Neutronic Analysis of the Multipurpose Hybrid Research Reactor for High-tech Applications (MYRRHA) with a Monte Carlo Code SERPENT

i

Neutronic Analysis of the Multipurpose 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 2012:57

ISSN 0280-316X

ISRN KTH/FYS/- -12:57–SE

ii

Abstract

Safety of nuclear power plants and their highly radio-toxic waste are the main concerns in nuclear technology. Hence, new reactor designs with enhanced safety properties and the ability to recycle the nuclear waste are vital for the future of nuclear power technology. The Multipurpose Hybrid Research Re- actor for High-tech Applications (MYRRHA) project designed at SCK·CEN in Belgium is one of the promising designs in this area. This multipurpose nuclear facility endeavors to fulfill some of the criteria of Gen-IV reactors such as sustainability, safety, and proliferation-resistance. MYRRHA is de- signed as a pool-type reactor core, which can be run either as critical reactor or sub-critical system, which is driven with a spallation source neutron of a proton accelerator. The key design features of MYRRHA are mixed oxide fuel 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 components of an ADS will be presented and suitable options for sub-critical mode of MYRRHA will be mentioned. The geometry and chosen options for the crit- ical mode of MYRRHA will be included in non-public appendix. This thesis focuses 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 of

MYRRHA obtained by MCNP/MCNPX codes versus simulations performed

with a new Monte Carlo neutron transport code - SERPENT. The safety

feedbacks, Doppler constant and effective delayed neutron fraction, will be

presented. Neutron flux in the fuel and power distribution over the core

for MYRRHA are calculated and compared to former outcomes. This thesis

presents different accident scenarios related to MYRRHA core, to verify lower

reactivity feedback coefficient due to voiding and to ensure the safety of

MYRRHA core from a neutronic point of view. Finally, burn-up calculations

have been performed in order to investigate the spent fuel and its quality,

and evaluate it with the result from earlier studies.

iv

Sammanfattning

S¨ akerheten och radioaktivt avfall ¨ ar de huvudsakliga problem inom k¨ arnkraft- steknik. D¨ arf¨ or ¨ ar nya reaktorer med f¨ orb¨ attrade s¨ akerhetsegenskaper och f¨ orm˚ agan att ˚ atervinna k¨ arnavfallet avg¨ orande f¨ or k¨ arnkraftens framtid. Fors- kningsreaktorn f¨ or h¨ ogteknologiska till¨ ampningar (Myrrha) vid SCK·CEN i Belgien ¨ ar en av de lovande designer inom detta omr˚ ade. Denna m˚ angsidiga k¨ arntekniska anl¨ aggning str¨ avar efter att uppfylla vissa av kriterierna f¨ or gen- eration 4-reaktor s˚ asom uth˚ allighet, s¨ akerhet och f¨ oljandet av icke-spridnings- f¨ ordraget. Myrrha ¨ ar en bass¨ angreaktor som kan k¨ oras antingen kritisk eller underkritisk. I det underkritiska utf¨ orandet drivs reaktorn med en pro- tonaccelerator och ett spallationsm˚ al. De viktigaste designk¨ annetecknen f¨ or Myrrha ¨ ar MOX-br¨ ansle samt anv¨ andandet av eutektisk bly-vismut-legering som kylmedel och spallationsm˚ al.

Denna avhandling presenterar kortfattat information om acceleratordrivna system (ADS) i allm¨ anhet, och Myrrha i synnerhet. De viktigaste komponen- terna i ett ADS kommer att presenteras och vissa komponenter f¨ or Myrrha i det underkritiska utf¨ orandet kommer att n¨ amnas. Geometrin och beskrivnin- gen f¨ or Myrrha i det kritiska utf¨ orandet kommer att ing˚ a i en icke-offentlig bilaga. Denna avhandling fokuserar fr¨ amst p˚ a analys av Myrrha i det kri- tiska utf¨ orandet och d¨ armed de kritiska parametrarna som ¨ ar mycket viktiga ur s¨ akerhetssynpunkt i systemet.

Avhandlingen j¨ amf¨ or n˚ agra av de grundl¨ aggande parametrar f¨ or Myrrha som har erh˚ allits genom MCNP/MCNPX med resultat fr˚ an Serpent, som

¨

ar en ny Monte Carlo-neutrontransportskod. De s¨ akerhetsparametrar som har ber¨ aknats ¨ ar doppler-konstant och effektiv br˚ akdel f¨ ordr¨ ojda neutroner.

Neutronfl¨ odet i br¨ anslet och effektf¨ ordelningen ¨ over h¨ arden ber¨ aknas och j¨ amf¨ ors med de tidigare resultaten. Olika haveriscenarier relaterade till voidning av Myrrhah¨ arden har tagits fram f¨ or att verifiera negativ reak- tivitets˚ aterkoppling och att garantera s¨ akerheten ur en neutronisk synvinkel.

