UPTEC F11 011
Examensarbete 30 hp
Februari 2011
Simulation of Reactor Transient
and Design Criteria of Sodiumcooled Fast Reactors
Filip Gottfridsson
Abstract
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
The need for energy is growing in the world and the market of nuclear power is now
once more expanding. Some issues of the current light-water reactors can be solved
by the next generation of nuclear power, Generation IV, where sodium-cooled
reactors are one of the candidates. Phénix was a French prototype sodium-cooled
reactor, which is seen as a success. Although it did encounter an earlier
unexperienced phenomenon, A.U.R.N., in which a negative reactivity transient
followed by an oscillating behavior forced an automatic emergency shutdown of the
reactor. This phenomenon lead to a lot of downtime of the reactor and is still
unsolved. However, the most probable cause of the transients is radial movements of
the core, referred to as core-flowering.
This study has investigated the available documentation of the A.U.R.N. events. A
simplified model of core-flowering was also created in order to simulate how radial
expansion affects the reactivity of a sodium-cooled core. Serpent, which is a
Monte-Carlo based simulation code, was chosen as calculation tool. Furthermore, a
model of the Phénix core was successfully created and partly validated. The model of
the core has a k_eff = 1.00298 and a neutron flux of (8.43+-0.02)!10^15
neutrons/cm^2 at normal state. The result obtained from the simulations shows that
an expansion of the core radius decreases the reactivity. A linear approximation of
the result gave the relation: change in k_eff/core extension = - 60 pcm/mm. This value
corresponds remarkably well to the around - 60 pcm/mm that was obtained from the
dedicated core-flowering experiments in Phénix made by the CEA.
Core-flowering can recreate similar signals to those registered during the A.U.R.N.
events, though the absence of trace of core movements in Phénix speaks against this.
However, if core-flowering is the sought answer, it can be avoided by design. The
equipment that registered the A.U.R.N. events have proved to be insensitive to noise.
Though, the high amplitude of the transients and their rapidness have made some
researcher believe that the events are a combination of interference in the equipment
of Phénix and a mechanical phenomenon. Regardless, the origin of A.U.R.N. seems to
be bound to some specific parameter of Phénix due to the fact that the transients
only have occurred in this reactor.
A safety analysis made by an expert committee, appointed by CEA, showed that the
A.U.R.N. events are not a threat to the safety of Phénix. However, the origin of these
negative transients has to be found before any construction of a commercial size
sodium-cooled fast reactor can begin. Thus, further research is needed.
Handledare: Hans Henriksson
Ämnesgranskare: Henrik Sjöstrand
Examinator: Tomas Nyberg
ISSN: 1401-5757, UPTEC F11 011
Sponsor: Vattenfall AB
Acknowledgements
I would like to thank the following persons for their guidance and criticism
Andrei Fokau
Anna-Maria Wiberg
Bruno Fontaine
Hans Henriksson
Henrik Sjöstrand
Peter Wolniewicz
I especially would like to thank Bruno Fontaine for all the valuable information and guidance
he has provided, which have been essential for this thesis. I am also grateful for the time Andrei
Fokau spent in order to help me learn Monte-Carlo simulation codes.
Contents
1 Introduction
1.1 Background . . . . . .
1.2 Aims and Objectives .
1.3 Limitations . . . . . .
1.4 Outline of this report .
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2 Fundamentals of fast reactors
2.1 Overview . . . . . . . . . . . . . . . . . . . . . .
2.2 Fission . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Breeding . . . . . . . . . . . . . . . . . . . . . . .
2.4 Transmutation of long-lived radio-active elements
2.5 Core design of fast reactors . . . . . . . . . . . .
2.5.1 Configuration of fast breeder reactors . .
2.6 Effective neutron multiplication factor, kef f . . .
3 Sodium-cooled fast reactors
3.1 Sodium-cooled fast reactors in the world
3.2 Sodium-cooled reactor design . . . . . .
3.2.1 Advantages and disadvantages .
3.2.2 Technical overview . . . . . . . .
3.3 Phénix . . . . . . . . . . . . . . . . . . .
3.3.1 A.U.R.N. . . . . . . . . . . . . .
3.3.2 Core-flowering . . . . . . . . . .
3.3.3 Core-flowering tests of Phénix . .
3.4 ASTRID . . . . . . . . . . . . . . . . . .
3.4.1 Preliminary design . . . . . . . .
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13
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4 Method and materials
4.1 Monte-Carlo simulation code . . . . . . . . . . . . . .
4.1.1 Difficulties using Monte-Carlo simulation code
4.1.2 Choice of Monte-Carlo simulation code . . . . .
4.1.3 Advantages and disadvantages of Serpent . . .
4.2 Model of Phénix . . . . . . . . . . . . . . . . . . . . .
4.3 Model of core-flowering . . . . . . . . . . . . . . . . . .
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5 Result
5.1 Model of Phénix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Core-flowering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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6 Discussion
6.1 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 A.U.R.N. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
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38
7 Conclusions
7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Suggestions for further work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
41
42
References
43
List of Figures
45
List of Tables
47
Nomenclature
48
Appendices
49
A Definitions of the units in the Four Factor Formula
A-1
B Code of the Phénix Model
B-1
C Output data from a test run of the Phénix model
C-1
D Results of the PFBR-model
D-1
"The first country to develop
a fast breeder reactor
will have a commercial advantage
for the exploitation of nuclear
energy"
Enrico Fermi - 1945
1
Introduction
The need of energy in the world is growing and since we now are facing possible climate changes
the search for alternative energy sources to fossil fuels is greater than ever. Nuclear power has
for some time been a non-expanding market, though today the view has changed. It is now seen
as one of the alternatives to fossil fuel due to its low emission of CO2 and low environmental
impact. However, nuclear power has its disadvantages, for example the waste produced in current
reactors needs to be stored for more than 300 000 years [1]. A new generation of nuclear power
plants named Generation IV is under development, which can solve some of the problems related
to the current nuclear power. The aim of Generation IV is to have safer, more reliable and
efficient power plants with a physical protection against terrorism in a closed fuel cycle [2]. The
goal is also to improve the environment, for example by introducing nuclear-produced hydrogen
for transportation.
1.1
Background
There are six different reactor designs of Generation IV [2], Sodium-cooled Fast Reactor (SFR),
Lead-cooled Fast Reactor (LFR), Molten Salt Reactor (MSR), Very High Temperature Reactor (VHTR), Gas-cooled Fast Reactor (GFR) and SuperCritical-Water Reactor (SCWR). All of
these designs are being developed throughout the world in order to achieve the goal of commercialization.
It is possible to have different neutron spectra by using different coolants. For example using liquid metal as coolant results in having a fast neutron spectrum1 in the reactor, more about
this in Chapter 2, which in turn leads to the possibility to use up to 99.9 % of the fuel. This
can be compared to the fuel usage of todays water reactors’ usage of a few percent. Recycling of
the spent nuclear fuel is then possible and it can result in a reduction of storage time from 300
000 years to several 1000 years [1]. Hence, the process of storing might be easier for a country
to manage. The main drawbacks of using these coolants are the increase of temperatures and
1 Fast
neutron spectrum: The neutron spectrum is dominated by fast/high energetic neutrons.
1
INTRODUCTION
Aims and Objectives
the high irradiation in the core, which makes it difficult to develop feasible materials that can
sustain such severe environment.
The sodium-cooled fast reactor is the candidate of Generation IV that lies furthest ahead in
research and development [2]. Even though sodium-cooled fast reactors are part of a new generation of nuclear power, the idea is quite old. In fact, the first reactor connected to the electrical
grid, EBR-I, was cooled with a combination of sodium and potassium [3]. However, the commercialization of sodium-cooled fast reactors is still far away in time due to the lack of proper
materials.
Downtime due to sodium-leaks is one of the most common issues with the operation of SFRs,
though earlier unexperienced very rapid negative reactivity transients2 have caused major problems in the French reactor Phénix. The French call these transients A.U.R.N., which is short for
Arrêt d’Urgence par Réactivité Négative. In English this means automatic emergency shutdown
by negative reactivity. No final explanation of A.U.R.N.s has yet been established, though the
most probable cause is radial movement of the core called core-flowering. This is one of the issues
that needs to be solved before introducing SFRs of commercial size.
