neutronic analysis of the critical myrrha core with serpent …536181/fulltext01.pdf · neutronic...

i

Neutronic Analysis of theMultipurpose Hybrid Research

Reactor for High-tech Applications(MYRRHA) with a Monte Carlo

Code SERPENT

Sara Asiyeh Changizi

School of Reactor Physics

KTH Royal Institute of Technology

Sweden

TRITA-FYS 2012:57ISSN 0280-316X

ISRN KTH/FYS/- -12:57–SE

Abstract

Safety of nuclear power plants and their highly radio-toxic waste are the mainconcerns in nuclear technology. Hence, new reactor designs with enhancedsafety properties and the ability to recycle the nuclear waste are vital for thefuture of nuclear power technology. The Multipurpose Hybrid Research Re-actor for High-tech Applications (MYRRHA) project designed at SCK·CENin Belgium is one of the promising designs in this area. This multipurposenuclear facility endeavors to fulfill some of the criteria of Gen-IV reactorssuch as sustainability, safety, and proliferation-resistance. MYRRHA is de-signed as a pool-type reactor core, which can be run either as critical reactoror sub-critical system, which is driven with a spallation source neutron of aproton accelerator. The key design features of MYRRHA are mixed oxidefuel and lead-bismuth eutectic as coolant and spallation target.

This thesis introduces briefly some basic information about Accelera-tor Driven System-ADS, MYRRHA in particular. The main componentsof an ADS will be presented and suitable options for sub-critical mode ofMYRRHA will be mentioned. The geometry and chosen options for the crit-ical mode of MYRRHA will be included in non-public appendix. This thesisfocuses mainly on analysis of critical mode of MYRRHA operation, hence,the critical parameters determine the critically safety of this system.

This thesis benchmarks and compares some of the basic parameters ofMYRRHA obtained by MCNP/MCNPX codes versus simulations performedwith a new Monte Carlo neutron transport code - SERPENT. The safetyfeedbacks, Doppler constant and effective delayed neutron fraction, will bepresented. Neutron flux in the fuel and power distribution over the corefor MYRRHA are calculated and compared to former outcomes. This thesispresents different accident scenarios related to MYRRHA core, to verify lowerreactivity feedback coefficient due to voiding and to ensure the safety ofMYRRHA core from a neutronic point of view. Finally, burn-up calculationshave been performed in order to investigate the spent fuel and its quality,and evaluate it with the result from earlier studies.

Sammanfattning

Sakerheten och radioaktivt avfall ar de huvudsakliga problem inom karnkraft-steknik. Darfor ar nya reaktorer med forbattrade sakerhetsegenskaper ochformagan att atervinna karnavfallet avgorande for karnkraftens framtid. Fors-kningsreaktorn for hogteknologiska tillampningar (Myrrha) vid SCK·CEN iBelgien ar en av de lovande designer inom detta omrade. Denna mangsidigakarntekniska anlaggning stravar efter att uppfylla vissa av kriterierna for gen-eration 4-reaktor sasom uthallighet, sakerhet och foljandet av icke-spridnings-fordraget. Myrrha ar en bassangreaktor som kan koras antingen kritisk ellerunderkritisk. I det underkritiska utforandet drivs reaktorn med en pro-tonaccelerator och ett spallationsmal. De viktigaste designkannetecknen forMyrrha ar MOX-bransle samt anvandandet av eutektisk bly-vismut-legeringsom kylmedel och spallationsmal.

Denna avhandling presenterar kortfattat information om acceleratordrivnasystem (ADS) i allmanhet, och Myrrha i synnerhet. De viktigaste komponen-terna i ett ADS kommer att presenteras och vissa komponenter for Myrrha idet underkritiska utforandet kommer att namnas. Geometrin och beskrivnin-gen for Myrrha i det kritiska utforandet kommer att inga i en icke-offentligbilaga. Denna avhandling fokuserar framst pa analys av Myrrha i det kri-tiska utforandet och darmed de kritiska parametrarna som ar mycket viktigaur sakerhetssynpunkt i systemet.

Avhandlingen jamfor nagra av de grundlaggande parametrar for Myrrhasom har erhallits genom MCNP/MCNPX med resultat fran Serpent, somar en ny Monte Carlo-neutrontransportskod. De sakerhetsparametrar somhar beraknats ar doppler-konstant och effektiv brakdel fordrojda neutroner.Neutronflodet i branslet och effektfordelningen over harden beraknas ochjamfors med de tidigare resultaten. Olika haveriscenarier relaterade tillvoidning av Myrrhaharden har tagits fram for att verifiera negativ reak-tivitetsaterkoppling och att garantera sakerheten ur en neutronisk synvinkel.Slutligen har en utbranningsberakning genomforts for att kunna undersokabranslets kvalitet och jamfora det med resultat fran tidigare studier.

vi Sammanfattning

Acknowledgements

Without cooperation and information from SCK·CEN, Belgian Nuclear Re-search Centre, this master thesis would have not been possible. Therefore,I will use this opportunity to acknowledge the support I have received fromSCK.CEN, specially the head of the expert group at SCK·CEN, Dr. GertVan den Eynde, that improved this thesis by his valuable comments. I wouldlike to express my gratitude to my supervisor, Prof. Waclaw Gudowski forall his advices and patience. I also express my appreciation for very nice andfriendly environmental at reactor physics department at KTH, especiallymy supportive friends Karl Samuelsson and Erdenechimeg Suvdantsetseg fortheir very helpful and wise advice. Finally, merci Behzad for all your sup-ports! I want to dedicate this thesis to my beloved mother.

Sara Asiyeh Changizi, June 14, 2012

viii Sammanfattning

x List of Abbreviations and Symbols

List of Abbreviations andSymbols

ADS Accelerator Driven SystemAm AmericiumBoC Beginning of CycleBREST Russian acronym for Pb-cooled fast reactorBR2 Belgian Reactor 2EoC End of CycleFA Fuel assemblyFoM Figure of MeritH HydrogenHe HeliumHYPER the Hybrid Power Extraction ReactorGen-IV Generation IV of nuclear power reactorsINVFS In Vessel Fuel StorageIPS In Pile Sections assembliesLBE Lead Bismuth EutecticLFR Lead-Cooled Fast ReactorLWR Light Water Reactorkeff kEFFective , effective neutron multiplication factorMA Minor ActinideMCNP Monte Carlo N-Particle transport codeMYRRHA Multi-purpose hybrid research reactor for high-tech applicationsMOX fuel Mixed OXide fuelNTE Neutron Transport EquationT91 FMS T91 Ferritic-Martensitic SteelPb LeadPEACER Proliferation-resistant, Environment-friendly, Accident-tolerant,

Continuable and Economical ReactorPu PlutoniumPVR Pressure Vessel ReactorSCRAM Safety Control Rod Axe ManSVBR Russian acronym for lead-bismuth fast reactorTRU Transuranic wasteU Uranium

Contents

Sammanfattning v

List of Abbreviations and Symbols ix

List of Figures xiii

List of Tables xv

1 Introduction 1

2 Introduction to MYRRHA, a Flexible Design 52.1 Accelerator Driven System and MYRRHA . . . . . . . . . . . 5

3 Tools and Methods 93.1 Neutron Transport Equation . . . . . . . . . . . . . . . . . . . 9

3.1.1 The Integral Form of the Transport Equation . . . . . 103.2 Monte Carlo Approach . . . . . . . . . . . . . . . . . . . . . . 113.3 SERPENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.4 Modeling in SERPENT . . . . . . . . . . . . . . . . . . . . . . 15

4 Results 194.1 The Criticality Calculation with SERPENT . . . . . . . . . . 19

4.1.1 Neutron Flux, Power Distribution and Cross Sections 204.1.2 Effective Neutron Multiplication Factor of Fuel Tem-

perature Changes and Doppler Constant . . . . . . . . 264.1.3 Effective Delayed Neutron Fraction . . . . . . . . . . . 31

4.2 Accident Condition Analysis . . . . . . . . . . . . . . . . . . . 324.2.1 Partial and Total Voiding of the Active Zone of the Core 324.2.2 Mixture of Steam and LBE Inside the Active Zone . . 464.2.3 Steam bubble saturation model . . . . . . . . . . . . . 484.2.4 Total Voiding of the Core . . . . . . . . . . . . . . . . 494.2.5 Fuel Relocation at the Top of the Active Zone . . . . . 50

xii CONTENTS

4.3 Burn-up Calculation . . . . . . . . . . . . . . . . . . . . . . . 534.4 Analysis of Figure of Merit for the SERPENT Model . . . . . 61

5 Comparison 655.1 The Criticality Calculation with SERPENT . . . . . . . . . . 655.2 Accidental Condition Analysis . . . . . . . . . . . . . . . . . . 685.3 Burn-up Calculation . . . . . . . . . . . . . . . . . . . . . . . 70

6 Conclusion 73

References 75

List of Figures

2.1 Spallation target - Pink particles are energetic protons, whichcreate neutrons (green particles) in spallation targets . . . . . 7

3.1 A scheme, which explains the different steps in analog MonteCarlo approach . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.1 Power distribution in the fissile zones of the core for fresh fuel,power peak factor 1.33 for model nr 1 Relative error ±0.0004 . 21

4.2 Power distribution in the fissile zones of the core for fresh,power peak factor 1.34 for model nr 2 Relative error ±0.0004 . 22

4.3 Power distribution in the fissile zones of the core for spent fuel,power peak factor 1.33 for model nr 1 Relative error ±0.0005 . 23

4.4 Power distribution in the fissile zones of the core for spent fuel,power peak factor 1.34 for model nr 2 Relative error ±0.0005 . 24

4.5 Neutron flux spectrum in the fuel . . . . . . . . . . . . . . . . 25

4.6 Cross sections and fission probability for nuclides in fresh fuel 25

4.7 Capture cross section spectrum of 238U and 240Pu . . . . . . . 26

4.8 Fuel temperature dependence of keff for MYRRHA, model nr 1 28

4.9 Fuel temperature dependence of keff for MYRRHA, model nr 2 29

4.10 This is how voiding is performed - Left picture shows cases 1,4 and 7 in which black area is voided about 50%, 75% and100% while the rest (blue area) is voided about 0%, 50% and75%, respectively. The picture in middle shows cases 2, 5 and8 in which the black area is voided about 50%, 75% and 100%and the rest (blue area) is voided about 0%, 50% and 75%,respectively. The picture at right shows cases 3, 6 and 9 inwhich all 3 zones (A, B and C) are voided about 50%, 75%and 100%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.11 3 different zones in one fuel assembly darker blue=zone A,purple =zone B, orange= zone C . . . . . . . . . . . . . . . . 34

4.12 Dark blue represents the voided LBE in one fuel assembly . . 34

xiv LIST OF FIGURES

4.13 The overview of the core one fuel assembly is voided, orangecolor represents voided LBE . . . . . . . . . . . . . . . . . . . 35

4.14 The overview of the core the six hottest fuel assemblies arevoided, orange color represents voided LBE . . . . . . . . . . . 35

