Generation IV Reactors

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Generation IV Reactors

PhD Thesis

Hunor S´ andor Gy¨ orgy

Supervisor: Szabolcs Czifrus

Budapest University of Technology and Economics Institute of Nuclear Techniques

Budapest

2017

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1 Introduction 6

1.1 Introduction of thorium . . . 7

1.1.1 Properties of thorium . . . 7

1.1.2 Past experiences of thorium utilization in nuclear reactors . 10 1.1.3 Future plans of thorium utilization . . . 11

1.2 Generation IV reactors . . . 15

1.3 Applied codes . . . 16

2 Sensitivity analyses of ALLEGRO reactor with and without thorium for infinite lattice model 20 2.1 Description of the models and burnup calculations of the ALLEGRO fuel assembly . . . 20

2.2 Burnup calculation of the reference and Th-containing ALLEGRO fuel assembly . . . 21

2.3 Investigation of the effect of the different parameters on ALLEGRO 28 2.3.1 Description of the models used in sensitivity analyses . . . . 29

2.3.2 The effect of material properties . . . 30

2.3.3 Geometrical parameters . . . 32

2.3.4 Operating parameters . . . 40

2.3.5 Summary of the effect of the investigated parameters . . . . 41

3 Calculations with infinite lattice models 44 3.1 SuperCritical-Water-cooled Reactor . . . 45

3.1.1 Reference fuel assembly of HPLWR . . . 45

3.1.2 Thorium-containing HPLWR fuel assemblies . . . 49

3.2 Very-High-Temperature Reactor . . . 56

3.2.1 Reference fuel assembly of VHTR . . . 56

3.2.2 Thorium-containing VHTR fuel assemblies . . . 60

3.3 Gas-cooled Fast Reactor . . . 66

3.3.1 Reference fuel assembly of GFR2400 . . . 66

3.3.2 Thorium-containing GFR2400 fuel assemblies . . . 69 2

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3 CONTENTS

3.4 Lead-cooled Fast Reactor . . . 74

3.4.1 Reference fuel assembly of ELSY . . . 74

3.4.2 Thorium-containing ELSY fuel assemblies . . . 77

3.5 Sodium-cooled Fast Reactor . . . 82

3.5.1 Reference fuel assembly of ESFR . . . 82

3.5.2 Thorium-containing ESFR fuel assemblies . . . 85

3.6 Molten Salt Reactor . . . 90

3.7 Comparison of the results . . . 93

4 Investigation of the possible thorium utilization in SFR reactor 96 4.1 Description of the reference full-core SFR . . . 96

4.2 Performed calculations . . . 99

4.3 The results of the reference case . . . 99

4.4 First thorium-containing SFR fuel cycle . . . 102

4.5 Thorium utilization in the full core of SFR (TSFR-FC) . . . 106

4.5.1 First few fuel cycles of TSFR-FC . . . 106

4.5.2 One possible final version of TSFR-FC . . . 111

4.6 Thorium utilization in the inner core of SFR (TSFR-IC) . . . 114

4.6.1 First few fuel cycles of TSFR-IC . . . 114

4.6.2 One possible final version of TSFR-IC . . . 117

4.7 Comparison of the TSFR core concepts . . . 119

5 Conclusions 130 Bibliography 140 A Cross sections 152 B Power distribution of the TSFR cores 154 B.1 TSFR-FC . . . 154

B.2 TSFR-IC . . . 157

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BOC Beginning Of Cycle

BOL Beginning Of Life (first cycle of the core) EFPD Effective Full Power Day

ELSY European Lead-cooled SYstem (concept of LFR)

EOC End Of Cycle

ESFR European Sodium-cooled Fast Reactor (concept of SFR) GFR Gas-cooled Fast Reactor

HM Heavy Metal

HPLWR High-Performance Light Water Reactor (concept of SCWR)

LEU Low Enriched Uranium

LFR Lead-cooled Fast Reactor LWR Light Water Reactor

MCNP Monte Carlo N-Particle code MOX Mixed OXide fuel type

MSFR Molten Salt Fast Reactor (concept of MSR) MSR Molten Salt Reactor

PWR Pressurized Water Reactor

SCALE Standardized Computer Analyses for Licensing Evaluation program package

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5 LIST OF ABBREVIATIONS

SCWR SuperCritical Water-cooled Reactor SFR Sodium-cooled Fast Reactor

TRISO TRistructural-ISOtropic fuel type

TSFR-FC Thorium-containing SFR with Full-Core thorium utilization TSFR-IC Thorium-containing SFR with Inner-Core thorium utilization VHTR Very High-Temperature Reactor

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Introduction

Today nuclear reactors operate mainly with uranium-plutonium cycle. Since the beginning of nuclear power development, thorium was considered as an alternative fuel option for reactors. The great availability makes this material a potential replacement of uranium. However, it does not contain any fissile isotope so it is impossible to start a fission chain reaction based solely on thorium. Neverthe- less, thorium can be converted to fissile ²³³U. In the past, several facilities were constructed to research thorium and nowadays theoretical as well as experimental research programs aim to determine how thorium could be optimally utilized in nuclear reactors.

Generation IV reactors, being an evolutionary step in the history of nuclear reactors, are in the mainstream research direction of nuclear industry. The unique designs and the advanced features may turn these concepts into the energy source of the future.

Expectedly, when the limited uranium deposits are going to be an issue, Gen- eration IV reactors will operate instead of the nowadays used Generation II and III reactors. This is the motive of this PhD thesis: how thorium can be utilized in the future nuclear reactors. The research focuses on the reactor-core concepts and investigates the possibility whether thorium breeding is achievable with little change to the existing Generation IV designs.

In the further part of this chapter (Introduction) the most important information about thorium and Generation IV reactors are reviewed. The second chapter focuses on the demonstration reactor of the Gas-cooled Fast Reactor (GFR), the ALLEGRO. Two main topics are discussed, namely the utilization of thorium within the demo reactor and how the different geometrical, material and opera- tional parameters influence the infinite multiplication factor of this reactor. The third chapter contains models and calculations of Generation IV reactor concepts.

Besides the reference cases which result in the base lines for later comparisons, the effect of thorium was also investigated. In the second and third chapters of

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7 CHAPTER 1. INTRODUCTION

the thesis, a fuel assembly is modelled with reflective boundary conditions (infinite lattice models).

Based on the conclusions of the third chapter, in the fourth chapter the Euro- pean concept of Sodium-cooled Fast Reactor (SFR) is investigated in more detail.

Firstly, the most important parameters are determined for the reference core. Af- terwards, the first thorium-containing SFR is discussed. From the results of this core, two different design approaches are investigated which partly or fully utilize thorium. This chapter also contains a comparison of these cores which includes safety and stability related parameters as well. As a closure, the last chapter is the summary and conclusions of my research.

1.1 Introduction of thorium

1.1.1 Properties of thorium

Thorium was discovered by Berzelius in 1829 [1]. He named the mineral which he investigated thorite which referred to Thor, the ancient Norse god of thunder.