Slutligen har en utbr¨ anningsber¨ akning genomf¨ orts f¨ or att kunna unders¨ oka

br¨ anslets kvalitet och j¨ amf¨ ora det med resultat fr˚ an 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 from SCK.CEN, specially the head of the expert group at SCK·CEN, Dr. Gert Van den Eynde, that improved this thesis by his valuable comments. I would like to express my gratitude to my supervisor, Prof. Waclaw Gudowski for all his advices and patience. I also express my appreciation for very nice and friendly environmental at reactor physics department at KTH, especially my supportive friends Karl Samuelsson and Erdenechimeg Suvdantsetseg for their 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 and Symbols

ADS Accelerator Driven System

Am Americium

BoC Beginning of Cycle

BREST Russian acronym for Pb-cooled fast reactor BR2 Belgian Reactor 2

EoC End of Cycle

FA Fuel assembly

FoM Figure of Merit

H Hydrogen

He Helium

HYPER the Hybrid Power Extraction Reactor Gen-IV Generation IV of nuclear power reactors INVFS In Vessel Fuel Storage

IPS In Pile Sections assemblies LBE Lead Bismuth Eutectic LFR Lead-Cooled Fast Reactor LWR Light Water Reactor

k _eff k EF F ective , effective neutron multiplication factor

MA Minor Actinide

MCNP Monte Carlo N-Particle transport code

MYRRHA Multi-purpose hybrid research reactor for high-tech applications MOX fuel Mixed OXide fuel

NTE Neutron Transport Equation T91 FMS T91 Ferritic-Martensitic Steel

Pb Lead

PEACER Proliferation-resistant, Environment-friendly, Accident-tolerant, Continuable and Economical Reactor

Pu Plutonium

PVR Pressure Vessel Reactor SCRAM Safety Control Rod Axe Man

SVBR Russian acronym for lead-bismuth fast reactor TRU Transuranic waste

U 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 5

2.1 Accelerator Driven System and MYRRHA . . . . 5

3 Tools and Methods 9 3.1 Neutron Transport Equation . . . . 9

3.1.1 The Integral Form of the Transport Equation . . . . . 10

3.2 Monte Carlo Approach . . . . 11

3.3 SERPENT . . . . 14

3.4 Modeling in SERPENT . . . . 15

4 Results 19 4.1 The Criticality Calculation with SERPENT . . . . 19

4.1.1 Neutron Flux, Power Distribution and Cross Sections 20 4.1.2 Effective Neutron Multiplication Factor of Fuel Tem- perature Changes and Doppler Constant . . . . 26

4.1.3 Effective Delayed Neutron Fraction . . . . 31

4.2 Accident Condition Analysis . . . . 32

4.2.1 Partial and Total Voiding of the Active Zone of the Core 32 4.2.2 Mixture of Steam and LBE Inside the Active Zone . . 46

4.2.3 Steam bubble saturation model . . . . 48

4.2.4 Total Voiding of the Core . . . . 49

4.2.5 Fuel Relocation at the Top of the Active Zone . . . . . 50

xii CONTENTS

4.3 Burn-up Calculation . . . . 53 4.4 Analysis of Figure of Merit for the SERPENT Model . . . . . 61

5 Comparison 65

5.1 The Criticality Calculation with SERPENT . . . . 65 5.2 Accidental Condition Analysis . . . . 68 5.3 Burn-up Calculation . . . . 70

6 Conclusion 73

References 75

List of Figures

2.1 Spallation target - Pink particles are energetic protons, which create neutrons (green particles) in spallation targets . . . . . 7 3.1 A scheme, which explains the different steps in analog Monte

Carlo 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 ²³⁸ U and ²⁴⁰ Pu . . . . 26 4.8 Fuel temperature dependence of k _eff for MYRRHA, model nr 1 28 4.9 Fuel temperature dependence of k _eff 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% 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 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 in which 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, orange

color represents voided LBE . . . . 35

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

4.15 k _eff of one voided fuel assembly, fresh fuel, model nr 1 . . . . . 37

4.16 k _eff of one voided fuel assembly, fresh fuel, model nr 2 . . . . . 38

4.17 k _eff of one voided fuel assembly, spent fuel, model nr 1 . . . . 39

4.18 k _eff of one voided fuel assembly, spent fuel, model nr 2 . . . . 40

4.19 k _eff of voiding the six fuel assemblies, fresh fuel, model nr 2 . . 42

4.20 k _eff of voiding the six fuel assemblies, spent fuel, model nr 2 . 43 4.21 k _eff of voiding all 68 fuel assemblies fresh fuel, model nr 1 . . . 44

4.22 k _eff of voiding all 68 fuel assemblies spent fuel, model nr 2 . . 45

4.23 Voiding of 16 fuel assemblies, model nr 2 . . . . 46

4.24 16 fuel assemblies are voided according to table 4.9, model nr 2 47 4.25 One bubble at top . . . . 48

4.26 3 bubbles at top . . . . 48

4.27 Void in all 6 IPS - vertical view . . . . 48

4.28 horizontal view . . . . 48

4.29 He release into all assemblies, yellow represents Helium . . . . 50

4.30 Scenario number 1 model nr 1 . . . . 51

4.31 Scenario number 1 model nr 1 . . . . 51

4.32 Scenario number 2 model nr 1 . . . . 51

4.33 Scenario number 3 model nr 1 . . . . 51

4.34 Mass evolution of fuel . . . . 54

4.35 Uranium-235 and Uranium-238 mass evolution . . . . 55

4.36 Americium-241 and Americium-242m mass evolution . . . . . 56

4.37 Plutonium mass evolution . . . . 57

4.38 k _eff evolution in time . . . . 58

4.39 Standard deviation σ and k _eff versus wall-clock time . . . . 61

4.40 FOM and k _eff versus wall-clock time, 120000 neutron sources and 1000 cycles . . . . 62

4.41 FOM and k _eff versus wall-clock time, 40000 neutron sources and 5000 cycles . . . . 62

4.42 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 fresh

fuel, power peak factor 1.34 . . . . 67

List of Tables

4.1 k _eff for different fuel temperatures, model nr 1 . . . . 27

4.2 k _eff for different fuel temperatures, model nr 2 . . . . 30

4.3 β _eff . . . . 31

4.4 Different scenarios for simulating void in the fuel assembly [3] 34 4.5 k _eff of one voided fuel assembly, model nr 1 . . . . 36

