Simulation of Reactor Transient and Design Criteria of Sodium- Cooled Fast Reactors

UPTEC F11 011 Examensarbete 30 hp Februari 2011

Simulation of Reactor Transient and Design Criteria of Sodium- cooled Fast Reactors

Filip Gottfridsson

Abstract Simulation of Reactor Transient and Design Criteria of Sodium- cooled Fast Reactors Filip Gottfridsson

Teknisk- naturvetenskaplig fakultet UTH-enheten The need for energy is growing in the world and the market of nuclear power is now once more expanding. Some issues of the current light-water reactors can be solved Besöksadress: by the next generation of nuclear power, Generation IV, where sodium-cooled Ångströmlaboratoriet Lägerhyddsvägen 1 reactors are one of the candidates. Phénix was a French prototype sodium-cooled Hus 4, Plan 0 reactor, which is seen as a success. Although it did encounter an earlier unexperienced phenomenon, A.U.R.N., in which a negative reactivity transient Postadress: followed by an oscillating behavior forced an automatic emergency shutdown of the Box 536 751 21 Uppsala reactor. This phenomenon lead to a lot of downtime of the reactor and is still unsolved. However, the most probable cause of the transients is radial movements of Telefon: the core, referred to as core-flowering. 018 – 471 30 03

Telefax: This study has investigated the available documentation of the A.U.R.N. events. A 018 – 471 30 00 simplified model of core-flowering was also created in order to simulate how radial expansion affects the reactivity of a sodium-cooled core. Serpent, which is a Hemsida: Monte-Carlo based simulation code, was chosen as calculation tool. Furthermore, a http://www.teknat.uu.se/student model of the Phénix core was successfully created and partly validated. The model of the core has a k_eff = 1.00298 and a neutron flux of (8.43+-0.02)!10^15 neutrons/cm^2 at normal state. The result obtained from the simulations shows that an expansion of the core radius decreases the reactivity. A linear approximation of the result gave the relation: change in k_eff/core extension = - 60 pcm/mm. This value corresponds remarkably well to the around - 60 pcm/mm that was obtained from the dedicated core-flowering experiments in Phénix made by the CEA. Core-flowering can recreate similar signals to those registered during the A.U.R.N. events, though the absence of trace of core movements in Phénix speaks against this. However, if core-flowering is the sought answer, it can be avoided by design. The equipment that registered the A.U.R.N. events have proved to be insensitive to noise. Though, the high amplitude of the transients and their rapidness have made some researcher believe that the events are a combination of interference in the equipment of Phénix and a mechanical phenomenon. Regardless, the origin of A.U.R.N. seems to be bound to some specific parameter of Phénix due to the fact that the transients only have occurred in this reactor. A safety analysis made by an expert committee, appointed by CEA, showed that the A.U.R.N. events are not a threat to the safety of Phénix. However, the origin of these negative transients has to be found before any construction of a commercial size sodium-cooled fast reactor can begin. Thus, further research is needed.

Handledare: Hans Henriksson Ämnesgranskare: Henrik Sjöstrand Examinator: Tomas Nyberg ISSN: 1401-5757, UPTEC F11 011 Sponsor: Vattenfall AB

Acknowledgements

I would like to thank the following persons for their guidance and criticism

Andrei Fokau

Anna-Maria Wiberg

Bruno Fontaine

Hans Henriksson

Henrik Sjöstrand

Peter Wolniewicz

IespeciallywouldliketothankBruno Fontaine for all the valuable information and guidance he has provided, which have been essential for this thesis. I am also grateful for the time Andrei Fokau spent in order to help me learn Monte-Carlo simulation codes.

Contents

1 Introduction 1 1.1 Background ...... 1 1.2 Aims and Objectives ...... 2 1.3 Limitations ...... 2 1.4 Outline of this report ...... 3

2 Fundamentals of fast reactors 5 2.1 Overview ...... 5 2.2 Fission ...... 5 2.3 Breeding ...... 6 2.4 Transmutation of long-lived radio-active elements ...... 7 2.5 Coredesignoffastreactors ...... 7 2.5.1 Conﬁguration of fast breeder reactors ...... 7 2.6 Eﬀective neutron multiplication factor, keff ...... 9

3 Sodium-cooled fast reactors 13 3.1 Sodium-cooled fast reactors in the world ...... 13 3.2 Sodium-cooled reactor design ...... 14 3.2.1 Advantages and disadvantages ...... 14 3.2.2 Technical overview ...... 14 3.3 Phénix...... 16 3.3.1 A.U.R.N...... 17 3.3.2 Core-ﬂowering ...... 21 3.3.3 Core-ﬂoweringtestsofPhénix...... 22 3.4 ASTRID...... 22 3.4.1 Preliminary design ...... 23

4 Method and materials 25 4.1 Monte-Carlosimulationcode ...... 25 4.1.1 Diﬃculties using Monte-Carlo simulation code ...... 25 4.1.2 Choice of Monte-Carlo simulation code ...... 26 4.1.3 Advantages and disadvantages of Serpent ...... 27 4.2 Model of Phénix ...... 27 4.3 Model of core-ﬂowering ...... 30

5 Result 33 5.1 Model of Phénix ...... 33 5.2 Core-ﬂowering...... 33 6 Discussion 37 6.1 Simulations ...... 37 6.2 A.U.R.N...... 38

7 Conclusions 41 7.1 Conclusions ...... 41 7.2 Suggestions for further work ...... 42

References 43

List of Figures 45

List of Tables 47

Nomenclature 48

Appendices 49

A Deﬁnitions of the units in the Four Factor Formula A-1

B Code of the Phénix Model B-1

C Output data from a test run of the Phénix model C-1

D Results of the PFBR-model D-1

"The ﬁrst country to develop afastbreederreactor will have a commercial advantage for the exploitation of nuclear energy"

Enrico Fermi - 1945 1 Introduction

The need of energy in the world is growing and since we now are facing possible climate changes the search for alternative energy sources to fossil fuels is greater than ever. Nuclear power has for some time been a non-expanding market, though today the view has changed. It is now seen as one of the alternatives to fossil fuel due to its low emission of CO2 and low environmental impact. However, nuclear power has its disadvantages, for example the waste produced in current reactors needs to be stored for more than 300 000 years [1]. A new generation of nuclear power plants named Generation IV is under development, which can solve some of the problems related to the current nuclear power. The aim of Generation IV is to have safer, more reliable and eﬃcient power plants with a physical protection against terrorism in a closed fuel cycle [2]. The goal is also to improve the environment, for example by introducing nuclear-produced hydrogen for transportation.

1.1 Background

There are six diﬀerent reactor designs of Generation IV [2], Sodium-cooled Fast Reactor (SFR), Lead-cooled Fast Reactor (LFR), Molten Salt Reactor (MSR), Very High Temperature Reac- tor (VHTR), Gas-cooled Fast Reactor (GFR) and SuperCritical-Water Reactor (SCWR). All of these designs are being developed throughout the world in order to achieve the goal of commercialization.

It is possible to have diﬀerent neutron spectra by using diﬀerent coolants. For example using liquid metal as coolant results in having a fast neutron spectrum1 in the reactor, more about this in Chapter 2, which in turn leads to the possibility to use up to 99.9 % of the fuel. This can be compared to the fuel usage of todays water reactors’ usage of a few percent. Recycling of the spent nuclear fuel is then possible and it can result in a reduction of storage time from 300 000 years to several 1000 years [1]. Hence, the process of storing might be easier for a country to manage. The main drawbacks of using these coolants are the increase of temperatures and

1Fast neutron spectrum: The neutron spectrum is dominated by fast/high energetic neutrons.

1 INTRODUCTION Aims and Objectives the high irradiation in the core, which makes it diﬃcult to develop feasible materials that can sustain such severe environment.

The sodium-cooled fast reactor is the candidate of Generation IV that lies furthest ahead in research and development [2]. Even though sodium-cooled fast reactors are part of a new generation of nuclear power, the idea is quite old. In fact, the ﬁrst reactor connected to the electrical grid, EBR-I, was cooled with a combination of sodium and potassium [3]. However, the commercialization of sodium-cooled fast reactors is still far away in time due to the lack of proper materials.

Downtime due to sodium-leaks is one of the most common issues with the operation of SFRs, though earlier unexperienced very rapid negative reactivity transients2 have caused major problems in the French reactor Phénix. The French call these transients A.U.R.N., which is short for Arrêt d’Urgence par Réactivité Négative. In English this means automatic emergency shutdown by negative reactivity. No ﬁnal explanation of A.U.R.N.s has yet been established, though the most probable cause is radial movement of the core called core-ﬂowering. This is one of the issues that needs to be solved before introducing SFRs of commercial size.

1.2 Aims and Objectives

This master thesis investigates the cause of the A.U.R.N. events. The objectives are to survey published reports and use Monte-Carlo simulation code in order to simulate core-flowering and analyze how it affects the reactivity of an SFR core. Simplified models of the phenomenon have been used in order to make the simulations possible. The aims of the study are to determine a possible cause of the negative reactivity transients, give a solution on how to avoid the problem and point to further research. Furthermore, some design criteria and core configurations of SFRs are discussed and how they can affect the behavior of the reactor.

The study was carried out at Vattenfall Research and Development AB. This thesis is valuable for Vattenfall in their long-term coverage of future reactor concepts, especially for the understanding of the issues the diﬀerent concepts are facing.

1.3 Limitations

This study does not give a direct explanation to the A.U.R.N. events that occurred in Phénix. It rather discusses the registered transients and their complexity and points to further research. Furthermore, the study does not investigate any of the consequences of A.U.R.N. nor does it dis- cuss any economical aspects of the events. A.U.R.N.s is still an unsolved phenomenon, therefore the information is very limited. There are few reports published in English that describe possible explanations and most of them only describe the problem, not its origin. The simulations however, are only used in order to analyze core-ﬂowering and how it aﬀects the reactivity of an SFR core. The results from the simulations have been compared with experimental data, though the simulations cannot be used to make any conclusions of the origin of the negative reactivity transients.

2Transient: A rapid/brief change in the power of the reactor.

2 Outline of this report INTRODUCTION

Serpent as Monte-Carlo simulation code has many advantages, though it cannot handle dynamic flows, such as coolant flow. Complex structures that are not included in the geometric library of the code are difficult to create. Sub-assemblies3 suffering from core-flowering have therefore in the simulations the same structure as in the normal state. Another limitation in the model is that the gap between the assemblies must increase symmetrically in the whole core, which means it is not possible to have any asymmetrical deformation of the lattice.

Phénix has been used for irradiation experiments, which resulted in the usage of different set-ups of assemblies with different cladding material etc. No complete core description of Phénix was found. Thus, the parameters and materials used in order to create the model for this study are obtained from several references. Some parameters vary in the different references and the values of these parameters have been set according to the source that seems most convenient. It should be noted that the parameters used is not set in order to have an optimized model. Furthermore, the models of both Phénix and PFBR (Prototype Fast Breeder Reactor, an Indian SFR that is under construction) are simplified in this project and cannot completely describe the environment of the core, such as the release of fission gas and fuel swelling due to irradiation.

1.4 Outline of this report

Summary of the chapters of the report: • Fundamentals of fast reactors - The chapter describes the basic physics and core conﬁgu- rations of fast reactors. Calculation of keff is also presented. • Sodium-cooled Fast Reactors - This chapter treats the technology of SFRs and focuses on the Phénix reactor and its experience of the A.U.R.N. events.

• Method and Materials - The selection of simulation code and how it was used is discussed. AdescriptionofthePhénixmodelandthemodelofcore-ﬂoweringisalsopresented. • Result - The results from the simulations of the Phénix and core-ﬂowering models are presented.

• Discussion - This chapter discusses the results, the models and the survey of the published reports. • Conclusions - The conclusions of the study is presented in this section. • Appendices - The code of the Phénix model are presented and a summary of the Monte Carlo simulation code used. Also, the results from the second model PFBR are presented.

3Sub-assembly: Fuel element containing the fuel pins in FRs. Corresponds to the fuel-assembly in LWRs.

2 Fundamentals of fast reactors

This chapter presents the basic theory of fast reactors and some of their advantages. Different core configurations are also presented and finally a description and calculation of the keff .

2.1 Overview

SFR is a Fast Reactor, FR, which in short means it uses fast neutrons1 instead of thermal neu- trons2 that are standard for water-moderated Light-Water Reactors, LWRs. FRs do not have amoderator3 as LWR. Hence, the neutrons of the FRs maintain their high energy. Thermal neutrons are wanted in LWRs, since they have a higher possibility to cause ﬁssions than fast neutrons, read more in Section 2.2,thoughtheycausebuild-upoflong-livedactinides4, which explains why nuclear waste from LWR needs to be stored for so long. However, reactors using a fast neutron spectrum have the advantages of better neutron economy, production of fuel while operating, see Section 2.3 and the possibility to transmute the long-lived actinides into shorter- lived isotopes see Section 2.4. In addition to the material issues, FRs have the disadvantage of aweakernegativefeedback[1].

Plutonium is the primary choice for FRs, in order to have a closed fuel cycle possible with current reactors. The fuel of FRs require a high-enriched fuel, around 20 % or more, due to the low possibility of ﬁssion when using fast neutrons [4].