Uranium in nature contains 0.71% fissile ²³⁵U. A fuel from natural uranium can be used directly for heavy water or carbon moderated reactors. However, in light water reactors enrichment is necessary to be able to achieve self-sustaining chain reaction. From the fertile ²³⁸U fissile plutonium isotopes can be generated. The plutonium extracted from spent fuel can be reprocessed and mixed with (depleted) uranium. This is the so-called mixed oxide (MOX) fuel cycle. Most of the nuclear reactors are using uranium-plutonium fuel cycle nowadays [2].

Thorium can be the prospective fuel for nuclear reactors and its reserves rep- resent an attractive potential energy supply with little or no CO₂ emissions. The great availability makes this material a supplement or potential replacement of uranium. Thorium occurs in the crust of earth about 7 ppm which concentration is about three times the availability of uranium (2.5-3 ppm). The commercially available thorium reserves are several million tons [3]. Natural thorium consists of essentially one isotope,²³²Th. This is an alpha decaying isotope with a half life of 1.4·10¹⁰years. Thorium is a fertile material which, upon capturing a neutron, may undergo several nuclear decay processes, leading to the fissile ²³³U. This process is analogous to the one in which ²³⁹Pu is generated from ²³⁸U. Both changes can be seen in Fig. 1.1. The neutron capture, which leads to the fissile ²³³U isotope, is interrupted by two intermediate nuclei, ie. ²³³Th and ²³³Pa. It is important to highlight that ²³³Pa has a significant neutron capture cross section and leads to

234U which is not fissile. From another perspective, ²³³Pa is similar to²³⁹Np in the case of U-Pu cycle; however, ²³⁹Np has a much shorter half-life (about 2.35 days vs. 27 days for²³³Pa) and smaller neutron capture cross section. Because of these

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Figure 1.1: The transmutation cycles of thorium and uranium

properties, ²³³Pa can be a significant neutron poison in the case of Th-U, or for the mixed Th-U and U-Pu cycles [1].

Because of the fact that natural uranium contains fissile²³⁵U the development of the uranium fuel cycle was an obvious and easier choice than thorium. Nuclear reactors apply oxide type fuels nowadays, e.g. uranium dioxide. A similar isostruc- tural compound (thorium dioxide) can be used for thorium as well, which can be the basis of thorium-containing reactor designs. Thorium has a significantly lower density (11.72 g/cm³) than that of uranium (19.1 g/cm³). The theoretical density of thorium dioxide is 10.00 g/cm³ while the value of this parameter is 10.96 g/cm³ for uranium dioxide. Some advantageous properties make thorium dioxide an ap- pealing alternative. Thorium dioxide is one of the most refractory and chemically nonreactive solid substance. Thorium based fuel materials have higher melting point than the uranium based ones: for thorium metal it is 1750 ^◦C compared to 1135 ^◦C for uranium metal and 3300 ^◦C for ThO₂ while 2800 ^◦C for UO₂. The same relation is valid for the thermal conductivity: the values for thorium metal is 54 W/(m·K) while for uranium metal it is 27.6 W/(m·K) (at room temperature).

The thermal conductivity of ThO₂, similarly to UO₂, decreases with the temperature but at 800^◦C it is 5 W/(m·K) (the value for UO₂ is 3-4 W/(m·K)). Thorium has also a lower thermal expansion coefficient than uranium. The thermal properties suggest that the thorium cycle occurs more favourably than uranium either as metal or oxide form from a safety point of view [3, 4].

As it was mentioned before, thorium can be transmuted into the fissile, non- naturally occurring uranium isotope, ²³³U which has excellent nuclear properties.

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232Th, however, is not fissile itself. To improve resource utilization, it is necessary to have recycling with breeding. For U-Pu fuel cycle, the so-called Purex process has been used for industrial reprocessing for more than 30 years. There are a few reprocessing methods available for thorium fuels nowadays, e.g. Thorex, Thorex2, acid Thorex, non-aqueous techniques, etc. [5–7]. The Thorex process has been investigated for many years in laboratories [8]. With the above mentioned methods very good recoveries can be achieved [9]. Nevertheless, these need more development since they are not appropriate for large-scale separation. An efficient dissolution process, corrosion resistant materials of construction, modifications to deal with ThO₂-PuO₂ fuels are a few of the main challenges [6, 10]. The cost of reprocessing ThO₂-UO₂ fuel is estimated to be approximately 30% higher than that of reprocessing the low-enrichment uranium oxide fuel [11]. Recently India is developing a laser-based separation technique. With this technique the produced uranium can be cleaned from the ²³²U side product by separating it out [7]. Nev- ertheless, considerable data are available about the reprocessing studies from the past, which can help to find suitable processes and designs quickly [6].

The excellent chemical stability of thorium dioxide suggests the possibility of direct disposal. Nevertheless, it is a good choice for burning excess plutonium in once-through fuels since thorium is being lower in the periodic table than uranium or plutonium. This results in much lower quantities of long-lived minor actinides [7, 8].

It is also important to highlight that the recycling of thorium-based fuels is more complex due to the ²³²U contaminant. This uranium isotope has a half-life of 69 years and its daughter products are intense gamma and alpha emitters with short half-lives (e.g. ²⁰⁸Tl emits gamma radiation with 2.6 MeV energy). This requires that the entire spent fuel handling process must be done under proper remote conditions. However, this feature makes thorium-based fuels inherently proliferation resistant as well. A further disadvantage is the fact that a significant amount of knowledge base on thorium fuel cycle is very old and not all documen- tation may be available [1, 11].

It is essential to have an initial fissile ”seed” or ”driver fuel” in case thorium is applied within the reactor core. ²³³U which can be occurred as the result of neutron capture can be retrieved via reprocessing and separation. With the application of thorium it may be possible to produce more fissile material than is consumed by the reactor. The parameter which can be defined as the ratio of production and consumption of fissile materials is the conversion ratio [12]:

CR = Average rate of fissile atom production Average rate of fissile atom consumption.

If this parameter is equal to or is above 1.0, the reactor is called ”breeder”.

This type of systems produces more fissile material than it consumes and with the

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utilization of this, a closed fuel cycle can be achieved. Accordingly, the system does not need any external fissile material so it can operate independently. The value of the conversion ratio is about 0.5-0.6 for the conventional PWRs. The utilization of plutonium MOX recycling increases this parameter to around 0.7.

With more harder neutron spectrum higher conversion ratio can be achieved which enhances the importance of fast reactors [2].

The Fissile Inventory Ratio (FIR) can also provide information about the breeding capabilities of nuclear reactors. This parameter can be defined by the following equation [13]:

FIR = Fissile inventory in discharged fuel Fissile inventory in charged fuel .

