Julian Robert Lebenhaft. B.Sc. (Chemistry with Physics) 1977 M.Sc. (Chemical Physics) 1978 Ph.D. (Chemical Physics) 1982 University of Toronto

Transcription

1 MCNP4B MODELING OF PEBBLE-BED REACTORS By Julian Robert Lebenhaft B.S. (Chemistry with Physis) 1977 M.S. (Chemial Physis) 1978 Ph.D. (Chemial Physis) 1982 University of Toronto Submitted to he Department of Nulear Engineering in partial fulfillment of the requirements for the degree of Nulear Engineer and Master of Siene in Nulear Engineering at the Massahusetts Institute of Tehnology Otober 21 MASSACHUSErFS INSTITUTE OF TECHNOLOGY DEC 5 23 LIBRARIES 21 Julian R. Lebenhaft. All rights reserved. The author hereby grants to MIT permission to reprodue and distribute publily paper and eletroni opies of this thesis doument in whole or in part. V\I Signature of Author: Certified by: Certified by: Aepted by: 6v Department of Nulear Engineering Otober 15, 21 Mihael J. Drisoll Professor Emeritus of Nulear Engineering Thesis Supervisor Pavel Hejzlar Program Diretor, Center for Advaned Nulear Energy Systems Reader M~? Jeffrey A. Coderre Assistant Professor of Nulear Engineering Chairman, Department Committee on Graduate Students.ARCHIVES

2 MCNP4B MODELING OF PEBBLE-BED REACTORS By Julian Robert Lebenhaft Submitted to the Department of Nulear Engineering on Otober 15, 21 in partial fulfillment of the requirements for the Degrees of Nulear Engineer and Master of Siene in Nulear Engineering ABSTRACT The appliability of the Mvlonte Carlo ode MCNP4B to the neutroni modeling of pebblebed reators was investigated. A modeling methodology was developed based on an analysis of ritial experiments arried out at the HTR-PROTIEUS and ASTRA failities, and the ritial loading of the HTR-1 reator. A body-entred ubi lattie of spheres with a speified paking fration approximates the pebble bed, and exlusion zones offset the ontribution of partial spheres generated by the geometry routines in MCNP4B at the ore boundaries. The oated fuel partiles are modeled in detail and are distributed over the fuelled region of the fuel sphere using a simple ubi lattie. This method predited the ritial ore loading aurately in all ases. The alulation of ontrol-rod worths in the more deoupled tall annular ASTRA ore gave results within 1% ompared to the reported experiments. An approximate method was also developed for the MCNP4B modeling of pebble-bed reators with burnup. The nulide densities of homogenized layers in the VSOP94 reator model are transferred to the orresponding MCNP4B model with the lattie of spheres represented expliitly. The method was demonstrated on the PBMR equilibrium ore, and used for a parallel study of burnup k- and isotopis on a single pebble. Finally, a study was arried out of the proliferation potential of a modular pebble-bed reator for both normal and off-normal operation. VSOP94 analysis showed that spent fuel from pebble-bed reators is proliferation resistant at high disharge burnup, beause of its unfavourable plutonium isotopi omposition and the need to divert -157, pebbles to aumulate suffiient 239 Pu for a nulear weapon. The isotopis of first-pass fuel pebbles are more favourable, but even more pebbles (-258,) would be needed. However, a superell MOCUP model was used to demonstrate that -2, pebbles would be needed if loaded with depleted uranium. But the assoiated reativity loss would neessitate a ompensatory inrease in ore height of approximately 5 m. Suh a hange in ore loading, as well as the properties of the speial pebbles, would be notied in a safeguarded faility. Thesis Supervisor: Mihael J. Drisoll Title: Professor Emeritus of Nulear Engineering 2

3 ACKNOWLEDGEMENTS I would like to express my deepest gratitude to Professor Mihael J. Drisoll, who helped guide this thesis researh through numerous onversations and "bak of the envelope" alulations. His prompt omments were partiularly useful during the writing of this report. I would also like to thank Prof. Drisoll for generously funding my trips to South Afria and Europe, whih proved to be ruial for both my researh and areer prospets. Thanks are also due to Professors Andrew C. Kadak and Ronald G. Ballinger, the Prinipal Investigators of the Advaned Modular Pebble Bed Reator Projet. Prof. Kadak's onstrutive omments during his review of the thesis were muh appreiated. Funding for this researh was provided by the Idaho National Engineering and Environmental Laboratory (INEEL) under the Strategi INEEL/MIT Nulear Researh Collaboration Program for Sustainable Nulear Energy. It has been my pleasure to ollaborate with Hans D. Gouger, Kevan D. Weaver and J. Steven Herring of the INEEL. My olleagues at ESKOM in South Afria deserve speial mention for their tehnial assistane during the ourse of this researh. Dr. Eben J. Mulder provided key PBMR related physis data, inluding the VSOP94 model and engineering drawings of the referene ore, and Diana Naidoo supplied the ASTRA doumentation. The hospitality of the entire PBMR staff during my visits to Centurion is gratefully aknowledged. Finally, I would like to thank Dr. Walter Y. Kato for his assistane in obtaining a variety of unpublished reports through his numerous international ontats, and for his friendship and valuable advie throughout my stay at MIT. 3

4 TABLE OF CONTENTS 1. INTRODUCTION Sope and Objetives Gas-Cooled Reators Overview of Researh PEBBLE BED REACTOR PHYSiCS Diffusion Theory Resonane Absorption Neutron Streaming Thermalization in Graphite The VSOP94 Code The Monte Carlo Method The Boltzmann Equation The MCNP Code Summary MCNP4B MODELING OF PEBBLE-BED REACTORS Regular Latties Edge Effets in MCNP4B Double Heterogeneity Conlusions HTR-PROTEUS FACILITY Desription of the PROTEUS Faility Fuel and Moderator Spheres The Stohasti Cores The MCNP4B Model Summary THE HTR-1 REACTOR Desription of the HTR-1 Reator Physis Benhmark Problems Referene Core Physis Model MCNP4B Model of HTR

5 5.4.1 Reator Struture Control Absorbers Core Boron Content MCNP4B Calulations Disussion Summary ASTRA Desription of the ASTRA Faility Desription of the Experiments Performed at the ASTRA Faility MCNP4B Model of the ASTRA Faility Strutural Components Core Results of MCNP4B Analysis Disussion Summary MCNP4B MODELLING OF PEBBLE BED CORES WITH BURNUP The Pebble Bed Modular Reator The VSOP94 Model of the PBMR Link Between VSOP94 and MCNP4B Modifiations to VSOP Program MCARDS MCNP4B Model of the PBMR MCNP4B/VSOP94 Results Disussion Summary PLUTONIUM PRODUCTION IN PEBBLE BED REACTORS Modelling Methods Superell Model Prodution Pebbles Analysis and Results Regular Fuel Pebbles 138 5

6 8.2.2 Superell Analysis of Prodution Pebbles Disussion CONCLUSIONS AND FUTURE DIRECTIONS REFERENCES 152 APPENDIX A MCNP4B Models of the HTR-PROTEUS Faility 171 APPENDIX A. 1: MCNP4B model of HTR-PROTEUS Core APPENDIX A.2: MCNP4B model of HTR-PROTEUS Core APPENDIX A.3: MCNP4B model of HTR-PROTEUS Core APPENDIX B MCNP4B Models of HTR APPENDIX B-1: MCNP4B model of HTR-1 Benhmark Problem B1 186 APPENDIX B-2: MCNP4B model of HTR-1 Benhmark Problem B APPENDIX C MCNP4B Models of ASTRA Faility 217 APPENDIX C. 1: MCNP4B model of ASTRA, 'super' ell ore representation 218 APPENDIX C.2: Infinite ASTRA lattie using exat 'super' ell model 236 APPENDIX C.3: Infinite ASTRA lattie using borated fuel shell 241 APPENDIX C.4: MCNP4B model of ASTRA using BCC ore representation 244 APPENDIX D MCNP4B/VSOP94 Models of PBMR 26 APPENDIX D. 1-VSOP94 input file for referene PBMR ore 261 APPENDIX D.2: MCNP4B model of PBMR 272 APPENDIX D.3: Modified subroutine VORSHU 33 APPENDIX D.4: Program MCARDS 345 6

7 APPENDIX E Plutonium Prodution in a Modular Pebble Bed Reator APPENDIX E. 1: MOCUP Superell model of prodution pebble APPENDIX E.2: Exel analysis of VSOP94 equilibrium ore results TABLES Table 1-1. Table 1-2. Table 1-3. Table 1-4. Table 3-1. Table 4-1. Table 4-2. Table 4-3. Table 4-4. Table 4-5. Table 4-6. Table 4-7. Table 4-8. Table 5-1. Table 5-2. Table 5-3. Table 5-4. Table 5-5. Typial parameters of British Magnox Reators Typial parameters of AGRs Main harateristis of HTGR prototypes Main harateristis of MHTGRs Properties of regular latties Atom densities in PROTEUS graphite refletor LEU-HTR fuel and moderator sphere data Atom densities in HTR-PROTEUS fuel spheres Atom densities in HTR-PROTEUS moderator spheres HTR-PROTEUS experimental ore onfigurations Experimental results for HTR-PROTEUS stohasti ores Lattie parameters for MCNP4B model of HTR-PROTEUS ores HTR-PROTEUS ritiality analysis HTR-1 reator ore parameters Homogenized nulide densities in HTR-1 refletor zones Composition of HTR-1 ontrol-rod stainless steel HTR-1 ontrol rod geometry and material speifiations HTR-1 model pebble-bed geometry speifiations

8 Table 5-6. Table 5-7. Table 5-8. Table 5-9. Table 5-1. Table 6-1. Table 6-2. Table 6-3. Table 6-4. Table 6-5. Table 6-6. Table 6-7. Table 6-8. Table 6-9. Table 6-1. Table Table 7-1. Table 7-2. Table 7-3. Table 7-4. Table 7-5. Table 8-1. Table 8-2. Material ompositions of HTR-1 pebble-bed ore MCNP4B simulation results for HTR-1 Calulated differential reativity worth of HTR-1 ontrol rod Diffusion ode benhmark results by other CRP-5 partiipants MCNP benhmark results for other CRP-5 partiipants and MIT ASTRA ore speifiations ASTRA spherial elements ASTRA regulating rod material speifiation Basi ritial onfiguration of ASTRA faility ASTRA ore lattie parameters Individual ontrol rod worths in ASTRA faility Reativity worth of two-rod ombinations in ASTRA Reativity worth of three-rod ombinations in ASTRA Differential worth of ASTRA ontrol rod CR5 Dependene of ASTRA ontrol rod worth on distane from ore Interferene oeffiients for ASTRA rod ombinations PBMR referene ore speifiations Referene speifiations for PBMR fuel elements Fission produt hain 44 in VSOP94 Modified VSOP94 Card V21 Temperature reativity oeffiients in the PBMR Plutonium Isotopi Composition of PBMR Spent Fuel Plutonium isotopi omposition of PBMR first-pass fuel

9 Table 8-3. Neutron fluxes alulated with superell MCNP4B model 14 Table 8-4. Pu-239 prodution alulated with superell MCNP4B model 141 Table 8-5. Isotopi omposition of plutonium in irradiated solid U 2 target 141 Table 9-1. Summary of key MCNP4B ritiality alulations 145 9

10 FIGURES Figure 2-1. Figure 2-2. Figure 2-3. Figure 2-4. Figure 2-5. Figure 2-6. Figure 2-7. Figure 2-8. Figure 3-1. Figure 3-2. Figure 3-3. Figure 3-4. Figure 3-5. Figure 3-6. Figure 4-1. Figure 4-2. Figure 4-3. Figure 4-4. Figure 5-1. Figure 5-2. Figure 5-3. TRISO oated fuel partile Neutron esape probabilities in a pebble-bed ore Paking density of 1/8" spheres in a 65 mm-od ylinder Paking density of 1/" spheres in infinite ylinders of varying diameter The graphite lattie Struture of the VSOP94 ode Overlay of VSOP94 and CITATION meshes Relation between vetors Body entred ubi strutures Partial spheres generated by MCNP4B The sphere exlusion zone MCNP4B model of a oated fuel partile MCNP4B model of a fuel pebble MCNP4B model of a pebble-bed ore Top view of HTR-PROTEUS faility A shemati representation of the HTR-PROTEUS faility Vertial view of MCNP4B model of HTR-PROTEUS Horizontal view of MCNP4B model of HTR-PROTEUS Vertial ross setion of the HTR-1 reator Horizontal ross setion of the HTR- 1 reator Referene ore physis alulation model

11 Figure 5-4. Figure 5-5. Figure 5-6. Figure 5-7. Figure 5-8. Figure 6-1. Figure 6-2. Figure 6-3. Figure 6-4. Figure 6-5. Figure 6-6. Figure 6-7. Figure 6-8. Figure 6-9. Figure 6-1. Figure Figure Figure Figure Figure Figure Struture of the HTR- 1 ontrol rod Vertial ross setion of the MCNP4B model of' HTR- 1 Horizontal ross setion of the MCNP4B model of HTR-1 MCNP4B model of HTR-1 ontrol rod Calulated differential reativity worth of a ontrol rod Horizontal ross setion of ASTRA faility Vertial ross setion of ASTRA faility Engineering drawing of an ASTRA ontrol rod Engineering drawing of the ASTRA manual regulating rod MCNP4B model of ASTRA faility-horizontal view Bottom of ASTRA ontrol rod-vertial view Joint between two halves of an ASTRA ontrol rod Lower pin bolder in an ASTRA ontrol rod-horizontal view Air-filled setions of pins in an ASTRA ontrol rod-horizontal view Absorber setions of pins in an ASTRA ontrol rod-horizontal View Upper pin holder in an ASTRA ontrol rod-horizontal View Spider at top of ASTRA ontrol-rod assembly ASTRA super ell MCNP4B model-horizontal view 1 ASTRA super ell MCNP4B model-horizontal view 2 ASTRA super ell MCNP4B model-vertial view Approximate MCNP4B Model of ASTRA Faility-Vertial

12 View 16 Figure Approximate MCNP4B Model of ASTRA Faility-Horizontal View Figure Differential worth of ASTRA ontrol rod CR5 Figure 7-1. A vertial view of the PBMR Figure 7-2. A horizontal view of the PBMR ore Figure 7-3. VSOP94 model of the PBMR Figure 7-4. MCNP4B model of the PBMR- Vertial View Figure 7-5. MCNP4B model of the PBMR-Horizontal Viev, Figure 7-6. Channel for small absorber balls in MCNP4B model of PBMR Figure 7-7. Power density in PBMR equilibrium ore Figure 7-8. Fast neutron flux in PBMR equilibrium ore jfigure 7-9. Thermal neutron flux in PBMR equilibrium ore 128 IFigure 7-1. Proposed MCNP-based ode system for pebble-bed reators with bumup ] Figure 8-1. Superell MCNP4B model of plutonium prodution sphere I Figure 8-2. Different onfigurations of plutonium prodution pebbles: I (a) solid ore; (b) shells; () dense BISO Figure 9-1. Six-ell BCC model used in the plutonium prodution study

13 1. INTRODUCTION Although high-temperature gas-ooled reators (HTGRs) exist today only as pilot-sale failities, the growing reognition of their unique harateristis makes them leading andidates for the future eletriity generating market. These harateristis inlude inherent safety, simpliity of design and expeted low apital ost, fuel-yle flexibility and high thermal effiieny. HTGRs are graphite-moderated and -refleted reators, whih are loaded with a unique type of fuel and are ooled by helium gas. Two types of HTGRs exist, whih differ in the shape of their fuel eements-prismati and spherial. The fous of this thesis is on the physis aspets of the latter type of reator, the pebblebed reator. After a statement of the thesis sope and objetives, this hapter will provide a historial overview of HTGR development, and a summary of the researh reported here. 1.1 Sope and Objetives From the 196s until the present, the neutroni design of pebble-bed reators has been arried out using diffusion-theory odes. These inlude the German VSOP' suite of odes [1-1], the modem Duth ode PANTHERMIX [1-2, 1-3], and PEBBED that is urrently under development at the INEEL [1-4]. The VSOP ode, as well as the unique features of pebble-bed reator physis, will be desribed briefly below. However, the subjet of this thesis is the neutroni modeling of pebble-bed ores using the Monte-Carlo ode MCNP4B [1-5]. Prior to the researh reported here, MCNP (Versions 4A and 4B) modeling of pebble-bed ores has been limited to the analysis of HTR-PROTEUS ritial l Very Speial Old Programs. 13

14 experiments involving regular latties [1-6]. Randomly paked ores had only been investigated using MCNP-BALL, whih is a version of MCNP3B that was modified to inlude a stohasti geometry feature [1-7]. The goal of the researh undertaken at MIT was to determine whether randomly paked ores ould be desribed with suffiient auray by regular latties, an approximation that is imposed by the use the repeatedgeometry feature in MCNP4B. Suh a methodology was developed and validated against several ritial experiments, inluding the stohasti HTR-PROTEUS ores, the HTR-1 start-up ore and the ASTRA ritials. 1.2 Gas Cooled Reators The history of gas-ooled reators dates bak to the plutonium-prodution piles built in the US at Hanford in the 194s, and in the UK at Windsale in the 195s. In the US, gas ooling of nulear reators was subsequently rejeted in part beause of antiipated diffiulties with the prourement of blowers and pressure vessels. However, a different route was followed in the UK, where the first power reators were natural-uranium fueled, graphite-moderated and utilized atmospheri air-ooling. This hoie of reator was initially ditated by the availability of nulear materials, but the inherent safety features of gas-ooled reators were soon reognized. The early gas-ooled reators were the British Magnox reators, whih were CO 2 ooled, graphite moderated, and used metalli natural uranium lad with a magnesiumaluminium alloy. Beause the operating temperature of this reator is limited to 5 C to prevent CO 2 oxidation of the ladding, the maximum oolant temperature ahieved is 365 C. The power density is very low (approximately.5 MW/m 3 ) and, even with on- 14

15 line refueling, the disharge burnup of fuel in Magnox reators is about 6 MWd/kgU. The first Magnox reator began operating at Calder all ir 1956, nd the last of these firtgeneration reators will be shut down by 21. Typial parateter of th reators are given in Table 1-1. Typial Parameters Item First power Net power [MW(e)] Net design effiieny (%) Ative ore: Length (m) Diameter (m) Power density (MW/m 3 ) Speifi power (kw/kg 235 U) Maximum burnup (MWd/kgU) Number of fuel hannels Fuel hannel diameter (mm) Elements per hannel Fuel element: Diameter (mm) Length (mm) Max ladding temperature ( C) Coolant: Pressure (MPa) Temperature (IC) Power per irulator (MW) Steam (Inlet/Outlet): Pressures (MPa) Temperatures ( C) Pressure vessel type Thikness (mm) Length (m) Diameter (m) Table 1-I Rea 11-1 of British Mag'ox Reators - Calder -nke Oldbury Wylfa Hall >i A g~~~~~~ Q I5 472~~~115 4' 418~ ~ ~~~~~~~. 1.5/.4 4.'7/1.3 4o/ / /3 5 4/ Steel ~ Steel PCRV PCRV Steel ;... _- IIC 15

16 ... _ A_. _ I. _ The Advaned Gas Reator (AGR) represents an evolutionary improvement over the Magnox reator. The use of 2.5% enrihed uranium oxide fuel and stainless steel ladding permits a higher gas temperature (56 C), inreases fuel disharge burnup to Table 1-2 Typial Parameters of AGRS [1-8] Item First power Net power [MW(e)] Net design effiieny (%) Ative ore: Length (m) Diameter (m) Power density (MW/m 3 ) Speifi power (kw/kg 235 U) Maximum burnup (MWd/kgU) Fuel enrihment (% 235 U) Number of fuel hannels Graphite sleeve ID (mm) Elements per hannel Fuel element: Number of rods Rod diameter (mm) Rod length (mm) Max ladding temperature (C) Coolant: Pressure (MPa) Temperature (C) Power per irulator (MW) Cirulator pressure rise (MPa) Steam: Pressures (MPa) Temperatures (C) Reheat (MPa/ C) Pressure vessel type Thikness (mm) Length (m) Diameter (m) WA GR None Steel u Brinkley FIinkley Point B /538 p'crv Dungeness B /565 PCRV Heysham 2 1 non,.. 1Yb/ , /538 PCRV A_ - 16

17 2 MWd/kgU, and dereases the size of the ore. The first AGR began operation at Windsale in 1963 and fourteen suh reators were subsequently built and operated. Typial parameters of the British Magnox reators are given in Table 1-2. The design of the high temperature gas-ooled reator (HTGR) was initiated in the UK at the same time as the AGR. The goal of this program was an all-erami, helium-ooled and graphite moderated reator utilizing the thorium fuel yle. The first suh reator, the 2 MW(t) DRAGON High Temperature Reator, ahieved ritiality at Winfrith in August 1964, and was soon followed by two other prototypes: the 4 MW(e) Peah Bottom Unit 1 in Marh 1966 in the US, and the 15 MW(e) AVR in August 1967 in West Germany. Both DRAGON and Peah Bottom utilized fuel assemblies that ontained oated fuel partiles uniformly dispersed throughout annular graphite ompats. The original fuel partiles were omposed of 93% enrihed uranium and thorium arbide surrounded by a single pyrolyti arbon oating. This primitive oating proved inadequate, and BISO fuel partiles were introdued that were oated with a double layer of pyrolyti arbon. BISO fuel was used suessfully in Peah Bottom, where very low ativity levels were subsequently experiened in the primary ooling system. Fuel was irradiated suessfully in DRAGON to burnups exeeding 1 MWd/kgU. The main harateristis of HTGRs are given in Table 1-3. A key feature of the HTGR is the use of oated fuel partiles that are dispersed in a graphite matrix. The purpose of this design is to avoid orrosion to the fuel element and to enhane the retention of fission produts with the graphite. However, this basi 17

18 onept an be satisfied by several fuel geometries. The British and US reators relied on the traditional rod geometry, either hexagonal (DRAGON) or ylindrial (Peah Bottom). A ompletely different approah was followed in Germany, where the development of spherial fuel elements led to the design of the pebble-bed reator. The fuel spheres are loaded from the top and disharged from the bottom of the reator ore. This is a partiularly attrative onept beause of its apparent simpliity and flexibility. Table 1-3 Main Charateristis of HTGR Prototypes [1-8] Item Dragon Peah Bottom A VR Country UK USA Germany Thermal power (MW) Net eletrial power (MW) 4 15 First power operation Helium pressure (MPa) Helium temperaturest 35/75 345/725 2/85 Ative ore: Diameter (m) Height (m) Core power density (MW/m 3 ) Fuel element: Design Hex rods Cylinders Spheres Number 37 x , Diameter (mm) Length (mm) Max fuel burnup (MWd/kgU) > Steam onditions (MPa/ C)t 1/ /54 Net yle effiieny (%) T Inlet/Outlet The first prototype pebble-bed reator was the Arbeitsgemeinshaft Versuhsreaktor (AVR), whih was started up at Jiilih, West Germany, in August The AVR was a helium-ooled, graphite-moderated, high-temperature reator with a thermal power rating of 46 MW and an eletri power output of 15 MW. The ore, the steam generator and the two helium irulators were ontained in a double-walled pressure vessel. With the 18

19 exeption of a water ingress aident from a leak in the steam generator in 1978, the AVR operated suessfully for 21 years. During these years, the AVR was used to test a variety of fuels and to demonstrate the inherent safety of the pebble-bed reator. These prototype HTGRs were followed in 1974 by the following third-generation gasooled reators: the General Atomis 33 MW(e) nulear power station at Fort St. Vrain, USA, whih utilized hexagonal graphite fuel elements with TRISO oated fuel partiles; and the Thorium High Temperature Reator (THTR), a 3 MW(e) pebble-bed reator that was built in Shmehausen, West Germany, between 1971 and Both reators used a PCRV to enlose the ore and primary ooling system. The Fort St. Vrain reator was shut down prematurely beause of numerous mehanial problems, while the THTR was shutdown beause of both mehanial problems and an unfavourable politial limate in Germany after the Chernobyl aident. Interest is being expressed one again in HTGRs beause of their inherent safety, simpliity and potential for ompeting eonomially with other forms of eletriity generation. Several ountries are atively pursuing the development of HTGRs for a variety of appliations. These inlude two prismati reators: the 3 MW(t) High Temperature Engineering Test Reator (HTTR), whih is urrently undergoing ommissioning tests at the Oarai Researh Establishment in Japan, and the General Atomis GT-MHR intended for the disposition of exess weapons-grade plutonium. A small pebble-bed reator, the HTR-1, was reently onstruted in China, and the Pebble Bed Modular Reator (PBMR) projet is at an advaned design stage in South Afria. Details of the HTR-1 and PBMR appear elsewhere in this report. Table 1-4 summarizes 19

20 the main harateristis of the fourth-generation modular HTGRs. Numerous paper studies are underway elsewhere, inluding the Duth oneptual design of a small (4 MWt) pebble-bed type HTGR [1-9, 1-1]. Table 1-4 Main Charateristis of MHTGRs Item HTTR HTR-1 GT-MHR PBMR Country Japan China USA/ South USA Sfra Russia Afria Thermal power (MW) Net eletrial power (MW) Helium pressure (MPa) Helium temperatures 395/95 25/7 49/85 491/85 Ative ore: Diameter (m) Height (m) Core power density (MW/m 3 ) Fuel element: UO2 U 2 PuO 2 U 2 Design Prismati Spherial Prismati Spherial Enrihment (% UL Number 15 27, , Diameter (mm) 36t Length (mm) 58-8 Max fuel burnup8, 8, (MWd/kgHM) Flat-to-flat distane. The work desribed in this report is part of a larger effort at MIT on the development of an advaned modular pebble-bed reator [1-11]. The objetive of this projet is to develop a oneptual design for a 11 MWe helium-ooled, gas turbine powered nulear power plant that will be ompetitive with natural gas. Funded by the Idaho National Engineering and Environmental Laboratory (INEEL), the projet has foused on fuel performane modeling, reator physis, safety analysis, balane of plant design, and the appliation of modularity to the onstrution of the plant. The design features an 2

21 intermediate heat exhanger that deouples the gas turbine from the primary ooling system. 1.3 Overview of Researh The remainder of this thesis is organized as follows. Chapter 2 overs pebble-bed reator physis, treating in detail the unique features assoiated with neutron transport in suh reators and the omputer odes used to perform this researh (VSOP94 and MCNP4B). The disussion inludes both diffusion theory and Monte Carlo methods. The appliation of diffusion theory to ore physis alulations requires the preparation of few-group ross setions and diffusion oeffiients [1-12]. These parameters are obtained by the homogenization of fine-group ross setions, whih are generated from detailed alulations in a large number of energy groups with a oarser spatial dependene. An important part of this spetrum alulation is the aurate determination of resonane absorption of neutrons in 238 U. The ollision probability form of the transport equation is used for this alulation, whih requires the determination of the Danoff fator appearing in the expression for the probability that a neutron experienes its next ollision in the moderator. The Danoff fator is the moderator esape probability [1-12]. Us, of oated fuel partiles reates a double heterogeneity on both the mirosopi and marosopi levels (the oated partile and the pebble) that ompliates the alulation of the Danoff fator. An additional peuliarity of pebble-bed reator physis is the need to introdue a streaming orretion to the alulation of the diffusion oeffiient beause of the effet of voids between pebbles on neutron leakage. 21

22 Use of the Monte Carlo method in onjuntion with a point-wise ross-setion library eliminates the need to prepare few-group parameters or to alulate the Danoff and diffusion streaming orretions. The Monte Carlo method is an effetive numerial tool for solving the Boltzmann transport equation [1-13], and its implementation in odes suh as MCNP is beoming inreasingly the method of hoie for the analysis of light water and liquid metal reators. Its appliation to HTGRs has been limited until reently to the analysis of homogenized ores [1-14], the HTR-PROTEUS ritial experiments involving regularly paked pebble beds [1-6, 1-15, 1-16], and the prismati Very High Temperature Reator Critial assembly in Japan [1-17]. Signifiant progress was made last deade in Japan, where a new sampling method was developed for irregularly distributed fuel elements [1-7]. In this approah, the loation of the modeled fuel element is generated probabilistially along the flight path of the neutron by sampling from nearest-neighbour distribution funtions for the fuel spheres and the oated fuel partiles. The MCNP4B modeling methodology is desribed in Chapter 3. In ommon with all fullore MCNP4B models, the pebble-bed reator struture an be modeled in detail. The hallenge lies in the representation of the randomly paked ore, whih must be approximated by a regular lattie of spheres. Of several possible types of paking, the body-entred ubi (or body-entred tetragonal) was found to be aurate and onvenient. The large number of fuel and moderator spheres in suh reators preludes the expliit speifiation of the ore geometry, and regular latties of spheres are used instead. Analysis of several ritial experiments showed that MCNP4B an be used for aurate ritiality alulations of pebble-bed ores using appropriately modeled regular latties to approximate the random loading [1-18]. 22

23 Analyzing three sets of ritial experiments validated this modeling methodology. The HTR-PROTEUS experiments [1-19] are disussed in Chapter 4. MCNP4B analysis of three stohasti ores showed the need for a peripheral buffer zone to ompensate for partial fuel spheres at the refletor interfae. These partial spheres, whih are introdued into the model by the repeated-struture feature of ode, have the effet of adding extra fuel into the ore. The same approah was then applied suessfully to the predition of the initial ritial loading of the HTR-1 reator (a total sphere loading of 16,83 alulated versus 16,89 measured). This analysis was part of a larger IAEA physis benhmark problem [1-2], whih is the subjet of Chapter 5. A single zone and two types of spheres (fuel and moderator) haraterize both the HTR-PROTEUS and the HTR-1 ores. A onsiderably more ompliated pebble-bed ore geometry was assembled for the ASTRA experiments [1-21]. This onfiguration onstituted a saled mok-up of the PBMR annular ore, with an inner refletor zone, an outer fuel zone and an intermediate mixing zone. Moreover, a small number of absorber spheres were added to the fuelled zones. The polygonal shape of the ASTRA ore vessel preluded the use of an expliit exlusion zone, beause a distribution of partial spheres of all sizes does not our in this ase. However, the equivalent redution in the amount of fuel was ahieved by using a redued paking fration. The presene of an absorber and the more neutronially deoupled ore resulted in poorer agreement with experiments. The MCNP4B modeling of the ASTRA experiments is disussed in Chapter 6. The ultimate goal of the MCNP4B methodology desribed here is the modeling of a large pebble-bed ore suh as that of the Pebble Bed Modular Reator [1-22]. Although not 23

24 investigated in this report, the approah used to model the ASTRA ritials is diretly appliable to the PBMR start-up ore. More important is the ability to analyze a pebblebed reator with a representative equilibrium burnup distribution. The omposition of depleted fuel an be readily determined in a stati ore, but a key feature of pebble-bed reators is the ontinuous reyling of fuel spheres [1-23]. In theory, the stohasti nature of suh ores lends itself to diret Monte Carlo simulation. However, the large number of pebbles found in a typial ore (for example, there are approximately 37, pebbles in the PBMR) renders the diret simulation of three-dimensional pebble flow impratial at this time. An alternative proedure is to perform the fuel management study using a diffusion theory-burnup ode and to transfer the equilibrium fuel ompositions to the detailed MCNP4B model. Chapter 7 desribes one suh approah, whih involves a semiautomated link between VSOP94 and MCNP4B. The method is demonstrated in priniple on the PBMR equilibrium ore using the referene VSOP model of the reator and an equivalent MCNP4B model. The final topi overed in Chapter 8 is a preliminary investigation of the proliferation potential of the referene PBMR fuel yle performed in ollaboration with the INEEL. Four physis odes were used to estimate the prodution of plutonium in the reator, inluding VSOP94, MCNP4B, ORIGEN2 [1-24] and MOCUP [1-25]. The Monte Carlo analysis was arried out at the INEEL using a simple-ell model representing an infinite lattie of pebbles [1-26], and at MIT using a superell model onsisting of a single prodution pebble in the enter of a driver ore representative of the PBMR. The 239 Pu prodution was estimated from a tally of the 238 U(n,y) 23 9 U reation rate for an MCNP4B snapshot simulation, and by traking the isotopi omposition of the prodution pebble in 24

25 a MOCUP depletion alulation. The results were ompared with VSOP94 preditions for the omposition of disharged fuel. The analysis onfirmed that spent fuel from pebble-bed reators is proliferation resistant at high disharge burnups ( 8 MWd/kgU), beause of its unfavourable plutonium isotopi omposition and the large number of pebbles that would have to be diverted-about half a ore load. The isotopis of first-pass fuel pebbles are more favourable, but an even larger number would be needed to aumulate 6 kg of 239 Pu. However, the analysis also showed that it is possible to produe a signifiant quantity of plutonium in a pebble-bed reator by inserting speial pebbles with a high loading of depleted uranium. Only 2, pebbles would have to be diverted over a minimum period of 1.5 years, in the unlikely event that the assoiated loss in reativity an be ompensated undeteted by raising the ore height or other means. The thesis onludes with a disussion of the results and reommendations for future researh in Chapter 9. All models and omputer programs developed during the ourse of this thesis researh are doumented in the Appendies. 25

26 2. PEBBLE BED REACTOR PHYSICS The physis analysis of pebble-bed reators shares muh in ommon with other thermal reators. With the exeption of early KENO analysis of homogenized ores [2-1], the neutroni design of pebble-bed reators has been arried out exlusively using SN and diffusion-theory odes, whose few-group parameters are generated by averaging finegroup ross setions [2-2, 2-3]. The fine-group parameters are obtained from a detailed spetrum alulation using a large number of energy groups with a oarse spatial dependene. However, the alulations are ompliated by some features of pebble-bed reators, inluding the use of spherial fuel elements, the double heterogeneity assoiated with the embedded oated fuel partiles, and the irregular paking of fuel spheres in the ore. Of partiular interest are resonane absorptions and neutron streaming in pebble beds. These speial features are disussed in this hapter both beause of their general importane and as motivation for the use of Monte Carlo methods, whih offer an alternative and often-simpler route for pebble-bed reator physis alulations. 2.1 Diffusion Theory [2-2, 2-3] In ommon with all HTGRs, pebble-bed reators are graphite-moderated and -refleted. While graphite has a relatively high atomi weight for a moderator, its very low absorption ross-setion makes it inferior only to heavy water and beryllium as a moderator. The nature of this moderator ditates the slowing down proess and the hoie of energy struture for few-group reator alulations. The upper bound of the thermal group is hosen suh that the probability for a neutron gaining energy in a ollision beomes negligible. For HTGRs, this ours at approximately 2 ev, and the range above 26

27 the thermal group is usually subdivided into three energy groups that ontain the resolved resonanes, the unresolved resonanes, and higher energies where the resonane struture of the heavy metal ross-setions is unimportant. The group boundaries used in the VSOP94 model of the PBMR are 1.86 ev, 29 ev and 1 kev Resonane Absorption Fission neutrons are born with an average energy of approximately 2 MeV, and are rapidly slowed down through ollisions with arbon atoms. In order to sustain the hain reation, a suffiient number of neutrons must be thermalized without being absorbed in the large resonanes of 238 U. Moreover, as burnup proeeds, the 24pu isotope also beomes an important resonane absorber. These resonane bsorptions have a signifiant effet on the physis of HTGRs, espeially on ore reativity, plutonium breeding and burnup. Beause of the heterogeneous fuel geometry and the large hanges in ross setion exhibited by resonane materials, resonane absorptions are often treated using ollision probability methods for solving the integral Boltzmann equation. The resonanes of 238 U are distint (resolved) up to about 1-4 kev. Above this energy, the resonane ross-setions are alulated using statistial distribution laws for the widths and separations of the unresolved resonanes. The spherial fuel element used in pebble-bed reators is a 6 m-diameter graphite ball with a (nominal) 5 m-diameter inner-fuelled zone. The fuel typially is ontained in oated partiles that are randomly embedded in the graphite matrix. The TRISO oated fuel partile onsists of a 5 gm-diameter UO2 kernel surrounded by an inner lowdensity arbon buffer layer (9 im thik), an inner high-density pyrolyti arbon layer (7 27

28 jgm), a silion arbide layer (6 m) and an outer pyrolyti arbon layer (6 pum). The funtion of these layers is to retain fission produts, while the graphite matrix further protets the fuel against orrosion and moderates neutrons. See Figure PyC layers UO 2 kernel Buffer SiC Figure 2-1. TRISO oated fuel partile (General Atomis, San Diego). The ombination of TRISO oated fuel partiles and fuel spheres reates a doubleheterogeneity on the mirosopi and marosopi levels, whih must be fatored into the expressions for fuel esape probabilities that appear in the resonane absorption alulations. This is usually ahieved via the alulation of the Danoff orretion, defined as the fator by whih the fuel esape probability is redued in a olletion of fuel lumps relative to that for an isolated fuel lump [2-4]. Thus, the Nordheim geometri esape probability is given by [2-5] P(E) = P(E) r] 1-[1-o, (E)P(E)b ' (2-1) where Po(E) is the probability that a neutron esapes the fuel lump where it is born, is the mean penetration hord length and IYa (E) is the marosopi absorption ross setion. 28

29 However, the Nordheim treatment does not apply diretly to the double heterogeneity found in pebble-bed reators, beause the small size of the fuel kernel results in Po(E) 1. Teuhert and Breitbarth alulated an alternative esape probability by following the path of a neutron in oated partiles and fuel spheres [2-6]. The possible path is subdivided into parts for whih the traversing probability an be evaluated numerially, and is expressed in terms of eight ollision probabilities as follows: P(E) = W +W 2 (W 3 +W 4 )+W 2 W W7 (2-2) 1-W8 where the Wi are the ollision probabilities in region I (see Figure 2-2). The first term gives the probability that a neutron born in a fuel kernel undergoes its next ollision in the same kernel; the seond gives the probability that the neutron leaves the kernel unollided and suffers its next ollision in the graphite matrix of the originating sphere (in either the fuelled zone or shell); while the third gives the probability that the neutron leaves the sphere, penetrates any number of other spheres without ollision and suffers its next ollision in graphite. This expression was implemented in the VSOP ode [2-7]. Figure 2-2. Neutron esape probabilities in a pebble-bed ore [2-7]. 29

30 Resonane absorptions are often treated using an equivalene relation, whih transforms the ompliated heterogeneous alulation into an equivalent one for a homogeneous medium. This is done by defining an energy-independent lattie esape ross setion 1, suh that [2-4] P (E) =, (2-3) Z(E)+ e where A,(E) is the marosopi total ross setion for the fuel at energy E. Segev derived the following aurate formula foi e [2-8]: e, = 1 (2-4) a yff where 1o is the mean penetration hord length in the fuel lump, a is a user seleted Bell fator, and yff is an effetive Danoff fator for the lattie: 1 Yeff 1> and 1 v, ( V (2-5) 3 VC I 3

31 Here, I is the mean penetration hord length, 1s the moderator ross-setion, VI the volume of the moderator, and V, is the volume of the nominal ell. The equivalent ross setion of the outer (pebble-bed) lattie is given by 1 L L (2-6) 1 A r where L is the mean penetration hord length, Fis the Danoff fator and A is the Bell fator for the outer lattie. Beause these equations assume the general form programmed for the esape ross-setion in the (two-dimensional) WIMS lattie ode [2-9], he above theoretial development defines an alternative alulational route for pebble-bed reators. An approah of this type is used in the Duth OCTOPUS reator physis analysis ode system [2-1] Neutron Streaming Numerous researhers have investigated the random paking of same-sized spheres in three dimensions sine early in the 2 'h entury [2-11]. Sott arried out a series of experiments, whih involved the filling of ylindrial tubes with '/s in. steel ball bearings [2-12]. The manner of filling the tubes determined the type of paking. When the tubes were filled by pouring and then shaken for several minutes, the resulting paking was termed "dense random paking." The tubes were then tipped horizontally, rotated slowly about the longitudinal axis, and gradually returned to the upright position. The resulting paking was termed "loose random paking." The experiments were arried out in four rigid ylinders with different diameters, and the paking densities in ylinders of infinite 31

32 length were determined from extrapolations as in Figure 2-3, plotted against reiproals 1 of diameters as in Figure 2-4. As --, the limiting paking densities D loose random paking and.63 for dense random paking. are.6 for,,, rf -. - "'"~'""r s n~ aam poking.9 u.p Lose rndon paking C- I U.2 1 1rl rn(mn- ) Figure 2-3. Paking density of 18" spheres in a 65mm-OD ylinder [2-1 1 ] A. VI. 65; a. I OZ.. ll,, SO.411A fiose m poking.u late rtmdom paddirg U _ - L _ ID (mnwt' M 'I I li~j v~y m Figure 2-4. Paking density of 1/8" spheres in infinite ylinders of varying diameter [2-11 ]. 32

33 The oordination number is defined as the number of spheres in ontat with any given sphere. The oordination number an be used as a means for quantifying the arrangement of three-dimensional arrays of spheres. Only even oordination numbers are possible in regularly arranged three-dimensional ubi latties, although odd oordination numbers are possible in hexagonal and random arrangements of sphei s. Wadsworth investigated the distribution of oordination numbers for smooth hard spheres using /4 in.-diameter steel ball bearings [2-13]. He made three important onlusions: a) In random paking, the void fration is only a funtion of the sphere-to-ontainer diameter ratio and is insensitive to the method of staking. h) The random paking in flat-bottomed ylinders tends towards rhombohedral (hexagonal) lose paking and the degree of inompleteness is random. ) A ritial diameter exists for foring omplete rhombohedral paking at the flat bottom of a ontainer. This value was estimated to be 2 sphere diameters radially and axially. The loading of spheres in pebble-bed reators is usually assumed to be loose random paking with a.61 density, with regular onfigurations appearing only near the walls and on the bottom of the ore. Neutron leakage, and hene ritiality, is affeted by the shape and distribution of avities in the pebble bed. The ore may be homogenized if the avities are evenly distributed and are small relative to the neutron mean free path. However, this approximation no longer applies for larger avities. Lieberoth and Stojadinovid derived a theoretial expression for the neutron diffusion onstant D, whih was verified using a Monte Carlo analysis of a system with 3 spheres [2-14]. Thus, 33

34 assuming that no orrelation exists between the passage lengths in the avities and in the spheres, where D = 1+, <-X tfqr + lor, (2-7) DH (1+) 3 [ 2212 R 2 2,R 2 - I + (1 + 2E,,R)exp(- 21,oR) - and (h2) (h)2 (2-8) (h) (2-9) Here, 2;,t is the total marosopi ross setion in the homogeneous model, R is the radius of a sphere, h is the hord length in a avity and t is the esape hord length in a sphere (the angular brakets denote an average). Spetrum and diffusion alulations in heterogeneous reators are often performed on a homogenized ore. In this approah, whih is used in the VSOP94 physis ode, the ross setions are multiplied by energy dependent self-shielding fators, while the diffusion onstant for the homogeneous model is saled as shown in Equation Thermalization in Graphite The fission neutrons are slowed down through ollisions with the arbon atoms until they equilibrate with the thermal motion of the graphite. The energies of the thermalized 34

35 neutrons are distributed about the neutron temperature (whih is slightly higher than the moderator temperature beause of leakage and absorption hardening) aording to the Maxwellian distribution. Thermalized neutrons an gain energy in a ollision with a arbon atom. Beause the arbon atoms are part of a graphite lattie (see Figure 2.5), the exhange of energy is restrited to the quanta of the rystal vibrational energy (phonons). The interation between the thermal neutrons and the arbon atoms is given by a double differential ross setion, whih is ommonly expressed in terms of a measured sattering law S(a,3), where a and 3 are dimensionless exhanges of momentum and energy. This sattering law an be related to the frequeny distribution of phonons in the graphite, whih an be alulated theoretially. The VSOP94 ode implements the graphite phonon alulation by Young and Koppel [2-15]. Co Figure 2-5. The graphite lattie [2-16] The VSOP94 Code [2-7] VSOP94 is a omputer ode system for reator physis and fuel yle simulation, whih is the main physis ode for the neutroni design of pebble-bed reators. It omprises neutron ross-setion libraries and routines for the following neutroni alulations: 35