2.2 Fission

The energy source of FRs is ﬁssion, like in LWRs. It means that a nucleus of an atom, when bombarded by neutrons, n, splits into two minor nuclei, which are referred to as ﬁssion products.

1Fast neutrons: High energetic neutrons, 1MeV. ∼ 2Thermal neutrons: Low energetic neutrons 1 eV, also known as slow neutrons. ∼ 3Moderator: Medium that decreases the speed/energy of the neutrons. 4Actinides: Elements with atomic numbers between 90-103.

5 FUNDAMENTALS OF FAST REACTORS Breeding

Elements, which are able to fission when bombarded with thermal neutrons and neutrons with high energies, are called fissile isotopes. Common examples are 235Uand239Pu. Fissile isotopes are needed in order to sustain a nuclear chain reaction5. The fissile isotope 235Uisthemain choice of fuel for LWRs. The reaction formula for fission of the isotope is [3]

235 236 n + U U ∗ Fissionproducts+ 2¯.5n + energy (2.1) → → Plutonium, 239Pu, is commonly used as fuel in a FRs [3]

239 240 n + Pu Pu∗ Fissionproducts+ 2¯.9n + energy (2.2) → → 2.3 Breeding

The isotope 238U has a very low probability of ﬁssion when bombarded by neutrons below 1 MeV, though it can capture a neutron, and then through beta-decay convert to the ﬁssile isotope 239Pu

238 239 239 n + U U ∗ Np+ β− (2.3) → → 239 239 Np Pu+ β− (2.4) → Isotopes, which can transmute into ﬁssile isotopes by neutron capture, are referred to as fertile isotopes and the process is called conversion. The degree of conversion that occurs in the reactor is fissile material produced CR = (2.5) fissile material destroyed

One favorable feature of FRs is breeding, which means that the production of fuel is higher than the fuel consumed. Breeding is possible in a FR due to the fact that a fast neutron spectrum has the advantages of higher production of neutrons per fission and a higher σf /σc-ratio 6 (where σf is the cross-section for fission and σc is the cross-section for neutron capture of the fissile isotope). The reactor is a breeder if the conversion ratio is greater than 1 [3]. In such a case, the conversion ratio is referred to as breeding ratio fissile material produced BR = > 1 (2.6) fissile material destroyed

In FRs, fuel enriched with 239Pu is a better choice than 235U, commonly used in LWR, most due to the fact that the η-value, number of neutrons produced per absorption, see equation 2.7,of 239Pu is greater at higher energies of the neutrons. This is desired in a breeding reactor, since η needs to be > 2 to make breeding possible. In other words, for each neutron absorption, two new neutrons have to be produced. The value of η is calculated by the equation

5Nuclear chain reaction: When ﬁssion of one nucleus produces at least one more ﬁssion, thus leading to self-propagation. 6Cross-section: Expresses the likelihood of interaction between particles.

6 Transmutation of long-lived radio-active elements FUNDAMENTALS OF FAST REACTORS

ν = number of neutrons produced per fission

σf ν η = (2.7) σf + σc Note that η in equation 2.7 is the value for a single isotope, not the η-value of a reactor.

2.4 Transmutation of long-lived radio-active elements

Breeding is not the only feature of FRs, transmutation of transuranium elements7 is another important feature. The objective of transmutation is to convert long-lived radiotoxic nuclei to shorter-lived isotopes.

The build-up of long-lived actinides is a serious disadvantage of the current nuclear power. The presence of actinides, such as Am, Cm and Pu, makes spent fuel radiotoxic for a long time. It takes more than 300 000 years for the nuclear waste to reach a radioactive level below natural uranium, see Figure 2.1.Hence,spentnuclearfuelfromLWRsneedstobestoredduringthis period. Fission products also contribute to the radiotoxicity of nuclear waste, though not as much as the transuranium elements.

Using reactors with a fast neutron spectrum gives the advantage of a more favorable burnup/buildup- ratio of actinides than LWRs. This can reduce the storage time for nuclear waste down to several thousands of years [1]. However, introducing minor actinides8 into the fuel brings safety related problems, which are further discussed in reference [1], such as an increase in coolant void worth9. One way to avoid some of the problematic safety issues related to fuel enriched with minor actinides is to have "target sub-assemblies", containing the minor actinides. These assemblies are dedicated for high burnup of nuclei.

2.5 Core design of fast reactors

FRs do not have a square lattice of fuel pins as LWRs and instead use a triangular lattice in order to optimize the burnup and breeding potential. Hence, the core of FRs has a hexagonal geometry with hexagonal sub-assemblies, which diﬀers from the square geometry of the fuel-assemblies10 in LWRs. The fuel pin and sub-assembly/fuel-assembly arrangement for FRs and LWRs are presented in Figure 2.2. The core of LWRs is designed to have a fuel-to-moderator ratio that optimizes the neutron economic and this is achieved by using a square geometry. However, the lack of moderator in FRs makes a minimized and more compact core superior.

2.5.1 Configuration of fast breeder reactors There are two basic configurations for a Fast Breeder Reactor, FBR: external and internal breeding. Figure 2.3 visualizes the two concepts. The external breeding configuration has all fertile

7Transuranium elements: Elements with atomic number higher than 92. 8Minor actinides: Actinides other than uranium and plutonium. 9Coolant void worth: The feedback in reactivity from coolant boiling. 10Fuel-assembly: Fuel element containing the fuel pins in LWRs.

7 Transmutation of nuclear waste

Radiotoxic inventory [Sv/g] During the first 20 years of cooling, the major contri- 100 bution to the radiotoxic inventory comes from fission 85 90 137 10 TRU products, more specifically Kr, Sr and Cs. The comparatively short half-life of these nuclides however 1 FP within 400 years reduces the contribution to the speci-

0.1 fic radiotoxic inventory from the fission products Uranium in nature below levels of natural uranium with progeny. It takes 0.01 over 300 000 years for the transuranium elements to reach the same level. Even though the spent fuel is not 0.001 t[y] completely harmless after this time, natural radiation 101 102 103 104 105 106 sources constitute similar levels of hazard. The radiotoxic inventory of uranium in nature is 18 mSv/g (to Figure 1.1: Specific radiotoxic 96% given by uranium daughters) and may serve as inventory of spent PWR fuel. one of several possible reference levels in the context FUNDAMENTALS OF FAST REACTORS Core design of fast reactors of transmutation.

Radiotoxic inventory [Sv/g] If we are to reduce the radiotoxic inventory by tran- 100 smutation, the priority should therefore be given to fissioning of the transuranium elements [Claiborne72]. 10 240 TRU Pu Not all of these elements constitute a significant 239Pu 238 hazard, though. Figure 1.2 shows the relative contri- 1 Pu 241Am 243Am butions to the specific radio-toxic inventory from the 0.1 long lived α-emitters. During the first 1000 years, 242Pu 241Am is the major offender. In the long term, 240Pu 0.01 Unat and 239Pu dominate the hazard. From the figure it may 237Np t [y] be inferred that removal of both plutonium and ame- 101 102 103 104 105 106 ricium is required in order to reduce the time needed for the radio-toxic inventory of spent nuclear fuel to Figure 2.1: The presenceFigure evolution 1.2: of Contributions transuranium elements of in spent nuclearreac fuel.h t [1]he level of natural uranium below 20 000 years. individual transuranium nucli- Neptunium on the other hand, does not contribute material located in a blanketdes zone to the outside radiotoxic the core of pureinventory fissile material. of Internalsig breedingnifican con-tly to the radio-toxic inventory, especially if figuration instead has a corespent of bothPWR fissile fuel. and fertile material surrounded by a fertile blanket 241 zone. The external arrangement was considered for the early FBRs, though wasthe neversou imple-rce term consisting of Am-decay is elimina- mented due to the rapid change in reactivity during fuel burnup, which is a consequenceted. We ofm noay therefore focus our efforts on the tran- in-core breeding. Internal breeding has the advantages of high breeding ratio and reduction of void coefficients. smutation of plutonium and americium. An important corollary is that the curium which is produced when transmuting americium must also be recycled. Other- In-core configuration: Homogeneous and heterogeneous wise, the reduction of the long term radiotoxic inven- All FBRs so far, have had a core design where internal breeding in the core is possible, which is also known as in-core breeding concept. There are two variants of this arrangement:tory in homo-the waste stream would be limited to about a geneous and heterogeneous. A core with all assemblies of pure fertile material,factor located of in bothten [Delpech99]. radial and axial regions has a so called homogeneous configuration due to the uniform spread of fertile and fissile material. The regions of fertile material have two main functions; neutron shielding and breeding of fuel. 11 The heterogeneous configuration has a core of fissile sub-assemblies where the blanket-assemblies of pure fertile material are distributed throughout the fissile regions. The advantages of this configuration are better breeding ratios and reduced sodium void coefficients, though it has the disadvantage of high enrichment of fissile material.

Different parameters of the core have different impact depending on the core configuration. In a homogeneous core, the neutronic performance is more sensitive to the fuel sub-assembly design and less sensitive to the layout of the core than in a heterogeneous configuration [5].

8 Eﬀective neutron multiplication factor, keff FUNDAMENTALS OF FAST REACTORS

Figure 2.2: This ﬁgure shows the fuel pin and the sub-assembly/fuel-assembly arrangements of FRs and LWRs. Note the LWR fuel-assemblies have more space between the fuel pins than those of FRs. a) Sub-assembly arrangement of FRs. b) Fuel-assembly arrangement of LWRs. c) Fuel pin arrangement of FRs. d) Fuel pin arrangements of LWRs.

2.6 Eﬀective neutron multiplication factor, keff

Eﬀective neutron multiplication factor, often referred to as keff ,isanimportantparameterin all nuclear reactors. The value of keff determines how the nuclear chain reaction proceeds. The value of keff can be calculated by the four factor formula [6] where η is obtained from equation 2.7

=Fastfissionfactor f =T hermal utilization p =Resonance Escape P robability P =Non leakage Probabilities, −

9 FUNDAMENTALS OF FAST REACTORS Eﬀective neutron multiplication factor, keff

Figure 2.3: Overview of the internal and external conﬁguration of a FBR.

keff is then determined by

keff = k P (2.8) ∞ · = η p f P (2.9) · · · · number of neutrons in current generation = (2.10) number of neutrons in previous generation

In words, keff describes how many ﬁssions one ﬁssion leads to. There are three crucial states of areactor:

keff < 1(subcritical, decreasing number of neutrons)

keff =1(critical, stationary number of neutrons)

keff > 1(supercritical, increasing number of neutrons)

Under normal operation conditions in a commercial reactor it is desired to have keff =1,in order to have a sustainable nuclear chain reaction. Furthermore, the value of keff must not be »1 to avoid severe accidents. Accelerator-Driven Systems, ADS, is an example of a reactor with asubcriticalcorethatusesaproton-canonasanoutsideneutronsourcetohaveasustainable neutron economy. The reactivity of a reactor [7], ρ,isdeﬁnedas

keff 1 ρ = − (2.11) keff

10 Eﬀective neutron multiplication factor, keff FUNDAMENTALS OF FAST REACTORS

The following states of a reactor are obtained from the Equation 2.11

ρ<0(subcritical) ρ =0(critical) ρ>0(supercritical)

3 Sodium-cooled fast reactors

This chapter describes the technique of SFRs and their current status in the world. Detailed information about the French reactor Phénix and information gathered from the investigation of the A.U.R.N. events are also presented.

3.1 Sodium-cooled fast reactors in the world

Since the establishment of nuclear power, more than 20 SFR units have been constructed in the world and together they have provided over 400 years of operation experience [8]. Reactors of experimental and prototype size have dominated the SFR fleet, see Table 3.1 and due to technological and economical difficulties of using sodium as coolant, Superphénix and BN-600 remain as the only two SFRs of industrial/commercial size ever constructed. Superphénix has been shutdown and is currently being decommissioned, while BN-600 is still in operation. Su- perphénix experienced a lot of technological difficulties and minor accidents during its operation before it finally was forced to shutdown in 1998. The BN-600 did also encounter problems in the early years, though it should be noted that the reactor have, several times, been the best power-generating unit in Russia, both with respect to reliability and safety [9]. A third reactor of industrial size was designed in the project European Fast Reactor, EFR, which was initiated in 1980. Unfortunately, the project was cancelled in 1998 before any construction had taken place.

During the last decade FRs have once again blossomed and countries are once more expanding their SFR programs. New countries are joining the international co-operations, such as the Generation IV Forum [10] and building reactors of their own to gather data and operating experience of SFRs. China for instance, has recently ﬁnished their construction of CEFR, China Fast Experimental Reactor, an experimental SFR with thermal capacity of 60 MW. France, which is one of the leading countries in SFR-technology, is for the moment planning the design of their second prototype reactor, ASTRID. The construction of ASTRID will probably take place in the middle of 2020. Moreover, Russia and India are expanding their SFR ﬂeet with the ongoing construction of BN-800 [11] and PFBR.