The delayed neutrons change the dynamic response time of the system to the reactivity changes which make the fission chain reaction within the reactor con- trollable via control systems (e.g. control rods). The less the delayed neutron fraction is, the more responsive control system is necessary for safe and stable operation [12, 14]. The delayed neutron fraction of ²³³U is 0.276%. This value is significantly lower than that of²³⁵U (0.650%) but slightly larger than that of²³⁹Pu (0.210%) [15].

1.1.2 Past experiences of thorium utilization in nuclear re- actors

In the past, several facilities were constructed to research thorium. Since thorium dioxide has great stability at high temperatures, the development how it can be applied in high temperature reactors began in which the coolant was gas. Small pyrolic carbon layers and silicon carbide coated particles (TRISO) were designed in which enriched uranium/thorium oxide was applied. These fuel particles were embedded in graphite balls similar to the ones which were used in German pebble- bed reactors [16]. From 1960s there were a few high temperature prototype reactors which used thorium/uranium in their lifetime: Peach Bottom HTR in the US, DRAGON HTGR in England, and AVR pebble bed reactors in Germany. The experiments were followed by industrial prototypes: Fort St. Vrain Reactor in Platteville HTGR, which is based on the Peach Bottom HTR and the THTR which was a more advanced pebble-bed reactor [16, 17]. These systems, however, had some costly technological incidents and it was decided to close them. In summary, it can be deduced from the experiments that very high burnups could have been achieved with these kind of reactors and they could be used as converters for supplementary fissile materials. A major drawback is the costly fuel fabrication and when thorium is applied, the necessity of reprocessing [16].

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Thorium was used in other reactor types as well. The Elk River BWR used U-Th fuel in the 60s, and despite its fruitful operation, it was closed because its limited power. The Edison Indian Point-1 PWR operated between 1962 and 1980 and in its core thorium-based fuel was used as well. In the Shippingport PWR a special experiment was performed in which thermal breeding was investigated with thermal or epithermal neutrons with uniquely designed fuel assemblies. The research demonstrated that slightly higher ²³³U production can be achieved than that burnt. In the Netherlands, between 1974 and 1977 a small sized homogeneous slurry reactor worked, which used UO₂/ThO₂ micro-particles. In this system the fuel was suspended in a liquid moderator instead of taking the form of bars surrounded by a moderator [16].

In the US, the Molten Salt Reactor Experiment (MSRE) was performed. The reactor used homogeneous molten fluorides and with thermal breeder configuration it could have run with U/Th salts [16].

In Russia and in France the use of thorium was studied in fast neutron spectrum as well, e.g. in BN-800 (see [3] but unfortunately no detailed information is available). The ability of iso-generation of fissile material was demonstrated; however, the performances achieved in this field were lower than those for uranium- plutonium cycle. It is caused by the fission cross section of thorium, which is about three times smaller for fast neutrons than that of ²³⁸U [3].

The conclusion of this experiments is that thorium can be utilized in almost any type of reactor. With seed-blanket configuration the reprocessing effort can be reduced but the complexity of the core increases [16].

1.1.3 Future plans of thorium utilization

According to the recent scenarios of thorium utilization strategies, in short term (before 2030) thorium is planned to be used as additive or in separated thorium- containing fuel rods. Thorium would be applied about 5-10% in uranium/plutonium oxide fuels. This can help to flatten the core power and reduce the necessary amount of burnable poisons e.g. gadolinium and even produce ²³³U. The aim of this short term scenarios is to collect irradiation experiences (possibly in Gen III LWR reactors) and it can be a first step of thorium utilization. However, it is not planned to use thorium to save uranium or improve the waste management.

In medium term (from 2030 to 2050) the fast reactor development is the main objective of the nuclear community. Thorium is going to be used in LWRs to reduce the uranium consumption and it will also be important to find the optimal breeding for recycling. Not only as it is planned in the early short term investigations where thorium is planned to be used in mainly homogeneously with uranium and plutonium, in this case heterogeneous fuel assemblies are suggested as well, where thorium and ²³³U are spatially separated from uranium and plutonium.

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If the required industrial reprocessing technologies are available, the 100%

thorium-cycle may be achievable in very long term (after 2050). One aim of this is the replacement of Generation II and III reactors. Additionally, the plutonium inventories should be dedicated to breed ²³³U from thorium. There are also Generation IV reactor concepts which utilize thorium such as MSR or the Canadian design of supercritical water reactor. In addition, hybrid reactor concepts (e.g. accelerator-driven systems) can also be a possible approach of thorium application in the future [2].

Connected to the above mentioned scenarios, nowadays theoretical as well as experimental research programs, such as the irradiation program in the Halden reactor aim to determine how thorium could be optimally utilized in nuclear reactors [2, 11]. One aim of the ”Seven-Thirty” program is to provide data for licensing thorium based fuels in today’s LWRs. In these experiments (Th,Pu)O₂ and (Th,U)O₂ pellets are investigated which can be manufactured on an industrial scale for operating reactors [18]. Investigations were performed for Th-MOX- fuelled PWRs and a combined Th-MOX and UO₂ cores as well. These cores can provide a cheap and easy way to reduce plutonium stockpile [19].

For the use of thorium, many extensive studies have been developed during the years. In the literature one can find almost any kind of reactor modified in a way that thorium would be possible to apply within it. There are investigations which focus on the use of thorium in PWR reactors. For this reactor type many different concepts can be found in which the fuel is LEU/Th homogeneous mixture, or Pu/Th based fuels or it is planned to apply the recycled²³³U with thorium. There are many designs (e.g. heavy water cooled PWR configuration [20]), the detailed description of which is not part of this thesis (a few examples can be found in Ref. [21–24]).

The Reduced-moderation Boiling Water Reactors (RBWR) is recently considered as a thorium break-even fuel cycle. This type of reactors are similar to ABWR but the pins are arranged in a tight triangular lattice. The core is loaded with Th-Pu-(MA) and Th-²³³U fuel pins [20, 25].

Another option for thorium utilization can be the CANDU reactor with its pressurized heavy water design because it is possible to use thorium oxide as its fuel [26].

In India, where it is planned to meet 30% of its total power requirements in 2050 by using thorium-fuelled reactors [26], the currently operating Pressurized Heavy Water Reactors (PHWR) are parts of a long-term plan in which India is going to utilize thorium eventually. As the first stage, with PHWR reactors fissile plutonium is produced which can be used later in the second stage in plutonium- based fast breeder reactors. The final stage is planned to use ²³³U/thorium-based breeders. A few heavy water reactors already apply thorium within their core in

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order to flatten the neutron flux [27, 28]. In the CIRUS research reactor (medium flux heavy water reactor) irradiation tests were performed with thorium-based fuels. The large scale utilization of thorium is planned to be in Advanced Heavy Water Reactors (AHWR). These reactors are of vertical pressure tube type, heavy water moderated, boiling light water cooled reactors whose fuel is a mixed oxide of (Th-Pu) and (Th-²³³U) [28]. The research reactor named KAMINI, moderated and cooled by light water operates with the fissile ²³³U which is produced in the Fast Breeder Test Reactor (FBTR). The latter one is a sodium-cooled system in which the transmutation of a few thorium bundles is tested as well [16].