36 nulear data proessing and preparation of temperature-dependent few-group parameters; repeated neutron spetrum evaluation; two- and three- dimensional diffusion alulations based on neutron flux synthesis with fuel depletion and shutdown features; fuel management inluding pebble reyling; fuel yle ost analysis; and quasi-stati thermal hydraulis. VSOP94 is a general-purpose ode, whih has also been applied suessfully to light- and heavy-water reators. The struture of the ode is shown in Figure 2-6. The ZUT-DGL ode is used to generate the fast spetrum involving resonanes in both the resolved and unresolved ranges [2-17]. The orresponding few-group parameters are prepared by the GAM-I ode in the PI approximation, whih aounts for leakage and anisotropi sattering [2-18]. The required fast and epithermal data, whih are provided in a GAM library with 68 energy groups ranging from 1 MeV to.414 ev, were extrated from the ENDF/B-IV, ENDF/B-V and JEF-I evaluations. In the thermal range, the spetrum alulations are arried out with the THERMOS ode, whih is based on the integral form of the Boltzmann transport equation [2-19]. The THERMOS library is given in 3 energy groups ranging from to 2.5 ev, and is prepared by the THERMALIZATION ode (whih is a preursor of the GATHER ode [2-2]) from a 96-group library taking into aount the speifi design of the fuel elements and reator [2-21]. Both the ZUT-DGL and THERMOS odes have been modified to allow for the double-heterogeneity present in the pebble-bed reator [2-22]. The graphite sattering matries are based on the Young phonon spetrum in graphite [2-15]. 36

37 Several auxiliary odes are used to prepare the geometrial data needed by the main routines. The DATA-2 ode prepares the fuel element input data from its geometry speifiation [2.23]. The auxiliary ode BIRGIT prepares a two-dimensional (R-Z) geometri design of the ore, whih speifies a pebble flow pattern of pebbles in finite Mr-CeOACAI&T3I: OETlC SIWB ES. Figure 2-6. Struture of the VSOP94 ode [2-7]. 37

38 bathes grouped into layers in different flow hannels (see Figure 2-7). The bathes are used to represent fuel spheres that have traversed the ore a given number of times and hene have a speifi burnup. The layers and flow hannels allow for axial and radial burnup variations in the ore. The material ompositions are homogenized within eah bath. Burnup is modeled by depleting the fuel in eah homogenized bath by the speified time step, then shuffling its ontents to the next layer in eah hannel. Bathes at the bottom of the ore are either disarded or reyled depending on the burnup. V5O CAITION vrs vy) Cam pecll.rs v(l.j) File 2-7. Overlay of VSOP94 and CITATION meshes [2-7] 38

39 A two- or three-dimensional neutron flux map is generated with the CITATION diffusion ode in several energy groups (usually four groups are hosen) [2-24]. This is utilized in a burn-up alulation for up to 2 different ore regions using a sheme developed from the FEVER ode, whih follows expliitly the build-up history of 4 fission produts in eah region [2-25]. The diffusion alulation is repeated for short burn-up intervals, while the neutron spetrum is realulated at larger time intervals. Beause the diffusion alulation is arried out on a regular grid pattern, a matrix transformation (and its inverse) is provided between the VSOP flow pattern and the CITATION mesh for the marosopi ross setions and neutron fluxes. The THERMIX ode is inluded in VSOP94 to perform both stati and time-dependent thermal hydrauli alulations for pebble-bed reators [2-26]. The temperatures of the fuel and moderator regions are fed bak to the spetrum evaluations for subsequent ore neutroni alulations. The fuel management and ost module KPD performs the in-ore and out-of-pile fuel shuffling, as well as general evaluations of the reator and fuel element irradiation history [2-27]. 2.2 The Monte Carlo Method The Monte Carlo method onsists of simulating a large number of neutron (and/or photon) histories by using a random number generator to sample appropriate probability distribution funtions for trak lengths between ollisions, sattering angles, type of interation, et. In this fashion, eah neutron is followed from birth throughout its life to its removal from the system through absorption or leakage. When a large number of suh 39

40 histories are followed, the neutron distribution beomes known and quantities of interest suh as the neutron flux an be tallied. [2-28, 2-29] The Boltzmann Equation The Monte Carlo method is ideally suited for the alulation of integrals. For example, onsider the simple integral I= f(x)d (b - a) f(xi) (2-1) The xi are hosen randomly instead of at regular intervals, and the purely statistial error is inversely proportional to [N' independently of the dimension of the integral. Beause the Boltzmann transport equation an be ast in integral form, it is lear that the Monte Carlo method is ideally suited for simulating neutron and photon transport in nulear reators. The following brief desription of the Monte Carlo sampling of the Boltzmann equation is based on the disussion in Referene 2-3. R ;XI Figure 2-8. Relation between vetors [2-3]. 4

41 The steady-state Boltzmann equation for the diretional flux density (r?,f,e)is as follows: -V(, Q, E) + X, (F,, E)b(, 2, E) = de'z,(f,'-, E'-- E)(, fi, E')+ S(r,, E), (2-11) The first term on the left-hand side of the equation denotes the leakage of neutrons traveling in diretion 6, and the seond term gives the rate of neutron loss by absorption and sattering. On the right-hand side, a(r,l' -,E'-E)dE' is the differential sattering ross setion from energy E' and diretion n' into the interval dedq, and the first term represents the rate at whih neutrons appear at position with energy E due to sattering. The term S(Fr,,E) denotes the rate at whih neutrons appear at with energy E and moving in diretion Q, with ontributions from both fission and extraneous soures. This integro-differential equation an be onverted into the following integral form of the Boltzmann equation: O(, Q, E) = JdR exp - Jt, (F- R'R,E)dR 1 x [Sfd6'dE'X, (,'-- Q,E'-4 E)(F?,i,E') + S(F,Q,E], (2-12) where ' is related to F and Q via '= F-R R, and R =]j. (see Figure 2-8). This equation is next expressed in operator form as y(f,, E) = IdF'.T(',fQ,E)(',,E) (2-13) 41

42 and X(,, E) = S(F, C, E) + ffd' de'.c(h',e', ', E'f ),' (,', E'), (2-14) where the ollision density Vyis defined as y(,,e) = dfr'.t(',r h,e) (2-15) and the density X of ollided partiles leaving position, X(r,,E) = ljjd'de's (,'--,E'-- E)(f,, E')+ S(f,,E). (2-16) The transport and ollision operators are defined respetively as follows: T(r', Q, E) =,(F, E)exp(- Z, ( ",E)ds 1 r?'-o - 2-Q r-r r-r - PI' -1 (2-17) and C(Q',E',,E ) - Z(Q'- 2,E' E) El, I F) X-, if, fl',e') (2-18) The propagation of neutrons is modeled in a reursive manner. Starting with a soure term S(F',f2',E'), Xo( (F',,E') = S(F',',E'), Vo/ (, ',E') = JId'T(F', I f',e')x(r',f',e') (2-19) (2-2) and Xr, (FQ,E) = JJdf'dE'C(2',E'--- i,ei )VO(F,i',E') (2-21) 42

43 Subsequent steps are given by and yi (FQ',E') = J 'T(',,E ( E') (2-22) X.(?,, E) = ffd(2'de'c(q',e'-,e I F)Yv~(F/,',E'). (2-23) The transport operator T propagates the neutron from ' to by sampling over the interval (, R) aording to Equation If is outside the boundaries of the reator model, the neutron has esaped and the history is terminated; otherwise, an interation takes plae. The ollision operator, whih desribes this interation via Equation 2-23, may be rewritten as E (,2, E) E. (Q'E Q, E F) (2-24), (.n, E) Y, (?, 2, E) = P(F,,E) C,((Q',E'- Q,E F), whih expresses the ollision operator in terms of a sattering kernel multiplied by a orretion fator for absorption. The sattering kernel may be further written as follows: C (', = NA QE I E'-- )-E (=',E'- IF) (2-25),(?,QE) ( Q',E'),j(O', F-4 K2, E), 43

44 where NA is the atomi number density for nulide A, and r, is the mirosopi ross setion for reation type j. By sampling randomly in the interval (,1), the braketed terms are used to determine the interating nulide and the type of reation, and the normalized sattering funtion fai is used to generate the sattering angle, ul = os 8. The partile energy E is determined from E = E(I, E') and CQ is alulated so as to satisfy the relation pu = C2 Q '. The neutron history is terminated if E is below the energy utoff, otherwise ' and E' are reset to and E. Monte Carlo odes suh as MCNP do not require expliit treatment of the slowing-down proess when ontinuous-energy ross-setions are used, beause the values of ross setions an be looked up diretly at any energy level. The ross setions for eah reation are given on one energy grid, whih is suffiiently dense to permit the reprodution of the evaluated ross setions within a 1% error. For example, for the ENDF/B-V evaluation, the energy grid for H ontains approximately 25 points, while 197Au uses approximately 22,5. [2-31] The Monte Carlo method offers further simplifiations over the analogous diffusiontheory approah. For example, the ability to speify the exat geometry of the reator preludes the need for neutron-streaming orretions, whih are needed when a homogenized representation of the ore is used The MCNP Code MCNP (Monte Carlo N-Partile) is a general-purpose, ontinuous-energy, generalizedgeometry, time-dependent, oupled neutron-photon-eletron, Monte-Carlo transport ode 44

45 system [2-31]. The alulations reported in this thesis were performed with version 4B2 of the ode, although a later version (4C) is now available. The generalized geometry apability of MCNP4B, ombined with the use of ontinuous ross-setion data, make it possible to model nulear reators with great auray. The goal of the researh reported here was to investigate the appliability of MCNP4B to pebble-bed reators with randomly paked ores. MCNP an model an arbitrary three-dimensional onfiguration of materials arranged in geometri ells, whih are bounded by first- and seond-degree surfaes and some speial fourth-degree surfaes. Point-wise, ontinuous-energy ross-setion libraries are typially used. However, multigroup data may also be used for fixed-soure adjoint alulations. The ross-setion evaluation aounted for all neutron interations, and both free gas and S(a; fl thermal treatments are used. Fission soures as well as fixed and surfae soures are available. For photons, the ode takes aount of inoherent and oherent sattering with and without eletron binding effets, the possibility of fluoresent emission following photoeletri absorption, and absorption in pair prodution with loal emission of annihilation radiation. A very general soure and tally struture is available. The tallies have extensive statistial analysis of onvergene, and rapid onvergene is enabled by a wide variety of variane redution methods. Normal energy ranges are -2 MeV for neutrons and 1 kev - 1 GeV for photons and eletrons. The large number of randomly situated fuel and moderator spheres, and the large number of fuel partiles per sphere (approximately 14), in pebble-bed reators preludes the expliit speifiation of the ore geometry, and regular latties of spheres are used 45

46 instead. The repeated-struture feature of MCNP4B permits the definition of an array onsisting of hexahedral or hexagonal unit ells. This an be used to approximate the randomly paked pebble-bed ore. 2.3 Summary An overview of pebble-bed reator physis was presented in this hapter. The doubleheterogeneity of the pebble-bed ore, whih is related to the presene of small fuel grains embedded in graphite spheres, requires the orret treatment of mutual shielding between grains. For diffusion-theory ore alulations, the effet of this shielding is embodied in the Danoff orretion for resonane absorptions. Although ompliated, this proedure is fully automated in odes like VSOP94. The Monte Carlo ode MCNP4B offers an alternative approah by relying on a point-wise representation of nulear reation ross setions, in whih a large number of energy points are used to desribe aurately the resonane urve. Therefore, the effet of mutual shielding between the fuel grains is inluded automatially. This feature of MCNP4B, as well as its ability to model reator geometry in detail, is explored in this report. 46

47 3. MCNP4B MODELLING OF PEBBLE-BED REACTORS Construting an MCNP4B model onsists of establishing the geometry of the reator from engineering drawings, representing eah subsystem by a ell whose boundaries are defined mathematially by a logial ombination of surfaes, and speifying the density and omposition of eah suh ell [3-1]. In the ase of pebble-bed reators, the struture of the reator an be modeled as aurately as is required by the appliation. The hallenge lies in modeling the randomly paked pebble-bed ore, whih must be approximated by a regular lattie of spheres. 3.1 Regular Latties Several latties are available inluding simple ubi (SC), body-entred ubi (BCC) or tetragonal (BCT), fae-entred ubi (FCC), simple hexagonal (SH), and hexagonal lose paked (HCP) [3-2]. These latties differ in the number of spheres present in the unit ell and the maximum paking fration (see Table 3-1). Table 3-1 Properties of Regular Latties Number of Spheres Coordination Maximum Paking in Unit Cell Number Fration SC BCC or BCT FCC SH HCP The simple ubi and simple (point-on-point) hexagonal latties an be eliminated for most ores, beause of their leakiness and low paking densities. The hoie among the 47

48 remaining latties depends on their ability to represent speifi sphere ombinations, sine the paking fration an be ahieved by adjusting the ell size; the size of the unit ell a is related to the radius of the sphere R and the paking frationfas follows: a =F~ R. ~3f For example, a ore haraterized by a 1:1 fuel-to-moderator (3-1) sphere ratio is modeled most easily by a BCC or BCT lattie beause their unit ell ontains two spheres (see Figure 3-1). All spheres ontained within the FCC and HCP latties are positioned along the bounding planes of the unit ell, making it impossible to model more ompliated mixtures of spheres (suh as the ombination of moderator, fuel and absorber spheres enountered in the ASTRA ritial experiments) beause adjaent spheres overlap inorretly. Therefore, although the paking of spheres in pebble beds is expeted to approx.imate a rhombohedral lattie (see Setion 2.1.2), a loose HCP lattie may not be a proper hoie. Figure 3-1. Body Centred Cubi Struture 48

49 As the subsequent hapters show, the BCC lattie was found to work well for the loose paking typially enountered in pebble-bed reators. The effet that the hoie of paking arrangement has on neutron streaming was investigated in Referene 3-3. Critiality alulations were performed for both BCT and HCP latties, using a spherial ore (with a radius of 14 m) paked with spheres; both refleted and unrefleted onfigurations were onsidered. The results of the analysis showed that the keff is not very sensitive to the speifi sphere arrangement for refleted systems for whih leakage effets are less important. Sphere mixtures other than the 1:1 fuel-to-moderator ratio present a problem. Reduing the size or density of the moderator sphere an approximate a small deviation, suh as the 57:43 perent ratio used for the HTR-1 start-up ore. Alternatively, a repeating ell may be onstruted from several BCC (or BCT) unit ells suh that the exat ombination of spheres an be defined. For example, ten layers of five BCC unit ells (for a total of 1 spheres) an be used to model the HTR-1 ore. More ompliated ore loadings may also be modeled in this fashion, although the results are sensitive to the (ideally stohasti) manner in whih the spheres are distributed throughout the repeating ell. 3.2 Edge Effets in MCNP4B A side effet assoiated with the repeated-struture feature in MCNP4B is the appearane of partial spheres at the ore boundary (Figure 3-2), beause this adds extra fuel to the ore. Murata first identified this problem during the development of MCNP-BALL [3-4]. A orretion had to be made to the sampling algorithm for spherial fuel spheres in order 49

50 to reprodue the speified paking fration. This was ahieved by generating a nearest neighbour distribution funtion for a slightly higher paking fration,f: f'=f V.636, (3-1) V-AV where f is the atual paking fration, V is the ore volume, and AV is the volume of an exlusion zone of thikness R (the radius of a fuel sphere in a one-zone ore). Sampled fuel spheres that overlapped the ore boundary were rejeted. Graphite refletor Exlusion zone Moderator sphere Figure 3-2. Partial spheres generated by MCNP4B A more diret approah was hosen for the MCNP4B modeling of irular pebble-bed ores in the present work. An exlusion zone was introdued at the boundaries of the ore, whih effetively redued the size of the sphere fill volume by AV. The size of this exlusion zone was the radius of a sphere, saled by the ratio of the number of fuel spheres to the total number of spheres in the unit ell. Thus, for the 57:43 perent sphere 57 ratio speified for the HTR-1 reator, this orresponded to 3x =1.71 m

51 Beause there is a distribution of differently sized partial spheres around the ore edge, deleted portions of physially realizable spheres are made up by leftover portions of physially unrealizable spheres (see Figure 3-3). This proedure does not work for the ASTRA faility with its polygonal ore, beause suh a anellation does not our on average. Therefore, a redued paking fration was used instead in order to eliminate partial spheres Figure 3-3. The sphere exlusion zone 3.3 Double Heterogeneity For a high-fidelity MCNP model of a pebble-bed reator, the double heterogeneity of the ore must also be reprodued aurately. The oated fuel partiles were modeled exatly (Figure 3-4), and the random distribution of these fuel partiles in the fuel sphere was approximated using a simple-ubi regular array without an exlusion zone (Figure 3-5). Figure 3-6 shows a slie through the BCC ore representation. 51

52 Graphitee matrix Fuel kernel I Pyrolyti Carbon Carbon bu fer Silion Carbide L Pyrolyti Carbon I ii i Figure 3-4. MCNP4B Model of a Coated Fuel Partile. / 1 ',,_o O o Oo o o o,,.io O ',1 O ' I--o o ' oo o 4 : o;o o o~o o oto oo oio o ' 1 o11 ' O O1 i'- ~.o O o '1 O1 OI: o 1 o o Io l~o OOi ' 1S LL.--- e--cr i 1 '1O 1i '" io, O OfOOO.' :,,! ooo '.,,~oo,o o.ololo oo o~olo o o o -o1.,o,1 OO o,,.4 _,, + _ ~ a o.4 i Moderator sphere (iraphite shell (iraphite matrix Coated fuel partile Helium Figure 3-5. MCNP4B Model of a Fuel Pebble 52

53 Helium Fuel sphere Moderator sphere Figure 3-6. MCNP4B Model of a Pebble-Bed Core 3.4 Conlusions The BCC lattie is a onvenient, and a neutronially aurate, representation of a randomly paked, refleted pebble-bed ore. It is haraterized by the size of the ubi unit ell, whih is determined from the speified paking fration and the detailed design of the omponent spheres. Compliated mixtures of different spheres an be assembled by ombining BCC unit ells into larger repeating ells. Use of the repeated-struture feature of MCNP4B generates partial spheres at the ore boundaries, whose effet an be minimized by either introduing an exlusion zone or by reduing the paking fration. 53

54 4. THE HTR-PROTEUS FACILITY The PROTEUS zero-power experimental faility is loated at the Paul Sherrer Institute in Switzerland. The faility has been used for a variety of ritial experiments involving both light-water and gas-ooled reator ores. The various ritial assemblies are usually onfigured in PROTEUS as a subritial test zone in the entre of an annular thermal driver zone. However, for the LEU-HTR experiments, the faility was set up as a ritial pebble-bed ore surrounded radially and axially by a graphite refletor. PROTEUS was initially prepared for the HTR experiments between January and August 198, but was subsequently reonfigured to aommodate advaned light-water reator experiments. The faility was rebuilt for the LEU-HTR tests in 1991 [4-1], and the experimental program ontinued until [4-2] 4.1 Desription of the PROTEUS Faility The HTR-PROTEUS faility onsists of a graphite ylinder with a entral avity. The height of the ylinder is 334 mm and its radius is 3262 mm. The avity starts 78 mm above the bottom of the lower axial refletor, and is a 22-sided polygon with a flat-to-flat separation distane of 125 mm. The removable upper axial refletor is a 78 mm-high graphite ylinder inside an aluminium tank, whih fits onto an aluminium safety ring loated 1764 mm above the floor of the avity. An air gap is present between the upper refletor and the pebble-bed ore. [4-3, 4-4] The radial refletor has numerous hannels, whih aommodate absorber rods and instrumentation. The faility uses eight shutoff rods loated on a radius of 689 mm, four 54

55 ontrol rods on a radius of 789 mm or 96 mm, and one servo-driven regulating rod at a distane of 9 mm from the ore entre. The shutoff rods are made of 35 mm-diameter borated-steel (5 wt%) rod setions enlosed in stainless-steel tubes with an outer diameter of 4 mm. For the first ore, the ontrol rods were the Zebra-type made of aluminium with admium shutters. However, these were replaed with standard stainless-steel ontrol rods for all subsequent ores. A photograph showing a top view of the HTR- PROTEUS faility appears in Figure 4-1, while Figure 4-2 provides a shemati side view Figure 4-1. Top View of HTR-PROTEUS Faility The refletor onsists of graphite of various ages and moisture ontent. Table 4-1 gives the atom densities for the refletor used in the MCNP models of the faility. These values were later revised to inorporate a higher onentration of impurities (expressed as an equivalent natural boron ontent) resulting in a 22 m/s ross-setion of 4.9 mbarn. An average value of g/m 3 was reommended for the density of the graphite. 55

56 Table 4-1 Atom Densities in PROTEUS Graphite Refletor nulei/barn-m Nulide Axial Refletors Radial Refletor B 9.e-9 9.2e-9 'B 3.6e-8 3.7e-8 Carbon 8.6 le e-2 -. 'I"CPI"TpJC I i ' ' t, ,. I E. ' : il),,.:, - U a Figure 4-2. A shemati Representation of the HTR-PROTEUS Faility 4.2 Fuel and Moderator Spheres The geometry and mass speifiations of the LEU-HTR fuel spheres and moderator spheres are summarized in Table 4-2. The 6 m-diameter fuel spheres ontain TRISO oated fuel partiles, with 16.7 wt% enrihed UO2, embedded in a graphite matrix. The atom densities in the fuel and moderator spheres are given in Tables 4-3 and 4-4, respetively. The presene of impurities in the graphite is approximated by a boron 56

57 ontent that results in an effetive 22 m/s absorption ross setion of 4.79 mbarn. The presene of moisture in the spheres is ignored in these speifiations, beause the moisture ontent was shown to be less than.1 wt%. The diameter and mass of the fuel pebbles was measured at the beginning and end of the experiments to address onerns regarding the potential erosion of the graphite during loading and unloading operations. No hange in mass ourred, although some surfae indentation was observed. [4-4] Table 4-2 LEU-HTR Fuel and Moderator Sphere Data Property Value Mass of uranium per fuel pebble g 235U mass per fuel pebble 1. g Mass of arbon per fuel pebble g Radius of fuel pebble fuelled zone 2.5 m Radius of fuel/moderator pebble 3. m Radius of U 2 fuel kernel Thikness of arbon buffer oating Thikness of inner PyC oating Thikness of SiC oating Thikness of outer PyC oating.251 m.915 m.399 m.353 m.4 m Density of U 2 fuel 1.88 g/m 3 Density of arbon buffer oating 1.1 g/m Density of inner PyC oating 1.9 g/m Density of SiC oating 3.2 m Density of outer PyC oating 1.89 g/m Number of CFPs per fuel sphere 9393 Mass of arbon in moderator sphere g Radius of moderator sphere 3. m 57

58 Atom Table 4-3 Densities in HTR-PROTEUS Fuel Spheres Nulide Atom Density (nulei/barn-m) U/ 2 kernel Graphite Matrix Graphite Shell ' B e e-8,B e e-7 Carbon e e-2 Oxygen e-2.. Silion e U e U 2U2.196e-2.. Table 4-4 Atom Densities in HTR-PROTEUS Moderator Spheres Nulide Atom Density (nulei/barn-m) ' B e-8 "B e-8 Carbon e The Stohasti Cores As summarized in Table 4-5, a total of eleven ores were investigated during the HTR- PROTEUS experimental program. The majority of the ores utilized deterministi sphere arrangements, whih failitated the studying of effets suh as neutron streaming, moderation and water ingress (simulated with polyethylene rods) beause of the easy aess to the ore. Moreover, beause k and the related spetral indies are independent of the pebble-bed geometry, it was possible to use the deterministi ores for the zeroleakage neutron balane measurement. [4-5] However, ritiality measurements were also arried out on three stohasti ores (4.1, 4.2 and 4.3), whih used a 1:1 fuel-to-moderator (F/M) sphere ratio to ahieve ritiality 58

59 at a reasonable ore height. The experimental results for these ores are summarized in Table 4-6 (the ontrol-rod reativity worths were also measured but are not reported here) [4-21. The reported kff are on the order of 1.13, beause of orretions for various experimental effets and ontrol-rod insertions needed to maintain ritiality [4-6]. Table 4-5 HTR-PROTEUS Experimental Core Configurations Core FF/M Paking Prominent Feature i 2:1 HCP_ Used Zebra Cd/Al shutters instead of ontrol rods. IA 2:1 HCP 2:1 HCP Investigated influene of upper reator avit 3 2:1 HCP Water ingress using 8.9 mm OD polyethylene rods. 4 1:1 Random Stohasti ores. 5 2:1 POP. 6 2:1 POP Simulated water ingress with polyethylene/opper rods. 7 2:1 POP Water ingress using 8.3 mm OD polyethylene rods. 8 2:1 POP Partial water ingress using 15 m-long polyethylene rods. 9 1:1 POP 1T 1:1 POP Water ingress using 6.5 mm OD polyethylene rods. ' Hexagonal Close Paked; Point-on-Point (olumn hexagonal). Table 4-6 Experimental Results for HTR-PROTEUS Stohasti Cores Parameter Core 4.1 Core 4.2 Core 4.3 ket Critial loading (F 52, ,494 49, 49 Critial height m m m Neutron flux 5 x 1 7 n/m 2 /s 5 x 7 n/m 2 /s 5 x 1 n/m/s Air temperature 19.8 C 19.6 C 21.2 C Air pressure 975 mbar 98 mbar O mbar Humidity 44% 5% 5% _ ' Correted for the presene of ontrol rods in the radial refletor. 59

60 The paking frations of the three ores differed beause the spheres were loaded differently [4-7]. Core 4.1 was prepared by lamping the fuel and moderator sphere delivery tubes together in parallel, and eah sphere was allowed to fall into the ore from its respetive tube. To avoid any unwanted ordering effets, a seond method was used to load ores 4.2 and 4.3 for whih the fuel and moderator sphere hannels were ombined by means of a simple funnel arrangement. The pebble bed was lightly flattened after eah loading step, and its height was determined by measuring the average distane from the safety ring to the bottom of a rod plaed horizontally on top of the ore. A 1 m error is assoiated with this proedure at the l onfidene interval. 4.4 The MCNP4B Model A detailed MCNP4B model of the HTR-PROTEUS faility was prepared based on the alulational benhmark speifiations given in Referene 4-4. This physis benhmark was part of the IAEA Coordinated Researh Program (CRP) on the "Validation of Safety Related Reator Physis Calulations for Low-Enrihed HTGRs." To simplify the modeling task, details of the hannels in the refletor tank and the absorber rods were not inluded in the speifiations. Moreover, an equivalent ore radius was provided, whih proved ruial for defining a sphere exlusion zone. However, the removable upper axial refletor was modeled aurately. Figures 4-3 and 4-4 are vertial and horizontal plan views of the MCNP4B model, and further generi details of the ore region appear in Chapter 3. Table 4-7 summarizes the pebble-bed lattie parameters. 6

61 iigure 4-3 Vertial View of MC'NP4[3 lmodel oft ITR-PR()TIt 'S i:igulre lorizontal View of MICNP4B Mlodel of It-tR-PROTJ. 'S 1

62 A 1.5 m sphere exlusion zone was used to ompensate for the presene of partial spheres (with a 1:1 fuel-to-moderator sphere ratio) around the ore periphery. The three MCNP4B models for ores 4.1 through 4.3 are inluded as Appendies A-1, -2 and -3. Table 4-7 Lattie Parameters for MCNP4B Model of Stohasti HTR-PROTEUS Cores Core Paking Fration Cell Size (m) The results of the MCNP4B ritiality analyses are summarized in Table 4-8, along with the measured kff and the results of an MCNP-BALL analysis arried out by Murata [4-7]. The two sets of alulations are seen to be in exellent agreement, although the ores are predited to be more reative than measured. The over-estimation of the alulated keff has been attributed to the speified omposition of the graphite refletor [4-6]. Table 4-8 HTR-PROTEUS Critiality Analysis Core Critial Paking Effetive Multipliation Constant Height (m) Fration Experiment MCNP4Bt MCNP-BALL 16J :± ± : i ± ± ±.11 Using ENDF/B-VI ross-setion data evaluated at 3 K;.5 million neutron histories. 62

63 4.5 Summary The HTR-PROTEUS experiments involving stohasti ores were modeled suessfully using a BCC lattie and a 1.5 m exlusion zone. The alulated ritial heights of the three experiments agreed losely with the preditions MCNP-BALL, a Japanese ode that models the irregularly paked pebble-bed ores exatly. Beause the model was based on inorret PSI speifiations of the impurity ontent in the refletor, the resulting effetive multipliation onstants were larger than those measured by approximately.7% Ak/k. The orret equivalent boron onentrations were not available. The suess of this modeling methodology justified its appliation to the analysis of the HTR-1 reator desribed in Chapter 5. 63

64 5. THE HTR-1 REACTOR The HTR-1 is an experimental 1 MW(t) pebble-bed reator reently onstruted at the Institute of Nulear Energy Tehnology (INET), Beijing. The main objetives of this high-temperature gas-ooled reator projet are as follows [5-1]: to aquire tehnial expertise in the design, onstrution and operation of pebble-bed reators; to provide an experimental faility for the testing of spherial fuel elements; to demonstrate the inherent safety features of the modular pebble-bed reator; to develop ogeneration and losed-yle gas-turbine tehnology; and to investigate high-temperature proess heat appliations. The safe operation of the reator requires the ability to alulate aurately its neutron physis parameters using omputer odes. These odes are typially validated using data from ritial experiments performed both in zero-power researh reators and during the ommissioning of the atual reator. To failitate this validation proess for HTGRs, the International Atomi Energy Ageny (IAEA) sponsored two benhmark problems in two separate Coordinated Researh Programs (CRPs). The first was already disussed in Chapter 4. The seond, whih is entitled "Evaluation of High-Temperature Gas-Cooled Reator Performane," is related to the ommissioning of the HTR-1 reator and is the subjet of this Chapter [5-2]. 64

65 5.1 Desription of the HTR-1 Reator The HTR-1 is a pebble-bed reator that uses spherial fuel elements with embedded' oated fuel partiles. The fuel partiles ontain kernels with low-enrihed uranium (17% 235 U) whose design burnup is 8, MWd/t. Detailed speifiations of the graphite fuel elements are given in Table 5-1. The full ore onsists of approximately 27, fuel elements randomly paked in a ylindrial avity with a mean height of 1.97 m, a diameter of 1.8 m and a volume of 5. m 3. The ore is surrounded by a struture onsisting of a graphite refletor and a borated arbon shield. The radial refletor, whih is 1 m thik, ontains penetrations for ten ontrol rods, seven absorber ball units, three irradiation sites and twenty oolant hannels. Helium gas flows up these oolant hannels before reversing diretion at the top of the ore and flowing downward into the pebble bed. The ore inlet and outit,ilant temperatures are 25 C and 7 C, respetively, at a pressure of 3. MPa. Vertial and horizontal ross setions of the ore are shown in Figures 5-1 and 5-2. The initial approah to ritial was ahieved on Deember 1, 2. The disharge tube and the one at the bottom of the ore was filled with moderator pebbles, then a mixture of fuel and moderator pebbles was added randomly until the ritial height was reahed with the ontrol rods fully withdrawn. The ratio of fuel balls to moderator pebbles used was 57% to 43%, and the initial loading was arried out at room temperature (15 C) and in atmospheri air. The ritial loading was 9627 fuel spheres and 7263 moderator spheres for a total of 16,89 spheres [5-3]. 65

66 I I I I I I Control rod hannel Smllt absorber bttl hannel /Heliup flow hannel Figure 5-1. Vertial Cross Setion of the HTR-1 Reator [5-2] 66

67 ji Figure 5-2. Horizontal Cross Setion of the HTR-1O Reator [5-2] 67

68 Table 5- HTR-1 Reator Core Parameters Parameter Ylue Units Struture Density of refletor graphite 17 6 g / Equivalent boron ontent of refletor graphite impurities ppm Density of borated arbon brik (inluding B 4 C) Weight ratio of B 4 C in borated arbon brik.g.m Moderator Pebbles Diameter of moderator pebble. Density of graphite.84 Equivalent natural boron ontent of impurities in graphite.125 m g/m Fuel Pebbles Diameter of fuel ebble 6. Cm Diameter of fuel zone 5. m Density of graphite in matrix and outer shell 1.73 g/m Uranium loading per fuel pebble Enrihment of 235U wt. % Equivalent natural boron ontent of impurities in uranium 4 ppm -Equivalent natural boron ontent ofimpurities in raphite. 13 ppm Volumetri filling fration of balls in the ore.61 Coated Fuel Partile Radius of fuel kernel.25 m UO2density 1.4 gjm Thikness of first-pyrolyti arbon oating m Thikness of seond yrolyti oating....4 m Thikness of silion-arbide oating.35 m Thikness of third pyrolyti arbon oating.4 m Density of first pyrol i oating ~ -1 _./C Density of seond pyroli oating. '.9 g/m Density of silion-arbide oating... g/m Density of third pyrolyti oating 1.9,Xm! With the ontrol rods inserted, the ore will then be pressurized and ompletely filled using the same mixture of fuel and moderator balls. The initial ritial ore height was hosen so as to limit the maximum exess reativity held down by the ontrol absorber 68

69 rods to the amount required to provide suffiient xenon override. The exess reativity margin will be ontrolled subsequently by the ontinuous refuelling of the reator. 5.2 Physis Benhmark Problems INET proposed the following benhmark problems for the HTR-1 to test the auray of physis odes in alulating the effetive multipliation fator for various pebble-bed reator onfigurations [5-2]. These are designated B 1, B2, B3 and B4: a) Problem B1. Predit the initial old ritial loading (kff = 1.), either in terms of the number of pebbles or the height of the pebble bed, with the ontrol absorbers fully withdrawn. Assume a ore temperature of 15 C and atmospheri air. b) Problem B2. Calulate the effetive multipliation fator, keff, of the ore filled ompletely to a height of 1.97 m under a helium pressure of 3. MPa and at the following ore temperatures: 2 C (B21), 12 C (B22) and 25 C (B23). Assume that all ontrol absorbers are fully withdrawn. ) Problem B3. Calulate the total reativity worth of the ten ontrol rods (B31) and of one ontrol rod (B32) for a full ore at a temperature of 2 C and a helium pressure of 3. MPa. d) Problem B4. Calulate the total reativity worth of the ten ontrol rods (B41) and the differential reativity worth of one ontrol rod (B42) for a ore loading height of 126 m at a temperature of 2 C and a helium pressure of 3. MPa. 69

70 These alulations are to be performed for the speified fuel-to-moderator pebble ratio of 57% to 43%. The given ore temperatures assume a uniform temperature profile throughout the reator, inluding the fuel pebbles and the surrounding graphite struture. The height of the ore refers to the fuelled portion only, i.e., exluding the onus filled with moderator pebbles. The auray of the odes was to be determined by omparing the ode preditions with measurements during the initial approah to ritial and lowpower physis ommissioning tests at the HTR- 1 faility. 5.3 Referene Core Physis Model A simplified reator desription was inluded in the physis benhmark speifiation to provide a ommon starting point for the modeling of the HTR- 1 with a variety of odes. Figure 5-3 shows the reommended two-dimensional model of the reator with zone identifiation numbers, and Table 5-2 gives the orresponding spatially homogenized material ompositions of the reator struture. Benhmark problems B3 and B4 require the expliit modeling of the ontrol rods. The design of the ontrol rod is depited in Figure 5-4, and its geometry and material speifiations are summarized in Table 5-3. Boron arbide (B 4 C) is used as the neutron absorber. Eah ontrol rod ontains five B 4 C annular segments with outer stainless-steel sleeves, and whih are joined together by stainless steel joints. 5.4 MCNP4B Model of HTR-1 The HTR-1 physis benhmark problem was speified in a manner suitable for both diffusion-theory and Monte Carlo odes. The resultant simplifiation of the reator 7

71 -... _ - - model (see Setion 5-3) redues the auray with whih MCNP4B an reprodue experimental measurements. Moreover, the speifiation of a fuel-to-moderator pebble ratio of 57% to 43% further redues the auray with whih the repeated-struture Centerline o.o E I Cavity i 1I o II I - I I I , 9f I I 4f ; R(m) Control Rod Region Mixture balls E Helium Flow Region -I. ' as.yt 4 I'l I-- Dummy balls , U RIl va l.- I 4 _ I 13 I _ I _ 16 18,1 L, r I I Z3! tl _L 7 O _ I 7 '8 _A.A - I 73 / ';3 _ 79 Z(m),I, Ir r= Figure 5-3. Referene Core Physis Calulation Model [5-2] 71

72 - i Zone , ,55,72,74, 75, 76, 78, 79 18,56, , 3, 25, 49 5, 52,54.66,67, 69,71, , , a 41b 42 43, ,59,61, I i mj Table 5-2 Homoenlzed.._... Nulide._--~~`- Denslies..~ In Refleetnr -. Znnea nulei/bhrner-m,. _ Carbon E OE E E E-2.OOOOOE E E E E E E E E E I1E E-2 Boron E E E E E-7.OOOOOE E E E E E E E E E E E-3 Desription Bottom refletor with hot helium flow borings Borated arbon briks Top graphite refletor Cold helium hamber Top refletor Top ore avity (helium filled) Dummy balls (= graphite with redued density) Bottom refletor struture Bottom refletor struture Bottom refletor struture Bottom refletor struture Bottom refletor struture Bottom refletor struture Bottom refletor struture Bottom refletor struture Bottom refletor struture Borated arbon briks E E E E E E E E-2 ( E-2)' E-2 (9.4339E-2) E-2 ( E-2) E-2 (9.4339E-2) E-2 ( E-2) E-2 (9.4339E-2) E E E E E E E E E E E E E E E E E-2.OOOOOE E E E E E E E-3 ( E-3) 1.4E-5 ( E-5) 1.4E-5 ( E-5) 3.645E-7 (5.655E-7) 3.464E-7 (4.7335E-7) 3.645E-7 (5.655E-7) 3.645E E E E E-3.OOOOOE E E E E E E E-3.OOOOE E E-3.OOOOOE+. _ Carbon briks Borated arbon briks Bottom refletor struture Bottom refletor struture Bottom refletor struture Bottom refletor struture Bottom refletor struture Borated arbon briks Bottom refletor struture Bottom refletor struture Bottom refletor struture Graphite refletor with ontrol rod holes Bottom refletor struture Bottom refletor struture Bottom refletor struture Bottom refletor struture Bottom refletor struture Borated arbon briks Carbon briks Bottom refletor struture Bottom refletor struture Bottom refletor struture Graphite refletor, old helium flow region Graphite refletor, old helium flow region Graphite refletor, old helium flow region Borated arbon briks Carbon briks 3raphite refletor struture Borated arbon briks Dummy balls (modeled as arbon briks) 1 Values in brakets are atom densities adjusted to aount for hannels in the graphite struture. 72

73 l s -- I 'a Q Ip a i I I Boron arbide rt m_,jim I Inner sleeve Outer sleeve Fe S o I t- Figure 5-4. Struture of the HTR-1 Control Rod [5-2] 73

74 I r, C.-,l l- I -,,,.. r Cavity I I Control rod region Mixture spheres Helium flow region w- Moderator spheres I = J :'II I I 1 I LI I I I Disharge tube i 1 Figure 5-5. Vertial Cross Setion of the MCNP Model of HTR-1 74

75 feature in MCNP4B an model the pebble-bed ore, beause all regular pakings of mono-sized spheres exept for simple-hexagonal have even oordination numbers [5-4]. This fuel-to-moderator sphere ratio was seleted by INET to ensure ritiality of the full ore Reator Struture The MCNP model onsists of the reator struture, whih inludes the graphite refletor and the borated arbon briks that surround the refletor, and the pebble-bed ore. A vertial ross-setional view of the modeled struture is shown in Figure 5-5. This model is idential to Figure 5-3 (inluding the zone numbers) exept for the presene of ontrol, irradiation and oolant hannels. These hannels are shown in the horizontal rosssetional view of the reator (Figure 5-6). refletor oolant hannel ore ontrol site shutoff site Figure 5-6. Horizontal Cross Setion of the MCNP Model of HTR-1 75

76 5.4.2 Control Absorbers Details regarding the stainless-steel joints between the ontrol absorber segments were not inluded in the benhmark problem definition. The model was prepared assuming that the joints preserve the annular geometry of the absorber segments to allow oolant flow. The omposition of the stainless steel is given in Table 5-3, and the geometry of the ontrol-rod hannels is otherwise modeled as speified in Table 5-4. The MCNP4B model of a ontrol rod is shown in Figure 5-7. The vertial position of eah ontrol rod an be hanged individually. boron.'_~ arbide s/s ;;O sleeve -S CZ U; '- helium, graphite horizontal view Figure 5-7. MCNP4B model of HTR- 1 ontrol rod Sine information about the ontrol-rod drive shafts was also not provided, the ontrol rods were modeled without suh omponents. The absorber-ball and irradiation hannels 76

77 were assumed to be empty (helium filled). The atom densities of the spatially homogenized zones that ontain the various hannels were orreted for the presene of these holes (shown in Table 5-2 in brakets). Table 5-3 HTR-1 Composition of Control-Rod Stainless Steel (density = 7.9 g/m 3 ) Element Wt% i Cr 18 Fe 68.1 Ni 1 Si 1 Mn 2 C.1 Ti.8 Table 5-4 HTR-1 Control Rod Geometry and VNaterial Speifiations Desription Value Units Control rod hannel radius 6.5 m Radial position of hannel entre 12.1 m Length of B 4 C segment 48.7 m Length of bottom metalli end 4.5 m Length of metalli joints 3.6 m Length of top metalli end 2.3 m Inside radius of inner stainless-steel sleeve 2.75 m Thikness of stainless-steel sleeve.2 m Thikness of gap between sleeve and B 4 C.5 m Thikness of B 4 C annulus 2.25 m Density of B 4 C 1.7 g/m 3 Length of ontrol rod m Core The speifiation of a 57:43 fuel-to-moderator pebble ore loading ompliates the modeling of the ore using perent ratio for the initial HTR-1 the repeated-struture feature of 77

78 MCNP4B. Exept for the simple (point-on-point) hexagonal paking, regular latties onstruted of simple unit ells with equal-sized spheres are haraterized by even oordination numbers and, therefore, annot be used to model an uneven fuel-tomoderator ratio while preserving the original geometry of the pebbles. As disussed in Chapter 3, three approahes are assailable. If a single BCC unit ell is used, then either the size or the density of the graphite moderator sphere an be redued in a manner that reprodues the speified fuel-to-moderator sphere ratio. Alternatively, a 'super' unit ell an be used ontaining a total of 1 spheres, whih permits the expliit loading of 57 fuel spheres and 43 moderator spheres. In the first method, the radius of the moderator sphere is redued from 3 m to m, and the size of the unit ell must be redued from m to m in order to preserve the paking fration (f=.61). This proedure assures that the fuel loading, the mass of heavy metal per unit ore volume, is the same as for the 57:43 perent random paking. The two-sphere ontent of the BCC unit ell minimizes the size adjustment for the moderator pebbles. The original size of the fuel sphere was maintained to preserve the effet of the single heterogeneity on the 238 U resonane esape probability, whih is expeted to dominate reativity effets, while minimizing the perturbation due to the double heterogeneity of the lattie. This method was used for the analysis presented in this report. In the seond method, whih has not been attempted to date, the graphite 43 3 density would have to be redued to -x 1.84 = 1.58 g/m 3 5 The super unit ell was onstruted from 2 x 5 x 5 = 5 unit BCC ells, with a = m. Therefore, the repeating ell spans the following ranges: < x < , 78

79 y < and <z< Beause eah BCC unit ell ontains two spheres, the large repeating ell holds 1 spheres in total. The 57 fuel and 43 moderator spheres were distributed deterministially but evenly among the ell lattie points. The alulated k of the ore was essentially idential to the unit BCC model ( at a ore height of 128. m vs. 1.5 ±.89 at m), although the exeution time of the super ell model was nearly an order of magnitude longer. Beause the results were generally found to be sensitive to the pattern used to distribute the spheres (see disussion in Chapter 6), the primitive unit ell approah is reommended. Details of the model may be found in the MCNP4B input file inluded in Appendix B. A sphere exlusion zone was used around the sides and at the top of the ore (see Chapter 57 3). The dimensions of the exlusion zone are 3x- = 1.71 m. An exlusion zone was 1 not required at the bottom of the fuelled portion of the ore, beause the onus was filled entirely with moderator spheres. Thus, fuel spheres ould be positioned suh that only moderator spheres overlapped the bottom boundary of the fuelled ore. The individual TRISO oated fuel partiles, whih were modeled, were distributed in the fuelled region of the fuel pebbles using a simple-ubi lattie expliitly. The dimensions of the SC unit ell were hosen to reprodue the speified uranium loading of 5 g per fuel pebble. Table 5-5 summarizes the geometry speifiations of the pebble-bed ore as modeled with MCNP4B. Details of the MCNP4B model appear in Chapter 3. 79