13 SODIUM-COOLED FAST REACTORS Sodium-cooled reactor design

Table 3.1: Table of some SFRs in world. Note that BN-600 and Superphénix are the only two reactors of commercial size. [11]

Name Country Thermal power (MWth1)Type CriticalStatus EBR-I USA 1.4 Experimental 1951 Shutdown RAPSODIE France 24 Experimental 1967 Shutdown BOR-60 Russia 60 Experimental 1968 Operating JOYO Japan 50 Experimental 1977 Operating CEFR China 60 Experimental 2010 Operating BN-350 Kazakhstan 1000 Demonstration 1972 Shutdown Phénix France 563 Demonstration 1973 Shutdown Monju Japan 714 Demonstration 1992 Operating BN-600 Russia 1470 Commercial 1980 Operating Superphénix France 3000 Commercial 1985 Shutdown

3.2 Sodium-cooled reactor design

SFRs are, as previously mentioned, fast reactors that use liquid sodium as coolant and this type is the most technologically developed concept of Generation IV [2]. It is similar to Pressurized Water Reactors, PWRs, in its design with primary and secondary circuits.

3.2.1 Advantages and disadvantages The current primary objective of SFR concept is to burn high-level waste, especially burnup of plutonium and other actinides in order to reduce the storage time. Sodium as coolant has the advantage of a good breeding performance and a high boiling point at an atmospheric pressure, which provides a safety margin against void, gas bubbles, in the core. Furthermore, sodium is not corrosive, it has a high thermal conductivity, high thermal inertia and the possibility to remove decay heat2 from the core by natural convection. These advantages combined with the fact that the SFR concept have been both tested and proven on industrial scale make sodium a feasible coolant for future reactors.

Sodium is unfortunately a very reactive metal, especially in contact with water, which can cause sodium ﬁres and hydrogen explosions, even air is chemically incompatible with sodium. This makes the design of steam generators in SFRs more complicated. Other problems are sodium void in the core, which has a positive feedback in reactivity and the metal’s opaqueness, which makes in-core inspections diﬃcult. The extra technology that is necessary in order to compensate for these disadvantages makes SFR expensive, which results in low economic competitiveness.

3.2.2 Technical overview The primary circuit with sodium cools the core and the secondary system with sodium transfer the heat from the primary circuit through Intermediate Heat Exchangers, IHX, to the steam generators, see Figure 3.1. The secondary system prevents the release of radioactive material in

1MWth: Thermal power. 2Decay heat: Heat produced after the reactor has been shutdown.

14 Sodium-cooled reactor design SODIUM-COOLED FAST REACTORS the event of a sodium-water reaction. The sodium in the primary and secondary circuit must be kept pure to avoid sodium oxide and hydride deposits, which in turn can lead to blockage in the ventilation of the sub-assemblies. Alternatives, which do not react violently with sodium, in the secondary circuit, are being considered. Super-critical carbon dioxide in a so called Brayton cycle is currently being developed as energy carrier. This concept is more eﬃcient than the cycles used in the present reactors. Since carbon dioxide does not react as violent with sodium as water an intermediate system would be unnecessary. Most SFR designs have multiple secondary circuits that are each connected to a multiple number of steam generators. For example, Phénix had three secondary loops with one steam generator each, while BN-600 had three secondary loops with eigth steam generators each.

There are two different configurations of the primary circuit: the common pool configuration and the less common loop configuration, favored in Japan. In the pool configuration, see Fig- ure 3.1, the entire primary circuit is integrated in the main vessel, while in the loop configuration each module has separate casings. The advantage of the pool configuration is large thermal inertia and the system is insensitive to loss of coolant flow, on the other hand the loop configuration has the benefit of easier inspections and repairs. The loop configuration also has better defense against earthquakes, which is one of the reasons why it is chosen by Japan.

Table 3.2: A summary of the design parameters for the SFR concept of Generation IV. [2]

Reactor Parameters Reference Value Outlet Temperature 530-550 °C Pressure 1 Atmospheres ∼ Rating 1000-5000 MWth Fuel Oxideormetalalloy Cladding Ferritic or ODS ferritic Average Burnup 150 200GWD/MTHM3 ∼ − Conversion Ratio 0.5-1.30 Average Power Density 350 MWth/m 3

Noble gas, mostly argon, is used as cover gas over the hot pool of sodium in the primary vessel. It is used to create a layer between the inner structures and components of the main vessel and the liquid sodium. The layer acts as an inert atmosphere, which prevents sodium aerosols from leaving deposits in sensitive areas. Furthermore, nitrogen is used as an inert gas between the main vessel and safety vessel and in systems surrounding the pipings carrying sodium. The reason for not having nitrogen as cover gas above the hot pool is that nitrogen reacts with sodium. Argon gas however, is too expensive to have in the systems surrounding the pipings etc.

Two diﬀerent fuels are considered for SFRs: mixed oxide fuel, MOX-fuel, and metal-fuel. The MOX-fuel is a combination of PuO2 and UO2. It is the primary choice of fuel for SFR due to the extensive experience gathered from earlier operation and testing. Metal fuel is a combination of uranium-plutonium-zirkonium metal alloy and it has the advantage of better thermal conductivity with no moderation from oxygen, which in turn results in better breeding performance, though this type of fuel has a lower melting point than oxide based fuel.

3GWD/MTHM: GWdays/metric tone heavy metal.

15 SODIUM-COOLED FAST REACTORS Phénix

Figure 3.1: Overview of the SFR pool design. The system has a primary circuit integrated in the main vessel and the heat is transferred from the primary circuit to the steam generators by intermediate circuits. [2]

3.3 Phénix

In 1971, the construction of the second French SFR, Phénix, was complete. Phénix was the first demonstrational/prototype SFR in the world and it had a capacity of 580 MWth/250 MWe4. The power plant was connected to the grid for the first time in 1973. The reactor was of pool- type configuration and was cooled by three intermediate systems, which in turn were connected to one steam generator each [12]. The desirable temperature of the sodium outlet from the core lies at 560°Candtheinletliesat400°C. Phénix had a homogenous core with two enrichment zones of fissile fuel [13]. The fissile core was surrounded by a fertile blanket, both in radial and axial directions, of mainly depleted or natural uranium. Most of the fuel breeding in Phénix took place in the blanket zone. Phénix used the free standing core restraint concept for keeping the sub-assemblies of the core together, which means that the core support structure is located at the lower part of the sub-assemblies. The concept allows free outward bowing of fuel- and blanket assemblies until the core radius makes contact with the shield assemblies, which are located at the periphery of the core. Several experimental sub-assemblies were placed in the core of Phénix for different irradiation experiments.

The main objectives of Phénix were not only to test the feasibility of SFR technology on larger scale but to perform irradiation experiments, like minor actinide burning [12]. For these experiments, Phénix used diﬀerent set-ups of sub-assemblies with diﬀerent inventories. All data

4MWe: Electrical power.

16 Phénix SODIUM-COOLED FAST REACTORS

Figure 3.2: Chart of downtime at Phénix due to accidents and maintenance. Note the percentage of negative reactivity transients, which is the fourth time-wasting issue, if scheduled work is not taken into account. [14] gathered from the operation of Phénix have been used for the development of Superphénix and EFR.

Phénix encountered many incidents during its time in operation and most of these were related to sodium leaks in the intermediate heat exchangers, see Figure 3.2. Phénix suffered long downtimes after minor incidents due to the fact that a political decision was required for a restart of the reactor, even though the facility recovered fast from the damages. In the late 1980’s and in the beginning of 1990’s, Phénix encountered several automatic shutdowns of the reactor due to negative transients. These events caused long downtimes of the reactor, see Figure 3.2,inorder to investigate their origin, more information about this is presented in Section 3.3.Afterthe fourth automatic shutdown, the power of the reactor was decreased to 350 MWth [12] due to an independent reason related to residual power removal system [15]. In 1992, a program for the life-time extension of Phénix was initiated and the renovation was finished in 2002. Phénix then proceeded with its operation until the reactor was finally shutdown in 2009. The last experiment performed was to investigate how the core is affected by core-flowering.

Although Phénix encountered many incidents and experienced a lot of downtime, it is still seen as a success, since it provided a lot of valuable information and operating experience of SFRs.

3.3.1 A.U.R.N. In the end of 1980’s Phénix encountered, while operating at full power, an earlier unexperienced phenomenon that lead to an automatic shutdown of the reactor. The signal of the neutron cham-

17 SODIUM-COOLED FAST REACTORS Phénix bers5 registered very rapid oscillations with high amplitudes, see Figure 3.3.Duringthetime period between 1989-1990, Phénix suffered from this event four times. These transients were named "Arrêt d’urgence par réactivité négative", A.U.R.N. In English this means automatic emergency shutdown by negative reactivity. The events occurred while operating at or close to full power; the first three at 580 MWth and the last one at 500 MWth. A.U.R.N. were all detected by the neutron chambers, which are located beneath the reactor vessel and measure the neutron flux.

During all events the registered signal of the neutron chamber had the following behavior: 1. An almost linear reactivity drop with high amplitude 2. Asymmetricalincreasetoamaximumbelowtheinitialvalue 3. A new decrease, though with lower amplitude then the initial reactivity drop 4. A secondary peak, which slightly exceeds the initial power of the reactor 5. Decrease in the power of the reactor due to the insertion of the control rods6 into the core

Figure 3.3: Two separate registered signals obtained from the neutron chambers during the last two A.U.R.N. events in Phénix in 1990. Note the oscillating behavior and the secondary peak, which in both cases slightly exceed the initial power. [14]

This phenomenon only lasted for several hundreds of milliseconds before the reactor was shutdown automatically by the control rods. The control rods were triggered by the ﬁrst reactivity drop due to the fact that the amplitude of the drop went below the threshold for negative reactivity transient. The power drop in the signal varies in the four diﬀerent events and in the last two it reached down to 28% and 45% of the nominal power. Assuming that the power signal from the neutron chamber directly corresponds to the thermal power of the core; the fastest 7 drop reached in the A.U.R.N. events corresponds to a loss in keff of 320 pcm and the highest

5Neutron chamber: An unmoderated detector containing one ore more neutron counters. It calculates the neutron ﬂux of the core, which can be translated to a corresponding thermal power. 6Control rods: Rods made of elements that can absorb many neutrons and are used for controlling the reactor. 7 pcm: per cent mille of ∆keff /keff .

18 Phénix SODIUM-COOLED FAST REACTORS increase corresponds to an increase of 37 pcm above the initial value [12].

Other instruments in Phénix were active during the A.U.R.N. events, such as geophone, cover gas pressure, the primary pump discharge, position readings of one of the six control rods etc., though none of them except the geophone registered any abnormal activity. Interference in the measurement channels was the ﬁrst possible explanation of the phenomenon due to the fact that two out of the three neutron chambers were replaced during the 10-yearly inspection [12]. How- ever, this explanation was later discarded after a control rod drop test, which proved that the equipment was insensitive to noise.

The information gathered from the third event led to the explanation that a large volume of gas passed through the core. This was conﬁrmed by the observation of an increase in the pressure of the cover gas and the possibility of a plugging in the special venting of the sub-assemblies. The reactor was then stopped and preventive measures were taken before start-up. This scenario however, was abandoned after the occurrence of the fourth event.

Low power tests, between 5 and 40 MWth, after the third event were performed in order to recreate the registered signals of the neutron chambers, though without any success [12].

Expert Committee After the fourth A.U.R.N., the operations of Phénix were stopped and the French Atomic Energy Commission, CEA (Commissariat à l’Énergie Atomique et aux énergies alternatives), conducted an extensive investigation program. An expert committee was appointed, whose objectives were, quoted from reference [12]: • Examine every possible cause of the reactor anomalies • Provide elements of response for these anomalies • Examine every possible consequence in the event that these abnormal conditions should occur in diﬀerent conditions • Make proposals for preventive measures After almost two years of investigation, the committee had not found a complete explanation of the phenomenon, though the most probable cause was radial movement of the sub-assemblies. Furthermore, in the safety analysis, which was based on all plausible scenarios that could cause A.U.R.N., it was concluded that the safety of the reactor was not aﬀected. A new approach was proposed, in which the surveillance of the reactor should be reinforced in order to obtain as much information as possible in case of a new negative reactivity transient. Secondly, tests were to be performed at low power followed by 10 days at high power, to test the instrumentation of Phénix and also to verify the reactor and core behavior before start-up of the reactor.

The new approach that was provided by the committee led to the installation of additional equipment in order to have a full surveillance of the reactor and to detect any anomaly. Some examples of new equipment: • SONAR device installed above the core • Acoustic detector inside the core • Magnetic ﬁeld measurement of the reactor vessel

19 SODIUM-COOLED FAST REACTORS Phénix

Furthermore, instrumentation designed for fast measurements were installed in Phénix. In the end of 1991 and in the beginning of 1992, tests were performed with the new equipment. They were to:

• Verify the neutronic condition of the core.

• Conﬁrm the reactivity change during a normal automatic drop of the control rods.

• Gather more information to evaluate the diﬀerent explanations.

• Obtain a description of the dynamic behavior of the reactor instrumentation.

• Validate the additional equipment installed after the events.

These tests succeeded to verify the new surveillance of the reactor and it provided enough information to be able to discard several assumptions made for diﬀerent scenarios, which were to explain the occurrence of A.U.R.N. in Phénix. The earlier seen correct behavior of the core and the primary hydraulics were conﬁrmed during these tests.

No A.U.R.N. event was registered after the installation of the new equipment.