4.15 keff of one voided fuel assembly, fresh fuel, model nr 1 . . . . . 374.16 keff of one voided fuel assembly, fresh fuel, model nr 2 . . . . . 384.17 keff of one voided fuel assembly, spent fuel, model nr 1 . . . . 394.18 keff of one voided fuel assembly, spent fuel, model nr 2 . . . . 404.19 keff of voiding the six fuel assemblies, fresh fuel, model nr 2 . . 424.20 keff of voiding the six fuel assemblies, spent fuel, model nr 2 . 434.21 keff of voiding all 68 fuel assemblies fresh fuel, model nr 1 . . . 444.22 keff of voiding all 68 fuel assemblies spent fuel, model nr 2 . . 454.23 Voiding of 16 fuel assemblies, model nr 2 . . . . . . . . . . . . 464.24 16 fuel assemblies are voided according to table 4.9, model nr 2 474.25 One bubble at top . . . . . . . . . . . . . . . . . . . . . . . . 484.26 3 bubbles at top . . . . . . . . . . . . . . . . . . . . . . . . . . 484.27 Void in all 6 IPS - vertical view . . . . . . . . . . . . . . . . . 484.28 horizontal view . . . . . . . . . . . . . . . . . . . . . . . . . . 484.29 He release into all assemblies, yellow represents Helium . . . . 504.30 Scenario number 1 model nr 1 . . . . . . . . . . . . . . . . . . 514.31 Scenario number 1 model nr 1 . . . . . . . . . . . . . . . . . . 514.32 Scenario number 2 model nr 1 . . . . . . . . . . . . . . . . . . 514.33 Scenario number 3 model nr 1 . . . . . . . . . . . . . . . . . . 514.34 Mass evolution of fuel . . . . . . . . . . . . . . . . . . . . . . . 544.35 Uranium-235 and Uranium-238 mass evolution . . . . . . . . . 554.36 Americium-241 and Americium-242m mass evolution . . . . . 564.37 Plutonium mass evolution . . . . . . . . . . . . . . . . . . . . 574.38 keff evolution in time . . . . . . . . . . . . . . . . . . . . . . . 584.39 Standard deviation σ and keff versus wall-clock time . . . . . . 614.40 FOM and keff versus wall-clock time, 120000 neutron sources

and 1000 cycles . . . . . . . . . . . . . . . . . . . . . . . . . . 624.41 FOM and keff versus wall-clock time, 40000 neutron sources

and 5000 cycles . . . . . . . . . . . . . . . . . . . . . . . . . . 624.42 FOM for small statistical variations . . . . . . . . . . . . . . . 63

5.1 Power distribution in the fissile zones of the core for fresh fuel,power peak factor 1.34, model nr 2 . . . . . . . . . . . . . . . 66

5.2 Power distribution in the fissile zones of the core [3] for freshfuel, power peak factor 1.34 . . . . . . . . . . . . . . . . . . . 67

List of Tables

4.1 keff for different fuel temperatures, model nr 1 . . . . . . . . . 274.2 keff for different fuel temperatures, model nr 2 . . . . . . . . . 304.3 βeff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.4 Different scenarios for simulating void in the fuel assembly [3] 344.5 keff of one voided fuel assembly, model nr 1 . . . . . . . . . . 364.6 keff of one voided fuel assembly, model nr 2 . . . . . . . . . . . 364.7 keff of voiding the six hottest fuel assemblies for model nr 2 . . 414.8 keff of voiding all 68 fuel assemblies, model nr 1 & 2 . . . . . 414.9 LBE densities for different steam fractions in the core . . . . . 474.10 keff for different steam fractions, model nr 2 . . . . . . . . . . 474.11 bubble in the core - model nr 2 . . . . . . . . . . . . . . . . . 494.12 keff during He release into all assemblies - Model nr 2 . . . . 494.13 keff during fuel relocation at the top of the active zone with

no regard to molten cladding - model nr 1 . . . . . . . . . . . 524.14 Composition of fresh fuel . . . . . . . . . . . . . . . . . . . . . 534.15 Composition evolution of the fuel in g/cm3 as a function of

time (days) - model nr 1 . . . . . . . . . . . . . . . . . . . . . 594.16 Composition evolution of the fuel in g/cm3 as a function of

time (days) - model nr 2 . . . . . . . . . . . . . . . . . . . . . 604.17 Composition evolution of the fuel in g/cm3 as a function of

time (days) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.1 Comparison of keff in two different codes . . . . . . . . . . . . 685.2 keff of voiding one fuel assembly, model nr 1 . . . . . . . . . . 695.3 keff of voiding one fuel assembly, model nr 2 . . . . . . . . . . 695.4 keff of voiding the six hottest fuel assemblies - model nr 2 . . . 705.5 keff in case of fuel relocation to the top of the active zone . . . 705.6 Composition evolution of the fuel in g/cm3 as a function of

time (days) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

xvi LIST OF TABLES

Chapter 1

Introduction

Although, conventional light-water reactors produce significant amount ofpower with very low CO2-emission at costs stable over time [16] in a conve-nient manner, they have a few major drawbacks. Along energy production,these conventional light-water reactors produce highly radio-toxic nuclearwaste. Even though, only a few percent of the spent fuel is the transuranicelements (TRU) such as plutonium and americium isotopes, they are themost problematic part of the present nuclear waste. They have half-lives upto millions of years and are highly radio-toxic. Hence, the cost and risk ofstoring these types of waste in a repository for a long time will not be neg-ligible [1]. Furthermore, these light water reactors, which utilizing mainlythermal neutrons, extract only a few percent of the energy in the fuel. Spentfuel still contains a lot of its original energy [1]. Increasing the number ofthermal reactors will only drain the low-cost natural uranium reserves infuture; therefore, it is vital to look at a more efficient and sustainable option.

Fast reactors with closed fuel cycle are the future of nuclear power technol-ogy. They may extract more energy from natural uranium by factor of sixty1,besides, they provide a substantial improvement of nuclear waste manage-ment. This is the direct result of more efficient atomic fission. Fast reactorsuse fast neutron spectrum contrasting the conventional light-water reactorsthat are depended on thermalized neutrons. Hence, an appropriate coolantwith good heat-transfer property, which does not thermalize the neutrons,is required. The option coolants for these types of reactors are liquid-metalssuch lead, sodium and lead-bismuth.

Heavy metal coolant such as Lead-Bismuth Eutectic (LBE) was the sub-ject of many researches as coolant for fast reactors since early 1950s, however,

1International Atomic Energy Agency (IAEA), Support for Innovative Fast Reac-tor Technology Development and Deployment, http://www.iaea.org/NuclearPower/FR/,08/06/2012

2 Introduction

the other liquid-metal coolant, namely sodium, was chosen. Because, sodiumhas the capability for coping with core having higher power density, which isresulted in lower doubling time for producing plutonium [14]. At the sametime, LBE was the coolant for a number of submarine reactors in the formerSoviet Union, which resulted in many researches about the coolant technol-ogy and material. Additionally, about 20 fast neutron reactors have producedelectricity commercially, which give 400 reactor-years of operating experienceto the end of 2010 2. These reactors mainly have been used as breeder andlately as high-level waste burners.

At the moment, these types of reactors are the subject of many studies foraccelerator-driven system. They are planned for high-level radiation wastetransmutation. Briefly, an ADS is designed to be an inherent safe nuclearreactor, which can consume its own waste in an efficient and safe manner.ADS has a sub-critical core i.e. keff < 1 and requires an external neutronsource to remain stable sub-critical. A proton accelerator and a spallationtarget that is generally heavy liquid-metal provide these neutrons in ADS.The energetic protons hit the spallation target and generate neutrons in thesub-critical core.

The interest in LBE coolant has been resumed for civilian fast reactorssince 1990. The lead-cooled BREST and LBE-cooled SVBR are the mostknown projects, which motivated several other projects in the field of ADS,and in particular lead cooling. Favorable features of lead are many suchas lower reactivity feedback coefficient in case of voiding, better shieldingagainst energetic neutrons and gamma rays and chemically inertly againstwater [7]. However, significantly lower melting temperature of LBE comparedto pure Pb (396 K vs 600 K [2]) has led to development of ADS with LBEas coolant instead of pure lead. Moreover, high boiling temperature of LBE(1943K±50K [7]) reduces the chances of coolant boiling. Also the possibilityof passive decay heat removal with natural convection in lead makes thesekinds of reactors more attractive. The major drawback of Pb and LBEcoolants is the corrosion issues [21]. The other apparent drawbacks of suchcoolants are the complicated service, repair, and small margin to freezing forthese types of reactors [14].

There have been several programs in the field of developing ADS tech-nology that perform experiments and researches in this area, such as MUSEprogram at the Cadarache Research Center of the CEA in France. Sev-eral experiments have been completed in this program to demonstrate theviability of neutronic measurements and core description of a sub-critical re-

2World Nuclear Association, Fast Neutron Reactors, http://www.world-nuclear.org/info/inf98.html, 08/06/2012

3

actor run by an external source in MASURCA facility. MUSE program wasdedicated to conduct tests and provide methods for sub-critical reactivitymeasurement [24]. The GUINEVERE project is another project, which isperformed in order to complete the results from MUSE program. After somemodifications in a facility called VEnus at Mol-site in Belgian and connec-tion to a deuteron accelerator, an experiment is started. The objective of thiszero-power facility is to address some of main issues of operational processesin ADS, reactivity monitoring, and sub-criticality characterization [5].

There is also another zero-power facility, called Yalina at Nuclear Re-search in Sosny. Building a full scale ADS, which can produce adequateenergy to transmute nuclear waste is very costly and has not done before.This has been also the motivation behind Yalina facility, to build a low costzero-power, sub-critical assembly, which can provide knowledge about thestatic and dynamic neutronics properties of ADS. It strives to be a small testfacility for the future ADS in full scale [11].

Studies about developing both ADS and LFR, at the Korea Atomic En-ergy Research Institute and Seoul National University in the Republic ofKorea, are also pursuing. The objective of this development is to investi-gate safe transmutation technology along with proliferation-resistance. Theyhave designed an ADS, called HYPER, in which LBE is both coolant andspallation target. Its purpose is to transmute transuranic waste and fissionproducts such as 129I and 99Tc [7]. PEACER is another LBE-cooled reactorthat has been developed at Seoul National University since 1998.

In Japan also these type of studies are under the progress. They have de-veloped a 800MW ADS that is able to transmutate 250 kg of minor actinidesand long-lived fission products yearly at the Japan Atomic Energy ResearchInstitute [7].

MYRRHA project at SCK·CEN in Belgium follows the same path in de-veloping ADS technology. It is one of the examples of many studies in thefield of lead-bismuth eutectic technology. MYRRHA project at SCK·CEN ismultipurpose nuclear facility, which endeavor to demonstrate ADS technol-ogy and waste transmutation. It will also address structural and materialstudies for other type of reactors such as fusion reactors. This pool-typereactor uses MOX-fuel and lead-bismuth eutectic, which is both coolant andspallation target. MYRRHA is a flexible design, which can operate in criticalmode as well.

This thesis introduces briefly some primary information about ADS, MYR-RHA in particular. The main components of ADS will be presented and theselected options for sub-critical MYRRHA will be mentioned. The criticalmode of MYRRHA will be presented in non-public appendix. To enhance theunderstanding of the code SERPENT, one chapter is dedicated to neutron

4 Introduction

transport equation, Monte Carlo method and SERPENT. The descriptionof the SERPENT model of MYRRHA in critical mode is presented in non-public appendix. The thesis presents results for critical mode of MYRRHAbecause critically safety will determine licensing process and will put signifi-cant constraints on MYRRHA design parameters [12].