Extended research field is connected to the thorium-fuelled sodium-cooled fast reactors. The parameters of these cores vary widely. One can find a core whose thermal power is 1000 MW and based on the SuperPRISM reactor but modified to achieve high conversion ratio. The core is fuelled with metalic thorium and contains 192 driver and 103 blanket assemblies [20]. At the University of California in Berkeley a 3000 MWth sodium-cooled reactor is developed which uses UThH fuel (SFR-ThH) and this results in an intermediate spectrum within its core [29].

A break-even SFR core is researched in Ref. [25] where the core applied nitride fuel and thorium is placed in a blanket around the seed part. There are also plans to discuss how the different type of reactors such as the MSR and PWR can synergism with SFR cores with Th-²³³U fuel cycle [21]. Another concept is the seed- and-blanket (S&B) configuration core of SFR where an annular core is designed.

In the central region an internal blanket can be found then the seed and finally the outermost blanket. The blanket parts of the core are fuelled with thorium.

After each cycle a fraction of the seed can be recycled and the blanket is shuffled inward [30, 31]. A significant part of this thesis focuses on sodium-cooled fast reactors, specifically on the European concept. In this work different fuel loading approaches are discussed in which the originally designed core which is planned to operate with MOX fuel can utilize thorium with little changes. This research can correspond to the medium and long term aims of the thorium utilization strategies.

In the literature, the Lead-cooled Fast Reactors are also investigated in terms of thorium utilization. The researched LFR contains (Th,TRU)O₂ fuel whose geometry is similar to STAR-LM LFR design. The core is designed with hydride moderators to reduce the spectral hardening during coolant voiding [32].

From the successful past experiences mentioned before, the researches of Molten Salt Reactors are still running and these are also part of the Generation IV reactors [20, 26, 33]. It was also demonstrated earlier that the high temperature reactors which fuel is thorium-based particles are promising. Since this kind of reactors are also part of the Generation IV framework, researches are conducted in order to develop these as well [24, 26]. One example can be that in Russia, a high-temperature gas-cooled reactor installation (HTGRI) is researched in which

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thorium can be used. The designed fuel of this core contains micro-fuel particles from plutonium and ²³²Th. This type of reactor is similar to the HTGR reactors [34].

Analyses occur for the so-called Fusion-Fission Hybrid systems with thermal and fast spectrum. In these systems inertial confinement fusion (ICF) is utilized to generate thermal power and D-T neutrons which are used for breeding thorium in the surrounding subcritical blanket. In the thermal case, graphite is used for moderating the neutrons [21].

There is another promising unique concept for the use of thorium which is worth mentioning, namely its use in accelerator driven subcritical systems e.g. the Thorium-Driven Fast-Neutron Energy Amplifier [15].

One can find unconventional suggestions for thorium utilization as well. One of the most extreme concepts is the idea to exploit thermonuclear explosions for breeding (via explosions in a 200 meter diameter cavity which is surrounded by thorium) [35].

As it can be seen from this short review, the options of thorium utilization are extensively investigated. Many concepts and suggestions were born in the last 50 years but the industrial use is still awaited.

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1.2 Generation IV reactors

Nuclear energy offers a very effective low carbon source of energy while the demand for electric power is increasing due to the increasing world population and longer health expectancy. This is the reason why many countries are building or planning to build nuclear reactors nowadays. In addition, the development of nuclear energy becomes more important to sustain energy supply in global perspective.

Nuclear reactors can be classified into four categories. The Generation I nuclear energy systems were prototype reactors which operated in the 1950s and the early 1960s. Mainly Generation II reactors are operating these days which are the commercial reactors. These were constructed from the late 1960s to early 1990s.

Today the technology of Generation III reactors is available. These are advanced, evolutionary models of the Generation II nuclear energy systems. To keep up the significant role of the nuclear reactors, new systems will be necessary to replace the retiring plants. Innovative designs of the Generation IV reactors obtain significant attention because of the improved safety and reliability, sustainability, economics, physical protection and proliferation resistance. These nuclear energy systems are capable of extending their benefits to e.g. generate hydrogen, district heating or desalinate water etc. [33, 36].

One of the challenging technology goals is the sustainability, which means the ability to meet the needs of the present generation while enhancing and not jeop- ardizing the ability of the future generations to meet society’s needs indefinitely into the future. This includes the conservation of resources, protection of the en- vironment via resource utilization and waste management as well. For the better utilization of the resources recycling of the used fuel is inevitable. Additionally, Generation IV nuclear energy systems focus on substantial reduction in the amount of wastes and their decay heat as well since the long-term repository spaces are limited.

Closing the fuel cycle can be a viable option to handle this issue. With recycling, plutonium and uranium can be recovered from the spent fuel and can be used for making new fuel. Nowadays recycling is not economical due to the large amount of widely available cheap uranium. However, this will change when the resources are depleting; then the closed fuel cycle will be preferable. Other benefits can be realized as well, such as the reduced amount of high-level radioactive residues, the transmutation of long-lived heavy elements, etc.

The economic requirement means the competitiveness of nuclear energy. With the number of innovative advances in the systems and the fuel cycle efficiency the costs can be decreased. The cost of nuclear energy is competitive with coal or oil but the construction costs should be reduced. In addition, the licensing needs to be more predictable as well. The innovative fabrication, construction techniques and possible modular designs help to reduce the economical risks of nuclear projects.

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The safe and reliable operation, the improved accident management and minimized consequences are the highest priorities of these systems. To achieve these goals, reactors are designed with inherent safety features. Besides, the public confidence in nuclear safety needs to be increased. Proliferation resistance and physical protection mean controlling and securing nuclear material and nuclear facilities which can be achieved by appropriate design. Today nuclear reactors have a robust design and added precautions against the acts of terrorism. Future nuclear energy systems are going to be designed with even higher degree of resistance to nuclear material diversion or undeclared production. The improved physical protection against terrorist attacks is also an emphasised purpose. Significant R&D is needed in every field to entirely fulfill these requirements [36].

The Generation IV International Forum (GIF) is an international co-operation framework, whose main purpose is to coordinate the development of GenIV systems and support R&D among the member countries. The members of the Genera- tion IV International Forum (GIF) selected six reactor types out of nearly 100 concepts in 2002 which can be promising. These are the Very-High-Temperature Reac- tor (VHTR), the SuperCritical-Water-cooled Reactor (SCWR), the Sodium-cooled Fast Reactor (SFR), the Gas-cooled Fast Reactor (GFR), the Molten Salt Reactor (MSR) and the Lead-cooled Fast Reactor (LFR). Detailed descriptions of these reactors can be found in the third chapter. These reactor types are planned to be in operation after 2030 when many currently operating nuclear power plants will be at or near the end of their operating licenses. Many different concepts are investigated (different size e.g. small modular or large monolithic, different fuel assembly concepts, etc.). Each reactor type is innovative and consists challenges both in fuel cycle and in reactor technologies. Four of the six reactor types are definitely fast reactors, which, with the aid of extensive recycling, can reduce the radiotoxicity of all wastes by several orders of magnitude via actinide management [36].