Explanations of A.U.R.N. A.U.R.N. remains a mystery and it has been hard for researchers to make any conclusions or find suitable explanations of the phenomenon, especially since it was only registered by the neutronic equipment. The expert committee gathered all possible scenarios, which can occur in a reactor for their investigation. Assumptions including the effects of fuel burnup and temperature have been eliminated due to the kinetics of A.U.R.N.s. Furthermore, the effects related to absorbing, moderating or reflecting parts have also been removed from the possible scenarios by the expert committee. Other phenomena such as effects related to sodium void, movements of the control rods and movement of the core have been investigated. Although many assumptions related to sodium void have been eliminated, there are still some left, for example implosion of sodium bubbles [16], though other assumptions such as sodium boiling and gas passing through the core, cannot provide a satisfying scenario due to their mechanisms. The involvement of the control rods have been examined, including their mechanism, the absorber pin bundle, the rotating plug that supports the rods. The high amplitude of the signals registered during the negative transient events requires a very high acceleration of the control rods and these investigations reveal that the required acceleration is not realistic. Therefore, control rod movements as a single explanation was abandoned. The first explanation that could cause such abnormal behavior in the signal of the neutron chambers was as mentioned before, interference in the measurements. Though, the equipment was later on proved to be insensitive to noise. Furthermore, there were up to seven different measurement channels from which the signal is computed, with different electronics and components that displayed the same abnormal activity, which makes the registered events even more consistent. However, it is possible that the high amplitude of the signals could be explained by failure in the electronics, though the deviation and oscillating behavior is most probably due to variation in the neutron flux.

Finally, after eliminating most of the plausible phenomena that can occur in a reactor, the expert committee concluded that assumptions involving movements of the core are most con- vincing. Outward movement of the sub-assemblies causing the core to expand, followed by a contraction, is a scenario which can induce a similar signal pattern as A.U.R.N. The expert

20 Phénix SODIUM-COOLED FAST REACTORS committee’s investigation of the phenomenon and its relation to A.U.R.N led to the following results and conclusions:

• Extensive modelling and tests performed on outward movement of the core, regardless of its origin, show that a pulse source inside the core can induce stresses, which in turn gives asimilarreactivitytransienttotheonesobservedduringtheA.U.R.N.sevents.

• Axial movements of the sub-assemblies in the core can theoretically reproduce similar signals, though this requires an unrealistic amount of energy. Consequently, the only realistic scenario of core movements involves radial movement of the sub-assemblies.

• The origin of the possible core movements in Phénix is still unidentified. Investigations have been made with scenarios based on transversal excitation from the diagrid; abnormal behavior of the core block structures; spontaneous reconfiguration of the core; a pressure hammer from gas passing in a pump; gas expansion occurring above the core or under the cover plug; loss of absorber pin tightness; oil passing through the core causing a mechanical effect by vaporization and cracking. All of these explanations have been discarded as possible origins.

CEA are going to recruit two Ph.D. students with the mission to investigate the remaining possible scenarios. They will hopefully solve the mystery of the negative transients.

3.3.2 Core-ﬂowering

Core-ﬂowering is a type of core-movement and it means that one sub-assembly expands and induces stresses on the surrounding sub-assemblies, causing the core to expand in radial direction. The result from core extension is displacement of the sub-assemblies in the core leading to an increase of the gap between the units. This decreases the keff of the core which is directly related to its thermal power. Little extension of the core leads to considerable decrease in the reactivity. For illustration see Figure 3.4.

Figure 3.4: Sub-assemblies under normal operation in a). Sub-assemblies suﬀering from core- ﬂowering at top b) and in the centre c).

21 SODIUM-COOLED FAST REACTORS ASTRID

3.3.3 Core-flowering tests of Phénix The latest scenario being investigated by CEA, is based on neutronic and thermal hydraulic interaction between a blanket-assembly and a moderated experimental sub-assembly, named DAC-assembly [16]. The increase of plutonium, as a result of breeding in the blanket combined, with the moderation effect of the experimental sub-assembly causes an increase in power between the two assemblies. This combined with the low flow-rate of sodium in the DAC sub-assembly causes the sodium to boil, which creates bubbles of sodium vapor. Implosion of these bubbles could induce the assumed core-flowering leading to the reactivity oscillations registered during the A.U.R.N. events.

After the life-time extension of Phénix 1998-2003, the operation of the facility restarted and new experiments for the development of SFRs were carried out. In the end of 2009 core-flowering tests were made by inserting the DAC experimental sub-assemblies, similar to those used in 1989 and 1990, into the core. The purpose of these tests was to investigate the thermal hydraulic and neutronic interactions between the experimental sub-assembly and blanket-assemblies. An Eddy current flowmeter was used for measuring the mass flow of sodium inside the DAC sub-assemblies see Figure 3.5 [17]. The thermal balance for both assemblies were measured at different mass flows of sodium. The power of the blanket and thermal exchanges between the sub-assemblies are to be determined by these experiments. Unfortunately, no results nor conclusions from the blanket-DAC experiments have yet been published.

Another experiment was carried out during the last year of Phénix to increase the knowledge of core-flowering. This was done while the reactor was running at zero power8, 100 kW [15]. A ∼ mechanical device, see Figure 3.6,wasinsertedintotwodifferentpositions;firstatthecenterof the core and then at a peripheral location of the core. The mechanical device put pressure on the surrounding sub-assemblies, causing the gap between all sub-assemblies to increase. The induced stress then resulted in a radial extension of the core, see Section 3.3.2 and Figures in Section 4.3.

The effect of core-flowering was measured at different temperatures in the interval of [180, 350]°C and the radius of the core was extended with 3-5 mm [15]. The result was that a small increase of the core radius gives a significant drop in reactivity. In this experiment the correlation between the negative feedback in keff and core extension lies around -60 pcm/mm, when the device was placed in the center of the core [17]. The effect was strongly reduced when the mechanical device was placed at the peripheral position.

3.4 ASTRID

Astrid is a French SFR prototype-project and the construction of the reactor will take place in the 2020’s. The ASTRID project is aiming at accomplishing some of the Generation IV criteria, though it will not be a "ﬁrst of a kind", since it is only going to be a prototype. The main goals of the project are to prove the technology of SFR on an industrial scale, perform transmutation of radioactive waste and irradiation experiments and the facility is to be used for the needed development of in-service inspections and repairs [18]. Considerable amount of information have been gathered from the experience of operating both Phénix and Superphénix, which now lies as a basis for the reactor design of ASTRID. More details in the design of ASTRIDs is to be published in 2012 and the ﬁnal design is to be delivered in 2014 [19].

8Zero power: the power plant runs at a low power without any active steam-generators.

22 IAEA TecDoc : Status of liquid metal cooled fast reactor technology ASTRID SODIUM-COOLED FAST REACTORS

Figure 2 - Thermal-hydraulic measuring pole on the DAC Figure 3.5: Schematic of the Eddy current ﬂow meter used for measuring the mass ﬂow of sodium in the moderated experimental sub-assembly DAC. [17] IAEA TecDoc : Status of liquid metal cooled fast reactor technology

Figure 3 - Experimental sub-assembly with moderator (DAC)

5. Training

In agreement with the ASN (Nuclear Safety Authority), a training program for the operating teams was set up. It consisted of presenting the operators with the test aims, their sequencing and related risks. To ensure successful testing, this program also saw the operators take part in drawing up the operational documents, called Trial Instruction Programs, as well as in running sessions on the SIMFONIX simulator, when this was possible.

Figure 3.6: A picture of the mechanicalFigure 12 – device,Device to push which apart was sub-assemblies used for testing how core-flowering is affecting the reactivity of the core. [17] The mechanical device was placed at two different core positions: at the center and at a peripheral one. The effect of core flowering was measured at different temperatures in the range 180 °C to 350 °C . The mechanical behaviour of the core was close to what was expected. Very small changes on core 3.4.1 Preliminary designradius give significant reactivity modifications, around - 60 pcm/mm in when the device is operated at the central position. This effect is strongly reduced at the peripheral position of the device. Astrid will in the preliminary designThe core be compactness a 600 MWe was no unit significantly [18], affected though by unlikethe temperature Phénix level. it will not breed any fuel. The blankets with fertile inventory surrounding the active core in earlier designs will be replaced by steel-reflectors.7. Further The core steps will of be the of program heterogeneous design to reduce the sodium void worth and the reactivity excessNow begins [19]. a new The phase main of in-depth vessel interpretation is a pool-type of the test configuration, results by the DEN though facilities at the origin ASTRID will follow the Russianof concept the request. of Consequently BN-600 with the neutron multiple physicists steam, thermal-hydraulics generators per experts interme- and fuel specialists will be able to capitalize on these results to complete the validation of the corresponding computer codes, ERANOS and DARWIN for neutronics, TRIO U and CATHARE for thermal-hydraulics and GERMINAL for fuel. The young engineers, specially recruited at CEA to prepare and conduct the tests along with the plant’s teams, will joined the fast reactor projects at CEA Cadarache center in23 their respective specialist areas after having experienced a unique period in their professional career.

Conclusion

A large program of tests was carried out for almost one year after the last industrial operation cycle of the Phenix sodium cooled fast reactor. The program covered core physics, thermal hydraulics and fuel issues and also the investigations of the automatic scrams occurred in 89 and 90. Several specific devices were designed, fabricated, qualified and used during the tests to complete the standard instrumentation of the reactor and to perform the tests. A big amount of information was recorded and will be used in the next period to fulfill the main objectives of the program on sodium fast reactors codes. This work was also the opportunity to involve young engineers in the preparation and performance of the tests.

SODIUM-COOLED FAST REACTORS ASTRID diate system. In the preliminary design, there are six intermediate circuits of sodium, which are connected to four steam generators of 100 MWe each [19]. The fuel pin design will be similar to those used in Superphénix, with a hole in the center to limit the maximum temperature of the pellet. The pin will have a large diameter, larger than in Superphénix and a small diameter spacing wire. The choice of fuel is for the moment MOX-fuel.

In-service inspections will have a large impact on the design of the reactor vessel and its external components. Hence, the focus will lie on simplification of the structures, accessibility, capability of component removal and repair, core discharge and arrangements for the possibility of primary circuit draining. There are several instruments that have been used in Phénix and Superphénix for inspection of the core, though the equipment needs upgrades and modifications before it can be used for the operations of ASTRID. More safety features for reactor shutdown will be introduced in order to enhance the protection against severe accidents, such as extra shutdown levels. A core catcher is going to be used as protection in the case of fuel-pin failure and core-melting. The possibility of core-flowering and core compaction is to be reduced in ASTRID by design; fuel elements will be reinforced to limit their movement [20].

Design parameters of ASTRID that are still open for discussion [19]: • Energy conversion • Primary circuit design • Devices to eliminate severe accidents

• Core catcher technology and location • Steam generators materials and technology • Innovative technologies for sodium ﬁres detection and mastering

24 4 Method and materials

The Monte-Carlo simulation code used for the study is discussed in this chapter. Descriptions of the core models and the simpliﬁed model of core-ﬂowering are also presented.

4.1 Monte-Carlo simulation code

The Monte-Carlo simulation code Serpent was chosen for the study in order to simulate how core-flowering affects the reactivity of the reactor. The main reasons for using this code were the advantage of free-of-charge and the access to the predefined SFR core of PFBR created by Peter Wolniewicz. Other advantages taken into account were predefined geometries and the fact that the Monte-Carlo Simulation code provides a simple way of creating complex lattices. The value of keff was obtained from the simulations in order to investigate how the reactivity of the core was affected by core-flowering.

Serpent has a manually deﬁned source of neutrons. The keff is calculated by neutron transport calculations and this process is referred to as a cycle. The calculated value of keff is after each cycle weighted against the values obtained from previous cycles. This has to be done in order to converge the value of keff .Aminimumnumberofcyclesarerequiredinordertohave aproperconvergenceofkeff . Inactive cycles are also used to have a better convergence of keff . The inactive cycles of a simulation are the initial cycles that correct the distribution of the keff values. However, the obtained values of keff are discarded in the inactive cycles.

4.1.1 Diﬃculties using Monte-Carlo simulation code

There are several problems when using Monte Carlo simulation code for calculation of keff . The three main issues that need to be taken into account are [21]:

• model error, bias

• statistical error

25 METHOD AND MATERIALS Monte-Carlo simulation code

• convergence

These issues can in most cases be avoided without any considerable impact on the results. First the convergence rate of keff can be more eﬃcient by using a good initial guess and a number of inactive cycles, which reduce the total number of cycles for convergence [21]. There is always a risk, when simulating diﬀerent states of a core, that the statistical error is larger than the change in keff between the simulations. In such a case it is impossible to make any essential conclusion from the result. The main way to prevent this is by increasing the number of simulations and have a large number of cycles per simulation. The bias of keff is proportional to 1/M , where M is the amount of neutrons per cycle. The bias is negligible if M>10000,thoughincaseofa large model M should be > 100000 neutrons/cycle [21].

4.1.2 Choice of Monte-Carlo simulation code

Two diﬀerent Monte Carlo-simulation codes were considered for the study: Serpent and MCNP. MCNP stands for general-purpose Monte Carlo N-Particle code and is developed by Los Alamos National Laboratory in the United States. It is capable of neutron, photon, electron, or coupled neutron/photon/electron transport, though it also includes the opportunity to calculate eigen- values, for example keff ,forcriticalsystems.