This thesis benchmarks and compares some of the basic parameters ofMYRRHA obtained by MCNP/MCNPX codes versus simulations performedwith a new Monte Carlo neutron transport code - SERPENT. Neutronicsafety feedback parameters, namely Doppler constant and effective delayedneutron fraction, will be presented. Neutron flux spectrum in the fuel andpower distribution over the core for MYRRHA are calculated and comparedto the former outcomes. Different accident scenarios related to MYRRHAcore are simulated to verify lower reactivity feedback coefficient due to void-ing and to ensure the safety of MYRRHA core in a neutronics point of view.Finally, burn-up calculations have been performed in order to investigate thespent fuel and its quality, and evaluate it with the result from earlier studies.

Chapter 2

Introduction to MYRRHA, aFlexible Design

In this chapter, we will look more closely to Accelerator-Driven Systems(ADS) technology, MYRRHA in particular, along with MYRRHA’s objec-tives. The main components of ADS will be presented and suitable optionsfor sub-critical mode of MYRRHA will be included. The geometry and amore detailed design data of critical mode of MYRRHA will be included inthe appendix A in the confidential format. In the end, the reason why thecritical mode of MYRRHA is chosen for this thesis will be explained.

2.1 Accelerator Driven System and

MYRRHA

ADS is receiving more attention in nuclear power research and developmentsolutions at the moment. There are some important factors that make ADSespecially remarkable. This concept makes it possible to design a core in away that is not adequate otherwise. Introducing minor actinides (MA), suchas Americium to the reactor fuel may challenge safety neutronic parameters,for instance reduction of Doppler constant, increase of coolant temperaturecoefficient and reduction of effective delayed neutron fraction in case of Am[25]. However, the ability to adjust sub-critically level in sub-critical sys-tems provides larger margins in these kinds of systems. Therefore, ADS isable to tolerate more presence of minor actinides than other systems. Thismakes them the most attractive option to recycle the nuclear waste. To makeADS technology credible compared to other options, it should decrease theradio-toxicity of the nuclear waste at least by a factor of 100 [6]. ADS candedicatedly burn both their as well as MA produced by LWRs.

6 Introduction to MYRRHA, a Flexible Design

The ability of altering sub-critically level in ADS converts them to a safeand reliable design. This design makes it sure not to have keff equal or morethan one even in case of structure failure, core meltdown, flooding etc. Thedelicate balance, which is required in a critical core, is not necessary in ADS.

SCK·CEN has been working on a new reactor design, in order to re-place the old BR2 reactor with a reactor, which can develop innovative fuelsand materials for the future Gen-IV fast reactor concepts. This is a flexibledesign, which can operate in both sub-critical and critical modes. In sub-critical mode, the proton accelerator provides high energetic protons, whichcreates neutrons in the spallation target. These neutrons feed the core so thereactor can attain a stable sub-critical mode. The coolant is lead-bismutheutectic, and fuel is MOX in both modes. The objective of MYRRHA isto be a tentative model for future experiment and development of lead fastreactor technology. It will demonstrate ADS technology and facilitate theexperimentation of innovative MA fuel. It will produce isotopes for nuclearmedicine and industry as well. MYRRHA will also assist material and com-ponents testing for other types of reactors [23]. This reactor will bring tooperation at full power around 2023 1.

Chosen fuel for MYRRHA is MOX, which contains Pu from reprocessingof spent fuel from LWR. It is enriched to about %33 plutonium. Pu in spentfuel is recycled as PuO2 and then is combined with depleted UO2 [22]. Thisspent fuel can contain also other transuranic waste. In this way, not onlythe extracting energy from the fuel is more efficient, also the other toxicfissionable elements can be recycled instead of going to a final repository.

One of the main components of ADS core is accelerator. It determines theoverall sub-critically level in the system. It is the accelerator that providesenergetic protons, which creates neutrons in the spallation target. MYRRHAhas a proton accelerator of 600 MeV in terms of energy and 4 mA in termsof intensity. The reliability and availability of ADS are depended on the reli-ability and availability of accelerators, and this is determined by the numberof tolerable beam trips. The two types of accelerators that are selected forMYRRHA are the isochronous cyclotron and the Continuous Wave linac,which LINAC is the primary reference and cyclotron is the back-up optionto LINAC [23].

Spallation target (figure 2.1) is the next important component of ADS.This is the interface between the accelerator and the sub-critical reactor.There are two configurations for the target concept: a window target and awindowless target configuration. In the first configuration, there is a win-

1SCK·CEN, MYRRHA: Multi-purpose hybrid research reactor for high-tech applica-tions, http://myrrha.sckcen.be/en/MYRRHA, 120508

2.1 Accelerator Driven System and MYRRHA 7

Figure 2.1: Spallation target - Pink particles are energetic protons,which create neutrons (green particles) in spallation targets

dow, which physically separates the beam and the target unit. The materials,which are exposed directly to the energetic beam, undergo severe radiationdamage. In the second configuration, there is no window between the beamand target; hence, the beam impinges the target without anything interven-ing. The absence of the window results in other challenges such as plasmaformation at the target surface [23]. In MYRRHA, the first configuration, awindow target, is preferred above other[8].

Since 1998, MYRRHA design has been improved and in this thesis, wewill work with the latest version called FASTEF, which is the critical modeof MYRRHA. Since there are several publications about this design and itsspecifics, extensive work has performed for this mode of MYRRHA. Thereare also former results performed in MCNP for critical mode, which enablesthe comparison of the results. However, while MYRRHA is designed to runa lot of experiments in a sub-critical mode of operation, the important safetyparameters are related to criticality safety [12]. Additionally, simulatingexternal source in SERPENT 1.1.13 is still very much under development[19]. Thus, to be assured of reliability of the results, simulations have beenperformed in critical source mode. The geometry and more detailed designdata of critical mode of MYRRHA will be on hand in the non-public appendixA with a brief summery of MYRRHA parameters.

8 Introduction to MYRRHA, a Flexible Design

Chapter 3

Tools and Methods

In this chapter, for better understating of SERPENT, which is the main codefor this thesis, Monte Carlo method is briefly presented. To understand thismethod, knowledge about neutron transport equation is necessary. Therefore,the NTE and its solution are presented in this chapter. Furthermore, a briefdescription of SERPENT and modeling in this code are presented.

3.1 Neutron Transport Equation

Neutron defines as a classic object and can be completely defined by itslocation r, its direction of travel Ω, and its energy E at time t.Due to sufficiently low neutron density, one can assume an educated guessof no neutron-neutron collision. Population of neutrons describes as neutronangular density N(r,Ω, E, t), which defines the density of neutrons in volumedr about r, traveling in direction dΩ about Ω, with energy dE about E, andtime dt about t. Collisions are point-like and instantaneous.Angular flux Ψ is the product of the angular density and the speed v. Whenthis is integrated over all directions, it will give total or scalar flux.

Ψ(r,Ω, E, t) = N(r,Ω, E, t)v (3.1)

φ =

∫4π

Ψ(r,Ω, E, t)dΩ (3.2)

The scalar flux is proportional to the reaction rate per unit volume. Theconstant Σ, which relates scalar flux to reaction rate is called macroscopiccross section. By solving neutron transport equation, one can find scalarflux which can be used for calculating measurable quantities i.e. reactionrate (equation 3.3).

10 Tools and Methods

R = Σφ (3.3)

The balance between gain and loss of neutrons represents neutron trans-port equation. The change of neutron density per time step in a volume isformulated as follows:

dN

dt= (Gain)− (Loss) (3.4)

Hence, neutron transport equation in terms of angular flux will be as follow:

1

v

∂Ψ(r, E,Ω, t)

∂t+ Ω · 5Ψ(r, E,Ω, t) + Σt(r, E, t)Ψ(r, E,Ω, t) =∫

4π

dΩ′∫ ∞0

dE′Σs(r, E

′ 7→ E,Ω′ 7→ Ω, t)Ψ(r, E

′,Ω

′, t) + S(r, E,Ω, t)

(3.5)

Where r is position vector in Cartesian coordinate, v neutron velocity vector,Ω unit vector in direction of motion, E energy, and t time. Thus, the neutronis at position r moving in direction Ω with energy E. Ψ(r, E,Ω, t) is angularneutron flux, Σt(r, E, t) total macroscopic cross section, Σs(r, E

′ 7→ E, Ω′ 7→

Ω, t)dE′dΩ

′scattering in cross section of a neutron from an incident energy

E′

and direction Ω′

to the energy E and direction Ω in dE′

and dΩ′

andfinally S(r, E,Ω, t) is the source term.

First term represents the change rate in number of neutrons, second termleakage rate, the movement of neutrons into or out of the volume, third termthe detailed collision rate, forth term neutrons which scatter and enter thevolume from all direction and energy (Ω

′, E

′) and finally the fifth term is the

source. Thus, production rate subtracting destruction rate will represent thechange rate of neutrons in the volume of interest.

3.1.1 The Integral Form of the Transport Equation

By defining β as the optical thickness [10] and integrating the angular fluxalong its characteristic for a given S, the integral form of transport equationis obtained as below [13]

β =

∫ s

0

Σt(r− s′Ω, E)ds

′(3.6)

Ψ(r, E,Ω, t) =

∫e−β

∫∫Σs(r− sΩ,Ω

′, E 7→ E

′)Ψ(r − sΩ,Ω′

, E′, t− s/v)

+

∫ s

0

dse−βS(r − sΩ,Ω, E, t− s/v)

(3.7)

3.2 Monte Carlo Approach 11

Boltzmann transport equation can be written in operator notation [10]as

Ψ = KΨ + S′

(3.8)

where K is the integral operator (equation 3.9) and S′

is the attenuatedsource (equation 3.10).

K =

∫ ∞0

e−β∫∫

Σs(r− sΩ,Ω′, E

′, t− s

v)dΩ

′dE

′ds (3.9)

S′=

∫ ∞0

e−βS(r− sΩ,Ω, E, t− s

v)ds (3.10)

A solution to the equation 3.8 is defining series as below [10].

Ψ0 = S′,Ψ1 = KΨ0, . . .Ψn+1 = KΨn (3.11)

Whenever these series converge, a solution 3.12, which is called von Neu-mann series solution, for the equation 3.8 is obtained.

Ψ =inf∑n=0

Ψn (3.12)

Ψ0 is angular flux from source when it does not go through any collisions,Ψ1 has gone through one collision and etc. at the requested point.

Monte Carlo method provides an estimation to the von Neumann se-ries solution (see equation 3.12) to the integral formulation of the transportequation (see equation 3.8) [10].

3.2 Monte Carlo Approach

The aim of this section is to give some primary information about how MonteCarlo method is applied to neutron particle transport. This method is basedon the use of sequence of random numbers to obtain sample values for theproblem. Monte Carlo method imitates the particle flight path and differentinteractions between the neutrons and materials. From this outcome variousvariables can be calculated. As it mentioned in the previous section, MonteCarlo method provides an estimation to the solution of NTE.

One should first define a geometry, which neutron will be investigatedin along with the source term. By Monte Carlo method even complicatedgeometry have solution. The description of the geometry includes the size,


shapes and locations of objects and also their material. The description ofthe geometry is one of the important parts of the method.

When the geometry is defined, the next step will be the execution ofneutron flight path through out the material. The simulation of this path iscalled random walk. The Monte Carlo random walk creates a set of neutroncollision points with information about the consequence of these collisions i.e.neutron energy and direction after the collisions. However, this informationabout neutron motion is not measurable quantities. The Monte Carlo methodresults are generally scores, and by these scores one can calculate measurablequantity such as reaction rates.