1.3 Applied codes

For the calculations of the following two chapters, the code MCNP6 is used. The different reactor types are evaluated according to the rate of change of the infinite multiplication factor and the isotope composition [37–39].

MCNP is a general-purpose, continuous-energy, generalized-geometry, time- dependent Monte Carlo N-Particle code which can simulate neutron, photon, elec- tron or other particles transport. It is capable to determine the eigenvalues of fissile systems, calculate shielding, dosimetry, detector response and many other applications as well [40]. Originally, many special-purpose codes were developed by the Los Alamos National Laboratory such as the MCS, MCN, MCP, MCG. Firstly, the MCN which was a three dimensional neutron transport code was merged with

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MCG, which was a gamma transport code. This was called MCNG. Later, the photon physics was also added, and the MCNP was created [41].

MCNP is capable to use the evaluated nuclear data files (ENDF) [42]. In the calculations the ENDF/B-VII.1 was used which consists of 423 nuclides in seven temperatures. These pointwise cross section data are given for all reactions which can be inevitable for reactor simulations. Thermal neutrons can be described as free gas or S(α,β) models in MCNP [40].

The code is capable of calculating adjoint-weighted reactor point kinetics parameters, e.g. delayed neutron fractions. An algorithm was implemented into the code by the developers which performs adjoint weighting of tallies during a forward power iteration method which does not increase the computation time significantly [43].

The Monte Carlo-based depletion methodology consists of a transport solver and a Bateman equation solver. In case of MCNP6 the Bateman equation solver is the CINDER’90 code which calculates the atom densities to the next time step.

At every time step, the transport solver determines destruction and creation co- efficients for the Bateman solver, while the Bateman solver provides new atom densities at the next time step for the transport solver [38, 39, 44].

For the burnup calculations which are presented in Chapter 4 (full-core investigations) a three-dimensional continuous-energy Monte Carlo reactor physics burnup calculation code, Serpent 2 was used. The program is developed by the VTT Technical Research Centre of Finland. The reason why MCNP was replaced by Serpent 2 is that regarding the speed of burnup calculations, the performance of this code is better than other general-purpose Monte Carlo codes because it uses the Woodcock delta-tracking method and a single unionized energy grid for all microscopic and macroscopic cross sections. The main advantage of the delta- tracking method can be experienced when the spatial dimensions of the geometry are shorter than the mean-free-path of the neutron. In such cases, neutrons can move directly to their next collision site without stopping the track at each boundary crossing. This can make the transport simulation faster. The reaction rate integrals and cell flux tallies are calculated based on the collision estimator which is theoretically not so efficient. However, analyses showed that there is no significant difference in efficiency between the two methods (the collision estimator and the track-length estimator) in reactor calculation because of the high collision density. Limitation can be the calculation of shielding or far located places from the reactor core [45].

Serpent 2 is also capable of the calculation of point kinetics parameters. For the estimation of this values, the iterated fission probability method was implemented [46].

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For depletion calculations, besides the conventional algorithms (Euler and predictor-corrector method with linear interpolation for the corrector calculation) higher order methods are available as well. The Bateman depletion equations are solved with CRAM matrix exponential method. The results of the program were compared with benchmarks and it was compared to other codes as well [45,47,48].

Compared to other general-purpose Monte Carlo codes, the reaction rate tallies required for the task do not need to be defined separately for each problem in Ser- pent 2. Another important difference is that even a large number of tallies do not change the running time significantly. The first version of the code, ie. Serpent 1 had an important limitation on the depletion zones that the memory usage was excessive in three dimensions due to the unionized energy grid approach. This issue was fixed in Serpent 2 via different optimization possibilities [45].

The geometry routine of Serpent is similar to that of MCNP. A model can be built from elementary surface types. Using universes, transformations and repeated structures (square and hexagonal lattices) it is possible to divide the geometry into multiple levels. The Doppler-broadening can be taken into account by a built-in routine [45].

The current version of Serpent is capable to run neutron transport simulations in external and k-eigenvalue critically source modes. Dynamic simulation mode is under development, which is going to be useful to simulate short reactivity initiated transients. The gamma transport modules were recently added as well [45]. The code is widely used for group constant generation, fuel cycle analysis, etc. for Gen III and Gen IV reactors [49].

The Monte Carlo criticality calculations are affected by cycle-to-cycle correla- tions in the fission source. This can cause an uncertainty which can be even more than five times the statistical uncertainties mainly when the dominance ratio is close to 1 [50]. The dominance ratio (k₁/k₀) can be defined as the ratio of the eigenvalue of the fundamental node (k₀ = k_eff) and the eigenvalue of the first higher node (k₁). This parameter is connected to the stability of the system regarding fluctuations (xenon, void, etc.). When the dominance ratio is close to 1.0 the system is more susceptible to oscillations [51]. To avoid this issue, these systems require many independent calculations [50]. In some cases the uncertainties can be underpredicted by a factor of 40 or more [52]. To obtain good statistics, it is necessary to perform a simulation with large computational time. The convergence of the fission source is one of the highest concern. For this, the Shannon entropy was introduced which can help to decide whether the fission source has reached the sta- tionary distribution [53]. This can depend on the number of histories, cycles and the model as well. Besides the fission source convergence and the cycle-to-cycle convergence issues, the undersampling fission source regions also contribute to the increased uncertainties [52]. Although the uncertainties of Monte Carlo burnup

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calculations are not subject of this thesis, in the literature one can find many related articles and investigations. The predictor–corrector methods are known to be conditionally stable (i.e. stable in the case of appropriately small time steps), however numerical instabilities can occur even when integral quantities such as k_eff seem stable [54]. Beside the method, the statistical error and the uncertainties in the cross sections can lead to additional errors as well. It was investigated in Ref. [55] that for a fast reactor burnup calculation which includes two time steps, the statistical errors cause less than 1% error (same in Ref. [56]), while the cross section errors result in 2-5% error in nuclide densities. For fission products the error can exceed 7%. Similar results can be found in Ref. [57] which also highlights the importance of the reliable stochastic transport calculations (flux error should be less than 10%) since it can significantly contribute to the isotopic concentration errors. The reviewed investigations suggest that with good input parameter choices the statistical error of the stochastic calculations can be reduced. To decrease the cross section uncertainties caused errors more reliable nuclear data are necessary.

Another program was also used in this work for several supporting calculations.