Serpent is a three-dimensional continuous-energy Monte Carlo neutron transport code developed at VTT Technical Research center of Finland. It also has the capability of performing burnup calculations. The code is speciﬁcally designed for reactor physics applications and the original intended use was the production of homogenized multi-group constants for reactor simulator calculations.

A comparison has been made [22] between the two diﬀerent Monte-Carlo simulations codes, which can be seen in Table 4.1 and Table 4.2. The simulation had 20 inactive and 500 active cycles and a source of 20 000 neutrons, which gives a total of 10 000 000 neutron histories. The JEFF-3.1.1 was used as a cross-section library.

Table 4.1: A comparison of k between MCNP and Serpent. [22] ∞

Case MCNP Serpent ∆(%) PWR pin-cell, 1 MWd/kgU burnup 1.28319 (0.013) 1.28294 (0.013) -0.019 PWR pin-cell, 20 MWd/kgU burnup 1.07180 (0.017) 1.07182 (0.016) 0.002 PWR pin-cell, 40 MWd/kgU burnup 0.91631 (0.021) 0.91611 (0.018) -0.022 SFR assembly 1.76744 (0.008) 1.76758 (0.008) 0.008 Mixed PWR MOX/UOX lattice 1.06929 (0.018) 1.06943 (0.017) 0.013

This thesis has a limitation in time and from the information obtained in Table 4.2 it can be concluded that Serpent is much faster than MCNP. In the SFR case, which is most essential, Serpent is 57 times faster than MCNP and the result only diﬀers with 0.008 %. Hence, MCNP was excluded as a simulation tool. Serpent is more time-eﬃcient and is specialized in lattice calculation and is therefore the best alternative for the simulations of this thesis.

26 Model of Phénix METHOD AND MATERIALS

Table 4.2: A comparison of computation time (in minutes) between MCNP and Serpent. [22]

Case MCNP Serpent MCNP/Serpent PWR pin-cell, 1 MWd/kgU burnup 821.0 21.4 38.3 PWR pin-cell, 20 MWd/kgU burnup 799.8 20.6 38.7 PWR pin-cell, 40 MWd/kgU burnup 809.7 21.3 38.0 SFR assembly 1368.3 23.9 57.2 Mixed PWR MOX/UOX lattice 143.3 17.2 8.3

4.1.3 Advantages and disadvantages of Serpent Serpent has only been on the market for a year. Although it seems now that most of the major bugs are ﬁxed, there are still some smaller ones left [23]. The latest report from the developer of Serpent tells that the minor bugs should not have a signiﬁcant impact on the results [24]. Since the code is still under development it does not have all the features that MCNP can provide, such as interactive geometric plotter for measurement and overview of the geometry, which are perfect for troubleshooting.

Woodcock’s delta-tracking method is used for the calculation of the neutron path in Serpent, which can lead to problems when heavy absorbers are present. However, this was not a problem for the simulations of the study due to the fact that a fast reactor was simulated, which meant that the value of the cross-sections of heavy absorbers were low. Therefore it should not have an impact on the results.

Another disadvantage of Serpent is that the code is not well suited for calculations of shielding and detectors due to the use of delta-tracking [25]. Instead, a collision estimator is used, which is less eﬃcient. In most cases however, the results from lattice calculations are not aﬀected.

Additional to the standard data libraries of Serpent, the code supports any continuous-energy MCNP data library. All numerical output from the simulations are stored in an .m-ﬁle, which is useful for analyzing the results in external programs, like MATLAB.

4.2 Model of Phénix

The model of Phénix created for the study is a simpliﬁed model of the Phénix core. The control rods are completely withdrawn from the core. Sodium ﬁlls the cells of the control rod and the sub-assemblies lie close to each other with a tiny space in-between. The wrapping material of the sub-assemblies has in this model the same material composition as the cladding of the fuel pins. The information gathered for the design has been obtained from the references [13, 26, 27].

The parameters of the model are presented in Table 4.3 and all material data are presented in Table 4.4 and 4.5.

27 METHOD AND MATERIALS Model of Phénix

Table 4.3: Parameters of the simpliﬁed model of Phénix. Most values are obtained from [13, 26, 27], other values have been set in order to have a reasonable geometry.

Reactor parameter Reference Value Fuel pin

Fuel type MOX (PuO2-UO2) Pellet diameter 5.42 mm Cladding outer diameter 6.65 mm Air-gap space 0.075 mm Thickness of cladding 0.45 mm Fissile height 850 mm Pitch 7.8 mm Pins/sub-assembly 271 Lower axial blanket within fuel pin 300 mm Upper axial blanket within fuel pin 260 mm Blanket pin

Blanket material Depleted uranium oxide (UO2) Pellet diameter 12.5 mm Cladding outer diameter 13.4 mm Thickness of cladding 0.45 mm Overall Length 1668 mm Pitch 14.5 mm Pins/sub-assembly 61 Sub-assembly Geometry Hexagonal Diameter across ﬂats 124 mm Wall thickness 3.5 mm Overall length S/A fuel 1410 mm Overall length S/A blanket 1668 mm Pitch 127 mm Core conﬁguraton Core design Homogeneous internal breeding Nr. of enrichment zones 2 Enrichment of Pu in MOX-fuel 18 % and 23 % Nr. of high-enriched S/A 48 Nr. of low-enriched S/A 55 Nr. of blanket S/A 90 Nr. control rods 6

28 Model of Phénix METHOD AND MATERIALS

Table 4.4: Composition of fuel and blanket.

Composition of fuel/blanket Proportion (%) Plutonium [1] 238Pu 3.5 % 239Pu 51.9 % 240Pu 23.8 % 241Pu 12.9 % 242Pu 7.9 % Uranium [28] (In MOX-fuel) 235U0.7% 238U99.3% Depleted uranium [28] 235U0.3% 238U99.7%

Table 4.5: Composition of of the cladding and wrapper steel. [29]

Material Proportion (%) Austenitic Steel Nr. 14970 C0.007% Cr 14.60 % Ni 15.00 % Mo 1.25 % Si 0.46 % Mn 1.70 % Ti 0.46 % Fe 66.44 %

29 METHOD AND MATERIALS Model of core-ﬂowering

Figure 4.1: Two-dimensional view of the core model of Phénix seen from the z-axis/above, with zoom at the active core and the fuel-assemblies. The red assemblies are dedicated cells for the control rods, which are withdrawn in this model. The blue sub-assemblies are blankets and the green and white ones are fuel-assemblies.

4.3 Model of core-ﬂowering

Monte-Carlo simulation codes have, as mentioned in Section 1.3,alimitednumberofgeometrical structures. In order to make a simulation of core-flowering, a simplification of the phenomenon was made; all structural bending of the sub-assemblies due to core-flowering, have not been taken into account. Instead the gap between the sub-assemblies was increased, which is the consequence of the structural bending, see Figures 4.2 and 4.3, which in turn causes core extension/increase of the core radius. The extra space added to the gap between the sub-assemblies, λ,increases

30 Model of core-ﬂowering METHOD AND MATERIALS symmetrically in this model, see Figure 4.4. The relation between the core extension and the extra space between the sub-assemblies depends on the number of sub-assemblies and core con- ﬁguration. The PFBR-model has a homogeneous design. If λ =1mm the corresponding core extension is 9 mm. For the Phénix-model, which is similar in design with a homogeneous core but with less number of sub-assemblies, the relation is 1:7.

The two different cores were first simulated with normal conditions, λ =0.Ahighnumber of neutrons were used to reduce the bias and enough cycles were made to make sure that the result converged properly. The simulations of core-flowering were made with λ =0.4, 0.8, 1.2, 1.6, 2 mm. The initial guess for keff was 1.00 and 100 inactive cycles were used in order to have a faster convergence rate. The nuclear data library used for these simulations was JEFF-3.1.1. Adetectorwasdefinedinthecenterofthemodelinordertoobtainhowtheneutronfluxis affected by core-flowering. How the detector is defined can be found in Chapter B.Theresults and the parameters for the simulations of Phénix are presented in Chapter 5 and the same can be obtained for the model of PFBR in the appendix, see Chapter D.

Figure 4.2: Plan view of how the sub-assemblies are aﬀected by core-ﬂowering in the simulations.

31 METHOD AND MATERIALS Model of core-ﬂowering

Figure 4.3: Side view of how the sub-assemblies are aﬀected by core-ﬂowering in the simulations. Each block corresponds to a block with hexagonal geometry.

Figure 4.4: The gap between the sub-assemblies increases symmetrically in the model of core- ﬂowering.

32 5 Result

In this chapter the results obtained from the model of Phénix and the model of core-ﬂowering are presented.

5.1 Model of Phénix

Under normal operation conditions, λ =0,thekeff of the Phénix model had a value of 1.00298. Detectors obtained the neutron flux in the center of the core. The obtained value from the simulation of the core under normal conditions was (8.43167 0.0175) 1015 neutrons/cm2, ± · compared with the measured neutron flux of Phénix, 7 1015 neutrons/cm2 [12]. This gives an · error/difference of around 20 % between the measured and the simulated value. The amount of fissile inventory in the model was estimated to be 1105 kg, by Serpent sampling 10 000 000 random points. According to reference [13], Phénix had a fissile inventory of 930 kg. This means that the amount of fissile material in the Phénix model is 19 % greater than measured. The inventory of 239Pu came to be 462 kg, which is much less than the value of 730 kg given in the same reference. Although the fissile inventory and the neutron flux differ quite a lot from the value given in the references, the values are sufficient for being a simplified model of the Phénix core.

5.2 Core-ﬂowering

The results from the simulations of core-ﬂowering, using the Phénix model, are presented in Table 5.1 and in Figure 5.1. It was obtained that the reactivity decreases when the core radius expands. A linear approximation, see Figure 5.1,givesthechange,∆keff /core extension = - 60 pcm/mm. Assuming that the signal from the neutron chambers directly corresponds to the thermal power of the core, the high amplitude of the signals from the A.U.R.N. events would require a core extension of around 5 mm. However, it does not seem that the relation between the reactivity and the increase of the core radius is linear due to the fact that three points of simulation data lie outside the linear approximation. This could mean that the relation is of

33 RESULT Core-ﬂowering higher order, though there is not enough data to tell. A similar relation was obtained from the results of PFBR that is presented in Chapter D and the linear approximation gave the change ∆keff /core extension = - 47.6 pcm/mm.

Table 5.1: The results of keff from the simulations of core-ﬂowering. The model of the Phénix- core was used for these simulations.

λ (mm) Extension Neutron Number of keff Standard of the core population cycles deviation, (mm) σ (10−5) 0 0.0 500000 2000 1.00298 5 0.4 2.8 500000 2000 1.00137 5 0.8 5.6 500000 2000 0.999605 5 1.2 8.4 500000 2000 0.997987 5 1.6 11.2 500000 2000 0.996145 4 2.0 14.0 500000 2000 0.994585 5

The results from the detector defined at the center of the Phénix model’s core are presented in Table 5.2 and in Figure 5.2. The neutron flux decreases as the core radius expands. However, at λ =1.6 mm there is a sudden increase. This is probably due to the statistical noise that is noticeable in the results. The relation between the neutron flux and core-extension is most likely of higher order. Note that thermal power of the core has the same value in all simulations.

Table 5.2: The results of the neutron ﬂux in the core center obtained from the simulations of core-ﬂowering, where λ is the increase in the gap between the sub-assemblies. The model of the Phénix-core was used for these simulations.

λ (mm) Extension Neutron Number Neutron ﬂux Standard 15 2 of the core population of cycles (10 cm− ) deviation, (mm) σ (1015) 0 0.0 500000 2000 8.43167 0.017454 0.4 2.8 500000 2000 8.38752 0.017194 0.8 5.6 500000 2000 8.35513 0.017128 1.2 8.4 500000 2000 8.34142 0.017434 1.6 11.2 500000 2000 8.36601 0.017485 2.0 14.0 500000 2000 8.34229 0.017485

34 Core-ﬂowering RESULT

Change in reactivity due to core extension

1.003 Simulation data Linear approximation 1.002

1.001

1 y = − 0.0006*x + 1 f

f 0.999

e k 0.998

0.997

0.996

0.995

0 2 4 6 8 10 12 14 Extension of the core [mm]

Figure 5.1: This figure displays how the keff of the Phénix model is affected by core extension due to core-flowering. A linear approximation gives ∆keff /core extension = -60 pcm/mm, though it does not seem to be a good approximation due to the fact that three points lie outside the line. However, in the interval [0 6] mm, the relation is in principle linear.

35 RESULT Core-ﬂowering

x 1015 Change in neutron flux due to core extension 8.46

8.44

8.42 ] 2

8.4

8.38 Neutrons flux [1/cm

8.36

8.34

8.32 −2 0 2 4 6 8 10 12 14 16 Extension of the core [mm]

Figure 5.2: The figure displays how the neutron flux in the center of the Phénix core model is affected by core-flowering. It can be seen that the relation between core extension and neutron flux is not linear. Note the peak at 11.2 mm, which shows a sudden increase in neutron-flux. This is probably a result of the statistical noise, which is noticeable in the large error bars. Note that thermal power of the core has the same value in all simulations.