4.6 k _eff of one voided fuel assembly, model nr 2 . . . . 36

4.7 k _eff of voiding the six hottest fuel assemblies for model nr 2 . . 41

4.8 k _eff of voiding all 68 fuel assemblies, model nr 1 & 2 . . . . . 41

4.9 LBE densities for different steam fractions in the core . . . . . 47

4.10 k _eff for different steam fractions, model nr 2 . . . . 47

4.11 bubble in the core - model nr 2 . . . . 49

4.12 k _eff during He release into all assemblies - Model nr 2 . . . . 49

4.13 k _eff during fuel relocation at the top of the active zone with no regard to molten cladding - model nr 1 . . . . 52

4.14 Composition of fresh fuel . . . . 53

4.15 Composition evolution of the fuel in g/cm ³ as a function of time (days) - model nr 1 . . . . 59

4.16 Composition evolution of the fuel in g/cm ³ as a function of time (days) - model nr 2 . . . . 60

4.17 Composition evolution of the fuel in g/cm ³ as a function of time (days) . . . . 60

5.1 Comparison of k _eff in two different codes . . . . 68

5.2 k _eff of voiding one fuel assembly, model nr 1 . . . . 69

5.3 k _eff of voiding one fuel assembly, model nr 2 . . . . 69

5.4 k _eff of voiding the six hottest fuel assemblies - model nr 2 . . . 70

5.5 k _eff in case of fuel relocation to the top of the active zone . . . 70

5.6 Composition evolution of the fuel in g/cm ³ as a function of

time (days) . . . . 71

xvi LIST OF TABLES

Chapter 1 Introduction

Although, conventional light-water reactors produce significant amount of power with very low CO 2 -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 nuclear waste. Even though, only a few percent of the spent fuel is the transuranic elements (TRU) such as plutonium and americium isotopes, they are the most problematic part of the present nuclear waste. They have half-lives up to millions of years and are highly radio-toxic. Hence, the cost and risk of storing these types of waste in a repository for a long time will not be neg- ligible [1]. Furthermore, these light water reactors, which utilizing mainly thermal neutrons, extract only a few percent of the energy in the fuel. Spent fuel still contains a lot of its original energy [1]. Increasing the number of thermal reactors will only drain the low-cost natural uranium reserves in future; 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 sixty ¹ , besides, they provide a substantial improvement of nuclear waste manage- ment. This is the direct result of more efficient atomic fission. Fast reactors use fast neutron spectrum contrasting the conventional light-water reactors that are depended on thermalized neutrons. Hence, an appropriate coolant with good heat-transfer property, which does not thermalize the neutrons, is required. The option coolants for these types of reactors are liquid-metals such 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,

1 International 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, sodium has the capability for coping with core having higher power density, which is resulted in lower doubling time for producing plutonium [14]. At the same time, LBE was the coolant for a number of submarine reactors in the former Soviet Union, which resulted in many researches about the coolant technol- ogy and material. Additionally, about 20 fast neutron reactors have produced electricity commercially, which give 400 reactor-years of operating experience to the end of 2010 ² . These reactors mainly have been used as breeder and lately as high-level waste burners.

At the moment, these types of reactors are the subject of many studies for accelerator-driven system. They are planned for high-level radiation waste transmutation. Briefly, an ADS is designed to be an inherent safe nuclear reactor, which can consume its own waste in an efficient and safe manner.

ADS has a sub-critical core i.e. k _eff < 1 and requires an external neutron source to remain stable sub-critical. A proton accelerator and a spallation target that is generally heavy liquid-metal provide these neutrons in ADS.

The energetic protons hit the spallation target and generate neutrons in the sub-critical core.

The interest in LBE coolant has been resumed for civilian fast reactors since 1990. The lead-cooled BREST and LBE-cooled SVBR are the most known projects, which motivated several other projects in the field of ADS, and in particular lead cooling. Favorable features of lead are many such as lower reactivity feedback coefficient in case of voiding, better shielding against energetic neutrons and gamma rays and chemically inertly against water [7]. However, significantly lower melting temperature of LBE compared to pure Pb (396 K vs 600 K [2]) has led to development of ADS with LBE as coolant instead of pure lead. Moreover, high boiling temperature of LBE (1943K ±50K [7]) reduces the chances of coolant boiling. Also the possibility of passive decay heat removal with natural convection in lead makes these kinds of reactors more attractive. The major drawback of Pb and LBE coolants is the corrosion issues [21]. The other apparent drawbacks of such coolants are the complicated service, repair, and small margin to freezing for these 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 MUSE program at the Cadarache Research Center of the CEA in France. Sev- eral experiments have been completed in this program to demonstrate the viability of neutronic measurements and core description of a sub-critical re-

2 World 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 was dedicated to conduct tests and provide methods for sub-critical reactivity measurement [24]. The GUINEVERE project is another project, which is performed in order to complete the results from MUSE program. After some modifications in a facility called VEnus at Mol-site in Belgian and connec- tion to a deuteron accelerator, an experiment is started. The objective of this zero-power facility is to address some of main issues of operational processes in 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 adequate energy 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 cost zero-power, sub-critical assembly, which can provide knowledge about the static and dynamic neutronics properties of ADS. It strives to be a small test facility 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 of Korea, are also pursuing. The objective of this development is to investi- gate safe transmutation technology along with proliferation-resistance. They have designed an ADS, called HYPER, in which LBE is both coolant and spallation target. Its purpose is to transmute transuranic waste and fission products such as 129I and 99Tc [7]. PEACER is another LBE-cooled reactor that 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 actinides and long-lived fission products yearly at the Japan Atomic Energy Research Institute [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 the field of lead-bismuth eutectic technology. MYRRHA project at SCK·CEN is multipurpose nuclear facility, which endeavor to demonstrate ADS technol- ogy and waste transmutation. It will also address structural and material studies for other type of reactors such as fusion reactors. This pool-type reactor uses MOX-fuel and lead-bismuth eutectic, which is both coolant and spallation target. MYRRHA is a flexible design, which can operate in critical mode as well.