80 Table 5-5 HTR-1 Model Pebble-Bed Geometry Speifiations Parameter Value Units Fuel-to-moderator pebble volume ratio Radius of fuel pebble 3. m Radius of fueled region 2.5 m Paking fration.61 Moderator pebble radius m BCC unit ell size m SC unit ell size m The material ompositions of the fuel kernels and the graphite moderator that were used in the MCNP model are given in Table 5-6. The ompositions of the pyrolyti arbon and silion arbide layers in the rriso oating of the fuel kernels are as speified in the benhmark problem speifiation (Table 5-1). Table 5-6 Material Compositions of HTR-1 Pebble-Bed Core Isotope Graphite moderator: C l B lib total Atom Density (I/b-m) E E E E-2 Fuel kernel: 235 U E-3 238U E E-2 B E-8 "B E-8 total E-2 8

81 5.4.4 Borgn Content Impurities in graphite and uranium are speified in the benhmark problem definition in terms of equivalent onentrations of natural boron. The absolute isotopi abundane of 1 B is not given and the nominal value of 19.9% was used. This is a signifiant soure of modeling unertainty, sine a natural variation in 1 B from 19.1% to 2.3% has been measured [5-5] MCNP4B Calulations The HTR-1 physis benhmark problems omprise a set of ritiality alulations, in whih the effetive multipliation fator (keff) is determined for several ore onfigurations. These onfigurations are ahieved by varying the height of the pebble bed, adjusting the position of the ontrol rods, or hanging isothermally the temperature of the ore. Determination of the initial ritial loading is subjet to the unertainty assoiated with the partial fuel spheres at the ore boundaries. Moderator spheres play no role in the determination of the exlusion zone next to a graphite refletor. It was possible to set up the lower level of the fuelled region preisely, beause the bottom of the ore is filled with moderator spheres only. However, a separate orretion is still required at the top of the ore beause of the overlapping of spheres in the BCC lattie. The ritial loading is alulated using the redued ore volume, but the top exlusion distane should not be used when determining the ritial height. 81

82 The total reativity worth of the ten ontrol rods is derived from krff values with the ontrol rods first fully inserted and then fully withdrawn; similarly for a single ontrol rod. The differential reativity worth of a single ontrol rod is determined by alulating the k for different insertion depths. The temperature-dependent MCNP alulations in this study (benhmark problems B21, B22 and B23) did not inlude the reativity effet due to the isothermal expansion of the refletor. Benhmark problems B, B3 and B4 were analyzed using the standard ENDF/B-VI ross-setion data proessed at 3 K. Benhmark problems B22 and B23, whih orrespond to K (12C) and K (25 C) respetively, were estimated using temperature-dependent ross setions prepared at the University of Texas at Austin [5-6]. Benhmark problem B21 was analyzed using both libraries. All the ross-setion libraries were originally evaluated using the NJOY nulear data proessing system [5-7]. The University of Texas ross-setion libraries (UTXS) are only available at 3 K, 45 K and 558 K in the temperature range of interest. The preditions for benhmark problems B21, B22 and B23 were therefore obtained by interpolation using a polynomial fit of the keff values determined at the UTXS temperatures. Problem B21 was alulated using both the standard ENDF/B-VI and UTXS libraries in order to determine the bias assoiated with the different nulear data evaluations. In addition, the UTXS libraries do not inlude all the nulides in the stainless steel used in the ontrol rods. Instead, the UTXS ases (B21, B22 and B23) used iron with a redued density of 5 g/m 3 as was speified in the earlier version of the benhmark 82

83 problem definition [5-8]. The assoiated bias was determined by running problem B41 with the iron ontrol rods for both the ENDF/B-VI and UTXS ross-setion libraries. The results for these ases are presented in Tables 5-7 and 5-8, and the differential reativity worth of a single ontrol rod appears in Figure 5-7. The results are based on 1 million (ative) neutron histories per ase, whih redued the estimated 1-a statistial unertainties to -.1%. Twenty non-ative yles, with 5 neutrons per yle, were used to establish a uniform soure distribution. Table 5-7 MCNP4B Simulation Results for HTR-1 - ritial Height (h) / keff (k) Cross Setions Comments h = m ENDF/B-VI 3 K; air k = ,841 spherest h = 128. m ENDF/B-VI lie, 3 MPa k = ,97 spherest k = ENDF/B-VI 3 K k = UTXS 3 K k = UTXS 45 K k = UTXS 558 K k = UTXS K; polynomial fit' k = UTXS K; polynomial fit k= UTXS K; polynomial fit k =.9628 ±.9 ENDF/B-VI AProd, = mk; 3 K k = ENDF/B-VI APone = 14.9 ink; 3 K k =.853 ±.86 ENDF/B-VI Aprods = mk; s/s CR k = ENDF/B-VI Equivalent iron CRs k = UTXS Equivalent iron CRs,.,,.i T k(t) = E-5*T E-9*TL, (T in ok); error not alulated. 1 Atual initial ritial loading was 16,89 (fuel and moderator) spheres [5-3]...~~~~ ~~ 83

84 Table 5-8 Calulated Differential Reativity Worth of HTR-1 Control Rod Insertion Depth (m) k.f. p (mk)* ± t mk = 1 x Aklk Insertion Distane (m) Figure 5-8. Calulated Differential Reativity Worth of a Control Rod 5.6. Disussion Tables 5-9 and 5-1 summarize the preliminary HTR-1 physis benhmark results reported at the IAEA Researh Coordination Meeting for the Coordinated Researh Projet on the "Evaluation of High Temperature Gas-Cooled Reator Performane," held 84

85 Otober 18-22, 1999, in Beijing [5-1]. Both diffusion-ode and MCNP results alulated by several international organizations are shown. There is onsiderable unertainty in the predition of the initial ritial loading with MCNP4B, beause of the approximations needed to aount for the partial spheres at ore boundaries. The approah followed at MIT has been to model the pebble bed as aurately as possible within the limitations of the regular lattie representation of the irregularly paked ore. However, the randomness of the ore also leads to the anellation of errors, whih allows oarser approximations. For example, the MCNP4A model developed at INET uses a simple hexagonal lattie and ignores partial spheres; the smaller paking fration and the more leaky ore appear to ompensate for the additional fiel. Table 5-9 Diffusion Code Benhmark Results by Other CRP-5 Partiipants Case Chinal Indonesia/Japan 2 Russia 3 Comments B m 17. m m Critial height B k-eff 2 C B k-eff 12 C B k-eff 25 C B mk mk All CRs - full ore B CR1 - full ore B mk- - AllCRs m B mk - CRI m VSOP [5-9]; 2 DELIGHT/CITATION-I OOOVP [5-1, 5-1 1]; 3 WIMS-D4/JAR [5-12] 85

86 Table 5-1 MCNP Benhmark Results for Other Partiipants and MIT Case China' Russia 2 MIT' Comments BI m m m Critial height 16,821-16,89 Critial loading B (4) k-eff 2 C B ± ±.9 (4) k-eff 12 C B k-eff 25 C B mk mk mk All CRs -full ore B mk - CR1 - full ore B mk mk AllCRs - 126m B mk mk CRI - 126m MCNP4A and ENDF/B-V; -MCNP4A and ENDF/B-VI;: MCNP4B and ENDFIB-VI (UTXS). There is learly large variation in the overall benhmark results. Nevertheless, there is exellent agreement between the MIT ritiality alulations using MCNP4B and the VSOP preditions at INET. This lends redibility to the MIT modeling approah beause VSOP had been previously validated through usage at the AVR and THTR. However, the absene of planned tlux measurements in the TR- 1 refletor preludes the opportunity to test the ability of MCNP4B to model deep neutron penetration in graphite. The analysis of the HTR-1 initial ore using MCNP has identified several defiienies in the definition of the physis benhmark problem. The isotopi omposition of natural boron in the graphite moderator and refletor has not been speified. Similar unertainty is believed to be the main reason for the inaurate predition of initial ritiality in the Japanese HTTR reator. Insuffiient information is provided on the design of the ontrol rods, speifially the stainless-steel joints and the drive shaft. The presene of the ontrol rods is ompletely ignored in the INET referene model, beause the all-rods-out ase is simulated in VSOP using a region with low density (homogenized graphite plus void). 86

87 An inrease in the temperature of the refletor is expeted to redue the reativity of the ore, beause the derease in the graphite density would redue the number of thermal neutrons sattered bak into to the ore. This effet was investigated for benhmrrk problem B23 by assuming a uniform expansion of the graphite refletor orresponding to an inrease in temperature from 27 C to 285 C. The resulting derease in reativity of approximately.1% Ak/k is inonsequential. Finally, ritiality alulations using the University of Texas at Austin ross-setion library (UTXS) were found to differ from the orresponding results obtained with standard ENDF/B-VI data. The UTXS-derived results are approximately.14 to.49 % Ak/k more reative, with the worst agreement (.49% Ak/k) observed for benhmark problem B41 in whih all ten ontrol-rods were fully inserted. The use of redued-density iron instead of stainless steel for the ontrol-rod sleeves appears to be an aeptable approximation, the reativity differene being less than.1% Ak/k. 5.7 Summary The MCNP4B modelling methodology desribed in the previous hapters was applied suessfully to the HTR-I start-up ore. This work was performed at MIT as part of the US ontribution to the IAEA Coordinated Researh Program on the evaluation of HTGR performane. Thie predited initial ritial loading agreed with the atual loading within.3% (16,841 total spheres versus 16,89 measured). Measured ontrol-rod reativity worths were not available at this report's writing time; however, the values alulated with MCNP4B agree well with VSOP preditions reported by INET. 87

88 6. THE ASTRA CRITICAL FACILITY A single fuelled zone, a binary mix of fuel and moderator spheres, and a irular ore haraterized the ore onfigurations analyzed in the previous two hapters. A muh more ompliated situation is enountered in the ore design of the Pebble Bed Modular Reator (PBMR), whih inludes an inner refletor region made of moderator spheres and a transition zone between the pure moderator and fuel zones [6-1]. Beause this represents a signifiant departure from other pebble-bed ore designs, a set of ritial experiments were ommissioned by PBMR (Pty) Limited in the ASTRA faility at the Russian Researh Centre-Kurhatov Institute, Mosow, on a mok-up of the annular PBMR ore [6-2]. The MCNP4B analysis of these experiments is the subjet of this hapter. 6.1 Desription of the ASTRA Faility The ASTRA faility onsists of a graphite ylinder with an outer diameter of 38 m and a height of 46 m [6-3]. This graphite struture, whih serves as both the radial and lower refletors, surrounds an otagonal ore that is loated 4 m above the bottom and with an equivalent outer diameter of 181 m. The ore was loaded stohastially with fuel, moderator and absorber spheres. A speial rig was used to ensure a lear separation between an inner refletor zone, a mixed fuel and moderator zone, and an outer fuel zone [6-4]. The proedure used to fill the ore resulted in random dense loading with a paking fration of.636. Experiments were performed both with and without an upper refletor. The unrefleted ritial ore height was determined to be 269 m, whih yields a height- 88

89 to-radius ratio of 3. A horizontal ross-setional view of the faility is shown in Figure 6-1, while a vertial ross-setional view appears in Figure 6-2. Absorber spheres were added to fuel spheres in the ratio of 5 to 95 to ompensate for the relatively high uranium enrihment (21% 235 U) used in the fuel spheres. The absorber spheres onsisted of boron-arbide kernels embedded in a graphite matrix. Thus, the transition zone ontained a 5:47.5:2.5 mixture of moderator spheres (MS), fuel spheres (FS) and absorber spheres (AS) spheres. The impurities in the graphite of the spherial elements were speified by an equivalent natural-boron ontent of I ppm (by weight). Details on the ore loading and the various types of spheres appear in Tables 6-1 and 6-2 [6-3]. Table 6- ASTRA Core Speifiations Item Value (m) Inside radius of inner refletor zone 5.25 Outside radius of inner refletor zone Outside radius of mixed zone (87.5, 37.5), (37.5, 87.5), (-37.5, 87.5) Corner points of ore otagon (-87.5, 37.5), (-87.5, -37.5), (-37.5, -87.5) (37.5, -87.5), (87.5, -37.5) Average paking fration.636 Relative amounts of fuel and absorber 95/5 spheres in fuel zone Relative amounts of moderator, fuel 5/47.5/27.5 and absorber spheres in mixed zone The faility has a large number of hannels to aommodate ontrol and shutoff absorbers, instruments and soures. The radial refletor onsists of individual graphite bloks (25 m x 25 m x 46 m) eah with a 5.7 m-radius axial hannel, whih an be 89

90 sealed using a graphite plug. There are five steel-lad boron-arbide ontrol rods, eight similar shutoff rods and one aluminum regulating-rod. Table 6-2 ASTRA Spherial Elements Sphere Outer Radius Fill Radius Density of Loading Type (m (m) raphite (g/m) (g/sp here) MS 3. -_ 1.68 FS U AS B The Kurhatov Institute has to date provided only limited details on the geometry of these absorber rods. The ontrol and shutoff rods onsist of two sets of 15 half-height (187.5 m) steel tubes arranged in a irle (7.6 m radius) and held together by a spider (see Figure 6-3). The tubes ontain boron arbide (B 4 C) powder whose density is 1.53 g/m 3. The overall height of the ontrol-rod assembly is m. A hollow aluminum ylinder serves as the manual regulating-rod (see Figure 6-4). Speifiations for the ontrol and shutoff rods appear in Referene 6-3. The omposition of the regulating rod appears in Table 6-3. Table 6-3 ASTRA Regulating Rod Material Speifiation Element WI. % Cu Zn 2.2 Si Cr.25 Mn Fe.5 Al Remainder 9

91 There are six vertial experimental tubes that extend the entire height of the ore: a large aluminum tube in the entre of the refletor with an inner radius of 5 m; and five small aluminum tubes, with an inner radius of.5 m, whih are loated in line radially 5.5 m, 25 m, 45 m, 65 m and 8 m from the entre of the ore. Four additional small experimental hannels are loated in the refletor along the same radial line as the in-pile tubes. 6.2 Desription of Experiments Performed at ASTRA Faility A large number of experiments were arried out on the annular pebble-bed ore in the ASTRA ritial faility. The goal of these experiments was to generate data suitable for the validation of omputer odes used for the neutroni design of pebble-bed reators. These experiments inluded the following: * Determination of the ritial height for a given ore loading. * Investigation of the total reativity worth of ontrol rods: - individual ontrol rods, - dependene of rod worth on radial position in the refletor, - interferene between ontrol rods. * Determination of the differential reativity worth of a ontrol rod. * Investigation of the effet of varying the ore height on ontrol-rod worth with and without an upper refletor. * Measurement of the spatial distribution of relative reation rates in the ore. * Measurement of the reativity worth of ore omponents. 91

92 IAivirnn?7n ( I I CR - Control Filled Rfletor MR1 - Manual ontrol.41 B[l.,k SR - Safety E1-E6 - Experimental hambers IUnfilled Experimental hannels for Refltr Blok PIRZPT,ZII,ZRTA - Ionization hambers and neutron Neutron soure hannel Figure 6-1. orizontal Cross-Setional View of ASTRA Faility [6-3] 92

93 AI Constrution I Nrs~~~~ I 4 LO. 3 IN! Cv): o L.! it f II ;,,r- I I I I -. - I. _ i. I I I Ionization Chambers Core Mixing Zone Internal Refletor Neutron Soure Neutron Counter [l:gure t-2 Vertlal C'ros.-stlonal View \ASTRA o :alilty [6-3] ),3

94 S13!4 I I i J L54 i. I Qua C41 11 r Il i ' I F igure 6-3. Engineering Drawing o f ASTRA Control Rod 94

95 V U. Figure 6-4. Engineering Drawing of ASTRA Manual Regulating Rod 95

96 Full details of the preliminary results of measurements and alulations may be found in Referenes 6-4 and 6-5. As was the ase for the analysis of the HTR-PROTEUS and HTR-1 in previous hapters, only experiments related to the determination of ontrolrod reativity worths in the referene ore are onsidered below [6-6]. The reativity worths were measured using a reativity meter based on the solution of the inverse pointkinetis equations; the auray of the reativity measurement was within.5% 3 eff [6-4]. Table 6-4 summarizes the basi ritial onfiguration investigated at the ASTRA faility, whih orresponds to a total of 38,584 spheres loaded aording to the speifiations given in Table 6-1 and without the top refletor. Table 6-4 Basi Critial Configuration of ASTRA Faility Item Value Number of spheres (FE/ME/AE/Total) 27,477 / 9,659 / 1,448 / 38,584 Average height of pebble bed (m) Position of all ontrol rods Fully withdrawn Position of all shutoff rods Fu!y withdrawn Position of manual regulating rod (m) ± 26 Measured k-eff MCNP4B Model of the ASTRA Faility This setion desribes the model of the ASTRA faility that was developed using MCNP4B. It was possible to model the strutural omponents of the faility very aurately, although assumptions had to be made regarding the engineering design of the ontrol-rod assemblies. However, most representation of the ore. Both 'super' ell of the modelling effort foused on the and simple BCC latties were investigated. 96

97 6.3.1 Strutural Components A very detailed MCNP4B model of the ASTRA faility has been prepared, whih reprodues aurately the strutural omponents of the ritial assembly (see Figure 6-5). Beause doumentation provided by the Kurhatov Institute did not inlude a omplete desription of the ontrol-rod support struture, the model inorporates a hypothetial design of the assembly that holds the boron-arbide tubes (see Figures 6-6 to 6-12). In addition, no information was available on air humidity during the experiments. Therefore, the HTR-PROTEUS onditions were assumed to apply (see Chapter 4). Details of the MCNP4B model may be found in the input file in Appendix C. Central experiment - tube Fuelled zone Inner refletor Graphite blok with plug Mixed zone Graphite blok with hole Figure 6-5. MCNP4B Model of ASTRA Faility-Horizontal View 97

98 'I I I ix V, I i: Figure 6-6. Bottom of ASTRA Control Rod----Vertial Viexw Figure 6-7. Joint Between Two Halves of ASTRA Control Rod---Vertial View 98

99 111 I "I. ' ''' r r '. Ir: i J1 : r Figure 6-8. Lower Pin Holder in ASTRA Control Rod-l-lorizontal View Figure 6-9. Air-Filled Setion of Pins in ASTRA Control Rod---I-IHorizontal View 99

100 Figure 6-1. Absorber Setions of Pins in ASTRA Control Rod -----I-orizontal View Figure Upper Pin Holder in ASTRA Control Rod---lorizontal View 1

101 Figure Spider at Top of ASTRA Control-Rod Assembly Core Three aspets of the ASTRA annular ore must be addressed when developing the MCNP4B model. First, a regular lattie representation of the randomly paked ore must be hosen that applies evenly aross the three zones. The model is ompliated bv the presene of absorber spheres, whih prelude the use of a simple BCC lattie if an exat model of these spheres is required. Seond, provisions should be made for the partial spheres that arise at the periphery of the ore when using the repeated-struture feature of the ode. Third, the overlapping of fuel ad absorber spheres at the interfaes between zones must be approximated. 11

102 The only diret representation of the mixture of moderator, fuel and absorber spheres possible is a 'super' ell ontaining 4 spheres. Suh a repeating ell was onstruted from 4 x 5 = 2 unit BCC ells, among whih the three types of spheres were distributed. Other unit ells were also investigated, inluding hexagonal lose paked (CP) and body-entred tetragonal (BCT) latties. A ell based on an HCP lattie proved to be too omplex for the MCNP4B geometry routines. Moreover, beause all the spheres in the HCP unit ell are loated along the ell edges, the ontinuity of different types of spheres aross ell boundaries annot be guaranteed. The BCT lattie has been used suessfully by others [6-7], but is haraterized by two degrees of freedom-the width and height of the unit ell. This introdues a degree of arbitrariness into the model, beause the hoie of ell dimensions affets the ore leakage. Therefore, the BCC unit ell was kept as the basis for the ore representation, with the size of the ubi ell adjusted so as to reprodue the required paking fration. The basi dimensions of the unit ell and other key parameters appear in Table Table 6-5 ASTRA Core Lattie Parameters Parameter Units Value Paking fration.625 Spheres: Dimension of BCC unit ell m X-axis range of superell m < x < Y-axis range of superell m < x < Z-axis range of superell m < z < Coated Fuel Partiles: Dimension of SC unit ell m Absorber Kernels: Dimension of SC unit ell m

103 The repeated ell was onstruted by staking five layers of four BCC unit ells eah. The loading of eah unit ell depended on the ore zone under onsideration. Thus, in the inner refletor zone, only graphite moderator spheres appeared in the unit ells. In the fuel zone, the repeated ell onsisted of eighteen fuel-only unit ells and two fuel unit ells with an absorber sphere in the entre position. The two fuel-with-absorber unit ells were loated diagonally apart in the seond and fourth layers of the superell. The mixed zone repeated eil onsisted of nineteen moderator unit ells with a fuel sphere in the entre position, and one moderator unit ell with an absorber sphere in the entre position. The latter unit ell was loated in the third layer of the repeated ell. The exat details may be found in the MCNP4B input file in Appendix C.1, and ross-setional views of the ore appear below in Figures 6-13 to 6-15 (blue spheres are moderator, purple are fuel and green are absorber spheres). Figure ASTRA Detailed MCNP4B Model-Horizontal View 1 13

104 Figure ASTRA Detailed MCNP4B Model--Horizontal View 2 Figure ASTRA Detailed MCNP4B Model ---Vertial View 14

105 However, numerial experiments with the 'super' ell model have shown that the results are overly sensitive to the manner in whih the absorber spheres are distributed within the repeated ell. This arbitrariness, as well as the long exeution times, led to the onlusion that an approximate representation using a simple BCC unit ell with borated fuel spheres is more appropriate. In the simplified model, the boron ontained in the absorber spheres is smeared into the graphite shells of the fuel spheres (see Figures 6-16 and 6-17). Beause of signifiant self-shielding among the boron arbide kernels, alulations were performed using infinite latties of fuel spheres with expliitly modelled absorber spheres and borated fuel spheres. The boron onentration in the homogenized ase was redued by 17% in order to math the exat kl results, and the same borated boron omposition was used in the ASTRA model. The MCNP4B model of the infinite lattie with a 'super' ell representation of the fuelled ore region appears in Appendix C.2, that of the orresponding approximate infinite lattie in Appendix C.3, and of ASTRA with borated fuel spheres in Appendix C.4. The otagonal shape of the ASTRA ore preludes the use of an exlusion zone as a means for eliminating the ontribution of partial spheres at the ore boundaries (see Chapter 3). However, an alternative approah is to redue the paking fration of the pebble bed. The paking fration of.625, whih is speified in the ASTRA ritial faility onfiguration report, already appears to inlude suh a orretion. The atual paking fration of.636 an be alulated from the known ore loading and volume. 15

106 Figure Approximate MCNP4B Model of ASTRA Faility--Vertial View - - I... 'O I Figure Approximate MCNP4B Model of ASTRA Faility---Horizontal View 16

107 A related modelling onsideration involves the treatment of the (irular) interfaes between the ore zones. Beause of the overlapping of spheres and the different proportions of (borated) fuel and moderator spheres in the various zones, the boundaries between these zones should be shifted. Thus, applying the reverse approah to that used in the HTR-PROTEUS and HTR-1 models, the outer radii of the inner refletor and mixed zones are shifted inward by 1.5 m to m and m, respetively. For example, the spheres in the fuel;,d zone would penetrate on average 3 m into the mixed zone, while the fuel and absorber spheres in the mixed zone would penetrate into the fuelled zone by 1.5 m on average. Therefore, the net inward adjustment of the interfae is = 1.5 m. The interfae between the mixed and inner refletor zones is also shifted inwards by 1.5 m, beause of the 5% moderator sphere loading in the mixed zone. The resulting keff of the referene ore onfirms the validity of these modelling hoies. 6.4 Results of MCNP4B Analysis The results of the MCNP4B ritiality analysis of the ASTRA ore presented below were generated with the approximate model, whih used fuel spheres with borated shells and no exlusion zones. The effetive multipliation onstant (keff) for the referene ritial height of m was alulated to be with all the absorber rods fully withdrawn. All ases were run for a total of 1 million ative histories from a soure file generated in a separate run. The reativity worths of individual ontrol rods are given in Table 6-6, pairs of rods in Table 6-7, and ombinations of three rods in Table 6-8. The differential reativity worth of ontrol rod CR5 appears in Table 6-9 and Figure

108 Table 6-6 Individual Control Rod Worths in ASTRA Faility Control Rod Refletor Reativity Worth (%. k/k) Position Measured Calulated CR1 D CR2 H ± CR4 K CR5 H ± MR1 I Table 6-7 Reativity Worth of Two-Rod Combinations in ASTRA Reativity Worth (% Ak/k) Measured Calulated CR1 + CR CR2 + CR5-4.1 ± CR4 + CR Table 6-8 Reativity Worths of Three-Rod Combinations in ASTRA Control Rods Reativity Worth (f% Ak/k) Measured Calulated CR1 + CR2 + CR5-6.6 ± ±.13 CR1 + CR4 + CR ± CR2 + CR4 + CR ± ±.13 18

109 Table 6-9 Differential Worth of ASTRA Control Rod CR5 Control Rod Control Rod Reativity Worth (% Ak/k) Position Insertion (m) Measured Calulated ± ± ± ± ± ± % -.2% -.4% -.6% 2 -.8% _. */t',. :..:,.::. ;' ',. :. -,..... Experiment -1., ",'..',,-'.:,,,, - - _1.% / %' -1 4% " -1.6% " O -1.8% -2.% Insertion Distane (m) - < ' -Ca Figure Differential Worth of ASTRA Control Rod CR5 The radial position dependene of the reativity worths of ontrol rods CR2 and CR4 is given in Table 6-1. Shown in the table are the refletor positions of the ontrol rods and the distane from the ore boundary. 19

110 Table 6-1 Dependene of ASTRA Control Rod Worth on Distane from Core Control Refletor Distane Reativi Worth (% Ak/k) Rod Position (m) Measured Calulated CR2 H CR2 H CR2 H CR2 L1 i CR4 K CR4 L t The relative error is 2.5% (ff= ). 6.5 Disussion The ASTRA ritial experiments have highlighted the limitations of applying MCNP4B to the modeling of pebble-bed reators. The ASTRA ore has the following features, whih were not found in the HTR-PROTEUS faility or the HTR-1 reator: (a) an otagonal ore vessel; (b) absorber spheres that make up 5% of the fuelled portion of the ore; and () an annular ore. Polygonal ores are not ommon in atual reator designs, but absorber spheres may be required in start-up ores. The otagonal ore preluded the inlusion of a buffer zone to ompensate for the appearane of partial spheres at ore boundaries, and a redued paking fration (given by the experimenters) was used instead. The proedure used by the Kurhatov Institute to estimate the redued paking fration is unknown, but the resulting model orretly predited the ritial height of the ore. However, the mixing of absorber spheres with the fuel spheres ompliated the onstrution of an exat ore model onsiderably. The effetive multipliation onstant of 11

111 the ore was found to depend strongly on the manner in whih the relatively small number of absorber spheres was distributed in the ore lattie, espeially in the narrow mixed zone where the required ratio of absorber to fuel spheres is more diffiult to realize beause of boundary effets. The resulting variability in keff (- +1% Ak/k) and the long running time (-24 h) of the detailed model led to the development of a more approximate but equally aurate model, in whih the boron from the boron arbide kernels was dispersed in the graphite shells of the fuel spheres. Beause dispersed boron leads to more absorptions than lumped boron arbide, its effetive atom density should be redued by an appropriate amount. The need for this orretion an be demonstrated by onsidering the optial path of a neutron in the absorber sphere. For a spherial B 4 C kernel with a diameter of 3 Am, the average hord length is = 4V =.2 m. The optial thikness for a single kernel is so r = IalO = (83.45)(.2) =.17, and the thermal flux depression in the absorber kernel relative to the moderator is approximately given by the semi-empirial orrelation m,,.87ro + exp(-.35r ) = 1.9 [6-8]. As noted earlier, the atual atom density orretion of 17% was dedued from diret numerial experiments. The annular ore appears to pose a more serious omputational hallenge for MCNP4B partly beause of the fuzzy interfaes between ore zones, but also beause of the greater neutroni deoupling aused by the large entral refletor region and the presene of boron absorber among the fuel spheres. The deoupling was evident from the sensitivity of the MCNP4B results on the definition of starting fission soure and the number of 111

112 neutron histories used to determine the effetive multipliation onstant. This possibly explains the differenes observed in the reativity worths of the symmetrially positioned ontrol rods CR2 and CR5. There appears to be a flux tilt aross the ore, whih hanged the reativity worths of CR4 and CR5 by -1%, CR2 by 2.72% and CR1 by -2.82%. Other deviations between the alulated and measured reativity worths are related to the unertain design of the ontrol rods and the manual regulating rod, whih show up as biases of % Ak/k (see Figure 6-14) and.27% Ak/k, respetively. Values of the interferene oeffiient for the two-rod and three-rod ombinations an be alulated from the results in Tables 6-6 to 6-8. The interferene oeffiient is defined as = AR/" p,, where AR is the total reativity worth of the entire rod system, pi is the worth of ontrol rod i, and n is the number of ontrol rods in the system [6-4]. The results are presented in Table Table 6-! 1 Interferene Coeffiients for ASTRA Rod Combinations Control Rods Measured Calulated CR1 + CR CR2 + CR CR4 + CR CR1 + CR2 + CR CR + CR4 + CR CR2 + CR4 + CR As disussed in Referene 6-4, Table 6-11 shows that a omplex pattern of interferene exists between the ontrol rods in the ASTRA faility. For ontrol rods CR2 and CR5, 112

113 whih are positioned symmetrially 18 apart, the interferene oeffiient is greater than unity ( = 1.9). Yet for ontrol rods CR4 and CR5, whih are 45 apart, the interferene oeffiient is less than unity ( =.96). The largest interferene oeffiient was measured for the ombination of CR 1, CR2 and CR5 (E = 1.11). 6.6 Summary A detailed MCNP4B model was developed of the PBMR mok-up in the ASTRA ritial faility at the Kurhatov Institute. This is an annular ore omposed of an inner refletor zone, a fuelled zone with 5% absorber spheres, and a transition zone with 5% moderator, 47.5% fuel and 2.5% absorber spheres. A primitive BCC lattie represents the randomly paked ore, with the boron from the absorber spheres smeared into the shells of the fuel spheres. A simple-ubi lattie is used to arrange the expliitly modelled oated fuel partiles inside the fuel spheres. The model predits the ritial height of the referene ore exatly ( ), although the more neutronially deoupled annular ore appears to make the spatial flux shape sensitive to the starting fission soure and number of neutron histories. As a result, the reativity worth of some ontrol rods was predited only within 1% of measurement. Greater auray would be required before this MCNP4B methodology an be applied to the annular PBMR ore. 113

114 7. MCNP4B MODELLING OF PEBBLE BED CORES WITH BURNUP The previous hapters established a method for the MCNP modelling of pebble-bed ores with fresh fuel. However, reator design and analysis is most frequently arried out using a ore with an equilibrium burnup distribution. The isotopi omposition of the fuel in most reators an be determined using a Monte Carlo burnup ode like MONTEBURNS [7-1] or MOCUP [7-2], whih ouple MCNP4B [7-3] to ORIGEN2 [7-4]. However, the reyling of fuel spheres in pebble-bed reators ompliates this alulation onsiderably, beause of the ontinuous movement and mixing of fuel in the ore. An alternative approah is presented in this hapter, whih utilizes a link between MCNP4B and VSOP94 [7-5]. The fuel management routine in VSOP94 is used to establish the equilibrium ore, and the program MCARDS is used to prepare the orresponding MCNP4B material ards from the nulide atom densities of the depleted fuel that were alulated by VSOP94. This method is demonstrated on the Pebble Bed Modular Reator. 7.1 The Pebble Bed Modular Reator The 268 MW(t) Pebble Bed Modular Reator (PBMR) urrently being designed in South Afria is the latest development in the ontinuing evolution of pebble-bed reators [7-6]. The advantages of modular HTGRs were already reognized by the 198s, even though higher fuel enrihments are required to ompensate for greater neutron leakage [7-7]. The inherent safety of a small reator unit (- 2 MWt) has the potential for signifiant ost redutions, beause of its simpler design, standardization and the elimination of a gastight ontainment building. Two modular pebble-bed reators were designed and liensed in 114

115 Germany by the late 198s: the 8 MW(e) HTR-MODUL by Siemens/Interatom [7-8] and the 1 MW(e) HTR-1 by HRB/BBC. Interest in an inner refletor surfaed in the early 199s, with the inlusion of a entral graphite olumn in the 5 MW(e) Advaned High Temperature Reator [7-9]. The ability to loate ontrol rods in the entral olumn of the AHTR-5 eliminated the need for the THTR-style in-ore rods, whih had to be pressed into the pebble bed [7-1]. An annular geometry was also proposed for inreasing the power of a modular pebble-bed reator from 2 MW(t) up to 35 MW [7-11]. The flux flattening effet of the entral refletor also inreases the reativity worth of ontrol rods loated in the side refletor. The PBMR features 18 ontrol rods and 17 small-absorber-ball shutdown hannels in the stati side refletor, and a moving inner refletor reated by dropping only graphite moderator spheres into the entre top of the ore. Vertial and horizontal ross-setional views of the reator are shown in Figures 7-1 and 7-2, and detailed speifiations of the PBMR referene ore and fuel sphere appear in Tables 7-1 and 7-2 [7-6]. Fuel spheres are dropped into the ore from nine equally spaed feeders loated on a irle of m radius, and are removed from the ore through a disharge tube at the bottom of the vessel. The fuel spheres are sanned with a y-detetor to determine the burnup and are reinserted at the top if the desired disharge burnup has not been reahed. 115

116 Table 7-1 PBMR Referene Core Speifiations Parameter Value Thermal power rating 268 MW Core diameter 3.5 m Average ore height 8.52 m Average burnup 8, MWd/tU Refuelling strategy Multiple pass (x 1) Fuel 8.13 at. % ( 235 U) Average irradiation time of fuel 874 days Number of fuel zones 2 Moderation ratio (N/Nu) 428 Number of fuel spheres 334, Number of graphite spheres 11, Perent fuel in entral/mixed/fuel zones /5/1 Thikness of top refletor 1.35 m Thikness of bottom refletor 2.61 m Width of radial zones in side refletor 6/13/22.5/19/14.5 m Graphite density in top refletor 1.54 g/m 3 Graphite density in bottom refletor 1.53 g/m 3 Graphite density profile in side refletor 1.7/1.17/1.7/1.48/1.7 g/m 3 Table 7-2 Referene Speifiations for PBMR Fuel Elements Parameter Value Fuel Sphere (FS): Pebble radius 3. m Radius of fuelled zone 2.5 m Uranium loading 9. g/fs Graphite density 1.75 g/m 3 Coated Fuel Partile: Diameter of UO2 kernel 5 Am Density of UO2 1.4 g/m 3 Coating materials C/PyC/SiC/PyC Layer thiknesses 95/4/35/4 gm Layer densities 1.5/1.9/3.18/1.9 g/m 3 116

117 Figure 7-1. A Vertial View of the PBMR [7-6] 117

118 FO UL S 1 NI 27& SEVIION "(:f-'c' Figure 7-2. A Horizontal View of the PBMR Core [7-6] 7.2 The VSOP94 Model of the PBMR The two-dimensional (R-Z geometry) VSOP94 model of the referene PBMR ore is shown shematially in Figure 7-3 [ 7-6 ].t The model inludes details of the ore, the refletors and the borated arbon thermal shields. The reator pressure vessel, the ore barrel and the assoiated helium gaps are lumped together in a single annular region. The I The VSOP model of the PBMR was kindly provided by Dr. E.J. Mulder, PBMR (Pty) Limited. 118

119 ontrol rods are modelled by homogenizing the boron arbide absorber into the surrounding graphite material. The various hannels for the shutdown system and helium oolant are modelled by reduing the density of the appropriate graphite regions. I If 3.DOEO42 CS 2.OOE'W 5,CoQ!1. Figure 7-3. VSOP94 Model of the PBMR [7-6] The model of the ore omprises 57 equally sized regions alled layers, eah of whih ontains a mixture of 1 different fuel bathes. t These bathes represent the number of times that the fuel spheres have been through the ore, from the first pass (bath 1) to the last pass (bath 1). The burnup of eah bath is alulated individually using a fissionprodut hain of 44 isotopes (see Table 7-3). The seond member of the hain is a nonsaturating fission produt hosen by omparison with ORIGEN-JOL-II ode preditions, whih orresponds to low absorbing fission produts not modeled expliitly [7-12]. The 43 expliit fission produts over 98.2% of the total fission-produt absorptions, while the non-saturating fission produt aounts for the remaining 1.98%. f Eah layer also ontains an I th bath in order to aommodate the presene of moderator spheres in the inner refletor. 119

120 Table 7-3 Fission Produt Chain 44 in VSOP94 Fuel depletion is modelled by means of burnup steps. Thus, approximately every 9 days, eah layer and its assoiated bathes are moved down to the position of the next layer. This movement of fuel ours in hannels, whih are used to reprodue the harateristi flow of pebbles within the ore vessel. This flow pattern was established by Pohl and Neubaher during the operation of the AVR [7-13], and from measurements performed by Kleine-Tebbe during the final defuelling of the THTR [7-14]. The layers at the bottom of the ore are disharged, and orresponding bathes (i.e., with the same number of passes through the ore) from different hannels are grouped and mixed together. The bath numbers are then inremented (to initiate an additional pass through the ore) and reinserted into the various hannels. The oldest bathes are disharged from the ore, while a tenth of the volume of eah top layer is filled with fresh fuel. The neutroni alulation is performed using 29 spetral zones, whih onsist of userspeified groupings of layers. A similar proedure is used for the refletor regions where 25 spetrum zones are defined. The temperatures of the spetral zones are established 12

121 using the thermal-hydraulis module in VSOP94. The referene VSOP94 input file is inluded as Appendix D Link Between VSOP94 and MCNP4B A onvenient way to model an equilibrium pebble-bed ore with MCNP4 is to perform a fuel management study with VSOP94 and transfer the resulting fuel ompositions to an MCNP4B model of the same reator. The most aurate method for establishing a link between the two odes would be to reate a superell VSOP94 model of a fuel kernel in a given layer, and deplete the fuel to the burnup determined from a separate VSOP94 fuel management study (see Setion 7.6 for further details). The resulting fuel ompositions ould then be used in a detailed MCNP4B model of the pebble-bed ore, whih would inlude an expliit representation of the oated fuel kernels and the fuel spheres. A more approximate but diret approah is presented here, in whih the nulide densities obtained from a whole-ore VSOP94 alulation are used diretly in an MCNP4B model of the reator. An MCNP4B model of the PBMR equilibrium ore was developed, whih uses a regular lattie of spheres with homogenized fuel and graphite interiors. This lattie is subdivided into annular regions that reprodue exatly the ore regions of the VSOP94 model. The fuel ompositions used in these regions are the orresponding bath-averaged VSOP94 nulide densities, whih are adjusted to allow for the effet of fuel homogenization on resonane absorptions in 23 8 U and 24 Pu. 121

122 7.3.1 Modifiations to VSOP94 Several modifiations had to be made to VSOP94 in order to extrat the neessary fuel ompositions. These hanges affeted subroutine CH 1 in hain 1 where the main problem definition data are read, and subroutine VORSHU in hain 7 where fuelling operations are simulated. Subroutine VORSHU is alled before fuel shuffling takes plae. It reads instrutions for the next burnup yle, alulates average bath properties and aounts for isotope deay during the reshuffling. The subroutine was modified to alulate the total atom numbers and reation rates for eah isotope per layer, and write this information to data files FORT.98 and FORT.99, respetively. Also written to file FORT.98 is the yle number, the layer number, the total number of all nulides in the given layer, the volume of the layer, and the paking fration. Two fields were added to the printout options ard V21 [7-5], whih speify the refuelling yle whose fuel ompositions are required. The speifiations of the modified ard are shown in Table 7-4, and listings of the soure ode are inluded as Appendix D Program MCARDS VSOP94 output file FORT.98 ontains, for eah layer, the total number of all nulides, the volume and the paking fration. This is followed by the number of atoms for eah nulide used in the VSOP94 alulation (65 nulides are used in the PBMR model). Output file FORT.99 ontains the total absorption reation rates that orrespond to these nulides. The FORTRAN program MCARDS reads these data and prepares an MCNP4B 122

123 material ard for eah layer. Beause a one-to-one mapping does not exist between the nulides available in the VSOP94 and MCNP4B libraries, ' B is added suh that the total absorption reation rate in eah layer is preserved. The materials ards are written onseutively to file MCARDS.DAT starting at material label M1 for the first layer with omment ards that speify the total atom density for the given layer, whih an be "ut and pasted" into the MCNP4B input file. The listings of the soure ode are inluded as Appendix D MCNP4B Model of the PBMR Beause detailed engineering drawings of the PBMR were not available, the MCNP4B model was based on the two-dimensional VSOP94 model of the reator. Key aspets of the VSOP94 model of the PBMR ore and strutural omponents were dupliated, inluding the pebble flow hannels and layers (Figures 7-4 and 7-5). The ontrol rods, and the shutdown and helium oolant hannels in the side refletor were modelled expliitly. However, the HTR-1 ontrol rods desribed in Chapter 5 were used instead of the proprietary PBMR design (Figure 5-7). The model also uses the oval shutdown hannels from the Chinese reator (Figure 7-6). A simple BCC lattie without exlusion zones was used to represent the randomly paked pebble bed. This lattie was subdivided into layers exatly as in the VSOP94 model of the ore. The spheres in eah layer onsisted of the homogenized mix of arbon, silion, heavy metal and fissionprodut nulides prepared with program MCARDS from the orresponding VSOP94 layer-averaged atom densities. Further details may be found in the MCNP4B input file inluded as Appendix D

124 Table 7-4 Modified VSOP94 Card V21 Card V21 Format ( 814) 1 IPRIN(1) Spetrum alulation: = : Thermal self shielding fators only. = 1: Same as, plus averaged thermal ross setions. = 2: Same as 1, plus fine-group neutron fluxes. = 3: Same as 2, plus broad-group averaged ross Setions for materials with onentration >. = 4: Same as 3, for all materials. 2 IPRIN(2) : No output. = 1: Print layout of bathes before shuffling. = 2: Same as 1, plus atom densities (only in ombination with IPRIN(3) 2 ). 3 IPRIN(3) Bumup alulation: = -1: Global neutron balane. : Detailed neutron balane. = 1: Same as, plus harateristi data for all fuel bathes. 4 IPRIN(4) : Skip spetrum alulation if a set of ross setions is available. Instrutions on ard V22 are negleted. = 1: Repeat spetrum alulation as defined on Card V22. 2: Same as 1, but only for the thermal spetrum. = 3: Same as 1, but not for zones without heavy metal (refletors). 4: Same as 2, but not for zones without heavy metal (refletors). 5 IPRIN(5) Cyle whose fuel ompositions are to be written to file. 6 IPRIN(6) II = : Do not write fuel ompositions to file. 1: Write fuel ompositions to file. 124

125 Top refletor Control rod hannel Helium avity Channel Inner refletor I Channel 2 Mixed zone Side refletor Channel 3 Fuel zone Channel 4 Fuel zone Channel 5 Fuel zone Bottom refletor Disharge pipe Figure 7-4. MCNP4B Model of the PBMR-Vertial View 125

126 Coolant hannel Control rod Shutdown site Inner refletor Fuel zone Side refletor Figure 7-5. MCNP4B Model of the PBMR--Horizontal View Figure 7-6. Channel for Small Absorber Balls in MCNP4B Model of PBMR 126

127 7.5 MCNP4B/VSOP94 Results Preliminary analysis of the PBMR using the MCNP4B/VSOP94 model desribed above, but with unadjusted VSOP94 nulide densities, yields an effetive multipliation onstant of Typial ore power and neutron flux distributions are shown in Figures 7-7 to 7-9 for fully homogenized layers. MCNP4B was unable to generate prompt fission power (F7) and neutron flux (F4) tallies for segments defined via an FS tally segmentation ard for the detailed ore. Although this result demonstrates in priniple the linkage between VSOP94 and MCNP4B, further developments are needed before the method an be applied to atual reator analysis. VSOP94 performs the diffusion alulations on homogenized regions of the ore, with self-shielding fators used to orret for double heterogeneity and a diffusion orretion to allow for neutron streaming in ore voids (see Chapter 2). Neutron streaming is handled in MCNP4B by modelling expliitly the lattie of spheres. Figure 7-7. Power Density in PBMR Equilibrium Core Control Rods 1/4 Inserted (z = m) E :,I - O8 -,ton -. (b 2- - ~1Ui -- 1' etl"- ( - Position (m) 1 7.E+-8.OOE+ * 6.E+-7.E+ 5.E+OO-6.E+ * 4.E+OO-5.OOE+ o 3.E+OO-4.E+ 3 2.E+OO-3.E+ 1.E+-2.E+ O.OOE+-1.OOE+ 127