These were performed with the aid of the Standardized Computer Analyses for Li- censing Evaluation (SCALE) program package which is a modelling and simulation suit developed by Oak Ridge National Laboratory. It provides a comprehensive, verified and validated tool set and able to handle issues in topics connected to reactor physics, criticality, shielding etc. The code package contains 89 computational modules for various tasks and these can even provide problem-dependent cross-section data as well. It is possible to edit and analyze the program created cross section data too. Since the program is capable to handle numerous issues, the introduction focuses on the Tools for Sensitivity and Uncertainty Analysis Methodology Implementation (TSUNAMI) module of SCALE which is responsible for uncertainty and sensitivity calculations and was used in this thesis. This SCALE control module integrates a material input processor, a cross-section data processor, cell-weighted cross-section data calculator, neutron transport solver, and cross-section sensitivity and uncertainty calculator. The transport solver is XSDRNPM for the one-dimensional modeling which is based on a discrete ordi- nates method. The SAMS module is responsible for the determination of the k_eff sensitivities based on nuclide type, reaction type and energy. For the uncertainties the program uses energy-dependent cross-section-covariance matrices. The SCALE uses a 44 group covariance library for k_eff uncertainty quantification [58].

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Sensitivity analyses of ALLEGRO reactor with and without thorium for infinite lattice model

2.1 Description of the models and burnup calcu- lations of the ALLEGRO fuel assembly

Since the investigation of the behaviour of fast reactors are recently a very popular research field, the calculations of this chapter of the thesis are focused on sensitivity analyses of one fast reactor concept. As an examined system, the demonstration reactor of the Gas-cooled Fast Reactor was chosen. The most reliable information were available for this core because of our collaboration in different projects such as the framework of the GoFastR project [59]. This reactor is called ALLEGRO, in which it would be possible to test the ceramic fuels designed for GFR2400 [60]. The coolant is helium because its absorption cross section is very small (transparent), chemically inert and in this way compatible with the structural materials [61].

First of all, burnup calculations were performed with infinite lattice models for the reference fuel assembly and for thorium-containing ones as well. In this way the effect of thorium can be examined. In the second part, sensitivity analyses were performed in which different geometric and material parameters are varied to understand how they change the infinite multiplication factor.

The thermal power of the demo reactor is planned to be 75 MWth (according to the present reference design). The average power density is 30.4 MW/t-HM.

The pressure of the coolant is 70 bars and the average coolant temperature will be 400^◦C.

The core of the ALLEGRO facility will contain 87 hexagonal fuel assemblies [59]. Two kinds of fuel are designed for this reactor. The starting config-

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21 CHAPTER 2. SENSITIVITY ANALYSES OF ALLEGRO

Figure 2.1: The geometry of the ALLEGRO fuel assembly (blue circles: (U,Pu)C pins)

uration is built up from MOX-containing fuel pins with stainless steel cladding.

The final ALLEGRO configuration will contain ceramic fuel pins. In the thesis the ceramic fuel case was examined. In both cases, above and under the core axial reflectors will be used, the material of which will be a mixture of ZrC and SiC.

The active length of a fuel rod is 0.86 m and the total length of a rod bundle is 1.35 m. The ceramic fuel assembly will contain 90 fuel pins with (U,Pu)C pellets.

A central tube is designed in every assembly to be the pillar of the structure. The cladding will also be made of a ceramic material (SiC) [62]. As an inner cover of the cladding, a thin rhenium layer is used, and in this way the interaction between the cladding and the fuel can be prevented [63, 64]. A more detailed description of the fuel pin can be found in the next section.

In the model, the PuC content was 28.44% and the natural uranium carbide content was 71.56%. Due to the fact that the helium density does not change significantly, this parameter of the coolant was modelled with an average value.

The fuel assembly model can be seen in Fig. 2.1.

2.2 Burnup calculation of the reference and Th- containing ALLEGRO fuel assembly

To understand the effects of the presence of thorium, the reference fuel assembly of ALLEGRO and further three cases were investigated and compared to each other. The calculations were performed for a single fuel assembly with reflective boundary conditions. In the models, which contain thorium, 6, 12 and 18 fuel pins were replaced with ThC fuel pins, respectively. The positions of the thorium

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Figure 2.2: The investigated cases for the ALLEGRO model (blue circles: (U,Pu)C pins, red circles: ThC pins)

pins can be seen in Fig. 2.2. Burnup calculations were performed to analyze the production of ²³³U and how other important parameters (multiplication factors, effective delayed neutron fractions, neutron spectra) change. Since the fabrication of the designed fuel pins of the demo ALLEGRO reactor may be expensive, in this investigations the thorium-containing pins do not include fissile isotopes because it would result in additional costs. Thus the calculations shown below can be treated as a testing, the aim of which is to analyze the effects of pure thorium carbide containing fuel pins in gas-cooled systems.

In the examinations, the investigated period was 500 effective full power days (EFPD). The time steps are the following: the first one was chosen to be after 2 EFPD and then calculations are performed for every 50th day. In the MCNP6 simulations 2500 neutrons are started in every cycle and for every time step 1000 active cycles were defined.

Firstly, the trends of the infinite multiplication factors are compared in Fig. 2.3.

The initial values are shifted so that all of the starting points be 1.0. Accordingly, the trends can be compared and the pace of decrease can be determined without biasing the tendencies. The results show that in the first approximately 100 days the normalized infinite multiplication factor is less than that of the reference case.

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0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0

0 . 9 6 5 0 . 9 7 0 0 . 9 7 5 0 . 9 8 0 0 . 9 8 5 0 . 9 9 0 0 . 9 9 5 1 . 0 0 0

Normalized infinite multiplication factor (-)

E f f e c t i v e f u l l p o w e r d a y ( d a y s )

R e f e r e n c e c a s e 1 s t c a s e ( 6 T h p i n s ) 2 n d c a s e ( 1 2 T h p i n s ) 3 r d c a s e ( 1 8 T h p i n s )

Figure 2.3: The change of the shifted infinite multiplication factors for the ALLEGRO reactor

The reason is that the produced²³³Pa has a long (27 days) half-life with significant neutron capture cross section and it decays to ²³³U, which is already fissile. At the end of the examined 500 effective full power days the infinite multiplication factor of the reference and the first cases decreases 2.5%. In the second case, the decrease is 2.2% while in the third case it is only 1.8%.

The average burnup in the ALLEGRO models was 15 MWd/kgHM at the end of the investigated cycle. Fig. 2.4 shows that the increasing amount of thorium decreases drastically the initial infinite multiplication factor. This is caused by the fissile material lost due to the replacement of original fuel with thorium-fuelled pins. The plutonium content is really high in the fuel pins (28.44%) so in this way the thorium rods cause a significant fissile isotope loss. Accordingly, the less decreasing tendency of the multiplication factor might not be able to compensate this initial decrease in a finite reactor.