This thesis introduces briefly some primary information about ADS, MYR-

RHA in particular. The main components of ADS will be presented and the

selected options for sub-critical MYRRHA will be mentioned. The critical

mode of MYRRHA will be presented in non-public appendix. To enhance the

understanding of the code SERPENT, one chapter is dedicated to neutron

4 Introduction

transport equation, Monte Carlo method and SERPENT. The description of the SERPENT model of MYRRHA in critical mode is presented in non- public appendix. The thesis presents results for critical mode of MYRRHA because 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 of MYRRHA obtained by MCNP/MCNPX codes versus simulations performed with a new Monte Carlo neutron transport code - SERPENT. Neutronic safety feedback parameters, namely Doppler constant and effective delayed neutron fraction, will be presented. Neutron flux spectrum in the fuel and power distribution over the core for MYRRHA are calculated and compared to the former outcomes. Different accident scenarios related to MYRRHA core 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 the

spent fuel and its quality, and evaluate it with the result from earlier studies.

Chapter 2

Introduction to MYRRHA, a Flexible 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 options for sub-critical mode of MYRRHA will be included. The geometry and a more detailed design data of critical mode of MYRRHA will be included in the appendix A in the confidential format. In the end, the reason why the critical 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 development

solutions at the moment. There are some important factors that make ADS

especially remarkable. This concept makes it possible to design a core in a

way that is not adequate otherwise. Introducing minor actinides (MA), such

as Americium to the reactor fuel may challenge safety neutronic parameters,

for instance reduction of Doppler constant, increase of coolant temperature

coefficient 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 is

able to tolerate more presence of minor actinides than other systems. This

makes them the most attractive option to recycle the nuclear waste. To make

ADS technology credible compared to other options, it should decrease the

radio-toxicity of the nuclear waste at least by a factor of 100 [6]. ADS can

dedicatedly 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 safe and reliable design. This design makes it sure not to have k _eff equal or more than one even in case of structure failure, core meltdown, flooding etc. The delicate 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 fuels and materials for the future Gen-IV fast reactor concepts. This is a flexible design, which can operate in both sub-critical and critical modes. In sub- critical mode, the proton accelerator provides high energetic protons, which creates neutrons in the spallation target. These neutrons feed the core so the reactor can attain a stable sub-critical mode. The coolant is lead-bismuth eutectic, and fuel is MOX in both modes. The objective of MYRRHA is to be a tentative model for future experiment and development of lead fast reactor technology. It will demonstrate ADS technology and facilitate the experimentation of innovative MA fuel. It will produce isotopes for nuclear medicine and industry as well. MYRRHA will also assist material and com- ponents testing for other types of reactors [23]. This reactor will bring to operation at full power around 2023 ¹ .

Chosen fuel for MYRRHA is MOX, which contains Pu from reprocessing of spent fuel from LWR. It is enriched to about %33 plutonium. Pu in spent fuel is recycled as PuO ₂ and then is combined with depleted UO ₂ [22]. This spent fuel can contain also other transuranic waste. In this way, not only the extracting energy from the fuel is more efficient, also the other toxic fissionable elements can be recycled instead of going to a final repository.

One of the main components of ADS core is accelerator. It determines the overall sub-critically level in the system. It is the accelerator that provides energetic protons, which creates neutrons in the spallation target. MYRRHA has a proton accelerator of 600 MeV in terms of energy and 4 mA in terms of intensity. The reliability and availability of ADS are depended on the reli- ability and availability of accelerators, and this is determined by the number of tolerable beam trips. The two types of accelerators that are selected for MYRRHA are the isochronous cyclotron and the Continuous Wave linac, which LINAC is the primary reference and cyclotron is the back-up option to 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 a windowless target configuration. In the first configuration, there is a win-

1 SCK·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 radiation damage. In the second configuration, there is no window between the beam and target; hence, the beam impinges the target without anything interven- ing. The absence of the window results in other challenges such as plasma formation at the target surface [23]. In MYRRHA, the first configuration, a window target, is preferred above other[8].

Since 1998, MYRRHA design has been improved and in this thesis, we

will work with the latest version called FASTEF, which is the critical mode

of MYRRHA. Since there are several publications about this design and its

specifics, extensive work has performed for this mode of MYRRHA. There

are also former results performed in MCNP for critical mode, which enables

the comparison of the results. However, while MYRRHA is designed to run

a lot of experiments in a sub-critical mode of operation, the important safety

parameters are related to criticality safety [12]. Additionally, simulating

external source in SERPENT 1.1.13 is still very much under development

[19]. Thus, to be assured of reliability of the results, simulations have been

performed in critical source mode. The geometry and more detailed design

data of critical mode of MYRRHA will be on hand in the non-public appendix

A 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 code for this thesis, Monte Carlo method is briefly presented. To understand this method, knowledge about neutron transport equation is necessary. Therefore, the NTE and its solution are presented in this chapter. Furthermore, a brief description 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 its location r, its direction of travel Ω, and its energy E at time t.

