Simulation of Reactor Transient and Design Criteria of

UPTEC F11 011

Examensarbete 30 hpFebruari 2011

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

Filip Gottfridsson

Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student

Abstract

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

Filip Gottfridsson

The need for energy is growing in the world and the market of nuclear power is nowonce more expanding. Some issues of the current light-water reactors can be solvedby the next generation of nuclear power, Generation IV, where sodium-cooledreactors are one of the candidates. Phénix was a French prototype sodium-cooledreactor, which is seen as a success. Although it did encounter an earlierunexperienced phenomenon, A.U.R.N., in which a negative reactivity transientfollowed by an oscillating behavior forced an automatic emergency shutdown of thereactor. This phenomenon lead to a lot of downtime of the reactor and is stillunsolved. However, the most probable cause of the transients is radial movements ofthe core, referred to as core-flowering.

This study has investigated the available documentation of the A.U.R.N. events. Asimplified model of core-flowering was also created in order to simulate how radialexpansion affects the reactivity of a sodium-cooled core. Serpent, which is aMonte-Carlo based simulation code, was chosen as calculation tool. Furthermore, amodel of the Phénix core was successfully created and partly validated. The model ofthe core has a k_eff = 1.00298 and a neutron flux of (8.43+-0.02)!10^15neutrons/cm^2 at normal state. The result obtained from the simulations shows thatan expansion of the core radius decreases the reactivity. A linear approximation ofthe result gave the relation: change in k_eff/core extension = - 60 pcm/mm. This valuecorresponds remarkably well to the around - 60 pcm/mm that was obtained from thededicated 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. Theequipment 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 someresearcher believe that the events are a combination of interference in the equipmentof Phénix and a mechanical phenomenon. Regardless, the origin of A.U.R.N. seems tobe bound to some specific parameter of Phénix due to the fact that the transientsonly have occurred in this reactor.

A safety analysis made by an expert committee, appointed by CEA, showed that theA.U.R.N. events are not a threat to the safety of Phénix. However, the origin of thesenegative transients has to be found before any construction of a commercial sizesodium-cooled fast reactor can begin. Thus, further research is needed.

Sponsor: Vattenfall ABISSN: 1401-5757, UPTEC F11 011Examinator: Tomas NybergÄmnesgranskare: Henrik SjöstrandHandledare: Hans Henriksson

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

I especially would like to thank Bruno Fontaine for all the valuable information and guidancehe has provided, which have been essential for this thesis. I am also grateful for the time AndreiFokau spent in order to help me learn Monte-Carlo simulation codes.

Contents

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Aims and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Outline of this report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Fundamentals of fast reactors 52.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Fission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Breeding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.4 Transmutation of long-lived radio-active elements . . . . . . . . . . . . . . . . . . 72.5 Core design of fast reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.5.1 Configuration of fast breeder reactors . . . . . . . . . . . . . . . . . . . . 72.6 Effective neutron multiplication factor, keff . . . . . . . . . . . . . . . . . . . . . 9

3 Sodium-cooled fast reactors 133.1 Sodium-cooled fast reactors in the world . . . . . . . . . . . . . . . . . . . . . . . 133.2 Sodium-cooled reactor design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2.1 Advantages and disadvantages . . . . . . . . . . . . . . . . . . . . . . . . 143.2.2 Technical overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.3 Phénix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.3.1 A.U.R.N. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.3.2 Core-flowering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.3.3 Core-flowering tests of Phénix . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.4 ASTRID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.4.1 Preliminary design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4 Method and materials 254.1 Monte-Carlo simulation code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.1.1 Difficulties using Monte-Carlo simulation code . . . . . . . . . . . . . . . 254.1.2 Choice of Monte-Carlo simulation code . . . . . . . . . . . . . . . . . . . . 264.1.3 Advantages and disadvantages of Serpent . . . . . . . . . . . . . . . . . . 27

4.2 Model of Phénix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.3 Model of core-flowering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

5 Result 335.1 Model of Phénix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.2 Core-flowering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

6 Discussion 376.1 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376.2 A.U.R.N. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

7 Conclusions 417.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417.2 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 developa fast breeder reactorwill have a commercial advantagefor the exploitation of nuclearenergy"

Enrico Fermi - 1945

1Introduction

The need of energy in the world is growing and since we now are facing possible climate changesthe search for alternative energy sources to fossil fuels is greater than ever. Nuclear power hasfor some time been a non-expanding market, though today the view has changed. It is now seenas one of the alternatives to fossil fuel due to its low emission of CO2 and low environmentalimpact. However, nuclear power has its disadvantages, for example the waste produced in currentreactors needs to be stored for more than 300 000 years [1]. A new generation of nuclear powerplants named Generation IV is under development, which can solve some of the problems relatedto the current nuclear power. The aim of Generation IV is to have safer, more reliable andefficient power plants with a physical protection against terrorism in a closed fuel cycle [2]. Thegoal is also to improve the environment, for example by introducing nuclear-produced hydrogenfor 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 ofthese designs are being developed throughout the world in order to achieve the goal of commer-cialization.

It is possible to have different neutron spectra by using different coolants. For example us-ing liquid metal as coolant results in having a fast neutron spectrum1 in the reactor, more aboutthis in Chapter 2, which in turn leads to the possibility to use up to 99.9 % of the fuel. Thiscan be compared to the fuel usage of todays water reactors’ usage of a few percent. Recycling ofthe spent nuclear fuel is then possible and it can result in a reduction of storage time from 300000 years to several 1000 years [1]. Hence, the process of storing might be easier for a countryto 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 cansustain such severe environment.

The sodium-cooled fast reactor is the candidate of Generation IV that lies furthest ahead inresearch and development [2]. Even though sodium-cooled fast reactors are part of a new gener-ation of nuclear power, the idea is quite old. In fact, the first reactor connected to the electricalgrid, EBR-I, was cooled with a combination of sodium and potassium [3]. However, the com-mercialization of sodium-cooled fast reactors is still far away in time due to the lack of propermaterials.

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 prob-lems in the French reactor Phénix. The French call these transients A.U.R.N., which is short forArrêt d’Urgence par Réactivité Négative. In English this means automatic emergency shutdownby negative reactivity. No final explanation of A.U.R.N.s has yet been established, though themost probable cause is radial movement of the core called core-flowering. This is one of the issuesthat 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 surveypublished reports and use Monte-Carlo simulation code in order to simulate core-flowering andanalyze how it affects the reactivity of an SFR core. Simplified models of the phenomenon havebeen used in order to make the simulations possible. The aims of the study are to determine apossible cause of the negative reactivity transients, give a solution on how to avoid the problemand point to further research. Furthermore, some design criteria and core configurations of SFRsare 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 forVattenfall in their long-term coverage of future reactor concepts, especially for the understandingof 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, thereforethe information is very limited. There are few reports published in English that describe pos-sible explanations and most of them only describe the problem, not its origin. The simulationshowever, are only used in order to analyze core-flowering and how it affects the reactivity of anSFR core. The results from the simulations have been compared with experimental data, thoughthe simulations cannot be used to make any conclusions of the origin of the negative reactivitytransients.

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 dy-namic flows, such as coolant flow. Complex structures that are not included in the geometriclibrary of the code are difficult to create. Sub-assemblies3 suffering from core-flowering havetherefore in the simulations the same structure as in the normal state. Another limitation inthe 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-upsof assemblies with different cladding material etc. No complete core description of Phénix wasfound. Thus, the parameters and materials used in order to create the model for this studyare obtained from several references. Some parameters vary in the different references and thevalues 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 IndianSFR that is under construction) are simplified in this project and cannot completely describe theenvironment 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 onthe 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.A description of the Phénix model and the model of core-flowering is also presented.

• Result - The results from the simulations of the Phénix and core-flowering models arepresented.

• Discussion - This chapter discusses the results, the models and the survey of the publishedreports.

• 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 MonteCarlo 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.

3

2Fundamentals of fast reactors

This chapter presents the basic theory of fast reactors and some of their advantages. Differentcore 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 havea moderator3 as LWR. Hence, the neutrons of the FRs maintain their high energy. Thermalneutrons are wanted in LWRs, since they have a higher possibility to cause fissions than fastneutrons, read more in Section 2.2, though they cause build-up of long-lived actinides4, whichexplains why nuclear waste from LWR needs to be stored for so long. However, reactors using afast neutron spectrum have the advantages of better neutron economy, production of fuel whileoperating, 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 ofa weaker negative feedback [1].

Plutonium is the primary choice for FRs, in order to have a closed fuel cycle possible withcurrent reactors. The fuel of FRs require a high-enriched fuel, around 20 % or more, due to thelow 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, whenbombarded by neutrons, n, splits into two minor nuclei, which are referred to as fission products.

1Fast neutrons: High energetic neutrons, ∼1 MeV.

