11 than with SOURCE IST 2.0P11. No thermodynamic or structural data was located for Cs2Zr3O7 in the literature. It appears to originate in unpublished work of D.A. Powers at Sandia National Laboratories referenced by Bixler [Bixler 1998]. It may have been postulated by analogy to polyuranates and polymolybdates, and have had thermodynamic properties estimated for it. It would appear from the date of this reference that Cs2Zr3O7(s) had not been included in the 1997 model of Corse [Corse 1997]. It is suggested that this postulated compound be deleted from the RMC model of irradiated uranium dioxide fuel.
7.4 Benchmarking 85Kr
Calculated Release Fraction
1
0.8
0.6
0.4
0.2
0 0
0.2
0.4
0.6
0.8
Experimental Release Fraction P11
Figure 24
SC11
Ideal
Calculated Vs. Experimental Releases for 85Kr
1
132 Since krypton is modelled as a non-reactive gas, no difference in release fractions is expected when modelling grain-boundary chemistry.
This expectation is
demonstrated by the data plotted in Figure 24 and in the data reported for Table 19. The longest-live precursor of
85Kr
(other than
85mKr,
85Kr
in
with a half-life of
4.48 h) is 85Br (half-life 2.87 minutes). Even if this nuclide were modelled in either SC11 or in SOURCE IST 2.0P11, the short half-life of the precursor means that the chemistry of that precursor would have negligible impact on the calculated release fraction.
7.5 Benchmarking 95Zr and 95Nb The experimental data for
95Zr
primarily indicates no releases of
95Zr
(see
Figure 25). In some cases, this is an implicit behaviour based on experience in previous tests and the assumption that there is no release. Thus in some tests, the gamma spectrum of
95Zr
is used to normalize the spectrum of other gammas
detected in the same energy region. There is an implicit assumption that 95Zr is not released. The SC11 results are in better agreement with this assumed behaviour. There is one outlier (from the line of ideal agreement) in the results from the SC11 prototype. In one case with about 41% fractional release, the prototype was predicting almost no release. In this experiment, much of the sample had vaporized and zirconium was being vaporized not from uranium dioxide plus fission and activation products, but from the low-volatile material that remains after the uranium dioxide itself has been vaporized. The mean signed difference for
95Zr
for
SC11 (see Table 19) is negative; whereas for SOURCE IST 2.0P11, it was positive.
133 This result indicates a negative bias in the calculated release fraction compared with the positive bias for SOURCE IST 2.0P11. The smaller root mean square difference indicates a smaller random scatter around the experimental results for the prototype code. The negative bias indicates that the results are not bounding. As such, this choice of analogue is not acceptable for safety analysis.
1
Calculated Release Fraction
0.8
0.6
0.4
0.2
0 0
0.2
0.4
0.6
0.8
1
Experimental Release Fraction P11
Figure 25
95Zr
Ideal
Calculated Vs. Experimental Releases for 95Zr
The experimental results for for
SC11
95Nb
releases are equal to or greater than the results
release (see Figure 25 and Figure 26). The use of zirconium as a chemical
analogue for niobium does not reproduce this different behaviour. Thus, it is probably preferable to add niobium species to a revised thermochemical database
134 than to use zirconium as an analogue. The mean signed difference (see Table 19) has gone from a large positive value of 0.402 (as a fraction) indicating that SOURCE IST 2.0P11 over-estimates the release fraction of
95Nb
to a negative fraction of
-0.121 indicating that the prototype under-estimates the release fraction of 95Nb by 12.1% of the end-of-NOC inventory. The root mean square difference is smaller with SC11 than with SOURCE IST 2.0P11.
1
Calculated Release Fraction
0.8
0.6
0.4
0.2
0 0
0.2
0.4
0.6
0.8
1
Experimental Release Fraction P11
Figure 26
SC11
Ideal
Calculated Vs. Experimental Releases for 95Nb
7.6 Benchmarking 103Ru and 106Ru The results of the prototype SC11 for 103Ru significantly reduce the over-estimated release fractions where experimental releases were small, except in one test (see
135 Figure 27).
In this test, the fuel was modelled as oxidizing to UO2.1 at high
temperature. From examination of the diagnostic output, the calculated release of ruthenium all comes from one time interval with oxidized fuel and high temperature. The magnitude of the mean signed difference between calculated and experimental releases and of the root mean square difference shown in Table 19 have both decreased for the prototype compared to SOURCE IST 2.0P11.