Due to sufficiently low neutron density, one can assume an educated guess of no neutron-neutron collision. Population of neutrons describes as neutron angular density N (r, Ω, E, t), which defines the density of neutrons in volume dr about r, traveling in direction dΩ about Ω, with energy dE about E, and time dt about t. Collisions are point-like and instantaneous.

Angular flux Ψ is the product of the angular density and the speed v. When this 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 = Z

4π

Ψ(r, Ω, E, t)dΩ (3.2)

The scalar flux is proportional to the reaction rate per unit volume. The

constant Σ, which relates scalar flux to reaction rate is called macroscopic

cross section. By solving neutron transport equation, one can find scalar

flux which can be used for calculating measurable quantities i.e. reaction

rate (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 is formulated 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) + Σ _t (r, E, t)Ψ(r, E, Ω, t) = Z

4π

dΩ

Z ∞

0

dE

Σ _s (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 neutron is at position r moving in direction Ω with energy E. Ψ(r, E, Ω, t) is angular neutron flux, Σ _t (r, E, t) total macroscopic cross section, Σ _s (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

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

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

, E

) and finally the fifth term is the source. Thus, production rate subtracting destruction rate will represent the change 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 flux along its characteristic for a given S, the integral form of transport equation is obtained as below [13]

β = Z s

0

Σ _t (r − s

Ω, E)ds

(3.6)

Ψ(r, E, Ω, t) = Z

e ^−β Z Z

Σ _s (r − sΩ, Ω

, E 7→ E

)Ψ(r − sΩ, Ω

, E

, t − s/v) +

Z s 0

dse ^−β S(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 attenuated source (equation 3.10).

K = Z ∞

0

e ^−β Z Z

Σ _s (r − sΩ, Ω

, E

, t − s

v )dΩ

dE

ds (3.9) S

=

Z ∞ 0

e ^−β S(r − sΩ, Ω, E, t − s

v )ds (3.10)

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

Ψ 0 = S

, Ψ 1 = KΨ 0 , . . . Ψ n+1 = KΨ n (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

X

n=0

Ψ _n (3.12)

Ψ ₀ is angular flux from source when it does not go through any collisions, Ψ 1 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 transport equation (see equation 3.8) [10].

3.2 Monte Carlo Approach

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

One should first define a geometry, which neutron will be investigated

in along with the source term. By Monte Carlo method even complicated

geometry have solution. The description of the geometry includes the size,

12 Tools and Methods

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

When the geometry is defined, the next step will be the execution of neutron flight path through out the material. The simulation of this path is called random walk. The Monte Carlo random walk creates a set of neutron collision points with information about the consequence of these collisions i.e.

neutron energy and direction after the collisions. However, this information about neutron motion is not measurable quantities. The Monte Carlo method results are generally scores, and by these scores one can calculate measurable quantity 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 scheme shows the different steps of decision making in analog ¹ Monte Carlo method.

Analog here means that the chain is terminated at capture site. To generate the ”history” of a neutron, the first step is to initiate a random start position and velocity. These initial inputs are assumed from initial condition. Then by 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 one of materials boundary or collides with other particles. In the scheme, this level 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 properties of new material will be obtained and the algorithm will be executed all over again. In the other hand, an interaction can be one of these collision types according to known branching ratios: scattering, fission or absorption. If the particle is absorbed the chain is terminated. In the case of scattering, previous velocity and scattering cross sections from the library determine the new 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 cross section library. These new neutrons will also go through the algorithm until all neutrons are absorbed and chain is terminated.

1 The other method is implicit treatment of capture reactions, in which the number of

neutrons that represents the simulated history is associated with a statistical weight. In

this method, the weight is reduced according to the capture probability, instead of to be

captured in site as in analog method [20].

3.2 Monte Carlo Approach 13


 Initial
velocity
and


position
for
neutrons
 Length
of
free
path,
which
is
 determined
from
library
 (material
properties)


Scattering
 Fission 
 Capture


New
 Velocity
 determined
 from
 scattering
 
cross
 section
 


Number
and
 velocity
of
 new

 neutrons
 determined
 from
fission
 cross
 section



Chain

 Terminated


Crossing
 boundaries
 Collision


types


Possible
 interactions
 or
event
 Velocity
and
position


for
neutrons


Figure 3.1: A scheme, which explains the different steps in analog

Monte Carlo approach

14 Tools and Methods

3.3 SERPENT

SERPENT is a three-dimensional continuous-energy Monte Carlo reactor physics burn-up calculation code. The significant of SERPENT is in two- dimensional lattice physics calculation, however, the universe-based geometry description makes the modeling in three dimensions possible as well. The advantage of SERPENT over other conventional tools is the faster run-time.

This is achieved by a more efficient tracking in the geometry routine and the use of same energy grid for all cross sections. This enables SERPENT to handle complicated objects and surfaces easier and reduces the running time [18].

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

f (E) = E − E _j−1

E _j − E _j−1 (3.13)

σ(E) = f (E)(σ _j − σ _j−1 ) + σ _j−1 (3.14) where E _j−1 and E _j are listed energy grid points with their corresponding listed σ in the libraries. Every time a cross section needs to be calculated an energy point E, which is between E _j−1 and E _j , required to be found.

This requires an iterative search algorithm, which in term of computing, is expensive.