1.2
Aims and Objectives
This master thesis investigates the cause of the A.U.R.N. events. The objectives are to survey
published reports and use Monte-Carlo simulation code in order to simulate core-flowering and
analyze how it affects the reactivity of an SFR core. Simplified models of the phenomenon have
been used in order to make the simulations possible. The aims of the study are to determine a
possible cause of the negative reactivity transients, give a solution on how to avoid the problem
and point to further research. Furthermore, some design criteria and core configurations of SFRs
are discussed and how they can affect the behavior of the reactor.
The study was carried out at Vattenfall Research and Development AB. This thesis is valuable for
Vattenfall in their long-term coverage of future reactor concepts, especially for the understanding
of the issues the different concepts are facing.
1.3
Limitations
This study does not give a direct explanation to the A.U.R.N. events that occurred in Phénix.
It rather discusses the registered transients and their complexity and points to further research.
Furthermore, the study does not investigate any of the consequences of A.U.R.N. nor does it discuss any economical aspects of the events. A.U.R.N.s is still an unsolved phenomenon, therefore
the information is very limited. There are few reports published in English that describe possible explanations and most of them only describe the problem, not its origin. The simulations
however, are only used in order to analyze core-flowering and how it affects the reactivity of an
SFR core. The results from the simulations have been compared with experimental data, though
the simulations cannot be used to make any conclusions of the origin of the negative reactivity
transients.
2 Transient:
2
A rapid/brief change in the power of the reactor.
Outline of this report
INTRODUCTION
Serpent as Monte-Carlo simulation code has many advantages, though it cannot handle dynamic flows, such as coolant flow. Complex structures that are not included in the geometric
library of the code are difficult to create. Sub-assemblies3 suffering from core-flowering have
therefore in the simulations the same structure as in the normal state. Another limitation in
the model is that the gap between the assemblies must increase symmetrically in the whole core,
which means it is not possible to have any asymmetrical deformation of the lattice.
Phénix has been used for irradiation experiments, which resulted in the usage of different set-ups
of assemblies with different cladding material etc. No complete core description of Phénix was
found. Thus, the parameters and materials used in order to create the model for this study
are obtained from several references. Some parameters vary in the different references and the
values of these parameters have been set according to the source that seems most convenient.
It should be noted that the parameters used is not set in order to have an optimized model.
Furthermore, the models of both Phénix and PFBR (Prototype Fast Breeder Reactor, an Indian
SFR that is under construction) are simplified in this project and cannot completely describe the
environment of the core, such as the release of fission gas and fuel swelling due to irradiation.
1.4
Outline of this report
Summary of the chapters of the report:
• Fundamentals of fast reactors - The chapter describes the basic physics and core configurations of fast reactors. Calculation of kef f is also presented.
• Sodium-cooled Fast Reactors - This chapter treats the technology of SFRs and focuses on
the Phénix reactor and its experience of the A.U.R.N. events.
• Method and Materials - The selection of simulation code and how it was used is discussed.
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 are
presented.
• Discussion - This chapter discusses the results, the models and the survey of the published
reports.
• Conclusions - The conclusions of the study is presented in this section.
• Appendices - The code of the Phénix model are presented and a summary of the Monte
Carlo simulation code used. Also, the results from the second model PFBR are presented.
3 Sub-assembly:
Fuel element containing the fuel pins in FRs. Corresponds to the fuel-assembly in LWRs.
3
2
Fundamentals of fast reactors
This chapter presents the basic theory of fast reactors and some of their advantages. Different
core configurations are also presented and finally a description and calculation of the kef f .
2.1
Overview
SFR is a Fast Reactor, FR, which in short means it uses fast neutrons1 instead of thermal neutrons2 that are standard for water-moderated Light-Water Reactors, LWRs. FRs do not have
a moderator3 as LWR. Hence, the neutrons of the FRs maintain their high energy. Thermal
neutrons are wanted in LWRs, since they have a higher possibility to cause fissions than fast
neutrons, read more in Section 2.2, though they cause build-up of long-lived actinides4 , which
explains why nuclear waste from LWR needs to be stored for so long. However, reactors using a
fast neutron spectrum have the advantages of better neutron economy, production of fuel while
operating, see Section 2.3 and the possibility to transmute the long-lived actinides into shorterlived isotopes see Section 2.4. In addition to the material issues, FRs have the disadvantage of
a weaker negative feedback [1].
Plutonium is the primary choice for FRs, in order to have a closed fuel cycle possible with
current reactors. The fuel of FRs require a high-enriched fuel, around 20 % or more, due to the
low possibility of fission when using fast neutrons [4].
2.2
Fission
The energy source of FRs is fission, like in LWRs. It means that a nucleus of an atom, when
bombarded by neutrons, n, splits into two minor nuclei, which are referred to as fission products.
1 Fast
neutrons: High energetic neutrons, ∼1 MeV.
neutrons: Low energetic neutrons ∼1 eV, also known as slow neutrons.
3 Moderator: Medium that decreases the speed/energy of the neutrons.
4 Actinides: Elements with atomic numbers between 90-103.
2 Thermal
5
FUNDAMENTALS OF FAST REACTORS
Breeding
Elements, which are able to fission when bombarded with thermal neutrons and neutrons with
high energies, are called fissile isotopes. Common examples are 235 U and 239 Pu. Fissile isotopes
are needed in order to sustain a nuclear chain reaction5 . The fissile isotope 235 U is the main
choice of fuel for LWRs. The reaction formula for fission of the isotope is [3]
Plutonium,
2.3
239
¯ + energy
n +235 U →236 U ∗ → F ission products + 2.5n
(2.1)
¯ + energy
n +239 P u →240 P u∗ → F ission products + 2.9n
(2.2)
Pu, is commonly used as fuel in a FRs [3]
Breeding
The isotope 238 U 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 239 Pu
n +238 U →239 U ∗ →239 N p + β −
239
N p →239 P u + β −
(2.3)
(2.4)
Isotopes, which can transmute into fissile isotopes by neutron capture, are referred to as fertile
isotopes and the process is called conversion. The degree of conversion that occurs in the reactor
is
f issile material produced
CR =
(2.5)
f issile material destroyed
One favorable feature of FRs is breeding, which means that the production of fuel is higher
than the fuel consumed. Breeding is possible in a FR due to the fact that a fast neutron spectrum has the advantages of higher production of neutrons per fission and a higher σf /σc -ratio
(where σf is the cross-section6 for fission and σc is the cross-section for neutron capture of the
fissile isotope). The reactor is a breeder if the conversion ratio is greater than 1 [3]. In such a
case, the conversion ratio is referred to as breeding ratio
BR =
f issile material produced
>1
f issile material destroyed
(2.6)
In FRs, fuel enriched with 239 Pu is a better choice than 235 U, commonly used in LWR, most due
to the fact that the η-value, number of neutrons produced per absorption, see equation 2.7, of
239
Pu is greater at higher energies of the neutrons. This is desired in a breeding reactor, since
η needs to be > 2 to make breeding possible. In other words, for each neutron absorption, two
new neutrons have to be produced. The value of η is calculated by the equation
5 Nuclear chain reaction: When fission of one nucleus produces at least one more fission, thus leading to
self-propagation.
6 Cross-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 f ission
η=
σf ν
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 another
important feature. The objective of transmutation is to convert long-lived radiotoxic nuclei to
shorter-lived isotopes.
The build-up of long-lived actinides is a serious disadvantage of the current nuclear power. The
presence of actinides, such as Am, Cm and Pu, makes spent fuel radiotoxic for a long time. It
takes more than 300 000 years for the nuclear waste to reach a radioactive level below natural
uranium, see Figure 2.1. Hence, spent nuclear fuel from LWRs needs to be stored during this
period. Fission products also contribute to the radiotoxicity of nuclear waste, though not as
much as the transuranium elements.
Using reactors with a fast neutron spectrum gives the advantage of a more favorable burnup/buildupratio of actinides than LWRs. This can reduce the storage time for nuclear waste down to several
thousands of years [1]. However, introducing minor actinides8 into the fuel brings safety related
problems, which are further discussed in reference [1], such as an increase in coolant void worth9 .