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 withhigh energies, are called fissile isotopes. Common examples are 235U and 239Pu. Fissile isotopesare needed in order to sustain a nuclear chain reaction5. The fissile isotope 235U is the mainchoice of fuel for LWRs. The reaction formula for fission of the isotope is [3]

n+235 U →236 U∗ → Fission products+ 2̄.5n+ energy (2.1)

Plutonium, 239Pu, is commonly used as fuel in a FRs [3]

n+239 Pu →240 Pu∗ → Fission products+ 2̄.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

n+238 U →239 U∗ →239 Np+ β− (2.3)239Np →239 Pu+ β− (2.4)

Isotopes, which can transmute into fissile isotopes by neutron capture, are referred to as fertileisotopes and the process is called conversion. The degree of conversion that occurs in the reactoris

CR =fissile material produced

fissile material destroyed(2.5)

One favorable feature of FRs is breeding, which means that the production of fuel is higherthan the fuel consumed. Breeding is possible in a FR due to the fact that a fast neutron spec-trum has the advantages of higher production of neutrons per fission and a higher σf/σc-ratio(where σf is the cross-section6 for fission and σc is the cross-section for neutron capture of thefissile isotope). The reactor is a breeder if the conversion ratio is greater than 1 [3]. In such acase, the conversion ratio is referred to as breeding ratio

BR =fissile material produced

fissile material destroyed> 1 (2.6)

In FRs, fuel enriched with 239Pu is a better choice than 235U, commonly used in LWR, most dueto the fact that the η-value, number of neutrons produced per absorption, see equation 2.7, of239Pu is greater at higher energies of the neutrons. This is desired in a breeding reactor, sinceη needs to be > 2 to make breeding possible. In other words, for each neutron absorption, twonew 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

η =σfν

σf + σc(2.7)

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 anotherimportant feature. The objective of transmutation is to convert long-lived radiotoxic nuclei toshorter-lived isotopes.

The build-up of long-lived actinides is a serious disadvantage of the current nuclear power. Thepresence of actinides, such as Am, Cm and Pu, makes spent fuel radiotoxic for a long time. Ittakes more than 300 000 years for the nuclear waste to reach a radioactive level below naturaluranium, see Figure 2.1. Hence, spent nuclear fuel from LWRs needs to be stored during thisperiod. Fission products also contribute to the radiotoxicity of nuclear waste, though not asmuch 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 severalthousands of years [1]. However, introducing minor actinides8 into the fuel brings safety relatedproblems, 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 ac-tinides is to have "target sub-assemblies", containing the minor actinides. These assemblies arededicated 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 orderto optimize the burnup and breeding potential. Hence, the core of FRs has a hexagonal geometrywith hexagonal sub-assemblies, which differs from the square geometry of the fuel-assemblies10in LWRs. The fuel pin and sub-assembly/fuel-assembly arrangement for FRs and LWRs arepresented in Figure 2.2. The core of LWRs is designed to have a fuel-to-moderator ratio thatoptimizes the neutron economic and this is achieved by using a square geometry. However, thelack of moderator in FRs makes a minimized and more compact core superior.

2.5.1 Configuration of fast breeder reactorsThere are two basic configurations for a Fast Breeder Reactor, FBR: external and internal breed-ing. 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

FUNDAMENTALS OF FAST REACTORS Core design of fast reactors

During the first 20 years of cooling, the major contri-

bution to the radiotoxic inventory comes from fission

products, more specifically 85Kr, 90Sr and 137Cs. The

comparatively short half-life of these nuclides however

within 400 years reduces the contribution to the speci-

fic radiotoxic inventory from the fission products

below levels of natural uranium with progeny. It takes

over 300 000 years for the transuranium elements to

reach the same level. Even though the spent fuel is not

completely harmless after this time, natural radiation

sources constitute similar levels of hazard. The radio-

toxic inventory of uranium in nature is 18 mSv/g (to

96% given by uranium daughters) and may serve as

one of several possible reference levels in the context

of transmutation.

If we are to reduce the radiotoxic inventory by tran-

smutation, the priority should therefore be given to

fissioning of the transuranium elements [Claiborne72].

Not all of these elements constitute a significant

hazard, though. Figure 1.2 shows the relative contri-

butions to the specific radio-toxic inventory from the

long lived α-emitters. During the first 1000 years, 241Am is the major offender. In the long term, 240Pu

and 239Pu dominate the hazard. From the figure it may

be inferred that removal of both plutonium and ame-

ricium is required in order to reduce the time needed

for the radio-toxic inventory of spent nuclear fuel to

reach the level of natural uranium below 20 000 years.

Neptunium on the other hand, does not contribute

significantly to the radio-toxic inventory, especially if

the source term consisting of 241Am-decay is elimina-

ted. We may therefore focus our efforts on the tran-

smutation of plutonium and americium. An important

corollary is that the curium which is produced when

transmuting americium must also be recycled. Other-

wise, the reduction of the long term radiotoxic inven-

tory in the waste stream would be limited to about a

factor of ten [Delpech99].

Transmutation of nuclear waste

11

Figure 1.1: Specific radiotoxic

inventory of spent PWR fuel.

Figure 1.2: Contributions of

individual transuranium nucli-

des to the radiotoxic inventory of

spent PWR fuel.

102 103 104 105 106

0.01

0.1

1

10

100

101

Radiotoxic inventory [Sv/g]

243Am

242Pu

239Pu

238Pu

240Pu

237Np

241Am

TRU

t [y]

Unat

0.001

0.01

0.1

1

10

100Radiotoxic inventory [Sv/g]

102 103 104 105 106101

TRU

FP

Uranium in nature

t[y]

Figure 2.1: The presence evolution of transuranium elements in spent nuclear fuel. [1]

material located in a blanket zone outside the core of pure fissile material. Internal breeding con-figuration instead has a core of both fissile and fertile material surrounded by a fertile blanketzone. The external arrangement was considered for the early FBRs, though was never imple-mented due to the rapid change in reactivity during fuel burnup, which is a consequence of noin-core breeding. Internal breeding has the advantages of high breeding ratio and reduction ofvoid coefficients.

In-core configuration: Homogeneous and heterogeneous

All FBRs so far, have had a core design where internal breeding in the core is possible, whichis also known as in-core breeding concept. There are two variants of this arrangement: homo-geneous and heterogeneous. A core with all assemblies of pure fertile material, located in bothradial and axial regions has a so called homogeneous configuration due to the uniform spreadof fertile and fissile material. The regions of fertile material have two main functions; neutronshielding and breeding of fuel.

The heterogeneous configuration has a core of fissile sub-assemblies where the blanket-assembliesof pure fertile material are distributed throughout the fissile regions. The advantages of thisconfiguration are better breeding ratios and reduced sodium void coefficients, though it has thedisadvantage 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-assemblydesign 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 ofFRs and LWRs. Note the LWR fuel-assemblies have more space between the fuel pins than thoseof FRs. a) Sub-assembly arrangement of FRs. b) Fuel-assembly arrangement of LWRs. c) Fuelpin 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 , is an important parameter inall 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 fromequation 2.7

� =Fast fission factor

f =Thermal utilization

p =Resonance Escape Probability

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

number of neutrons in previous generation(2.10)

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

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, inorder 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 witha subcritical core that uses a proton-canon as an outside neutron source to have a sustainableneutron economy. The reactivity of a reactor [7], ρ, is defined as

ρ =keff − 1

keff(2.11)

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)

11

3Sodium-cooled fast reactors

This chapter describes the technique of SFRs and their current status in the world. Detailedinformation about the French reactor Phénix and information gathered from the investigation ofthe 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 inthe world and together they have provided over 400 years of operation experience [8]. Reactorsof experimental and prototype size have dominated the SFR fleet, see Table 3.1 and due totechnological and economical difficulties of using sodium as coolant, Superphénix and BN-600remain as the only two SFRs of industrial/commercial size ever constructed. Superphénix hasbeen 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 operationbefore it finally was forced to shutdown in 1998. The BN-600 did also encounter problems inthe early years, though it should be noted that the reactor have, several times, been the bestpower-generating unit in Russia, both with respect to reliability and safety [9]. A third reactorof industrial size was designed in the project European Fast Reactor, EFR, which was initiatedin 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 expand-ing their SFR programs. New countries are joining the international co-operations, such as theGeneration IV Forum [10] and building reactors of their own to gather data and operating expe-rience of SFRs. China for instance, has recently finished their construction of CEFR, China FastExperimental Reactor, an experimental SFR with thermal capacity of 60 MW. France, which isone of the leading countries in SFR-technology, is for the moment planning the design of theirsecond prototype reactor, ASTRID. The construction of ASTRID will probably take place inthe middle of 2020. Moreover, Russia and India are expanding their SFR fleet with the ongoingconstruction 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 tworeactors of commercial size. [11]

Name Country Thermal power (MWth1) Type Critical StatusEBR-I USA 1.4 Experimental 1951 ShutdownRAPSODIE France 24 Experimental 1967 ShutdownBOR-60 Russia 60 Experimental 1968 OperatingJOYO Japan 50 Experimental 1977 OperatingCEFR China 60 Experimental 2010 OperatingBN-350 Kazakhstan 1000 Demonstration 1972 ShutdownPhénix France 563 Demonstration 1973 ShutdownMonju Japan 714 Demonstration 1992 OperatingBN-600 Russia 1470 Commercial 1980 OperatingSuperphénix 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 typeis the most technologically developed concept of Generation IV [2]. It is similar to PressurizedWater Reactors, PWRs, in its design with primary and secondary circuits.