There are several occasions that this iterative search algorithm must be performed, for example every time that the cross sections are required for sampling interactions, scoring reaction rates or sampling the distance to the next collision site. In burn-up calculation for instance which has a large number of nuclides, the running time will increase because the calculation of macroscopic cross sections need to be done by summing over all nuclides component. For MCNP5 for example, the difference between running time for 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 the

distance 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, the computing is less expensive and the run time is reduced. To understand the value of delta tracking in terms of the running time, one of the simulations is 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 changes in the result data.

3.4 Modeling in SERPENT

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

Cell, which is the basic block, defines the regional space. It can be filled with 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 referred in cells to define the boundaries. There are various types of surfaces, for instance sphere, plane, cube, hexagonal and etc. Along with specifying the type of surface, surface parameters such as coordinates, radii and etc. should be included in the surface definition.

The universe-based geometry starts first with constructing pins with their gaps and cladding. Several different kinds of pins such as fuel pin, dummies, etc. can be constructed in their own universe. Next step is constructing the assemblies with fuel pins arranged in a lattice, also in their universe. There are several types of lattice cards such as square, hexagonal ³ , cylindrical and etc. Each lattice is an universe, which should be fixed into a cell. These assemblies 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 to determine the continuous-energy cross sections in the transport simulation.

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

2 This technique can easily set to OFF in SERPENT.

3 X-type hexagonal lattice has been used in this thesis.

16 Tools and Methods

super-critically and equal to one critical core. This means, for example, the chain reaction continues at a constant rate when k _eff is one or the number of fission neutrons increases while k _eff is over one. By connecting k _eff and reactivity one can have a better understanding about the safety of the core.

The formula below shows the relation between them.

ρ = k _eff − 1

k _eff (3.15)

In SERPENT, the k-eigenvalue criticality source method is used as default mode. This means that the simulations run in cycles with fixed number of source neutrons per cycle. Since the number of generated source points is different from this fixed value, the source size will change accordingly.

The fission reaction distributed from previous cycle forms the next source distribution [19]. One should define the number of source neutrons per cycle and the number of active cycles run. The total number of active neutron histories determines the statistical accuracy of the results. Furthermore, if the system is far from critically (k _eff = 1), one can guess an initial value for k _eff . Otherwise, by default, the value of k _eff is set to unity. One should notice that the initial source-points are chosen in the fissile cells randomly by the program and source-point is not required from the user [19]. In SERPENT ⁴ , 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 collision estimate of neutron flux to evaluate the reaction rates:

R = 1/V Z

V

Z E

E

f (r, E)φ(r, E)d ³ rdE (3.16) where f (r, E) is the detector response function, which determines the type of calculation. Hence, in detector definition one should specify the type of reaction, and also the energy and spatial domains of this integral. For instance, to calculate neutron flux integrated over space and energy, detector parameters are as follow: f is equal to one, the energy domain sets to a desired grid, and the space defines as coordinates or inside a preferred material ⁵ .

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

4 SERPENT 1.1.13

5 There 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 spontaneous fission product yield along with the continuous-energy cross sections. To start a burn-up calculation in SERPENT, one should first identify the de- pleted materials ⁶ and defines the radiation history. There are three different options ⁷ in SERPENT to solve the Bateman equations. The user can choose the the most adequate option to make the burn-up calculations more accurate but 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 design significances are included. However, there are two models presented in this thesis. The first model is the simplified one and is based on MYRRHA data available in open literature. A good deal of work has done on this model and many results are obtained. The second model is the more detailed one and based on propriety MYRRHA design data. All assumptions and details are made according to MYRRHA design [3]. This model is the most identical one to MYRRHA. More details about these two models are presented in the appendix A.

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

7 “ First method: Transmutation Trajectory Analysis (TTA), based on the analytical solution 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 TTA

equations.” [19]

18 Tools and Methods

Chapter 4 Results

In this chapter, all results from various simulations are included in three sepa- rated sections: The criticality calculation with SERPENT, accident condition analysis and burn-up calculation performed by SERPENT. First a short de- scription of the problem is presented followed by the results and discussion section. 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 of normal operation such as k _eff , Doppler constant and effective delayed neutron fraction are presented. The neutron flux spectrum in the fuel and power distribution over the core are obtained. Same simulations are performed for both model nr 1 and nr 2 ¹ . Some of these simulations are performed for both models or partially for only one of them. To ensure the reliability of the outcome and safety during the operation, all the calculations are executed for fresh fuel at the beginning of cycle (BoC) and also spent fuel at the end of 5th cycle, which has different composition. The composition of the fresh and spent fuel are included in Appendix A [3].

1 Check out appendix A for more detail information about model nr 1 and 2 and their

design specific.

20 Results

4.1.1 Neutron Flux, Power Distribution and Cross Sections

In this section, neutron flux spectrum in the fuel and power maps over the core for both fresh and spent fuel are presented. Additionally, the most important cross sections, namely fission and capture cross sections and the fission probabilities of the most important nuclides, are included. Here to calculate the energy-integrated flux in the fuel, the writer defines a grid of 1500 equal lethargy-width bins with an energy boundary of [10 ⁻⁵ , 10 ² ]M eV i.e. the energy boundary is divided to 1500 equal lethargy-width bins ² . Results and discussion

Figures 4.1 and 4.2 show the power distribution over the core for fresh fuel in both models 1 and 2. Additionally, the power distribution for spent fuel for both models are shown in figures 4.3 and 4.4. Total linear power in the core is 1.606 MW/cm that grants the total power of 96.35 MW (1.606 ^{M W} _cm · 60cm = 96.35M W where 60 cm is the length of the active part) ³ . The neutron flux spectrum in the fuel is plotted (see figure 4.5). The normalized total neutron flux in the material fuel is 2.27e+15 neutrons/cm ² s. The figure 4.6 shows the spectrum-averaged cross sections and fission probabilities for all nuclides presents in the fresh fuel.