One way to avoid some of the problematic safety issues related to fuel enriched with minor actinides is to have "target sub-assemblies", containing the minor actinides. These assemblies are
dedicated for high burnup of nuclei.
2.5
Core design of fast reactors
FRs do not have a square lattice of fuel pins as LWRs and instead use a triangular lattice in order
to optimize the burnup and breeding potential. Hence, the core of FRs has a hexagonal geometry
with hexagonal sub-assemblies, which differs from the square geometry of the fuel-assemblies10
in LWRs. The fuel pin and sub-assembly/fuel-assembly arrangement for FRs and LWRs are
presented in Figure 2.2. The core of LWRs is designed to have a fuel-to-moderator ratio that
optimizes the neutron economic and this is achieved by using a square geometry. However, the
lack of moderator in FRs makes a minimized and more compact core superior.
2.5.1
Configuration of fast breeder reactors
There are two basic configurations for a Fast Breeder Reactor, FBR: external and internal breeding. Figure 2.3 visualizes the two concepts. The external breeding configuration has all fertile
7 Transuranium
elements: Elements with atomic number higher than 92.
actinides: Actinides other than uranium and plutonium.
9 Coolant void worth: The feedback in reactivity from coolant boiling.
10 Fuel-assembly: Fuel element containing the fuel pins in LWRs.
8 Minor
7
sources constitute simi
toxic inventory of uran
Figure 1.1: Specific radiotoxic
96% given by uranium
inventory of spent PWR fuel.
one of several possible
FUNDAMENTALS OF FAST REACTORS
Core design of fast reactors
of transmutation.
101
102
103
104
105
106
If we are to reduce the
smutation, the priority
fissioning of the transur
TRU
10 240Pu
Not all of these elem
239
Pu
hazard, though. Figure
238
1
241
Pu
Am
243
Am
butions to the specific r
long lived α-emitters.
0.1
242
241 Am is the major off
Pu
0.01 Unat
and 239Pu dominate the
237
Np
be inferred that remov
t [y]
ricium is required in or
102
103
104
105
106
101
for the radio-toxic inve
Figure
1.2:of Contributions
of in spent nuclear
Figure 2.1: The presence
evolution
transuranium elements
fuel.the
[1] level of natur
reach
individual transuranium nucliNeptunium on the oth
des
to
the
radiotoxic
inventory
of
material located in a blanket zone outside the core of pure fissile material. Internal
breeding con- to the radi
significantly
figuration instead has a core
of
both
fissile
and
fertile
material
surrounded
by
a
fertile
blanket
spent PWR fuel.
thenever
source
zone. The external arrangement was considered for the early FBRs, though was
imple-term consis
mented due to the rapid change in reactivity during fuel burnup, which is a consequence of no
ted. We may therefore
in-core breeding. Internal breeding has the advantages of high breeding ratio and reduction of
void coefficients.
smutation of plutonium
corollary is that the cu
transmuting americium
In-core configuration: Homogeneous and heterogeneous
wise, the reduction of t
All FBRs so far, have had a core design where internal breeding in the core is possible, which
tory in the waste stream
is also known as in-core breeding concept. There are two variants of this arrangement: homogeneous and heterogeneous. A core with all assemblies of pure fertile material,factor
located of
in both
ten [Delpech99
100
Radiotoxic inventory [Sv/g]
radial and axial regions has a so called homogeneous configuration due to the uniform spread
of fertile and fissile material. The regions of fertile material have two main functions; neutron
shielding and breeding of fuel.
The heterogeneous configuration has a core of fissile sub-assemblies where the blanket-assemblies
of pure fertile material are distributed throughout the fissile regions. The advantages of this
configuration are better breeding ratios and reduced sodium void coefficients, though it has the
disadvantage of high enrichment of fissile material.
Different parameters of the core have different impact depending on the core configuration.
In a homogeneous core, the neutronic performance is more sensitive to the fuel sub-assembly
design and less sensitive to the layout of the core than in a heterogeneous configuration [5].
8
Effective neutron multiplication factor, kef f
FUNDAMENTALS OF FAST REACTORS
Figure 2.2: This figure shows the fuel pin and the sub-assembly/fuel-assembly arrangements of
FRs and LWRs. Note the LWR fuel-assemblies have more space between the fuel pins than those
of FRs. a) Sub-assembly arrangement of FRs. b) Fuel-assembly arrangement of LWRs. c) Fuel
pin arrangement of FRs. d) Fuel pin arrangements of LWRs.
2.6
Effective neutron multiplication factor, kef f
Effective neutron multiplication factor, often referred to as kef f , is an important parameter in
all nuclear reactors. The value of kef f determines how the nuclear chain reaction proceeds.
The value of kef f can be calculated by the four factor formula [6] where η is obtained from
equation 2.7
� =F ast f ission f actor
f =T hermal utilization
p =Resonance Escape P robability
P =N on − leakage P robabilities,
9
FUNDAMENTALS OF FAST REACTORS
Effective neutron multiplication factor, kef f
Figure 2.3: Overview of the internal and external configuration of a FBR.
kef f is then determined by
(2.8)
kef f = k∞ · P
=η·�·p·f ·P
number of neutrons in current generation
=
number of neutrons in previous generation
(2.9)
(2.10)
In words, kef f describes how many fissions one fission leads to. There are three crucial states of
a reactor:
kef f < 1 (subcritical, decreasing number of neutrons)
kef f = 1 (critical, stationary number of neutrons)
kef f > 1 (supercritical, increasing number of neutrons)
Under normal operation conditions in a commercial reactor it is desired to have kef f = 1, in
order to have a sustainable nuclear chain reaction. Furthermore, the value of kef f must not be
»1 to avoid severe accidents. Accelerator-Driven Systems, ADS, is an example of a reactor with
a subcritical core that uses a proton-canon as an outside neutron source to have a sustainable
neutron economy. The reactivity of a reactor [7], ρ, is defined as
ρ=
10
kef f − 1
kef f
(2.11)
Effective neutron multiplication factor, kef f
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
3
Sodium-cooled fast reactors
This chapter describes the technique of SFRs and their current status in the world. Detailed
information about the French reactor Phénix and information gathered from the investigation of
the A.U.R.N. events are also presented.
3.1
Sodium-cooled fast reactors in the world
Since the establishment of nuclear power, more than 20 SFR units have been constructed in
the world and together they have provided over 400 years of operation experience [8]. Reactors
of experimental and prototype size have dominated the SFR fleet, see Table 3.1 and due to
technological and economical difficulties of using sodium as coolant, Superphénix and BN-600
remain as the only two SFRs of industrial/commercial size ever constructed. Superphénix has
been shutdown and is currently being decommissioned, while BN-600 is still in operation. Superphénix experienced a lot of technological difficulties and minor accidents during its operation
before it finally was forced to shutdown in 1998. The BN-600 did also encounter problems in
the early years, though it should be noted that the reactor have, several times, been the best
power-generating unit in Russia, both with respect to reliability and safety [9]. A third reactor
of industrial size was designed in the project European Fast Reactor, EFR, which was initiated
in 1980. Unfortunately, the project was cancelled in 1998 before any construction had taken place.
During the last decade FRs have once again blossomed and countries are once more expanding their SFR programs. New countries are joining the international co-operations, such as the
Generation IV Forum [10] and building reactors of their own to gather data and operating experience of SFRs. China for instance, has recently finished their construction of CEFR, China Fast
Experimental Reactor, an experimental SFR with thermal capacity of 60 MW. France, which is
one of the leading countries in SFR-technology, is for the moment planning the design of their
second prototype reactor, ASTRID. The construction of ASTRID will probably take place in
the middle of 2020. Moreover, Russia and India are expanding their SFR fleet with the ongoing
construction of BN-800 [11] and PFBR.