For better understanding Monte Carlo approach, a scheme of single neu-tron history for analog mode is introduced (see scheme 3.1). This schemeshows the different steps of decision making in analog1 Monte Carlo method.Analog here means that the chain is terminated at capture site. To generatethe ”history” of a neutron, the first step is to initiate a random start positionand velocity. These initial inputs are assumed from initial condition. Thenby knowing material properties from a library, for instance JEFF-3.1.1 nu-clear data, length of free flight is determined. Either neutron is crossing oneof materials boundary or collides with other particles. In the scheme, thislevel of decision making is called for possible interactions and event.

Event occurs when neutrons cross the boundaries and enter in a new ma-terial. If neutron crosses material boundary, new flight path from propertiesof new material will be obtained and the algorithm will be executed all overagain. In the other hand, an interaction can be one of these collision typesaccording to known branching ratios: scattering, fission or absorption. Ifthe particle is absorbed the chain is terminated. In the case of scattering,previous velocity and scattering cross sections from the library determine thenew velocity of neutrons after scattering. As the scheme shows, these neu-trons go back to the algorithm again with new velocities. In fission collision,the number and velocities of new neutrons are determined from fission crosssection library. These new neutrons will also go through the algorithm untilall neutrons are absorbed and chain is terminated.

1The other method is implicit treatment of capture reactions, in which the number ofneutrons that represents the simulated history is associated with a statistical weight. Inthis method, the weight is reduced according to the capture probability, instead of to becaptured in site as in analog method [20].

3.2 Monte Carlo Approach 13

Initialvelocityandpositionforneutrons

Lengthoffreepath,whichisdeterminedfromlibrary(materialproperties)

Scattering Fission Capture

NewVelocitydeterminedfromscatteringcrosssection

Numberandvelocityofnewneutronsdeterminedfromfissioncrosssection

ChainTerminated

Crossingboundaries

Collisiontypes

Possibleinteractionsorevent

Velocityandpositionforneutrons

Figure 3.1: A scheme, which explains the different steps in analogMonte Carlo approach


3.3 SERPENT

SERPENT is a three-dimensional continuous-energy Monte Carlo reactorphysics burn-up calculation code. The significant of SERPENT is in two-dimensional lattice physics calculation, however, the universe-based geometrydescription makes the modeling in three dimensions possible as well. Theadvantage of SERPENT over other conventional tools is the faster run-time.This is achieved by a more efficient tracking in the geometry routine and theuse of same energy grid for all cross sections. This enables SERPENT tohandle complicated objects and surfaces easier and reduces the running time[18].

The transport simulation is executed in SERPENT more efficient thanother conventional methods because of the use of different techniques. Anemployment of same energy grid for all cross sections [17] is the most im-portant technique. In other methods, each nuclide is associated with its ownenergy grid point, thus, every time that the energy index is needed, the codehas to repeat an iterative grid search, which slows down the calculation. Thecross section at energy point E is calculated by linear interpolation below[18]:

f(E) =E − Ej−1Ej − Ej−1

(3.13)

σ(E) = f(E)(σj − σj−1) + σj−1 (3.14)

where Ej−1 and Ej are listed energy grid points with their correspondinglisted σ in the libraries. Every time a cross section needs to be calculatedan energy point E, which is between Ej−1 and Ej, required to be found.This requires an iterative search algorithm, which in term of computing, isexpensive.

There are several occasions that this iterative search algorithm must beperformed, for example every time that the cross sections are required forsampling interactions, scoring reaction rates or sampling the distance to thenext collision site. In burn-up calculation for instance which has a largenumber of nuclides, the running time will increase because the calculationof macroscopic cross sections need to be done by summing over all nuclidescomponent. For MCNP5 for example, the difference between running timefor fresh fuel calculation and high burn-up is 5 times [17].

Additionally, in SERPENT another geometry routine is used namely,Woodcock delta-tracking [18]. In this technique instead of calculating thedistance to the next surface and comparing it to free path length in the ma-terial, which is the criteria of tracking in conventional methods, the particle

3.4 Modeling in SERPENT 15

continues its path over material boundaries without stopping. Hence, thecomputing is less expensive and the run time is reduced. To understand thevalue of delta tracking in terms of the running time, one of the simulationsis performed without delta tracking 2. The running time from 4 hours is in-creased to 9 hours and 30 minutes, a significant increase without any changesin the result data.

3.4 Modeling in SERPENT

To describe complicated geometry in SERPENT, universe-based geometrysimilar to MCNP is used [19]. In SERPENT, geometry is divided into sep-arated levels that are layered inside each other. Each universe level definesseparately with its boundaries and structures. In other word, a complex ge-ometry divides into smaller parts then level by level, these parts get togetherand shape the whole geometry.

Cell, which is the basic block, defines the regional space. It can be filledwith different materials or lattice. Cells determine the boundaries. Surfaces,on the other hand, define different types of geometry constructions. In SER-PENT, one should identify the surface by a number so it can be referredin cells to define the boundaries. There are various types of surfaces, forinstance sphere, plane, cube, hexagonal and etc. Along with specifying thetype of surface, surface parameters such as coordinates, radii and etc. shouldbe included in the surface definition.

The universe-based geometry starts first with constructing pins with theirgaps and cladding. Several different kinds of pins such as fuel pin, dummies,etc. can be constructed in their own universe. Next step is constructing theassemblies with fuel pins arranged in a lattice, also in their universe. Thereare several types of lattice cards such as square, hexagonal3, cylindrical andetc. Each lattice is an universe, which should be fixed into a cell. Theseassemblies then can be arranged in another lattice to shape the whole core.In the end, material can be defined by their nuclides components.

Summarizing geometry modeling in SERPENT, one should define: pins,lattices, surfaces, cells and materials. Moreover, defining the file path todetermine the continuous-energy cross sections in the transport simulation.

To measure the critically in the core, one defines effective multiplicationfactor keff, which is the ratio of the number of fission neutrons from onegeneration to the next generation. This can be also critically safety mea-surement in assessments [15]. keff below one indicates sub-critically, over one

2This technique can easily set to OFF in SERPENT.3X-type hexagonal lattice has been used in this thesis.


super-critically and equal to one critical core. This means, for example, thechain reaction continues at a constant rate when keff is one or the numberof fission neutrons increases while keff is over one. By connecting keff andreactivity one can have a better understanding about the safety of the core.The formula below shows the relation between them.

ρ =keff − 1

keff(3.15)

In SERPENT, the k-eigenvalue criticality source method is used as defaultmode. This means that the simulations run in cycles with fixed numberof source neutrons per cycle. Since the number of generated source pointsis different from this fixed value, the source size will change accordingly.The fission reaction distributed from previous cycle forms the next sourcedistribution [19]. One should define the number of source neutrons per cycleand the number of active cycles run. The total number of active neutronhistories determines the statistical accuracy of the results. Furthermore, ifthe system is far from critically (keff = 1), one can guess an initial value forkeff. Otherwise, by default, the value of keff is set to unity. One should noticethat the initial source-points are chosen in the fissile cells randomly by theprogram and source-point is not required from the user [19]. In SERPENT4,one can also simulate an external source, which is still under progress [19].

To evaluate user-defined reaction rates over energy and space in SER-PENT, a detector should be defined. One can conclude that detector eval-uates this integration 3.16 over space and energy [19]. It uses the collisionestimate of neutron flux to evaluate the reaction rates:

R = 1/V

∫V

∫ Ei

Ei+1

f(r, E)φ(r, E)d3rdE (3.16)

where f(r, E) is the detector response function, which determines thetype of calculation. Hence, in detector definition one should specify the typeof reaction, and also the energy and spatial domains of this integral. Forinstance, to calculate neutron flux integrated over space and energy, detectorparameters are as follow: f is equal to one, the energy domain sets to a desiredgrid, and the space defines as coordinates or inside a preferred material5.

SERPENT is able also to perform burn-up calculation as a stand-alonesimulation code. SERPENT code solves the set of Bateman equations. These

4SERPENT 1.1.135There are various types of defining a detector in SERPENT depends on what the user

wants to calculate.

3.4 Modeling in SERPENT 17

depletion equations describe the change of material composition due to ra-dioactive decay and reactions caused by neutrons. For burn-up calculation,one needs also radioactive decay data and neutron-induced and spontaneousfission product yield along with the continuous-energy cross sections. Tostart a burn-up calculation in SERPENT, one should first identify the de-pleted materials 6 and defines the radiation history. There are three differentoptions7 in SERPENT to solve the Bateman equations. The user can choosethe the most adequate option to make the burn-up calculations more accuratebut more time-consuming, or the simulations quicker.

A full detailed model of MYRRHA in SERPENT is presented in the Ap-pendix A. In this appendix, the full geometry of the fuel pin, fuel assemblies,fuel components are described. The temperature, density and other designsignificances are included. However, there are two models presented in thisthesis. The first model is the simplified one and is based on MYRRHA dataavailable in open literature. A good deal of work has done on this model andmany results are obtained. The second model is the more detailed one andbased on propriety MYRRHA design data. All assumptions and details aremade according to MYRRHA design [3]. This model is the most identicalone to MYRRHA. More details about these two models are presented in theappendix A.

6 “This version of SERPENT 1.1.13 handles burn-up in cylindrical or spherical materialregions.” [19]

7“ First method: Transmutation Trajectory Analysis (TTA), based on the analyticalsolution of linearized transmutation chains. Second method: An advanced matrix ex-ponential solution based on the Chebyshev Rational Approximation Method (CRAM).Third option: The variation TTA method, in which cyclic transmutation chains are han-dled by inducing small variations in the coefficients instead of solving the extended TTAequations.” [19]

Chapter 4

Results

In this chapter, all results from various simulations are included in three sepa-rated sections: The criticality calculation with SERPENT, accident conditionanalysis and burn-up calculation performed by SERPENT. First a short de-scription of the problem is presented followed by the results and discussionsection. In the end an analysis of figure of the merit is carried out.

4.1 The Criticality Calculation with

SERPENT

In this section, some primary neutronic parameters necessary for the safety ofnormal operation such as keff, Doppler constant and effective delayed neutronfraction are presented. The neutron flux spectrum in the fuel and powerdistribution over the core are obtained. Same simulations are performed forboth model nr 1 and nr 2 1. Some of these simulations are performed forboth models or partially for only one of them. To ensure the reliability of theoutcome and safety during the operation, all the calculations are executedfor fresh fuel at the beginning of cycle (BoC) and also spent fuel at the endof 5th cycle, which has different composition. The composition of the freshand spent fuel are included in Appendix A [3].

1Check out appendix A for more detail information about model nr 1 and 2 and theirdesign specific.

20 Results

4.1.1 Neutron Flux, Power Distribution and CrossSections

In this section, neutron flux spectrum in the fuel and power maps over thecore for both fresh and spent fuel are presented. Additionally, the mostimportant cross sections, namely fission and capture cross sections and thefission probabilities of the most important nuclides, are included. Here tocalculate the energy-integrated flux in the fuel, the writer defines a grid of1500 equal lethargy-width bins with an energy boundary of [10−5, 102]MeVi.e. the energy boundary is divided to 1500 equal lethargy-width bins2.

Results and discussion

Figures 4.1 and 4.2 show the power distribution over the core for fresh fuel inboth models 1 and 2. Additionally, the power distribution for spent fuel forboth models are shown in figures 4.3 and 4.4. Total linear power in the core is1.606 MW/cm that grants the total power of 96.35 MW (1.606MW

cm· 60cm =

96.35MW where 60 cm is the length of the active part)3. The neutron fluxspectrum in the fuel is plotted (see figure 4.5). The normalized total neutronflux in the material fuel is 2.27e+15 neutrons/cm2s. The figure 4.6 showsthe spectrum-averaged cross sections and fission probabilities for all nuclidespresents in the fresh fuel.