The production of ²³³U was investigated as well. Fig. 2.5 shows that in the examined time interval the change of fissile isotope content (which includes the produced²³³U and²³⁵U) is almost linear in the thorium-fuelled pins, which suggests that for a longer period significantly larger production can be achieved. The values are normalized with the initial mass of the thorium-fuelled pins. Tab. 2.1 shows the production ratio values (m_fissile/m_ThC) at the end of the simulation. It is noticeable that the more thorium is applied in the investigated fuel assembly, the more ²³³U can be produced. This result suggests that the thorium caused spectrum changes

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0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 1 . 1 6

1 . 1 8 1 . 2 0 1 . 2 2 1 . 2 4 1 . 2 6 1 . 2 8 1 . 3 0 1 . 3 2 1 . 3 4

1 . 3 6 C a l c u l a t e d r e s u l t s

F i t t e d l i n e a r

Initial infinite multiplication factor (-)

N u m b e r o f t h o r i u m - c o n t a i n i n g f u e l p i n s ( - )

k ^{i n i t}_{i n f}[ - ] = ( - 0 . 0 1 0 3 ±0 . 0 0 0 2 )⋅N T h - p i n s[ - ] + ( 1 . 3 5 4 1 ±0 . 0 0 1 8 )

Figure 2.4: The change of the initial multiplication factors in the ALLEGRO reactor

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0

0 . 0 % 0 . 2 % 0 . 4 % 0 . 6 % 0 . 8 % 1 . 0 % 1 . 2 % 1 . 4 %

Normalized233 U amount in the Th pins (-)

E f f e c t i v e f u l l p o w e r d a y ( d a y s ) 1 s t c a s e ( 6 T h p i n s )

2 n d c a s e ( 1 2 T h p i n s ) 3 r d c a s e ( 1 8 T h p i n s )

Figure 2.5: The normalized amount of fissile isotopes in the thorium rods for the ALLEGRO reactor (m_fissile/m_ThC)

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Table 2.1: The produced²³³U ratio in thorium-containing ALLEGRO at 500 EFPD Case Mass percentage

First case 1.2996%

Second case 1.3891%

Third case 1.4974%

help the fissile isotope production. According to the production ratio table, the achieved ²³³U content is about 1.5% at 500 EFPD.

The spectra can be seen in Fig. 2.6 for BOC and EOC in the case of the reference model and the third case. The values are integrated for the pins. The difference between the results was magnified for better visibility. The spectrum was calculated in 100 energy groups. Negative difference bars mean that in the thorium-containing case there are more neutrons in that energy group than there are in the reference case. If it is positive, the neutron flux is higher in the reference case.

As it is expected for a fast reactor, the neutron flux is negligible in the energy regions below 10⁻⁴ MeV. When the energy is less than 2 MeV, in the thorium- containing case there are more neutrons than in the reference case. Higher neutron flux is observed in the energy regions above 2 MeV in the reference case than in the 3rd case. These statements remain valid for BOC and EOC as well. This helps the production of ²³³U, since above 1 MeV the neutron capture cross section of

232Th strongly decreases (Fig. A.1).

The effective delayed neutron fractions are shown in Tab. 2.2. It can be seen, that these are very small values, which is caused by the high plutonium content.

The application of thorium does not change the values significantly at BOC or EOC.

Table 2.2: The effective delayed neutron fraction in ALLEGRO for BOC and EOC

BOC EOC

Reference case 0.00325±0.00015 0.00321±0.00013 First case 0.00339±0.00014 0.00321±0.00014 Second case 0.00317±0.00013 0.00338±0.00014 Third case 0.00325±0.00013 0.00322±0.00013

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1 E - 9 1 E - 8 1 E - 7 1 E - 6 1 E - 5 1 E - 4 1 E - 3 0 . 0 1 0 . 1 1 1 0 0 . 0 0 E + 0 0 0

1 . 0 0 E + 0 1 3 2 . 0 0 E + 0 1 3 3 . 0 0 E + 0 1 3 4 . 0 0 E + 0 1 3 5 . 0 0 E + 0 1 3 6 . 0 0 E + 0 1 3

1 E - 9 1 E - 8 1 E - 7 1 E - 6 1 E - 5 1 E - 4 1 E - 3 0 . 0 1 0 . 1 1 1 0

0 . 0 0 E + 0 0 0 1 . 0 0 E + 0 1 3 2 . 0 0 E + 0 1 3 3 . 0 0 E + 0 1 3 4 . 0 0 E + 0 1 3 5 . 0 0 E + 0 1 3 6 . 0 0 E + 0 1 3 Φ (1/(cm2 ⋅s))

E n e r g y ( M e V ) R e f e r e n c e c a s e ( B O C )

3 . c a s e ( B O C )

- 5 0 - 4 0 - 3 0 - 2 0 - 1 0

0

1 0 2 0 3 0 4 0 5 0

Difference (%)

D i f f e r e n c e

Φ (1/(cm2 ⋅s))

E n e r g y ( M e V ) R e f e r e n c e c a s e ( E O C )

3 . c a s e ( E O C )

- 5 0 - 4 0 - 3 0 - 2 0 - 1 0

0

1 0 2 0 3 0 4 0 5 0

Difference (%)

D i f f e r e n c e

Figure 2.6: The neutron spectrum in the ALLEGRO at BOC (upper) and EOC (lower)

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0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0

1 . 3 1 5 1 . 3 2 0 1 . 3 2 5 1 . 3 3 0 1 . 3 3 5 1 . 3 4 0 1 . 3 4 5 1 . 3 5 0 1 . 3 5 5

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0

1 . 1 3 5 1 . 1 4 0 1 . 1 4 5 1 . 1 5 0 1 . 1 5 5 1 . 1 6 0 1 . 1 6 5 1 . 1 7 0 1 . 1 7 5

Infinite multiplication factor of the reference case (-)

R e f e r e n c e c a s e ( I ) R e f e r e n c e c a s e ( I I )

Infinite multiplication factor of the 3rd case (-)

3 r d c a s e ( 1 8 T h p i n s ) ( I ) 3 r d c a s e ( 1 8 T h p i n s ) ( I I )

Figure 2.7: The effect of time steps on the infinite multiplication factor in the reference ALLEGRO (upper) and in the thorium-containing ALLEGRO (lower) fuel assembly

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Finally, a sensitivity analysis was performed on how the time steps influence the results. In this case about twice as many time steps were chosen than those applied in the previously showed investigations. This means that one time step was at 0, one at 2 EFPD, then the rest in every 25 EFPD. The last two time steps occurred at 450 and 500 EFPD respectively. This also meant that the computational time increased drastically. One calculation was performed for the reference fuel assembly and another one for the last thorium-containing case, when the number of thorium carbide pins is 18. Fig. 2.7 shows the results. For both the reference and the thorium-containing cases, the increase of the number of time steps does not influence the outcomes significantly. The difference in case of the reference assembly is less than 0.05% and in the thorium-containing case is less than 0.1%.

The results suggest that the originally chosen time steps can describe adequately the processes and changes.