3.2.1 Advantages and disadvantagesThe current primary objective of SFR concept is to burn high-level waste, especially burnup ofplutonium and other actinides in order to reduce the storage time. Sodium as coolant has theadvantage 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, sodiumis not corrosive, it has a high thermal conductivity, high thermal inertia and the possibility toremove decay heat2 from the core by natural convection. These advantages combined with thefact that the SFR concept have been both tested and proven on industrial scale make sodium afeasible coolant for future reactors.

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

3.2.2 Technical overviewThe primary circuit with sodium cools the core and the secondary system with sodium transferthe heat from the primary circuit through Intermediate Heat Exchangers, IHX, to the steamgenerators, 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 bekept pure to avoid sodium oxide and hydride deposits, which in turn can lead to blockage in theventilation of the sub-assemblies. Alternatives, which do not react violently with sodium, in thesecondary circuit, are being considered. Super-critical carbon dioxide in a so called Brayton cycleis currently being developed as energy carrier. This concept is more efficient than the cycles usedin the present reactors. Since carbon dioxide does not react as violent with sodium as water anintermediate system would be unnecessary. Most SFR designs have multiple secondary circuitsthat are each connected to a multiple number of steam generators. For example, Phénix hadthree secondary loops with one steam generator each, while BN-600 had three secondary loopswith eigth steam generators each.

There are two different configurations of the primary circuit: the common pool configurationand 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 configurationeach module has separate casings. The advantage of the pool configuration is large thermal iner-tia and the system is insensitive to loss of coolant flow, on the other hand the loop configurationhas the benefit of easier inspections and repairs. The loop configuration also has better defenseagainst 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 ValueOutlet Temperature 530-550 °CPressure ∼ 1 AtmospheresRating 1000-5000 MWthFuel Oxide or metal alloyCladding Ferritic or ODS ferriticAverage Burnup ∼ 150− 200GWD/MTHM3

Conversion Ratio 0.5-1.30Average Power Density 350 MWth/m3

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 andthe liquid sodium. The layer acts as an inert atmosphere, which prevents sodium aerosols fromleaving deposits in sensitive areas. Furthermore, nitrogen is used as an inert gas between themain vessel and safety vessel and in systems surrounding the pipings carrying sodium. The rea-son 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. TheMOX-fuel is a combination of PuO2 and UO2. It is the primary choice of fuel for SFR due to theextensive experience gathered from earlier operation and testing. Metal fuel is a combination ofuranium-plutonium-zirkonium metal alloy and it has the advantage of better thermal conduc-tivity 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 inthe main vessel and the heat is transferred from the primary circuit to the steam generators byintermediate circuits. [2]

3.3 Phénix

In 1971, the construction of the second French SFR, Phénix, was complete. Phénix was the firstdemonstrational/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 connectedto one steam generator each [12]. The desirable temperature of the sodium outlet from the corelies at 560°C and the inlet lies at 400°C. Phénix had a homogenous core with two enrichmentzones of fissile fuel [13]. The fissile core was surrounded by a fertile blanket, both in radial andaxial directions, of mainly depleted or natural uranium. Most of the fuel breeding in Phénix tookplace in the blanket zone. Phénix used the free standing core restraint concept for keeping thesub-assemblies of the core together, which means that the core support structure is located at thelower part of the sub-assemblies. The concept allows free outward bowing of fuel- and blanketassemblies until the core radius makes contact with the shield assemblies, which are located atthe periphery of the core. Several experimental sub-assemblies were placed in the core of Phénixfor different irradiation experiments.

The main objectives of Phénix were not only to test the feasibility of SFR technology on largerscale but to perform irradiation experiments, like minor actinide burning [12]. For these ex-periments, 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 percentageof negative reactivity transients, which is the fourth time-wasting issue, if scheduled work is nottaken into account. [14]

gathered from the operation of Phénix have been used for the development of Superphénix andEFR.

Phénix encountered many incidents during its time in operation and most of these were relatedto sodium leaks in the intermediate heat exchangers, see Figure 3.2. Phénix suffered long down-times after minor incidents due to the fact that a political decision was required for a restart ofthe reactor, even though the facility recovered fast from the damages. In the late 1980’s and inthe beginning of 1990’s, Phénix encountered several automatic shutdowns of the reactor due tonegative transients. These events caused long downtimes of the reactor, see Figure 3.2, in orderto investigate their origin, more information about this is presented in Section 3.3. After thefourth automatic shutdown, the power of the reactor was decreased to 350 MWth [12] due to anindependent reason related to residual power removal system [15]. In 1992, a program for thelife-time extension of Phénix was initiated and the renovation was finished in 2002. Phénix thenproceeded with its operation until the reactor was finally shutdown in 2009. The last experimentperformed 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 seenas 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 unexperiencedphenomenon that lead to an automatic shutdown of the reactor. The signal of the neutron cham-

17


bers5 registered very rapid oscillations with high amplitudes, see Figure 3.3. During the timeperiod between 1989-1990, Phénix suffered from this event four times. These transients werenamed "Arrêt d’urgence par réactivité négative", A.U.R.N. In English this means automaticemergency shutdown by negative reactivity. The events occurred while operating at or closeto full power; the first three at 580 MWth and the last one at 500 MWth. A.U.R.N. were alldetected by the neutron chambers, which are located beneath the reactor vessel and measure theneutron 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. A symmetrical increase to a maximum below the initial value

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 lasttwo 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 shut-down automatically by the control rods. The control rods were triggered by the first reactivitydrop due to the fact that the amplitude of the drop went below the threshold for negative reac-tivity transient. The power drop in the signal varies in the four different events and in the lasttwo it reached down to 28% and 45% of the nominal power. Assuming that the power signalfrom the neutron chamber directly corresponds to the thermal power of the core; the fastestdrop reached in the A.U.R.N. events corresponds to a loss in keff of 320 pcm7 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.

7pcm: per cent mille of ∆keff/keff .

18


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, covergas 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 themeasurement channels was the first possible explanation of the phenomenon due to the fact thattwo 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 theequipment was insensitive to noise.

The information gathered from the third event led to the explanation that a large volume ofgas passed through the core. This was confirmed by the observation of an increase in the pres-sure 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 scenariohowever, 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 torecreate 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 EnergyCommission, CEA (Commissariat à l’Énergie Atomique et aux énergies alternatives), conductedan 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 shouldoccur in different conditions

• Make proposals for preventive measures

After almost two years of investigation, the committee had not found a complete explanation ofthe 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 causeA.U.R.N., it was concluded that the safety of the reactor was not affected. A new approachwas proposed, in which the surveillance of the reactor should be reinforced in order to obtain asmuch information as possible in case of a new negative reactivity transient. Secondly, tests wereto be performed at low power followed by 10 days at high power, to test the instrumentation ofPhénix 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 additionalequipment in order to have a full surveillance of the reactor and to detect any anomaly. Someexamples of new equipment:

• SONAR device installed above the core

• Acoustic detector inside the core

• Magnetic field measurement of the reactor vessel

19


Furthermore, instrumentation designed for fast measurements were installed in Phénix. In theend of 1991 and in the beginning of 1992, tests were performed with the new equipment. Theywere 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 in-formation to be able to discard several assumptions made for different scenarios, which were toexplain the occurrence of A.U.R.N. in Phénix. The earlier seen correct behavior of the core andthe 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 findsuitable explanations of the phenomenon, especially since it was only registered by the neutronicequipment. The expert committee gathered all possible scenarios, which can occur in a reactorfor their investigation. Assumptions including the effects of fuel burnup and temperature havebeen 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 expertcommittee. Other phenomena such as effects related to sodium void, movements of the controlrods and movement of the core have been investigated. Although many assumptions related tosodium void have been eliminated, there are still some left, for example implosion of sodiumbubbles [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 controlrods have been examined, including their mechanism, the absorber pin bundle, the rotating plugthat supports the rods. The high amplitude of the signals registered during the negative transientevents requires a very high acceleration of the control rods and these investigations reveal that therequired acceleration is not realistic. Therefore, control rod movements as a single explanationwas abandoned. The first explanation that could cause such abnormal behavior in the signal ofthe neutron chambers was as mentioned before, interference in the measurements. Though, theequipment was later on proved to be insensitive to noise. Furthermore, there were up to sevendifferent measurement channels from which the signal is computed, with different electronics andcomponents that displayed the same abnormal activity, which makes the registered events evenmore consistent. However, it is possible that the high amplitude of the signals could be explainedby failure in the electronics, though the deviation and oscillating behavior is most probably dueto variation in the neutron flux.