13
SODIUM-COOLED FAST REACTORS
Sodium-cooled reactor design
Table 3.1: Table of some SFRs in world. Note that BN-600 and Superphénix are the only two
reactors of commercial size. [11]
Name
Country
Thermal power (MWth1 )
Type
Critical
Status
EBR-I
USA
1.4
Experimental
1951
Shutdown
RAPSODIE
France
24
Experimental
1967
Shutdown
BOR-60
Russia
60
Experimental
1968
Operating
JOYO
Japan
50
Experimental
1977
Operating
CEFR
China
60
Experimental
2010
Operating
BN-350
Kazakhstan
1000
Demonstration
1972
Shutdown
Phénix
France
563
Demonstration
1973
Shutdown
Monju
Japan
714
Demonstration
1992
Operating
BN-600
Russia
1470
Commercial
1980
Operating
Superphénix
France
3000
Commercial
1985
Shutdown
3.2
Sodium-cooled reactor design
SFRs are, as previously mentioned, fast reactors that use liquid sodium as coolant and this type
is the most technologically developed concept of Generation IV [2]. It is similar to Pressurized
Water Reactors, PWRs, in its design with primary and secondary circuits.
3.2.1
Advantages and disadvantages
The current primary objective of SFR concept is to burn high-level waste, especially burnup of
plutonium and other actinides in order to reduce the storage time. Sodium as coolant has the
advantage of a good breeding performance and a high boiling point at an atmospheric pressure,
which provides a safety margin against void, gas bubbles, in the core. Furthermore, sodium
is not corrosive, it has a high thermal conductivity, high thermal inertia and the possibility to
remove decay heat2 from the core by natural convection. These advantages combined with the
fact that the SFR concept have been both tested and proven on industrial scale make sodium a
feasible coolant for future reactors.
Sodium is unfortunately a very reactive metal, especially in contact with water, which can cause
sodium fires and hydrogen explosions, even air is chemically incompatible with sodium. This
makes the design of steam generators in SFRs more complicated. Other problems are sodium
void in the core, which has a positive feedback in reactivity and the metal’s opaqueness, which
makes in-core inspections difficult. The extra technology that is necessary in order to compensate
for these disadvantages makes SFR expensive, which results in low economic competitiveness.
3.2.2
Technical overview
The primary circuit with sodium cools the core and the secondary system with sodium transfer
the heat from the primary circuit through Intermediate Heat Exchangers, IHX, to the steam
generators, see Figure 3.1. The secondary system prevents the release of radioactive material in
1 MWth:
2 Decay
14
Thermal power.
heat: Heat produced after the reactor has been shutdown.
Sodium-cooled reactor design
SODIUM-COOLED FAST REACTORS
the event of a sodium-water reaction. The sodium in the primary and secondary circuit must be
kept pure to avoid sodium oxide and hydride deposits, which in turn can lead to blockage in the
ventilation of the sub-assemblies. Alternatives, which do not react violently with sodium, in the
secondary circuit, are being considered. Super-critical carbon dioxide in a so called Brayton cycle
is currently being developed as energy carrier. This concept is more efficient than the cycles used
in the present reactors. Since carbon dioxide does not react as violent with sodium as water an
intermediate system would be unnecessary. Most SFR designs have multiple secondary circuits
that are each connected to a multiple number of steam generators. For example, Phénix had
three secondary loops with one steam generator each, while BN-600 had three secondary loops
with eigth steam generators each.
There are two different configurations of the primary circuit: the common pool configuration
and the less common loop configuration, favored in Japan. In the pool configuration, see Figure 3.1, the entire primary circuit is integrated in the main vessel, while in the loop configuration
each module has separate casings. The advantage of the pool configuration is large thermal inertia and the system is insensitive to loss of coolant flow, on the other hand the loop configuration
has the benefit of easier inspections and repairs. The loop configuration also has better defense
against earthquakes, which is one of the reasons why it is chosen by Japan.
Table 3.2: A summary of the design parameters for the SFR concept of Generation IV. [2]
Reactor Parameters
Reference Value
Outlet Temperature
530-550 °C
Pressure
∼ 1 Atmospheres
Rating
1000-5000 MWth
Fuel
Oxide or metal alloy
Cladding
Ferritic or ODS ferritic
Average Burnup
∼ 150 − 200GWD/MTHM3
Conversion Ratio
Average Power Density
0.5-1.30
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 and
the liquid sodium. The layer acts as an inert atmosphere, which prevents sodium aerosols from
leaving deposits in sensitive areas. Furthermore, nitrogen is used as an inert gas between the
main vessel and safety vessel and in systems surrounding the pipings carrying sodium. The reason for not having nitrogen as cover gas above the hot pool is that nitrogen reacts with sodium.
Argon gas however, is too expensive to have in the systems surrounding the pipings etc.
Two different fuels are considered for SFRs: mixed oxide fuel, MOX-fuel, and metal-fuel. The
MOX-fuel is a combination of PuO2 and UO2 . It is the primary choice of fuel for SFR due to the
extensive experience gathered from earlier operation and testing. Metal fuel is a combination of
uranium-plutonium-zirkonium metal alloy and it has the advantage of better thermal conductivity with no moderation from oxygen, which in turn results in better breeding performance,
though this type of fuel has a lower melting point than oxide based fuel.
3 GWD/MTHM:
GWdays/metric tone heavy metal.
15
SODIUM-COOLED FAST REACTORS
Phénix
Figure 3.1: Overview of the SFR pool design. The system has a primary circuit integrated in
the main vessel and the heat is transferred from the primary circuit to the steam generators by
intermediate circuits. [2]
3.3
Phénix
In 1971, the construction of the second French SFR, Phénix, was complete. Phénix was the first
demonstrational/prototype SFR in the world and it had a capacity of 580 MWth/250 MWe4 .
The power plant was connected to the grid for the first time in 1973. The reactor was of pooltype configuration and was cooled by three intermediate systems, which in turn were connected
to one steam generator each [12]. The desirable temperature of the sodium outlet from the core
lies at 560°C and the inlet lies at 400°C. Phénix had a homogenous core with two enrichment
zones of fissile fuel [13]. The fissile core was surrounded by a fertile blanket, both in radial and
axial directions, of mainly depleted or natural uranium. Most of the fuel breeding in Phénix took
place in the blanket zone. Phénix used the free standing core restraint concept for keeping the
sub-assemblies of the core together, which means that the core support structure is located at the
lower part of the sub-assemblies. The concept allows free outward bowing of fuel- and blanket
assemblies until the core radius makes contact with the shield assemblies, which are located at
the periphery of the core. Several experimental sub-assemblies were placed in the core of Phénix
for different irradiation experiments.
The main objectives of Phénix were not only to test the feasibility of SFR technology on larger
scale but to perform irradiation experiments, like minor actinide burning [12]. For these experiments, Phénix used different set-ups of sub-assemblies with different inventories. All data
4 MWe:
16
Electrical power.
Phénix
SODIUM-COOLED FAST REACTORS
Figure 3.2: Chart of downtime at Phénix due to accidents and maintenance. Note the percentage
of negative reactivity transients, which is the fourth time-wasting issue, if scheduled work is not
taken into account. [14]
gathered from the operation of Phénix have been used for the development of Superphénix and
EFR.
Phénix encountered many incidents during its time in operation and most of these were related
to sodium leaks in the intermediate heat exchangers, see Figure 3.2. Phénix suffered long downtimes after minor incidents due to the fact that a political decision was required for a restart of
the reactor, even though the facility recovered fast from the damages. In the late 1980’s and in
the beginning of 1990’s, Phénix encountered several automatic shutdowns of the reactor due to
negative transients. These events caused long downtimes of the reactor, see Figure 3.2, in order
to investigate their origin, more information about this is presented in Section 3.3. After the
fourth automatic shutdown, the power of the reactor was decreased to 350 MWth [12] due to an
independent reason related to residual power removal system [15]. In 1992, a program for the
life-time extension of Phénix was initiated and the renovation was finished in 2002. Phénix then
proceeded with its operation until the reactor was finally shutdown in 2009. The last experiment
performed was to investigate how the core is affected by core-flowering.
Although Phénix encountered many incidents and experienced a lot of downtime, it is still seen
as a success, since it provided a lot of valuable information and operating experience of SFRs.
3.3.1
A.U.R.N.