1
Calculated Release Fraction
0.8
0.6
0.4
0.2
0 0
0.2
0.4
0.6
0.8
1
Experimental Release Fraction P11
Figure 27
SC11
Ideal
Calculated Vs. Experimental Releases for 103Ru
The case with an outlier in the top left corner for SC11 and 103Ru (see Figure 27) did not have reported data for
106Ru.
The absence of a corresponding point for
(see Figure 28) reflects the absence of experimental data for
106Ru
106Ru
rather than a
136 better calculated release fraction for the prototype. Except for a test case in which the experimental release was about 81% and the calculated release with the prototype SC11 was 37%, the
106Ru
results for the prototype represent an
improvement over SOURCE IST 2.0P11. The mean signed difference has decreased in magnitude (but changed in sign) and the root mean square difference is smaller (see Table 19).
1
Calculated Release Fraction
0.8
0.6
0.4
0.2
0 0
0.2
0.4
0.6
0.8
1
Experimental Release Fraction P11
Figure 28
SC11
Ideal
Calculated Vs. Experimental Releases for 106Ru
It is interesting to note that there are 10 tests with reported experimental release fractions for 103Ru, and 11 for both
103Ru
and
106Ru.
106Ru;
but only 5 tests reported release fractions for
In particular, there is no experimental release fraction for
137 103Ru
corresponding to the test with ~81% experimental release of
calculated release fraction of 37% with the prototype.
106Ru,
and a
The ruthenium in the
condensed phase is calculated by SC11 to be in a hexagonal closed-packed noblemetal phase.
7.7 Benchmarking 131I The situation with 131I is virtually unchanged between the two computer programs. This result is not surprising since iodine is not modelled as being soluble in urania, and has no low-volatile compounds modelled. It is expected that the iodine that reaches the fuel surface will vaporize and that more detailed chemical modelling will not substantially alter this behaviour. Thus, there is little difference between the solid diamonds (P11 calculations) and open squares (SC11 calculations). The statistical measures are also similar for the two codes (see Table 19).
Calculated Release Fraction
1 0.8 0.6 0.4 0.2 0
0 0
0.2
0.4
0.6
0.8
Experimental Release Fraction P11
Figure 29
SC11
Ideal
Calculated Vs. Experimental Releases for 131I
1
138
7.8 Benchmarking 133Xe and 135Xe The data sets available for 85Kr.
133Xe
and 135Xe are not as extensive for the longer-lived
Only two tests have data for both isotopes.
Given the expectation that
modelled noble-gas behaviour is not affected by modelling chemistry the results for 133Xe
(see Figure 30) are reassuring. The release fractions at the end of the test are
identical. The statistical measures for
133Xe
in Table 19 indicate a small negative
bias and minimal scatter for both codes.
1
Calculated Release Fraction
0.8
0.6
0.4
0.2
0 0
0.2
0.4
0.6
0.8
1
Experimental Release Fraction P11
Figure 30
SC11
P11-End
Ideal
Calculated Vs. Experimental Releases for 133Xe
The same situation exists with 135Xe (Figure 31). For the three in-reactor tests, the SOURCE IST 2.0P11 points have been decay-corrected for the short half-life of 135Xe.
139 The data at the end of the test (with no decay correction) are plotted as black open triangles. These three points indicate the same final release fraction with both computer programs. Since the decay correction does not depend on the computer program used, the mean difference and root mean square differences listed in Table 19 are the same for SC11 as for SOURCE IST 2.0P11.