Finally, after eliminating most of the plausible phenomena that can occur in a reactor, theexpert 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 acontraction, is a scenario which can induce a similar signal pattern as A.U.R.N. The expert

20


committee’s investigation of the phenomenon and its relation to A.U.R.N led to the followingresults and conclusions:

• Extensive modelling and tests performed on outward movement of the core, regardless ofits origin, show that a pulse source inside the core can induce stresses, which in turn givesa similar reactivity transient to the ones observed during the A.U.R.N.s events.

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

• The origin of the possible core movements in Phénix is still unidentified. Investigationshave been made with scenarios based on transversal excitation from the diagrid; abnormalbehavior of the core block structures; spontaneous reconfiguration of the core; a pressurehammer from gas passing in a pump; gas expansion occurring above the core or under thecover plug; loss of absorber pin tightness; oil passing through the core causing a mechanicaleffect by vaporization and cracking. All of these explanations have been discarded aspossible origins.

CEA are going to recruit two Ph.D. students with the mission to investigate the remainingpossible 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 andinduces 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 anincrease of the gap between the units. This decreases the keff of the core which is directly relatedto 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 hydraulicinteraction between a blanket-assembly and a moderated experimental sub-assembly, namedDAC-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 betweenthe two assemblies. This combined with the low flow-rate of sodium in the DAC sub-assemblycauses the sodium to boil, which creates bubbles of sodium vapor. Implosion of these bubblescould induce the assumed core-flowering leading to the reactivity oscillations registered duringthe A.U.R.N. events.

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

Another experiment was carried out during the last year of Phénix to increase the knowledge ofcore-flowering. This was done while the reactor was running at zero power8, ∼100 kW [15]. Amechanical device, see Figure 3.6, was inserted into two different positions; first at the center ofthe core and then at a peripheral location of the core. The mechanical device put pressure on thesurrounding sub-assemblies, causing the gap between all sub-assemblies to increase. The inducedstress 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]°Cand the radius of the core was extended with 3-5 mm [15]. The result was that a small increase ofthe core radius gives a significant drop in reactivity. In this experiment the correlation betweenthe negative feedback in keff and core extension lies around -60 pcm/mm, when the device wasplaced in the center of the core [17]. The effect was strongly reduced when the mechanical devicewas placed at the peripheral position.

3.4 ASTRID

Astrid is a French SFR prototype-project and the construction of the reactor will take place inthe 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 goalsof the project are to prove the technology of SFR on an industrial scale, perform transmutationof radioactive waste and irradiation experiments and the facility is to be used for the neededdevelopment of in-service inspections and repairs [18]. Considerable amount of information havebeen gathered from the experience of operating both Phénix and Superphénix, which now liesas a basis for the reactor design of ASTRID. More details in the design of ASTRIDs is to bepublished 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

ASTRID SODIUM-COOLED FAST REACTORSIAEA TecDoc : Status of liquid metal cooled fast reactor technology

Figure 2 - Thermal-hydraulic measuring pole on the DAC

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 3.5: Schematic of the Eddy current flow meter used for measuring the mass flow of sodiumin the moderated experimental sub-assembly DAC. [17]

IAEA TecDoc : Status of liquid metal cooled fast reactor technology

Figure 12 – Device to push apart sub-assemblies 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 radius 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. The core compactness was no significantly affected by the temperature level. 7. Further steps of the program Now begins a new phase of in-depth interpretation of the test results by the DEN facilities at the origin of the request. Consequently the neutron physicists, thermal-hydraulics experts 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 in 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.

Figure 3.6: A picture of the mechanical device, which was used for testing how core-flowering isaffecting the reactivity of the core. [17]

3.4.1 Preliminary design

Astrid will in the preliminary design be a 600 MWe unit [18], though unlike Phénix it will notbreed any fuel. The blankets with fertile inventory surrounding the active core in earlier designswill be replaced by steel-reflectors. The core will be of heterogeneous design to reduce the sodiumvoid worth and the reactivity excess [19]. The main vessel is a pool-type configuration, thoughASTRID will follow the Russian concept of BN-600 with multiple steam generators per interme-

23

SODIUM-COOLED FAST REACTORS ASTRID

diate system. In the preliminary design, there are six intermediate circuits of sodium, which areconnected to four steam generators of 100 MWe each [19]. The fuel pin design will be similarto those used in Superphénix, with a hole in the center to limit the maximum temperature ofthe pellet. The pin will have a large diameter, larger than in Superphénix and a small diameterspacing 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 ex-ternal components. Hence, the focus will lie on simplification of the structures, accessibility,capability of component removal and repair, core discharge and arrangements for the possibilityof primary circuit draining. There are several instruments that have been used in Phénix andSuperphénix for inspection of the core, though the equipment needs upgrades and modificationsbefore it can be used for the operations of ASTRID. More safety features for reactor shutdownwill be introduced in order to enhance the protection against severe accidents, such as extra shut-down levels. A core catcher is going to be used as protection in the case of fuel-pin failure andcore-melting. The possibility of core-flowering and core compaction is to be reduced in ASTRIDby 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

4Method and materials

The Monte-Carlo simulation code used for the study is discussed in this chapter. Descriptionsof 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 howcore-flowering affects the reactivity of the reactor. The main reasons for using this code were theadvantage of free-of-charge and the access to the predefined SFR core of PFBR created by PeterWolniewicz. Other advantages taken into account were predefined geometries and the fact thatthe Monte-Carlo Simulation code provides a simple way of creating complex lattices. The valueof keff was obtained from the simulations in order to investigate how the reactivity of the corewas affected by core-flowering.

Serpent has a manually defined source of neutrons. The keff is calculated by neutron trans-port calculations and this process is referred to as a cycle. The calculated value of keff is aftereach cycle weighted against the values obtained from previous cycles. This has to be done inorder to converge the value of keff . A minimum number of cycles are required in order to havea proper convergence of keff . 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 keffvalues. However, the obtained values of keff are discarded in the inactive cycles.

4.1.1 Difficulties using Monte-Carlo simulation codeThere are several problems when using Monte Carlo simulation code for calculation of keff . Thethree 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. Firstthe convergence rate of keff can be more efficient by using a good initial guess and a number ofinactive cycles, which reduce the total number of cycles for convergence [21]. There is always arisk, when simulating different states of a core, that the statistical error is larger than the changein keff between the simulations. In such a case it is impossible to make any essential conclusionfrom the result. The main way to prevent this is by increasing the number of simulations andhave a large number of cycles per simulation. The bias of keff is proportional to 1/M , whereM is the amount of neutrons per cycle. The bias is negligible if M > 10000, though in case of alarge 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 AlamosNational Laboratory in the United States. It is capable of neutron, photon, electron, or coupledneutron/photon/electron transport, though it also includes the opportunity to calculate eigen-values, for example keff , for critical systems.

Serpent is a three-dimensional continuous-energy Monte Carlo neutron transport code devel-oped at VTT Technical Research center of Finland. It also has the capability of performingburnup calculations. The code is specifically designed for reactor physics applications and theoriginal intended use was the production of homogenized multi-group constants for reactor sim-ulator 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 activecycles and a source of 20 000 neutrons, which gives a total of 10 000 000 neutron histories. TheJEFF-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) -0.019PWR pin-cell, 20 MWd/kgU burnup 1.07180 (0.017) 1.07182 (0.016) 0.002PWR pin-cell, 40 MWd/kgU burnup 0.91631 (0.021) 0.91611 (0.018) -0.022SFR assembly 1.76744 (0.008) 1.76758 (0.008) 0.008Mixed 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 beconcluded 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, MCNPwas excluded as a simulation tool. Serpent is more time-efficient and is specialized in latticecalculation 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/SerpentPWR pin-cell, 1 MWd/kgU burnup 821.0 21.4 38.3PWR pin-cell, 20 MWd/kgU burnup 799.8 20.6 38.7PWR pin-cell, 40 MWd/kgU burnup 809.7 21.3 38.0SFR assembly 1368.3 23.9 57.2Mixed PWR MOX/UOX lattice 143.3 17.2 8.3

4.1.3 Advantages and disadvantages of SerpentSerpent has only been on the market for a year. Although it seems now that most of the majorbugs are fixed, there are still some smaller ones left [23]. The latest report from the developer ofSerpent tells that the minor bugs should not have a significant impact on the results [24]. Sincethe 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 areperfect 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 problemfor the simulations of the study due to the fact that a fast reactor was simulated, which meantthat the value of the cross-sections of heavy absorbers were low. Therefore it should not have animpact on the results.