In the end of 1980’s Phénix encountered, while operating at full power, an earlier unexperienced
phenomenon that lead to an automatic shutdown of the reactor. The signal of the neutron cham-
17
SODIUM-COOLED FAST REACTORS
Phénix
bers5 registered very rapid oscillations with high amplitudes, see Figure 3.3. During the time
period between 1989-1990, Phénix suffered from this event four times. These transients were
named "Arrêt d’urgence par réactivité négative", A.U.R.N. In English this means automatic
emergency shutdown by negative reactivity. The events occurred while operating at or close
to full power; the first three at 580 MWth and the last one at 500 MWth. A.U.R.N. were all
detected by the neutron chambers, which are located beneath the reactor vessel and measure the
neutron flux.
During all events the registered signal of the neutron chamber had the following behavior:
1. An almost linear reactivity drop with high amplitude
2. 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 last
two A.U.R.N. events in Phénix in 1990. Note the oscillating behavior and the secondary peak,
which in both cases slightly exceed the initial power. [14]
This phenomenon only lasted for several hundreds of milliseconds before the reactor was shutdown automatically by the control rods. The control rods were triggered by the first reactivity
drop due to the fact that the amplitude of the drop went below the threshold for negative reactivity transient. The power drop in the signal varies in the four different events and in the last
two it reached down to 28% and 45% of the nominal power. Assuming that the power signal
from the neutron chamber directly corresponds to the thermal power of the core; the fastest
drop reached in the A.U.R.N. events corresponds to a loss in kef f of 320 pcm7 and the highest
5 Neutron 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.
6 Control rods: Rods made of elements that can absorb many neutrons and are used for controlling the reactor.
7 pcm: per cent mille of ∆k
ef f /kef f .
18
Phénix
SODIUM-COOLED FAST REACTORS
increase corresponds to an increase of 37 pcm above the initial value [12].
Other instruments in Phénix were active during the A.U.R.N. events, such as geophone, cover
gas pressure, the primary pump discharge, position readings of one of the six control rods etc.,
though none of them except the geophone registered any abnormal activity. Interference in the
measurement channels was the first possible explanation of the phenomenon due to the fact that
two out of the three neutron chambers were replaced during the 10-yearly inspection [12]. However, this explanation was later discarded after a control rod drop test, which proved that the
equipment was insensitive to noise.
The information gathered from the third event led to the explanation that a large volume of
gas passed through the core. This was confirmed by the observation of an increase in the pressure of the cover gas and the possibility of a plugging in the special venting of the sub-assemblies.
The reactor was then stopped and preventive measures were taken before start-up. This scenario
however, was abandoned after the occurrence of the fourth event.
Low power tests, between 5 and 40 MWth, after the third event were performed in order to
recreate the registered signals of the neutron chambers, though without any success [12].
Expert Committee
After the fourth A.U.R.N., the operations of Phénix were stopped and the French Atomic Energy
Commission, CEA (Commissariat à l’Énergie Atomique et aux énergies alternatives), conducted
an extensive investigation program. An expert committee was appointed, whose objectives were,
quoted from reference [12]:
• Examine every possible cause of the reactor anomalies
• Provide elements of response for these anomalies
• Examine every possible consequence in the event that these abnormal conditions should
occur in different conditions
• Make proposals for preventive measures
After almost two years of investigation, the committee had not found a complete explanation of
the phenomenon, though the most probable cause was radial movement of the sub-assemblies.
Furthermore, in the safety analysis, which was based on all plausible scenarios that could cause
A.U.R.N., it was concluded that the safety of the reactor was not affected. A new approach
was proposed, in which the surveillance of the reactor should be reinforced in order to obtain as
much information as possible in case of a new negative reactivity transient. Secondly, tests were
to be performed at low power followed by 10 days at high power, to test the instrumentation of
Phénix and also to verify the reactor and core behavior before start-up of the reactor.
The new approach that was provided by the committee led to the installation of additional
equipment in order to have a full surveillance of the reactor and to detect any anomaly. Some
examples of new equipment:
• SONAR device installed above the core
• Acoustic detector inside the core
• Magnetic field measurement of the reactor vessel
19
SODIUM-COOLED FAST REACTORS
Phénix
Furthermore, instrumentation designed for fast measurements were installed in Phénix. In the
end of 1991 and in the beginning of 1992, tests were performed with the new equipment. They
were to:
• Verify the neutronic condition of the core.
• Confirm the reactivity change during a normal automatic drop of the control rods.
• Gather more information to evaluate the different explanations.
• Obtain a description of the dynamic behavior of the reactor instrumentation.
• Validate the additional equipment installed after the events.
These tests succeeded to verify the new surveillance of the reactor and it provided enough information to be able to discard several assumptions made for different scenarios, which were to
explain the occurrence of A.U.R.N. in Phénix. The earlier seen correct behavior of the core and
the primary hydraulics were confirmed during these tests.
No A.U.R.N. event was registered after the installation of the new equipment.
Explanations of A.U.R.N.
A.U.R.N. remains a mystery and it has been hard for researchers to make any conclusions or find
suitable explanations of the phenomenon, especially since it was only registered by the neutronic
equipment. The expert committee gathered all possible scenarios, which can occur in a reactor
for their investigation. Assumptions including the effects of fuel burnup and temperature have
been eliminated due to the kinetics of A.U.R.N.s. Furthermore, the effects related to absorbing,
moderating or reflecting parts have also been removed from the possible scenarios by the expert
committee. Other phenomena such as effects related to sodium void, movements of the control
rods and movement of the core have been investigated. Although many assumptions related to
sodium void have been eliminated, there are still some left, for example implosion of sodium
bubbles [16], though other assumptions such as sodium boiling and gas passing through the core,
cannot provide a satisfying scenario due to their mechanisms. The involvement of the control
rods have been examined, including their mechanism, the absorber pin bundle, the rotating plug
that supports the rods. The high amplitude of the signals registered during the negative transient
events requires a very high acceleration of the control rods and these investigations reveal that the
required acceleration is not realistic. Therefore, control rod movements as a single explanation
was abandoned. The first explanation that could cause such abnormal behavior in the signal of
the neutron chambers was as mentioned before, interference in the measurements. Though, the
equipment was later on proved to be insensitive to noise. Furthermore, there were up to seven
different measurement channels from which the signal is computed, with different electronics and
components that displayed the same abnormal activity, which makes the registered events even
more consistent. However, it is possible that the high amplitude of the signals could be explained
by failure in the electronics, though the deviation and oscillating behavior is most probably due
to variation in the neutron flux.
Finally, after eliminating most of the plausible phenomena that can occur in a reactor, the
expert committee concluded that assumptions involving movements of the core are most convincing. Outward movement of the sub-assemblies causing the core to expand, followed by a
contraction, is a scenario which can induce a similar signal pattern as A.U.R.N. The expert
20
Phénix
SODIUM-COOLED FAST REACTORS
committee’s investigation of the phenomenon and its relation to A.U.R.N led to the following
results and conclusions:
• Extensive modelling and tests performed on outward movement of the core, regardless of
its origin, show that a pulse source inside the core can induce stresses, which in turn gives
a 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 similar
signals, though this requires an unrealistic amount of energy. Consequently, the only
realistic scenario of core movements involves radial movement of the sub-assemblies.
• The origin of the possible core movements in Phénix is still unidentified. Investigations
have been made with scenarios based on transversal excitation from the diagrid; abnormal
behavior of the core block structures; spontaneous reconfiguration of the core; a pressure
hammer from gas passing in a pump; gas expansion occurring above the core or under the
cover plug; loss of absorber pin tightness; oil passing through the core causing a mechanical
effect by vaporization and cracking. All of these explanations have been discarded as
possible origins.
CEA are going to recruit two Ph.D. students with the mission to investigate the remaining
possible scenarios. They will hopefully solve the mystery of the negative transients.
3.3.2
Core-flowering
Core-flowering is a type of core-movement and it means that one sub-assembly expands and
induces stresses on the surrounding sub-assemblies, causing the core to expand in radial direction.
The result from core extension is displacement of the sub-assemblies in the core leading to an
increase of the gap between the units. This decreases the kef f of the core which is directly related
to its thermal power. Little extension of the core leads to considerable decrease in the reactivity.
For illustration see Figure 3.4.
Figure 3.4: Sub-assemblies under normal operation in a). Sub-assemblies suffering from coreflowering at top b) and in the centre c).