1
Calculated Release Fraction
0.8
0.6
0.4
0.2
0 0
0.2
0.4 0.6 Experimental Release Fraction P11
Figure 31
SC11
Ideal
0.8
1
P11-End
Calculated Vs. Experimental Releases for 135Xe
7.9 Benchmarking 140Ba Except in one case with a small experimental release fraction and a small release fraction calculated by SOURCE IST 2.0, the results for
140Ba
(in Figure 32) with the
SC11 prototype are the same or in better agreement with the experimental values than the SOURCE IST 2.0P11 results. Both the mean difference and the root mean
140 square difference for
140Ba
in Table 19 are smaller in magnitude for the SC11
prototype than for the original SOURCE IST 2.0P11 results. There remains an overestimation of releases particularly at low release fractions.
1
Calculated Release Fraction
0.8
0.6
0.4
0.2
0 0
0.2
0.4
0.6
0.8
1
Experimental Release Fraction P11
Figure 32
SC11
Ideal
Calculated Vs. Experimental Releases for 140Ba
7.10 Benchmarking 144Ce The results for 144Ce are better with the original code than with the new prototype SC11 (see Figure 33). The prototype computer program is predicting that cerium oxides are almost entirely in the fuel fluorite solution phase. The small overestimate of the release fraction characterized by a small positive mean difference for 144Ce
and SOURCE IST 2.0P11 in Table 19 has been replaced by a larger
141 underestimation characterized by a larger magnitude of negative mean difference. The scatter, as characterized by the root mean square difference, is smaller with the prototype than with the original computer program.
1
Calculated Release Fraction
0.8
0.6
0.4
0.2
0 0
0.2
0.4
0.6
0.8
1
Experimental Release Fraction P11
Figure 33
SC11
Ideal
Calculated Vs. Experimental Releases for 144Ce
The single point with the largest release fraction is for a test in which the sample matrix vaporized. In this case, the predicted solid phase was a mixed oxide with zirconium and rare earths. The solid phase included cerium, but not praseodymium. In the absence of an actinide oxide phase, the new model has only the gas phase as a source of oxygen. The current model does not track the oxygen associated with
142 fission products. It is also unclear whether the model for the UO2 fluorite phase with impurities should be employed after the uranium dioxide has volatilized.
7.11 Benchmarking 125Sb and 154Eu and Assessment of Chemical Analogues In the prototype SC11, tellurium is used as analogue for antimony. In SOURCE IST 2.0P11, antimony chemistry had been modelled directly. The results plotted in Figure 34 and tabulated in Table 19 show that the root mean square difference (a measure of scatter) is almost the same, but the magnitude of the mean difference has increased and the sign has changed. What had been a small conservative bias is now a larger underestimate of release fractions. It would appear that restoring chemical modelling of antimony should be considered.
Calculated Release Fraction
1
0.8
0.6
0.4
0.2
0 0
0.2
0.4
0.6
0.8
Experimental Release Fraction P11
Figure 34
SC11
Ideal
Calculated Vs. Experimental Releases for 125Sb
1
143 For
154Eu
(see Figure 35), the mean difference and root mean square difference in
Table 19 are smaller using the new prototype SC11 and using strontium as an analogue for europium. It would appear that the use of strontium as an analogue for europium is a reasonable approximation. Olander has referenced the unpublished work by Kaye and Thompson (at RMC) on deficiencies in the data for europium hydroxides [Olander 1999].
1
Calculated Release Fraction
0.8
0.6
0.4
0.2
0 0
0.2
0.4
0.6
0.8
Experimental Release Fraction P11
Figure 35
SC11
Ideal
Calculated Vs. Experimental Releases for 154Eu
1
144
145
8 Discussion The discussion of benchmarking of nuclide inventories in SOURCE IST 2.0P11 is provided in Section 8.1. Benchmarking of inventories of chemical elements in SC11 is discussed in Section 8.2.
Benchmarking of release fractions is discussed in
Section 8.3.
8.1 Discussion of Benchmarking of SOURCE IST 2.0P11 Nuclide Inventories The nuclide benchmarking exercise is described in Section 5.1.