Another disadvantage of Serpent is that the code is not well suited for calculations of shield-ing 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-energyMCNP data library. All numerical output from the simulations are stored in an .m-file, which isuseful 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 controlrods are completely withdrawn from the core. Sodium fills the cells of the control rod and thesub-assemblies lie close to each other with a tiny space in-between. The wrapping material ofthe sub-assemblies has in this model the same material composition as the cladding of the fuelpins. 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 presentedin 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 ValueFuel pinFuel type MOX (PuO2-UO2)Pellet diameter 5.42 mmCladding outer diameter 6.65 mmAir-gap space 0.075 mmThickness of cladding 0.45 mmFissile height 850 mmPitch 7.8 mmPins/sub-assembly 271Lower axial blanket within fuel pin 300 mmUpper axial blanket within fuel pin 260 mmBlanket pinBlanket material Depleted uranium oxide (UO2)Pellet diameter 12.5 mmCladding outer diameter 13.4 mmThickness of cladding 0.45 mmOverall Length 1668 mmPitch 14.5 mmPins/sub-assembly 61Sub-assemblyGeometry HexagonalDiameter across flats 124 mmWall thickness 3.5 mmOverall length S/A fuel 1410 mmOverall length S/A blanket 1668 mmPitch 127 mmCore configuratonCore design Homogeneous internal breedingNr. of enrichment zones 2Enrichment of Pu in MOX-fuel 18 % and 23 %Nr. of high-enriched S/A 48Nr. of low-enriched S/A 55Nr. of blanket S/A 90Nr. 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)235U 0.7 %238U 99.3 %Depleted uranium [28]235U 0.3 %238U 99.7 %

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

Material Proportion (%)Austenitic Steel Nr. 14970C 0.007 %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, withzoom at the active core and the fuel-assemblies. The red assemblies are dedicated cells for thecontrol rods, which are withdrawn in this model. The blue sub-assemblies are blankets and thegreen and white ones are fuel-assemblies.

4.3 Model of core-flowering

Monte-Carlo simulation codes have, as mentioned in Section 1.3, a limited number of geometricalstructures. In order to make a simulation of core-flowering, a simplification of the phenomenonwas made; all structural bending of the sub-assemblies due to core-flowering, have not been takeninto account. Instead the gap between the sub-assemblies was increased, which is the consequenceof the structural bending, see Figures 4.2 and 4.3, which in turn causes core extension/increaseof 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 theextra 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 = 1 mm the corresponding coreextension is 9 mm. For the Phénix-model, which is similar in design with a homogeneous corebut with less number of sub-assemblies, the relation is 1 : 7.

The two different cores were first simulated with normal conditions, λ = 0. A high numberof neutrons were used to reduce the bias and enough cycles were made to make sure that the re-sult converged properly. The simulations of core-flowering were made with λ = 0.4, 0.8, 1.2, 1.6, 2mm. The initial guess for keff was 1.00 and 100 inactive cycles were used in order to have afaster convergence rate. The nuclear data library used for these simulations was JEFF-3.1.1.A detector was defined in the center of the model in order to obtain how the neutron flux isaffected by core-flowering. How the detector is defined can be found in Chapter B. The resultsand the parameters for the simulations of Phénix are presented in Chapter 5 and the same canbe 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

5Result

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

5.1 Model of Phénix

Under normal operation conditions, λ = 0, the keff 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 thesimulation 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 anerror/difference of around 20 % between the measured and the simulated value. The amountof fissile inventory in the model was estimated to be 1105 kg, by Serpent sampling 10 000 000random points. According to reference [13], Phénix had a fissile inventory of 930 kg. This meansthat the amount of fissile material in the Phénix model is 19 % greater than measured. Theinventory of 239Pu came to be 462 kg, which is much less than the value of 730 kg given in thesame reference. Although the fissile inventory and the neutron flux differ quite a lot from thevalue given in the references, the values are sufficient for being a simplified model of the Phénixcore.

5.2 Core-flowering

The results from the simulations of core-flowering, using the Phénix model, are presented inTable 5.1 and in Figure 5.1. It was obtained that the reactivity decreases when the core radiusexpands. A linear approximation, see Figure 5.1, gives the change, ∆keff/core extension = -60 pcm/mm. Assuming that the signal from the neutron chambers directly corresponds to thethermal power of the core, the high amplitude of the signals from the A.U.R.N. events wouldrequire a core extension of around 5 mm. However, it does not seem that the relation betweenthe reactivity and the increase of the core radius is linear due to the fact that three points ofsimulation 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 theresults 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) Extensionof the core(mm)

Neutronpopulation

Number ofcycles

keff Standarddeviation,σ (10−5)

0 0.0 500000 2000 1.00298 50.4 2.8 500000 2000 1.00137 50.8 5.6 500000 2000 0.999605 51.2 8.4 500000 2000 0.997987 51.6 11.2 500000 2000 0.996145 42.0 14.0 500000 2000 0.994585 5

The results from the detector defined at the center of the Phénix model’s core are presented inTable 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 isnoticeable in the results. The relation between the neutron flux and core-extension is most likelyof 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 ofcore-flowering, where λ is the increase in the gap between the sub-assemblies. The model of thePhénix-core was used for these simulations.

λ (mm) Extensionof the core(mm)

Neutronpopulation

Numberof cycles

Neutron flux(1015 cm−2)

Standarddeviation,σ (1015)

0 0.0 500000 2000 8.43167 0.0174540.4 2.8 500000 2000 8.38752 0.0171940.8 5.6 500000 2000 8.35513 0.0171281.2 8.4 500000 2000 8.34142 0.0174341.6 11.2 500000 2000 8.36601 0.0174852.0 14.0 500000 2000 8.34229 0.017485

34

Core-flowering RESULT

0 2 4 6 8 10 12 14

0.995

0.996

0.997

0.998

0.999

1

1.001

1.002

1.003

Change in reactivity due to core extension

Extension of the core [mm]

k e f f

y = − 0.0006*x + 1

Simulation dataLinear approximation

Figure 5.1: This figure displays how the keff of the Phénix model is affected by core extension dueto core-flowering. A linear approximation gives ∆keff/core extension = -60 pcm/mm, though itdoes 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

−2 0 2 4 6 8 10 12 14 168.32

8.34

8.36

8.38

8.4

8.42

8.44

8.46x 1015 Change in neutron flux due to core extension

Extension of the core [mm]

Neu

trons

flux

[1/c

m2 ]

Figure 5.2: The figure displays how the neutron flux in the center of the Phénix core model isaffected by core-flowering. It can be seen that the relation between core extension and neutronflux 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. Notethat thermal power of the core has the same value in all simulations.

36

6Discussion

The A.U.R.N. events, the results obtained from the simulations and the uncertainties in the toolsand 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 thiscode 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 arepresent. This however, should not be an issue in this thesis since no heavy absorber is presentin any of the core models. Even if the models had control rods inserted into the core, the highenergies of the neutrons should significantly reduce this error. Serpent has been validated againstMCNP with satisfying results and therefore the results calculated by Serpent should be consis-tent. The models in the Monte-Carlo simulation code cannot describe dynamic environmentssuch as coolant flow, which brings some uncertainties to the results.

There are some uncertainties in the models used for the simulations. First, a simplified modelof the Phénix’s core was used and it should be noted that three different references have beenused in order to find all crucial parameters. Some parameters have different values in the dif-ferent references. The reason for the variation in value of the parameters is most probably dueto 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 wasused in Phénix during the A.U.R.N. events and the core-flowering experiments. This adds someuncertainties to the comparison between the results collected from the simulations and the ex-periments. However, it is still interesting that the change in keff obtained from the simulationsis similar to the experimental data.

The model of core-flowering is also a simplification of the true phenomenon. It does not takeinto 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 hasa significant impact on the keff . Furthermore, the gap between the sub-assemblies increasessymmetrically 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 convergedand 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 obtainedfrom the neutron flux detector.

The model of Phénix has been partly validated against the real core, where the neutron fluxand the fissile inventory were compared. The simulations differed from the measured values with∼14%. The keff of the model under normal conditions lies at 1.00298, which is quite a high valuefor a reactor. This is most probably the consequence of using different references for the creationof the model. The neutron flux and the amount of fissile inventory in the model of Phénix differquite a lot from the values obtained from references. However, this is most probably a conse-quence of having different compositions of plutonium, wrapper materials and depleted uraniumthan 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 fluxclearly decrease when the core expands, which was the initial guess of the study. Small increaseof the core radius leads to a significant change in the keff , which confirms the core-floweringexperiments made in Phénix. The relation between keff and core expansion does not seem tobe linear in the results obtained from the simulations, which was unexpected. Hence, the rela-tion between keff and core expansion might be of a higher order, though there is not enoughsimulation data to tell. However, in the interval [0, 6] mm the relation is almost linear and thecore, in the core-flowering experiments of Phénix, was only extended up to 5 mm. The results ofthe simulations correspond remarkably well to the experimental data, which indicates that thesimulations were a success. It is however hard to validate how significant impact the uncertain-ties have on the results. Hence, it might be dangerous to make any more conclusions about thecore’s behavior from these simulations (especially about the sudden increase in the neutron fluxat 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 400years of operating experience of SFRs in the world. Hence, the origin of the negative reactivitytransients is most probably related to some specific parameter of Phénix. This makes the scenariowhere an experimental sub-assembly, DAC-assembly, is responsible for provoking core-floweringmost 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 thatthe events could somehow be related to the power of the reactor. Regardless, it is not possible tomake 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 duringthe A.U.R.N. events. The free standing core concept that Phénix used, allows radial bowing ofthe assemblies, which makes core-flowering possible to occur. However, this should leave sometrace 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 giveany further explanation nor conclusion of how core-flowering is related to the negative reactivitytransients.