36 6 Discussion

The A.U.R.N. events, the results obtained from the simulations and the uncertainties in the tools and models used are discussed in this chapter.

6.1 Simulations

The limitation of time in the study determined the choice of Monte-Carlo simulation code. Ser- pent was chosen due to its efficient computation time. MCNP was considered and although this code has been more validated compared to Serpent, its long computation time makes it unsuit- able. Serpent has some problems with calculations of the neutron paths if heavy absorbers are present. This however, should not be an issue in this thesis since no heavy absorber is present in any of the core models. Even if the models had control rods inserted into the core, the high energies of the neutrons should significantly reduce this error. Serpent has been validated against MCNP with satisfying results and therefore the results calculated by Serpent should be consistent. The models in the Monte-Carlo simulation code cannot describe dynamic environments such as coolant flow, which brings some uncertainties to the results.

There are some uncertainties in the models used for the simulations. First, a simplified model of the Phénix’s core was used and it should be noted that three different references have been used in order to find all crucial parameters. Some parameters have different values in the different references. The reason for the variation in value of the parameters is most probably due to the different set-up of fuel elements used in Phénix during its time in operation. Hence, the SFR model created has most probably used a different set-up of sub-assemblies than was used in Phénix during the A.U.R.N. events and the core-flowering experiments. This adds some uncertainties to the comparison between the results collected from the simulations and the experiments. However, it is still interesting that the change in keff obtained from the simulations is similar to the experimental data.

The model of core-ﬂowering is also a simpliﬁcation of the true phenomenon. It does not take into account that sub-assemblies swell, which in turn induces the stress to the surrounding sub-

37 DISCUSSION A.U.R.N. assemblies. Instead, all sub-assemblies are at a normal state without any bending or swelling. This leaves some uncertainties in the model, though it is not certain that the bending itself has asigniﬁcantimpactonthekeff .Furthermore,thegapbetweenthesub-assembliesincreases symmetrically in the model.

In order to have a consistent result, over 100 000 neutrons were used per cycle. Moreover, 2 000 cycles were used for each simulation in order to have a result where keff has converged and the statistical error is reduced. The results of keff did not have any major concerns regard- ing statistical errors, which can be an issue when using Monte-Carlo simulation codes. However, better and longer simulations are needed to reduce the statistical noise in the results obtained from the neutron ﬂux detector.

The model of Phénix has been partly validated against the real core, where the neutron flux and the fissile inventory were compared. The simulations differed from the measured values with 14%. The k of the model under normal conditions lies at 1.00298, which is quite a high value ∼ eff for a reactor. This is most probably the consequence of using different references for the creation of the model. The neutron flux and the amount of fissile inventory in the model of Phénix differ quite a lot from the values obtained from references. However, this is most probably a consequence of having different compositions of plutonium, wrapper materials and depleted uranium than used in Phénix when the measured values were obtained.

In the results of the simulations it can be obtained that the reactivity and the neutron flux clearly decrease when the core expands, which was the initial guess of the study. Small increase of the core radius leads to a significant change in the keff , which confirms the core-flowering experiments made in Phénix. The relation between keff and core expansion does not seem to be linear in the results obtained from the simulations, which was unexpected. Hence, the relation between keff and core expansion might be of a higher order, though there is not enough simulation data to tell. However, in the interval [0, 6] mm the relation is almost linear and the core, in the core-flowering experiments of Phénix, was only extended up to 5 mm. The results of the simulations correspond remarkably well to the experimental data, which indicates that the simulations were a success. It is however hard to validate how significant impact the uncertainties have on the results. Hence, it might be dangerous to make any more conclusions about the core’s behavior from these simulations (especially about the sudden increase in the neutron flux at λ = 1.6mm), when suffering from core-flowering.

6.2 A.U.R.N.

The strange events of A.U.R.N. that occurred in Phénix are an important issue in SFR-technology. It is strange that the phenomenon only occurred in Phénix, especially since there are over 400 years of operating experience of SFRs in the world. Hence, the origin of the negative reactivity transients is most probably related to some speciﬁc parameter of Phénix. This makes the scenario where an experimental sub-assembly, DAC-assembly, is responsible for provoking core-ﬂowering most probable.

No negative reactivity transients have been registered since the the fourth event of A.U.R.N. After that event, the power of Phénix was decreased. This leads to the possible conclusion that the events could somehow be related to the power of the reactor. Regardless, it is not possible to make this conclusion without ﬁrst comparing other parameters such as the sub-assembly set-up

38 A.U.R.N. DISCUSSION of the core before and after the power of the facility was reduced.

Radial movement of the core due to core-flowering, is the current most plausible explanation. It can cause similar patterns in the signals of the neutron chambers to those registered during the A.U.R.N. events. The free standing core concept that Phénix used, allows radial bowing of the assemblies, which makes core-flowering possible to occur. However, this should leave some trace inside the core, especially since it requires strong induced stresses of the sub-assemblies. The remarkable thing is that no trace has so far been found, which speaks against this scenario [15]. Although simulations of core-flowering have been made, the results from these cannot give any further explanation nor conclusion of how core-flowering is related to the negative reactivity transients.

What makes A.U.R.N. so diﬃcult to understand are the high amplitudes of the signals, the speed of the phenomenon and the amount of energy required in order to cause such change. These unsolved issues make some researchers to still believe that failure or noise in the electronic equipment is responsible for the abnormality in the signals of the neutrons chambers. However, in the tests the equipment proves its consistency. Furthermore, no physical phenomenon has been proven to be able to induce similar signals in the neutron chambers, which is not related to the thermal power of the core. On the other hand, no mechanical phenomenon can provide a satisfying scenario. Hence, it is possible that the abnormalities were induced by a combination of a mechanical phenomenon and some failure in the electrical equipment [15].

Although there are some possible scenarios for the A.U.R.N. events, its true origin has to be found in order to increase the understanding of the SFR concept and for the future development towards commercialization. Phénix is no longer available for neutronic experiments, though hopefully enough data have been gathered to solve this mystery. Hopefully, some kind of trace of A.U.R.N. or core-ﬂowering can be found during the decommissioning of Phénix and the dismantling of the core. It is therefore important that crucial parts of the reactor, during the dismantling process, are examined thoroughly. Finally, in order to exclude A.U.R.N. from occurring in current LWRs, the origin of the phenomenon must be found.

7 Conclusions

7.1 Conclusions

In this thesis a study of the A.U.R.N. events that occurred in the French reactor Phénix has been carried out. Furthermore, a model of the Phénix core was created and simulations of how core-ﬂowering aﬀects the keff have been made.

The simplified model of the core of Phénix was successfully created and validated, though unfortunately the model’s neutron flux and the amount of fissile isotopes differed from measured values of Phénix. This model can be used for further simulations, such as burnup calculations. Regardless of the validation of the Phénix model, the simulations gave satisfying results with the same value as was measured during the experiments of core-flowering made in the final year of Phénix. Thus, it was concluded that the relation between keff and the core extension could be of higher order (>1), though it is linear in the realistic intervals of the core-extension. However, these results cannot provide any essential conclusion about the origin of core-flowering nor if core-flowering is the single answer to the A.U.R.N. events. Though core-flowering as explanation is not inconsistent with the results of this study.

The most reasonable explanation of A.U.R.N. seems to be core-flowering, since it can recreate similar patterns in the signals of the neutron chambers. The absence of any kind of trace of this movement is remarkable though, which implies the uncertainties in this scenario. Due to the high amplitude of the signals, it is possible that there was interference or failure in the electrical equipment. However, the origin of the core-flowering and why it occurred remain unsolved. Furthermore, if core-flowering is the single reason for A.U.R.N., the high amplitude of the signals would require a core extension of around 5 mm, assuming that the signal from the neutron chambers directly corresponds to the thermal power of the core. If core-flowering is the sought answer, then future A.U.R.N. events can be avoided by design. By limiting the fuel elements’ movement the phenomenon can be reduced significantly, for example through strengthening of the fuel elements.

41 CONCLUSIONS Suggestions for further work

The irradiation experiments of the sub-assemblies with high burnup of fuel might be one answer to the origin of A.U.R.N., especially since it was one of the major differences between Phénix and Superphénix, which did not experience any similar transients. A moderated experimental sub-assembly and its possible involvement in inducing a core-flowering in Phénix is being investigated. Regardless of the origin of the negative reactivity transients, the safety of Phénix was not affected, such as support structures of the core. Furthermore, the automatic emergency shutdown of the reactor proved its efficiency during these events by shutting down the operation after a few hundreds of milliseconds. This type of event should therefore not be able to cause a severe accident, though it is still an issue for the commercialization of the SFR concept.

Further research is needed for finding the explanation behind A.U.R.N.s. It is important to find the explanation since the origin is unknown and therefore cannot be excluded from occurring in LWRs, even though it is not likely. The importance of finding the answer can be seen as CEA is still investigating the phenomenon and is going to recruit Ph.D. students for the investigation.

7.2 Suggestions for further work

In the study a simplified model of Phénix was created, however there are still some parameters in the model that can be improved. For instance, no reference for the wrapper material was found for the model and it was therefore set to the same material as the cladding of the fuel pins. It would also be intriguing to find a design of and more information about the DAC-assemblies and make further simulations of how these can affect the reactivity and neutron flux of the core.

The simulations of core-flowering using the Phénix model indicated that the change in keff is not linear. In order to confirm this, more simulation data should be gathered using the same models, but with other values of λ. It would also be of great interest to investigate how the neutron flux in- and outside the core is affected in this model.

Some very crude simulations of how core-flowering affects a LWR core showed an increase in reactivity instead of a decrease. This is not strange since an increase of the gap between the sub-assemblies increases the moderation effect. However, better and more simulations should be carried out before making any conclusions about this.

In order to gain more understanding of core-ﬂowering, more simulations should be carried out using other codes than Serpent to obtain a better model of the phenomenon. Deterministic codes, such as CAST3x, could be used for making more complex calculations.

Since the A.U.R.N. events have only occurred in Phénix, the origin of the events should be bound to some parameters that are specific for Phénix. Thus, it would be convenient to investigate different set-ups of sub-assemblies of Phénix used before and after the events. Furthermore, an investigation of the differences between Superphénix and Phénix might give some answers to A.U.R.N.s since the design of Superénix is based on data gathered from the operation of Phénix.

42 References

[1] J. Wallenius. Transmutation of nuclear waste, 2008. Not yet published. [2] Issued by the U.S. DOE Nuclear Energy Research Advisory Committee and the Generation IV International Forum. A technology Roadmap for Generation IV Nuclear Energy System. Generation IV International Forum http: // www. gen-4. org/ ,December2002. [3] A. E. Waltar and A. B. Reynolds. Fast Breeder Reactors.PergamonPress,1980. [4] World Nuclear Association. Fast neutron reactors. http: // www. world-nuclear. org/ , December 2010. [5] Y. Orechwa and S. F. Su. Homogeneous-Heterogeneous Core Evaluation and Structural- Material Selection. Information Bridge - http: // www. osti. gov/ bridge ,1982. [6] K. E. Holbert. Four factor formula. http: // holbert. faculty. asu. edu/ ,December 2010. Handout. [7] B. Rouben. Introduction to reactor physics. Atomic Energy of Canada Ltd.,September 2002. [8] R. Nakai. Design and Assessment Approach on Advanced SFR Safety with Emphasis on CDA Issue. http://www-pub.iaea.org/,December2009. [9] N. N. Oshkanov, O. M. Saraev, M. V. Bakanov, P. P. Govorov, O. A. Potapov, Yu. M. Ashurko, V. M. Poplavskii, B. A. Vasilev, Yu. L. Kamaninand, and V. N. Ershov. 30 years of experience in operating the BN-600 soidum-cooled fast reactor. Atomic Energy,108,2010. [10] Website of The Generation IV International Forum. http://www.gen-4.org/.2010-11-24. [11] Ph. Dafour. Sodium Fast Reactors Descriptions. ESFR Seminar,November2010. Cadarache. [12] J-F. Sauvage. Phénix, 30 years of history: the heart of a reactor. CEA. GONIN, 2006. [13] FBR-database of IAEA. http://www-frdb.iaea.org/.2010-11-18. [14] L. Martin and B. Vray. Phénix Plant, 2008. CEA, unpublished. [15] B. Fontaine CEA. Interview. 2010-11-18. [16] A. Vasile, B. Fontaine., M. Vanier, P. Gauthé, V. Pascal, G. Prulhière, P. Jaecki, D. Ten- chine, L. Martin, J.F. Sauvage, D. Verwaerde, R. Dupraz, and A. Woaye-Hune. The PHÉNIX ﬁnal tests. Abstract ICAPP 2011,2010. [17] A. Vasile, B. Fontaine, M. Vanier, D. Tenchine, P. Gauthé, V. Pascal., G. Prulhière, P. Jaecki, L. Martin., J-F. Sauvage, and R. Dupraz. IAEA TecDoc: Status of liquid metal cooled fast reactor technology: The Phénix end of life tests. IAEA,2010.Notyetpublished.