128 Figure 7-9. Thermal Neutron Flux in PBMR Equilibrium Core Control Rods 1/4 Inserted (z = m) * 3E E+14 *2.5E+14-3E+14 * 2E E E+14-2E+14 1E E+14 *5E+13-1E+14-5E+13 I,f s 128

129 However, the nulide densities alulated by VSOP94 for eah layer must also be adjusted to ompensate for the approximate MCNP4B representation of fuel-sphere interiors. The effet of this homogenization was shown to derease the reativity of the ore -4% Ak/k by using an idential MCNP4B model in whih the ore layers were fully homogenized. Therefore, the 238 U (and 24 Pu that ontributes to the resonane absorptions at high burnup) atom densities alulated by VSOP94 should be redued (i.e., adjust,2=niao by modifying Ni instead of ao) to ompensate for this hange in reativity. This would result in a keff of -1.4 if temperature effets are not inluded in the simulation. Two-dimensional VSOP analysis of the PBMR ore has established a total temperature reativity oeffiient of x 1 ' 5 Ak/ C (see T-.le 7-5) [7-6], whih would redue the reativity of the ore by -4% Aklk assuming an average fuel temperature of 95 C. The MCNP4B alulations reported here were performed at room temperature, beause rosssetion libraries at typial HTGR operating temperatures were not available. Table 7-5 Temperature Reativity Coeffiients in the PBMR [7-6] Reator Component zk/ C Fuel x 1-5 Moderator in fuelled region of ore -3.3 x 1-5 Central refletor +.93 x 1-5 Outer refletors x 1-5 Total x

130 7.6 Disussion Monte Carlo methods are beoming the tool of hoie for the physis design and analysis of nulear reators. Models prepared with a Monte Carlo o:e suh as MCNP4B re apable of alulating very aurately all key ore parameters, inluding the effetive multipliation onstant, the reativity worths of ontrol rods and shutdown absorbers, fission powers and neutron fluxes. The ability of MCNP4B to transport photons also makes it useful for shielding and heat deposition alulations. Furthermore, advanes in omputer hardware have made lengthy Monte Carlo runs ost effetive. Full-ore alulations are inreasingly being performed with ode systems that ouple Monte Carlo and stand-alone fuel depletion odes. An example of suh a Monte Carlo burnup ode is MOCUP, whih ouples MCNP4B and ORIGEN2. However, this ode annot be urrently applied to pebble-bed reators for several reasons: (a) the reirulation of fuel spheres in the ore; (b) modelling the 1 4 disrete fuel partiles in eah fuel sphere in a large pebble-bed ore is beyond the apabilities of the odes; and () the number of MCNP4B runs required to reah an equilibrium burnup distribution would be omputationally prohibitive. Therefore, the best approah at this time is to perform the fuel management study separately using a diffusion- or transport-theory ode and use the resulting fuel ompositions in a snapshot MCNP4B alulation with a very detailed model of the reator. The method desribed in this hapter for obtaining the MCNP input for the omposition of fuel spheres in a pebble-bed ore with burnup is limited in its auray, beause of the need to aount for the effets of homogenization on resonane absorptions. Therefore, a 13

131 different approah is needed if the resulting MCNP4B model is to be of benhmark quality. Suh a model should treat the double heterogeneity of the pebble bed ore with the same degree of auray as the HTR-PROTEUS and HTR-1 models desribed in Chapters 4 and 5 (although one possible simplifiation is to lump the oatings of the fuel kernels together with the graphite matrix [7-15]). The omposition of the fuel kernels ould be generated diretly using a lattie ode with an aurate burnup apability, or a Monte Carlo burnup ode. The proposed method is shown shematially in Figure 7-1 for the Duth WIMS/PANTHERMIX ode system (see Chapter 2), although VSOP94 ould also be used to perform these alulations. In the suggested proedure, a fuel management study would be performed to determine the burnup distribution in the ore for a given refuelling strategy. These burnups (in MWD/THM) would be alulated using diffusion theory for a finite number of ore regions (or layers in VSOP94). A neutronis ode would then be used to deplete the fuel to the required burnup with a standard superell model onsisting of a single fuel sphere, with an expliit representation of the oated fuel partiles, surrounded by a driver region. This proedure is similar to the single pebble, multi-kernel burnup alulations reported in Referenes 7-15 and Beause eah fuel sphere is expeted to visit every region of the ore during its multiple passes, an average fuel omposition orresponding to the equilibrium ore ould be used for the driver fuel. Any number of odes may be used to perform the superell depletion alulation, inluding MOCUP and WIMS [7-18]. The model would have to be run to generate 131

132 separate fuel ompositions for the burnup in eah ore region, and the MCNP4B material ards would be prepared with a modified version of MCARDS. A more diret approah, whih does not rely on a diffusion-theory ode, would be to use the MONTEBURNS Monte Carlo burnup ode to perform the entire fuel management study. The ore would be modeled as in Setion 7.4, although with an expliit representation of the double heterogeneity. Simple annular zones ould be used to simplify the generation of flux and power distributions. The same fuel omposition would be used in all fuel spheres in a given ore region. MONTEBURNS already has the apability for shuffling fuel, but the ode would have to be modified to perform the mixing of fuel spheres with different burnup that ours when disharged fuel spheres are reinserted at the top of the ore. 7.7 Summary An approximate method for the MCNP4B modelling of pebble-bed reators with burnup was presented. In this approah, the nulide densities of the homogenized layers in the VSOP94 model of the reator are used in the orresponding MCNP4B model with an adjustment for its expliit representation of the sphere lattie. The method was demonstrated in priniple on the PBMR equilibrium ore, although temperaturedependent ross setions would have to be generated for MCNP4B before the model an be applied to reator design problems. Two alternative approahes were proposed, whih takes advantage of the ability to model the double heterogeneity of the PBMR ore diretly with MCNP4B. In the first method, 132

133 whih uses a lattie ode suh as WIMS or the Monte-Carlo burnup ode MOCUP, a superell model of a fuel kernel would be used to deplete the fuel to the desired burnup in a representative ore environment. The resulting nulide densities ould then be used without adjustment in a detailed (doubly heterogeneous) MCNP4B model. In both this and the MCNP4BNSOP94 approahes, average fuel ompositions are generated for a finite number of ore regions (similar to the layers of VSOP94) to make the problem omputationally manageable. In the seond method, the Monte Carlo burnup ode MONTEBURNS would be used to perform the entire fuel management study diretly. However, this approah would require modifiations to the ode to failitate the reyling of fuel spheres with different burnup. 133

134 . ear Data STEP I t _. PANTHERMIX Neutron Transport and Burnup Lattie Code (WIMS) Cross Setion Proessing Utility Programs (New) I Mirosopi Cross-setions Group parameters Diffusion Theory Code..[ m STEP II Superell Burnup Calulation Temperature Distrihltinn Thermohydrauli Code (THERMIX) Equilibrium ore power distribution A. I r-- 11 l Dplted ue Composition at b/u Intervals Calulate fuel ompositions at given b/u MCARDS _.I Vr. r -- MCNP material ards 1 I Core Burnup Distribution MCNP4B/C or MCNP-BALL snapshots Figure 7-1. Proposed MCNP-Based Code System for Pebble-Bed Reators with Burnup 134

135 8. PLUTONIUM PRODUCTION IN A PEBBLE BED REACTOR Nulear power is expeted to play a signifiant role in meeting future eletriity needs while reduing emissions of air pollutants and greenhouse gases [8-1]. However, several issues ontinue to trouble government and industry poliymakers and segments of the publi. These inlude nulear power plant safety, waste, eonomis and weapons material proliferation. The modular pebble-bed reator is a leading ontender in a new generation of nulear reators, and is reognized for its simple design, thermodynami effiieny, natural safety and environmental friendliness. The graphite pebbles with the embedded TRISO oated fuel partiles serve as an exellent waste form for the diret disposal of spent fuel in a geologial repository [8-2]. The fous of this hapter is the proliferation resistane of pebble-bed reators. Preliminary alulations were performed with the VSOP94, MCNP4B and ORIGEN2 physis odes to estimate the prodution of plutonium in a pebble-bed reator. The ESKOM Pebble Bed Modular Reator (PBMR) was used as the referene reator [8-3]. The study examined the isotopi omposition of normally disharged fuel, first-pass fuel spheres and depleted-uranium prodution spheres'l Modeling Methods A desription of the VSOP94 and MCNP4B physis odes appears in Chapter 2. The VSOP94 suite of odes, whih relies on diffusion theory to solve the neutron transport equation, an be used to perform fuel management studies for pebble-bed reators with multiple-pass refuelling strategies [8-4]. The Monte Carlo ode MCNP4B is apable of aurate alulations involving the transport of neutrons and photons, inluding the determination of 238 U apture rates [8-5]. ' The onept of depleted-uranium prodution spheres was proposed by J.S. Herring of the INEEL. 135

136 ORIGEN2 is a general-purpose point-depletion and generation ode for alulating isotopis, deay heat, radiation soure terms and radioativity levels [8-6]. MOCUP is a Monte Carlo burnup ode that ouples MCNP4B and ORIGEN2 [8-7]. Models of the PBMR were used to examine the amount and isotopi omposition of plutonium present in the normally disharged fuel spheres, fuel spheres diverted after a single pass through the ore, and speial prodution spheres loaded with depleted UO2. The analysis onsisted of a superell alulation of plutonium prodution with speial spheres using MCNP4B, and a fullore simulation of normal fuel spheres using VSOP Superell Model The superell model represents an attempt to represent aurately the environment that the prodution pebble experienes during its passage through the ore. It onsists of an MCNP4B model, in whih a single prodution pebble is plaed in the enter of a refleted spherial ore onsisting of a regular lattie of driver fuel pebbles (see Figure 8-1). The nulide onentrations of the driver fuel were extrated from the VSOP94 model of the PBMR and orresponded to an average over all regions of the equilibrium ore (see Chapter 7). The size of the superell was adjusted to yield a ritial assembly (kff - 1), and its power was normalized so as to math the VSOP94 ore-averaged total neutron flux. The 239 Pu prodution is estimated from a tally of the 238 U(n,y) 239 U reation rate for the stand-alone MCNP4B, or by traking the isotopi omposition of the prodution ball in a MOCUP depletion alulation; the omposition of the driver fuel is stati. The superell model permits the modeling of the inner refletor and transition zones. 2 The VSOP model of the PBMR referene ore was provided by Dr. E.J. Mulder, PBMR (Pty) Ltd. 136

137 LZZZ Prodution Prodution Driver pebble ell ore Figure 8-1. Superell MCNP4B Model of Prodution Sphere Prodution Pebbles Three onfigurations of plutonium prodution pebbles ontaining depleted (.2% 2 35 U) UO, were onsidered (see Figure 8-2): () a solid ore (2.1 m radius); (h) ten alternating shells (2 mm thik) of depleted fuel and pyrolyti arbon; () a densely paked simple ubi array of BISO oated depleted fuel partiles (.25 m inner and.38 m outer radius of pyrolyti arbon oating, and a.5 paking fration). The BISO oating does not inorporate a silion-arbide layer, and using suh fuel partiles would avoid problems assoiated with the removal of silion arbide during reproessing (the depleted uranium will not add a signifiant amount of fissionprodut ontamination to the reator ooling system). 137

138 i (67) (h) (C) Figure 8-2. Different onfigurations of prodution pebbles: (a) solid ore; (h) shells; () dense BISO. 8.2 Analysis and Results The following setions provide some details of the analysis performed and a summary of the results obtained. Plutonium prodution in regular fuel pebbles was analyzed with VSOP94, while the speial prodution pebbles was investigated using the superell model desribed above. A further disussion of the proliferation resistane of pebble-bed reator ftiel yles appears in Referene 8-8, and the simple-ell MCNP4B and MOCUP analysis of plutonium prodution in pebble-bed reators performed at the INEEL may be found in Referene I Regular Fuel Pebbles VSOP94 analysis of the referene PBMR ore showed (see Appendix E.2) that a diversion of 157, spent fuel pebbles would be needed over 1.2 years to obtain 6 kg of 239Pu (whih is taken to be a weapon's worth of plutonium). However, as is shown in Table 8-1 for a fuel disharge burnup of 8 NMWd/kgU, the isotopi omposition of plutonium in spent fuel at high burnup is not well suited for nulear weapons prodution. Moreover, the perentage of 39 Pu is lower than 4%, whih is a reognized level tor lower proliferation risk [8-9]. 138

139 Table JIdAUaLU WILI V a.jry1 '. Fuel pebbles, whih are diverted after a single pass through the ore, have a more favourable plutonium isotopi omposition (Table 8-2). However, beause of the shorter irradiation times (on average 73 days per pass), as many as 258, fuel pebbles would have to be diverted for 6 kg of 239 Pu (the amount of 239 Pu needed for a weapon varies between 4 and 8 kg). Sine fuel pebbles are normally reinserted at the top of the ore, the diversion of all first-pass fuel pebbles would result in an exessive loss of reativity. Therefore, the duration of the diversion would be longer than the two years alulated for the normal disharge rate of suh pebbles unless fresh fuel an be added. Table 8-2 Plutonium Isotopi Composition of PBMR First-Pass Fuel t Isotope % PU 239 PU pu PU pu O. 1 I Calulated with VSOP94 for referene fuel yle. 139

140 8.2.2 Superell Analysis of Prodution Pebbles The purpose of using a superell model of the prodution pebble is to simulate more aurately the neutron flux and spetrum that the pebble would experiene during its single pass through the ore. Calulations were performed for the three designs of prodution pebble desribed in Setion 8.1.2, using a driver-fuel assembly representative of (a) the PBMR average ore and (b) the PBMR inner refletor region. The MCNP4B analysis inluded tallies of the 238 U(n,y) reation rates in the depleted uranium target and the eighth of a driver fuel pebble in eah of the eight orners of the BCC prodution ell. The average neutron flux in the prodution ell was also tallied. In addition, a MOCUP depletion alulation was arried out for the prodution pebble with a solid UO2 target to determine the plutonium isotopi omposition at the end of the irradiation period. The results are presented in Tables 8-3 to 8-5. Table 8-3 Neutron Fluxes Calulated With Superell MCNP4B Model (neutrons-m2. s' l) Case Group 1 a Group 2 b Group 3 Group 4 d Comments VSOP referene 2.47e e e e+14 Solid U e e e e+13 target (3.41%) (2.91%) (4.91%) (2.26%) Average U 2 target 3.58e e e e+13 ore shells (3.4%) (2.84%) (4.81%) (2.32%) Densely paked 3.58e e e e+ 13 BISO targets (3.47%) (2.96%) (5.18%) (2.27%) VSOP referene 1.7e e e e+14 Inner Solid U e e e+14 refletor target (11.3%) (24,1%) (38.4%) (1.72%) ).1 MeV < E _ 2 MeV; ) 29 ev < E.1 MeV; ) 1.86 ev < E 29 ev; ) ev < E 1.86 ev. 14

141 The standalone MCNP4B tallies were normalized using four million starting neutron histories for the ore-averaged ases and eight million for the refletor ase 3, while the MOCUP alulation was limited to one million neutron histories at eah burnup step beause of time onstraints. The reported perent relative errors (shown in brakets) orrespond to the I-a onfidene interval. Table Pu Prodution Calulated with Superell MCNP4B Model Prodution Reation Rate (1/s) g 239 Pu / pass Pebbles for Pebble driver target driver target 2Comments Solid U e e ,866 target (21.9%) (5.65%) (21.9%) (5.65%) Shell U e e ,526 Average targets (21.%) (6.63%) (21.%) (6.63%) + 1,29 ore Dense BISO 1.27e e ,312 targets (16.2%) (6.18%) (16.2%) (6.18%) Solid UO e e ,132 Inner target (4.67%) (3.86%) (4.67%) (3.86%) refletor Table 8-5 Isotopi Composition of Plutonium in Irradiated Solid U 2 Targett Isotope % 23Pu - 239u pu pu.3 242pU p MO Calulated with superell MOCUP model. 8.3 Disussion The analysis has onfirmed that spent fuel from pebble-bed reators is proliferation resistant at high disharge burnup (>8 MWd/kgU), beause of its unfavourable plutonium isotopi omposition and the large number of pebbles that would have to be diverted-about half a ore 3 The large number of histories is needed to redue the relative errors of the neutron flux and reation rate tallies to aeptable levels (ideally < 5%). 141

142 load. The isotopis of first-pass fuel pebbles are more favourable, but an even larger number would be needed to aumulate 6 kg of 239 Pu. In addition, the large number of oated fuel partiles that must be raked to remove the SiC oating make TRISO fuel diffiult to reproess. Suh reproessing tehnology is yet to be demonstrated on irradiated fuel. However, it is also possible to produe a signifiant quantity of plutonium in a pebble-bed reator by inserting speial pebbles with a high loading of depleted uranium. Analysis has also shown that the prodution of plutonium in suh pebbles is limited by y-heating and resonane self-shielding in the target regions [8-1]. As with any new fuel onept, the manufaturing of the speial pebbles would require a sophistiated fuel development program and irradiation researh failities not ommonly found in ountries laking a nulear infrastruture. Fewer pebbles would be needed (13, to 2,), although the duration of the diversion will depend on the ability to ompensate for their reativity effet. If the prodution pebbles omprise 1% of the ore inventory, it would take a minimum of 1.5 years to aumulate the required amount of material at the normal fuel-pebble removal rate. By extrapolation from HTR-1 ritiality alulations 4, the reativity worth of the PBMR ore height may be estimated to be.2 %/m. Therefore, the height of the ore would have to be raised by approximately 5 m to ompensate for 1 %Ak/k loss in reativity. It is unlikely that suh a hange in ore height would go unnotied in a safeguarded reator. The substitution of fuel pebbles with ones ontaining depleted uranium targets, or diverting regular pebbles after a single pass, ould have a signifiant effet on the normal operation of the 4 For HTR-1, Ap/AH -.5 %/m. Sine the PBMR ore is 5 times taller, then this value sales as (1/5)2 assuming a osine flux shape. Thus, ap/ah pbml I.2 O/o/m. 142

143 reator. 5 A detailed analysis must be arried out using the VSOP94 fuel management ode to model suh effets, espeially to determine the throughput of speial pebbles. However, sine the preparation of VSOP94 input files is time onsuming, the preliminary alulations were performed with MCNP4B and MOCUP using simplified models of the PBMR ore that limit the auray of the analysis. The standalone MCNP4B alulations are expeted to be onservative beause they neglet the depletion of bred plutonium. The superell MCNP4B models predit a harder neutron spetrum than VSOP94 and, therefore, also tend to overestimate the 238 U(n,y) reation rate. The potential diversion of speial plutonium prodution pebbles requires the use of extrinsi barriers to assure nonproliferation. While there are differenes in estimates of the atual number (13, to over 2,) and the time needed to aumulate these pebbles (1 to 2 years), the final onlusion is that intrinsi barriers alone are not suffiient for on-line refueling of pebble-bed reators. IAEA safeguards and enhaned monitoring systems would be required to prevent the insertion of these pebbles, monitoring devies to detet their prodution, and seals to avoid tampering with the losed refueling system of the plant [8-11]. As is typial for IAEA safeguards programs for light-water reators, inspetions of fuel fabriation plants and fresh fuel deliveries would be required. Automati weighing stations would also be required for fuel pebbles prior to their insertion into the ore to detet the heavier prodution pebbles. Pebble-bed reators already possess on-line burnup meters and failed pebble detetors to sort pebbles for reinsertion. However, by making "defeted" prodution pebbles, this system ould also be used to remove first-pass pebbles for plutonium reovery. The detetion s It may be possible to design prodution pebbles that are reativity neutral, e.g., by adding an outer fuel shell. 143

144 system would have to be enhaned to detet spetral differenes aused by the presene of prodution pebbles. These tehnologies require an additional researh and development effort to ensure that nonproliferation objetives are met. This study also suggests that additional work on fuel management strategies may be helpful in improving intrinsi barriers by reduing 239 Pu prodution through the adjustment of enrihments and neutron spetra. Alternative intrinsi barriers are the OTTO (_ne through then out) fuel yles, whih inlude the Duth PAP (peu-a-peu) onept [8-12] and the proposed PAP2 fuel with burnable poison [8-13], and potentially utilizing Th/LEU fuel to provide additional proliferation resistane of spent fuel. Irradiations of short duration are not possible in suh nonreirulating ores (other than by the premature dumping of the entire inventory). A final remark is appropriate regarding the relative proliferation risk of this tehnology. The pebble-bed reator is not a likely target for a terrorist or sub-national group, beause of the sophistiated nature of the fabriation and reproessing of prodution pebbles. Plutonium prodution assemblies an be inserted into any reator. However, while a single fuel assembly may suffie in a light-water reator, thousands of pebbles would have to be diverted from a pebble-bed reator to produe a single weapon. Any reator may beome a national threat by a ountry that hooses to abdiate the NPT and IAEA safeguards inspetions. It is the purpose of international safeguards to provide advaned notie of suh ativity. 144

145 9. Conlusions and Future Diretions The researh desribed in this report explored the appliability of the standard version of MCNP to the neutroni modeling of pebble-bed reators. Previous MCNP (versions 4A or 4B) investigations only onsidered ritial experiments involving regularly paked ores [9-1, 9-2]. The key issue for the pratial appliation of MCNP4B to pebble-bed reators is the use of regular latties to desribe their randomly paked ores. This modeling effort was very suessful for the simple ore onfigurations enountered in the HTR-PROTEUS ritial experiments and the HTR-1 start-up ore. The annular ASTRA ore, whih is representative of modem modular HTGR designs, proved to be muh more diffiult to model aurately. A summary of key results is provided in Table 9-1; further details may be found in the referened hapters. Table 9-1 Summary of key MCNP4B Critiality Calulations Experiment Parameter Measurement Calulation Chapter HTR-PROTEUS Core 4.1 keff 1.134± ' 4 Core 4.2 keff 1.129± ±.1 t 4 Core 4.3 kegf 1.132± ±.11 t 4 HTR-1 Critial load 16,89 16,841 5 ASTRA keff Control rod 1 zip 1.77 % % 6 Control rod 2 zip 1.84 % % 6 Control rod 4 zip 1.4 % % 6 Control rod % % 6 t A reativity bias is present beause of graphite impurities; % Ak/k. The method developed for the MCNP4B modeling of pebble-bed ores involves the use of a regular lattie of spheres, arranged either as a primitive BCC lattie or based on a repeating ell onstruted from a number of BCC unit ells as shown in Figure 9-1. The 145

146 oated fuel partiles are modeled in detail and are distributed over the fuelled portion of the fuel sphere using a simple ubi lattie. The enlarged ell approah is needed for modeling expliitly more ompliated ore onfigurations, espeially when more nore than two types of spheres are present in the ore (suh as fuel, moderator, absorber, et.). The results of suh a model me were found to depend very strongly on the distribution of )f spheres in the ell, and a generi modeling methodology is diffiult to define. However, ase-by- ase treatment an be suessful when supported by appropriate sensitivity studies. 6.9 m i If Figure 9-1. Si: Six-ell BCC model used in the plutonium prodution study [9-3] -3) Beause the repeat( repeated-struture feature of MCNP4B introdues partial spheres!s at the periphery of the or( ore, a orretion is required in order to eliminate exess fuel ontributed by partial fuel spher, spheres. This an be done either by reduing the volume of the ore )re while keeping the sphere paking fration unhanged, or by reduing the paking fration while keeping the ore volume unhanged. Both approahes rely on an exlusion zone, whih balanes the ontribi ontributions from physially realizable and unrealizable partial spheres. For 146

147 irular ores, the proedure is straightforward beause a distribution of partial spheres of various sizes exists at the ore boundary. The size of the exlusion zone is given by the radius of the sphere saled by the number ratio of fuel spheres to all spheres in the unit ell. However, suh a distribution does not exist in polygonal ores and the exlusion zone must be determined expliitly from the volumes of partial spheres at the boundaries. This is possible beause the positions of the spheres are known in a regular lattie, and an expression is available for the volume of a spherial segment [V = /3h 2 ( 3R-h), where R is the radius of the sphere and h is the height of the segment]. Ultimately of interest is the ability to model a realisti ore with any number of types of spherial elements, inluding fuel spheres with different fissile materials, enrihments and burnup. A ore representation onstruted from a repeating ell with 1 spheres (arranged in 5 BCC unit ells) ould be used in priniple to desribe suh ore loadings. However, as the ASTRA analysis has demonstrated, suh a deterministi approah is very diffiult and not likely to be aurate. If MCNP4B (or version 4C) is to be used, the reommended method is to use average material ompositions in a finite number of ore regions (suh as the layers from the VSOP94 model), with an expliit treatment of the fuel kernels whose ompositions are best generated with a separate fuel management ode as disussed in Chapter 7. A 3% redution in omputation time is reportedly possible by smearing the multiple oatings of the fuel kernels into a single layer [9-4]. However, the best approah would appear to be to shift the Monte Carlo modeling effort to the stohasti geometry treatment of the MCNP-BALL ode developed by JAERI [9-5], beause this would eliminate the diffiulties assoiated with speifying the pebble-bed 147

148 ore expliitly. In this method, the geometry of the ore is sampled during the neutron transport alulation using nearest-neighbour distribution funtions (NND). Suh distribution funtions, whih give the probability of finding the nearest neighbour in a spherial shell between radius r and r+dr, are generated using the Monte Carlo paking ode MCRDF. (An exlusion zone is used during the sampling proess to avoid inluding spheres that overlap the vessel boundary, although here the paking fration is inreased to ahieve the orret inventory of spheres.) The NNDs are sampled during the transport of eah neutron to determine its path through a sphere or oated fuel partile. This eliminates the need for the a priori speifiation of the pebble-bed geometry, beause the positions of other spheres or oated fuel partiles do not enter the alulation. The urrent version of MCNP-BALL was developed by JAERI from MCNP3B by revising five existing subroutines and adding five new ones, and validated through analysis of the stohasti-ore experiments at the HTR-PROTEUS faility [9-6]. However, all future appliations and modifiations of MCNP-BALL should be based on an MCNP4C implementation of the ode. The most important enhanements required in MCNP-BALL relate to the modeling of separate ore regions with different fuel ompositions. Apart from the reommendation to shift from MCNP4B (or 4C) to MCNP-BALL, several other aspets of the researh disussed in this report require a follow-up. The most important of these onern the ASTRA ritial assembly and the addition of a burnup apability to the MCNP4B modeling of pebble-bed reators. 148

149 (a) ASTRA The remaining experiments performed in ASTRA should be analyzed, inluding the investigation of ritial parameters as a funtion of ore height, the spatial distribution of relative reation rates, and the reativity effets of spherial elements. The latter measurements were arried out for both individual and groups of spheres (fuel, moderator and absorber) in the entral hannel. [9-7] Calulation of the ASTRA ontrol-rod worths was found to be sensitive to the number of neutron histories (both the total number and the number per yle) and the definition of the fission soure term used to initiate the run. This suggests that the annular ore may be more neutronially deoupled than was previously thought to be the ase. This should be investigated, inluding the effet of the boron absorber on the neutroni stability of the ore (for example, by defining the starting fission soure in one half of the ore only and following the behaviour of the effetive multipliation fator for suessive yles). (b) Burnup The method proposed in Chapter 7 for alulating the nulide densities of depleted fuel should be implemented. This should be done initially by using VSOP94 to determine the equilibrium ore burnup distribution, followed by a superell MONTEBURNS [9-8] alulation of layer-averaged fuel ompositions (see Figure 7-1). This ould then be followed up by an investigation of whether MONTEBURNS ould be used to perform the fuel management study diretly. New routines would have to be added to 149

150 MONTEBURNS to sinmulate the out-of-pile deay of fission produts and the mixing of fuel spheres with different burnup in eah ore region. An interlaboratory burnup benhmark should be promoted similar to those done in the past for light-water reator UOX and MOX fuel [9-9]. This would onsist of a numerial benhmark omparison of the burnup reativity and isotopis apabilities of the omputer odes urrently used by the international ommunity engaged in HTGR analysis and design. The proposed benhmark would ontinue the work initiated in Referene 9-1, in whih a single spherial unit ell was depleted with MONTEBURNS at several levels of omplexity. The unit ell examined was taken from an ECN report [9-11], whih modeled the LEUPRO-1 ritial assembly tested at the HTR-PROTEUS faility. Suh an international benhmark was reently proposed [9-12]. Several other areas also deserve further investigation. A more systemati study of neutron streaming in different types of latties should be undertaken to determine the optimum paking order. As disussed in Chapter 3, a rhombohedral lattie is expeted to provide a better representation of the arrangement of spheres in a pebble-bed reator. A "super" lattie onstruted from suh unit ells was found to be too ompliated for detailed modeling of the ASTRA ore, but an approximate model that uses borated fuel spheres in a primitive rhombohedral unit ell may give better results than a BCC unit ell. The preditions for the reativity worths of the ontrol rods in the HTR- 1 reator, whih were alulated using the MCNP4B model desribed in Chapter 5, should be ompared with the measured values when these beome available. Good agreement in the worth of ontrol rods signifies that the MCNP4B model is apable of prediting aurately the 15

151 neutron flux in the ore, and, more importantly, in the radial refletor where diffusion theory treatments are suspet. In onlusion, a omprehensive examination of the appliability of the MCNP4B Monte Carlo ode to the modeling of pebble-bed reators was undertaken in the ourse of this researh. A modeling methodology was developed based on an analysis of three ritial experiments-htr-proteus, ASTRA and the HTR-1 start-up ore. The method uses a body-entred ubi ore representation, and exlusion zones to ompensate for the ontribution of partial spheres generated by MCNP4B at the ore boundaries. The ritial ore heights were predited orretly in all ases. However, the alulation of the reativity worths of ontrol rods in the more deoupled annular ASTRA ore was less aurate. An approximate proedure was also developed for the MCNP4B modeling of pebble-bed reators with burnup. The nulide densities of the homogenized layers in the VSOP94 model of the reator are used in the orresponding MCNP4B model with an expliit representation of the sphere lattie. The method was demonstrated in priniple on the PBMR equilibrium ore. The proedure for extrating fuel ompositions from VSOP94 was also used to reate a superell MOCUP model of a speial pebble loaded with depleted uranium. The model was then used to alulate the plutonium prodution apability of the PBMR. For the modeling of realisti ores, the main reommendation of this report is a shift from MCNP4B (or version 4C), and its use of regular latties of spheres to represent the ore, to the stohasti geometry approah implemented in the JAERI ode MCNP-BALL. 151

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166 [7-11] A.I. van Heek, "Inreasing the Power of the High Temperature Reator Module," Nulear Engineering and Design, 15, 1994, pp [7-12] H.J. Riitten, "The Depletion Computer Code ORIGEN-JUL," KFA Jiilih, JUL- 2739, Marh [7-13] Unpublished tehnial memoranda reporting on the investigation of pebble flow urves for the AVR: a) Pohl and Neubaher, Das Kugelflieflverhalten im Innen- und A uflenore - Enduaswertung des IC-Durhlaufversuhs - Simulation des KugelflieBfens im AC AVR GmbH, Ref. No.: H5-X1, P1/Neu/Bot, b) Pohl, "Generation of a new model for the flow of spheres for the AVR ore following ode," AVR GmbH, Ref. No.: H5-X1, P1/Bot, [7-14] A. Kleine-Tebbe, Arbeiten zu einen ringformigen Kugelhaufenkern, KFA Reseah Report, September [7-15] Z. Karriem, C. Stoker and F. Reitsma, "MCNP Modelling of HTGR Pebble-Type Fuel," presented at the M&C 2, Pittsburgh, Pennsylvania, May 7-12, 2. [7-16] J.R. Johnson, "Monte Carlo Study of Pebble Bed Reator Fuel Reativity and Isotopis", SB Thesis, Nulear Engineering Department, MIT, June 21. [7-17] J.R. Johnson, J.R. Lebenhaft and M.J. Drisoll, "Burnup Reativity and Isotopis of an HTGR Fuel Pebble," to be presented at the 21 ANS Winter Conferene. 166

167 [7-18] J.R. Askew, A.J. Fayers and P.B. Kemshell, "A General Desription of the Lattie Code WIMS," Journal of British Nulear Soiety, X, 1966, pp Chapter 8 [8-1] "From Renaissane to Reality-Vision 22," Nulear Energy Institute, Washington, D.C., 21. [8-2] P.E. Owen and K.R. Czerwinski, "Waste Charateristis of Spent Nulear Fuel from a Pebble Bed Reator," MIT, Report MIT-NFC-TR-23, June 2. [8-3] E.J. Mulder, "Core Basi Design Report for the PBMR Nulear Power Plant Projet," PBMR (Pty) Ltd., Report , November 2. [8-4] E. Teuhert et al., "V.S.O.P. ('94) Computer Code System for Reator Physis and Fuel Cyle Simulation - Input Manual and Comments," Forshungszentrurr. Jiilih, Jiil-2897, April [8-5] J.F. Briesmeister, "MCNP - A General Monte Carlo N-Partile Transport Code, Version 4B," Los Alamos National Laboratory, LA M, Version 4B, Marh [8-6] A.G. Croff, "ORIGEN Isotope Generation and Depletion Code Matrix Exponen-tial Method," RSICC, Oak Ridge National Laboratory, CCC-371 (ORNL/TM-7175), July

168 [8-7] "MOCUP: MCNP/ORIGEN Coupling Utility Programs," RSICC, Oak Ridge National Laboratory, PSR-365 (INEL-95/523), Otober [8-8] E. Teuhert and K.A. Haas, "Nonproliferation Issue of the Pebble Bed High Tempera-ture Reator," Nulear Tehnology, 72, February 1986, pp [8-9] "Tehnologial Opportunities to Inrease the Proliferation Resistane of Global Civilian Nulear Power Systems (TOPS)," report by the TOPS task fore to the Nulear Researh Advisory Committee (NERAC), January 21. [8-1] J.S. Herring, J.R. Lebenhaft, K.D. Weaver and M.J. Drisoll, "Plutonium Prodution in a Pebble Bed Reator," MIT/INEEL, unpublished tehnial report, August 2. [8-1 1] E.F. Dean, "Analysis of the Proliferation Resistant Safeguards Appliable to the Fuel Handling and Storage System of the Modular Pebble Bed Reator," B.S. Thesis, Department of Nulear Engineering, MIT, September 21. [8-12] B. R. W. Haverkate, A. I. Heek and J. N. T. Jehee, "Nulear Cogeneration Based on the HTR Tehnology," Proeedings of the 6'h International Conferene on Nulear Engineering, ICONE-6258, 1-14 May [8-13] E. Mulder and E. Teuhert, "OTTO-PAP2 - An Alternative Option to the PBMR Fuelling Philosophy," Tehnial Committee Meeting on HTGR Tehnology Development, Commerializing the HTGR, IAEA, Vienna, November

169 Chapter 9 [9-1] F.C. Difilippo, "Appliations of Monte Carlo Methods for the Analysis of MHTGR Case of the PROTEUS Benhmark," Oak Ridge National Laboratory, Report ORNL/TM-12711, April [9-2] A. Hogenbirk, R.C.L. van der Stad, A.J. Janssen, H. Th. Klippel and J.C. Kuijper, "HTR-PROTEUS Benhmark Calulations. Part 1: Unit ell results LEUPRO-1 and LEUPRO-2," Netherlands Energy Researh Foundation, Report ECN-C-95-87, September [9-3] J.S. Herring, J.R. Lebenhaft, K.D. Weaver and M.J. Drisoll, "Plutonium Prodution in a Pebble Bed Reator," MIT/INEEL, unpublished tehnial report, August 2. [9-4] Z. Karriem, C. Stoker and F. Reitsma, "MCNP Modelling of HTGR Pebble-Type Fuel," presented at the M&C 2, Pittsburgh, Pennsylvania, May 7-12, 2. [9-5] 1. Murata, "Studies on Monte Carlo Partile Transport in Irregularly Distributed Fuel Elements for High Temperature Gas-Cooled Reators," PhD Thesis, Osaka University, Japan, [9-6] I. Murata, A. Takahashi, T. Mori and M. Nakagawa, "New Sampling Method in Continuous Energy Monte Carlo Calulation for Pebble Bed Reators," Journal of Nulear Siene and Tehnology, 34(8), August 1997, pp

170 [9-7] V.P. Garin, et al., "Measurement of reativity effets of omponents and materials important for the PBMR reator, and of spatial distribution of reation rates, neutron fluxes and power in axial and radial diretions in the ASTRA Faility Assembly," Stage A Report, Russian Researh Centre, Kurhatov Institute, Mosow, February 2. [9-8] H.R. Trellue and D.I Poston, "User's Manual, Version 2. for MONTEBURNS, Version 5B," Los Alamos National Laboratory, Report LA-UR , [9-9] X. Zhao, "Miro-Heterogeneous Thorium Based Fuel Conepts for Pressurized Water Reators," Ph.D. thesis, Nulear Engineering Department, MIT, June 21. [9-1] J.R. Johnson, "Monte Carlo Study of Pebble Bed Reator Fuel Reativity and Isotopis", SB Thesis. Nulear Engineering Department, MIT, June 21. [9-11] A. Hogenbirk, R.C.L. van der Stad, A.J. Janssen, H. Th. Klippel and J.C. Kuijper, "HTR-PROTEUS Benhmark Calulations. Part 1: Unit ell results LEUPRO-I and LEUPRO-2," Netherlands Energy Researh Foundation, Report ECN-C-95-87, September [9-12] J.R. Johnson, J.R. Lebenhaft and M.J. Drisoll, "Burnup Reativity and Isotopis Of an HTGR Fuel Pebble," presented at the Amerian Nulear Soiety Winter Meeting, Reno, Nevada, November 11-15,

171 ADpendix A [A-I] J.F. Briesmeister (Ed.), "MCNP-A General Monte Carlo N-Partile Transport Code, Version 4B," Los Alamos National Laboratory, Report LA M, Marh

172 APPENDIX A. MCNP4B Models of the HTR-PROTEUS Faility This Appendix ontains the MCNP4B input files with models of the three HTR- PROTEUS stohasti ores. A desription of the MCNP4B ode, model reation and input ards may be found in the manual [A-l]. Details of the HTR-PROTEUS faility appear in Chapter 4. All the alulations reported in this report were performed on a DEC Alpha Personal Workstation 6au running under the Digital UNIX Version 4.E operating system. MCNP4B and VSOP94 were ompiled using the Digital FORTRAN 77 ompiler (V BH and Driver V5.2-1). 172

173 APPENDIX A. 1: MCNP4B Model of HTR-PROTEUS Core 4.1 HTR-PROTEUS EXPERIMENT IRREGULAR CORE MCNP4B model of ritial experiment 4.1 in the PROTEUS faility using the detailed geometry speifiation from the alulational benhmark. The random paking is modeled using a loose BCC, with F/M ratio of one, and a detailed model of oated fuel partiles. Uses a 1.5 m exlusion zone and a detailed top refletor. J.R. Lebenhaft, MIT, January 21 _ - - CELL CARDS C 1-1: 11: 22 $ outside world reator struture e $ bottom axial refletor e $ Al ring e $ radial refletor e $ air above rad refletor e $ air between Al and refl e $ outer Al ylinder e $ inner Al ylinder e $ lower Al plate e $ upper Al plate - outer e $ upper Al plate - inner e $ middle Al ylinder e $ inner air avity e $ outer air avity e $ inner axial refletor e $ outer axial refletor ore avity e e e e-5 fill=l (1) #3-2 $ air above ore enter $ rest of air above ore $ radial exlusion zone $ bottom exlusion zone $ pebble bed universe 1: BCC lattie of pebbles lat=1 fill=2 u=i universe 2: ontents of unit ell 32-6 fill=3 u=2 $ [ e-2-61 u=2 $ [ 1 1 1] e-2-62 u=2 $ [ I 1-1] e-2-63 u=2 $ [ ] 173

174 e e e e e e universe 3: ontents of fuel pebble e universe 4: embedded oated fuel partiles lat=1 fill=5 u= universe 5: oated fuel partile e u=2 $ 1-1 1] u=2 $ [-1 1 1] u=2 $ [-1 1-1] u=2 $ [-l -1-11] u=2 $ [-1-1 1] $ air between u=2 $ pebbles u=3 $ graphite shell fill=4 u=3 $ fueled region u=5 u=5 u=5 u=5 u=5 u=5 $ U2 kernel $ PyC layer 1 $ PyC layer 2 $ SiC layer $ PyC layer 3 $ graphite matrix SURFACE CARDS reator struture surfaes pz. pz 78. pz 79.5 pz pz 251. pz 252. pz pz 267. pz pz 33. pz z z 2.38 z z z 6. z 61. z z z 62.5 z 7. z $ bottom of reator $ bottom of pebble bed $ bottom exlusion zone $ top of ore $ lower surfae of Al ring $ upper surfae of Al ring $ upper surfae of bot. Al plate $ lower surfae of top Al plate $ upper surfae of top Al plate $ top of radial refletor $ top of reator $ inside of inner Al ylinder $ outside of inner Al ylinder $ inside of middle Al ylinder $ outside of middle Al ylinder $ inner surfae of Al ring $ radial exlusion zone $ inside of outer Al ylinder $ outside of outer Al ylinder $ inner surfae of radial refletor $ outer surfae of Al ring $ outer surfae of radial refletor 174

175 Pebble bed suriaes unit ell in ore px px py py pz pz balls in unit ells 6 so s s s s s s s s inside fuel pebble 85 so unit ell for CFP lattie px px py py pz pz $ 1 ] $ [-1 ] $ 1 ] $ [ -1 ] $ [ 1] $ [ -1] $ fueled region oated fuel partile so.251 $ U2 kernel so.3425 $ buffer so.3824 $ inner PyC so.4177 $ SiC so.4577 $ outer PyC RUN PARAMETERS problem type mode kode n ksr totnu print dbn 9j

176 prdmp j neutron importane imp:n 1 14r 1 4r 1 1 9r r transformations trl material speifiations axial refletor ml e e-8 mtl grph.1t radial refletor m e e-8 mt2 grph.1t m m4 humid air e e e Oe-5 pebble graphite shell m e e-7 mt6 grph.1t moderator pebble (N = e-2) m e e-8 mt8 grph.1t fuel kernel (N = e-2) m e e-2 mtll m12 mt12 buffer e e-8 grph.1t PyC e e-7 grph.1t SiC m e e e-8 mt13 grph. Olt $ outside world $ reator struture $ ore avity $ u=l: lattie $ u=2: unit ell $ u=3: fuel pebble $ u=4: CFP lattie $ u=5: CFP e e-9 $ aluminum e e e e e e e-8 176

177 APPENDIX A,2: MCNP4B Model of HTR-PROTEUS Core 4.2 HTR-PROTEUS EXPERXMENT IRREGULAR CORE MCNP4B model of ritial experiment 4.2 in the PROTEUS faility using the detailed geometry speifiation from the alulational benhmark. The random paking is modeled using a loose BCC, with F/M ratio of one, and a detailed model of oated fuel partiles. Uses a 1.5 m exlusion zone and a detailed top refletor. J.R. Lebenhaft, MIT, January CELL CARDS 1 reator struture e e e e e e e e e e e e e e e-2 ore avity e e e e-5 24 fill=l (1) -1: 11: #3-2 universe 1: BCC lattie of pebbles lat=1 fill=2 u=l universe 2: ontents of unit ell e e e e-2-64 $ outside world $ bottom axial refletor $ Al ring #3 $ radial refletor $ air above rad refletor $ air between Al and ref $ outer Al ylinder $ inner Al ylinder $ lower Al plate $ upper Al plate - outer $ upper Al plate - iner $ middle Al ylinder $ inner air avity $ outer air avity $ inner axial refletor $ outer axial refletor $ air above ore enter $ rest of air above ore $ radial exlusion zone $ bottom exlusion zone 56 $ pebble bed fill=3 u=2 $ [ u=2 $ [ 1 1 u=2 $ [ 1 1 u=2 $ [ 1-1 u=2 $ 1-1 ] 1] -1] -1] 1] 177

178 e e e e e pebbles universe 3: ontents of fuel pebble e u=2 u=2 u=2 u=2 u=3 fill=4 u=3 universe 4: embedded oated fuel partiles lat=1 fill=5 u=4 universe 5: oated fuel partile e-2 99 $ $ ] $ ] $ ] u=2 $ air between u=5 u=5 u=5 u=5 u=5 u=5 $ graphite shell $ fueled region $ U2 kernel $ PyC layer 1 $ PyC layer 2 $ SiC layer $ PyC layer 3 $ graphite matrix C SURFACE CARDS reator struture surfaes pz. pz 78. pz 79.5 pz pz 251. pz 252. pz pz 267. pz pz 33. pz z z 2.38 z z z 6. z 61. z z z 62.5 z 7. z $ bottom of reator $ bottom of pebble bed $ bottom exlusion zone $ top of pebble bed $ lower surfae of Al ring $ upper surfae of Al ring $ upper surfae of bottom Al plate $ lower surfae of top Al plate $ upper surfae f top Al plate $ top of radial refletor $ top of reator $ inside of inner Al ylinder $ outside of inner Al ylinder $ inside of middle Al ylinder $ outside of middle Al ylinder $ inner surfae of Al ring $ radial exlusion zone $ inner surfae of outer Al ylinder $ outer surfae of outer Al ylinder $ inner surfae of radial refletor $ outer surfae of Al ring $ outer surfae of radial refletor 178