What makes A.U.R.N. so difficult to understand are the high amplitudes of the signals, thespeed 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 electronicequipment 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 hasbeen proven to be able to induce similar signals in the neutron chambers, which is not relatedto the thermal power of the core. On the other hand, no mechanical phenomenon can provide asatisfying scenario. Hence, it is possible that the abnormalities were induced by a combinationof 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 befound in order to increase the understanding of the SFR concept and for the future devel-opment towards commercialization. Phénix is no longer available for neutronic experiments,though hopefully enough data have been gathered to solve this mystery. Hopefully, some kindof trace of A.U.R.N. or core-flowering can be found during the decommissioning of Phénix andthe dismantling of the core. It is therefore important that crucial parts of the reactor, duringthe dismantling process, are examined thoroughly. Finally, in order to exclude A.U.R.N. fromoccurring in current LWRs, the origin of the phenomenon must be found.

39

7Conclusions

7.1 Conclusions

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

The simplified model of the core of Phénix was successfully created and validated, though un-fortunately the model’s neutron flux and the amount of fissile isotopes differed from measuredvalues 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 thesame value as was measured during the experiments of core-flowering made in the final year ofPhénix. Thus, it was concluded that the relation between keff and the core extension could beof 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 ifcore-flowering is the single answer to the A.U.R.N. events. Though core-flowering as explanationis 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 recre-ate similar patterns in the signals of the neutron chambers. The absence of any kind of trace ofthis movement is remarkable though, which implies the uncertainties in this scenario. Due to thehigh amplitude of the signals, it is possible that there was interference or failure in the electri-cal 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 sig-nals would require a core extension of around 5 mm, assuming that the signal from the neutronchambers directly corresponds to the thermal power of the core. If core-flowering is the soughtanswer, 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 ofthe fuel elements.

41

CONCLUSIONS Suggestions for further work

The irradiation experiments of the sub-assemblies with high burnup of fuel might be one an-swer to the origin of A.U.R.N., especially since it was one of the major differences betweenPhénix and Superphénix, which did not experience any similar transients. A moderated experi-mental sub-assembly and its possible involvement in inducing a core-flowering in Phénix is beinginvestigated. Regardless of the origin of the negative reactivity transients, the safety of Phénixwas not affected, such as support structures of the core. Furthermore, the automatic emer-gency shutdown of the reactor proved its efficiency during these events by shutting down theoperation after a few hundreds of milliseconds. This type of event should therefore not be ableto 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 tofind the explanation since the origin is unknown and therefore cannot be excluded from occur-ring in LWRs, even though it is not likely. The importance of finding the answer can be seenas CEA is still investigating the phenomenon and is going to recruit Ph.D. students for theinvestigation.

7.2 Suggestions for further work

In the study a simplified model of Phénix was created, however there are still some parameters inthe model that can be improved. For instance, no reference for the wrapper material was foundfor the model and it was therefore set to the same material as the cladding of the fuel pins. Itwould also be intriguing to find a design of and more information about the DAC-assemblies andmake 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 keffis not linear. In order to confirm this, more simulation data should be gathered using the samemodels, but with other values of λ. It would also be of great interest to investigate how theneutron 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 inreactivity instead of a decrease. This is not strange since an increase of the gap between thesub-assemblies increases the moderation effect. However, better and more simulations should becarried out before making any conclusions about this.

In order to gain more understanding of core-flowering, more simulations should be carried outusing other codes than Serpent to obtain a better model of the phenomenon. Deterministiccodes, 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 bebound to some parameters that are specific for Phénix. Thus, it would be convenient to investi-gate 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 toA.U.R.N.s since the design of Superénix is based on data gathered from the operation of Phénix.

42

References

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[7] B. Rouben. Introduction to reactor physics. Atomic Energy of Canada Ltd., September2002.

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[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 yearsof 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, November 2010.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 PHÉNIXfinal 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 metalcooled fast reactor technology: The Phénix end of life tests. IAEA, 2010. Not yet published.

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[19] P. Le Coz. The ASTRID project. ESFR Seminar, November 2010. Cadarache.

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[21] F. Brown, W. Martin, J. Leppänen, Wim H., and B. Cochet. Reactor Physics Analysis withMonte Carlo. ANS PHYSOR-2010 Conference Workshop, 2010.

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[24] PSG / Serpent - a Continuous-energi Monte Carlo Reactor Physics Burnup CalculationCode. http://montecarlo.vtt.fi/. 2010-10-20.

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44

List of Figures

2.1 The presence evolution of transuranium elements in spent nuclear fuel. [1] . . . . 82.2 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 fuelpins than those of FRs. a) Sub-assembly arrangement of FRs. b) Fuel-assemblyarrangement of LWRs. c) Fuel pin arrangement of FRs. d) Fuel pin arrangementsof 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 inthe main vessel and the heat is transferred from the primary circuit to the steamgenerators by intermediate circuits. [2] . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2 Chart of downtime at Phénix due to accidents and maintenance. Note the per-centage of negative reactivity transients, which is the fourth time-wasting issue, ifscheduled work is not taken into account. [14] . . . . . . . . . . . . . . . . . . . 17

3.3 Two separate registered signals obtained from the neutron chambers during thelast two A.U.R.N. events in Phénix in 1990. Note the oscillating behavior and thesecondary 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 ofsodium in the moderated experimental sub-assembly DAC. [17] . . . . . . . . . . 23

3.6 A picture of the mechanical device, which was used for testing how core-floweringis 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 arededicated cells for the control rods, which are withdrawn in this model. The bluesub-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. 314.3 Side view of how the sub-assemblies are affected by core-flowering in the simula-

tions. Each block corresponds to a block with hexagonal geometry. . . . . . . . . 324.4 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 extensiondue to core-flowering. A linear approximation gives ∆keff/core extension = -60pcm/mm, though it does not seem to be a good approximation due to the fact thatthree points lie outside the line. However, in the interval [0 6] mm, the relation isin 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 isaffected by core-flowering. It can be seen that the relation between core extensionand neutron flux is not linear. Note the peak at 11.2 mm, which shows a suddenincrease in neutron-flux. This is probably a result of the statistical noise, whichis noticeable in the large error bars. Note that thermal power of the core has thesame value in all simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

D.1 This figure shows how the keff of the model of PFBR is affected by core extension.A linear approximation gives ∆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 onlytwo reactors of commercial size. [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∞ between MCNP and Serpent. [22] . . . . . . . . . . . . . . . 264.2 A comparison of computation time (in minutes) between MCNP and Serpent. [22] 274.3 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. . 284.4 Composition of fuel and blanket. . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.5 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 thePhénix-core was used for these simulations. . . . . . . . . . . . . . . . . . . . . . 34

5.2 The results of the neutron flux in the core center obtained from the simulationsof 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

47

Nomenclature

A.U.R.N. Arrêt d’Urgence par Réactivité Négative (automatic emergency shutdown by nega-tive 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 inIndia., 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

49

Appendices

51

ADefinitions of the units in the Four Factor

Formula

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

� = Fast fission factor

f = Thermal ultilization

p = Resonance escape probability

P = Non − leakage probabilities

� =total fission neutrons from thermal and fast fission

fission neutrons from thermal fission

f =thermal neutrons absorbed by fuel

total thermal neutrons absorbed

P =absorption

production

p =Number of neutrons slowing to thermal energy

total number of fast neutrons available for slowing

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

A-1

BCode of the Phénix Model

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

s e t t i t l e "Phenix"

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

% −−− Low enr i ched f u e l

pin 1 % low−f u e l pinl ow fue l 0 .275 % f u e l p e l l e t outer rad iu svoid 0 .2825 % c ladd ing inner rad iu sc ladd ing 0 .3275 % c ladd ing outer rad iu ssodium % coo lant out s id e o f c lad

% −−− High enr i ched f u e l

pin 2 % high−f u e l pinh i gh f u e l 0 .275 % f u e l p e l l e t outer rad iu svoid 0 .2825 % c ladd ing inner rad iu sc ladd ing 0 .3275 % c ladd ing outer rad iu ssodium % coo lant out s id e o f c lad

% −−− Blanket pin

pin 3blanket 0 .625 % blanket pin

B-1

CODE OF THE PHÉNIX MODEL

c ladd ing 0 .67sodium % coo lant out s id e o f c lad

% −−− Coolant

pin 9 % dummy pin f o r f i l l i n g the l a t t i c esodium

% −−−−−−−−−−−−−−−−− La t t i c e s −−−−−−−−−−−−−−−−−

% −−− Fuel Sub−assembly , low−enr i chedl a t 10 2 0 0 19 19 0 .78

9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 99 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 99 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 1 99 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 1 1 99 9 9 9 9 1 1 1 1 1 1 1 1 1 1 1 1 1 99 9 9 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 99 9 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 99 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 99 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 99 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9 99 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9 9 99 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9 9 9 99 1 1 1 1 1 1 1 1 1 1 1 1 1 9 9 9 9 99 1 1 1 1 1 1 1 1 1 1 1 1 9 9 9 9 9 99 1 1 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 99 1 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 99 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9