43 REFERENCES REFERENCES

[18] F. Gauché, J. Rouault, JC. Garnier, Guedeney, L. Martin, F. Baqué, Verwaerde, J.F. Sauvage, and J.P. Serpantié. The status of Fast Reactors program in France in 2010. IAEA TWG-F,November2010.PreparedbyA.Vasile. [19] P. Le Coz. The ASTRID project. ESFR Seminar, November 2010. Cadarache.

[20] A. MacLachlan. CEA ﬁnalizing design options for Gen IV sodium reactor. Platts Nucleonics Week,March2010. [21] F. Brown, W. Martin, J. Leppänen, Wim H., and B. Cochet. Reactor Physics Analysis with Monte Carlo. ANS PHYSOR-2010 Conference Workshop,2010.

[22] J. Leppänen. Standard comparison between Serpent 1.1.13 and MCNP5. http: // montecarlo. vtt. fi/ ,2010. [23] J. Leppänen. Progress Report 2009. http: // montecarlo. vtt. fi/ ,2010. [24] PSG / Serpent - a Continuous-energi Monte Carlo Reactor Physics Burnup Calculation Code. http://montecarlo.vtt.fi/.2010-10-20. [25] J. Leppänen. Performance of Woodcock delta-tracking in lattice physics applications using the Serpent Monte Carlo reactor physics burnup calculation code. Annals of Nuclear Energy, 2010. [26] F. Varaine. Core speciﬁcations and design. ESFR Seminar, November 2010. Cadarache.

[27] F. Delage, A. Courcelle, Y. Guerin, M. Pelletier, and M. Zabiego. Fuel pin & fuel assembly design: Fuel manufacturing, behaviour and requirements. ESFR Seminar,November2010. Cadarache.

[28] World Nuclear Association. Uranium and depleted uranium. http: // www. world-nuclear. org/ ,December2009. [29] M. Teradaa, R. A. Antunesb, A. F. Padilhab, H. Gomes de Meloc, and I. Costaa. Comparison of the Corrosion Resistance of DIN W. Nr. 1.4970 (15%Cr-15%Ni-1.2%Mo-Ti) and ASTM F- 138 (17%Cr-13%Ni-2.5%Mo) Austenitic Stainless Steels for Biomedical Applications, 2005.

[30] JEFF 3.1.1 - Nuclear Data Library. http://www.oecd-nea.org/janis/,December2010.

44 List of Figures

2.1 The presence evolution of transuranium elements in spent nuclear fuel. [1] . . . . 8 2.2 This ﬁgure shows the fuel pin and the sub-assembly/fuel-assembly arrangements of FRs and LWRs. Note the LWR fuel-assemblies have more space between the fuel pins than those of FRs. a) Sub-assembly arrangement of FRs. b) Fuel-assembly arrangement of LWRs. c) Fuel pin arrangement of FRs. d) Fuel pin arrangements of LWRs...... 9 2.3 Overview of the internal and external conﬁguration of a FBR...... 10

3.1 Overview of the SFR pool design. The system has a primary circuit integrated in the main vessel and the heat is transferred from the primary circuit to the steam generators by intermediate circuits. [2] ...... 16 3.2 Chart of downtime at Phénix due to accidents and maintenance. Note the percentage of negative reactivity transients, which is the fourth time-wasting issue, if scheduled work is not taken into account. [14] ...... 17 3.3 Two separate registered signals obtained from the neutron chambers during the last two A.U.R.N. events in Phénix in 1990. Note the oscillating behavior and the secondary peak, which in both cases slightly exceed the initial power. [14] . . . . 18 3.4 Sub-assemblies under normal operation in a). Sub-assemblies suffering from core- flowering at top b) and in the centre c)...... 21 3.5 Schematic of the Eddy current flow meter used for measuring the mass flow of sodium in the moderated experimental sub-assembly DAC. [17] ...... 23 3.6 A picture of the mechanical device, which was used for testing how core-flowering is affecting the reactivity of the core. [17] ...... 23

4.1 Two-dimensional view of the core model of Phénix seen from the z-axis/above, with zoom at the active core and the fuel-assemblies. The red assemblies are dedicated cells for the control rods, which are withdrawn in this model. The blue sub-assemblies are blankets and the green and white ones are fuel-assemblies. . . 30 4.2 Plan view of how the sub-assemblies are affected by core-flowering in the simulations. 31 4.3 Side view of how the sub-assemblies are affected by core-flowering in the simulations. Each block corresponds to a block with hexagonal geometry...... 32 4.4 The gap between the sub-assemblies increases symmetrically in the model of core- flowering...... 32

5.1 This figure displays how the keff of the Phénix model is affected by core extension due to core-flowering. A linear approximation gives ∆keff /core extension = -60 pcm/mm, though it does not seem to be a good approximation due to the fact that three points lie outside the line. However, in the interval [0 6] mm, the relation is in principle linear...... 35

45 LIST OF FIGURES LIST OF FIGURES

5.2 The figure displays how the neutron flux in the center of the Phénix core model is affected by core-flowering. It can be seen that the relation between core extension and neutron flux is not linear. Note the peak at 11.2 mm, which shows a sudden increase in neutron-flux. This is probably a result of the statistical noise, which is noticeable in the large error bars. Note that thermal power of the core has the same value in all simulations...... 36

D.1 This ﬁgure shows how the keff of the model of PFBR is aﬀected by core extension. Alinearapproximationgives∆keff /Core extension = -47.6 pcm/mm...... D-2

46 List of Tables

3.1 Table of some SFRs in world. Note that BN-600 and Superphénix are the only tworeactorsofcommercialsize. [11] ...... 14 3.2 A summary of the design parameters for the SFR concept of Generation IV. [2] . 15

4.1 A comparison of k betweenMCNPandSerpent. [22] ...... 26 ∞ 4.2 A comparison of computation time (in minutes) between MCNP and Serpent. [22] 27 4.3 Parameters of the simpliﬁed model of Phénix. Most values are obtained from [13, 26, 27], other values have been set in order to have a reasonable geometry. . 28 4.4 Compositionoffuelandblanket...... 29 4.5 Composition of of the cladding and wrapper steel. [29] ...... 29

5.1 The results of keff from the simulations of core-flowering. The model of the Phénix-core was used for these simulations...... 34 5.2 The results of the neutron flux in the core center obtained from the simulations of core-flowering, where λ is the increase in the gap between the sub-assemblies. The model of the Phénix-core was used for these simulations...... 34

D.1 The results from the simulations of the PFBR-core ...... D-1

Nomenclature

A.U.R.N. Arrêt d’Urgence par Réactivité Négative (automatic emergency shutdown by negative reactivity), page 2 CEA Commissariat à l’énergie atomique et aux énergies alternatives (French Alternative En- ergies and Atomic Energy Commission), page 19 EFR European Fast Reactor, page 13

FBR Fast Breeder Reactor, page 8 FR Fast Reactor, page 5 GFR Gas-cooled Fast Reactor, page 1

IHX Intermediate Heat Exchangers, page 14 LFR Lead-cooled Fast Reactor, page 1 LWR Light-Water Reactor, page 5 MOX-fuel Mixed Oxide fuel, page 15

MSR Molten Salt Reactor, page 1 PFBR Prototype Fast Breeder Reactor. A sodium-cooled fast reactor under construction in India., page 3 PWR Pressurized Water Reactor, page 14

S/A Sub-assembly, page 28 SCWR Super-Critical Water Reactor, page 1 SFR Sodium-cooled Fast Reactor, page 1

TRU Transuranium Elements, page 8 VHTR Very High Temperature Reactor, page 1

Appendices

A Deﬁnitions of the units in the Four Factor Formula

In this section the deﬁnitions of the diﬀerent units of the four factor formula are presented

= Fastfissionfactor f = T hermal ultilization p = Resonance escape probability P = Non leakage probabilities − total fission neutrons from thermal and fast fission = fission neutrons from thermal fission thermal neutrons absorbed by fuel f = total thermal neutrons absorbed absorption P = production Number of neutrons slowing to thermal energy p = total number of fast neutrons available for slowing

k = keff without any leakage of neutrons, a reactor with no boundaries. ∞

A-1

B Code of the Phénix Model

The code used to create the model of Phenix in Serpent:

set title "Phenix"

% Fuel/Pins −−−−−−−−−−−−−−−−− −−−−−−−−−−−−−−−−−

% Low e n r i c h e d f u e l −−− pin 1 % low fuel pin − lowfuel 0.275 % fuel pellet outer radius void 0.2825 % cladding inner radius cladding 0.3275 % cladding outer radius sodium % coolant outside of clad

% High enriched fuel −−− pin 2 % high fuel pin − highfuel 0.275 % fuel pellet outer radius void 0.2825 % cladding inner radius cladding 0.3275 % cladding outer radius sodium % coolant outside of clad

% Blanket pin −−− pin 3 blanket 0.625 % blanket pin

B-1 CODE OF THE PHÉNIX MODEL cladding 0.67 sodium % coolant outside of clad

% Coolant −−− pin9 %dummypinforfillingthelattice sodium

% Lattices −−−−−−−−−−−−−−−−− −−−−−−−−−−−−−−−−− % Fuel Sub assembly , low enriched −−− − − lat 10 2 0 0 19 19 0.78

9999999999999999999 9999999991111111119 9999999911111111119 9999999111111111119 9999991111111111119 9999911111111111119 9999111111111111119 9991111111111111119 9911111111111111119 9111111111111111119 9111111111111111199 9111111111111111999 9111111111111119999 9111111111111199999 9111111111111999999 9111111111119999999 9111111111199999999 9111111111999999999 9999999999999999999

% Fuel Sub assembly , high enriched −−− − − lat 20 2 0 0 19 19 0.78

9999999999999999999 9999999992222222229 9999999922222222229 9999999222222222229 9999992222222222229 9999922222222222229 9999222222222222229 9992222222222222229 9922222222222222229 9222222222222222229 9222222222222222299

B-2 CODE OF THE PHÉNIX MODEL

9222222222222222999 9222222222222229999 9222222222222299999 9222222222222999999 9222222222229999999 9222222222299999999 9222222222999999999 9999999999999999999

%Dummyassembly withsodium lat 110 2 0 0 19 19 0.78

9999999999999999999 9999999999999999999 9999999999999999999 9999999999999999999 9999999999999999999 9999999999999999999 9999999999999999999 9999999999999999999 9999999999999999999 9999999999999999999 9999999999999999999 9999999999999999999 9999999999999999999 9999999999999999999 9999999999999999999 9999999999999999999 9999999999999999999 9999999999999999999 9999999999999999999

% Blanket assembly −− − lat 30 2 0 0 11 11 1.45

99999999999 99999333339 99993333339 99933333339 99333333339 93333333339 93333333399 93333333999 93333339999 93333399999 99999999999

B-3 CODE OF THE PHÉNIX MODEL

%Core l a t t i c e lat 200 3 0 0 21 21 12.7 % Pitch 12.7 cm 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 33 33 33 33 33 33 33 22 22 22 22 22 22 22 22 22 22 22 22 33 33 33 33 33 33 33 33 33 33 22 22 22 22 22 22 22 22 22 22 33 33 33 33 51 51 51 33 33 33 33 22 22 22 22 22 22 22 22 22 33 33 33 51 51 51 51 51 51 33 33 33 22 22 22 22 22 22 22 22 33 33 51 51 50 50 50 50 50 51 51 33 33 22 22 22 22 22 22 22 33 33 51 51 50 50 50 80 50 50 51 51 33 33 22 22 22 22 22 22 33 33 51 51 50 80 50 50 50 50 50 51 51 33 33 22 22 22 22 22 33 33 33 51 50 50 50 50 50 50 80 50 51 33 33 33 22 22 22 22 22 33 33 51 50 50 50 50 50 50 50 50 50 51 33 33 22 22 22 22 22 33 33 33 51 50 80 50 50 50 50 50 50 51 33 33 33 22 22 22 22 22 33 33 51 51 50 50 50 50 50 80 50 51 51 33 33 22 22 22 22 22 22 33 33 51 51 50 50 80 50 50 50 51 51 33 33 22 22 22 22 22 22 22 33 33 51 51 50 50 50 50 50 51 51 33 33 22 22 22 22 22 22 22 22 33 33 33 51 51 51 51 51 51 33 33 33 22 22 22 22 22 22 22 22 22 33 33 33 33 51 51 51 33 33 33 33 22 22 22 22 22 22 22 22 22 22 33 33 33 33 33 33 33 33 33 33 22 22 22 22 22 22 22 22 22 22 22 22 33 33 33 33 33 33 33 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22

% Surfaces −−−−−−−−−−−−−−−−− −−−−−−−−−−−−−−−−− surf 1 hexyprism 0 0 5.85 42.5 42.5 % inner sub ass struct − − surf 2 hexyprism 0 0 6.2 42.5 42.5 % outer sub ass struct − − surf 3 hexyprism 0 0 5.85 83.4 83.4 % inner sub ass struct − − surf 4 hexyprism 0 0 6.2 83.4 83.4 % outer sub ass struct − − surf 5 hexyprism 0 0 5.85 42.5 68.5 % inner sub ass struct − surf 6 hexyprism 0 0 5.85 72.5 42.5 % inner sub ass struct − − − surf 7 hexyprism 0 0 6.2 42.5 68.5 % outer sub ass struct − surf 8 hexyprism 0 0 6.2 72.5 42.5 % outer sub ass struct − − − surf 100 sph 0 0 0 300 % Region of Neutrons surf 200 sph 0 0 0 400 % Sphere of interest surf 500 cyl 0 0 105 % Reactor tank