179 pebble bed surfaes Unit ell in ore px px py py pz pz Balls in unit ells 6 so s s s s s s s s inside fuel pebble 85 unit ell for CFP lattie 87 px px py py pz pz $ (-1 ] $ ( 1 ] $ ( 1 ] $ [ -1 ] $ [ 1] $ [ -1] so 2.5 $ fueled region oated fuel partile 95 so.251 $ U2 kernel 96 so.3425 $ buffer 97 so.3824 $ inner PyC 98 so.4177 $ SiC 99 so.4577 $ outer PyC --- RUN PARAMETERS problem type mode n kode ksr totnu print dbn 9j 3 179

180 prdmp j neutron importane imp:n 1 14r 1 4r 1 1 9r r transformations trl.. mll mtll m12 mt material speifiations axial refletor ml e e-8 mtl grph.lt radial refletor m e e-8 mt2 grph.lt m humid air m e e e e-5 pebble graphite shell m e e-7 mt6 grph.lt moderator pebble (N = e-2) m e e-8 mt8 grph.lt fuel kernel (N = e-2) m e e-2 buffer e e-8 grph.lt PyC e e-7 grph.1t SiC m e e e-8 mt13 grph.lt $ outside world $ reator struture $ ore avity $ u=1: lattie $ u=2: unit ell $ u=3: fuel pebble $ u=4: CFP lattie $ u=5: CFP e e-9 $ aluminum e e e e e e e-8 18

181 APPENDIX A.3: MCNP4B Model of HTR-PROTEUS Core 4.3 HTR-PROTEUS EXPERIMENT IRREGULAR CORE MCNP4B model of ritial experiment 4.3 in the PROTEUS faility using the detailed geometry speifiation from the alulational benhmark. The random paking is modeled using a loose BCC, with F/M ratio of one, and a detailed model of oated fuel partiles. Uses a 1.5 m exlusion zone to aount for partial pebbles at ore edge, and a detailed representation of the top refletor. J.R. Lebenhaft, MIT, January 21 CELL CARDS 1-1: 11: 22 $ outside world reator struture e $ bottom axial refletor e $ Al ring e #3 $ radial refletor e $ air above rad refletor e $ air between Al and ref e $ outer Al ylinder e $ inner Al ylinder e $ lower Al plate e $ upper Al plate - outer e $ upper Al plate - inner e $ middle Al ylinder e $ inner air avity e $ outer air avity e $ inner axial refletor e $ outer axial refletor ore avity e e e e-5 fill=l(1) universe 1: BCC lattie of pebbles lat=l fill=2 u=l universe 2: ontents of unit ell e e #3 $ air above ore enter $ rest of air above ore $ radial exlusion zone $ bottom exlusion zone 56 $ pebble bed fill=3 u=2 $ [ u=2 $ 1 u=2 $ [ 1 ] 1 1] 1-1] 181

182 e e e e e e e universe 3: ontents of fuel pebble e-2 5 lat=l u= universe 4: embedded oated fuel partiles fill= universe 5: oated fuel partile e u=2 u=2 u=2 u=2 u=2 u=2 $ [ ] $ 1-1 1] $ [-1 1 1] $ [-1 1-1] $ [ ] $ [-1-1 1] u=2 $ air bet pebbles u=3 $ graphite shell fill=4 u=3 $ fueled region u=5 u=5 u=5 u=5 u=5 u=5 $ U2 kernel $ PyC layer 1 $ PyC layer 2 $ SiC layer $ PyC layer 3 $ graphite matrix SURFACE CARDS reator struture surfaes pz. pz 78. pz 79.5 pz pz 251. pz 252. pz pz 267. pz pz 33. pz z z 2.38 z z z 6. z 61. z z z 62.5 z 7. z $ bottom of reator $ bottom of pebble bed $ bottom exlusion zone $ top of pebble bed minus exlusion $ lower surfae of Al ring $ upper surfae of Al ring $ upper surfae of bottom Al plate $ lower surfae of top Al plate $ upper surfae of top Al plate $ top of radial refletor $ top of reator $ inside of inner Al ylinder $S outside of inner Al ylinder $ inside of middle Al ylinder $ outside of middle Al ylinder $ inner surfae of Al ring $ radial exlusion zone $ inner surfae of outer Al ylinder $ outer surfae of outer Al ylinder $ inner surfae of radial refletor $ outer surfae of Al ring $ outer surfae of radial refletor 182

183 pebble bed surfaes Unit ell in ore px px py py pz pz Balls in unit ells 6 so s s s s s s s s inside fuel pebble so unit ell for CFP lattie 87 px px py py pz pz oated fuel partile so.251 so.3425 so.3824 so.4177 so $ [-1 ] $ [ 1 ] $ [ 1 ] $ [ -1 ] $ [ 1] $ [ -1] $ fueled region $ U2 kernel $ buffer $ inner PyC $ si $ outer PyC mode kode ksr totnu print RUN PARAMETERS problem type n

184 dbn 9j 3 prdmp j neutron importane imp:n 1 14r 1 4r 1 1 9r r transformations trl.. ml mtl material speifiations axial refletor e-2 grph.1t radial refletor m e-2 mt2 grph. Olt m humid air m e e-7 mll mtll m12 mt e e e Oe-5 pebble graphite shell m e e-7 mt6 grph.lt moderator pebble (N = e-2) m e e-8 mt8 grph.1t fuel kernel (N = e-2) mlo e e-C2 buffer e e-8 grph. lt PyC e e-7 grph. Olt SiC m mt13 grph.1t 4.863e e e-8 $ outside world $ reator struture $ ore avity $ u=l: lattie $ u=2: unit ell $ u=3: fuel pebble $ u=4: CFP lattie $ u=5: CFP e e-9 $ aluminum e e e e e e e-8 184

185 APPENDIX B. MCNP4B Models of HTR-1 This Appendix ontains the MCNP4B input files with models of the HTR-1 reator. The model of the initial ritial ore for benhmark problem B, whih uses the standard ENDF/B-VI ross-setion libraries, appears in Appendix B. I. The model of the reator for benhmark problem B2. 1, with a full ore and using the University of Texas at Austin libraries, appears in Appendix B.2. Details of the HTR-1 reator appear in Chapter

186 APPENDIX B-1: MCNP4B Model of HTR-1 Benhmark Problem BI HTR-1 PEBBLE-BED REACTOR MCNP4B model of the HTR-1 initial ore, based on IAEA benhmark problem CRP-5 speifiation. Benhmark problem B1. Modeling assumptions: A BCC lattie of spheres in ore with.61 paking fration and a 1:1 mix of fuel and moderator pebbles in ylindrial portion of ore, but adjusted with moderator pebble size redued to approximate a 57:43 fuel-to-moderator ratio. The ontrol, irradiation, KLEPX and He hannels were modeled expliitly. A 1.71 m radial exlusion zone orrets for ore-edge fuel pebbles. Prepared by J.R. Lebenhaft (MIT) Deember 2 Revision history: January 21, J. Lebenhaft - detailed model of ontrol rods CELL CARDS 1 1: -17: 29 Graphite reator struture $ outside world $ zone 1 $ zone 2 $ zone 3 $ zone 4 $ zone $ zone 6 $ zone 7 $ zone 81 $ zone 8 $ zone 9 $ zone 1 $ zone 11 $ zone 12 $ zone 13 $ zone 14 $ zone 15 $ zone 16 $ zone 17 $ zone 18 $ zone 19 $ zone 2 $ zone 21 $ zone 22 $ zone 23 $ zone

187 e e e e e (275:-276: (277 (281:-282: (283 (287:-288: (289 (293:-294:(295 (299:-3:(31 (35:-36:(37 (311:-312: ( (275:-276: (277 (281:-282:(283 (287:-288: (289 (293:-294: (295 (299:-3:(31 (35:-36:(37 (311:-312:( : (275:-276:(277 (281:-282:(283 (287:-288: (289 (293:-294: (295 (299:-3:(31 (35:-36:(37 (311:-312: ( (275:-276:(277 (281:-282: (283 (287:-288:(289 (293:-294:(295 (299:-3:(31 (35:-36:(37 (311:-312:( (275:-276:(277 (281:-282: (283 (287:-288:(289 (293:-294:(295 (299:-3:(3. (35:-36:(37 (311:-312:( ) :(28-278)) 285) :( ) 291) :(292-29)) 297) :( )) 33) :(34-32)) 39) :(31-38)) 315) :(316 M14)) ) 285) 291) 297) 33) 39) 315) ) 285) 291) 297) 33) 39) 315) ) :(28 :(286 :(292 : (298 : (34 : (31 : (316 :(28 285) :( ) :( ) :(298 33) :(34 39) :(31 315) :( ) 285) 291) 297) 33) 39) 315) -278)) -284)) -29)) -296)) -32)) -38)) -314)) : (28 : (286 : (292 : (298 : (34 : (31 : ( )) -284 ) -29)) -296)) -32 ) -38)) -314)) )) -284 ) -29)) -296 ) -32 ) -38)) -314 ) :(28 :(286 : (292 :(298 :(34 : (31 :( ) ) -284 ) -29)) -296) ) -32) ) -38)) -314 ) $ zone 25 $ zone 26 $ zone 8 $ zone 27 $ zone 28 $ zone 29 $ zone 82 $ zone 3 187

188 e e (275: -276: (281: -282: (287: -288: (293: -294: (299: -3: (35: -36: (311:-312: (275: -276: (281: -282: (287: -288: (293: -294: (299: -3: (35: -36: (311:-312: (277 (283 (289 (295 (31 (37 ( (277 (283 (289 (295 (31 (37 ( ): 285) 291): 297): 33): 39): 315) ): 285): 291): 297): 33): 39): 315): (28 (286 (292 (298 (34 (31 (316 (28 (286 (292 (298 (34 (31 ( )) -284)) -29)) -296)) -32)) -38)) -314)) -278)) -284)) -29)) -296)) -32)) -38)) -314)) $ zones 31-4 $ zone 41a - $ at bottom $ of CR $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone 41b a 66b

189 Cavity above ore e C Cylindrial Region of Core e lat=l fill=11 u= fill=1 (1) Universe 1: BCC lattie of fuel and dummy spheres Universe 11: unit ell e e e e e e e e e e lat=1 fill=14 u= fil Universe 12: details of fuel element =12 u=11 u=ll1 u=ll u=11 u=11 u=ll1 u=11 u=11 u=11 Universe 13: embedded oated fuel partiles Universe 14: oated fuel partile e $ zone 7 $ zone 71 $ zone 72 $ zone 73 $ zone 75 $ zone 76 $ zone 77 $ zone 78 $ zone 79 $ air $ fuel $ mod $ mod $ mod $ mod $ mod $ mod $ mod $ mod $ radial gap $ pebble bed [ [ 1 [ 1 [ 1 [ 1 [-1 [-1 [-1 [-1 u=11 $ air in between u=12 $ graphite shell fill=13 u=12 $ fuel region u=14 $ U2 kernel u=14 $ PyC layer 1 u=14 $ PyC layer 2 u=14 $ SiC layer o O] 1 1] 1-1] ] -1 1] 1 1] 1-1] -1-1] -1 1] 189

190 e Conus Region of Core (dummy balls) fill=2 (2) Universe 2: BCC lattie of dummy spheres lat=l fill=21 u= Universe 21: unit ell e e e e e e e e e e Control rod sites Universe 25: ontents of CR guide tubes e e segment e Universe 26: ontrol rod fill=25(15) fill=25(16) fill=25(17) fill=25(18) fill=25(19) fill=25(2) fill=25(21) fill=25(22) fill=25(23) fill=25(24) u=14 $ PyC layer 3 u=14 $ graphite matrix u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=25 u=25 fi11=26 u=25 $ mod $ mod $ mod $ mod $ mod $ mod $ mod $ mod $ mod [ [ 1 [ 1 [ 1 [ 1 [-1 [-1 [-1 [-1 ] 1 1] 1-1] -1-1) -1 1] 1 1] 1-1] -1-1] -1 1] u=21 $ air in between $ CR1 $ CR2 $ CR3 $ CR4 $ CR5 $ CR6 $ CR7 $ CR8 $ CR9 $ CR1 $ air around CR $ air below CR $ CR u=26 $ lower end u=26 u=26 u=26 $ inner sleeve $ gap $ B4C 19

191 e segment e e segment e e segment e e segment e e e e _ Absorber ball KLAK sites e e e e e e e u=26 $ gap u=26 $ outer u=26 $ joint 1 u=26 u=26 u=26 u=26 u=26 $ inner $ gap $ B4C $ gap $ outer u=26 $ joint 2 u=26 u=26 u=26 u=26 u=26 $ inner $ gap $ B4C $ gap $ outer u=26 $ joint 3 u=26 u=26 u=26 u=26 u=26 $ inner sleeve $ gap $ B4C $ gap $ outer sleeve u=26 $ joint 4 u=26 u=26 u=26 u=26 u= u=26 u=26 u= $ inner $ gap $ B4C $ gap $ outer (-277:-279) (278:-28) (-283:-285) (284:-286) (-289:-291) (29:-292) (-295:-297) (296:-298) (-31:- 33) (32:-34) (-37:-39) (38:-31) (-313:-315) (314:-316) sleeve sleeve sleeve sleeve sleeve sleeve sleeve $ upper end $ entre hannel $ above rod $ KL1 $ KL2 $ KL3 $ KL4 $ KL5 $ KL6 $ KL7 191

192 C Helium flow hannels e e e e e e e e-5 5 b.58e e e e e e e e e e e e e e e-5 Irradiation hannels $ HE1 $ HE2 $ HE3 $ HE4 $ HE5 $ HE6 $ HE7 $ HE8 $ HE9 $ HE1 $ HE11 $ HE12 $ HE13 $ HE14 $ HE15 $ HE16 $ HE17 $ HE18 $ HE19 $ HE2 $ IR1 $ IR2 $ IR3 SURFACE CARDS 1 pz. 2 pz pz pz pz pz pz pz pz pz pz pz pz pz pz pz pz pz pz z $ Top of borated C briks at reator top $ Bottom of borated C reator top $ Upper surfae of old He hamber $ Lower surfae of old He hamber $ Surfae between axial regions 3 and 82 $ Lower surfae of top refletor $ Top of fueled region (full ore) $ Top of fueled region (initial ritial) $ Upper surfae of one region $ Lower surfae of one region $ Surfae between axial regions 8 and 9 $ Surfae between axial regions 9 and 1 $ Surfae between axial regions 1 and 12 $ Surfae between axial regions 13 and 14 $ Surfae between axial regions 6 and 7 $ Surfae between axial regions 16 and 17 $ Surfae between axia regions 7 and 81 $ Bottom of reator $ Bottom of CR guide hole $ radial fuel exlusion zone 192

193 2 z z z z z z z z z z kz Fuel element 41 so 2.5 Unit ell in ore 45 px px py py pz pz Pebbles in unit BCC ells 51 so s s s s s s s s Coated Fuel Partiles so.25 so.34 so.38 so.415 so.455 $ Inner surfae of radial refletor $ Inner surfae of ontrol rod region $ Outer surfae of ontrol rod region $ Inner surfae of He f 'w region $ Outer surfae of He flow region $ Outer surfae of side graphite refletor $ Outside of radial borated C briks $ Outer surfae of bottom one Unit ell for CFP lattie in graphite matrix px px py py pz pz Control rod hannels $ fuel region $ [-1 ] $ [ 1 ] $ [ 1 ] $ [ -1 ] $ [ 1] $ [ -1] $ $ $ $ $ $ $ $ $ entre fuel redued radius moderator spheres $ kernel $ 1st PyC layer $ 2nd PyC layer $ SiC layer $ 3rd PyC layer 193

194 26 /z $ CR1 261 /z $ CR2 262 /z $ CR3 263 /z $ CR4 264 /z $ CR5 265 /z $ CR6 266 /z $ CR7 267 /z $ CR8 268 /z $ CR9 269 /z $ CR1 Small absorber ball hannels.. KL px px py py /z /z KL px px py py /z /z KL px px py py /z /z KL px px py py /z /z KL px px py py /z /z KL px px py

195 38 1 py 39 1 /z 31 1 /z KL7 11 px 11 px 11 py 11 py 11 /z 11 /z Helium flow hannels /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z Irradiation Channels 34 /z /z /z pz rod pz bottom pz pz Control Rods bottom pz pz bottom pz pz pz pz $ HE1 $ HE2 $ HE3 $ HE4 $ HE5 $ HE6 $ HE7 $ HE8 $ HE9 $ HE1 $ HE11 $ HE12 $ HE13 $ HE14 $ HE15 $ HE16 S HE17 $ HE18 $ HE19 $ HE2 $ IR1 $ IR2 $ IR3 $ bottom of ontro $ segment 1 - $ segment 1 - top $ segment 2 - $ segment 2 - top $ segment 3 - $ segment 3 - top $ segment 4 - bottom $ segment 4 - top $ segment 5 - bot 195

196 pz pz z z z 3.1 z z 5.31 z 5.51 $ segment 5 - top $ top of rod $ inner sleeve - in $ inner sleeve - out $ absorber - inside $ absorber - outside $ outer sleeve - in $ outer sleeve - out RUN PARAMETERS NEUTRON IMPORTANCES imp:n 1 74r r 1 9r 1 2r 1 32r 1 1lr 1 6r 1 19r 1 2r TRANSFORMATIONS Center positions of unit ells in fill zones trl tr Small absorber ball hannels (entered on r = m) *tr5 *tr *tr7 *tr8 *tr *trlo *trll tr15 tr16 tr17 tr18 tr19 tr2 tr21 tr22 tr23 tr24 Control rod radial positions Control rod insertion (length = m) $ outside world $ graphite struture $ helium avity $ fuel region $ ontrol rod sites $ ontrol rod guide tubes $ ontrol rod $ onus $ KLAK sites $ Helium flow hannels $ Irradiation sites $ fuel sphere $ mod sphere $ CR1 $ CR2 $ CR3 $ CR4 $ CR5 $ CR6 $ CR7 $ CR8 $ CR9 $ CR1 $ KL1 $ KL2 $ KL3 $ KL4 $ KL5 $ KL6 $ KL7 196

197 tr tr MATERIAL SPECIFICATIONS Graphite Struture ml e e e-8 mtl grph.lt m mt2 grph.lt m mt3 grph.lt m mt4 grph.lt m mt5 grph.lt m mt7 grph.lt m mt8 grph.lt m mt9 grph.lt m mtlo grph.lt mll mtll grph.lt m mtl2 grph.lt m mt13 grph.1t m mt14 grph.lt e e e e e e e e e e e e e e e e e e-4 8.5G79e e e e e e e e e e e e e e e e e e-5 $ fully out $ fully in 197

198 m mt15 grph.olt m mt16 grph.olt m mt17 grph.olt m mt18 grph.olt m mtl9 grph.olt m mt2 grph.olt m mt21 grph.olt m mt22 grph.olt m mt23 grph.olt m mt24 grph.olt m mt25 grph.olt m mt26 grph.olt m mt27 grph.olt m mt28 grph.olt e e e e e e e e e e e e e e e e e e e e e e e e e e-7 m e e-& e e e e e e e e e e e e e-8 198

199 511.6 mt29 grph. Olt m mt3 grph.olt m mt31 grph.olt m mt32 grph.olt m mt33 grph.olt m mt35 grph.olt m mt36 grph.olt m mt37 grph.olt m mt38 grph.olt m mt39 grph.olt m mt4 grph.olt m mt41 grph.olt m mt43 grph.olt m mt44 grph.olt e e e e e e e e e e e e e e e e e e e e e e e e e e e-3 m e e e e e e e e e e e e e e e e-7 199

200 mt45 m5 grph. lt Humid air m e e-5 1.e m Fuel element.. fuel kernel (N = e-2) m e e e-8.. graphite layers of CFP m SiC layer of CFP m moderator graphite (N = m64 Control rod e e-9 mt64 grph.lt.. graphite matrix in fuel m e e-8 mt65 grph.lt e e e e e-2) e-9 pebble (N = e-2) e-8 PROBLEM TYPE mode n totnu kode sdef pos= axs= 1 rad=dl ext=d2 sil spl 1 si sp2 1 Printing and utoff ards print dbn 9j 3 prdmp j $ B4C 2

201 APPENDIX B-2: MCNP4B Model of HTR-1 Benhmark Problem B2.1 HTR-1 PEBBLE-BED REACTOR (CASE B21 UTX) MCNP4B model of the HTR-1 initial ore, based on IAEA benhmark problem CRP-5 speifiation. Benhmark problem B21. Modeling assumptions: A BCC lattie of spheres in ore with.61 paking fration and a 1:1 mix of fuel and moderator balls in ylindrial portion of ore, but with a redued moderator pebble size to approximate a 57/43 f/m pebble ratio. The ontrol, irradiation, KLAK and He hannels are modeled expliitly. Pressurized helium atmosphere. Benhmark problem B2.1, alulated using the U of Texas ross setions at 3K. Prepared by J.R. Lebenhaft (MIT) May 21. Revision history: January 21, J. Lebenhaft - detailed model of ontrol rod; radial ore exlusion zone to orret for partial pebbles at boundary. May 21, J. Lebenhaft - revised moderator density and boron ontent; redued fueled region in fuel spheres; orreted size of CFP unit ell. CELL CARDS 1 1: -17: 29 Graphite reator struture $ outside world $ zone 1 $ zone 2 $ zone 3 $ zone 4 $ zone $ zone 6 $ zone 7 $ zone $ zone 8-23 $ zone 9-21 $ zone 1-23 $ zone $ zone $ zone $ zone $ zone 15 21

202 e e e e e (275:-276:(277 (281:-282:(283 (287:-288:(289 (293:-294:(295 (299:-3:(31 (35:-36:(37 (311:-312:( (275:-276:(277 (281:-282:(283 (287:-288:(289 (293:-294:(295 (299:-3:(31 (35:-36:(37 (311:-312:( (275:-276:(277 (281:-282:(283 (287:-288:(289 (293:-294:(295 (299:-3:(31 (35:-36:(37 (311:-312:( (275:-276:(277 (281:-282:(283 (287:-288:(289 (293:-294:(295 (299:-3:(31 (35:-36:(37 (311:-312:( ): 285): 291): 297): 33): 39): 315): ): 285): 291): 297 ): 33): 39): 315): ) 285) 291): 297): 33): 39): 315): ): 285): 291): 297): 33): 39): 315): (28 (286 (292 (298 (34 (31 ( )) -284)) -29)) -296)) -32)) -38)) -314)) 264 2C,5 (28 (286 (292 (298 (34 (31 ( )) -284)) -29)) -296)) -32)) -38)) -314)) (28 (286 (292 (298 (34 (31 ( )) -284)) -29)) -296)) -32)) -38)) -314)) (28 (286 (292 (298 (34 (31 ( )) -284)) -29)) -296)) -32)) -38)) -314)) $ zone 16 $ zone 17 $ zone 18 $ zone 19 $ zone 2 $ zone 21 $ zone 22 $ zone 23 $ zone 24 $ zone 25 $ zone 26 $ zone 8 $ zone 27 $ zone 28 $ zone 29 $ zone 82 $ zone 3 22

203 e e (275: -276: (281: -282: (287: -288: (293: -294: (299: -3: (35: -36: (311: -312: (275: -276: (281:-282: (287:-288: (293:-294: (299:-3: (35:-36: (311:-312: (275: -276 (281: -282: (287: -288: (293: -294: (299:-3: (35:-36: (311:-312: (277 (283 (289 (295 (31 (37 ( (277 (283 (289 (295 (31 (37 ( (277 (283 (289 (295 (31 (37 ( ) :(28-278)) 285) :( )) 291) :(292-29)) 297) :( )) 33) :(34-32)) 39) :(31-38)) 315) :( )) ): 285) 291): 297): 33): 39): 315): ): 285): 291): 297): 33): 39): 315): (28 (286 (292 (298 (34 (31 ( (28 (286 (292 (298 (34 (31 ( )) -284) ) -29)) -296)) -32) ) -38)) -314)) $ zones 31 to $ zone 41a $ CR bottom -278)) -284)) -29)) -296)) -32)) -38)) -314)) $ zone 41b $ zone 42 $ zone 43 $ zone 44 $ zone 45 $ zone 46 $ zone 47 $ zone 74 $ zone 66a $ zone 66b $ zone 48 $ zone 49 $ zone 5 $ zone 51 $ zone 52 $ zone 53 $ zone 54 $ zone 55 $ zone 56 $ zone 57 $ zone 58 23

204 e-3 C Cavity above ore Cylindrial Region of Core e lat=1 fill=11 u= fill=1 (1) Universe 1: BCC lattie of fuel and dummy spheres Universe 11: unit ell e e e e e e e e e fill=12 u=11 u=11 u=11 u=11 u=11 u=11 u=11 u=11 u= Universe 12: details of fuel element e Universe 13: embedded oated fuel partiles $ radial gap $ pebble bed $ fuel $ mod $ mod $ mod $ mod $ mod $ mod $ mod $ mod $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone $ zone [ [1 1 [1 1 [ 1-1 [1-1 [-1 1 [-1 1 [-1-1 [ ] -1] 1] 1] -1] -1] 1] u=11 $ helium between u=12 $ graphite shell fill=13 u=12 $ fuel region 24

205 lat=l fill=14 u=13 Universe 14: oated fuel partile e e Conus Region of Core (dummy balls) fill=2 (2) Universe 2: BCC lattie of moderator spheres lat=l fill=21 u=2 Universe 21: unit ell e e e e e e e e e e Control rod sites Universe 25: ontents of CR guide tubes e e fill=25(15) fill=25(16) fill=25(17) fill=25(18) fill=25(19) fill=25(2) fill=25(21) fill=25(22) fill=25(23) fill=25(24) u=14 $ U2 kernel u=14 $ PyC layer 1 u=14 $ PyC layer 2 u=14 $ SiC layer u=14 $ PyC layer 3 u=14 $ graphite matrix u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=25 u=25 fill=26 u=25 $ mod $ mod $ mod $ mod $ mod $ mod $ mod $ mod $ mod [ [ 1 [ 1 [ 1 [ 1 [-1 [-1 [-1 [-1 ] 1 1] 1-1] -1-1] -1 1] 1 1] ] -1 1] u=21 $ helium between $ CR1 $ CR2 $ CR3 $ CR4 $ CR5 $ CR6 $ CR7 $ CR8 $ CR9 $ CR1 $ He around CR $ He below CR $ CR 25

206 segment Universe 26: ontrol rod e e segment e e segment e e segment e e segment e e ' e e u=26 $ lower end u=26 u=26 u=26 u=26 u=26 $ inner sleeve $ gap $ B4C $ gap $ outer sleeve u=26 $ joint 1 u=26 u=26 u=26 u=26 u=26 $ inner sleeve $ gap $ B4C $ gap $ outer sleeve u=26 $ joint 2 u=26 u=26 u=26 u=26 u=26 $ inner sleeve $ gap $ B4C $ gap $ outer sleeve u=26 $ joint 3 u=26 u=26 u=26 u=26 u=26 $ inner sleeve $ gap $ B4C $ gap $ outer sleeve u=26 $ joint 4 u=26 u=26 u=26 u=26 u=26 u=26 u=26 u=26 $ inner sleeve $ gap $ B4C $ gap $ outer sleeve $ upper end $ entre hannel $ above rod 26

207 Absorber ball KLAK sites e e e e e e e Helium flow hannels e e e e e e e e e e e e e e e e e e e e-3 Irradiation hannels e e e (-277:-279) (278:-28) (-283:--285) (284:-286) (-289:-291) (29:-292) (-295:--297) (296:-298) (-31:--33) (32:-34) (-37:-39) (38:-31) (-313:-315) (314:-316) $ HE1 $ HE2 $ HE3 $ HE4 $ HE5 $ HE6 $ HE7 $ HE8 $ HE9 $ HE1 $ HE11 $ HE12 $ HE13 $ HE14 $ HE15 $ HE16 $ HE17 $ HE18 $ HE19 $ HE2 $ IR1 $ IR2 $ IR3 $ KL1 $ KL2 $ KL3 $ KL4 $ KL5 $ KL6 $ KL7 SURFACE CARDS 1 pz. 2 pz pz pz pz pz pz pz pz pz pz $ Top of borated C briks at reator top $ Bottom of borated C reator top $ Upper surfae of old He hamber $ Lower surfae of old He hamber $ Surfae between axial regions 3 and 82 $ Lower surfae of top refletor $ Top of fueled region minus 1.71 m $ Upper surfae of one region $ Lower surfae of one region $ Surfae between axial regions 8 and 9 $ Surfae between axial regions 9 and 1 27

208 12 pz pz pz pz pz pz pz z z z z z z z z z z z kz Fuel element $ Surfae between axial regions 1 and 12 $ Surfae between axial regions 13 and 14 $ Surfae between axial regions 6 and 7 $ Surfae between axial regions 16 and 17 $ Surfae between axia regions 7 and 81 $ Bottom of reator $ Bottom of CR guide hole $ radial fuel exlusion zone so 2.5 $ fuel region Unit ell in ore px px py py pz pz Balls in unit ells so 3. s s s s s s s s Coated Fuel Partiles so.25 so.34 so.38 so.415 so.455 $ Outer radius of fueled region $ Inner surfae of ontrol rod region $ Outer surfae of ontrol rod region $ Inner surfae of He flow region $ Outer surfae of He flow region $ Outer surfae of side graphite refletor $ Outside of radial borated C briks $ Outer surfae of one at bottom of ore $ [-1 ] $ [ 1 ] $ [ 1 ] $ [ -1 ] $ [ 1] $ [ -1] $ kernel $ 1st PyC layer $ 2nd PyC layer $ SiC layer $ 3rd PyC layer Unit ell for CFP lattie in graphite matrix 28

209 25 px px py py pz pz C C C C C C C C C C C Control rod hannels /z /z /z /z /z /z /z /z /z /z Small absorber ball hannels.. KL1 5 px 5 px 5 py 5 py 5 /z 5 /z.. KL2 6 px 6 px 6 py 6 py 6 /z 6 /z.. KL3 7 px 7 px 7 py 7 py 7 /z 7 /z.. KL4 8 px 8 px 8 py 8 py 8 /z 8 /z.l. J5 9 px 9 px $ CR1 $ CR2 $ CR3 $ CR4 $ CR5 $ CR6 $ CR7 $ CR8 $ CR9 $ CR1 29

210 C C C C C C C C PY PY /z /z.. KL6 1 px 1 px 1 py 1 py 1 /z 1 /z.. KL7 11 px 11 px 11 py 11 py 11 /z 11 /z Helium flow hannels /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z C Irradiation Channels C 34 /z /z /z pz pz pz pz pz Control Rods $ HE1 $ HE2 $ HE3 $ HE4 $ HE5 $ HE6 $ HE7 $ HE8 $ HE9 $ HE1 $ HEll $ HE12 $ HE13 $ HE14 $ HE15 $ HE16 $ HE17 $ HE18 $ HE19 $ HE2 $ IR1 $ IR2 $ IR3 $ bottom of CR $ segment 1' - bottom $ segment 1 - top $ segment 2 - bottom $ segment 2 - top 21

211 pz pz pz pz pz pz pz z z z 3.1 z z 5.31 z 5.51 $ segment 3 - bottom $ segment 3 - top $ segment 4 - bottom $ segment 4 - top $ segment 5 - bottom $ segment 5 - top $ top of rod $ inner sleeve - in $ inner sleeve - out $ absorber - inside $ absorber - outside $ outer sleeve - in $ outer sleeve - out RUN PARAMETERS NEUTRON IMPORTANCES imp: n 1 74r r 1 1lr 1 9r 1 2r 1 32r 1 6r 1 19r 1 2r TRANSFORMATIONS $ outside world $ graphite struture $ helium avity $ fuel region $ onus $ ontrol rod sites $ ontrol rod guide tubes $ ontrol rod $ KLAK sites $ Helium flow hannels $ Irradiation sites Center positions of unit ells in fill zones trl $ fuel ball region tr $ dummy ball region Small absorber ball hannels (entered on r = m) *tr $ KL1 *tr $ KL2 *tr $ KL3 *tr $ KL4 *tr $ KL5 *trlo $ KL6 *trll $ KL7 tr15 tr16 tr17 tr18 tr19 tr2 Control rod radial positions $ CR1 $ CR2 $ CR3 $ CR4 $ CR5 $ CR6 211

212 tr21 tr22 tr23 tr Control rod insertion (length = m) tr tr MATERIAL SPECIFICATIONS Graphite Struture ml e e e-8 mtl grph.lt m mt2 grph.lt m mt3 grph.lt m mt4 grph.olt m mts grph.olt m mt7 grph.olt m mt8 grph.olt m mt9 grph.olt m mtlo grph.lt mll mtll grph.olt m mt12 grph.olt e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e-5 $ CR7 $ CR8 $ CR9 $ CR1 $ fully out $ fully in 212

213 m mt13 grph.olt m mt14 grph.olt m mt15 grph.olt m16 6, mt16 grph.olt m mtl7 grph.olt m mt18 grph.olt m mt19 grph.olt m mt2 grph.olt m mt21 grph.olt m mt22 grph.olt m mt23 grph.olt m mt24 grph.olt m mt25 grph.olt m mt26 grph.olt m e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e-6 213

214 e-5 mt27 grph.olt m mt28 grph.olt m mt29 grph.olt m mt3 grph.olt m mt31 grph.olt m mt32 grph.olt m mt33 grph.olt m mt35 grph.olt m mt36 grph.olt m mt37 grph.olt m mt38 grph.olt m mt39 grph.olt m mt4 grph.olt m mt41 grph.olt e e e e e e e e e e e e e e e e e e e e e e e e e e-3 m e e e e e e e e e e e e e e e e-8 214

215 mt43 grph.1t m e e e-3 mt44 grph.1t m e e e-7 mt45 grph.1t Helium oolant (4.814e-3 g/ at 3K) m Control-rod metalli struture (iron at a redued density of 5 g/m3) m Control-rod B4C absorber m Fuel element.. fuel kernel (N = e-2) m e e e e e-8.. graphite layers of CFP m SiC layer of CFP m graphite matrix in fuel pebble (N = e-2) m e e e-9 mt64 grph.1t.. graphite matrix in fuel pebble (N = e-2) m e e e-8 mt65 grph.1t define U of Texas ross-setion libraries at 3K xsl he E-8 $ He-3 xs he E-8 $ He-4 xs b E-8 $ B-1 xs b11l E-8 $ B-ll xs nat E-8 $ C-nat xs o E-8 $ -16 xs7 xs fe E-8 $ Fe fe E-8 $ Fe

216 xs fe E-8 $ Fe-57 xslo fe E-8 $ Fe-58 xsll u E-8 $ U-235 xs u E-8 $ U-238 PROBLEM TYPE mode n totnu kode sdef pos= axs= 1 rad=dl ext=d2 sil spl 1 si sp2 1 Printing and utoff ards print dbn 9j 3 prdmp j

217 APPENDIX C. MCNP4B Models of ASTRA Faility Appendix C ollets the MCNP4B input files for the models of the ASTRA faility. Appendix C. 1 ontains the model with an exat 'super' ell ore representation. Appendix C.2 ontains the model of an infinite lattie with the exat 'super' ell representation of the fuelled region of the ASTRA ore. In Appendix C.3, the same infinite lattie is approximated by a primitive BCC unit ell with borated fuel spheres. This approximate ore representation is applied to the ASTRA ore in Appendix C.4. Details on the ASTRA faility may be found in Chapter

218 APPENDIX C.1: MCNP4B model of ASTRA, superell ore representation ASTRA - PBMR CRITICAL EXPERIMENT MCNP4B model of the PBMR mokup in ASTRA faility at the Kurhatov Institute, Mosow. Control/shutoff rod positions: CELLS reator struture SD rods fully withdrawn CR2 in position 1 all other CRs in position 1 MR1 at referene ritial height No top refletor Paking fration =.625 BCC lattie No exlusion zones J.R. Lebenhaft, MIT, July : 26: (35:-36: 37:-38: fill=1 (5) radial refletor lattie 5 lat=l u=1 fill=-12:4-8: ; (51) (41) (52) : (53) 6 25(45) (58) 6 22(42) : 4:-41:-42) (57) 5 O O O (54) 7 7 h = m h = m h = m h = m (44) (56) 6 26(46) 35(55) 5 23(43) $ outside world $ bottom refletor $ top refletor $ radial refletor

219 u=5 universe 6: graphite blok with empty enter hole e-5-54 u=6 $ graphite u=6 $ air universe 7: graphite blok with filled enter hole u=7 $ graphite e u=7 $ air gap u=7 $ graphite plug universe 8: graphite blok with small experimental hannel and empty enter hole (199:-2:-198) e e u=8 $ graphite u=8 $ hannel u=8 $ hole universe 9: graphite blok with small experimental hannel and plug in enter hole (199:-2:-198) e e e e e e-5 universe 11: ontrol-rod spider u=9 u=9 u=9 u= $ graphite $ hannel $ air gap $ plug u=1ll $ outer ring u=1ll $ enter u=1ll $ x-tie u=1ll $ y-tie u=ll $ gap - top right u=1ll $ gap - top left u=11 $ gap - bot right u=ll $ gap - bot left universe 12: ontrol rod end-plate u=12 $ outer ring e e u=12 $ pin 1 holder u=12 $ pin 2 holder 219

220 e e e e e e e e e e e e e e e e e universe 15: ontrol/shutdown pin assembly fill=16(21) fill=16(22) fill=16(23) fill=16(24) fill=16(25) 5-1 fill=16(26) fill=16(27) fill=16(28) fill=16(29) fill=16(3) fill=16(31) fill=16(32) fill=16(33) fill=16(34) fill=16(35) e universe 16: ontents of absorber pin u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=15 u=15 u=15 u=15 u=15 u=15 u=15 u=15 u=15 u=15 u=15 u=15 u=15 u=15 u=15 $ pin 3 holder $ pin 4 holder $ pin 5 holder $ pin 6 holder $ pin 7 holder $ pin 8 holder $ pin 9 holder $ pin 1 holder $ pin 11 holder $ pin 12 holder $ pin 13 holder $ pin 14 holder $ pin 15 holder $ enter $ x-tie $ y-tie $ gap - top right $ gap - top left $ gap - bot right $ gap - bot left $ pin $ pin $ pin $ pin $ pin $ pin $ pin $ pin $ pin $ pin $ pin $ pin $ pin $ pin $ pin u=15 $ air u=16 $ s/s u=16 $ B4C lad _ universe 17: air-filled portion of ontrol/shutdown pins fill=18(21) u=17 $ pin fill=18(22) u=17 $ pin 2 22

221 e universe 18: ontents of absorber pin universe 19: upper pin holder e e e universe 2: hollow interior fill=18(23) fill=18(24) fill=18(25) fill=18(26) fill=18(27) fill=18(28) fill=18(29) fill=18(3) fill=18(31) fill=18(32) fill=18(33) fill=18(34) fill=18(35) fill=2(21) fill=2(22) fill=2(23) fill=2(24) fill=2(25) fill=2(26) fill=2(27) fill=2(28) fill=2(29) fill=2(3) fill=2(31) fill=2(32) fill=2(33) fill=2(34) fill=2(35) u=17 $ pin 3 u=17 u=17 u=17 u=17 $ pin 4 $ pin 5 $ pin 6 $ pin 7 u=17 u=17 u=17 u=17 u=17 u=17 u=17 u=17 $ pin $ pin $ pin $ pin $ pin $ pin $ pin $ pin u=17 $ air u=18 $ s/s lad u=18 $ air u=19 u=19 u=19 u=19 u=19 u=19 u=19 u=19 u=19 u=19 u=19 u=19 u=19 u=19 u=19 $ pin 1 $ pin 2 $ pin 3 $ pin 4 $ pin 5 $ pin 6 $ pin 7 $ pin 8 $ pin 9 $ pin 1 $ pin 11 $ pin 12 $ pin 13 $ pin 14 $ pin 15 u=19 $ air u=2 $ s/s holder u=2 $ air universe 21: ontrol rod CR1 (with small experiment hannel) (199:-2:-198) e e u=21 $ graphite u=21 $ expt. hannel u=21 $ surrounding air 221

222 e universe 22: ontrol rod CR e e fill=21 universe 23: ontrol rod CR e e fill=21 universe 24: ontrol rod CR e e fill=21 universe 25: ontrol rod CR e e universe 26: manual rod MR e e u=21 $ air below rod fill=21 u=21 $ rod u=22 u=22 u=22 u=22 u=23 u=23 u=23 u=23 u=24 u=24 u=24 u=24 $ graphite $ surrounding air $ air below rod $ rod $ graphite $ surrounding air $ air below rod $ rod $ graphite $ surrounding air $ air below rod $ rod _ universe 31: ontrol rod SR e e u=25 u=25 u=25 fill=21 u=25 $ graphite $ surrounding air $ air below rod $ rod u=26 $ graphite u=26 $ surrounding air u=26 $ air below rod fill=22 u=26 $ rod u=31 $ graphite u=31 $ surrounding air u=31 $ air below rod fill=21 u=31 $ rod universe 32: ontrol rod SR u=32 $ graphite 222

223 e e universe 33: ontrol rod SR e e universe 34: ontrol rod SR e e universe 35: ontrol rod SR e e universe 36: ontrol rod SR e e universe 37: ontrol rod SR e e universe 38: ontrol rod SR e e universe 21: details of ontrol/shutoff rod u=32 u=32 fill=21 u=32 u=33 u=33 u=33 fill=21 u=33 u=34 u=34 u=34 fill=21 u=34 u=35 u=35 u=35 fill=21 u=35 u=36 u=36 u=36 fill=21 u=36 u=37 u=37 u=37 fill=21 u=37 u=38 u=38 u=38 fill=21 u=38 $ surrounding air $ air below rod $ rod $ graphite $ surrounding air $ air below rod $ rod $ graphite $ surrounding air $ air below rod $ rod $ graphite $ surrounding air $ air below rod $ rod $ graphite $ surrounding air $ air below rod $ rod $ graphite $ surrounding air $ air below rod $ rod $ graphite $ surrounding air $ air below rod $ rod u=21 $ lower endplate 223

224 e e universe 22: details of manual rod e e fill=12 fill=17 fill=15 fill=17 fill=19 fill=ll fill=12 fill=17 fill=15 fill=17 fill=19 fill=ll u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=22 u=22 u=22 u=22 u=22 u=22 u=22 $ lower pin holder $ empty pin zone $ absorber $ empty pin zone $ upper pin holder $ spider $ middle gap $ middle joint $ lower endplate $ lower pin holder $ empty pin zone $ absorber region $ empty pin zone $ upper pin holder $ spider $ air above rod $ solid bottom $ inner wall $ air gap $ outer wall $ solid top $ enter gap $ upper mid plate ore avity e e e-5 ore regions 529 fill=5(2) 53 fill=52(3) fill=54(4) experimental hannels fill=68 fill=7 fill=75 fill=8 fill=85 fill=9 $ above fuel zone $ above mixed zone $ above inner reflet $ inner refletor $ mixed zone $ fuel outer zone $ entral hannel $ El $ E2 $ E3 $ E4 $ E5 224

225 universe 5: inner refletor lat=l fill=51(7) u= lat=l u=51 fill=o:l :1-2: u n iverse universe 52: mixed fuel/moderator/absorber zone lat=l fill=53(7) u= ,3 lat=l u=53 fill=o:l :1-2: universe 54: outer fuel zone lat=l fill=55(7) u= lat=l u=55 fill=o:1 :1-2: Universe 56: b unit ell (moderator) u= u= u= u= u=56 225

226 air between spheres e u= Universe 57: b unit ell (moderator + 1 fuel sphere) air between spheres e u= e u=57 u=57 u=57 u=57 fill=62(645) u=57 u=57 u=57 u=57 u=57 Universe 58: b unit ell (moderator + 1 absorber sphere) air between spheres u=58 fill=65(645) Universe 59: b unit ell (fuel) u=56 u=56 u=56 u=56 u=58 u=58 u=58 u=58 u=58 u=58 u=58 u=58 u=58 fill=62(641) u=59 fill=62(642) u=59 226