% −−− Fuel Sub−assembly , high−enr i ched

l a t 20 2 0 0 19 19 0 .78

9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 2 2 2 2 2 2 2 2 2 99 9 9 9 9 9 9 9 2 2 2 2 2 2 2 2 2 2 99 9 9 9 9 9 9 2 2 2 2 2 2 2 2 2 2 2 99 9 9 9 9 9 2 2 2 2 2 2 2 2 2 2 2 2 99 9 9 9 9 2 2 2 2 2 2 2 2 2 2 2 2 2 99 9 9 9 2 2 2 2 2 2 2 2 2 2 2 2 2 2 99 9 9 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 99 9 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 99 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 99 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 9 9

B-2


9 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 9 9 99 2 2 2 2 2 2 2 2 2 2 2 2 2 2 9 9 9 99 2 2 2 2 2 2 2 2 2 2 2 2 2 9 9 9 9 99 2 2 2 2 2 2 2 2 2 2 2 2 9 9 9 9 9 99 2 2 2 2 2 2 2 2 2 2 2 9 9 9 9 9 9 99 2 2 2 2 2 2 2 2 2 2 9 9 9 9 9 9 9 99 2 2 2 2 2 2 2 2 2 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9

% Dummy assembly with sodiuml a t 110 2 0 0 19 19 0 .78

9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9

% −− Blanket−assemblyl a t 30 2 0 0 11 11 1 .45

9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 3 3 3 3 3 99 9 9 9 3 3 3 3 3 3 99 9 9 3 3 3 3 3 3 3 99 9 3 3 3 3 3 3 3 3 99 3 3 3 3 3 3 3 3 3 99 3 3 3 3 3 3 3 3 9 99 3 3 3 3 3 3 3 9 9 99 3 3 3 3 3 3 9 9 9 99 3 3 3 3 3 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9

B-3


%Core l a t t i c el a t 200 3 0 0 21 21 12 .7 % Pitch 12 .7 cm22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 2222 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 2222 22 22 22 22 22 22 22 22 22 22 33 33 33 33 33 33 33 22 22 2222 22 22 22 22 22 22 22 22 33 33 33 33 33 33 33 33 33 33 22 2222 22 22 22 22 22 22 22 33 33 33 33 51 51 51 33 33 33 33 22 2222 22 22 22 22 22 22 33 33 33 51 51 51 51 51 51 33 33 33 22 2222 22 22 22 22 22 33 33 51 51 50 50 50 50 50 51 51 33 33 22 2222 22 22 22 22 33 33 51 51 50 50 50 80 50 50 51 51 33 33 22 2222 22 22 22 33 33 51 51 50 80 50 50 50 50 50 51 51 33 33 22 2222 22 22 33 33 33 51 50 50 50 50 50 50 80 50 51 33 33 33 22 2222 22 22 33 33 51 50 50 50 50 50 50 50 50 50 51 33 33 22 22 2222 22 33 33 33 51 50 80 50 50 50 50 50 50 51 33 33 33 22 22 2222 22 33 33 51 51 50 50 50 50 50 80 50 51 51 33 33 22 22 22 2222 22 33 33 51 51 50 50 80 50 50 50 51 51 33 33 22 22 22 22 2222 22 33 33 51 51 50 50 50 50 50 51 51 33 33 22 22 22 22 22 2222 22 33 33 33 51 51 51 51 51 51 33 33 33 22 22 22 22 22 22 2222 22 33 33 33 33 51 51 51 33 33 33 33 22 22 22 22 22 22 22 2222 22 33 33 33 33 33 33 33 33 33 33 22 22 22 22 22 22 22 22 2222 22 22 33 33 33 33 33 33 33 22 22 22 22 22 22 22 22 22 22 2222 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 2222 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22

% −−−−−−−−−−−−−−−−− Sur f a c e s −−−−−−−−−−−−−−−−−

s u r f 1 hexyprism 0 0 5 .85 −42.5 42 .5 % inner sub−as s s t r u c ts u r f 2 hexyprism 0 0 6 .2 −42.5 42 .5 % outer sub−as s s t r u c t

s u r f 3 hexyprism 0 0 5 .85 −83.4 83 .4 % inner sub−as s s t r u c ts u r f 4 hexyprism 0 0 6 .2 −83.4 83 .4 % outer sub−as s s t r u c t

s u r f 5 hexyprism 0 0 5 .85 42 .5 68 .5 % inner sub−as s s t r u c ts u r f 6 hexyprism 0 0 5 .85 −72.5 −42.5 % inner sub−as s s t r u c t

s u r f 7 hexyprism 0 0 6 .2 42 .5 68 .5 % outer sub−as s s t r u c ts u r f 8 hexyprism 0 0 6 .2 −72.5 −42.5 % outer sub−as s s t r u c t

s u r f 100 sph 0 0 0 300 % Region o f Neutronss u r f 200 sph 0 0 0 400 % Sphere o f i n t e r e s ts u r f 500 cy l 0 0 105 % Reactor tank

% −−−−−−−−−−−−−−−−− Ce l l s −−−−−−−−−−−−−−−−−

c e l l 1000 80 sodium −4c e l l 1001 80 sodium 4

B-4


% −−− Universe 100 , low−enr i ched sub−assembly

c e l l 1 50 f i l l 10 −1 −2c e l l 2 50 c ladd ing 1 −2c e l l 56 50 f i l l 15 −6 −8 1 2c e l l 53 50 c ladd ing 6 −8 1 2c e l l 54 50 f i l l 15 −5 −7 1 2c e l l 55 50 c ladd ing 5 −7 1 2c e l l 5 50 sodium 2 5 6 7 8

% −−− Universe 200 , high−enr i ched sub−assembly

c e l l 6 51 f i l l 20 −1 −2c e l l 7 51 c ladd ing 1 −2c e l l 8 51 f i l l 15 −6 −8 1 2c e l l 50 51 c ladd ing 6 −8 1 2c e l l 51 51 f i l l 15 −5 −7 1 2c e l l 52 51 c ladd ing 5 −7 1 2c e l l 10 51 sodium 2 6 5 8 7

% −−− Universe 300 , blanket−assembly

c e l l 11 33 f i l l 30 −3 −4c e l l 12 33 c ladd ing 3 −4c e l l 13 33 sodium 4

% −−− Universe 22 , dummy−assembly with sodium f o r l a t t i c e

c e l l 1111 22 f i l l 110 −4c e l l 1311 22 sodium 4

% −−− Universe 0 , the corec e l l 101 0 f i l l 200 −500 −100c e l l 102 0 void 500 −100c e l l 103 0 out s id e 100

% −−−−−−−−−−−−−−−−− Plo t t i ng −−−−−−−−−−−−−−−−−

% plo t 3 800 800 % Plo t t i ng the whole geometry% p lo t 2 800 800 % Plo t t i ng s ide−view% plo t 2 800 800 0 −3.1 3 .1 −150 150 % Plo t t i ng f u e l p ins% p lo t 3 800 800 0 −69.5 69 .5 −69.5 69 .5 % Plot o f inne r core

% −−−−−−−−−−−−−−−−− Mater i a l s −−−−−−−−−−−−−−−−−

% −−− High enr i ched f u e l

B-5


mat h i gh f u e l −10.98 rgb 255 255 255 % −10.977792238.12 c 0 .7646 % U−238 99.3%92235.12 c 0 .0054 % U−235 0.07%94238.12 c 0 .0081 % Pu−238 3.5%94239.12 c 0 .1194 % Pu−239 51.9%94240.12 c 0 .0547 % Pu−240 23.8%94241.12 c 0 .0297 % Pu−241 12.9%94242.12 c 0 .0182 % Pu−242 7.9%8016.12 c 2 % O2

% −−− Low enr i ched f u e l

mat l ow fue l −10.97 rgb 0 255 0 % −10.968392238.12 c 0 .8143 % U−23892235.12 c 0 .0057 % U−23594238.12 c 0 .0063 % Pu−23894239.12 c 0 .0934 % Pu−23994240.12 c 0 .0428 % Pu−24094241.12 c 0 .0232 % Pu−24194242.12 c 0 .0142 % Pu−2428016.12 c 2 % O2

% −−− Cladding , SS 316

% SS 316%mat c ladd ing −7.9402 rgb 255 255 0%26000.06 c 0 .66 % Natural Fe%28000.06 c 0 .13 %%24000.06 c 0 .17%42000.06 c 0 .025%25055.06 c 0 .015