% Cells −−−−−−−−−−−−−−−−− −−−−−−−−−−−−−−−−− cell 1000 80 sodium 4 − cell 1001 80 sodium 4

B-4 CODE OF THE PHÉNIX MODEL

% Universe 100, low enriched sub assembly −−− − − cell 1 50 fill 10 1 2 − − cell 2 50 cladding 1 2 − cell 56 50 fill 15 6 812 − − cell 53 50 cladding 6 812 − cell 54 50 fill 15 5 712 − − cell 55 50 cladding 5 712 − cell 5 50 sodium 2 5 6 7 8

% Universe 200, high enriched sub assembly −−− − − cell 6 51 fill 20 1 2 − − cell 7 51 cladding 1 2 − cell 8 51 fill 15 6 812 − − cell 50 51 cladding 6 812 − cell 51 51 fill 15 5 712 − − cell 52 51 cladding 5 712 − cell 10 51 sodium 2 6 5 8 7

% Universe 300, blanket assembly −−− − cell 11 33 fill 30 3 4 − − cell 12 33 cladding 3 4 − cell 13 33 sodium 4

% Universe 22, dummy assembly with sodium for lattice −−− − cell 1111 22 fill 110 4 − cell 1311 22 sodium 4

% Universe 0, the core −−− cell 101 0 fill 200 500 100 − − cell 102 0 void 500 100 − cell 103 0 outside 100

% Plotting −−−−−−−−−−−−−−−−− −−−−−−−−−−−−−−−−− %plot3800800 %Plottingthewholegeometry %plot2800800 %Plottingside view − %plot28008000 3.1 3.1 150 150 % Plotting fuel pins − − %plot38008000 69.5 69.5 69.5 69.5 % Plot of inner core − − % Materials −−−−−−−−−−−−−−−−− −−−−−−−−−−−−−−−−−

% High enriched fuel −−−

B-5 CODE OF THE PHÉNIX MODEL

mat highfuel 10.98 rgb 255 255 255 % 10.9777 − − 92238.12c 0.7646 % U 238 99.3% − 92235.12c 0.0054 % U 235 0.07% − 94238.12c 0.0081 % Pu 238 3.5% − 94239.12c 0.1194 % Pu 239 51.9% − 94240.12c 0.0547 % Pu 240 23.8% − 94241.12c 0.0297 % Pu 241 12.9% − 94242.12c 0.0182 % Pu 242 7.9% − 8016.12c 2 % O2

% Low e n r i c h e d f u e l −−− mat lowfuel 10.97 rgb 0 255 0 % 10.9683 − − 92238.12c 0.8143 % U 238 − 92235.12c 0.0057 % U 235 − 94238.12c 0.0063 % Pu 238 − 94239.12c 0.0934 % Pu 239 − 94240.12c 0.0428 % Pu 240 − 94241.12c 0.0232 % Pu 241 − 94242.12c 0.0142 % Pu 242 − 8016.12c 2 % O2

% Cladding , SS 316 −−− %SS316 %mat c l a d d i n g 7.9402 rgb 255 255 0 − %26000.06c 0.66 % Natural Fe %28000.06c 0.13 % %24000.06c 0.17 %42000.06c 0.025 %25055.06c 0.015

%15 15 Ti − mat cladding 7.8974 rgb 255 255 0 − 6000.06c 0.0009 24000.06c 0.146 28000.06c 0.150 42000.06c 0.0125 14000.06c 0.0046 25055.06c 0.0170 22000.06c 0.0046 26000.06c 0.6644

% Sodium , coolant −−− mat sodium 0.968 rgb 255 0 0 − 11023.06c 1

B-6 CODE OF THE PHÉNIX MODEL

% Blanket , U 238 −−− − mat blanket 10.5 rgb 0 0 255 − 92238.06c 0.997 % depleted Uranium, U 238 − 92235.06c 0.003 % depleted Uranium, U 238 − 8016.06c 2 % O2

% Detectors −−−−−−−−−−−−−−−−− −−−−−−−−−−−−−−−−− det 1 % Detector for measuring the average flux of the core dz 42.5 42.5 20 − dl 200 dv 1.29E6

det 3 % Detector for measuring the neutron flux at the core ’ s center dx 111 − dy 111 − dz 111 − du 0 dv 8

% Libraries −−−−−−−−−−−−−−−−− −−−−−−−−−−−−−−−−− set acelib "/xs/sss_jeff31u .xsdata"

% Values for normalization −−−−−−−−−−−−−−−−− −−−−−−−−−−−−−−−−− set power 5.63E8 % thermal power of the core

% Start values −−−−−−−−−−−−−−−−− − −−−−−−−−−−−−−−−−− set pop 10000 3000 50 1.001

B-7

C Output data from a test run of the Phénix model

Here is a test run of the core model of Phénix used for the report. Note that only two active cycles are presented since there is no value in displaying them all.

_.= ..== . − − − − {} __ .’Oo ’. / <’ ) < − −− {} .’O’. /o. .O\ / . ‘ − −−− {} /. .o\ /O/ \ o\ /O/ − \‘ ‘/ \O‘ ’o / \ O‘ ‘o / − − − ‘ . ‘’.____.’‘.____.’ − − PSG2 / S e r p e n t

AContinuous energy Monte Carlo Reactor Physics Burnup Calculation Code − Version 1.1.13 (August 25, 2010) Contact : Jaakko . Leppanen@vtt . fi − −− Parallel calculation mode not available − Geometry and mesh plotting available − Begin calculation on Mon Jan 10 13:30:44 2011

Reading input f i l e "Phenix " . . .

Processing geometry ... OK .

Reading directory f i l e s . . .

C-1 OUTPUT DATA FROM A TEST RUN OF THE PHÉNIX MODEL

OK .

Calculating isotope fractions ... OK .

Reading data from ACE f i l e s : Isotope 6000.06c (C nat ) . . . − Isotope 8016.06c (O 16)... − Isotope 8016.12c (O 16)... − Isotope 11023.06c (Na 23)... − Isotope 14000.06c (Si nat ) . . . − Isotope 22000.06c (Ti nat ) . . . − Isotope 24000.06c (Cr nat ) . . . − Isotope 25055.06c (Mn 55)... − Isotope 26000.06c (Fe nat ) . . . − Isotope 28000.06c (Ni nat ) . . . − Isotope 42000.06c (Mo nat ) . . . − Isotope 92235.06c (U 235)... − Isotope 92235.12c (U 235)... − Isotope 92238.06c (U 238)... − Isotope 92238.12c (U 238)... − Isotope 94238.12c (Pu 238)... − Isotope 94239.12c (Pu 239)... − Isotope 94240.12c (Pu 240)... − Isotope 94241.12c (Pu 241)... − Isotope 94242.12c (Pu 242)... − OK .

Reading energy arrays : Isotope 6000.06c (C nat ) . . . − Isotope 8016.06c (O 16)... − Isotope 8016.12c (O 16)... − Isotope 11023.06c (Na 23)... − Isotope 14000.06c (Si nat ) . . . − Isotope 22000.06c (Ti nat ) . . . − Isotope 24000.06c (Cr nat ) . . . − Isotope 25055.06c (Mn 55)... − Isotope 26000.06c (Fe nat ) . . . − Isotope 28000.06c (Ni nat ) . . . − Isotope 42000.06c (Mo nat ) . . . − Isotope 92235.06c (U 235)... − Isotope 92235.12c (U 235)... − Isotope 92238.06c (U 238)... − Isotope 92238.12c (U 238)... − Isotope 94238.12c (Pu 238)... − Isotope 94239.12c (Pu 239)... − Isotope 94240.12c (Pu 240)... − Isotope 94241.12c (Pu 241)... − Isotope 94242.12c (Pu 242)... −

C-2 OUTPUT DATA FROM A TEST RUN OF THE PHÉNIX MODEL

OK .

Main grid thinned from 198270 to 198270 points using tolerance 0.00E+00. − 34737 important points added resulting in a total of 198270 points. − Final grid size 198046 points (1.00E 11 < E < 2 0 . 0 ) . − − Total 2387 points in nubar grid . − 2energygroupsinfewgroup structure . − − Processing XS data: Isotope 6000.06c (C nat ) . . . − Isotope 8016.06c (O 16)... − Isotope 8016.12c (O 16)... − Isotope 11023.06c (Na 23)... − Isotope 14000.06c (Si nat ) . . . − Isotope 22000.06c (Ti nat ) . . . − Isotope 24000.06c (Cr nat ) . . . − Isotope 25055.06c (Mn 55)... − Isotope 26000.06c (Fe nat ) . . . − Isotope 28000.06c (Ni nat ) . . . − Isotope 42000.06c (Mo nat ) . . . − Isotope 92235.06c (U 235)... − Isotope 92235.12c (U 235)... − Isotope 92238.06c (U 238)... − Isotope 92238.12c (U 238)... − Isotope 94238.12c (Pu 238)... − Isotope 94239.12c (Pu 239)... − Isotope 94240.12c (Pu 240)... − Isotope 94241.12c (Pu 241)... − Isotope 94242.12c (Pu 242)... − OK .

Finalizing XS data ... OK .

Preparing statistics . . . OK .

Setting partial reaction lists for material cross sections... OK .

Calculating material total cross sections : material highfuel ... material lowfuel ... material cladding ... material sodium ...

C-3 OUTPUT DATA FROM A TEST RUN OF THE PHÉNIX MODEL

material blanket ... OK .

Starting the transport calculation cycle ...

Sampling initial source . . . OK .

Inactive cycle 1 / 10: k eff = 0.45696 (DT thresh = 0.9000) − Inactive cycle 2 / 10: k eff = 0.78370 (DT thresh = 0.9000) − Inactive cycle 3 / 10: k eff = 0.93937 (DT thresh = 0.9000) − Inactive cycle 4 / 10: k eff = 0.96630 (DT thresh = 0.9000) − Inactive cycle 5 / 10: k eff = 1.00147 (DT thresh = 0.9000) − Inactive cycle 6 / 10: k eff = 1.00093 (DT thresh = 0.9000) − Inactive cycle 7 / 10: k eff = 1.00404 (DT thresh = 0.9000) − Inactive cycle 8 / 10: k eff = 1.00514 (DT thresh = 0.9000) − Inactive cycle 9 / 10: k eff = 0.98590 (DT thresh = 0.9000) − Inactive cycle 10 / 10: k eff = 1.00188 (DT thresh = 0.9000) − Begin active cycles −−−−− −−−−−

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− Serpent 1.1.13 Criticality source simulation −− Title : "Phenix"

Active cycle 1 / 100 (5000 source neutrons)

Delta tracking on: thresh = 0.90 , eff = 0.53 , frac = 0.85 − Running time : 0:00:21 Estimated running time : 0:05:40 Estimated running time left : 0:05:19

k eff (analog) = 0.99988 +/ 0.00000 [0.99988 0.99988] − − k eff (implicit) = 0.99780 +/ 0.00000 [0.99780 0.99780] − −

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− (...)

Serpent 1.1.13 Criticality source simulation −− Title : "Phenix"

Active cycle 100 / 100 (5000 source neutrons)

C-4 OUTPUT DATA FROM A TEST RUN OF THE PHÉNIX MODEL

Delta tracking on: thresh = 0.90 , eff = 0.53 , frac = 0.87 − Running time : 0:03:13 Estimated running time : 0:03:13 Estimated running time left : 0:00:00 k eff (analog) = 1.00267 +/ 0.00186 [0.99903 1.00632] − − k eff (implicit) = 1.00271 +/ 0.00109 [1.00056 1.00485] − −

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− Finished after 100 active cycles of 5000 source neutrons. Total calculation time 3.22 minutes .

Notes :

Unable to read available memory from /proc/meminfo . − Consider manual override .

Unresolved resonance probability tables available for 10 − nuclides but sampling NOT in use.

2neutronsemittedabovemaximumenergy20.00MeV. −

C-5

D Results of the PFBR-model

The parameters and the results of the keff ,obtainedfromthesimulationofthePFBRmodel can be seen in Table D.1. The result is displayed in ﬁgure Figure D.1. The linear approximation of the result gives the relation ∆keff /Core extension = -47.6 pcm/mm.

Table D.1: The results from the simulations of the PFBR-core

Increase in Extension Neutron Number of keff Standard the S/A of the core population cycles deviation, 5 gap, λ(mm) (mm) σ(10− ) 0 0.0 500000 2356 1.16338 4 0.2 1.8 300000 1000 1.16240 7 0.4 3.6 300000 1300 1.16166 7 0.8 7.2 300000 1300 1.15987 7 1.2 10.8 300000 1300 1.15829 7 1.6 14.4 300000 1300 1.15653 7 2.0 18.0 250000 5000 1.15472 4

D-1 RESULTS OF THE PFBR-MODEL

Figure D.1: This ﬁgure shows how the keff of the model of PFBR is aﬀected by core extension. Alinearapproximationgives∆keff /Core extension = -47.6 pcm/mm.

D-2