21
SODIUM-COOLED FAST REACTORS
3.3.3
ASTRID
Core-flowering tests of Phénix
The latest scenario being investigated by CEA, is based on neutronic and thermal hydraulic
interaction between a blanket-assembly and a moderated experimental sub-assembly, named
DAC-assembly [16]. The increase of plutonium, as a result of breeding in the blanket combined,
with the moderation effect of the experimental sub-assembly causes an increase in power between
the two assemblies. This combined with the low flow-rate of sodium in the DAC sub-assembly
causes the sodium to boil, which creates bubbles of sodium vapor. Implosion of these bubbles
could induce the assumed core-flowering leading to the reactivity oscillations registered during
the A.U.R.N. events.
After the life-time extension of Phénix 1998-2003, the operation of the facility restarted and new
experiments for the development of SFRs were carried out. In the end of 2009 core-flowering
tests were made by inserting the DAC experimental sub-assemblies, similar to those used in 1989
and 1990, into the core. The purpose of these tests was to investigate the thermal hydraulic and
neutronic interactions between the experimental sub-assembly and blanket-assemblies. An Eddy
current flowmeter was used for measuring the mass flow of sodium inside the DAC sub-assemblies
see Figure 3.5 [17]. The thermal balance for both assemblies were measured at different mass
flows of sodium. The power of the blanket and thermal exchanges between the sub-assemblies
are to be determined by these experiments. Unfortunately, no results nor conclusions from the
blanket-DAC experiments have yet been published.
Another experiment was carried out during the last year of Phénix to increase the knowledge of
core-flowering. This was done while the reactor was running at zero power8 , ∼100 kW [15]. A
mechanical device, see Figure 3.6, was inserted into two different positions; first at the center of
the core and then at a peripheral location of the core. The mechanical device put pressure on the
surrounding sub-assemblies, causing the gap between all sub-assemblies to increase. The induced
stress then resulted in a radial extension of the core, see Section 3.3.2 and Figures in Section 4.3.
The effect of core-flowering was measured at different temperatures in the interval of [180, 350]°C
and the radius of the core was extended with 3-5 mm [15]. The result was that a small increase of
the core radius gives a significant drop in reactivity. In this experiment the correlation between
the negative feedback in kef f and core extension lies around -60 pcm/mm, when the device was
placed in the center of the core [17]. The effect was strongly reduced when the mechanical device
was placed at the peripheral position.
3.4
ASTRID
Astrid is a French SFR prototype-project and the construction of the reactor will take place in
the 2020’s. The ASTRID project is aiming at accomplishing some of the Generation IV criteria,
though it will not be a "first of a kind", since it is only going to be a prototype. The main goals
of the project are to prove the technology of SFR on an industrial scale, perform transmutation
of radioactive waste and irradiation experiments and the facility is to be used for the needed
development of in-service inspections and repairs [18]. Considerable amount of information have
been gathered from the experience of operating both Phénix and Superphénix, which now lies
as a basis for the reactor design of ASTRID. More details in the design of ASTRIDs is to be
published in 2012 and the final design is to be delivered in 2014 [19].
8 Zero
22
power: the power plant runs at a low power without any active steam-generators.
IAEA TecDoc : Status of liquid metal cooled fast reactor technology
ASTRID
SODIUM-COOLED FAST REACTORS
Figure 2 - Thermal-hydraulic measuring pole on the DAC
Figure 3.5: Schematic of the Eddy current flow meter used for measuring the mass flow of sodium
in the moderated experimental sub-assembly DAC. [17]
IAEA TecDoc : Status of liquid metal cooled fast reactor technology
Figure 3 - Experimental sub-assembly with moderator (DAC)
5. Training
In agreement with the ASN (Nuclear Safety Authority), a training program for the operating teams was
set up. It consisted of presenting the operators with the test aims, their sequencing and related risks.
To ensure successful testing, this program also saw the operators take part in drawing up the
operational documents, called Trial Instruction Programs, as well as in running sessions on the
SIMFONIX simulator, when this was possible.
Figure 3.6: A picture of the mechanical
device, which was used for testing how core-flowering is
Figure 12 – Device to push apart sub-assemblies
affecting the reactivity of the core. [17]
3.4.1
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 corebe
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codes, ERANOS and DARWIN for neutronics, TRIO U and CATHARE for thermal-hydraulics and
GERMINAL for fuel.
The young engineers, specially recruited at CEA to prepare and conduct the tests along with the
plant’s teams, will joined the fast reactor projects at CEA Cadarache center in23
their respective
specialist areas after having experienced a unique period in their professional career.
Conclusion
A large program of tests was carried out for almost one year after the last industrial operation cycle of
the Phenix sodium cooled fast reactor.
The program covered core physics, thermal hydraulics and fuel issues and also the investigations of
the automatic scrams occurred in 89 and 90.
Several specific devices were designed, fabricated, qualified and used during the tests to complete the
standard instrumentation of the reactor and to perform the tests.
A big amount of information was recorded and will be used in the next period to fulfill the main
objectives of the program on sodium fast reactors codes.
This work was also the opportunity to involve young engineers in the preparation and performance of
SODIUM-COOLED FAST REACTORS
ASTRID
diate system. In the preliminary design, there are six intermediate circuits of sodium, which are
connected to four steam generators of 100 MWe each [19]. The fuel pin design will be similar
to those used in Superphénix, with a hole in the center to limit the maximum temperature of
the pellet. The pin will have a large diameter, larger than in Superphénix and a small diameter
spacing wire. The choice of fuel is for the moment MOX-fuel.
In-service inspections will have a large impact on the design of the reactor vessel and its external components. Hence, the focus will lie on simplification of the structures, accessibility,
capability of component removal and repair, core discharge and arrangements for the possibility
of primary circuit draining. There are several instruments that have been used in Phénix and
Superphénix for inspection of the core, though the equipment needs upgrades and modifications
before it can be used for the operations of ASTRID. More safety features for reactor shutdown
will be introduced in order to enhance the protection against severe accidents, such as extra shutdown levels. A core catcher is going to be used as protection in the case of fuel-pin failure and
core-melting. The possibility of core-flowering and core compaction is to be reduced in ASTRID
by design; fuel elements will be reinforced to limit their movement [20].
Design parameters of ASTRID that are still open for discussion [19]:
• Energy conversion
• Primary circuit design
• Devices to eliminate severe accidents
• Core catcher technology and location
• Steam generators materials and technology
• Innovative technologies for sodium fires detection and mastering
24
4
Method and materials
The Monte-Carlo simulation code used for the study is discussed in this chapter. Descriptions
of the core models and the simplified model of core-flowering are also presented.
4.1
Monte-Carlo simulation code
The Monte-Carlo simulation code Serpent was chosen for the study in order to simulate how
core-flowering affects the reactivity of the reactor. The main reasons for using this code were the
advantage of free-of-charge and the access to the predefined SFR core of PFBR created by Peter
Wolniewicz. Other advantages taken into account were predefined geometries and the fact that
the Monte-Carlo Simulation code provides a simple way of creating complex lattices. The value
of kef f was obtained from the simulations in order to investigate how the reactivity of the core
was affected by core-flowering.
Serpent has a manually defined source of neutrons. The kef f is calculated by neutron transport calculations and this process is referred to as a cycle. The calculated value of kef f is after
each cycle weighted against the values obtained from previous cycles. This has to be done in
order to converge the value of kef f . A minimum number of cycles are required in order to have
a proper convergence of kef f . Inactive cycles are also used to have a better convergence of kef f .
The inactive cycles of a simulation are the initial cycles that correct the distribution of the kef f
values. However, the obtained values of kef f are discarded in the inactive cycles.
4.1.1
Difficulties using Monte-Carlo simulation code
There are several problems when using Monte Carlo simulation code for calculation of kef f . The
three main issues that need to be taken into account are [21]:
• model error, bias
• statistical error
25
METHOD AND MATERIALS
Monte-Carlo simulation code
• convergence
These issues can in most cases be avoided without any considerable impact on the results. First
the convergence rate of kef f can be more efficient by using a good initial guess and a number of
inactive cycles, which reduce the total number of cycles for convergence [21]. There is always a
risk, when simulating different states of a core, that the statistical error is larger than the change
in kef f between the simulations. In such a case it is impossible to make any essential conclusion
from the result. The main way to prevent this is by increasing the number of simulations and
have a large number of cycles per simulation. The bias of kef f is proportional to 1/M , where
M is the amount of neutrons per cycle. The bias is negligible if M > 10000, though in case of a
large model M should be > 100000 neutrons/cycle [21].