227 fi11=62(643) u= fill=62(644) u= fill=62(645) u= fill=62(646) u= fill=62(647) u= fill=62(648) u= fill=62(649) u=59 air between spheres e u=59 Universe 6: b unit ell (fuel + 1 absorber sphere) fill=62(641) u= fill=62(642) u= fill=62(643) u= fill=62(644) u= fill=65(645) u= fill=62(646) u= fill=62(647) u= fill=62(648) u= fill=62(649) u=6 air between spheres e u=6 Universe 62: details of fuel sphere u=62 $ shell fill=63 u=62 $ fuel region Universe 63: embedded oated fuel partiles lat=1 fill=64 u=63 Universe 64: oated fuel partile u=64 $ U2 kernel u=64 $ PyC layer u=64 $ PyC layer u=64 $ SiC layer u=64 $ PyC layer u=64 $ graphite 227

228 C C C C universe 65: absorber sphere universe 66: absorber region u=65 $ shell fill=66 u=65 $ absorber lat=l fill=67 u=66 $ simple ubi universe 67: absorber kernel u=67 $ B4C u=67 $ graphite universe 68: entral hannel u=68 $ Al wall e-5-27 u=68 $ air universe 7: experimental tube El u=7 $ Al wall e u=7 $ air universe 75: experimental tube E u=75 $ Al wall e u=75 $ air universe 8: experimental tube E u=8 $ Al wall e-5-19 u=8 $ air universe 85: experimental tube E u=85 $ Al wall e u=85 $ air universe 9: experimental tube E u=9 $ Al wall e u=9 $ air 8 9 SURFACES pz. $ bottom of reator pz 4. $ bottom of ore 228

229 C C ore height pz 38.9 pz 38.9 pz pz pz pz z z z z z 19. ore boundary (x-y plane) 35 px px py py p 1. 4 p p p refletor bloks (x-y plane) z 5.6 z 5.7 px 12.5 px py 12.5 py z pebble-bed lattie px px py py pz pz inside fuel pebble $ top of outer fuel zone $ top of mixed fuel zone $ top of inner refletor $ bottom of Al struture $ bottom of upper refletor $ top of reator $ enter tube - inner surfae $ enter tube - outer surfae $ inner refletor boundary $ mixed- zone boundary $ outer surfae of reator $ $ $ $ $ $ $ $ right left top bottom top right top left bottom left bottom right $ graphite plug $ hole in graphite blok $ right $ left $ top $ bottom $ universe boundary $ -x $ +x $ -y $ +y $ bottom $ top so 2.5 $ fueled region unit ell for CFP lattie px px py py

230 8 pz pz oated fuel partile so so so so so inside absorber sphere 87 unit absorber ell 88 px px py py pz pz so.3 absorber pins outer surfaes $ U2 kernel $ buffer $ inner PyC $ si $ outer PyC so 2. $ radius of absorber region /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z z.55 b unit ell px px PY PY pz pz aluminum experiment tubes - outer surfaes $ absorber kernel radius $ absorber outer surfae $ -x $ +x $ -Y $ +y $ bottom $ top 23

231 C/z C/z C/z C/z C/z aluminum experiment tubes - inner surfaes /z /z -25. /z -45. /z -65. /z px py py small experiment hannels ontrol and shutoff rod surfaes z.3 z 1.5 z 3.1 z 4.5 px.5 px -.5 py.5 py -.5 manual z z z z CR1 pz pz pz pz pz pz pz pz pz pz pz pz pz pz pz pz MR1 rod $ El $ E2 $ E3 $ E4 $ E5 $ El $ E2 $ E3 $ E4 $ E5 $ radius of pin end-region $ joint $ inside of pin holder $ outside of pin holder $ pin support $ pin support $ pin support $ pin support $ inside of inner surfae $ outside of inner surfae $ inside of outer surfae $ outer surfae of rod $ bottom of lower endplate $ bottom of lower pin holder $ bottom of lower pins $ bottom of B4C in lower pins $ top of B4C in lower pins $ bottom of lower pin holder $ bottom of lower spider $ bottom of middle gap $ bottom of upper endplate $ bottom of pin holder $ bottom of upper pins $ bottom of B4C in upper pins $ top of B4C in upper pins $ bottom of upper holder $ bottom of upper spider $ top of upper spider 231

232 C pz. 45 pz pz pz pz upper pin holder /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z ontrol rod end-plate /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z spheres s s s s so s s s s $ bottom of rod $ bottom of air gap $ top of air gap $ bottom of top plate $ top of rod $ [-a/2 $ ( a/2 $ [-a/2 $ [ a/2 $ [ $ (-a/2 $ [ a/2 $ [-a/2 $ [ a/2 -a/2 -a/2 a/2 a/2 -a/2 -a/2 a/2 a/2 -b/2] -b/2] -b/2] -b/2] ] b/2] b/2] b/2] b/2] 232

233 C C C C mode kode sdef sil spl si2 sp2 totnu print dbn prdmp RUN PARAMETERS problem type n pos= 4 axs= imp:n I r 1 2r 1 3r 1 7r 1 22r 1 17r 1 17r 1 17r 1 4r 1 3r 1 3r 1 3r 1 16r 1 6r 1 2r 1 2r 1 5r 1 5r 1 9r 1 9r 1 9r 1 9r 1 9r 1 8r 1 4r i j 3 j neutron importane 1 rad=dl ext=d2 1 3r 1 3r 1 3r 1 3r 1 3r 1 3r 1 3r 1 3r 1 3r 1 3r $ outside world $ reator struture $ u=1: radial refletor lattie $ u=5: solid graphite blok $ u=6: graphite blok with hole $ u=7: graphite blok/plug $ u=8: graphite blok/hole/hannel $ u=9: graphite blok/plug/hannel $ u=11: ontro rod end-plate $ u=12: lower pin holder $ u=15 and 16: B4C pins $ u=17 and 18: gap in pins $ u=19 and 2: pin holder $ u=21 to 25: CRs $ u=26: MR1 $ u=31 to 38: SD rods $ u=21: details of CR $ u=22: details of MR $ avity above ore $ ore regions $ experimental hannels $ u=5 to 55: unit ells $ u=56: moderator $ u=57: moderator + 1 fuel $ u=58: moderator + 1 absorber $ u=59: fuel $ u=6: fuel + absorber $ u=62 to 64: fuel sphere $ u=65 to 67: absorber sphere $ u=65: enter hannel $ u=7: El $ u=75: E2 $ u=8: E3 $ u=85: E4 $ u=9: E5 233

234 transformations tr2 tr3 tr4 tr5 tr absorber pins - inner surfaes tr tr tr tr tr tr tr tr tr tr tr tr tr tr tr ontrol rod positions tr tr tr tr tr tr shutdown rod positions tr tr tr tr tr tr tr tr sphere positions tr tr tr tr tr645.. tr tr tr tr $ inner refletor origin $ mixed zone origin $ fuel zone origin $ refletor origin $ origin of unit ell fill $ CR1 $ CR2 $ CR3 $ CR4 $ CR5 $ MR1 $ SD1 $ SD2 $ SD3 $ SD4 $ SD5 $ SD6 $ SD7 $ SD8 position (ritial) out 234

235 C C material speifiations C ml $ U2 m $ PyC mt2 grph.lt m mt3 grph.lt m mt4 grph.lt m mt5 grph.lt m e ontrol and shutdown rods refletor graphite m e-6 mt9 grph.lt e e-6 aluminum experiment tubes m humid air mll m e e e-5 aluminum manual rod e e $ si $ graphite $ B4C $ s/steel 235

236 APPENDIX C.2: Infinite ASTRA lattie using exat superell model ASTRA SUPERCELL MODEL MCNP4B superell model with 4 fuel spheres with borated shells. The CFPs are modeled expliitly. The boron and arbon in these spheres reprodue the 95/5 fuel-to-absorber sphere ratio. The repeating unit geometry is an enlarged BCC ell CELLS fill=1 3 lat=l fill=2(7) u=l universe 1: super ell 6: -59: 62: lat=l u=2 fill=:1 :1-2: Universe 59: b unit ell (fuel) fill=62(641) fill=62(642) fill=62(643) fill=62(644) fill=62(645) fill=62(646) fill=62(647) fill=62(648) fill=62(649) u=59 u=59 u=59 u=59 u=59 u=59 u=59 u=59 u=59 18 air between spheres e u=59 Universe 6: bt unit ell (fuel + 1 absorber sphere) fill=62(641) u=6 $ outside world $ periodi BC $ inside world 236

237 fill62(642) fill=62(643) fill=62(644) fill=65 (645) fill=62(646) fill=62(647) fill=62(648) fill=62 (649) air between spheres e u=6 Universe 62: details of fuel sphere lat=l fill=64 u= Universe 63: embedded oated fuel partiles Universe 64: oated fuel partile _ universe 65: absorber sphere universe 66: absorber region 62 lat=l fill=67 u= universe 67: absorber kernel u=6 u=6 u=6 u=6 u=6 u=6 u=6 u=6 u=62 $ shell fill=63 u=62 $ fuel region u=64 u=64 u=64 u=64 u=64 u=64 u=65 fill=66 u=65 $ U2 kernel $ PyC layer 1 $ PyC layer 2 $ SiC layer $ PyC layer 3 $ graphite $ shell $ absorber $ simple ubi u=67 $ B4C u=67 $ graphite SURFACES 237

238 pebble-bed lattie px -59 px -62 py -61 py px px py py pz pz inside fuel pebble 75 unit ell for CFP lattie 76 px px py py pz pz oated fuel partile 82 so so so so so.53 inside absorber sphere 87 so 2. unit absorber ell $ -x $ +x $ -y $ +y $ -x $ +x $ -y $ +y $ bottom $ top so 2.5 $ fueled region px px py py pz pz so.3 b unit ell px px PY PY $ $ S $ $ U2 kernel buffer inner PyC si outer PyC $ radius of absorber region $ absorber kernel radius $ -x $ +x $ -Y $ +y 238

239 pz pz spheres s s s s so s s s s $ bottom $ top $ [-a/2 $ [ a/2 $ [-a/2 $ [ a/2 $ [ $ [-a/2 $ [ a/2 $ [-a/2 $ [ a/2 -a/2 -a/2 a/2 a/2 -a/2 -a/2 a/2 a/2 -b/2] -b/2] -b/2] -b/2] ] b/2] b/2] b/2] b/2] TRANSFORMATIONS tr $ origin of unit ell fill sphere positions tr641 tr642 tr643 tr644 tr645 tr646 tr647 tr648 tr MATERIALS ml $ U2 m $ PyC mt2 grph.olt m $ si mt3 grph.olt m e e-6 $ graphite mt4 grph.olt m $ B4C mt5 grph.1t mll humid air e e e e e-7 239

240 C C RUN PARAMETERS mode n kode sdef pos=o axs= 1 rad=dl ext=d2 sil spl 1 si sp2 1 imp:n $ outside world 1 $ inside world 1 $ u=l 1 $ u=2: super ell 1 9r $ u=59 1 9r $ u=6 1 8r $ u=62 to u=64 1 4r $ u=65 to u=67 totnu print dbn 9j 3 prdmp j

241 APPENDIX C.3: Infinite ASTRA lattie using borated fuel shell ASTRA SUPERCELL MODEL MCNP4B model of an infinite BCC lattie of fuel spheres with borated shells. 1 2 CELLS fill=1 3 fill=2 lat=l u=l : -59: 62: Universe 2: b unit ell fill=62(641) fill=62(642) fill=62(643) fill=62(644) fill=62(645) fill=62(646) fill=62(647) fill=62(648) fill=62(649) u=2 u=2 u=2 u=2 u=2 u=2 u=2 u=2 u=2 $ outside world $ periodi BC $ lattie air between spheres e u=2 Universe 62: details of fuel sphere u=62 $ borated shell fill=63 u=62 $ fuel region Universe 63: embedded oated fuel partiles lat=1 fill=64 u=63 Universe 64: oated fuel partile u=64 $ U2 kernel u=64 $ PyC layer u=64 $ PyC layer u=64 $ SiC layer 241

242 u=64 $ PyC layer 3 u=64 $ graphite SURFACES 59-6 px 6-59 px py py b unit ell (paking fration =.625) 69 px px py py pz pz inside fuel pebble 75 so px px py py pz pz unit ell for CFP lattie oated fuel partile 82 so so so so so.53 spheres pebble-bed lattie s s s s so s s s s $ $ $ $ $ $ $ $ $ $ -x +x -Y +y -x +x -y +y bottom top $ fueled region $ U2 kernel $ buffer $ inner PyC $ si $ outer PyC $ [-a/2 $ [ a/2 $ [-a/2 $ [ a/2 $ [ $ [-a/2 $ [ a/2 $ [-a/2 $ [ a/2 -a/2 -a/2 a/2 a/2 -a/2 -a/2 a/2 a/2 -b/2] -b/2] -b/2] -b/2] ] b/2] b/2] b/2] b/2] TRANSFORMATIONS 242

243 C tr641 tr642 tr643 tr644 tr645 tr646 tr647 tr648 tr649 sphere positions C MATERIALS ml m mt2 grph.lt m mt3 grph.olt m e mt4 grph.olt m e-5 mt6 grph.lt humid air mll e e e-5 RUN PARAMETERS mode n kode e e e e-7 sdef pos= axs= 1 rad=dl ext=d2 sil spl 1 si sp2 1 imp:n 1 1 9r 1 8r totnu print dbn 9j 3 prdmp j $ U2 $ PyC $ si $ graphite $ borated shell $ outside world $ inside world $ u=l $ u=2: b unit $ u=62 to u=64 243

244 APPENDIX C.4: MCNP4B model of ASTRA using BCC ore representation ASTRA - PBMR EXPERIMENT MCNP4B model of the PBMR mokup in ASTRA faility at the Kurhatov Institute, Mosow. Task 3: Differential reativity worth of ontrol rods. No top refletor SD rods fully withdrawn CR2 in position 1 all other CRs in position 1 MR1 at referene ritial height Paking fration =.625 Simple BCC lattie withi borated fuel spheres No exlusion zones J.R. Lebenhaft, MIT, August 21 CELLS 1-8: 26: 32 reator struture (35:-36: 37:-38: fill=1(5) radial refletor lattie lat=l u=l fill=-12:4-8:8 : (51) (41) (52) (53) 6 25(45) : 4:-41:-42) (57) 5 h = m h = m h = m h = m _ (44) 5 5 $ outside world $ bottom refletor $ top refletor $ radial refletor (56) 6 26(46) 35(55) 23(43)

245 (58) 6 22(42) 6 34(54) u=5 universe 6 graphite blok with empty enter hole e e universe 7: graphite blok with filled enter hole 53 u=6 $ graphite u=6 $ air universe 8: graphite blok with small experimental hannel and empty enter hole (199:-2:-198) e e u=7 $ graphite u=7 $ air gap u=7 $ graphite plug u=8 $ graphite u=8 $ hannel u=8 $ hole universe 9: graphite blok with small experimental hannel and plug in enter hole (199:-2:-198) e e universe 11: ontrol-rod spider e e e e universe 12: ontrol rod end-plate u=9 u=9 u=9 u=9 $ graphite $ hannel $ air gap $ plug u=11 $ outer ring u=11 $ enter u=11 $ x-tie u=11 $ y-tie u=11 $ gap - top right u=11 $ gap - top left u=11 $ gap - bot right u=11 $ gap - bot left 245

246 e e e e e e e e e e e e e e e e e e e e u=12 $ outer ring universe 15: ontrol/shutdown pin assembly universe 16: ontents of absorber pin fill=16(21) fill=16(22) fill=16(23) fill=16(24) fill=16(25) fill=16(26) fill=16(27) fill=16(28) fill=16(29) fill=16(3) fill=16(31) fill=16(32) fill=16(33) fill=16(34) fill=16 (35) u=12 u-12 u-12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=15 u=15 u=15 u=15 u=15 u=15 u=15 u=15 u=15 u=15 u=15 u=15 u=15 u=15 u=15 $ pin 1 holder $ pin 2 holder $ pin 3 holder $ pin 4 holder $ pin 5 holder $ pin 6 holder $ pin 7 holder $ pin 8 holder $ pin 9 holder $ pin 1 holder $ pin 11 holder $ pin 12 holder $ pin 13 holder $ pin 14 holder $ pin 15 holder $ enter $ x-tie $ y-tie $ gap - top right $ gap - top left $ gap - bot right $ gap - bot left $ pin 1 $ pin 2 $ pin 3 $ pin 4 $ pin 5 $ pin 6 $ pin 7 $ pin 8 $ pin 9 $ pin 1 $ pin 11 $ pin 12 $ pin 13 $ pin 14 $ pin 15 u=15 $ air u=16 $ s/s lad u=16 $ B4C 246

247 universe 17: air-filled portion of ontrol/shutdown pins e e universe 18: ontents of absorber pin universe 19: upper pin holder e universe 2: hollow interior e-5-21 C C fill=18(21) fill=18(22) fill=18(23) fill=18(24) fill=18(25) fill=18(26) fill=18(27) fill=18(28) fill=18(29) fill=18(3) fill=18(31) fill=18(32) fill=18(33) fill=18(34) fill=18(35) fill=2(21) fill=2(22) fill=2(23) fill=2(24) fill=2(25) fill=2(26) fill=2(27) fill=2(28) fill=2(29) fill=2(3) fill=2(31) fill=2(32) fill=2(33) fill=2(34) fill=2(35) u=17 u=17 u=17 u=17 u=17 u=17 u=17 u=17 u=17 u=17 u=17 u=17 u=17 u=17 u=17 $ pin 1 $ pin 2 $ pin 3 $ pin 4 $ pin 5 $ pin 6 $ pin 7 $ pin 8 $ pin 9 $ pin 1 $ pin 11 $ pin 12 $ pin 13 $ pin 14 $ pin 15 u=17 $ air u=18 $ s/s lad u=18 $ air u=19 u=19 u=19 u=19 u=19 u=19 u=19 u=19 u=19 u=19 u=19 u=19 u=19 u=19 u=19 $ pin $ pin $ pin $ pin $ pin $ pin $ pin $ pin $ pin $ pin $ pin $ pin $ pin $ pin $ pin u=19 $ air u=2 $ s/s holder u=2 $ air 247

248 universe 21: ontrol rod CR1 (with small experiment hannel) (199:-2:-198) 5.58e e e universe 22: ontrol rod CR e e universe 23: ontrol rod CR e e universe 24: ontrol rod CR e e universe 25: ontrol rod CR e e universe 26: manual rod MR e e u=21 u=21 u=21 u=21 fill=21 u=21 u=22 u=22 u=22 fill=21 u=22 fill=21 fill=21 u=23 u=23 u=23 u=23 u=24 u=24 u=24 u=24 u=25 u=25 u=25 fill=21 u=25 u=26 u=26 u=26 fill=22 u=26 $ graphite $ expt. hannel $ surrounding air $ air below rod $ rod $ graphite $ surrounding air $ air below rod $ rod $ graphite $ surrounding air $ air below rod $ rod $ graphite $ surrounding air $ air below rod $ rod $ graphite $ surrounding air $ air below rod $ rod $ graphite $ surrounding air $ air below rod $ rod _ universe 31: ontrol rod SR e e u=31 u=31 u=31 fill=21 u=31 $ graphite $ surrounding air $ air below rod $ rod 248

249 universe 32: ontrol rod SR e e universe 33: ontrol rod SR e e universe 34: ontrol rod SR e e universe 35: ontrol rod SR e e universe 36: ontrol rod SR e e-C universe 37: ontrol rod SR e e universe 38: ontrol rod SR u=32 u=32 u=32 fill=21 u=32 u=33 u=33 u=33 fill=21 u=33 u=34 u=34 u=34 fill=21 u=34 u=35 u=35 u=35 fill=21 u=35 u=36 u=36 u=36 fill=21 u=36 fill= e e fill=21 u=37 u=37 u=37 u=37 u=38 u=38 u=38 u=38 $ graphite $ surrounding air $ air below rod $ rod $ graphite $ surrounding air $ air below rod $ rod $ graphite $ surrounding air $ air below rod $ rod $ graphite $ surrounding air $ air below rod $ rod $ graphite $ surrounding air $ air below rod $ rod $ graphite $ surrounding air $ air below rod $ rod $ graphite $ surrounding air $ air below rod $ rod 249

250 C C universe 21: details of ontrol/shutoff rod e e universe 22: details of manual rod e e ore avity e-5 zone refletor 5.58e e-5 ore regions 529 fill=5(2) 53 fill=52(3) fill=54(4) fill=12 fill=17 fill=15 fill=17 fill=19 fill=ll1 fill=12 fill=17 fili=15 fill=17 fill=19 fill= experimental hannels u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=22 u=22 u=22 u=22 u=22 u=22 u=22 $ lower endplate $ lower pin holder $ empty pin zone $ absorber $ empty pin zone $ upper pin holder $ spider $ middle gap $ middle joint $ lower endplate $ lower pin holder $ empty pin zone $ absorber region $ empty pin zone $ upper pin holder $ spider $ air above rod $ -nlid bottom $ inner wall $ air gap $ outer wall $ solid top $ enter gap $ upper mid plate $ above outer fuel $ above mixed zone 184 $ above inner $ inner refletor $ mixed zone $ fuel outer zone 25

251 universe 5: inner refletor lat=l fill=51 u=5 Universe 51: b unit ell (moderator) air between spheres e u=51 universe 52: mixed fuel/moderator/absorber zone lat=l fill=53 u=52 Universe 53: BCC unit ell (moderator/borated e fill=65 $ entral hannel fill=7 $ El fill=75 $ E2 fill=8 $ E3 fill=85 $ E4 fill=9 $ E5 fuel) fill=6 u=53 u=53 u=53 u=53 u=53 u=53 u=53 u=53 u=53 u=51 u=51 u=51 u=51 u=51 u=51 u=51 u=51 u=51 $ [ [ 1 $ [1 $ [ 1 $ [1 $ [-1 $ [-1 $ [-1 $ [-1 u=53 $ air o ] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] 251

252 universe 54: outer borated fuel zone lat=l fill=55 u=54 Universe 55: BCC unit ell -121 fill=6 u=55 $ [ ] -122 fill=6(11) u=55 $ [ 1 1 1] -123 fill=6(12) u=55 $ [ 1 1-1] -124 fill=6(13) u=55 $ ( ] -125 fill=6(14) u=55 $ [ 1-1 1] -126 fill=6(15) u=55 $ [-1 1 1] -127 fill=6(16) u=55 $ [-1 1-1] -128 fill=6(17) u=55 $ [ ] -129 fill=6(18) u=55 $ [-1-1 1] e u=55 $ air Universe 6: details of fuel element u=6 $ borated shel1-75 fill=61 u=6 $ fuel region Universe 61: embedded oated fuel partiles lat=l fill=62 u=61 Universe 62: oated fuel partile u=62 $ U2 kernel u=62 $ PyC layer u=62 $ PyC layer u=62 $ SiC layer u=62 $ PyC layer u=62 $ graphite universe 65: entral hannel u=65 $ Al wall e-5-27 u=65 $ air universe 7: experimental tube El u=7 $ Al wall 252

253 e universe 75: experimental tube E e universe 8: experimental tube E e-5-19 universe 85: experimental tube E e universe 9: experimental tube E e SURFACES 8 pz. 9 pz 4. ore height 17 pz pz pz pz 27 z 28 z 3 z 31 z 32 z 35 px 36 px 37 py 38 py 39 p 4 p 41 p 42 p pz 36.8 pz ore boundary (x-y plane) refletor bloks (x-y plane) $ bottom of reator $ bottom of ore u=7 $ air u=75 $ A wall u=75 $ air u=8 $ Al wall u=8 $ air u=85 $ Al wall u=85 $ air u=9 $ Al wall u=9 $ air $ top of outer fuel zone $ top of mixed fuel zone $ top of inner refletor $ bottom of Al struture $ bottom of upper refletor $ top of reator $ enter tube - inner surfae $ enter tube - outer surfae $ inner refletor boundary (36.25) $ mixed- zone boundary (52.75) $ outer surfae of reator $ right $ left $ top $ bottom $ top right $ top left $ bottom left $ bottom right 253

254 53 z z px px py py z pebble-bed lattie 69 px px py py pz pz inside fuel pebble 75 so 2.5 unit ell for CFP lattie 76 px px py py pz, pz oated fuel partile so.25 so.34 so.41 so.47 so.53 absorber pins - outer surfaes /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z $ graphite plug $ hole in graphite blok $ right $ left $ top $ bottom $ universe boundary $ -x $ +x $ -Y $ +Y $ bottom $ top $ fueled region $ U2 kernel $ buffer $ inner PyC $ si $ outer PyC 254

255 11 CZ. 55 spheres in unit ell C C aluminum experiment tubes - outer surfaes /z /z /z /z /z aluminum experiment tubes - inner surfaes C/z C/z C/z C/z C/z 198 px 199 py 2 py so S S s S S s s small experiment hannels ontrol and shutoff rod surfaes z.3 z 1.5 z 3.1 z 4.5 px.5 px -.5 py.5 py -.5 manual z z z z rod Control rod 215 pz. 216 pz.1 $ absorber outer surfae $ El $ E2 $ E3 $ E4 $ E5 $ El $ E2 $ E3 $ E4 $ E5 $ radius of pin end-region $ joint $ inside of pin holder $ outside of pin holder $ pin support $ pin support $ pin support $ pin support $ inside of inner surfae $ outside of inner surfae $ inside of outer surfae $ outer surfae of rod $ bottom of lower endplate $ bottom of lower pin holder 255

256 pz pz pz pz pz pz pz pz pz pz pz pz pz pz Manual regulating rod 45 pz. 45 pz pz pz pz upper pin holder /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z ontrol rod end-plate /z /z /z /z /z /z /z /z /z /z /z /z /z /z $ bottom of lower pins $ bottom of B4C in lower pins $ top of B4C in lower pins $ bottom of lower pin holder $ bottom of lower spider $ bottom of middle gap $ bottom of upper endplate $ bottom of pin holder $ bottom of upper pins $ bottom of B4C in upper pins $ top of B4C in upper pins $ bottom of upper holder $ bottom of upper spider $ top of upper spider $ bottom of rod $ bottom of air gap $ top of air gap $ bottom of top plate $ top of rod 256

257 535 /z mode kode sdef sil spl si2 sp2 totnu print dbn prdmp imp:n RUN PARAMETERS problem type n pos= 4 axs= 1 rad=dl ext=d j 3 j neutron importane 1 1 2r 2r 3r 7r 22r 17r 17r 17r 4r 3r 3r 3r 16r 6r 2r 2r Sr lor lor lor 8r r 1 3r 1 3r 1 3r 1 3r 1 3r 1 3r 1 3r 1 3r 1 3r $ outside world $ reator struture $ u=l1: radial refletor lattie $ u=5: solid graphite blok $ u=6: graphite blok with hole $ u=7: graphite blok/plug $ u=8: graphite blok/hole/hannel $ u=9: graphite blok/plug/hannel $ u=11: ontro rod end-plate $ u=12: lower pin holder $ u=15 and 16: B4C pins $ u=17 and 18: gap in pins $ u=19 and 2: pin holder $ u=21 to 25: CRs $ u=26: MR1 $ u=31 to 38: SD rods $ u=21: details of CR $ u=22: details of MR $ avity above ore $ ore regions $ experimental hannels $ u=5 to 51: inner refletor $ u=52 to 53: mixed zone $ u=54 to 55: fuel zone $ u=6 to 62: CFPs $ u=65: enter hannel $ u=7: El $ u=75: E2 $ u=8: E3 $ u=85: E4 $ u=9: E5 257

258 tr2 tr3 tr4 tr5 trll tr12 tr13 tr14 tr15 tr16 tr17 tr18 tr21 tr22 tr23 tr24 tr25 tr26 tr27 tr28 tr29 tr3 tr31 tr32 tr33 tr34 tr35 tr41 tr42 tr43 tr44 tr45 tr46 tr51 tr52 tr53 tr54 tr55 tr56 tr57 tr58 transformations unit ell positions absorber pins - inner surfaes ontrol rod positions shutdown rod positions material speifiations $ inner refletor origin $ mixed zone origin $ fuel zone origin $ refletor origin $ CR1 $ CR2 $ CR3 $ CR4 $ CR5 $ MR1 $ SD1 $ SD2 $ SD3 $ SD4 $ SD5 $ SD6 $ SD7 $ SD8 position (ritial) out 258

259 ml m mt2 grph.olt m mt3 grph.olt m e-7 mt4 grph.olt m mt5 grph.olt m e-5 mt6 grph.olt e e-6 ontrol and shutdown rods m refletor graphite m e e-6 mt9 grph.olt aluminum experiment tubes m humid air mll m e e l.oe-5 aluminum manual rd e e $ U2 $ PyC $ si $ graphite $ matrix $ B4C $ borated shell $ s/steel 259

260 APPENDIX D. MCNP4BNSOP94 Models of PBMR This Appendix ontains the key files used to model the PBMR ore with burnup. The VSOP94 input file for the referene PBMR ore is attahed as Appendix D.1, while the orresponding MCNP4B model is in Appendix D.2. The modified VSOP94 subroutine VORSHU is inluded as Appendix D.3. Program MCARDS, whih generates the MCNP4B material ards from the layeraveraged fuel ompositions extrated from VSOP94, is in Appendix D.4. Details on the PBMR reator, the VSOP94 and MCNP4B models and the link between these odes appear in Chapter 7. 26

261 APPENDIX D.1--VSOP94 input file for referene PBMR ore *1999 MS;.3%BE IN MS; 265 MW; 44 FISPRD; 9 G/K; 18 RODS + 16 KLAK V 2 V 3 V 4 V 1 1 K1 V V V V v V V V V 11 1 K2 V V V V V V V V V V K3 V V V V V V V V '1 298 V V V K4 V V V V V V V V V V V V K5 V V V V V V V V

262 o V V V V V V V KON V11 V 12 V 12 1 B 1 V11 V 12 V 12 V 12 V 12 2 B 2 Vll V 12 V 12 3 B 3 V11 V 12 V 12 4 B 4 V11 V 12 5 B 5 Vll V 12 V 12 6 B 6 V11 V 12 V 12 7 B 7 V11 V 12 V 12 8 B 8 V11 V 12 V 12 9 B 9 V11 1 B1 V11 V 12 V Bll V11 12 B12 V11 13 B13 Vll 14 B14 V11 15 B15 V11 16 B16 V11 V 12 V 12 V B17 V11 18 B18 V11 19 B19 V11 2 B2 V11 V 12 V 12 V B21 V11 22 B22 V11 262

263 B23 V11 24 B24 V11 27 B27 V11 28 B28 V11 29 B29 V11 3 B3 V11 31 B31 V11 32 B32 V11 33 B33 V11 34 B34 V11 35 B35 V11 V 12 V 12 V 12 V B36 V11 37 B37 V11 38 B38 V11 39 B39 V11 4 B4 V11 V 12 V 12 V 12 V B41 V11 42 B42 V11 43 B43 V11 44 B44 V11 V 12 V 12 V 12 V B45 V11 46 B46 V11 47 B47 V11 48 B48 V11 49 B49 V11 V 12 V 12 5 B5 V11 V 12 V 12 V 12 V B51 V11 V 12 V 12 V 12 V B52 Vll 53 B53 Vll 54 B54 V11-55 B55 V11 V 15 V 16 V 21 V

264 V 23 G 1 G2/R19 G2/R19 G2/R19 G2/R19 G2/R19 G2/R19 G2 G 3 G 3 G 3 G 3 G 4 G 4 G 4 G 4 G 4 G 4 G 5 T 1 T 2 T3/R2 T3/R2 T3/R2 T3/R2 T3/R2 T3/R2 T3 T 2 T3/R2 T3/R2 T3/R2 T3/R2 T3/R2 T3/R2 T3 T T T T 5 T T 6 T 7 T 9 T 9 T 9 T 9 T 9 T 9 1. T T 7 T 8 T 9 T 9 T 9 T 9 264

265 *773* MEDUL H/R=85/175; CITA 2-Z **KOPPLUNG: VSOP - CITATION** $1MILL T 9 T 9. T 6 T 7 T 8 T 9 1. T 6. T 7 T 8 T 9 T 9 T 9 T 9 T 11 o-1 CO-2 CO-3 Cl-l C1-2 C1-3 C1-4 C1-5 C3-1 C3-2 C3-3 C3-4 C7-1 C7-2 C7-3 C7-4 C7-5 CX-1 K 1 K 2.6 K 3 K 4. K 5 K 6 TP1 K 7 K 8 K 9 K 1 TP2 K 7 K 8 K 9 K 1 TP3 K 7 K 8 K 9 K 1.99 R 1. R 1. R 1. R 1. R 1. R 1. R 1 265

266 E E E ' R 1. R 1 1. R 1 R 1. R 2 R 3 R 5 R 5 R 5 R 9 R 14 R 16 R G2/R19. G2/R19. G2/R19. G2/R G2/R19. G2/R19. G2/R , 4. 31' ' ( 6.3 T3/R2 T3/R2 T3/R2 T3/R2 T3/R2 T3/R2 T3/R2 T3/R2. T3/R2. T3/R2. T3/R T3/R2. T3/R2. T3/R2 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 266

267 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24.R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 267

268 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R 9 R14.1 R24I.143 R R R R R R R R R24 1. R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24., R R R24 268

269 R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R24 269

270 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R24 R 9 R 9 R 9 R 9 R 9 R 9 R 9 R 9 R 9 R 9 R 9 R 9 R 9 R 9 R 9 R 9 R 9 R 9 R 9 R 9 R 9 R 9 R 9 R 9 R 9 R 9 R 9 R 9 R 9 27

271 R R R R R 9 271

272 APPENDIX D.2: MCNP4B MODEL OF PBMR ESKOM PEBBLE BED MODULAR REACTOR MCNP4B model of the Eskom PBMR using geometry and material speifiations from the VSOP model of the reator ore. Detailed desription of a multi zoned ore using a BCC lattie with homogenized pebbles. J.R. Lebenhaft, MIT, June 2. CELL CARDS 1 5: -25: 41 $ outside world reator struture (using VSOP speifiations) 1.128e e e e e e e e e e B1 upper shield B28 upper shield B49 vessel and gaps B52 top graphite B3 radial refletor, middle B29 bottom shield B44 radial shield B52 top graphite B2 old helium hamber B29 radial refletor, middle e e e e e e e e e e e e e e e e e e e e e e ontrol/shutdown zone e (44:-441: (444:-445: 442:-443) 446:-447) (448:-449: 45:-451) $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ B53 helium gap B3 top refletor B1-B14 radial reflet, inside B3 radial refletor, middle B4 radial refletor, outside B4 helium avity B31 radial refletor, middle B41 radial refletor, outside B45 radial shield, inside B32-B34 rad refletor, mid/out B42-B55 rad refletor, out/bot B46-B48 rad shield, insulate B7 bottom refletor B14 radial refletor, inside B5 bottom shield, insulate B51 B8 hot He hamber B54 shield of disharge tube B54 B15 B15 B9 Bxx onus refletor B6 disharge pipe wall 272

273 helium hannel zone e ontrol sites (452:-453: (456:-457: (46:-461: (464:-465: (468:-469: 454:-455) 458: -459) 462:-463) 466: -467) 47: -471) (472:-473: 474:-475) (476:-477: (48:-481: 478: -479) 482:-483) (484:-485: 486:-487) (488:-489: 49: -491) (492:-493: (496:-497: (5:-51: 494:-495) 498: -499) 52:-53) (54:-55: 56: -57) (58:-59: 51: -511) (271:-272:(273 (277:-278:(279 (283:-284:(285 (289:-29:( ): 281): 287): 293): (295:-296: ( ): (31:-32:(33 (37:-38:(39 (313:-314:(315 (319:-32:(321 (325:-326:(327 (331:-332:(333 35): 311): 317): 323): 329): 335): (337:-338: ( ): (343:-344:(345 (349:-35:(351 (355:-356:(357 (361:-362:(363 (367:-368:( ): 353): 359): 365): 371): (276 (282 (288 (294 (3 (36 (312 (318 (324 (33 (336 (342 (348 (354 (36 (366 ( )) -28)) -286)) -292)) -298)) -34)) -31)) -316)) -322)) -328)) -334)) -34)) -346)) -352)) -358)) -364)) -37)) fill=3(61) fill=3(62) fill=3(63) fill=3(64) fill=3(65) fill=3(66) fill=3(67) fill=3(68) fill=3(69) fill=3(7) fill=3(71) fill=3(72) $ CR1 $ CR2 $ CR3 $ CR4 $ CR5 $ CR6 $ CR7 $ CR8 $ CR9 $ CR1 $ CR11 $ CR12 273

274 shutdown sites e e e e e e e e e e e e e e e e e helium oolant hannels e e e e e e e e e e e e e e e e e e e e e e A29e e e e e e fill=3(73) fill=3(74) fill=3(75) fill=3(76) fill=3(77) fill=3(78) 272 (-273:-275) (274:-276) 278 (-279:-281) (28:-282) 284 (-285:-287) (286:-288) 29 (-291:-293) (292:-294) 296 (-297:-299) (298:-3) 32 (-33:-35) (34:-36) 38 (-39:-311) (31:-312) 314 (-315:-317) (316:-318) 32 (-321:-323) (322:-324) 326 (-327:-329) (328:-33) 332 (-333:-335) (334:-336) 338 (-339:-341) (34:-342) 344 (-345:-347) (346:-348) 35 (-351:-353) (352:-354) 356 (-357:-359) (358:-36) 362 (-363:-365) (364:-366) 368 (-369:-371) (37:-372) $ CR13 $ CR14 $ CR15 $ CR16 $ CR17 $ CR18 $ KL1 $ KL2 $ KL3 $ KL4 $ KL5 $ KL6 $ KL7 $ KL8 $ KL9 $ KL1 $ KLll $ KL12 $ KL13 $ KL14 $ KL15 $ KL16 $ KL17 274

275 e e e e e e e e-3.. universe 32: e e e-3 ore disharge pipe ' : ontrol site universe universe 3: ontrol site e e rod universe 31: absorber lattie lat=l fill=32 u= unit ell fill=31 u=3 $ ontrol rod region u=3 $ graphite surroundings u=3 $ region below ontrol u=32 u=32 u=32 u=32 u=32 u=32 u=32 u=32 fill=5 hannel 1 ( ): ( ): ( ): ( ): ( ): ( ) fill=1 u=5 fill=78(58) hannel 2 33 ( ): ( ): ( ): ( ): ( ): ( ) fill=ll1 u=5 hannel 3 34 ( ): ( ): ( ): ( ): ( ): ( ) $ graphite surroundings $ helium-filled gap $ upper half joint $ outer sleeve of abs $ absorber $ inner sleeve of abs $ lower half joint $ helium-filled inside 275

276 fill=12 u=5 hannel 4 35 ( ): ( ): ( ): ( ): ( ): ( ) fill=13 u=5 hannel 5 36 ( ): ( ): ( ): ( ): ( ): ( ): (15-159) fill=14 u=5 ore layers.. hannel 1 5 fill=21 (1) u=1 $ layer fill=22 (2) u=1 $ layer fill=23 (3) u=1 $ layer fill=24 (4) u=1 $ layer fill=25 (5) fill=26 (6) fill=27(7) u=1 u=1 u=1 $ layer 5 $ layer 6 $ layer fill=28 (8) u=1 $ layer 8-57 fill=29 (9) u=1 $ layer hannel O.. hannel hannel fill=3(1) fill=31(11) fill=32(12) fill=33(13) fill=34(14) fill=35(15) fill=36(16) fill=37(17) fill=38(18) fill=39(19) fill=4(2) fill=41(21) fi11=42(22) fill=43(23) fill=44(24) fill=45(25) fill=46(26) fill=47(27) fill=48(28) fill=49(29) fill=5(3) fill=51(31) 86 fill=52(32) u=11 u=ll u=11 u=11 u=11 u=11 u=11 u=11 u=11 u=11 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 u=12 $ layer 1 $ layer 11 $ layer 12 $ layer 13 $ layer 14 $ layer 15 $ layer 16 $ layer 17 $ layer 18 $ layer 19 $ layer $ layer $ layer $ layer $ layer $ layer $ layer $ layer $ layer $ layer $ layer u=13 $ layer 31 u=13 $ layer

277 hannel fill=53(33) fill=54(34) fill=55(35) fill=56(36) fill=57(37) fill=58(38) fill=59(39) fill=6(4) fill=61(41) fill=62(42) fill=63(43) fill=64(44) fill=65(45) fill=66(46) fill=67(47) fill=68(48) fill=69(49) fill=7(5) fill=71(51) fill=72 (52) fill=73(53) fill=74(54) fill=75(55) fill=76(56) fill=77(57) u=13 u=13 u=13 u=13 u=13 u=13 u=13 u=13 u=13 u=13 u=14 u=14 u=14 u=14 u=14 u=14 u=14 u=14 u=14 u=14 u=14 u=14 u=14 u=14 u=14 hannel 1: inner graphite refletor with trae U universe 21: layer lat=l fill=8 u= unit ell with graphite balls e e e e e e e e e e universe 22: layer u=8 u=8 u=8 u=8 u=8 u=8 u=8 u=8 u= $ layer 33 $ layer 34 $ layer 35 $ layer 36 $ layer 37 $ layer 38 $ layer 39 $ layer 4 $ layer 41 $ layer 42 $ layer 43 $ layer 44 $ layer 45 $ layer 46 $ layer 47 $ layer 48 $ layer 49 $ layer 5 $ layer 51 $ layer 52 $ layer 53 $ layer 54 $ layer 55 $ layer 56 $ layer 57 $ I O] $ [ 1 1 1] $ [ 1 1-1] $ [ ] $ [ $ [-1 1 1] $ [-1 1-1] $ [ ] $ '-1-1 1] u=8 $ helium between balls 277

278 lat=l fill=81 u=22 unit ell with graphite balls e e e e e e e e e e u=81 u=81 u=81 u=81 u=81 u=81 u=81 u=81 u=81 $ [ $ [1 Sf1 $ [1 $ [1 $ [-1 $ [-1 $ [-1 $ [-1 O] 1 1] 1-1] ] 1 1] 1-1] -1-1] -1 1] u=81 $ helium between balls universe 23: layer lat=1 fill=82 u= unit ell with graphite balls e e e e e e e e e e universe 24: layer 4 48 lat=1 fill=83 u= unit ell with graphite balls e e e e e e e e e e u=82 u-82 u=82 u=82 u=82 u=82 u=82 u=82 u= $ 1 $ [ 1 $ 1 $ [ 1 $ 1 1 $ [-i $ [-1 $ [-1 $ [-1 ] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] u=82 $ helium between balls u=83 u=83 u=83 u=83 u=83 u=83 u=83 u=83 u=83 $ [O $ [ 1 $ [ 1 $ [1 $ [ 1 $ [-1 $ [-1 $ [-1 $ [-1 ] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] 278

279 u=83 $ helium between balls universe 25: layer lat=l1 fill=84 u= unit ell with graphite balls e e e e e e e e e e-3 universe 26: layer unit lat=l fill=85 ell with graphite balls e e e e e e e e e e universe 27: layer unit u=84 u=84 u=84 u=84 u=84 u=84 u=84 u=84 u=84 $ 1 $ [ (1 $ [-1 $ [-1 $ [-1 $ [-1 O] 1 1] ] -1 1] 1 1] 1-1) -1-1] -1 1] u=84 $ helium between balls 21 u=26 u=85 u=85 u=85 u=85 u=85 u=85 u=85 u=85 u= lat=l fill=86 u=27 ell with graphite balls e u= e u= e u= e u= e u= e u= e u= e u= e u= e $ [ 1 5(1 5(1 $ [-1 $ [-1 $ [-1 $ [-1 O] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] u=85 $ helium between balls $ [O $ [ 1 $ [1 511 $ [ 1 $ [-1 $ [-1 $ (-1 $ [-1 ] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] 279

280 universe 28: layer unit ell with graphite e e e e e ]6558e e e e e universe 29: layer unitt ell with graphite balls lat=l fill=87 u=28 balls u=87 u=87 u=87 u=87 u=87 u=87 u=87 u=87 u= lat=l fill= e e e e e e e e e e universe 3: layer hannel 2: mixed fuel and moderator u=86 $ helium between balls $ [ $[1 $ [11 $ [1 $[1 $ [-1 $ [-1 $ [-1 $ [-1 ] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] u=87 $ helium between balls 21 u=29 u=88 u=88 u=88 u=88 u=88 u=88 u=88 u=88 u= lat=l fill=89 u=3.. ontents of unit ell e e e e e e e e e e $ [O $ [1 $ [ 1 $ 1 $ [1 $ [-1 $ [-1 $ [-1 $ [-1 ] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] u=88 $ helium between balls u=89 u=89 u=89 u=89 u=89 u=89 u=89 u=89 u=89 $ unit ell boundaries $ [O $ [1 $ [ 1 $ [1 $ [ 1 $ [-1 $ [-1 $ [-1 $ [-1 ] 1 1] 1-1] -1-1] -1 1) 1 1] 1-1] -1-1] -1 1] 28