% 15−15 Timat c ladd ing −7.8974 rgb 255 255 0

6000.06 c 0 .000924000.06 c 0 .14628000.06 c 0 .15042000.06 c 0 .012514000.06 c 0 .004625055.06 c 0 .017022000.06 c 0 .004626000.06 c 0 .6644

% −−− Sodium , coo lant

mat sodium −0.968 rgb 255 0 011023.06 c 1

B-6


% −−− Blanket , U−238

mat blanket −10.5 rgb 0 0 25592238.06 c 0 .997 % dep le ted Uranium , U−23892235.06 c 0 .003 % dep le ted Uranium , U−2388016.06 c 2 % O2

% −−−−−−−−−−−−−−−−− Detector s −−−−−−−−−−−−−−−−−

det 1 % Detector f o r measuring the average f l u x o f the coredz −42.5 42 .5 20d l 200dv 1 .29E6

det 3 % Detector f o r measuring the neutron f l u x at the core ’ s c en te rdx −1 1 1dy −1 1 1dz −1 1 1du 0dv 8

% −−−−−−−−−−−−−−−−− L i b r a r i e s −−−−−−−−−−−−−−−−−

s e t a c e l i b "/ xs/ s s s_ j e f f 3 1u . xsdata "

% −−−−−−−−−−−−−−−−− Values f o r norma l i za t i on −−−−−−−−−−−−−−−−−

s e t power 5 .63E8 % thermal power o f the core

% −−−−−−−−−−−−−−−−− Start−va lue s −−−−−−−−−−−−−−−−−

s e t pop 10000 3000 50 1 .001

B-7

COutput 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 activecycles are presented since there is no value in displaying them all.

_ .−=−. .−==−.{ } __ . ’ O o ’ . / −<’ )−−<{ } . ’ O’ . / o .− . O \ / .−−−‘{ } / .− . o\ /O / \ o\ /O /\ ‘− ‘ / \ O‘− ’ o / \ O‘− ‘ o /

‘−.− ‘ ’ .____. ’ ‘ .____. ’

PSG2 / Serpent

A Continuous−energy Monte Carlo Reactor Phys ics Burnup Ca l cu la t i on Code

− Vers ion 1 . 1 . 1 3 ( August 25 , 2010) −− Contact : Jaakko . Leppanen@vtt . f i

− Pa r a l l e l c a l c u l a t i o n mode not a v a i l a b l e

− Geometry and mesh p l o t t i n g a v a i l a b l e

Begin c a l c u l a t i o n on Mon Jan 10 13 : 30 : 44 2011

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

Proce s s ing geometry . . .OK.

Reading d i r e c t o r y f i l e s . . .

C-1

OUTPUT DATA FROM A TEST RUN OF THE PHÉNIX MODEL

OK.

Ca l cu l a t ing i s o t op e f r a c t i o n s . . .OK.

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

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

C-2


OK.

− Main gr id thinned from 198270 to 198270 po in t s us ing t o l e r an c e 0 .00E+00.

− 34737 important po in t s added r e s u l t i n g in a t o t a l o f 198270 po in t s .

− Fina l g r id s i z e 198046 po in t s ( 1 . 00E−11 < E < 20 . 0 ) .

− Total 2387 po in t s in nubar g r id .

− 2 energy groups in few−group s t r u c tu r e .

Proce s s ing XS data :I so tope 6000.06 c (C−nat ) . . .I s o tope 8016.06 c (O− 16 ) . . .I s o tope 8016.12 c (O− 16 ) . . .I s o tope 11023.06 c (Na− 23 ) . . .I s o tope 14000.06 c ( Si−nat ) . . .I s o tope 22000.06 c (Ti−nat ) . . .I s o tope 24000.06 c (Cr−nat ) . . .I s o tope 25055.06 c (Mn− 55 ) . . .I s o tope 26000.06 c (Fe−nat ) . . .I s o tope 28000.06 c (Ni−nat ) . . .I s o tope 42000.06 c (Mo−nat ) . . .I s o tope 92235.06 c (U−235 ) . . .I s o tope 92235.12 c (U−235 ) . . .I s o tope 92238.06 c (U−238 ) . . .I s o tope 92238.12 c (U−238 ) . . .I s o tope 94238.12 c (Pu−238 ) . . .I s o tope 94239.12 c (Pu−239 ) . . .I s o tope 94240.12 c (Pu−240 ) . . .I s o tope 94241.12 c (Pu−241 ) . . .I s o tope 94242.12 c (Pu−242 ) . . .OK.

F i n a l i z i n g XS data . . .OK.

Prepar ing s t a t i s t i c s . . .OK.

Se t t i ng p a r t i a l r e a c t i on l i s t s f o r mate r i a l c r o s s s e c t i o n s . . .OK.

Ca l cu l a t ing mate r i a l t o t a l c r o s s s e c t i o n s :mate r i a l h i gh f u e l . . .mate r i a l l ow fue l . . .mate r i a l c l add ing . . .mate r i a l sodium . . .

C-3


mate r i a l b lanket . . .OK.

S ta r t i ng the t ranspor t c a l c u l a t i o n cy c l e . . .

Sampling i n i t i a l source . . .OK.

Ina c t i v e cy c l e 1 / 10 : k−e f f = 0.45696 (DT thresh = 0 .9000)I na c t i v e cy c l e 2 / 10 : k−e f f = 0.78370 (DT thresh = 0 .9000)I na c t i v e cy c l e 3 / 10 : k−e f f = 0.93937 (DT thresh = 0 .9000)I na c t i v e cy c l e 4 / 10 : k−e f f = 0.96630 (DT thresh = 0 .9000)I na c t i v e cy c l e 5 / 10 : k−e f f = 1.00147 (DT thresh = 0 .9000)I na c t i v e cy c l e 6 / 10 : k−e f f = 1.00093 (DT thresh = 0 .9000)I na c t i v e cy c l e 7 / 10 : k−e f f = 1.00404 (DT thresh = 0 .9000)I na c t i v e cy c l e 8 / 10 : k−e f f = 1.00514 (DT thresh = 0 .9000)I na c t i v e cy c l e 9 / 10 : k−e f f = 0.98590 (DT thresh = 0 .9000)I na c t i v e cy c l e 10 / 10 : k−e f f = 1.00188 (DT thresh = 0 .9000)

−−−−− Begin a c t i v e c y c l e s −−−−−

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

Serpent 1 . 1 . 1 3 −− C r i t i c a l i t y source s imu la t i on

T i t l e : "Phenix"

Active cy c l e 1 / 100 (5000 source neutrons )

Delta−t r a ck ing on : thresh = 0 .90 , e f f = 0 .53 , f r a c = 0.85

Running time : 0 : 0 0 : 2 1Estimated running time : 0 : 0 5 : 4 0Estimated running time l e f t : 0 : 0 5 : 1 9

k−e f f ( analog ) = 0.99988 +/− 0.00000 [ 0 . 99988 0 . 99988 ]k−e f f ( imp l i c i t ) = 0.99780 +/− 0.00000 [ 0 . 99780 0 . 99780 ]

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

( . . . )

Serpent 1 . 1 . 1 3 −− C r i t i c a l i t y source s imu la t i on

T i t l e : "Phenix"

Active cy c l e 100 / 100 (5000 source neutrons )

C-4


Delta−t r a ck ing on : thresh = 0 .90 , e f f = 0 .53 , f r a c = 0.87

Running time : 0 : 0 3 : 1 3Estimated running time : 0 : 0 3 : 1 3Estimated running time l e f t : 0 : 0 0 : 0 0

k−e f f ( analog ) = 1.00267 +/− 0.00186 [ 0 . 99903 1 . 00632 ]k−e f f ( imp l i c i t ) = 1.00271 +/− 0.00109 [ 1 . 00056 1 . 00485 ]

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

Fin i shed a f t e r 100 a c t i v e c y c l e s o f 5000 source neutrons .Total c a l c u l a t i o n time 3 .22 minutes .

Notes :

− Unable to read av a i l a b l e memory from /proc /meminfo .Consider manual ove r r i d e .

− Unresolved resonance p r obab i l i t y t ab l e s a v a i l a b l e f o r 10nuc l i d e s but sampling NOT in use .

− 2 neutrons emitted above maximum energy 20 .00 MeV.

C-5

DResults of the PFBR-model

The parameters and the results of the keff , obtained from the simulation of the PFBR modelcan be seen in Table D.1. The result is displayed in figure Figure D.1. The linear approximationof 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 inthe S/Agap, λ(mm)

Extensionof the core(mm)

Neutronpopulation

Number ofcycles

keff Standarddeviation,σ(10−5)

0 0.0 500000 2356 1.16338 40.2 1.8 300000 1000 1.16240 70.4 3.6 300000 1300 1.16166 70.8 7.2 300000 1300 1.15987 71.2 10.8 300000 1300 1.15829 71.6 14.4 300000 1300 1.15653 72.0 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.A linear approximation gives ∆keff/Core extension = -47.6 pcm/mm.

D-2

Documents

Simulation of Reactor Transient and Design Criteria of