4.1.2
Choice of Monte-Carlo simulation code
Two different Monte Carlo-simulation codes were considered for the study: Serpent and MCNP.
MCNP stands for general-purpose Monte Carlo N-Particle code and is developed by Los Alamos
National Laboratory in the United States. It is capable of neutron, photon, electron, or coupled
neutron/photon/electron transport, though it also includes the opportunity to calculate eigenvalues, for example kef f , for critical systems.
Serpent is a three-dimensional continuous-energy Monte Carlo neutron transport code developed at VTT Technical Research center of Finland. It also has the capability of performing
burnup calculations. The code is specifically designed for reactor physics applications and the
original intended use was the production of homogenized multi-group constants for reactor simulator calculations.
A comparison has been made [22] between the two different Monte-Carlo simulations codes,
which can be seen in Table 4.1 and Table 4.2. The simulation had 20 inactive and 500 active
cycles and a source of 20 000 neutrons, which gives a total of 10 000 000 neutron histories. The
JEFF-3.1.1 was used as a cross-section library.
Table 4.1: A comparison of k∞ between MCNP and Serpent. [22]
Case
MCNP
Serpent
∆(%)
PWR pin-cell, 1 MWd/kgU burnup
1.28319 (0.013)
1.28294 (0.013)
-0.019
PWR pin-cell, 20 MWd/kgU burnup
PWR pin-cell, 40 MWd/kgU burnup
1.07180 (0.017)
0.91631 (0.021)
1.07182 (0.016)
0.91611 (0.018)
0.002
-0.022
SFR assembly
1.76744 (0.008)
1.76758 (0.008)
0.008
Mixed PWR MOX/UOX lattice
1.06929 (0.018)
1.06943 (0.017)
0.013
This thesis has a limitation in time and from the information obtained in Table 4.2 it can be
concluded that Serpent is much faster than MCNP. In the SFR case, which is most essential,
Serpent is 57 times faster than MCNP and the result only differs with 0.008 %. Hence, MCNP
was excluded as a simulation tool. Serpent is more time-efficient and is specialized in lattice
calculation and is therefore the best alternative for the simulations of this thesis.
26
Model of Phénix
METHOD AND MATERIALS
Table 4.2: A comparison of computation time (in minutes) between MCNP and Serpent. [22]
4.1.3
Case
MCNP
Serpent
MCNP/Serpent
PWR pin-cell, 1 MWd/kgU burnup
821.0
21.4
38.3
PWR pin-cell, 20 MWd/kgU burnup
799.8
20.6
38.7
PWR pin-cell, 40 MWd/kgU burnup
809.7
21.3
38.0
SFR assembly
1368.3
23.9
57.2
Mixed PWR MOX/UOX lattice
143.3
17.2
8.3
Advantages and disadvantages of Serpent
Serpent has only been on the market for a year. Although it seems now that most of the major
bugs are fixed, there are still some smaller ones left [23]. The latest report from the developer of
Serpent tells that the minor bugs should not have a significant impact on the results [24]. Since
the code is still under development it does not have all the features that MCNP can provide,
such as interactive geometric plotter for measurement and overview of the geometry, which are
perfect for troubleshooting.
Woodcock’s delta-tracking method is used for the calculation of the neutron path in Serpent,
which can lead to problems when heavy absorbers are present. However, this was not a problem
for the simulations of the study due to the fact that a fast reactor was simulated, which meant
that the value of the cross-sections of heavy absorbers were low. Therefore it should not have an
impact on the results.
Another disadvantage of Serpent is that the code is not well suited for calculations of shielding and detectors due to the use of delta-tracking [25]. Instead, a collision estimator is used,
which is less efficient. In most cases however, the results from lattice calculations are not affected.
Additional to the standard data libraries of Serpent, the code supports any continuous-energy
MCNP data library. All numerical output from the simulations are stored in an .m-file, which is
useful for analyzing the results in external programs, like MATLAB.
4.2
Model of Phénix
The model of Phénix created for the study is a simplified model of the Phénix core. The control
rods are completely withdrawn from the core. Sodium fills the cells of the control rod and the
sub-assemblies lie close to each other with a tiny space in-between. The wrapping material of
the sub-assemblies has in this model the same material composition as the cladding of the fuel
pins. The information gathered for the design has been obtained from the references [13, 26, 27].
The parameters of the model are presented in Table 4.3 and all material data are presented
in Table 4.4 and 4.5.
27
METHOD AND MATERIALS
Model of Phénix
Table 4.3: Parameters of the simplified model of Phénix. Most values are obtained from [13, 26,
27], other values have been set in order to have a reasonable geometry.
Reactor parameter
Reference Value
Fuel pin
Fuel type
MOX (PuO2 -UO2 )
Pellet diameter
5.42 mm
Cladding outer diameter
6.65 mm
Air-gap space
0.075 mm
Thickness of cladding
0.45 mm
Fissile height
850 mm
Pitch
7.8 mm
Pins/sub-assembly
271
Lower axial blanket within fuel pin
300 mm
Upper axial blanket within fuel pin
260 mm
Blanket pin
Blanket material
Depleted uranium oxide (UO2 )
Pellet diameter
12.5 mm
Cladding outer diameter
13.4 mm
Thickness of cladding
0.45 mm
Overall Length
1668 mm
Pitch
14.5 mm
Pins/sub-assembly
61
Sub-assembly
Geometry
Hexagonal
Diameter across flats
124 mm
Wall thickness
3.5 mm
Overall length S/A fuel
1410 mm
Overall length S/A blanket
1668 mm
Pitch
127 mm
Core configuraton
28
Core design
Homogeneous internal breeding
Nr. of enrichment zones
2
Enrichment of P u in MOX-fuel
18 % and 23 %
Nr. of high-enriched S/A
48
Nr. of low-enriched S/A
55
Nr. of blanket S/A
90
Nr. control rods
6
Model of Phénix
METHOD AND MATERIALS
Table 4.4: Composition of fuel and blanket.
Composition of fuel/blanket
Proportion (%)
Plutonium [1]
238
Pu
3.5 %
239
Pu
51.9 %
240
Pu
23.8 %
241
Pu
12.9 %
242
Pu
7.9 %
Uranium [28] (In MOX-fuel)
235
U
0.7 %
238
U
99.3 %
Depleted uranium [28]
235
U
0.3 %
238
U
99.7 %
Table 4.5: Composition of of the cladding and wrapper steel. [29]
Material
Proportion (%)
Austenitic Steel Nr. 14970
C
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, with
zoom at the active core and the fuel-assemblies. The red assemblies are dedicated cells for the
control rods, which are withdrawn in this model. The blue sub-assemblies are blankets and the
green and white ones are fuel-assemblies.
4.3
Model of core-flowering
Monte-Carlo simulation codes have, as mentioned in Section 1.3, a limited number of geometrical
structures. In order to make a simulation of core-flowering, a simplification of the phenomenon
was made; all structural bending of the sub-assemblies due to core-flowering, have not been taken
into account. Instead the gap between the sub-assemblies was increased, which is the consequence
of the structural bending, see Figures 4.2 and 4.3, which in turn causes core extension/increase
of the core radius. The extra space added to the gap between the sub-assemblies, λ, increases
30
Model of core-flowering
METHOD AND MATERIALS
symmetrically in this model, see Figure 4.4. The relation between the core extension and the
extra space between the sub-assemblies depends on the number of sub-assemblies and core configuration. The PFBR-model has a homogeneous design. If λ = 1 mm the corresponding core
extension is 9 mm. For the Phénix-model, which is similar in design with a homogeneous core
but with less number of sub-assemblies, the relation is 1 : 7.
The two different cores were first simulated with normal conditions, λ = 0. A high number
of neutrons were used to reduce the bias and enough cycles were made to make sure that the result converged properly. The simulations of core-flowering were made with λ = 0.4, 0.8, 1.2, 1.6, 2
mm. The initial guess for kef f was 1.00 and 100 inactive cycles were used in order to have a
faster convergence rate. The nuclear data library used for these simulations was JEFF-3.1.1.