2See chapter 3, for more information about detectors and how they can be defined.3In SERPENT, total values represents per length.

4.1 The Criticality Calculation with SERPENT 21

Figure 4.1: Power distribution in the fissile zones of the core for freshfuel, power peak factor 1.33 for model nr 1

Relative error ±0.0004

22 Results

Figure 4.2: Power distribution in the fissile zones of the core for fresh,power peak factor 1.34 for model nr 2



Figure 4.3: Power distribution in the fissile zones of the core for spentfuel, power peak factor 1.33 for model nr 1


24 Results

Figure 4.4: Power distribution in the fissile zones of the core for spentfuel, power peak factor 1.34 for model nr 2



10−5

10−4

10−3

10−2

10−1

100

101

102

0

2

4

6

8

10

12

14

16

18x 10

15

E[MeV]

Neutron flux spectrum[cm−2

s−1

] in fuel

Figure 4.5: Neutron flux spectrum in the fuel

Pu238 Pu239 Pu240 Pu241 Pu242 U238 U2350

1

2

3

Pu238 Pu239 Pu240 Pu241 Pu242 U238 U2350

0.2

0.4

0.6

0.8

1

Fission XS (b)

Capture XS (b)

Fission Probability

Figure 4.6: Cross sections and fission probability for nuclides in freshfuel

26 Results

10−6

10−4

10−2

100

102

10−3

10−2

10−1

100

101

102

103

104

105

Incident neutron energy MeV

cap

ture

cro

ss s

ection

, b

arn

σ

c of U238

σc of Pu240

Figure 4.7: Capture cross section spectrum of 238U and 240Pu

4.1.2 Effective Neutron Multiplication Factor of FuelTemperature Changes and Doppler Constant

While all parameters have kept constant like coolant and structure tempera-ture, the fuel temperature is altered from 300 K to 1500 K. In this way, onecan investigate the sensitivity of the keff to the fuel temperature. By thesedata, Doppler constant can be calculated as well. Doppler broadening ofcapture resonance of fertile 238U and 240Pu results in more neutron capturesover a wider energy spectrum, consequently, keff will decrease. In other word,during the slowing down of neutrons, they are more prone to be captured in238U and 240Pu (see figure 4.7). Thus, Doppler constant is one of the mainsafety neutronic parameters. Although, Doppler feedback is more effectivefor resonances during the slowing down [25] and this coefficient is smaller infast reactors, Doppler constant is crucial to ensure the inherent safety.

One can calculate Doppler coefficient by this formula [25]:


αD ≡dρ

dT=

1

k2dk

dT(4.1)

and Doppler constant KD [25] by:

αD =KD

T(4.2)

k(T ) = k(0)−KDln(T ) (4.3)

By fitting a line according equation 4.3, an approximation of Dopplerconstant can be obtained.

Results and Discussion

To obtain the best result for Doppler constant, a logarithmic line is fittedto the data for different temperatures versus keff (figures 4.8 and 4.9) forboth fresh and spent fuel. As results demonstrate the Doppler constants arecomparable with typical reactivity insertion and they can have significant rolein core stability (table 4.1 and 4.2). Doppler constant increases for spent fuel.The reduction of fertile 238U and 240Pu besides the presence of 241Am are thereasons of this increase. However, one should notice the relatively large error.Generally, the Doppler effect is still significant and negative.

Table 4.1: keff for different fuel temperatures, model nr 1

Fuel temperature keff Fresh keff Spent

300K 1.05619±0.00019 1.00861±0.00019600K 1.05349±0.00019 1.00655±0.00019900K 1.05200±0.00018 1.00564±0.000211200K 1.05146±0.00018 1.00485±0.000191500K 1.05041±0.00013 1.00425±0.00014Doppler constant [pcm] -333±57 -266±58

28 Results

400 800 1,200 1,6001

1.02

1.04

1.06

temperature T

keff

Fresh fuel

Spent fuel

Line fit fresh fuel

Line fit spent fuel

Figure 4.8: Fuel temperature dependence of keff for MYRRHA, modelnr 1


400 800 1,200 1,600

1

1.02

1.04

1.06

temperature T in K

keff

Fresh fuel

Spent fuel

Line fit fresh fuel

Line fit spent fuel

Figure 4.9: Fuel temperature dependence of keff for MYRRHA, modelnr 2

30 Results

Table 4.2: keff for different fuel temperatures, model nr 2

Fuel temperature keff Fresh keff Spent

300K 1.05005±0.00015 1.00331±0.00016600K 1.04777±0.00016 1.00144±0.00017900K 1.04648±0.00015 1.00029±0.000161200K 1.04566±0.00016 0.99946±0.000161500K 1.04484± 0.00014 0.99873±0.00014Doppler constant [pcm] -306±47 -282±50


4.1.3 Effective Delayed Neutron Fraction

The fraction between all delayed neutrons, which induces fission, and totalnumber of fission-inducing neutrons is effective delayed neutron βeff. Delayedneutrons are produced by fission products. In MOX fuel, due to higher con-centration of Pu, βeff is lower, however, it is essential to obtain this value.Since larger βeff will results in a larger neutron generation time Λ (see equa-tion 4.4), which increases the response time. Furthermore, the core is moreresistant to power fluctuation and small perturbation.

Point kinetic model [4]:

dp(t)

dt=ρ(t)− β(t)

Λ(t)p(t) +

∑k

λkck(t) + s(t) (4.4)

where p(t) is power, ρ(t) reactivity, β(t) the delayed neutron fraction,Λ(t) neutron generation time, λk decay constant for the i’th delayed neutronprecursor group, ck(t) the decay precursor concentration and finally s(t) issource term. SERPENT generates an output for effective delayed neutronfraction. This value can be found in the output’s results.


As table 4.3 illustrates the βeff reduces in the end of cycle for both models.The presence of Americium from conversion of 238U and lower amount of 238Uresult in a reduction of βeff. Americium has high capture cross section forthermal neutron spectrum (around 500 keV) and delayed neutron has thislow energy (the average energy of the delayed neutrons is 300-700 keV) [26].Since in both models the fuel compositions are same βeff remains unchanged.

Table 4.3: βeff

βeff [pcm] at BOC βeff [pcm] at EOC

Model nr 1 329±1 324±1Model nr 2 328±1 324±1

32 Results

4.2 Accident Condition Analysis

In this section, some of severe accident scenarios are simulated in SERPENTand keff and ∆keff

4 for each scenario are presented. Different scenarios oftypical occurrence of void in the core such fuel pin rapture, releasing fissiongases like helium into the core, blow down of steam from steam generatorrapture, and complete voiding scenario will be simulated properly. Finallythe relocation of melted fuel to top of the core in three distinctive caseswill be examined. Some simulations are based on previously investigatedscenarios while the rest are defined by the writer. This will be an assessmentof MYRRHA core during some accident scenarios.

4.2.1 Partial and Total Voiding of the Active Zone ofthe Core

Coolant void worth indicates the reactivity changes in the core while there isvoid in the system. To ensure the inherent safety of the core, this parametershould always remain negative during the normal and accident scenarios. Ina LBE-cooled reactor, coolant serves both as a coolant and neutron reflector.Voiding the core results in less neutron moderation and faster neutrons whilethe core leakage will increase due to less density and neutron reflection.

While having lead in the coolant reduces the chance of coolant-boiling,there is still a possibility of coolant boiling such as fuel assembly blockageand sub-channel boiling [8]. There are also other scenarios that void canintroduce to the core, for instance rapture of steam generator and mixingsteam into the core or release of fission gas products due to high pressureat in the end of the cycle. This possibility should be taken seriously. Here,the partial loss of coolant in fuel assemblies is simulated. Voiding of one ormore fuel assemblies are performed, according to MCNP assumptions (seefigure 4.10 and table 4.4). One fuel assembly is divided into 3 different zones,namely A, B and C. The first 10 cm is zone A, 10-30 cm is zone B and therest is C (see figure 4.11). These simulations are performed for both freshand spent fuel in one fuel assembly (see figure 4.12) and the 6 hottest fuelassemblies (see figure 4.14) in the core. Finally, all 68 FA’s are voided in thesame manner.

4Difference between actual keff and nominal state.

4.2 Accident Condition Analysis 33

Figure 4.10: This is how voiding is performed - Left picture showscases 1, 4 and 7 in which black area is voided about 50%, 75% and 100%while the rest (blue area) is voided about 0%, 50% and 75%, respectively.The picture in middle shows cases 2, 5 and 8 in which the black areais voided about 50%, 75% and 100% and the rest (blue area) is voidedabout 0%, 50% and 75%, respectively. The picture at right shows cases3, 6 and 9 in which all 3 zones (A, B and C) are voided about 50%, 75%

and 100%.


As the figure 4.15 shows, the results of voiding one fuel assembly in model nr 1is not statistically significant. Hence, a more detailed investigation is neededto check out the feedback. In voiding one fuel assembly in model nr 2, moreneutron sources have been employed to acquire more detailed information offeedback. With doubling the number of neutron sources in model nr 2, apositive tendency is rather apparent for spent fuel (see figure 4.18) and stillunclear for fresh fuel. All these deviations are inside the confidence intervalof keff during normal operation (green lines). For easier assessment, all tableshave extra columns for ∆keff, which are the differences from nominal state,

Voiding the six hottest fuel assemblies is only performed for model nr2. There are some apparent positive tendencies toward positive reactivityfeedback in this scenario, especially, the case of complete voiding of all six

34 Results

Figure 4.11: 3 different zonesin one fuel assembly darker blue=zone A,

purple =zone B, orange= zone CFigure 4.12: Dark blue representsthe voided LBE in one fuel assembly

Table 4.4: Different scenarios for simulating void in the fuel assembly[3]

case 1 Zone A: 50 % LBE, Zone B and C: 100 % LBEcase 2 Zone A and B: 50 % LBE, Zone C: 100 % LBEcase 3 Zone A, B and C: 50 % LBEcase 4 Zone A: 25 % LBE, Zone B and C: 50 % LBEcase 5 Zone A and B: 25 % LBE, Zone C: 50 % LBEcase 6 Zone A, B and C: 25 % LBEcase 7 Zone A: 0 % LBE, Zone B and C: 25 % LBEcase 8 Zone A and B: 0 % LBE, Zone C: 25 % LBEcase 9 Zone A, B and C: 0 % LBE


Figure 4.13: The overview of the coreone fuel assembly is voided, orange

color represents voided LBE

Figure 4.14: The overview of the corethe six hottest fuel assemblies

are voided, orange color represents voided LBE

FAs, namely case number 9 (see figure4.19 and 4.20). Coolant void worthincreases for spent fuel because of the reduction of the ratio between fissileand fertile nuclides. One should notice that the result of case number 9 forspent fuel is completely out of confidence interval of keff during the normaloperation.

In case of voiding all fuel assemblies, the negative tendency is completelyevident, for both fresh and spent fuel. Both models nr 1 and 2 confirm thesame tendency.