281 universe 31: layer lat=l fill=93.. ontents of unit ell e e e e e e e e e e u=89 $ helium between balls 21 u=31 u=93 u=93 u=93 u=93 u=93 u=93 u=93 u=93 u=93 - universe 32: layer ontents of unit ell e e e e e e e e e e lat=l fill= $ unit ell boundaries $ [ $ [1 $ r 1 $ 1 $[1 $ [-1 $ [-1 $ [-1 $ [-1 ] 1 1] ] -1 1] 1 1] 1-1] -1-1] -1 1] u=93 $ helium between balls 21 u=32 u=97 u=97 u=97 u=97 u=97 u=97 u=97 u=97 u=97 $ unit ell boundaries [ [1 [1 $ [1 $ [ 1 $ [-1 $ [-1 $ [-1 $ [-1 O] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] u=97 $ helium between balls universe 33: layer lat=1 fill=11.. ontents of unit ell e e e e e e e e e e u=33 u=11 u=11 u=11 u=11 u=11 u=11 u=11 u=11 u=11 $ unit ell boundaries $ [O $ [1 $ [ 1 $ [ 1 $ [1 $ [-1 $ [-1 $ [-1 $ [-1 O] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] u=11 $ helium between balls 281

282 universe 34: layer lat=l.. ontents of unit ell e e e e e e e e e e universe 35: layer ontents of unit ell e e e e e e e e e e universe 36: layer ontents of unit ell e e e e e e e e e e fill=15 u= u=15 u=15 u=15 u=15 u=15 u=15 u=15 u=15 u= lat=l fill=19 u= $ unit ell boundaries $ [ $ [1 1 $ [ 1 $ [ 1 $ [-1 $ [-1 $ [-1 $ [-1 $ [-1 ] 1 1] 1-1] ] -1 1] 1 1] 1-1] -1-1] -1 1] u=15 $ helium between balls u=19 u=19 u=19 u=19 u=19 u=19 u=19 u=19 u= lat=l fill=113 u= $ unit ell boundaries $ [ $ [ 1 $ [ 1 $ [ 1 $ [1 $ [-1 $ [-1 $ [-1 $ [-1 ] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] u=19 $ helium between balls u=113 u=113 u=113 u=113 u=113 u=113 u=113 u=113 u=113 universe 37: layer $ unit ell boundaries 215 $ unit ell boundaries $ [ $ [ 1 $ [( 1 $ [ 1 $ [ 1 $ [-1 $ [-1 $ [-1 $ [-1 ] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] u=113 $ helium between balls 282

283 lat=1 fill=117 u=37.. ontents of unit ell e e e e e e e e e e u=117 u=117 u=117 u=117 u=117 u=117 u=117 u=117 u=117 $ [ ] $ [ 1 1 1] $ [1 1-1] $ ] $ [ 1-1 1] $ [ $ (-1 1-1] $ [ ] $ (-1-1 1] u=117 $ helium between balls universe 38: layer lat=i fill=121 u= ontents of unit ell e e e e e e e e e e $ unit ell boundaries universe 39: layer lat=1 fill=125 u= ontents of unit ell e e e e e e e e e e u=121 u=121 u=121 u=121 u=121 u=121 u=121 u=121 u=121 $ [O $ [ 1 $ [1 $ [ 1 $ [ 1 $ [-1 $ (-1 $ [-1 $ [-1 O] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] u=121 $ helium between balls u=125 u=125 u=125 u=125 u=125 u=125 u=125 u=125 u=125 $ unit ell boundaries $ [ $ [1 1 $[1 1 $ [ 1-1 $ [ 1-1 $ [-1 1 $ [-1 1 $ [-1-1 $ [-1-1 ] 1] -1] -1] 1] 1] -1] -1] 1] u=125 $ helium between balls 283

284 hannel 3: fuel universe 4: layer 2 63 lat=l fill=129 u= ontents of unit ell e e e e e e e e e e-3 universe 41: layer 614 lat=l fill=133 u=41.. ontents of unit ell u=129 u=129 u=129 u=129 u=129 u=129 u=129 u=129 u= u= e u= e u= e u= e u= e u= e u= e u= e u= e u= e u=133 universe 42: layer lat=1 fill=137 u= ontents of unit ell e e e e e e e u=137 u=137 u=137 u=137 u=137 u=137 u=137 $[ 1 $ 1 1 $ [ 1-1 $ [ 1-1 $ [-1 1 $ [-1 1 $ [-1-1 $ [-1-1 ] 1] -1] -1] 1] 1] -1] -1] 1] $ helium between balls $ unit ell $ 1 $ [1 $ [1 $ [-1 $ (-1 $ [-1 $ [-1 $ [-1 ] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] $ helium between balls $ unit ell $ [ O] $ [ 1 1 1] $ [ 1 1-1] $ [ ] $ [ 1-1 1] $ [-1 1 1] $ [-1 1-1] 284

285 e u= e u= e u=137 universe 43: layer lat=1 fill=141 u= ontents of unit ell e e e e e e e e e e universe 44: layer lat=l fill=145 u= ontents of unit ell e e e e e e e e e e-3 universe 45: layer lat=l fill=149 u= ontents of unit ell e e e u=141 u=141 u=141 u=141 u=141 u=141 u=141 u=141 u= u= u=145 u=145 u=145 u=145 u=145 u=145 u=145 u=145 u= $ [ ] $ ] $ helium between balls $ unit ell [ $ [1 $ [1 $ [ 1 $ [1 $ 1-1 $ [-1 $ [-1 $ [-1 $ ([ $ [1 $ [1 $[1 $ [-1 $ [-1 $ [-1 ] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] ] 1 1] ] -1 1] 1 1] 1-1] -1-1] -1 1] u=145 $ helium between balls u=149 u=149 u=149 $ helium between balls $ unit ell $ unit ell $ [ O] $ [ 1 1 1] $ [ 1 1-1) 285

286 e e e e e e e u=149 u=149 u=149 u=149 u-=149 u=149 $ [ ] $ [ 1-1 1] $ [-1 1 1] $ [-1 1-1] S [-1-11] $ [-1-1 1] u=149 $ helium between balls universe 46: layer lat=1 fill=153 u= ontents of unit ell e e e e e e e e e e universe 47: layer lat=l fill= universe 128: ontents of unit ell e e e e e e e e e e u=153 u=153 u=153 u=153 u=153 u=153 u=153 u=153 u=153 universe 48: layer lat=l fill=161 u= $ unit ell $ [ o $ [ 1 1 1] $ [ 1 1-1] $ [ ] $ [ 1-1 1] $ [-1 1 1] $ [-1 1-1] $ [ ] $ [-1-1 1] u=153 $ helium between balls 21 u=47 $ unit ell u=157 u=157 u=157 u=157 u=157 u=157 u=157 u=157 u=157 $ [ o O] $ [ 1 11] $ [ 1 1-1] $ [ ] $ [ 1-1 1] $ [-1 1 1] $ [-1 1-1] $ [ ] $ [-1-1 1] u=157 $ helium between balls $ unit ell 286

287 ontents of unit ell e e e e e e e e e e u=161 u=161 u=161 u=161 u=161 u=161 u=161 u=161 u=161 $ [O $ [ 1 $ [1 $ [1 $ [1 $ [-1 $ [-1 $ [-1 $ [-1 ] 1 1] 1-1] -1 -i] -1 1] 1 1] 1-1] -1-1] -1 1] u=161 $ helium between balls universe 49: layer lat=l fill=165 u=49.. ontents of unit ell e e e e e e e e e e u=165 u=165 u=165 u=165 u=165 u=165 u=165 u=165 u=165 universe 5: layer lat=1 fill=169 u= ontents of unit ell e e e e e e e e e e hannel $ unit ell $ [O $ [ 1 $ [ 1 $ [1 $ [ 1 $ [-1 $ [-1 $ [-1 $ [-1 ] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1) -1-1] -1 1i u=165 $ helium between balls u=169 u=169 u=169 u=169 u=169 u=169 u=169 u=169 u=169 _- - _ _- _ $ unit ell $ [ $ [1 $ [1 $ [ 1 $ [1 $ [-1 $ [-1 $ [-1 $ [-1 O] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] u=169 $ helium between balls 287

288 universe 51: layer 31 lat=l fill=173 u=51.. ontents of unit ell e e e e e e e e e e u=173 u=173 u=173 u=173 u=173 u=173 u=173 u=173 u=173 $ unit ell $ [ 1 [1 [1 $ [1 $ [-1 $ [-1 $ [-1 $ [-1 ] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] u=173 $ helium between balls universe 52: layer , at=l fill=177 U: =52. ontents of unit ell e e e e e e e e e e universe 53: layer lat=l fill=181 u=53.. ontents of unit ell e e e e e e e u=177 u=177 u=177 u=177 u=177 u=177 u=177 u=177 u=177 $ unit ell $ [O ] 1 1] $ [ 1 1-1] $ [ ] [ 1-1 1] $ [-1 1 1] $ [-1 1-1] [ ] $ [-1-1 1] u=177 $ helium between balls u=181 u=181 u=181 u=181 u=181 u=181 u=181 $ unit ell $ [ o] $ [ ] 1-1] $ [ ] $ [ 1-1 1] $ [-1 1 1] $ [-1 1-1] 288

289 e e e universe 54: layer lat=l fill=185 u= ontents of unit ell e le e e e e e e e e universe 55: layer lat=l fill=189 u= ontents of unit ell e e e e e e e e e e u=181 $ [ ] u=181 $ [-1-1 1] u=181 $ helium between balls u=185 u=185 u=185 u=185 u=185 u=185 u=185 u=185 u=185 $ unit ell $ [ ] $ [ ] $ [ 1 1-1] $ [ i -1-1] $ [ 1-1 1] $ [ ] $ [-1 1-1] $ ( ] $ [-1-1 1] u=185 $ helium between balls u=189 u=189 u=189 u=189 u=189 u=189 u=189 u=189 u=189 $ unit ell $ [O $ [1 [1 $ [1 $ [1 $ [-1 $ [-1 $ [-1 $ [-1 ] 1 1] 1-1] - -1] -1 1] 1 1] 1-1] -1-1] -1 1] u=189 $ helium between balls universe 56: layer lat=l fill=193 u=56 $ unit ell.. ontents of unit ell e u=193 $ [ ] 289

290 e e e e e e e e e universe 57: layer lat=1 fill=197 u=57 u=193 u=193 u=193 u=193 u=193 u=193 u=193 u= universe 189: ontents of unit ell e e e e e e e e e e-3 universe 58: layer lat=1 fill=21 u= ontents of unit ell e e e e e e e e e e $ [ 1 1 1] $ [ 1 1-1] $ [ ] $ [ 1-1 1] $ [-1 1 1] $ [-1 1-1] $ [ ] $ [-1-1 1] u=193 $ helium between balls u=197 u=197 u=197 u=197 u=197 u=197 u=197 u=197 u=197 $ unit ell $ [ $ [ 1 1 $[1 1 $ [ 1-1 $ [ 1-1 $ [-1 1 $ [-1 1 $ [-1-1 $ [-1-1 ] 1] -1] -1] 1] 1] -1] -1] 1] u=197 $ helium between balls u=21 u=21 u=21 u=21 u=21 u=21 u=21 u=21 u= universe 59: layer $ unit ell $ [ $ 1 $ [ 1 $ [ 1 $ [ 1 $ [-1 $ [-1 $ [-1 $ [-1 o o] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] u=21 $ helium between balls 29

291 lat=l fill=25 u=59.. ontents of unit ell e e e e e e e e e e-3 universe 6: layer lat=l fill=29 u= ontents of unit ell e e e e e e e e e e universe 61: layer lat=l u= fill=213.. ontents of unit ell e e e e e e e e e e u=25 u=25 u=25 u=25 u=25 u=25 u=25 u=25 u= [ $ 1 $ 1 $(1 $ [-1 $ [-1 $ [-1 $ [-1 O] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1) -1 1] u=25 $ helium between balls u=29 u=29 u=29 u=29 u=29 u=29 u=29 u=29 u= $ unit ell $ [ ] $ [ ]. 1 1] $ [ 1 1-1] $ [ ] $ r 1-1 1] $ [-1 1 1] $ [-1 1-1] $ [ ] $ [-1-1 1] u=29 $ helium between balls u=213 u=213 u=213 u=213 u=213 u=213 u=213 u=213 u=213 $ unit ell $ unit ell $ [O $ [ 1 $ [1 $ [1 $ [ 1 $ [-1 $ [-1 $ [-1 $ [-i ] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] 291

292 C universe 62: layer lat=1 fill=217 u= ontents of unit ell e e e e e e e e e e u=213 $ helium between balls u=217 u=217 u=217 u=217 u=217 u=217 u=217 u=217 u=217 hannel 5 universe 63: layer lat=1 fill=221 u= ontets of unit ell e e e e e e e e e e universe 64: layer lat=1 fill=225 u=64.. ontents of unit ell e e $ unit ell O $ [ 1 $ [ J. 1 $ [ 1-1 $ [ 1-1 $ [-1 1 $ [-1 1 $ [-1-1 $ [-1-1 O] 1] -1] -1] 1] 1] -1] -1] 1] u=217 $ helium between balls u=221 u=221 u=221 u=221 u=221 u=221 u=221 u=221 u=221 $ unit ell $ [ O $ [ 1 $ [ 1 1 $ [ 1-1 $ [ 1-1 $ [-1 1 $ [-1 1 $ [-1-1 $ [-1-1 ] 1] -1] -1 1]1] -1] -1] 1] u=221 $ helium between balls $ unit ell u=225 $ [ ] u=225 $ [ 1 1 1] 292

293 e u= e u= e u= e u= J3873e u= e u= e u= e u=225 universe 65: layer lat=1 fill=229 u= ontents of unit ell e e e e e e e e e e u=229 u-229 u=229 u=229 u=229 u=229 u=229 u=229 u= universe 66: layer lat=1 fill=233 u= ontents of unit ell e e e e e e e e e e universe 67: layer lat=1 fill=237 u=67 $ [ 1 1-1] $ [ ] $ [ 1-1 1] $ [-1 1 1] $ [-1 1-1] $ [ ] $ [-1-1 1] $ helium between balls $ unit ell $ [ $ [ 1 $ [ 1 $ [ 1 $ [ 1 [-1 $ [-1 [-1 $ [-1 ] 1 1] 1-1] -1-1] -1 1] 1 1] ] -1 1] u=229 $ helium between balls u=233 u=233 u=233 u=233 u=233 u=233 u=233 u=233 u=233 $ unit ell $ [ $ [ 1 L 1 [1 $ [1 $ [-1 $ [-1 $ [-1 $ [-1 O] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] u=233 $ helium between balls $ unit ell 293

294 .. ontents of unit ell e e e e e e e e e e universe 68: layer lat=1 fill=242 u=68.. ontents of unit ell e e e e e e e e e e-3 u=237 u=237 u=237 u=237 u=237 u=237 u=237 u=237 u=237 $ [ 1 $ 1 r1i $1 $ [-1 $ [-1 $ [-1 $ [-1 O] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] u=237 $ helium between balls $ unit ell u=242 u=242 u=242 u=242 u=242 u=242 u=242 u=242 u=242 universe 69: layer lat=1 fill=246 u= ontents of unit ell e e e e e e e e e e $[ $ 11 $ 1 $ 1 $ 1 $ [-1 $ [-1 $ [-1 $ [-1 O] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] u=242 $ helium between balls u=246 u=246 u=246 u=246 u=246 u=246 u=246 u=246 u=246 $ unit ell s[ 5(1 [1 $ [1 511 $ [-1 $ [-1 $ [-1 $ [-1 ] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] u=246 $ helium between balls 294

295 universe 7: layer lat=l fill= u=7.. ontents of unit ell e e e e e e e e e e u=25 u=25 u=25 u=25 u=25 u=25 u=25 u=25 u=25 universe 71: layer lat=l fill=254 u= ontents of unit ell e u= e u= e u= : e u= e u= e u= e u= e u= e u= e u=254 universe 72: layer lat=l fill=258 u= ontents of unit ell e e e e e e e $ unit ell $ ] $ [ 1 1 1] $ [ 1 1-1] $ [ ] $ [ 1-1 1] $ [-1 1 1] $ [-1 1-1] $ [ ] $ [-1-1 1] u=25 $ helium between balls u=258 u=258 u=258 u=258 u=258 u=258 u=258 $ unit ell [ $ [1 [1 [1 $ [1 $ [-1 $ [-1 $ [-1 $ [-1 ] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] $ helium between balls $ unit ell $ [ o $ [ 1 1 1] $ [ 1 1-1] $ ] $ 1-1 1] $ [ ] $ [-1 1-1] 295

296 e u= e u= e u=258 universe 73: layer lat=l fill=262 u= ontents of unit ell e e e e e e e e e e _. u=262 u=262 u=262 u=262 u=262 u=262 u=262 u=262 u= u=262 universe 74: layer lat=l fill=266 u= ontents of unit ell e u= e u= e u= e u= e u= e u= e u= e u= e u= e u=266 universe 75: layer lat=l fill=27 u=75.. ontents of unit ell e e e e u=27 u=27 u=27 u=27 $ [ ] $ [-1-1 1] $ helium between balls $ unit ell $ o $[ 1 $ [1 1 $ I 1-1 $ [ 1-1 $ [-1 1 $ [-1 1 $ [-1-1 $ [-1-1 O] 1] -1] -1] 1] 1] -1] -1] 1] $ helium between balls $ unit ell $ [ $ [ 1 [1 [1 $ [1 $ [-1 $ [-1 $ [-1 $ 1-1 O] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] $ helium between balls $ unit ell $ [ ] $ [ 1 1 1] $ [ 1 1-1] $ [ ] 296

297 e e e e e e universe 76: layer lat=l fill=274 u= ontents of unit ell e e e e e e e e e e-3 u=27 u=27 u=27 u=27 u=27 _ universe 77: layer lat=l fill=278 u= ontents of unit ell $ [ 1-1 1] $ [-1 1 1] $ [-1 1-1] $ [ ] $ [-1-1 1] u=27 $ helium between balls u=274 u=274 u=274 u=274 u=274 u=274 u=274 u=274 u= e u= e u= e u= e u= e u= e u= e u= e u= e u= e u=278 universe 78: disharge pipe 238 lat=l fill=282 u= ontents of unit ell $ unit ell $ [ O] $ [ 1 1 1] $ [ 1 1-1] $ [ ] $ [ 1-1 1] $ [-1 1 1] $ [-1 1-1] $ [ ] $ [-1-1 1] u=274 $ helium between balls $ unit ell $ [ $ [1 $ [1 $ 1 $ [ 1 $ [-1 $ [-1 $ [-1 $ [-1 O] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1 ] -1 1] $ helium between balls $ unit ell 297

298 e e e e e e R91e e e e u=282 u=282 u=282 u=282 u=282 u=282 u=282 u=282 u=282 $ [ $ [1 $ 1 $ [1 $ [1 $ [-1 $ [-1 $ [-1 $ [-1 ] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] u=282 $ helium between balls SURFACE CARDS C reator struture axial divisions 5 pz. 6 pz pz pz pz pz pz pz pz pz pz pz pz pz reator struture radial divisions 3 z z z 175. I35 z z z z z z z 331. onus 45 z layers in hannel 1 5 pz pz pz pz pz pz pz pz bottom of: $ layer 1 $ layer 2 $ layer 3 $ layer 4 $ layer 5 $ layer 6 $ layer 7 $ layer 8 298

299 layers in hannel 2 6 pz $ layer 1 61 pz $ layer pz $ layer pz $ layer pz $ layer pz $ layer pz $ layer pz $ layer pz $ layer 18 layers in hannel 3 7 pz $ layer 2 71 pz $ layer pz $ layer pz $ layer pz $ layer pz $ layer pz $ layer pz $ layer pz $ layer pz $ layer 29 layers in hannel 4 85 pz $ layer pz $ layer pz $ layer pz $ layer pz $ layer 35 9 pz $ layer pz $ layer pz $ layer pz $ layer pz $ layer 4 95 pz $ layer 41 layers in hannel 5 1 pz $ layer pz $ layer pz $ layer pz $ layer pz $ layer pz $ layer pz $ layer pz $ layer 5 18 pz $ layer pz $ layer pz $ layer pz $ layer pz $ layer pz $ layer 56 hannel 1 outer boundary 115 z z z

300 118 z z z hannel 2 outer boundary z z z z z z hannel 3 outer boundary z z z z z z hannel 4 outer boundary/hannel 5 inner boundary z z z z z z pz pz pz pz pz fuel element.. fuel region 21 so 2.5 unit ell boundaries in ore 25 px px py py pz pz balls in unit b ell so 3. s s s s s s $ [-1 ] $ [ 1 ] $ [ 1 ] $ [ -1 ] $ [ 1] $ [ -1] 3

301 '218 s s oated fuel partile (fp) so so so so so unit s ell for fp lattie in graphite matrix 225 px px py py pz pz shutdown sites.. KL px px py py /z /z KL px px py py /z /z KL px px py py /z /z I I.. KL px px py py /z I /z $ U2 kernel $ 1st PyC layer $ 2nd PyC layer $ SiC layer $ 3rd PyC layer KL5 85 px 85 px

302 A-- 29' 7 85 py 29i3 85 py 29S9 85 /z 3( 85 /z.. KL px 86 px 86 py 86 py 86 /z 86 /z 3; KL7 87 px 87 px 87 py 87 py 87 /z 87 /z.. KL8 88 px 88 px 88 py 88 py 88 /z 88 /z.. KL9 89 px 89 px 89 py 89 py 89 /z 89 /z.. KL1 9 px 9 px 9 py 9 py 9 C/z 9 C/z.. KLll 91 px 91 px 91 py 91 py 91 /z 91 /z.. KL12 92 px 92 px 92 py

303 34 92 py /z /z KL px px py py /z /z KL px px py py /z /z KL px px py py /z /z KL px px py py /z /z KL px px py py /z /z helium hannels in refletor 375 /z /z /z /z /z /z /z /z /z /z /z

304 /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z /z ontrol sites.. CR1 61 px px py py CR2 62 px px py py CR3 63 px px py py CR4 64 px px py py CR5 65 px px py py

305 .. CR px px py py CR px px py py CR px px py py CR px px py py CR px px py py CR px px py py CR px px py py CR px px py py CR px px py py CR px

306 pz 531 pz 532 pz 533 pz 534 z 535 z 536 z 537 z 538 z sleeve px py py CR16 76 px px py py CR17 77 px px py py CR18 78 px px py py -6.1 ontrol rods pz pz lattie boundaries px 6. px -6. py 6. PY -6. absorber unit ell surfaes for tallies pz pz pz pz pz pz pz pz radial zones $ bottom of rod (1/4 inserted) $ bottom of rod (1/2 inserted) $ top of joint (1/2 height) $ top of absorber setion $ bottom of absorber setion $ bottom of joint (1/2 height) $ inner surfae of s/s sleeve $ inner surfae of absorber $ outer surfae of absorber $ outer surfae of s/s sleeve $ inner surfae of graphite 36

307 561 z 562 z 563 z 564 z $ inner refletor $ mixed mod/fuel zone $ fuel zone 1 $ fuel zone 2 RUN PARAMETERS problem type mode n kode ksr totnu print dbn 9j 3 prdmp j neutron importane imp:n 1 33r r 1 16r 1 35r 1 1lr r 1 8r 1 9r 1 1r 1 1lr 1 14r 1 lor 1 1r 1 1r 1 1r 1 1r 1 1r 1 1r 1 1r 1 1r 1 1r 1 1r 1 1r 1 1Or 1 lor 1 1Or 1 1r 1 1r 1 1r 1 1r 1 1r 1 1Or 1 1r 1 1r 1 1r 1 1r 1 1r 1 1r 1 1Or r 1 1r 1 1r 1 1r 1 1r r 1 1r 1 1r 1 1r 1 1r 1 1r 1 1r $ outside world $ struture (VSOP speifiations) $ ontrol/shutdown zone $ helium hannel zone $ ontrol sites $ shutdown sites $ oolant hannels $ ontrol site $ ore $ disharge pipe $ urved boundaries of hannels 1-5 $ layer boundaries in hannels 1-5 $ layers 1-9 $ layers 1-19 $ layers 2-3 $ layers

308 1 1r 1 1r 1 1r 1 1r 1 O1r 1 O1r 1 1r 1 lor 1 1r 1 O1r 1 O1r 1 1Or 1 1r Or 1 1r 1 1r 1 1r 1 lor transformations hannel 1 trl tr tr tr tr tr tr tr tr hannel 2 trlo trll tr12 tr13 tr14 tr15 tr16 tr17 tr18 tr hannel 3 tr2 tr21 tr22 tr23 tr24 tr25 tr26 tr27 tr28 tr29 tr hannel 4 tr31 tr32 tr33 tr34 tr35 tr36 tr37 tr38 tr $ layers $ disharge pipe 38

309 tr tr tr hannel 5 tr43 tr44 tr45 tr46 tr47 tr48 tr49 tr5 tr51 tr52 tr53 tr54 tr55 tr56 tr disharge pipe tr ontrol sites *tr *tr *tr *tr *tr *tr *tr *tr *tr *tr *tr *tr *tr *tr *tr *tr *tr *tr shutdown sites *tr *tr *tr *tr *tr *tr *tr *tr $ CR $ CR $ CR $ CR $ CR $ CR $ CR $ CR $ CR $ CR $ CR $ CR $ CR $ CR $ CR $ CR $ CR $ CR $ KL $ KL $ KL $ KL $ KL $ KL $ KL $ KL8 39

310 *tr $ KL9 *tr $ KL1 *tr $ KL1l *tr $ KL12 *tr $ KL13 *tr $ KL14 *tr $ KL15 *tr $ KL16 *tr $ KL17 f7 f7:n 3 sd7 1 f17 tally speifiations - from model with homogenized layers fission soure for normalization (per unit mass) ore average fission power in inner refletor zone R-Z geometry, 9 x 8.5 m regions top to bottom R1 = 73 m f17:n 3 fs sd17 1 1r f27 average prompt fission power in mixed mod/fuel zone R-Z geometry, 9 x 8.5 m regions top to bottom R1 = 73 m, R2 = 17.8 m f27:n 3 fs sd27 f37 1 1lr average prompt fission power in inner fuel zone R-Z geometry, 9 x 8.5 m regions top to bottom R2 = m, R3 = m f37:n 3 fs sd37 1 1lr f47 average prompt fission power in middle fuel zone R-Z geometry, 9 x 8.5 m regions top to bottom R3 = m, R4 = m f47:n 3 fs sd47 1 1lr f57 average prompt fission power in outer fuel zone R-Z geometry, 9 x 8.5 m regions top to bottom R4 = m, R5 = 175 m f57:n 3 fs sd r f14 average neutron flux in inner refletor zone R-Z geometry, 9 x 8.5 m regions top to bottom R1 = 73 m f14:n 3 fs

311 sd14 el4 f24 f24:n fs24 sd24 e24 f34 f34:n fs34 sd34 e34 f44 f44:n fs44 sd44 e r 1.86e-6 2 average neutron flux in mixed mod/fuel zone R-Z geometry, 9 x 8.5 m regions top to bottom R1 = 73 m, R2 = 17.9 m r 1.86e-6 2 average neutron flux in inner fuel zone R-Z geometry, 9 x 79.8 m regions top to bottom R2 = 17.9 m, R3 = m r 1.86e-6 2 average neutron flux in middle fuel zone R-Z geometry, 9 x 79.8 m regions top to bottom R3 = m, R4 = m r 1.86e-6 2 f54 average neutron flux in outer fuel zone R-Z geometry, 9 x 79.8 m regions top to bottom R4 = m, R5 = 175 m f54:n 3 fs sd r e e-6 2 material speifiations ml mtl m2 mt2 m3 mt3 m6 m7 mt6 m8 mt7 m4 mt4 m49 mt49 m5 mt5 m51 mt51 strutural materials e-3 grph.6t e-3 grph.6t e-3 grph.6t e e-3 grph.6t e-3 grph.6t e-3 grph.6t e-2 grph.6t e-3 grph.6t e-2 grph.6t e e e e e e e e e e e e e e e e e e e-2 311

312 helium (4.814e-3 g/ at 3K)' m6 stainless steel m boron arbide (B4C) m fuel orresponding to equilibrium burnup VSOP yle 261; layer 1; total N = E-1 M E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-6 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-6 C VSOP yle 261; layer M E E E E E E E E E E E E E E E E E E E E E E E E E E E-2 2; total N = E E E E E E E E E E E E E E E-2 3; total N = E E E E E E E E E E E E E QOE E E E E E E E E E E E E E E E E E E E E E E E E E E E-1 312

313 E E E E E E E E E-6 C VSOP yle 261; layer 4; total N = E-1 M E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-6 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-6 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-6 C VSOP yle 261; layer M E E E E E-9 5; total N = E E E E E E E E E E E E E E E-2 6; total N = 1.165' E E E E E E E E E E E E E E E-2 7; total N = E E E E E-9 58E C E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-1 313

314 E E E E E E E E E E-6 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-6 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-6 C VSOP yle 261; layer M E E E E E E E E E E E E E E C ; tota ; total E E E E E E E E E E N = E E E E E E E E E E E E E E E E ; total L N = E E E E E E E E E E E E E E E E N = E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-7 314

315 E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer Mll E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E-, ; total N = 4.24( )819E E-' E-O' E-O E-O E-O E-1( ) E-O E E-O' E-1( ) E-1C E-O E-O E E-O ; total N = 4.24C)879E ; total ; total E E E-OE E-O E E-1C 1.649E E E E-1C 4.421E E E E E-2 N = E E E E E E E E E E E E E E E-2 N = E E E E E E E E E SO E E E E E-7 2,24784E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

316 E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer E E-7 6i E E E E E E-2 15; total N = E E E E E E E E E E E E E E E-2 16; total N = E E E E E E E E E E E E E E E-2 17; total N = 4.241: E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-4 239E ; total N = E E E E E E E E E E E E E E E E-4 316

317 M E , E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E E E E E E E E E E ; total N = E E E E E E E E E E E E E E E E ; total N = E E E E E E E E E E E E E E E E ; total N = E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-7 317

318 E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E-4 22; total N = E E E E E E E E E E E E E E E E E E E E CE E E E E E E E E E E-4 23; total N = E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-4 24; total N = E E E E E-7 9: E E E E E E E E E E E E E E E E E E E E E E E E E E-4 25; total N = E E E E E-7 318

319 E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E ;5392E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E E E E E E E E E E ; total N = E E E E E E E E E E E E E E E E ; total N = E E E E E E E E E E E E E E E E ; total N = E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-7 319

320 E E E E-4 C VSOP yle 261; layer M E E E ,52139E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E-2 29; total N = E E E E E E E E E E E E E E E-2 3; total N = ' E E E E E E E E E E E E E E E-2 31; total N = E E E E E E E E E E E E E E E E E E E ; total N = E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-7 32

321 E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-4 33; total N = E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-4 34; total N = E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-4 35; total N = E E E E E E E E E E E E E E E E E E E E E E E E E E E

322 E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E-O', E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E-7 h E E-4 36; total N = E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-4 37; total N = E E-6 ; E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-4 38; total N = E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-4 39; total N = E E E E E E E E E E E E E-7 322

323 E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP - le 261; layer M ,J E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-4 4; total N = E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-4 41; total N = E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-4 42; total N = E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-4 323

324 C, VSOP yle 261; layer M E E E E E E '74E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 VSOP yle 261; layer M E E E E E E E E-7 43; total N = E E E : E E E E E E : 5.429E E E E E E E E ; tota ; tota ; total N = E E E E E E E E E E E E E E E E L N = E E E E E E E E E E E E E E E E N = E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-ll E E E E E E E E E E E E E E E E-8 324

325 E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E b E E E-4 47; total N = E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-4 48; total N = E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-4 49; total N = E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-4 5; total N = E E E-4 325

326 E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E E E E E E E E E E ; total N = E E E E E E E E E E ' E E E E E E ; total N = E E E E E E E E E E E E E E E E ; total N = E E E E E E E E E E-1 688E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-8 326

327 E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E i.2786e E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer M E E E E E E E E E E E E E E E-4 C VSOP yle 261; layer E E E E E ; total N = E E E E E E E E E E E E E E E E ; total N = E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E I E E E E-4 I 56; total N = E I E E I E E IS E E E E E E E E E E E E-8 5$ E E E E E E E E E E E E E E-4 57; total N = E-1 M E E E E E E E E E-8 327

328 E E E E E E E E E E E E-4 mtloo grph.6t mtlol grph.6t mtlo2 grph.6t mtl3 grph.6t mtlc4 grph.6t mtlo5 grph.6t mtlo6 grph.6t mtlo7 grph.6t mtlo8 grph.6t mtlo9 grph.6t mtllo grph.6t mtlll grph.6t mtll2 grph.6t mtll3 grph.6t mtll4 grph.6t mtll5 grph.6t mtll6 grph.6t mtll7 grph.6t mtll8 grph.6t mt119 grph.6t mtl2o grph.6t mtl2l grph.6t mt122 grph.6t mt123 grph.6t mt124 grph.6t mt125 grph.6t mt126 grph.6t mt127 grph.6t mt128 grph.6t mt129 grph.6t mtl3o grph.6t mt131 grph.6t mt132 grph.6t mt133 grph.6t mt134 grph.6t mt135 grph.6t mt136 grph.6t mt137 grph.6t mt138 grph.6t mt139 grph.6t mtl4o grph.6t mtl41 grph.6t E E E E E E E E E E E E E E C E E E E E E E E E E-4 thermal s(alpha,beta) ross setions for graphite at 12K 328

329 mt142 grph.6t mt143 grph.6t mt144 grph.6t mt145 grph.6t mt146 grph.6t mt147 grph.6t mt148 grph.6t mt149 grph.6t mtl5 grph.6t mtl51 grph.6t mt152 grph.6t mt153 grph.6t mt154 grph.6t mt155 grph.6t mt156 grph.6t 329

330 APPENDIX D.3: Modified subroutine VORSHU SUBROUTINE VORSHU(NPRINT,IN1,MRY,NKEEP,DECAF,ICONPO,BU,VOLREG,VOL, 1 DEN,DENIOD,HM,THBURN,FADOS3,NOPOW,HMETAL,TCHG2, 2 KRESHZ,LRZN,TCHG1,N24,NALT,NTYP1,TEMZUT,TCELS, 3 VERA,IHZ,VOLIHZ,VOLWEG,HMETAV,DAV,DA2,SCELS, 4 SEMZUT,IREG,JAD11,IBOX,RVCB,HPOS, 5 ABSIG,LA,NHOT,SS,RPHIAV) C C C F U M A N MANAGES FUELLING OPERATIONS C C VORSHU MEANS: BEFORE SHUFFLING C C C C C C C C C Subroutine VORSHU was modified (J.R. Lebenhaft, MIT, January 2) to write layer-averaged atom densities and reation rates to files FORT.98 and FORT.99. PARAMETER (NMC = 95) COMMONS COMMON / BLOCK1 / 1 IPRIN(15) 2, JTPE3 3, JTPE6 4, JTPE9 5, N26 6, N2 7, NLUM 8, JSER 9, KINIT X, K42 COMMON / BLOCK1 / 1 MMAF 2, N2 3, MBOX 4, RINN EQUIVALENCE(JTPE2,NS) 1, (JTPE3,NT) COMMON / BLOCK3 / 1 JNN 2, N71 3, DELSEC 4, XYZ 5, ZF3 6, VOLUME 7, YIELD1(49) 8, YIELD4(49) 9, N27 X, N31 COMMON / BLOCK3 / 1 CORE 2, REACT(2) 3, LSER,JTPE1,JTPE4,JTPE7,JTPE1,KMAT,NDR,NC,NXE,MUHU (3),IRR9,NLB,KROT,IAVC,IBUCK,IRSUB,CRT,NK,ZF1,ZF4,FIWATT,YIELD2(49),NP237,N28,N41(2),RADR(2),XPPNEW(95),ZKFIND,JTPE2,JTPE5,JTPE8,NXS,JN,NO,POWER,NRSTRT,K96,KFR,PI,NEND33,JD11,NVSOP,KREG,DELDAY,NL,ZF2,ZJNUM,DIRAC(49,5),YIELD3(49),XNORM,N29,SERCON,NTYPE,YPPNEW(95),AWT(13) 33

331 C C C C C 4' 5, 6, 7, 8, 9, X, COMMON / 1 2, 3, 4, 5, 6, 7, 8, GS (13) JS KSIM LBUMP JSMAX SPECK(192) NSTO(96) BLOCK3 / JNSTOP ISPEKT(2) HMANFG XMNEW YPNEW1 NBOX XVSP (3) C2S COMMON / BLOCKR / 1 NRESHZ 2, XSPALT 3, FICOMP(13) 4, NKT 5, TSTORE 6, BRUCH 7, KLASSE(1) 8, MREP 9, FOJB(1) X, NBO 1 2 COMMON / DABLCK / NDA1 NDAll 3 3, JAD1(15) 4 I, NXT4 5 1, JSUM8 6 j, NXT9 7 7, 8 9 K1 NDA29 NXT13 X, ND13 COMMON / DABLCK / 1 2, 3, 4, COMMON / 1, 2, L8 Lll L29 IWRITE PROZ COMMON / ORIGEN / 1 LOB 2, VOR(5) COMMON 1, 1,GM (13),JSS,LSIM,NBUMP,JSSMAX,TIME(192),NSWIT,NLT,FIFA,REALNN(1),FITOT1,LAYER(2),IDIFF(2),ZPPNEW(95),MAKEUP,AAAA,NNNN,JEEP,TREPRO,KUGL,FIMAKL(2),MARX (1),NFUL(1),NCY,NXT1,NXT11,NDA8,JAD8 (2),JSUM9,K8,NXT29,N13,N14,L9,L13,L3,IREAD / INZWX, INZWXX, INZW(1), FABC(1), REPC(1), DMAT(14,4,4), NTIK,NOR,NTO (5),HCORE,KSS,JSIM,NQUIT,JSPEC,STORE(7,96),JNUM,JNSP,HMTOT,YMNEW,XPNEW1,FF(4),IVSP(3),COlS,ZMNEW,NSPALT,IDFISS(13),NWRITE,TDOWN,TFAB,JTYP,NOPILE,NAJB(1),NBTOT,JSUM1,JSUM11,NXT3,NXT8,NDA9,JAD9 (2),N33,NDA13,NXT28,L1,L28,L4,JSUM13 PRO (3) NNE, LISTEQ /GRENZE/ NURTHM THERGR,IDGAM,IDZUT,IDTHER,NGAM,IDESIN,JJGM,MSTU, MGHUS,NNOBG, NZT(1,2), 331

332 C C C C C C C C C C C C 2 3 COMMON /SPECTI/ I'?IK(1) IZUT(1,2,1),SIRA(68),NIRPI,NID,NDA3 NKER, ITEMP (2) COMMON /QVAR/ IVAR,ENDKEF,QVOLLL,QREDUZ,QREMAX,EPQ,EPC 1 DQDDC,DELC,DCN,SBU,TE(4,99),TA(99),N61,URZ 2 ZLEKA,ABXEN,TI (99),DQCMAX,PSPALT,JRESTW,JRESTR 3 I, JREST,TAU,Q,QMI,QMA,QRAT,DMOD,DAEM COMMON /OPT/ KENN,IOPUT,NIFKO,DZT,KONIN COMMON /MPUNKT/ IMPU,KMPU,EMPU,TTTEIN,TTTAUS COMMON /ANISO/ JH,IZONE(5),DU(5),KK,M1(6,4) COMMON / IFA / FA, FA1, FA2, IEND, N44 COMMON /UI/ DUM(155),EM9 COMMON / DECAYT / DECY(17) COMMON / MCNP / IPCYC DIMENSION 1, 2, 3, 4, 5, 6, 7, 8, 9, X, DIMENSION DIMENSION BU (6,KMAT) DEN(KMAT,N2) THBURN(N2) HMETAL (N2) LRZN(N2) NTYP1(N24) VERA (N2) VOLWEG(NDR) DA2(KMAT) IREG(NDR) RVCB (MBOX),VOLREG(NDR),DENIOD(N2),FADOS3(N2),TCHG2(N2),TCHG1 (N24),TEMZUT (NXS),IHZ(NDR),HMETAV(N2),SCELS(NXS),JAD11(JD11),VOL(N2),HM (N2),NOPOW (N2),KRESHZ(N2),NALT(N24),TCELS (5,NXS),VOLIHZ (NDR),DAV(KMAT),SEMZUT(NXS),IBOX(MBOX) ABSIG(LAO),NHOT(N2),SS(N26,N2), RPHIAV (N26, NDR) ADEN(KMAT), JP(KMAT),ABSRAT(KMAT) C C FORMATE C C 5 FORMAT (2I3,5E12.5,I6) 11 FORMAT (2413) 12 FORMAT(18I4) ') 114 FORMAT (//' FOR THE NEXT CYCLE THE TEMPERATURES OF THE RESONANCE A IBSORBERS AND SCATTERING NUCLIDES HAVE BEEN CHANGED:'/) 115 FORMAT (6E12.5) 116 FORMAT (//' REPROCESSING MIXTURE:',I1,918) 117 FORMAT (' FRACTIONS OF JUMBLE BOXES:',F6.2,9F8.2) 5 FORMAT ('' // 5('.'),' FOR OUT-OF-PILE BATCHES DECAY IS CALCULAT led FOR OUT-OF-PILE STORAGE TIME TSTORE 2,G12.5,5('. /// ) 51 FORMAT (I3,9X,I2,8X,E12.5,4(3X,E12.5)) 52 FORMAT ('O' // 5('.'),' FOR THE IN-PILE BATCHES DECAY IS CALCULAT 1ED FOR THE DOWNTIME FOR REFUELLING TDOWN 332

333 2,G12.5,5('.') /// ) 54 FORMAT (/ ' MATERIAL',18X,'CONCENTRATION') 55 FORMAT (' ******************************************************** 1***t***ff************* * * ********************************* 2 /3X, ' END OF OPERATING CYCLE',I4,5X,' RELOAD NO', 4,' 1 IS EXECUTED ' /X,121('*') //) 56 FORMAT (// ' OPTIONS FOR NEXT CYCLE 1/' IPRIN(1)=',I3,',P RIN(2 )',I,'IPRIN2 3,IPRIN(3)=',I3,',IPRIN(4)=',I3, 2',JNSTOP=',I3,',LIB=',13,',NPRINT=',I3,',IBUC'X=',I3,',MUHU(3)=',I3 3,',XE-EXPL.=',I3/' NXE=',I3,',DELDAY=',E12.5,',POWER=',E12.5,',ZKF 4IND=',E12.5,',TDOWN=',E12.5//) 57 FORMAT (4I3,3E12.5,4E6.) 51 FORMAT (I5,6X,G12.5,8X,G12.5) 511 FORMAT ('1','BATCHES BEFORE RELOAD NO ',I3//' BATCH TOT.VOLUME ( 1CCM) HEAVY METAL (GR) FIMA FUEL TYPE BURNUP CLASS 2 IRRADIATION AGE FDOSE'/) 512 FORMAT (1H,6A4,E12.5) 513 FORMAT ('+',45X,E12.5,6X,I2,12X,I2,9X,E12.5,5X,E12.5) 599 FORMAT ('1') C 61 FORMAT (/' AUF DIRECT-ACCESS-EINHEIT',I3,' WURDEN',I4,' SAETZE MITML C 1 KONZENTRATIONEN VERBUCHT.'/) ML FORMAT (/' ON DIRECT-ACCESS UNIT',I3,' - ',I4,' SETS WITH CONCENTRML ATIONS ARE WRITTEN.'/) ML FORMAT (18I4) 64 FORMAT (1216) 7 FORMAT (////' OUT OF PILE BATCHES BEFORE RELOAD NO.',I5//' TYP B lurnup CLASS VOLUME AVG.AGE AVG.BURNUP AVG.F 2-DOSE HM-GRAM'/) C 71 FORMAT (//' ***VORSICHT: DIE ZWISCHENBOX',I4,' MIT VOL. =',E12.5,'ML C 1 WIRD GELOESCHT.'/14X, 'SIE WIRD AUCH IN DER KOSTENRECHNUNG NICHT BML C 2ERUECKSICHTIGT.***'//) ML FORMAT (//' ***CAUTION: THE INTERMEDIATE BOX',14,' WITH VOL. =', ML E12.5,' WILL BE DELETED.'/14X, 'NO CONSIDERATION OF THIS BOX IN CALML CULATION OF COSTS.***'//) ML FORMAT (////' FROM RELOAD NO.',I5,' THE FOLLOWING STORAGE BOXES AR 1E PREPARED.'/' THEY ARE AVAILABLE AT THIS RELOAD NO.',I5,' (DECAY 2TIME IS NOT APPLIED).'//' BOX TYPE BURNUP CLASS VOLUME 3 AVG.IRR.TIME AVG.BURNUP AVG.F-DOSE TOT.HEAVY METAL (G 4R)'/) 721 FORMAT (I3,I7,9X,I2,8X,E12.5,3(3X,E12.5),6X,E12.5) C C IF (TSTORE.LT..) TSTORE=-TIME(1)/AAAA TST=ABS(TSTORE) DELSTO = DELDAY * JNSTOP C C NEW OPTIONS FOR NEXT CYCLE C DO 29 I=1,3 IVSP(I+24)= XVSP(I) =. 29 CONTINUE XTDOWN =. IVSP(28) = KONIN = JREST = IF(ITIK(1).GT. ) GO TO 3 333