Inventories
calculated with SOURCE IST 2.0P11 agreed with those calculated with ORIGEN-S (from SCALE 6.0) [Gauld 2009a] to within ±20% for 102 of 150 nuclides at all 24 output times in the test case. Of the remaining 48 nuclides, SOURCE IST 2.0P11 calculated inventories were higher than ORIGEN-S for 21 nuclides and lower for 27 nuclides. The 21 nuclides for which SOURCE-calculated inventories were higher can be broken down further.
Inventories calculated with SOURCE IST 2.0P11 were
consistently high (by more than 20% of the ORIGEN-S Inventory) for ten nuclides: 240mNp, 126Sb, 110mAg, 148mPm, 155Eu, 115mCd, 154Eu, 93Y, 236U
and 130Sb. For a further
four nuclides, SOURCE-calculated inventories were on average more than 20 higher than ORIGEN-S inventories. These nuclides or nuclear isomers were: 148Pm
and
133Te.
242mAm, 130I,
Additionally, for seven nuclides or nuclear isomers (83Kr,
127mTe, 130Xe, 130Xe, 105Rh,
125Sb,
and 132Sb), the SOURCE-calculated inventories were 20%
higher than ORIGEN-calculated inventories at one or more reported time step. The
146 27 nuclides for which SOURCE-calculated inventories are lower than ORIGENcalculated inventories can be broken down as 11 nuclides or nuclear isomers (238Pu, 109Pd, 82Br, 156Eu, 128Sb, 241Am, 240Np, 241Pu, 157Eu, 122Sb,
and
113mCd)
with all
inventories more than 20% lower than ORIGEN-S, five nuclides (106Rh, 153Sm, 153Eu, 242Pu
and 124Sb) with inventories with an average relative diference to ORIGEN-S of
greater than 20%, and 11 nuclides (112Ag, 112Pd, 113Ag, 129Te, 129Sb, 129I, 105Tc, 105Ru, 111Ag, 86Rb
and
135Cs)
with a SOURCE-calculated inventory more than 20% below
ORIGEN-S for at least one time step. The large number of nuclides and nuclear isomers for which SOURCE-calculated inventories were within 20% agreement with ORIGEN-S calculations suggests that the SOURCE 2.0 algorithm for calculating nuclide inventories is fundamentally sound. Furthermore, the decay data taken from Radionuclide Transformation [ICRP 1983] are comparable to those in the ORIGEN-S (SCALE 6.0) library [Gauld 2006b]. A recurring theme in the comments in subsections of Section 5.1.3.3 is a difference in nuclear cross-section between SOURCE IST 2.0P11 taken from the 14th Edition of the Chart of the Nuclides [Walker 1989] and those used in ORIGEN-S [Gauld 2009a]. The latter are preferred as they are averaged to the reactor neutron energy spectrum. As noted in Section 5.1.3.3.11, the chain yields for the decay chain with mass number 129 differ, significantly, between England and Rider [England 1994] and ORIGEN-S [Gauld 2009a]. The SOURCE 2.0 yields were taken from Engalnd and Rider. There are modelled nuclei that undergo radiative capture reactions that have not been modelled in SOURCE IST 2.0P11. The absence of a radiative neutron capture
147 cross-section was noted in a number of cases in Sections 5.1.3.3. For example, there are no cross-sections in the SOURCE IST 2.0P11 data set for 105Rh (n, γ) 106Rh or for 108Pd
(n, γ) 109Pd.
One long-lived parent that affects the growing in of decay
products has been identified to add to the SOURCE IST 2.0P11 nuclide set. It is 126Sn which is a parent of 126Sb (See Section 5.1.3.3.7). Four nuclides and one nuclear isomer have been identified to be removed from the SOURCE 2.0 nuclide list. The activation products neutron capture by
239Np
240mNp
and
240Np
from radiative
contribute only a small amount to the neptunium
inventory and can be eliminated from the SOURCE IST 2.0P11 nuclide set. There is uncertainty in the identification of the ground state (132Sb) and the first excited state (132mSb) of antimony in isobar 132. Neither isomer is a major contributor to dose to the public nor to the chemical inventory of antimony; therefore, the current 132Sb 79As
nuclide should be deleted from the SOURCE 2.0 nuclide set. Neither
77As
nor
is a major contributor to radiation dose, nor is arsenic a large contributor to the
chemical inventory of fuel; therefore both nuclides can be deleted from the SOURCE 2.0 nuclide set. Future applications of SOURCE 2.0 may require the addition of the nuclides 237Np,
237U,
and 238Np and associated cross-sections and half-lives. This has been done in
the SC11 nuclear data file.