36 Results

Table 4.5: keff of one voided fuel assembly, model nr 1

Fresh fuel ∆keff pcm Spent fuel ∆keff pcm

case 1 1.05021±0.00021 -19 1.00432±0.00019 7case 2 1.05016±0.00022 -25 1.00409±0.00019 -16case 3 1.05065±0.00019 24 1.00409±0.00019 -16case 4 1.05013±0.00019 -28 1.00411±0.00019 -14case 5 1.05041±0.00019 0 1.00417±0.00019 -8case 6 1.05003±0.00020 -38 1.00447±0.00019 22case 7 1.05009±0.00019 -32 1.00408±0.00018 -17case 8 1.05041±0.00019 0 1.00414±0.00019 -11case 9 1.05038±0.00015 -3 1.00423±0.00019 -2

Normal operation 1.05041±0.00013 1.00418±0.00023

Table 4.6: keff of one voided fuel assembly, model nr 2


case 1 1.04514±0.00014 30 0.998705±0.00014 -3case 2 1.04481±0.00014 -3 0.998652±0.00015 -11case 3 1.04485±0.00014 1 0.998838±0.00014 11case 4 1.04493±0.00014 9 0.998790±0.00014 6case 5 1.04510±0.00014 26 0.998849±0.00014 12case 6 1.04511±0.00013 27 0.998832±0.00014 10case 7 1.04514±0.00014 30 0.998790±0.00014 6case 8 1.04490±0.00014 6 0.998822±0.00013 9case 9 1.04495±0.00014 11 0.99054±0.00015 32



case1 case2 case3 case4 case5 case6 case7 case8 case9

1.0496

1.05

1.0504

1.0508

1.0512

keff

Figure 4.15: keff of one voided

fuel assembly, fresh fuel, model nr 1

38 Results


1.0444

1.0448

1.0452

1.0456

1.046

keff


fuel assembly, fresh fuel, model nr 2



1.0036

1.004

1.0044

1.0048

1.0052

keff


fuel assembly, spent fuel, model nr 1

40 Results


0.9982

0.9986

0.999

0.9994

0.9998

keff


fuel assembly, spent fuel, model nr 2


Table 4.7: keff of voiding the six hottest fuel assemblies for model nr 2


case 1 1.04490±0.00015 6 0.998628±0.00016 -10case 2 1.04500±0.00014 16 0.998679±0.00015 -5case 3 1.04536±0.00016 52 0.999015±0.00017 28case 4 1.04487±0.00015 3 0.998885±0.00016 15case 5 1.04506±0.00016 22 0.999378±0.00016 64case 6 1.04509±0.00016 25 0.999195±0.00016 46case 7 1.04508±0.00016 24 0.999027±0.00016 30case 8 1.04526±0.00015 42 0.999202±0.00016 47case 9 1.04532±0.00015 48 0.999593±0.00016 86


Table 4.8: keff of voiding all 68 fuel assemblies, model nr 1 & 2


case 1 1.04854±0.00019 -187 0.996428±0.00021 -230case 2 1.04728±0.00020 -313 0.996059±0.00022 -267case 3 1.04319±0.00020 -722 0.993353±0.00022 -538case 4 1.04357±0.00020 -684 0.992133±0.00021 -660case 5 1.04319±0.00020 -722 0.992303±0.00021 -643case 6 1.04158±0.00020 -883 0.990319±0.00021 -841case 7 1.04071±0.00020 -970 0.989283±0.00022 -945case 8 1.03969±0.00019 -1072 0.988555±0.00022 -1017case 9 1.03777±0.00020 -1264 0.987147±0.00020 -1158


42 Results


1.0444

1.0448

1.0452

1.0456

1.046

keff

Figure 4.19: keff of voiding the

six fuel assemblies, fresh fuel,model nr 2


0 case1 case2 case3 case4 case5 case6 case7 case8 case9 00.998

0.9985

0.999

0.9995

1

1.0005

keff

Figure 4.20: keff of voiding the

six fuel assemblies, spent fuel,model nr 2

44 Results


1.038

1.042

1.046

1.05

keff

Figure 4.21: keff of voiding

all 68 fuel assembliesfresh fuel, model nr 1



0.986

0.99

0.994

0.998

keff

Figure 4.22: keff of voiding

all 68 fuel assembliesspent fuel, model nr 2

46 Results

Figure 4.23: Voiding of 16 fuel assemblies, model nr 2

4.2.2 Mixture of Steam and LBE Inside the ActiveZone

Another accident scenario can be the mixing of secondary coolant with LBEand occurrence of bubbles inside FA. By applying simple gas law and staticpressure calculation, one can estimate how much the volume of a bubble willincrease from moving from the bottom to the top of the core. The bubble’svolume increases roughly 1% for every 60 cm moving upward to the surface.From this we can assume that the volumetric fraction of void will increases1% and LBE density decreases accordingly. Since, this volume-change is notsignificant to provide a significant change into the result, hence the volumeincrease of bubbles in the LBE are overstated by 1% for every 20 cm mov-ing upward instead of 60 cm. Furthermore, as the previous section showsvoid worth effect is worst for spent fuel case, thus, this simulation is onlyperformed for spent fuel and for the hottest fuel assemblies. Additionally,to discover how much the positive feedback can increase, more fuel assemblyhave been voided. In this case, we have voided 16 fuel assemblies partiallyand totally (see figure4.23). Fuel assembly is divided into 3 zones similar tothe previous section: the first 10 cm is zone A, from 10 cm to 20 cm is zoneB and the rest is zone C. Table 4.9 shows the LBE densities in the 3 zones.


As figure 4.24 shows, by voiding more fuel assemblies the positive feedbackdoes not grow over the confidence interval. Additionally, the worst scenarioi.e. voiding 100% of all 16 FAs will results in a negative feedback.


Table 4.9: LBE densities for different steam fractions in the core

5%[ gcm3 ] 10%[ g

cm3 ] 15% [ gcm3 ] 57% [ g

cm3 ]zone A 9.773 9.312 8.850 4.425zone B 9.635 9.081 8.665 4.333zone C 9.345 8.804 8.434 4.217

Table 4.10: keff for different steam fractions, model nr 2

keff - Spent fuel ∆keff pcm

5% steam in the mixture 0.998701±0.00014 010% steam in the mixture 0.998701±0.00014 2515% steam in the mixture 0.999069±0.00015 3957% steam in the mixture 0.999046±0.00016 32100% steam in the mixture 0.998544±0.00015 -19

5% 10% 15% 57% 100%0.998

0.9982

0.9984

0.9986

0.9988

0.999

0.9992

0.9994

0.9996

0.9998

keff

Figure 4.24: 16 fuel assemblies are voided according to table 4.9, modelnr 2

48 Results

4.2.3 Steam bubble saturation model

A few numbers of bubbles are placed at top of the core. At first, one singlebubble is placed at the top (see figure 4.25) and in the second case 3 bubblesare set (see figure 4.26). To attain a more apparent representation of voidinga reactor like MYRRHA, all 6 IPS in the active zone up to the top of thecore are voided i.e. LBE is replaced by void completely (see figure 4.27 and4.28).

Figure 4.25: One bubble at top Figure 4.26: 3 bubbles at top

Figure 4.27: Void in all 6 IPS - vertical view Figure 4.28: horizontal view


Table 4.11 shows the results which are not statically significant for two firstcases. For the medium-sized MYRRHA core, such bubble sizes will not besignificant enough to change keff. However, voiding all 6 IPS rods results in


Table 4.11: Bubble in the core - model nr 2

keff ∆keff pcm

No bubble 1.04484±0.00014 -Bubble (10 cm radii) at the top 1.04506±0.00014 22

3 Bubbles (10 cm radii) at the top 1.04485±0.00014 1Voided 6 IPS rods 1.03380±0.00020 -1104

a considerable negative feedback due to large leakage of neutrons (check out∆keff in table 4.11).

4.2.4 Total Voiding of the Core

Here, we assume total release of helium into the assemblies. In this scenariothe channels between assemblies are filled with helium (see figure 4.29).


In this case, the large amount of neutron leakage due to voiding gives re-sults in a significant negative feedback (see table 4.12). This simulation isperformed for only model nr 2.

Table 4.12: keff during He release into all assemblies - Model nr 2

keff ∆keff pcm

1.00431±0.00089 -4053

50 Results

Figure 4.29: He release into all assemblies, yellow represents Helium

4.2.5 Fuel Relocation at the Top of the Active Zone

One of the most severe accidents is that the fuel melts down. Thus, in thissection the reactivity alteration due to the melted fuel is investigated. Here,we will look into a few possible scenarios. We assume that the melted fuelwill float over the coolant and will stop beneath the exit cone of the fuelassembly [3]. The cladding is not considered in these simulations.

Scenario number one: In this scenario melted fuel will float over onlythe six hottest fuel assemblies (figures 4.30 and 4.31), the other assembliesare intact. By using the initial fuel mass which is 1252kg, one can estimatethe molten fuel height in the fuel assembly. Volume of one fuel assembly is1743cm3, and the area of one hexagonal assembly is 81.56cm2, hence, theheight of the fuel will be 21.4cm [3].

Scenario number two: In this one, we assume all fuel assemblies are dam-aged and melted fuel is floating over all fuel assemblies in the core (figure4.32).

Scenario number three: In this scenario, fuel is divided equally betweenall assemblies inside the core and accumulated over the top, in other words,a layer of molten fuel is floating at top of the core just below the grid. Theheight of the fuel will be 9.8cm in this scenario (figure4.33).


There is a significant negative feedback for the first case, however, thischanges for the second scenario and a significant positive feedback is ob-


Figure 4.30: Scenario number 1model nr 1




52 Results

Table 4.13: keff during fuel relocation at the top of the active zone

with no regard to molten cladding - model nr 1

keff ∆keff pcm

Scenario 1 1.03889±0.00028 -1152Scenario 2 1.28003±0.00023 2296Scenario 3 1.15229±0.00026 1018

Normal operation 1.05041±0.00013

served. Finally for the last scenario, the positive feedback is less than thesecond scenario; still, it is considerably large.

4.3 Burn-up Calculation 53

4.3 Burn-up Calculation

In this section, the burn-up of MYRRHA’s fuel after 5 cycles will be investi-gated. Fresh fuel has been placed into the core and burn-up of the fuel hasbeen over-viewed. Especially the focus has been on producing and burningminor actinides such as Am and Cm. A complete value of keff after eachcycle is computed and included in this section. It is important to recognizethe evolution of the fuel to finds out about the eventual different behavior ofthe fuel.

The burn-up calculation is performed with SERPENT 1.1.13 and crosssection library JEFF-3.1.1. For both models a burn-up calculation have beenexecuted. The fresh fuel composition is as follow [3]:

Isotope Initial concentration [g/cm3]O-16 1.245U-235 0.045U-238 6.197Pu-238 0.072Pu-239 1.746Pu-240 0.829Pu-241 0.187Pu-242 0.236Overall density: 10.557 g/cm3

Table 4.14: Composition of fresh fuel

A cycle is 90 days of operation and 30 days of inspection and re-shufflingand furthermore a 90 days of maintenance. Thus in 5 cycle fuel there will be450 days of irradiation and 210 days of decay.

Results

Evolution of fissile materials and the most important minor actinides areplotted in figure 4.34.

For better understanding of evolution of fuel nuclides, Uranium, Ameri-cium and Plutonium mass evolution are plotted separately (see figure 4.35,4.36, and 4.37).

Also evolution of keff is plotted (see figure 4.38). The average reactivityloss per cycle is about 0.015.