334 C C C C C C C C C C C C C ITIK (1) = ITIK(9) = IT1 = IVAR = URZ =. JRESTW = JRESTR = EPQ =. DMOD =.5 EM9 = 1.E-9 DQCMAX =. 3 CONTINUE IF(IVSP(1).GE. 1) GO TO 21 CARD R9 READ (NS,11) (IVSP(I), I=1,6),(IVSP(I), I=8,14),IVOID,(IVSP(I), I= 115,17),(IVSP(I), I=19,24),MUHU(8) N44 = IVSP(12) IF(IVOID.LE. ) GO TO 6 CARD R1 READ (NS,12) JH,(IZONE(I),Ml(I,1),Ml(I,2), I=1,JH) KK = JH + 1 M1(KK,1) = IVOID = 6 CONTINUE IF(IVSP(2).LT. 1) GO TO 4 KONIN = IVSP(2) / 1 IVSP(2) = IVSP(2) - 1 * KONIN 4 CONTINUE IF(IVSP(2).LT. 1) GO TO 1 IT1 = IVSP(2) / 1 IF(IT1.NE. 6) GO TO 9 ITIK(1) = ITIK(9) = IT1 = 5 IVSP(2) = 51 9 CONTINUE IVSP(2) = IVSP(2) - 1 * IT1 IF(IT1.EQ. ) GO TO 1 ITIK(1) = 1 IF(IT1.EQ. 1) GO TO 1 IF(IT1.LE. 4) GO TO 2 IVAR = IT1-4 IT1 = IT1-3 CARD Rll READ (NS,115) ENDK,QVOLLL,QREMAX,EPR,EPC,URZ IF(EPR.NE..) EPQ = EPR IF((ITIK(1).EQ. ).OR. (ENDK.NE. )) ENDKEF = ENDK 334

335 C C C C C C C CARD R12 READ (NS,115) DQDDG,DELC,DCM,DQCMAZ,PSPALT,DMOT IMPU = IF(DQDDG.NE..) DQDDC = DQDDG IF(DQCMAZ.NE..) DQCMAX = DQCMAZ IF(DMOT.NE..) DMOD = DMOT IF(DCM.NE..) DCN = DCM CARD R13 IF(ITIK(1).EQ. ) READ (NS,5) JRESTW,JRESTR,QO,QMI,QMA,QRAT,DAEM IF(ITIK(1).EQ. ) EMPU =. IF(QMI.NE. QMA) GO TO 2 QMI = EPQ QMA = EPQ 2 CONTINUE IF(QRAT.EQ..) QRAT = 1. ITIK(1) = 2 IF(ITIK(9).GT. ) GO TO 1 ITIK(9) = IT1-5 1 CONTINUE MUHU(29)= IF (IVSP(3).LT.1) GOTO 22 MUHU(29) =IVSP (3)/1 IVSP(3)=IVSP(3)-1 22 CONTINUE MUHU(1) = IVSP(23) 21 CONTINUE N61 = 6 IF(URZ.LT..) N61 = 4 NT=6 IVSP(1) = IVSP(1) - 1 ITIK(4) = IVSP(8) IPRIN(1) = IVSP(2) IPRIN(2) = IVSP(3) IPRIN(3) = VSP(4) IPRIN(4) = IVSP(1) LIB = IVSP(21) NPRINT = IVSP(5) NTIK = IVSP(2) ITIK(6) = NTIK IF((NTIK.EQ. 3).OR. (NTIK.EQ. 1)) ITIK(1) = NCYC = IVSP(14) NTYPE= IF (IVSP(11).EQ.2) NTYPE=2 IVSP(14) = IN2 = IVSP(9) NKEEP = IVSP(13) ISTORN = NKP = NKEEP - 1 * (NKEEP/1) IF(NKP.EQ. 2) ISTORN = 1 IVSP(13) = LOB =-IVSP(22) PU = POWER 335

336 C C C C C C C C C C C C C C C C HNUC =. CONPOI =. HPOS =. CARD R14 IF(IVSP(15).EQ. 1) READ (NS,57) (IVSP(I), I=25,28), (XVSP(I), I= 11,3),HNUC,HPOS,XTDOWN,CONPOI IF(IVSP(28).GT. ) NXE = 1 IF(CONPOI.LT..) JSER = 1 ICONPO = IFIX(CONPOI) IF(HNUC.GT..) IVSP(29) = IFIX(HNUC) HNUC =. IF(XTDOWN GT..) TDOWN = XTDOWN IF(XTDOWN.LT..) TDOWN =. IF(XVSP(1).NE..) DELDAY = XV, SP(1) IF(XVSP(2).NE..) POWER = XV, SP(2) IF(XVSP(3).NE..) ZKFIND = XV. SP(3) IF(IVSP(25).NE. ) JNSTOP = IV 'SP(25) IF(IVSP(26).NE. ) JNUM = IV, SP(26) IF(IVSP(24).GT. ) JNSTOP = -JNS' rop IVSP(24) = IVSP(15) = XVSP(2) = PU IF(IVSP(27).GT. ) MUHU(3) = IVS]?(27) IF(NCYC.LE. ) GO TO 42 IF(NCY.EQ. ) NCYC = -NCYC NCY = NCYC CARD R15 READ (NS,115) (FOJB(I), I=1,MREP) WRITE (NT,116) ( I, I=1,MREP) WRITE (NT,117) (FOJB(I), I=1,MREP) 42 CONTINUE IF(IVSP(16).LE. ) GO TO 43 IVSP(16) = CARD R16 READ (NS,63) (ISPEKT(I), I=1,18) ISPEKT(2) = DO 47 I=1,18 IF(ISPEKT(I).NE. ) ISPEKT(2) = I 47 CONTINUE 43 CONTINUE IF(IVSP(17).LE. ) GO TO 49 IVSP(17) = CARD R17 READ (NS,63) (IDIFF(I), I=1,18) IDIFF(2) = 336

337 C C C C C C C C C C C C C C C C DO 48 I=1,18 IF(IDIFF(I).NE. ) IDIFF(2) = 48 CONTINUE 49 CONTINUE IF(ITIK(6).EQ. 5) GO TO 41 IF((NTIK.LT. 1).OR. (NTIK.GT. 2)) GO TO 58 CARD R18 41 READ (NS,63) (ITEMP(I), I=1,18) ITEMP(2) = DO 59 1=1,18 IF(ITEMP(I).NE. ) ITEMP(2) = I 59 CONTINUE 58 CONTINUE IF(IVSP(19).EQ. ) GO TO 54 IF(IVSP(19).EQ. 2) GO TO 6 CARD R19 READ (NS,115) (SEMZUT(I), I=1,NXS) DO 56 I=1,NXS 56 IF(SEMZUT(I).GT..) TEMZUT(I) = SEMZUT(I) WRITE (NT,114) WRITE (NT,115) (TEMZUT(I), I=1,NXS) DO 53 J=1,NKER CARD R2 READ (NS,115) (SCELS(I), I=1,NXS) DO 57 I=1,NXS 57 IF(SCELS(I).GT..) TCELS(J,I) = SCELS(I) WRITE (NT,115) (TCELS(J,I), I=1,NXS) 53 CONTINUE IF(IVSP(19).EQ. 1) GO TO 54 6 CONTINUE DO 61 I=1,IDESIN DO 61 J=1,2 CARD R21 READ (NS,64)NZ, (IZUT(I,J,M), M=1,NZ) WRITE (NT,64) NZ,(IZUT(I,J,M), M=1,NZ) NZT(I,J) = NZ 61 CONTINUE 54 CONTINUE IVSP(19) = IF(IPRIN(3).EQ. -2) NT = 4 INZW(1) = IN2 IF(NPRINT.GE.) WRITE (NT,599) IN1=IPRIN(15)+1 INZW(3) = IN1 WRITE ( 6,55) IN1,IPRIN(15) 337

338 WRITE ( 6,56) (IPRIN(I),I=1,4),JNSTOP,LIB,NPRINT,IBUCK,MUHU(3),IV 1SP(28),NXE,DELDAY,POWER,ZKFIND,TDOWN C C CALCULATE AVERAGE BATCH PROPERTIES BEFORE RELOAD C IF (NPRINT.GE.1) WRITE (NT,511) IPRIN(15) NCX2 = MRY = DECAF =. NDA28 = 28 NXT28 = 1 IL = C C repeat for eah bath DO 191 IR=1,NRESHZ C C for fuel yle ipy C IF (IPRIN(15).EQ.IPCYC) THEN C write yle and bath number to file WRITE (96,*) 'CYCLE = ',IPCYC,' BATCH = ',IR WRITE (97,*) IR hek if new layer IF (MOD(IR,11).EQ.1) THEN IF ((IL.GE.1).AND.(IL.LE.57)) THEN C print data on previous layer WRITE (96,*) 'VOL OF LAYER ',IL,' = ',VOLAY WRITE (98,*) IPCYC,IL,ADENT,VOLAY,FF(1) WRITE (99,*) IL DO 13 I=1,KMAT, KMAX = MIN(I+4,KMAT) WRITE (98,*) (ADEN(K),K=I,KMAX) WRITE (99,*) (ABSRAT(K),K=I,KMAX) CONTINUE END IF C inrement layer ounter IL = IL C initialize variables DO 19 I=1,KMAT ADEN(I) = ABSRAT(I) = CONTINUE ADENT = VOLAY = END IF END IF C NCX1 = NCX2+1 NCX2 = KRESHZ(IR) IF ((IR.GT.1).AND.(NPRINT.EQ.2)) WRITE (NT,599) NALT(IR) = 1 DO 55 M=1,KMAT 55 DAV(M) =. PARVOL=. HMETAV(IR) =. HMGRM =. BURNRX =. 338

339 DOSNRX =. MRZ = IR1=NCX1 51 CONTINUE NCX = LRZN(IR1) DO 5 M=1,KMAT 5 DAV(M) = DAV(M) + DEN(M,NCX) * VOL(NCX) HMETAV(IR) = HMETAV(IR) + HMETAL(NCX)*VOL(NCX) HMGRM =HMGRM+HM(NCX) BURNRX=BURNRX+THBURN (NCX)*VOL(NCX) DOSNRX=DOSNRX+FADOS3(NCX)*VOL(NCX) PARVOL=PARVOL+VOL(NCX) MRZ = MRZ + 1 IR1 = IR1 + 1 IF(IR1.LE. NCX2) GO TO 51 MRY = imax(mry,mrz) VERA(IR)=PARVOL HMETAV(IR) = HMETAV(IR) / PARVOL HMDEN =HMETAV (IR) BURNRX=BURNRX/PARVOL DOSNRX=DOSNRX/PARVOL TCHG1(IR)=TCHG2(IR)+TIME (1) IF (NPRINT.GE.1) WRITE (NT,51) IR,PARVOL,HMGRM IF (NPRINT.EQ. 2) WRITE(NT,54) HMEND =. DAVT =. IF (IPRIN(15).EQ.IPCYC) THEN WRITE (96,*) 'VOLUME OF BATCH ',IR,' = ',PARVOL VOLAY = VOLAY + PARVOL END IF DO 52 M=1,KMAT DAV(M) = DAV(M)/PARVOL C C prepare layer averaged data for output if hosen yle C IF (IPRIN(15).EQ.IPCYC) THEN C print number of atoms of material M in bath WRITE (96,*) M,DAV(M)*PARVOL WRITE (97,*) DAV(M) C number of atoms of material M in layer ADEN(M) = ADEN(M) + DAV(M)*PARVOL C total number of atoms in layer ADENT = ADENT + ADEN(M) C set up pointers into sigma and flux arrays IF (IR.EQ.1) THEN LA = (NHOT(IR)-1)*KMAT DO 24 I=1,KMAT JP(I) = (LA+I-1)*N CONTINUE ELSE IF (NHOT(IR).NE.NHOT(IR-1)) THEN LA = (NHOT(IR)-1)*KMAT DO 25 I=1,KMAT JP(I) = (LA+I-1)*N CONTINUE END IF C prepare total absorption rate for material M in the bath C using effetive marosopi ross setion

340 DO 26 IG=1,N SSFAC = SS(IG,IR)*RPHIAV(IG,IL) ABSRAT(M) = ABSRAT(M) + ABSIG(JP(M)+IG)*SSFAC CONTINUE END IF C IF (M.LE. 13) HMEND = HMEND + DAV(M) IF (NPRINT.NE. 2) GO TO 52 WRITE (NT,512)(BU(N,M),N=1,6),DAV(M) 52 CONTINUE IF (TDOWN.EQ..) GO TO 19 C C DECAY DURING RESHUFFLE PERIOD C DAV(2) =. DAV(3) =. DAV(8) =. DAV(9) =. DAV(11) = IF (NXE.LE. ) 1DAV(14) =. TDOWM = TDOWN IF(TDOWM.LT..) TDOWM = ABS(TDOWN) * DELSTO TT = TDOWM*36.*24. IRi=NCX1 16 CONTINUE NX = LRZN(IR1) IF (NXE.GT. ) GO TO 155 DEC = EXP(-2.87E-5*TT) DEN(14,NX) = (DEN(14,NX) *DENIOD(NX)*(EXP(-.77E-5*TT) 1-1.))*EXP(-2.lE-5*TT) DENIOD(NX) = DENIOD(NX)*DEC 155 CONTINUE DEC = EXP(-TT*DECY(2)) DC = DEN(2,NX) * (1.-DEC) DEN(3,NX) = DEN(3,NX)+DC DEN(2,NX) = DEN(2,NX)*DEC DECAF = DECAF + DC * VOL(NX) DEC = EXP(-TT*DECY(8)) DC = DEN(8,NX) * (1.-DEC) DEN(9,NX) = DEN(9,NX)+DC DEN(8,NX) = DEN(8,NX)*DEC DECAF = DECAF + DC * VOL(NX) DEC = EXP(-TT*DECY(11)) DEN(11,NX) = DEN(11,NX)*DEC DAV(2) = DAV(2) + DEN(2,NX) * VOL(NX) DAV(3) = DAV(3) + DEN(3,NX) * VOL(NX) DAV(8) = DAV(8) + DEN(8,NX) * VOL(NX) DAV(9) = DAV(9) + DEN(9,NX) * VOL(NX) DAV(11) = DAV(11) + DEN(11,NX) * VOL(NX) IF (NXE.LE. ) 1DAV(14) = DAV(14) + DEN(14,NX) * VOL(NX) IR1 = IR1 + 1 IF(IR1.LE. NCX2) GO TO 16 DAV(2) = DAV(2)/PARVOL DAV(3) = DAV(3)/PARVOL DAV(8) = DAV(8)/PARVOL 34

341 C C C C DAV(9) = DAV(9)/PARVOL DAV(11) = DAV(11)/PARVOL IF (NXE.LE. ) 1DAV(14) = DAV(14)/PARVOL 19 CONTINUE FIND BURNUP (FIMA-VALUE) FOR THIS REGION IF (NOPOW(IR).EQ.) GOTO 182 FIMA=. GOTO CONTINUE FIMA = (HMETAV(IR)-HMEND)/HMETAV(IR) IF(FIMA.LE..) FIMA = EM9 183 CONTINUE NTP = NTYP1(IR) NTP1 = NTP-1 KL = IF (NTP1.LE. ) GO TO 175 DO 17 I=1,NTP1 KL = KL+KLASSE(I) 17 CONTINUE 175 CONTINUE IF(NOPOW(IR).GT. ) GO TO 184 KLZ = KLASSE(NTP) DO 18 I=1,KLZ IKLASS = I IF (FIMA.LT. FIMAKL(KL+I)) GO TO CONTINUE 184 CONTINUE IKLASS = 181 CONTINUE IF(NPRINT.GE.1) 1WRITE(NT,513) FIMA,NTP,IKLASS,TCHG1(IR),DOSNRX WRITE (97,*) PARVOL,FIMA JSATZ = 2+IR IF (JAD11(JSATZ).EQ. ) JADll1(JSATZ)=JSUM11 NXT11 = JAD11(JSATZ) WRITE (NDA11,REC=NXT11)(DAV(L),L=l,KMAT),PARVOL,TCHGI(IR),NTP 1, IKLASS,BURNRX,DOSNRX,HMGRM,HMDEN NXT11 = NXT IF (JSUM11.LT. NXT11) IF(IVSP(21).GE. ) GO TO 191 NTYP = NTP * WRITE (NDA28,REC=NXT28) NTYP NXT28 = NXT CALL WRDA(IWRITE,NDA28,NXT28,L28,DAV,KMAT) 191 CONTINUE IF(IVSP(21).GE. ) GO TO 6 IVSP(21) = NRS = NXT28-1 WRITE (6,61) NDA28,NRS 6 CONTINUE IF (NPRINT.GT. ) 1WRITE (NT,52) TDOWN IF (KUGL.LE. ) GO TO 199 JSUM11=NXT11 341

342 C IHZ(KR) = NUMBER OF BATCHES / LAYER C VOLIHZ(KR) = VOL. OF ONE LAYER C IRRE1 = DO 192 KR=1,NDR IRRE2 = IREG(KR) IHZ(KR) = IRRE2-IRRE1 VOLIHZ(KR) = VOLREG(KR) VOLWEG(KR) =. IRRE1 = IRRE2 192 CONTINUE IF(MBOX.LE. NBOX) GO TO 31 C C FILLING OF THE STORAGE BOXES FROM INTERMEDIATE BOXES C DO 132 I=1,MBOX 132 RVCB(I) =. K2 = KMAT + 8 ANUL =. NB1 = NBOX + 1 DO 33 I=NB1,MBOX RVCB(I) = 1. JSATZ = NRESHZ I IF (JAD11(JSATZ).EQ. ) JAD1(JSATZ)=JSUM11 NXT11 = JAD11(JSATZ) WRITE (NDA11,REC=NXT11) (ANUL, J=1,K2) NXT11 = NXT IF (JSUM11.LT. NXT11) JSUMll=NXT11 33 CONTINUE IF(MBOX.EQ. 1) GO TO 31 IF(ISTORN.EQ. 1) GO TO 31 DO 34 I=1,NBOX JSATZ = NRESHZ I JS2 = JSATZ NXT11 = JAD11(JSATZ) IF(NXT11.EQ. ) GO TO 34 READ (NDA11,REC=NXT11) (DAV(L), L=1,KMAT),PARVOL,XCHNRX,NTPNRX, 1 IKLNRX,BURNRX,DOSNRX,HMGRM,HMDEN NXT11 = NXT IF(IBOX(I).EQ. ) GO TO 32 JSATZ = NRESHZ IBOX(I) NXT11 = JAD11(JSATZ) READ (NDA11,REC=NXT11) (DA2(L), L=1,KMAT),PARVO2,XCHNR2,NTPNR2, 1 IKLNR2,BURNR2,DOSNR2,HMGR2,HMDE2 NXT11 = NXT PV = PARVOL + PARV2 PV1 = PARVOL / PV PV2 = PARVO2 / PV DO 35 L=1,KMAT 35 DA2(L) = DAV(L) * PV1 + DA2(L) * PV2 PARV2 = PV XCHNR2 = XCHNRX * PV1 + XCHNR2 * PV2 NTPNR2 = NTPNRX HMGR2 = HMGRM + HMGR2 HMDE2 = HMDEN * PV1 + HMDE2 * PV2 BURNR2 = BURNRX * PV1 + BURNR2 * PV2 DOSNR2 = DOSNRX * PV1 + DOSNR2 * PV2 342

343 C C C DN2 =. DO 36 L1,13 36 DN2 - DN2 + DA2(L) FIMA (HMDE2-DN2) / HMDE2 IF(FIMA.LE..) FIMA EM9 NTP1 NTPNR2-1 KL = IF(NTP1.LE. ) GO TO 39 DO 2 L=1,NTP1 KL = KL + KLASSE(L) 2 CONTINUE 39 CONTINUE KLZ = KLASSE(NTPNR2) DO 37 L=1,KLZ IKLNR2 = L IF(FIMA.LT. FIMAKL(KL+L)) GO TO CONTINUE IKLNR2 = 38 CONTINUE NXT11 = JAD11(JSATZ) WRITE(NDA11,REC=NXT11) (DA2(L), L=1,KMAT),PARV2,XCHNR2,NTPNR2, 1 IKLNR2,BURNR2,DOSNR2, HMGR2,HMDE2 NXT11 = NXT CONTINUE IF(IBOX(I).EQ..AND. PARVOL.GT..) WRITE (6,71) I,PARVOL NXT11 = JAD11(JS2) WRITE(NDA11,REC=NXT11) (ANUL, J=1,K2) NXT11 = NXT IBOX(I) = 34 CONTINUE IF(NPRINT.LT..OR. IPRIN(15).EQ. ) GO TO 4 IPRO = IFIX(PRO(299)) WRITE (NT,72) IPRO,IPRIN(15) DO 3 I=NB1,MBOX J = I - NBOX JSATZ = NRESHZ I NXT11l JAD11(JSATZ) READ(NDA11,REC=NXT11) (DA2(L), L=1,KMAT),PARV2,XCHNR2,NTPNR2, 1 IKLNR2,BURNR2,DOSNR2,HMGR2,HMDE2 NXT11 = NXT WRITE (NT, 721) J, NTPNR2, IKLNR2, PARVO2, XCHNR2, BURNR2, DOSNR2, HMGR2 3 CONTINUE 4 CONTINUE 31 CONTINUE DECAY OF OUT-OF-PILE BATCHES DURING LAST CYCLE AND RESHUFFLE TT=TST*36. *24. IF(NPRINT.GE. 1) WRITE (NT,7) IPRIN(15) DO 194 N=1,NOPILE IR=NRESHZ+N JSATZ=2+MBOX+IR NXT11=JAD11 (JSATZ) READ (NDA11,REC=NXT11) (DAV(L),L=1,KMAT),PARVOL,TXCHG,NTP,IKLASS, 1 BURNRX,DOSNRX,HMGRM,HMDEN NXT11 = NXT IF (IKLASS.LE. 1) GOTO

344 TXCiGTXCHG+TST*AAAA TCHG1 (IR) =TXCG IF (NXE.LE. ) 1DAV(14). DEC=EXP (-TT*DECY(2)) DC = DAV(2) * (1.-DEC) DAV(3)=DAV(3)+DC DAV(2)=DAV(2) *DEC DECAF DECAF + DC * PARVOL DEC=EXP(-TT*DECY(8)) DC = DAV(8) * (1.-DEC) DAV(9)=--DAV(9) +DC DAV(8)=DAV(8)*DEC DECAF - DECAF + DC * PARVOL DEC=EXP(-TT*DECY (l)) DAV(11)=DAV(11)*DEC NXT11=JAD11 (JSATZ) WRITE (NDA11,REC=NXT11) (DAV(L),L=1,KMAT), PARVOL,TXCHG,NTP,IKLASS, 1 BURNRX, DOSNRX, HMGRM,HMDEN NXT11 = NXT IF (NPRINT.LT. 1) GOTO 194 WRITE (NT,51) NTP, IKLASS,PARVOL,TXCHG,BURNRX,DOSNRX,HMGRM IF (NPRINT.NE. 2) GOTO 194 DO 193 L=1,KMAT WRITE (NT,512) (BU(I,L),I=1,6),DAV(L) 193 CONTINUE 194 CONTINUE IF (NPRINT.GT. ) 1WRITE (NT,5) TST 199 CONTINUE RETURN END 344

345 APPENDIX D.4: Program MCARDS program mards prepare mnp material ards using vsop fuel ompositions for eah layer. The ompositions are homogenized over the volume of a fuel sphere, with an adjustment to U238 omposition. parameter (niso = 51) parameter (kmat = 65) parameter (layers = 57) real nvsop(kmat),rate(kmat),nmnp(niso),vlay(layers) integer hit(kmat),ipoint(niso) harater*9 zaid(niso)*9,matnam*4 mnp material i.d. data zaid / 1 '9232.5',' ',' ',' ',' ', 2 ' ',' ',' ,' ','9424.5', 3 ' ',' ',' ',' ','3683.5', 4 '4295.5','4399.5','4411.5','4413.5','4513.5', 5 '4515.5','4615.5','4618.5','4719.5','48.5', 6 ' ',' ',' ',' ','6143.5', 7 '6145.5',' ',' ',' ',' ', 8 ' ','6215.5',' ',' ,' , 9 ' ',' ,' ,,, ',' ', x ' 51.5',' 511.5','26.5','14.5',' 6.5', y ' 816.5' / data pf/.61/,rfs/3./,pi/ /,sale/1./ mapping between vsop and mnp data hit / 14*1,,,1,,1,,8*1,1,,1,,3*1,,1,,1,,4*1,,3*1, 1,11*1,,1,,1,1 / initializations.. zaid pointer and mnp atom density arrays do 5 iz=l,niso ipoint(iz) = nmnp(iz) =. 5 ontinue.. vsop material atom densities and reation rates do 1 m=l,kmat nvsop(m) =. rate(m) =. 1 ontinue.. total reation rate for non-hits rden =. volume of fuel sphere vfs = (4.J3.)*pi*rfs**3 345

346 open (unit=98,file='fort.98',status='old') open (unit=99,file='fort.99',status='old') open (unit=1,file='mards_new.dat',status='new') start numbering mnp material ards at m1 matnum = 99 for eah layer. do 45 1=1, layers input vsop yle, layer number and total atom density read (98,*) ipy,laynuml,vlay(l),pf read (99,*) laynum2 if (laynuml.ne. laynum2) then stop 'mards error: layer number mismath' end if 15 ontinue input atom density and reation rate for eah material matnum = matnum + 1 do 15 m=l,kmat,5 kmax = min(m+4,kmat) read (98,*) (nvsop(k),k=m,kmax) read (99,*) (rate(k),k=m,kmax) alulate number of fuel spheres in layer vol = vlay(l) nfs = int(pf*vol/vfs) transfer atom densities to mnp file if nulides math or sum up reation rates otherwise im = iz = do 2 m=l,kmat mnp library exists and density not zero if ((hit(m).eq.l).and.(nvsop(m).ne..)) then inlude Pml48g with Pm148m (m=42) if (m.eq.43) then nmnp(im) = nmnp(im) + nvsop(m) B1 else if (m.eq.58) then im =im + 1 iz = iz + 1 nmnp(im) = nvsop(m) iblo = im ipoint(im) = iz orret [U238] for heterogeneity else if (m.eq.7) then im = im + 1 iz = iz + 1 nmnp(im) = sale*nvsop(m) ipoint(im) = iz all other nulides else im = im + 1 iz = iz + 1 nmnp(im) = nvsop(m) ipoint(im) = iz end if mnp library exists but density is zero 346

347 else if ((hit(m).eq.1).and.(nvsop(m).eq..)) then inrement zaid array pointer iz = iz + 1 if (m.eq.58) then im = im + 1 nmnp(im) =. iblo = im ipoint(im) = iz end if mnp library does not exist else rden = rden + nvsop(m)*rate(m) end if 2 ontinue nmax = im B1 atom density hosen to onserve total reation rate nmnp(iblo) = nmnp(iblo) + rden/rate(58) adjust atom densities to volume of spheres and alulate total atom density in layer totn =. do 22 i=l,niso nmnp(i) = nmnp(i)*vol/(nfs*vfs) totn = totn + nmnp(i) 22 ontinue prepare mnp material ard write (1,25) ipy,laynuml,totn 25 format ('C VSOP yle ',i4,'; layer ',i3, > '; total N = ',lpe14.7) do 4 i=l,nmax,3 jmax = min(i+2,nmax) if (i.eq.1) then numold = matnum all mhar(numold,matnam) write (1,3) matnam,((zaid(ipoint(j)),nmnp(j)), > j=i,jmax) 3 format(a4,1x,3(a9,lpe12.5,2x)) else write (1,35) ((zaid(ipoint(j)),nmnp(j)),j=i,jmax) 35 format(5x,3(a9,lpel2.5,2x)) end if 4 ontinue 45 ontinue end for loop lose (unit=97) lose (unit=98) lose (unit=99) stop end 347

348 subroutine mhar (num,number) prepare harater string Mn harater*4 number harater*l digit(1) data digit /'','1','2','3','4','5','6','7', '8,'9'/ number = 'M i= 4 if (num.gt. 999) stop 'number > 999' 1 ontinue n = mod(num,1) + 1 number(i:i) = digit(n) num = int(num/1) i=i if (i.gt. 1) go to 1 write (6,15) number format(lx,'material =',a4) return end 348

349 APPENDIX E. Plutonium Prodution in a Modular Pebble Bed Reator Appendix E. 1 ontains the MCNP4B input file with added lines for a MOCUP burnup alulation, whih uses a superell model to alulate plutonium prodution in a speial, depleted-uranium pebble. Details on this model and related analysis may be found in Chapter 8. Appendix E.2 ontains the Exel spreadsheets that were used to analyze the results of the VSOP94 fuel management for the preliminary PBMR ore (see Appendix D. 1). The nulide densities of fuel spheres in the bathes at the bottom of the ore were extrated from the VSOP94 output file prior to reload number 261. The five sets of eleven bathes orrespond to the five pebble flow hannels in the VSOP94 model. The mass of 239 pu was determined from these nulide densities. 349

350 APPENDIX E. 1: MOCUP Superell Model of Prodution Sphere CRITICAL DRIVER LATTICE WITH PRODUCTION PEBBLE IN CENTER MCNP4B model of a ritial spherial assembly onsisting of: - solid outer refletor - lattie of driver fuel pebbles with nulide ompositions that orrespond to the average VSOP model of equilibrium fuel yle - a prodution pebble in the enter with depleted uranium ore J.R. Lebenhaft, MIT, July 2 - MCNP4B model K.D. Weaver, INEEL - MOCUP additions ell ards e fill=l ore universe 2: prodution ell E e e e e e e e e-3 (12:-11: 14:-13:-15: 16) universe 6: ontents of prodution ball e e-2-4 $ outside world $ graphite refletor $ pebble bed fill=2 u=l $ prodution ell fill=5 u=l $ driver ore fill=6 u=2 u=2 u=2 u=2 u=2 u=2 u=2 u=2 u=2 $ prodution $ 1/8 driver $ 1/8 driver $ 1/8 driver $ 1/8 driver $ 1/8 driver $ 1/8 driver $ 1/8 driver $ 1/8 driver u=2 $ helium [ 1 [ 1 [ 1 1 [-1 [-1 [-1 [-1 u=6 $ graphite shell u=6 $ target region universe 5: driver lattie lat=l fill=1 u=5 $ driver ell ] 1 1] 1-1] -1-1] -1 1] 1 1] 1-1] -1-1] -1 1] 35

351 .. universe 1: ontents of driver ell e e e e e e e e e e u=1 $ u=1 $ u=1 $ u=1 $ u=1 $ u=1 $ u=1 $ u=1 $ u=1 $ 1 driver 1/8 driver 1/8 driver 1/8 driver 1/8 driver 1/8 driver 1/8 driver 1/8 driver 1/8 driver u=1 $ helium ] 1-1 1] (-1 1 1] [-1 1-1] [ [-1-1 1] surfae ards 1 2 universe boundaries so 25. so 2. 1 so so prodution ell boundaries 11 px px py py pz pz balls in unit b lattie 3 so s s s s s s s s prodution fuel 4 so 2.1 $ outer refletor $ driver region $ outer refletor $ driver region $ fueled region in ball run time ards -- material ards helium (12 K) 351

352 ml 23, U2 (U235/U =.2) m OOOE E OOOE OOE E OOOE OOOE E E E E E E E E E E OOE E E E E E E E E E E E OOOE E OOOE E OOE E E OOOE E E E E OOOE OOOE OOE E E E E E E OOOE OOE E E E E E E E E E E-24 m4 VSOP yle 261; layer average; total N = E E E E E E E E E E E E E E E E E E E E E E E E E-8 352

353 E E E E E E E E E E E E E E-2 mt4 grph.6t graphite matrix in fuel pebble (N = e-2) m e e e-8 mt64 grph.6t U238 for (n,gamma) reation rate tally m Tally Materials m71 m72 m73 m74 m75 m76 m77 m78 m79 m71 m711 m712 m713 m714 m715 m716 m717 m718 m719 m72 m721 m722 m723 m724 m725 m726 m727 m728 m729 m73 m731 m732 m733 m734 m735 m736 m E E E E E E E-4 353

354 m m m m m m m m m m m m m m m m m m m m m m m m m soures ksr tally speifiations fqo e f f7 fission soure for normalization (per unit mass) f7:n 3 sd7 1 f4 average neutron flux in prodution ell f4:n 4 sd e4 1.86e-6 29e-6 1e-3 2 f14 average U238 absorption rate in prodution ball f14:n (21 < 1 < 4 < 3) atom density of depleted U2 (1/b-m) fml e volume of target (m3) 354

355 sdl e e-6 2 f24 average U238 absorption rate in driver ball f24:n (( ) < 4 < 3) atom density of U238 (1/b-m) from m4 ard fm e sd e e-6 2 (total fuel volume = m*3) f54 Total Fissions Total Fission Neutrons fm54 ( (-6) (-6-7)) f54:n 21 begin_moup_flux_tallies time dependent flux f94 Cell-averaged neutron flux (neutrons/m**2 per soure neutron) f94:n 21 endmoup_flux_tallies begin_moup_reation_rate_tallies time dependent reation rates f94 (n,x) reations - fuel region f94:n 21 fm94 (1. 71 (12)) (1. 72 (12)) (1. 73 (12)) (1. 74 (12)) (1. 75 (12)) (1. 76 (12)) (1. 77 (12)) (1. 78 (12)) (1. 79 (12)) (1. 71 (12)) ( (12)) ( (12)) ( (12)) ( (12)) ( (12)) ( (12)) ( (12)) ( (12)) ( (12)) (1. 72 (12)) ( (12)) ( (12)) ( (12)) ( (12)) ( (12)) ( (12)) 355

356 ( (12)) ( (12)) ( (12)) (1. 73 (12)) ( (12)) ( (12)) ( (12)) ( (12)) ( (12)) ( (12)) ( (12)) ( (12)) ( (12)) (1. 74 (12)) ( (12)) (1. 81 (16) (17) (18) (12))$ (1. 82 (16) (17) (18) (12))$ (1. 83 (16) (17) (18) (12))$ (1. 84 (16) (17) (18) (12))$ (1. 85 (16) (17) (18) (12))$ (1. 86 (16) (17) (19:2) (12))$ (1. 87 (16) (17) (19:2) (12))$ (1. 88 (16) (17) (19:2) (12))$ (1. 89 (16) (17) (19:2) (12))$ (1. 81 (16) (17) (18) (12))$ ( (16) (17) (19) (12))$ ( (16) (17) (18) (12))$ ( (16) (17) (19:2) (12))$ ( (16) (17) (18) (12))$ ( (16) (17) (19:2) (12))$ ( (16) (17) (18) (12))$ ( (16) (17) (18) (12))$ ( (16) (17) (18) (12))$ ( (16) (17) (19:2) (12))$ (1. 82 (16) (17) (19:2) (12))$ ( (16) (17) (19:2) (12))$ end_moup_reation_rate_tallies neutro n mp neutron importane imp:n $ outside world 1 $ outer refletor 1 $ pebble bed 1 1 $ u=l: target, driver ore 1 9r $ u=2: prodution ell 1 1 $ u=6: prodution ball 1 $ u=5: driver lattie 1 9r ell $ u=1: unit driver fuel mode n phys:p lj 1 kode prdmp

357 print

358 APPENDIX E.2: Exel analysis of V8P94 equilibrium ore results Data used In alulations: Gram atomi weights U235 U236 U238 Pu239 Pu24 Pu241 Pu242 NP Avogadro'es number pebble volume paking fration 6.2E m

359 Composition of used fuel balls In bathes at bottom of ore before removal: disharge bumup MWdlI average endhment 4.33 % 9 g HM; g fissile per fuel sphere passes through ore 1 avg. fuel residene tim days bath (m3) volume atom density (1/b-m) HM U-235 U-236 U-238 NP-239 PU-239 PU-24 PU-241 PU-242 NP E E E-6 4.5E E-4 2.7E E E E E-1 1.7E E-6 6.8E E-4 2.6E E E E E-9 5.E E E E E E E-7 5,9E E-8 1.4E E E E-4 2.5E-8 3.3E E-7 9.E E E E-6 1.2E E-4 2.4E-8 3.7E E E E E E E-6 1.1E E E E E E E E E-6 1.1E-4 2.2E-8 3.7E-7 4.1E E E E E E E-4 2.1E-8 3.6E E E E-7 5.9E E E-6 1.9E-4 2.E-8 3.5E E-7 1.7E-7 2.2E E E-6 1,32E-6 1.8E E-8 3.3E E E E E E E E E E E E E E E E E E-8 2.8E-7 5.8E E-9 3.2E E E-6 5.6E E E E E E E E E E E E-8 4.3E-7 2.6E E E-8 1.3E E E E E E E E-8 317E-8 2.7E E E E E-8 4.5E E E E E E-6 1.8E E E E-7 4.1E E E E E E-6 1.1E E-8 4.5E-7 4.3E E E E E E-6 1.9E E E E E E E E E-6 1.9E-4 2.1E E E E-7 1.9E E E-6 1.3E-6 1 8E-4 2.9E E E E E E E E E E E E E E E E E E E E-8 33E-7 5.3E E-9 3.2E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-7 3.E-8 2.6E E E E E E E E E E E E E-6 1.5E-6 1.1E-4 1.9E E E-7 2.8E E E E E-6 113E-6 1.1E E E E E E E E E E-6 1.9E E E E E E-7 5.7E E E E-6 19E E E E-7 2.6E E-7 6.6E E E E-6 1.8E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-9 6.4E E E E E E E E E E E E E E E E E E E E-8 2.3E E E-6 9.4E E E E E E E-8 2.9E E E-6 1.4E-6 1.1E E E E-7 2.6E-7 8.5E E E E E-6 1.1E E E-7 3.6E E E E E E E-6 1.9E E E E E E E E E E-6 1.9E E-8 5.6E E E E E E E E-6 1.8E-4 1.6E E-7 3.8E E E E E E E E E E E E E E E E E E-8 3.5E-7 524E E-9 4.E E E E E E E-8 4.3E E E-8 4.3E-9 6.3E E E E E E E E E E E E E E E E E E E-7 325E-8 2.E E E E E E-8 5.3E E-7 1.8E-7 5.7E E E E-6 1.6E-6 1.1E E-8 5.4E E E E E E E E-6 1.1E E-8 5.3E E E E E E E-6 1.2E-6 1.9E E-8 5.1E E E E E E E E-6 1.9E E E E E E E E E E-6 1.8E E E-7 3.7E E-7 226E E E E E E E E E E E E-13 disharge volune = 4.27E+5 359

360 Meae of uranium and plutonium In bath a bottom of ee before removal: m (g) hannel beth U.238 U-238 U-238 PU-239 PU-24 PU-241 PU-242 NP-237 I E+ 1,1E-12.84E E E-2 1,14E-3 8,91EO5 4.26E E+ 1,52E-12.83E+1 8,54E.23.95E E E E E+ 1.94E-12.83E E.2 86,32E E2 4,32E E E+ 2.28E E E-2 8.6E-2 2.3E E E E-1 2,57E E+1 7.8E E-2 2,99E E E ,18E-1 2,79E-1 2.8E E-2 1.E E E E E E.12,79E E-2 1,5E E.2 3,33E-2 1.7E ,92E E E E-2 1.8E E E E E E E-2 1 1E E E E E E E E2 1.11E-1 4,49E E E E E E E-2 191E-2 1.9E E-4 6.2E E+2 8,71E+2.84E+3 7.7E+ 1.47E+ 1.33E E+2 1,4E E E+ 4 21E+ 6.85E E E E-2 1.8E E E+1 2,82E+31.9E E+ 1.5E+ 3,54E E ,9E E E E+18.42E+ 2.38E+ 8.15E-1 5.2E E E+1 2.8E E+19.66E+ 3.13E+ 1.45E+ 7.3E E E E E+1 1.5E+13.73E2.22E+ 9 5E E E E E+1 11E E+ 3.8E+ 1.2E E+1 3.7E E E+11.13E+1 4.5E+ 3.99E+1.43E E E E E E+14.72E+ 4.93E+ 1.68E E E+1 2.7E E+1 116E E+ 5.88E+ 1.88E E-1 6.,14E E+1 5 8E E E.36 43E E E E+15.67E E E+ 3 71E E E E E E+32.37E+1 7 3E+ 1.97E+ 1.84E E E E E+32.65E+1 1.1E E+6.74E-1 6.4E E E E+32.76E E+1 684E+ 1.54E+ 1 4E E+24.75E+1 5 6E+3 2.8E E+1 899E E+1.47E E+2 526E E E E+1 1.7E E+ 1.94E E E E E E E E E E+2 6.1E E+3 2.8E E E+1 772E+ 2.88E E E E E E E E+3.35E E+1 6 7E E E E E+1 1.7E E E E E-5 1 o1e-71.68e-8 2,44E-9 1.2E E E E E+31 67E+1 2,37E+ 3.22E E-2 789E E E+15.65E+32.42E E+ 1.85E+ 1.66E-1 3 3E E+2 3.3E E E+1 1 9E E+ 6.32E E E+2 48E E+32.82E+1 14E E+ 14E+ 12E E E+1 5.6E E E E+2.67E+ 146E ,86E E E+32.87E E E E+32.87E E+1 1.6E E+1.93E. 1.84E E E+ 2 4E E+2 6.E+15 55E E+1 1.9E E+1 7.6E+ 2 E E E E+32.86E E E E+ 3 34E E+1 6 6E E E E+1 I 29E+1 1,.6E+13 55E E-7 675E E-5 1 1E E E E E E E E+31.54E+12.66E+4.32E-1 24E E E E E E+ 2.17E+2.2E-1 3.2E E+23.41E E E E E+ 7.55E-1 6.2E E E E E E+1 7.9E+ 167E+ 1 1E E+2 4.8E+1 5 8E E+11 59E E+ 2.93E+ 1.44E E E E+32 57E E+1 1.9E+14.45E+ 1.89E E E E+32.56E+1 1.8E E E+O 2 36E E+2 6 5E E E+1 1 8E E E+ 2.82E E E E E E E E+ 3 28E E+1 6.1E E+32 38E E+1 1 3E+1 I 1E+1 348E E E E-5 1.1E E- 2.84E E-1 469E-11 omnpare total HM Pu wlith HM # pebble 3.32,E *-M E E ,9E E E-1 29.a 2.58E E E E E _ M E E E E E E E E ,37E E ivaa, E E+1 594S9.985.E E E E E E E E E E , E E ,4E E E E E EO E E E , , , Y 6187, , e E-O a ' 178 6,?t E E E E E E E E ME E E SU 3 77E-O HM Is the total heavy metal ontent repoted by VSOP. <- firt ps through ore <- disharge - graphlte bells with trae hule (not Inluded In larulatlos he <- first pas Ihrough ore <- disharge <- 1 1 mix of graphile and fueld <- first pass through ore <- disharge - graphite balls with trae fissie <- first pass through ore - disharge <- graphite balls with trae fissile <-first pass through ore <- isharge <-graphite balls wth trae fssle Total plutonium In bath groups: bath group total Pu s d bumup step grams Pu239 % Pu239 # pebbles time/peb % % % % % % % % % % min 4 min 4 min 4 min 4 min 4 min 4 min 4 rmin 4 min 4 min gpujfs #FS 8 kg gpu239/fs #FS/6kg , o sa ~ <-; ll p~, ' FS = fuel sphre, hnormidaled Analyss of VSOP disharge data: volume disarded paking ration pebble volume # pebbles disarded 4.51E+5 6.1E E E-.3 #peb for peb for g.a w. 1tban-m 9 HM ghmpeb 6 kg HM 8 kg HM Pu E Pu E Pu E Pu E ,266 38