148
8.2 Discussion of Benchmarking of Total Inventories of Chemical Elements This discussion is based on the benchmarking, nuclide set development and rebenchmarking exercise reported in Section 5.2. The SOURCE-calculated molar inventories of elements ranged from 1). The identifier can be constructed as an integer equal to 10000 Z + 10 A +I, where Z is the atomic number, A is the atomic mass number, and I indicates the isomeric state.
427 5. Record 7, the total number of parents of each nuclide by all modelled processes 6. Record 8, the position in Record 5 of the parent for the transition in the position in numerous records including Record 23 corresponding to the position of the value in Record 8 7. Record 22, decay constants (1/s) 8. Record 23, a compressed matrix containing partial cross-sections (barns) and partial half-lives (1/s) for neutronic transitions and decay transitions. This record and the index records 6, 7 and 8 allow the corresponding parent, progeny and reaction type (neutronic or decay) to be determined. 9. Record 24, the capture cross-section (barns) for the corresponding nuclide in Record 5 10. Record 25, the fission cross-section of nuclides in Record 3. Records 23 to 25 correspond to the first burnup interval. 11. Records 41, 45, 49, 53, 57, 61 and 65, as Record 23 but for the second through eighth burnup intervals, respectively. These records may contain 6 extra parameters at the end that allow the conversion of cross-sections from a thermal flux basis to a total flux basis. 12. Records 42, 46, 50, 54, 58, 62 and 66, as Record 24 for the second through eighth burnup intervals, respectively. 13. Records 43, 47, 51, 55, 59, 63 and 67, as Record 25 for the second through eighth burnup intervals, respectively.
428 H.2.2
Overview of arplibreader
The program arplibreader reads the candu37e library and creates a file that can be searched by the nuclide identification number for cross-section and decay constant data. Using the partial cross-section for production of a fission-product by fission and the fission cross-section of the fissionable nuclide, arplibreader calculates the independent fission yield for each fission-product nuclide from each fissionable nuclide. The partial microscopic cross-section (
,
) for producing a particular
fission-product nuclide (fp) from a given actinide (act) can be defined as the product of the independent fission yield for that fission-product nuclide from fission of the given actinide ( actinide (
,
) multiplied by the microscopic fission cross-section of the
):
,
Since both
,
and
=
,
.
(H-1)
are contined in the ORIGEN-ARP library, the independent
yield can be calculated by solving Equation (H-1) for the yield. The program arplibreader produced 28,954 lines of output for the candu37e library provided with ORIGEN-S in SCALE 5.1 [Gauld 2006a]. The cross-section data for the line corresponding to the capture cross-section for
234U
(n, γ) 235U is shown in the
first eight lines of column three in Table 30. The data are from Records 23, 41, 45, 49, 53, 57, 61 and 65 of the ORIGEN-S “candu37e” library ,Gauld 1995].
The
average and a weighted average were calculated separately. The weighted average is weighted by the difference between final and initial burnup for that value. These
429 values can be compared to 100 barns from the Chart of Nuclides 14th edition [Walker 1989]. The utility arplibreader provides a tool for extracting cross-section data for SC11 (or SOURCE 2.0) that are more consistent with the ORIGEN-S library. Table 30
Capture Cross-Section for 234U (n, γ) 235U
Starting Burnup (MW·h·kg-1) Ending Burnup (MW·h·kg-1) 0.00 11.52 11.52 23.04 23.04 46.08 46.08 92.16 92.16 138.24 138.24 184.32 184.32 230.40 230.40 276.48 Average Weighted Avergae by Incremental Burnup
Cross-Section (barns) 78.16 78.97 79.84 80.76 81.22 81.28 81.16 80.98 80.77 80.30