54 Results

0 100 200 300 400 500 600 70010

−4

10−3

10−2

10−1

100

101

102

103

Days

Mass [kg]

0

U235

U238

Pu238

Pu239

Pu240

Pu241

Pu242

Am241

Am242m

Cm242

Cm244

Figure 4.34: Mass evolution of fuel


0 200 400 600 8004

5

6

U235 [kg]

time (days) − model nr 2

0 200 400 600 800700

720

740

U238 [kg]

0 200 400 600 8004

5

6

U235 [kg]


0 200 400 600 800700

720

740

U238 [kg]

Figure 4.35: Uranium-235 and Uranium-238 mass evolution

56 Results

0 200 400 600 8000

0.01

0.02

Am

24

1 [

kg]


0 200 400 600 8000

1

2

Am

242

m [kg

]

0 200 400 600 8000

0.01

0.02

Am

24

1 [

kg]


0 200 400 600 8000

1

2

Am

242

m [kg

]

Figure 4.36: Americium-241 and Americium-242m mass evolution


0 100 200 300 400 500 600 7007

7.5

8

8.5

9

Days

Mass [kg]

0 100 200 300 400 500 600 700180

185

190

195

200

205

210

Days

Mass [kg]

0 100 200 300 400 500 600 70097.9

98

98.1

98.2

98.3

98.4

Days

Mass [kg]

0 100 200 300 400 500 600 70018

19

20

21

22

23

Days

Mass [kg]

0 100 200 300 400 500 600 70026.5

27

27.5

28

Days

Mass [kg]

Pu238 − model nr 1

P238 − model nr 2









Figure 4.37: Plutonium mass evolution

58 Results

0 100 200 300 400 500 600 7000.96

0.97

0.98

0.99

1

1.01

1.02

1.03

1.04

1.05

1.06

time [days]

keff

evolution

model nr 1

model nr2

Figure 4.38: keff evolution in time


Days U235 U238 Pu238 Pu239 Pu240 Pu241 Pu2420 0.0450 6.1970 0.0720 1.7460 0.8290 0.1870 0.236045 0.0441 6.1805 0.0708 1.7258 0.8289 0.1844 0.235190 0.0433 6.1639 0.0697 1.7067 0.8288 0.1819 0.2343120 0.0433 6.1639 0.0696 1.7078 0.8288 0.1812 0.2343165 0.0424 6.1472 0.0685 1.6878 0.8286 0.1787 0.2334210 0.0415 6.1303 0.0674 1.6690 0.8284 0.1763 0.2325240 0.0415 6.1303 0.0673 1.6701 0.8284 0.1756 0.2325285 0.0407 6.1133 0.0662 1.6504 0.8281 0.1734 0.2316330 0.0399 6.0961 0.0651 1.6319 0.8277 0.1711 0.2307375 0.0399 6.0961 0.0651 1.6330 0.8277 0.1701 0.2307420 0.0399 6.0961 0.0650 1.6330 0.8277 0.1691 0.2307465 0.0391 6.0788 0.0640 1.6135 0.8273 0.1670 0.2298510 0.0382 6.0613 0.0629 1.5953 0.8269 0.1649 0.2289540 0.0382 6.0613 0.0629 1.5964 0.8269 0.1643 0.2289585 0.0374 6.0436 0.0618 1.5773 0.8263 0.1623 0.2279630 0.0366 6.0259 0.0608 1.5594 0.8258 0.1604 0.2270660 0.0366 6.0259 0.0608 1.5605 0.8258 0.1598 0.2270

Abs. diff. -0.0084 -0.1711 -0.0112 -0.1855 -0.0037 -0.0272 -0.0090Rel. diff. -18.67% -2.76% -15.55% -10.62% -0.39% -14.54% -3.81%

Table 4.15: Composition evolution of the fuel in g/cm3 as a functionof time (days) - model nr 1

60 Results

Days U235 U238 Pu238 Pu239 Pu240 Pu241 Pu2420 0.0450 6.1970 0.0720 1.7460 0.8290 0.1870 0.236045 0.0441 6.1807 0.0708 1.7256 0.8289 0.1844 0.235190 0.0433 6.1643 0.0697 1.7064 0.8288 0.1818 0.2343120 0.0433 6.1643 0.0696 1.7075 0.8288 0.1811 0.2343165 0.0424 6.1477 0.0685 1.6874 0.8286 0.1787 0.2334210 0.0415 6.1309 0.0674 1.6684 0.8284 0.1763 0.2325240 0.0415 6.1309 0.0673 1.6695 0.8284 0.1756 0.2325285 0.0407 6.1141 0.0662 1.6497 0.8281 0.1732 0.2316330 0.0399 6.0970 0.0651 1.6310 0.8278 0.1710 0.2307375 0.0399 6.0970 0.0651 1.6321 0.8278 0.1700 0.2307420 0.0399 6.0970 0.0650 1.6321 0.8278 0.1690 0.2307465 0.0390 6.0799 0.0639 1.6125 0.8274 0.1668 0.2298510 0.0382 6.0625 0.0629 1.5941 0.8270 0.1648 0.2289540 0.0382 6.0625 0.0629 1.5952 0.8270 0.1641 0.2289585 0.0374 6.0451 0.0618 1.5759 0.8265 0.1621 0.2280630 0.0366 6.0275 0.0608 1.5579 0.8259 0.1602 0.2270660 0.0366 6.0275 0.0608 1.5590 0.8259 0.1595 0.2270

Abs. diff. -0.0084 -0.1695 -0.0112 -0.187 -0.0031 -0.0275 -0.009Rel. diff. -18.67% -2.69% -15.56% -10.71% -0.37% -14.70% -3.81%

Table 4.16: Composition evolution of the fuel in g/cm3 as a functionof time (days) - model nr 2

Code U235 U238 Pu238 Pu239 Pu240 Pu241 Pu242SERPENT - model nr 1 0.037 6.026 0.061 1.561 0.826 0.160 0.227SERPENT - model nr 2 0.037 6.028 0.061 1.559 0.826 0.160 0.227

Table 4.17: Composition evolution of the fuel in g/cm3 as a functionof time (days)

4.4 Analysis of Figure of Merit for the SERPENT Model 61

4.4 Analysis of Figure of Merit for the

SERPENT Model

The figure of merit has been defined in order to optimized the SERPENTsimulation time and to avoid excessively long calculation. Figure below 4.39shows the reduction of standard deviation in wall-clock time5.

0 500 1000 15000

1

2

3

4x 10

−3

time (min)

σ

0 500 1000 15001.04

1.045

1.05

1.055

time (min)

keff

Figure 4.39: Standard deviation σ and keff versus wall-clock time

The figure of merit defines as FOM = 1/(R2T ) is an practical statisticto check out the convergence of keff calculation, where T is the runtime toproduce N histories and R is the relative error σ

keff. As the curve demon-

strates FOM is generally constant because R2 is proportional to 1/N and Tto N. The value of FOM indicates the efficiency of the method, the higherFOM the better [9]. Furthermore, it estimates the time needed for desiredstatistical precision, which means T ' 1

R2FOM.

FOM must be constant then the results from Monte Carlo method countas consistent. However, for small statistical variations, it does not have tobe constant (see figure 4.42).

The figure 4.41 shows clearly that 300 minutes is more than enough forobtaining a reliable answer in reasonable time.

5CPU USAGE, ratio of CPU time to wall-clock time, is 0.99676.

62 Results

0 1 2 3 4 5 6 7 8 9 10

x 104

0

500

1000

1500

time(sec)

FO

M

0 1 2 3 4 5 6 7 8 9 10

x 104

1.045

1.05

1.055

time(sec)

keff

Figure 4.40: FOM and keff versus wall-clock time, 120000 neutron

sources and 1000 cycles

0 1 2 3 4 5 6 7 8 9

x 104

0

500

1000

1500

time(sec)

FOM

0 1 2 3 4 5 6 7 8 9

x 104

1.04

1.05

1.06

1.07

time(sec)

keff

Figure 4.41: FOM and keff versus wall-clock time, 40000 neutron

sources and 5000 cycles

4.4 Analysis of Figure of Merit for the SERPENT Model 63

4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5

x 104

850

900

950

1000

1050

1100

time(sec)

FO

M

Figure 4.42: FOM for small statistical variations

64 Results

Chapter 5

Comparison

In this chapter, a comparison between the outcome of this thesis and formerresults will be performed. It will clarify if they are in good agreement withprevious calculations or there are great contrasts among the results.

5.1 The Criticality Calculation with

SERPENT

Neutron Flux, Power Distribution and Cross Sections

In SERPENT, the total neutron flux in the fuel is 2, 27.1015neutrons/(cm2)which is in very good agreement with former results [3]. In the other hand,the power generation calculated by MCNP codes is equal to 95.77 MW andin SERPENT, this total power is measured to be equal 96.35 MW. Also,the power peaking factor of 1.34 is confirmed by model nr 2. The powerdistributions in SERPENT for both models are consistent with former powerdistributions (see figures 5.1 and 5.2). Comparing these results have shownthat the found values are in good agreement.

66 Comparison

Figure 5.1: Power distribution in the fissile zones of the core for freshfuel, power peak factor 1.34, model nr 2


Figure 5.2: Power distribution in the fissile zones of the core [3] forfresh fuel, power peak factor 1.34

68 Comparison

Effective Neutron Multiplication Factor

keffs of normal operation in SERPENT are 228 and 780 pcm less than keffaccounted in MCNP [3] (see table 5.1), however, this difference can be due tothe assumption made for modeling the vessel containing the core. There isapproximately 550 pcm difference in keffs of having two different models forvessels. This could be the main reason of difference between keffs in these twocodes. To make this difference as little as possible more detailed informationabout how MCNP code is written required. However, SERPENT confirmsthe super-critically of the system with a keff ≈1.05 in both models nr 1 and2.

5.2 Accidental Condition Analysis

Partial and Total Voiding of the Active Zone of theCore

To simulate voiding effect in MYRRHA, same assumptions as MCNP codeare made. As the tables 5.2 and 5.3 show, voiding only one fuel assemblywill not give a reliable answer to how feedback will change. Both models nr1 and 2 confirm this. This is also the conclusion of MCNP studies as well.Additionally, simulation of voiding one fuel assembly, loaded with spent fuelconfirms this once again.

Simulating void in the six hottest fuel assemblies in SERPENT code showsrather clear tendency about the void worth effect. As table 5.4 presents, theslightly positive feedback for all cases are apparent, however, in MCNP, thisfeedback does not show any clear tendency, except for the case nr 9. Simu-lation in SERPENT confirms also this and case nr 9 has the most positivefeedback among all cases. In case number 9 for spent fuel, the positive feed-back is more obvious and statistically significant.