2.3 Investigation of the effect of the different pa- rameters on ALLEGRO

In this section of the thesis, sensitivity analyses are performed which focus on how a small change in the rhenium layers, the pin pitch, the cladding, the fuel pellet diameter, the fuel density, the void, and the fuel temperature influence the multiplication factor. The examinations were carried out not only for the reference fuel assembly but for a thorium-containing case as well. The importance of this kind of investigations is that a small difference in the multiplication factor can result in a significant change in reactivity because of the low effective delayed neutron fraction. The calculations were performed for fresh fuels with the aid of the code MCNP6 for fuel assembly models with the ENDF/B-VII cross section library in this investigations as well. The boundary condition on the vertical surfaces of the examined unit cell were still reflective; nevertheless, in axial direction all the parts were modelled (bottom reflector, active length, upper reflector).

The given tolerances and measuring errors which can be found in Ref. [65] can help to assume the real effect of the parameters and in this way conclusions can be drawn for the actual importances. The values are given for oxide fuels but can be a good reference for carbide fuel as well. When tolerances are given, those data are applied. In the other cases, the measuring error is used because it can be reasonable to assume that since ALLEGRO is a demo reactor, the fabrication and manufacture of each fuel pellet, rod and fuel assembly is carefully inspected and supervised.

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2.3.1 Description of the models used in sensitivity analyses

The fuel pin model of ALLEGRO contains the uranium-plutonium carbide fuel, the gap, which is filled by helium gas, the two different layers of rhenium, and the silicon carbide wrapper. When thorium-containing pins are implemented in the model, the geometry remains the same and only the pellet part is changed to thorium carbide. The detailed reference design of the ceramic fuel pin can be seen in Fig. 2.8 and its axial overview is shown in Fig. 2.9.

Figure 2.8: The geometry of the initial design of the ceramic fuel pin

Figure 2.9: Axial overview of the ALLEGRO fuel assembly

The ceramic fuel composition provided in the initial design was used. As it was mentioned before, the active length of the fuel pin is 86 cm. Under this region, a 40 cm long gap is located, which is filled with helium. The role of this gap is that it ensures sufficient room for the gaseous fission products. Under and above the fuel pin a reflector section was modelled, the material of which is ZrC. The reflector parts also have covers in axial directions, which were B₄C shielding [59].

The MCNP6 model of the fuel assembly can be seen in Fig. 2.1. It contains 90 fuel pins with a pitch of 1.1 cm. The number of active cycles was 500 in each calculation of this section and the number of neutrons started was 10000 per cycle.

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The results of the reference and the thorium-containing fuel assemblies are shown in the same figure. In this way the trend of the changes can be compared.

In every case, the black data points and black y axis relates to the reference fuel assembly, while the red points with the red y axis are linked to the thorium- containing case respectively. In order to have a valid comparison, the interval of the vertical axes are the same. If information could have been available about the fabrication tolerances it is discussed in the related sections.

2.3.2 The effect of material properties

Firstly, the effect of the plutonium content and the pellet density is investigated.

These properties are determined by the fuel fabrication process. In both examinations, only the parameters of the (U,Pu)C pellets are varied and if thorium is applied, the material properties of those pins are not changed.

Plutonium content

As it was discussed before the designed fuel pins contain 28.44% plutonium carbide and 71.56% uranium carbide. The latter is natural uranium so it contains 0.72%

235U. In this part of the investigation, the plutonium content of the fuel pins was varied uniformly in every fuel assembly. Since the percentage of plutonium is changing, the uranium content is also different in the calculations. For the thorium-containing case, only the plutonium content of the reference pins were varied but the thorium-containing pins remained the same. The results are shown in Fig. 2.10. It is obvious that the increasing amount of plutonium increases the infinite multiplication factor and in this way the reactivity of the system in both cases. As a first order approximation, linear were fitted on the data. It can be seen that in this intervals these can give good descriptions for the changes of the multiplication factors. The slope of the linear regressions suggest that the presence of thorium decreases the influence of the plutonium. This means that thorium has a moderating effect on this parameter change. The equations of the linear can be seen in Fig. 2.10.

According to the parameters given in [65], the ²³⁵U content is within a ±0.05%

interval of the given percentage values in case of oxide fuel (e.g. 2.4%±0.05%, 4.0%±0.05%, etc.). This would suggest an at least 1.25% relative error for plutonium. The measurement of isotopes is performed with a mass-spectrometer.

Based on the data which can be found in Ref. [65], the relative measurement error of ²³⁵U in oxide fuel is 0.2%. If we assume that only the measurement error can contribute to the variance of the plutonium content, with the aid of this value it can be assumed that the plutonium content difference can be about 0.057%. Im-

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portant to mention that these data and values are given for oxide fuel; parameters could not have been found for carbide fuel. According to the fitted linear, this difference can cause about 137 pcm ∆k_inf/k_inf change in the reference core while about 119 pcm for the thorium-containing core.

2 8 . 3 5 2 8 . 4 0 2 8 . 4 5 2 8 . 5 0 2 8 . 5 5

1 . 3 5 0 1 . 3 5 1 1 . 3 5 2 1 . 3 5 3 1 . 3 5 4 1 . 3 5 5 1 . 3 5 6

2 8 . 3 5 2 8 . 4 0 2 8 . 4 5 2 8 . 5 0 2 8 . 5 5

1 . 1 6 5 1 . 1 6 6 1 . 1 6 7 1 . 1 6 8 1 . 1 6 9 1 . 1 7 0 1 . 1 7 1

k ^{T h}_{i n f}[ - ] = ( 0 . 0 2 1 0 ±0 . 0 0 0 7 )⋅c _{P u}[ % ] + ( 0 . 5 7 1 3 ±0 . 0 1 9 4 )

R e f e r e n c e f u e l a s s e m b l y F i t t e d l i n e a r f o r r e f e r e n c e c a s e

Infinite multiplication factor for the reference case (-)

P u c o n t e n t ( % )

k ^{r e f}_{i n f}[ - ] = ( 0 . 0 2 4 1 ±0 . 0 0 1 2 )⋅c _{P u}[ % ] + ( 0 . 6 6 7 8 ±0 . 0 3 4 3 )

Infinite mulitplication factor for Th-containing case (-)

W i t h t h o r i u m c o n t a i n i n g p i n s F i t t e d l i n e a r f o r t h o r i u m c a s e

P u c o n t e n t ( % )

Figure 2.10: The effect of the plutonium content on the infinite multiplication factor for the reference and for the thorium-containing fuel assembly

Fuel density

The designed plutonium pellet density was varied between±2% to investigate the effect of its influence on the infinite multiplication factor. As it can be seen in Fig. 2.11, the linear approximations of the calculated values are appropriate for this interval.

It is important to highlight that the thorium-containing system is more sensitive to the density changes than the reference case. Based on the results, the ∆k_inf/k_inf change is about 376 pcm if the density difference is 1% for the reference fuel assembly and it is about 431 pcm for the thorium-containing one. The typical measurement error is about ±0.07 g/cm³ in the case of UO₂ density. If it is assumed that the variance of density is about the same for (U,Pu)C fuel as well, this can cause about 241 pcm ∆k_inf/k_inf change for the reference and 277 pcm for the thorium-containing case. In summary, the infinite multiplication factor is