2 See chapter 3, for more information about detectors and how they can be defined.

3 In 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 fresh fuel, 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

Relative error ±0.0004

4.1 The Criticality Calculation with SERPENT 23

Figure 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

24 Results

Figure 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

4.1 The Criticality Calculation with SERPENT 25

10

10

10

10

10

10

10

10

0 2 4 6 8 10 12 14 16 18 x 10

E[MeV]

Neutron flux spectrum[cm

s

] in fuel

Figure 4.5: Neutron flux spectrum in the fuel

Pu238 Pu239 Pu240 Pu241 Pu242 U238 U235 0

1 2 3

Pu238 Pu239 Pu240 Pu241 Pu242 U238 U235 0

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 fresh

fuel

26 Results

10

10

10

10

10

10

10

10

10

10

10

10

10

10

Incident neutron energy MeV

capture cross section, barn

σ c of U238 σ c of Pu240

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

4.1.2 Effective Neutron Multiplication Factor of Fuel Temperature 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, one can investigate the sensitivity of the k _eff to the fuel temperature. By these data, Doppler constant can be calculated as well. Doppler broadening of capture resonance of fertile ²³⁸ U and ²⁴⁰ Pu results in more neutron captures over a wider energy spectrum, consequently, k _eff will decrease. In other word, during the slowing down of neutrons, they are more prone to be captured in

238 U and ²⁴⁰ Pu (see figure 4.7). Thus, Doppler constant is one of the main safety neutronic parameters. Although, Doppler feedback is more effective for resonances during the slowing down [25] and this coefficient is smaller in fast reactors, Doppler constant is crucial to ensure the inherent safety.

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

4.1 The Criticality Calculation with SERPENT 27

α _D ≡ dρ dT = 1

k ² dk

dT (4.1)

and Doppler constant K _D [25] by:

α D = K _D

T (4.2)

k(T ) = k(0) − K _D ln(T ) (4.3)

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

Results and Discussion

To obtain the best result for Doppler constant, a logarithmic line is fitted to the data for different temperatures versus k _eff (figures 4.8 and 4.9) for both fresh and spent fuel. As results demonstrate the Doppler constants are comparable with typical reactivity insertion and they can have significant role in core stability (table 4.1 and 4.2). Doppler constant increases for spent fuel.

The reduction of fertile ²³⁸ U and ²⁴⁰ Pu besides the presence of ²⁴¹ Am are the reasons 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 k _eff Fresh k _eff Spent

300K 1.05619±0.00019 1.00861±0.00019

600K 1.05349±0.00019 1.00655±0.00019

900K 1.05200±0.00018 1.00564±0.00021

1200K 1.05146±0.00018 1.00485±0.00019

1500K 1.05041±0.00013 1.00425±0.00014

Doppler constant [pcm] -333±57 -266±58

28 Results

400 800 1,200 1,600

1 1.02 1.04 1.06

temperature T

k

Fresh fuel

Spent fuel Line fit fresh fuel Line fit spent fuel

Figure 4.8: Fuel temperature dependence of keff for MYRRHA, model

nr 1

4.1 The Criticality Calculation with SERPENT 29

400 800 1,200 1,600

1 1.02 1.04 1.06

temperature T in K

k

Fresh fuel

Spent fuel Line fit fresh fuel Line fit spent fuel

Figure 4.9: Fuel temperature dependence of keff for MYRRHA, model

nr 2

30 Results

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

Fuel temperature k _eff Fresh k _eff Spent

300K 1.05005±0.00015 1.00331±0.00016

600K 1.04777±0.00016 1.00144±0.00017

900K 1.04648±0.00015 1.00029±0.00016

1200K 1.04566±0.00016 0.99946±0.00016

1500K 1.04484± 0.00014 0.99873±0.00014

Doppler constant [pcm] -306±47 -282±50

4.1 The Criticality Calculation with SERPENT 31

4.1.3 Effective Delayed Neutron Fraction

The fraction between all delayed neutrons, which induces fission, and total number of fission-inducing neutrons is effective delayed neutron β _eff . Delayed neutrons are produced by fission products. In MOX fuel, due to higher con- centration of Pu, β _eff is lower, however, it is essential to obtain this value.

Since larger β _eff will results in a larger neutron generation time Λ (see equa- tion 4.4), which increases the response time. Furthermore, the core is more resistant to power fluctuation and small perturbation.

Point kinetic model [4]:

dp(t)

dt = ρ(t) − β(t)

Λ(t) p(t) + X

k

λ _k c _k (t) + s(t) (4.4) where p(t) is power, ρ(t) reactivity, β(t) the delayed neutron fraction, Λ(t) neutron generation time, λ _k decay constant for the i’th delayed neutron precursor group, c _k (t) the decay precursor concentration and finally s(t) is source term. SERPENT generates an output for effective delayed neutron fraction. This value can be found in the output’s results.

Results and Discussion

As table 4.3 illustrates the β _eff reduces in the end of cycle for both models.

The presence of Americium from conversion of ²³⁸ U and lower amount of ²³⁸ U result in a reduction of β _eff . Americium has high capture cross section for thermal neutron spectrum (around 500 keV) and delayed neutron has this low energy (the average energy of the delayed neutrons is 300-700 keV) [26].