Table 5.1: Comparison of keff in two different codes

keff SERPENT keff MCNP ∆keff pcm

Model nr 1 1.05041±0.00013 1.05269±0.00006 -228Model nr 2 1.04484±0.00014 1.05269±0.00006 -785

5.2 Accidental Condition Analysis 69

Table 5.2: keff of voiding one fuel assembly, model nr 1

∆keff Fresh/Spent SERPENT, pcm ∆keff Fresh MCNP, pcm

case 1 -19/7 0case 2 -25/-16 1case 3 24/-16 7case 4 -28/-14 -3case 5 0/-8 -1case 6 -38/22 -5case 7 -32/-17 8case 8 0/-11 -7case 9 -3/-2 7


Table 5.3: keff of voiding one fuel assembly, model nr 2

∆keff Fresh/Spent SERPENT, pcm ∆keff Fresh MCNP, pcm

case 1 30/-3 0case 2 -3/-11 1case 3 1/11 7case 4 9/6 -3case 5 26/12 -4case 6 27/10 -5case 7 30/6 8case 8 6/9 -6case 9 11/32 7


70 Comparison

Table 5.4: keff of voiding the six hottest fuel assemblies - model nr 2

Fresh/Spent fuel SERPENT,pcm Fresh fuel MCNP,pcmcase 1 6/-10 -1case 2 16/-5 -7case 3 52/28 13case 4 3/15 -3case 5 22/64 -4case 6 25/46 1case 7 24/30 3case 8 42/47 -6case 9 48/86 26


Table 5.5: keff in case of fuel relocation to the top of the active zone

keff ∆keff pcm keff MCNP ∆keff pcm

Scenario 1 1.03889±0.00028 -1152 1.03708±0.00012 -1561Scenario 2 1.28003±0.00023 2260 1.27905±0.00013 2263


Fuel Relocation at the Top of the Active Zone

This simulation is performed only for model nr 1 with no regard to themelted clad. As table 5.5 shows there is about 400 pcm difference in theresults in scenario nr 1, however, for scenario nr 2 ∆keffs are in agreement.Generally, scenario nr 1 for both codes predict a significant reduction ofcritically and keff reduces approximately to 1.04 from 1.05. However, thetotal fuel relocation to the top of the core increases the keff dramatically tothe value of 1.28. In these two scenarios, as mentioned before, there is noregard to melted clad. Hence, a comparison will not give a clear and reliableanswer here.

5.3 Burn-up Calculation

The results in burn-up calculations are consistent with results from ALEPH[3], however, the most difference is in the amount of Pu239 and U238. InSERPENT simulation, the breeding is slightly lower, hence, keff reducesmore. After every cycle keff reduces about 0.015, however, in ALEPH this


value is about 0.010. Hence, keff in the end of the cycle will be less in SER-PENT than former calculation.

Code U235 U238 Pu238 Pu239 Pu240 Pu241 Pu242ALEPH[3] 0.038 5.930 0.066 1.630 0.832 0.174 0.227

SERPENT - model nr 1 0.037 6.026 0.061 1.561 0.826 0.160 0.227SERPENT - model nr 2 0.037 6.028 0.061 1.559 0.826 0.160 0.227

Table 5.6: Composition evolution of the fuel in g/cm3 as a function oftime (days)

72 Comparison

Chapter 6

Conclusion

The pool-type hybrid reactor, MYRRHA with MOX-fuel, has been the sub-ject of this thesis. The aim of this thesis has been to determine some mainsafety neutronic parameters for critical mode of MYRRHA using a MonteCarlo computer code, namely SERPENT, and benchmark those results withstudies performed by MCNP Monte Carlo code. Also, burn-up calculationfor fresh fuel has been performed and compared to previous burn-up calcu-lation in ALEPH-code. Additionally some accident scenarios for MYRRHAare simulated with SERPENT. Some simulations are based on previouslyinvestigated scenarios while the rest are defined by the writer.

In this thesis, calculations have been performed for fresh fuel load as wellas for burn-up core. In this way, one can also ensure the safety of the corein the end of the fuel cycle, when the composition of fuel is different andsome main feedbacks may be worsened, such as void worth. However, thecomparison has been performed only for fresh fuel due to the lack of data forcomparison in the case spent fuel.

Analysis revealed that Doppler effect and effective delayed neutron frac-tion ensure a well determined negative feedback mechanisms as expected foran inherently safe reactor and in good agreement with result from MCNP.The Doppler constant is comparable with typical reactivity insertion andit can have a significant role in core stability. The calculation of Dopplerconstant for spent fuel shows a certain degradation. However, statisticaluncertainties for calculation of Doppler constant for burn-up fuel are stillsignificant and this problem needs furtherer, more detailed studies.

Power distribution over the core of MYRRHA confirmed former powerdistribution calculated by MCNP. keff during normal operation in SERPENTis lower, however, this difference can mainly be due to the assumption madefor the vessel containing the core. Thus, by reviewing the assumption madein MCNP, for instance regarding the vessel, this difference can be reduced.

74 Conclusion

To simulate voiding effect in MYRRHA, same assumptions as MCNP codeare made. The variation of keff supports the former calculations in MCNP inthe way that the feedback of voiding LBE in small areas in a medium-sizedcore will not give clear statistical results. However, the tendency towards anincreased reactivity during voiding of the six hottest fuel assemblies is moreapparent than former calculations. This effect gets even larger for spent fuelas expected. To see how much this positive feedback can increase, othersimulations have been performed such as voiding of higher number of hotfuel assemblies, loaded with spent fuel. However, this does not increase thepositive feedback significantly and the feedback remains in the confidenceinterval of keff during normal operation. This scenario exhibits also thenegative feedback of voiding more FAs. Complete voiding scenario showssignificant negative feedback and ensures the safety in a neutronic point ofview for such accidents. All these scenarios have shown clearly that leakageof neutrons from the system in such accident scenarios is the dominant factorand keff will decrease accordingly.

In the end, burn-up calculations have been performed for both models.The results of burn-up calculations have been consistent with former calcu-lations performed using the code ALEPH. The most difference found in theamount of 239Pu. SERPENT simulations show that the breeding is slightlylower than previous calculations, hence, keff is reduced more. However, keffreductions per cycles show that the results are comparable.

Finally, summarizing the results, one can conclude that all these simu-lations have proven a similarity of results from SERPENT simulations withother computer codes and SERPENT is a valid tool to model critical modeof MYRRHA. Significant negative Doppler constant and effective delayedneutron fraction give rise to a more stable core. Negative feedbacks duringvarious voiding scenarios make sure that these scenarios will not jeopardizethe safety of MYRRHA in a neutronic point of view.

References

[1] OECD Nuclear Energy Agency. Advanced Nuclear Fuel Cycles and Ra-dioactive Waste Management. Nuclear Development. Nuclear EnergyAgency, Organisation for Economic Co-operation and Development,2006.

[2] A. Azad. Critical temperature of the lead-bismuth eutectic (lbe) alloy.Journal of Nuclear Materials, 341(1):45–52, 2005. Cited By (since 1996):5.

[3] Stefano Benedetti. Neutronic coupling between the myrrha core and thein-vessel fuel storages. Master’s thesis, Belgian Nuclear Higher Educa-tion Network, c/o SCK·CEN, 2010− 2011.

[4] J.E. Cahalan. SAS4A/SASSYS-1 Maintenance and operation handbook.Argonne National Laboratory, Oct 2002.

[5] Belgian Nuclear Research Centre. Guinevere: Generatorof uninterrupted intense neutron at the lead venus reactor.http://www.sckcen.be/en/Our-Research/Research-projects/

EU-projects-FP6-FP7/GUINEVERE, 2012. 08/06/2012.

[6] NUCLEAR ENERGY AGENCY ORGANIZATION FOR ECONOMICCO-OPERATION and DEVELOPMENT. Accelerator-driven Systems(ADS) and Fast Reactors (FR) in Advanced Nuclear Fuel Cycles, 2002.

[7] NUCLEAR ENERGY AGENCY ORGANIZATION FOR ECONOMICCO-OPERATION and DEVELOPMENT. Handbook on Lead-bismutheutectic alloy and lead properties,materials compatibility, thermal-hydraulic and technologies. OECD/NEA Nuclear Science Committee,2007.

[8] Van den Eynde Gert. Personal communication, 08/06/2012.

[9] William L. Dunn and J. Kenneth Shultis. Exploring Monte Carlo Meth-ods. Elsevier Science, 2011.

http://www.sckcen.be/en/Our-Research/Research-projects/EU-projects-FP6-FP7/GUINEVERE

http://www.sckcen.be/en/Our-Research/Research-projects/EU-projects-FP6-FP7/GUINEVERE

76 REFERENCES

[10] Stephen A. Dupree and Stanley K. Fraley. A Monte Carlo Primer: APractical Approach to Radiation Transport. Springer, 2001.

[11] Yousry Gohar and Donald L. Smith. YALINA Facility A Sub-CriticalAccelerator-Driven System (ADS) for Nuclear-Energy Research Facil-ity Description and an Overview of the Research Program (1997-2008).Nuclear Engineering Division, Argonne National Laboratory, January2010.

[12] Waclaw Gudowski. Personal communication, 08/06/2012.

[13] Alain Hebert. Applied Reactor Physics. ECOLE POLYTECHNIQUEDE MONTREAL, 2004.

[14] P. Hejzlar, N. E. Todreas, E. Shwageraus, A. Nikiforova, R. Petroski, andM. J. Driscoll. Cross-comparison of fast reactor concepts with variouscoolants. Nuclear Engineering and Design, 239(12):2672–2691, 2009.Cited By (since 1996): 8.

[15] R.M. Haley J. Venner and R. L. Bowden. k Effective as a Measure ofCriticality Safety. 7th International Conference on Nuclear CriticalitySafety, October 20-24, 2003 Japan.

[16] H. Khatib. Review of oecd study into ”projected costs of generatingelectricity-2010 edition”. Energy Policy, 38(10):5403–5408, 2010. CitedBy (since 1996): 2.

[17] J. Leppanen. Two practical methods for unionized energy grid con-struction in continuous-energy monte carlo neutron transport calcula-tion. Annals of Nuclear Energy, 36(7):878–885, 2009. Cited By (since1996): 5.

[18] J. Leppanen. Performance of woodcock delta-tracking in lattice physicsapplications using the serpent monte carlo reactor physics burnup cal-culation code. Annals of Nuclear Energy, 37(5):715–722, 2010. CitedBy (since 1996): 2.

[19] J. Leppanen. Serpent manual. VTT Technical Research Centre of Fin-land, December 2, 2010.

[20] Jaakko Leppanen. Development of a New Monte Carlo Reactor PhysicsCode. PhD thesis, Helsinki University of Technology, 2007.

[21] Eric P. Loewen. Idaho National Laboratory Lead or Lead-Bismuth Eu-tectic (LBE) Test Facility. Idaho National Laboratory, May 2005.

REFERENCES 77

[22] Odd Runevall. Helium Filled Bubbles in Solids Nucleation, Growth andSwelling. PhD thesis, Royal Institute of Technology, 2012.

[23] SCK.CEN. Myrrha: Multi-purpose hybrid research reactor for high-techapplications. http://myrrha.sckcen.be/en, 2012. 08/06/2012.

[24] R. Soule, W. Assal, P. Chaussonnet, C. Destouches, C. Domergue,C. Jammes, J. . Laurens, J. . Lebrat, F. Mellier, G. Perret, G. Rimpault,H. Servire, G. Imel, G. M. Thomas, D. Villamarin, E. Gonzalez-Romero,M. Plaschy, R. Chawla, J. L. Kloosterman, Y. Rugama, A. Billebaud,R. Brissot, D. Heuer, M. Kerveno, C. Le Brun, E. Liatard, J. . Loiseaux,O. Mplan, E. Merle, F. Perdu, J. Vollaire, and P. Baeten. Neutronicstudies in support of accelerator-driven systems: The muse experimentsin the masurca facility. Nuclear Science and Engineering, 148(1):124–152, 2004. Cited By (since 1996): 64.

[25] Janne Wallenius. Transmutation of nuclear waste. Leadcooled booksand games, December 2011, first edition.

[26] Youpeng Zhang. Transmutation of Am in sodium fast reactors and accel-erator driven system. PhD thesis, Royal institute of technology, Sweden,2012.

http://myrrha.sckcen.be/en

neutronic analysis of the critical myrrha core with serpent …536181/fulltext01.pdf · neutronic...

Documents