Since in both models the fuel compositions are same β _eff remains unchanged.

Table 4.3: βeff

β _eff [pcm] at BOC β _eff [pcm] at EOC

Model nr 1 329±1 324±1

Model nr 2 328±1 324±1

32 Results

4.2 Accident Condition Analysis

In this section, some of severe accident scenarios are simulated in SERPENT and k _eff and ∆k _eff ⁴ for each scenario are presented. Different scenarios of typical occurrence of void in the core such fuel pin rapture, releasing fission gases like helium into the core, blow down of steam from steam generator rapture, and complete voiding scenario will be simulated properly. Finally the relocation of melted fuel to top of the core in three distinctive cases will be examined. Some simulations are based on previously investigated scenarios while the rest are defined by the writer. This will be an assessment of MYRRHA core during some accident scenarios.

4.2.1 Partial and Total Voiding of the Active Zone of the Core

Coolant void worth indicates the reactivity changes in the core while there is void in the system. To ensure the inherent safety of the core, this parameter should always remain negative during the normal and accident scenarios. In a LBE-cooled reactor, coolant serves both as a coolant and neutron reflector.

Voiding the core results in less neutron moderation and faster neutrons while the 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 blockage and sub-channel boiling [8]. There are also other scenarios that void can introduce to the core, for instance rapture of steam generator and mixing steam into the core or release of fission gas products due to high pressure at 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 or more fuel assemblies are performed, according to MCNP assumptions (see figure 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 the rest is C (see figure 4.11). These simulations are performed for both fresh and spent fuel in one fuel assembly (see figure 4.12) and the 6 hottest fuel assemblies (see figure 4.14) in the core. Finally, all 68 FA’s are voided in the same manner.

4 Difference between actual keff and nominal state.

4.2 Accident Condition Analysis 33

Figure 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% 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 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 in which all 3 zones (A, B and C) are voided about 50%, 75%

and 100%.

Results and Discussion

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

Voiding the six hottest fuel assemblies is only performed for model nr

2. There are some apparent positive tendencies toward positive reactivity

feedback in this scenario, especially, the case of complete voiding of all six

34 Results

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

purple =zone B, orange= zone C

Figure 4.12: Dark blue represents the 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 % LBE case 2 Zone A and B: 50 % LBE, Zone C: 100 % LBE case 3 Zone A, B and C: 50 % LBE

case 4 Zone A: 25 % LBE, Zone B and C: 50 % LBE case 5 Zone A and B: 25 % LBE, Zone C: 50 % LBE case 6 Zone A, B and C: 25 % LBE

case 7 Zone A: 0 % LBE, Zone B and C: 25 % LBE

case 8 Zone A and B: 0 % LBE, Zone C: 25 % LBE

case 9 Zone A, B and C: 0 % LBE

4.2 Accident Condition Analysis 35

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

color represents voided LBE

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

are voided, orange color represents voided LBE

FAs, namely case number 9 (see figure4.19 and 4.20). Coolant void worth increases for spent fuel because of the reduction of the ratio between fissile and fertile nuclides. One should notice that the result of case number 9 for spent fuel is completely out of confidence interval of k _eff during the normal operation.

In case of voiding all fuel assemblies, the negative tendency is completely

evident, for both fresh and spent fuel. Both models nr 1 and 2 confirm the

same tendency.

36 Results

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

Fresh fuel ∆k _eff pcm Spent fuel ∆k _eff pcm

case 1 1.05021±0.00021 -19 1.00432±0.00019 7

case 2 1.05016±0.00022 -25 1.00409±0.00019 -16 case 3 1.05065±0.00019 24 1.00409±0.00019 -16 case 4 1.05013±0.00019 -28 1.00411±0.00019 -14

case 5 1.05041±0.00019 0 1.00417±0.00019 -8

case 6 1.05003±0.00020 -38 1.00447±0.00019 22 case 7 1.05009±0.00019 -32 1.00408±0.00018 -17

case 8 1.05041±0.00019 0 1.00414±0.00019 -11

case 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

Fresh fuel ∆k _eff pcm Spent fuel ∆k _eff pcm

case 1 1.04514±0.00014 30 0.998705±0.00014 -3

case 2 1.04481±0.00014 -3 0.998652±0.00015 -11

case 3 1.04485±0.00014 1 0.998838±0.00014 11

case 4 1.04493±0.00014 9 0.998790±0.00014 6

case 5 1.04510±0.00014 26 0.998849±0.00014 12

case 6 1.04511±0.00013 27 0.998832±0.00014 10

case 7 1.04514±0.00014 30 0.998790±0.00014 6

case 8 1.04490±0.00014 6 0.998822±0.00013 9

case 9 1.04495±0.00014 11 0.99054±0.00015 32

Normal operation 1.04484±0.00014 0.998731±0.00014

4.2 Accident Condition Analysis 37

case1 case2 case3 case4 case5 case6 case7 case8 case9 1.0496

1.05 1.0504 1.0508 1.0512

k

Figure 4.15: keff of one voided

fuel assembly, fresh fuel, model nr 1

38 Results

case1 case2 case3 case4 case5 case6 case7 case8 case9 1.0444

1.0448 1.0452 1.0456 1.046

k

Figure 4.16: keff of one voided

fuel assembly, fresh fuel, model nr 2

4.2 Accident Condition Analysis 39

case1 case2 case3 case4 case5 case6 case7 case8 case9 1.0036

1.004 1.0044 1.0048 1.0052

k

Figure 4.17: keff of one voided

fuel assembly, spent fuel, model nr 1