A detector was defined in the center of the model in order to obtain how the neutron flux is
affected by core-flowering. How the detector is defined can be found in Chapter B. The results
and the parameters for the simulations of Phénix are presented in Chapter 5 and the same can
be obtained for the model of PFBR in the appendix, see Chapter D.
Figure 4.2: Plan view of how the sub-assemblies are affected by core-flowering in the simulations.
31
METHOD AND MATERIALS
Model of core-flowering
Figure 4.3: Side view of how the sub-assemblies are affected by core-flowering in the simulations.
Each block corresponds to a block with hexagonal geometry.
Figure 4.4: The gap between the sub-assemblies increases symmetrically in the model of coreflowering.
32
5
Result
In this chapter the results obtained from the model of Phénix and the model of core-flowering
are presented.
5.1
Model of Phénix
Under normal operation conditions, λ = 0, the kef f of the Phénix model had a value of 1.00298.
Detectors obtained the neutron flux in the center of the core. The obtained value from the
simulation of the core under normal conditions was (8.43167 ± 0.0175) · 1015 neutrons/cm2 ,
compared with the measured neutron flux of Phénix, 7 · 1015 neutrons/cm2 [12]. This gives an
error/difference of around 20 % between the measured and the simulated value. The amount
of fissile inventory in the model was estimated to be 1105 kg, by Serpent sampling 10 000 000
random points. According to reference [13], Phénix had a fissile inventory of 930 kg. This means
that the amount of fissile material in the Phénix model is 19 % greater than measured. The
inventory of 239 Pu came to be 462 kg, which is much less than the value of 730 kg given in the
same reference. Although the fissile inventory and the neutron flux differ quite a lot from the
value given in the references, the values are sufficient for being a simplified model of the Phénix
core.
5.2
Core-flowering
The results from the simulations of core-flowering, using the Phénix model, are presented in
Table 5.1 and in Figure 5.1. It was obtained that the reactivity decreases when the core radius
expands. A linear approximation, see Figure 5.1, gives the change, ∆kef f /core extension = 60 pcm/mm. Assuming that the signal from the neutron chambers directly corresponds to the
thermal power of the core, the high amplitude of the signals from the A.U.R.N. events would
require a core extension of around 5 mm. However, it does not seem that the relation between
the reactivity and the increase of the core radius is linear due to the fact that three points of
simulation data lie outside the linear approximation. This could mean that the relation is of
33
RESULT
Core-flowering
higher order, though there is not enough data to tell. A similar relation was obtained from the
results of PFBR that is presented in Chapter D and the linear approximation gave the change
∆kef f /core extension = - 47.6 pcm/mm.
Table 5.1: The results of kef f from the simulations of core-flowering. The model of the Phénixcore was used for these simulations.
λ (mm)
0
0.4
0.8
1.2
1.6
2.0
Extension
of the core
(mm)
0.0
2.8
5.6
8.4
11.2
14.0
Neutron
population
Number of
cycles
kef f
500000
500000
500000
500000
500000
500000
2000
2000
2000
2000
2000
2000
1.00298
1.00137
0.999605
0.997987
0.996145
0.994585
Standard
deviation,
σ (10− 5)
5
5
5
5
4
5
The results from the detector defined at the center of the Phénix model’s core are presented in
Table 5.2 and in Figure 5.2. The neutron flux decreases as the core radius expands. However,
at λ = 1.6 mm there is a sudden increase. This is probably due to the statistical noise that is
noticeable in the results. The relation between the neutron flux and core-extension is most likely
of higher order. Note that thermal power of the core has the same value in all simulations.
Table 5.2: The results of the neutron flux in the core center obtained from the simulations of
core-flowering, where λ is the increase in the gap between the sub-assemblies. The model of the
Phénix-core was used for these simulations.
λ (mm)
0
0.4
0.8
1.2
1.6
2.0
34
Extension
of the core
(mm)
0.0
2.8
5.6
8.4
11.2
14.0
Neutron
population
Number
of cycles
Neutron flux
(1015 cm−2 )
500000
500000
500000
500000
500000
500000
2000
2000
2000
2000
2000
2000
8.43167
8.38752
8.35513
8.34142
8.36601
8.34229
Standard
deviation,
σ (101 5)
0.017454
0.017194
0.017128
0.017434
0.017485
0.017485
Core-flowering
RESULT
Change in reactivity due to core extension
1.003
Simulation data
Linear approximation
1.002
1.001
1
keff
y = − 0.0006*x + 1
0.999
0.998
0.997
0.996
0.995
0
2
4
6
8
10
Extension of the core [mm]
12
14
Figure 5.1: This figure displays how the kef f of the Phénix model is affected by core extension due
to core-flowering. A linear approximation gives ∆kef f /core extension = -60 pcm/mm, though it
does not seem to be a good approximation due to the fact that three points lie outside the line.
However, in the interval [0 6] mm, the relation is in principle linear.
35
RESULT
Core-flowering
15
8.46
Change in neutron flux due to core extension
x 10
8.44
Neutrons flux [1/cm2]
8.42
8.4
8.38
8.36
8.34
8.32
−2
0
2
4
6
8
10
Extension of the core [mm]
12
14
16
Figure 5.2: The figure displays how the neutron flux in the center of the Phénix core model is
affected by core-flowering. It can be seen that the relation between core extension and neutron
flux is not linear. Note the peak at 11.2 mm, which shows a sudden increase in neutron-flux.
This is probably a result of the statistical noise, which is noticeable in the large error bars. Note
that thermal power of the core has the same value in all simulations.
36
6
Discussion
The A.U.R.N. events, the results obtained from the simulations and the uncertainties in the tools
and models used are discussed in this chapter.
6.1
Simulations
The limitation of time in the study determined the choice of Monte-Carlo simulation code. Serpent was chosen due to its efficient computation time. MCNP was considered and although this
code has been more validated compared to Serpent, its long computation time makes it unsuitable. Serpent has some problems with calculations of the neutron paths if heavy absorbers are
present. This however, should not be an issue in this thesis since no heavy absorber is present
in any of the core models. Even if the models had control rods inserted into the core, the high
energies of the neutrons should significantly reduce this error. Serpent has been validated against
MCNP with satisfying results and therefore the results calculated by Serpent should be consistent. The models in the Monte-Carlo simulation code cannot describe dynamic environments
such as coolant flow, which brings some uncertainties to the results.
There are some uncertainties in the models used for the simulations. First, a simplified model
of the Phénix’s core was used and it should be noted that three different references have been
used in order to find all crucial parameters. Some parameters have different values in the different references. The reason for the variation in value of the parameters is most probably due
to the different set-up of fuel elements used in Phénix during its time in operation. Hence,
the SFR model created has most probably used a different set-up of sub-assemblies than was
used in Phénix during the A.U.R.N. events and the core-flowering experiments. This adds some
uncertainties to the comparison between the results collected from the simulations and the experiments. However, it is still interesting that the change in kef f obtained from the simulations
is similar to the experimental data.
The model of core-flowering is also a simplification of the true phenomenon. It does not take
into account that sub-assemblies swell, which in turn induces the stress to the surrounding sub-
37
DISCUSSION
A.U.R.N.
assemblies. Instead, all sub-assemblies are at a normal state without any bending or swelling.
This leaves some uncertainties in the model, though it is not certain that the bending itself has
a significant impact on the kef f . Furthermore, the gap between the sub-assemblies increases
symmetrically in the model.
In order to have a consistent result, over 100 000 neutrons were used per cycle. Moreover,
2 000 cycles were used for each simulation in order to have a result where kef f has converged
and the statistical error is reduced. The results of kef f did not have any major concerns regarding statistical errors, which can be an issue when using Monte-Carlo simulation codes. However,
better and longer simulations are needed to reduce the statistical noise in the results obtained
from the neutron flux detector.
The model of Phénix has been partly validated against the real core, where the neutron flux
and the fissile inventory were compared. The simulations differed from the measured values with
∼14%. The kef f of the model under normal conditions lies at 1.00298, which is quite a high value
for a reactor. This is most probably the consequence of using different references for the creation
of the model. The neutron flux and the amount of fissile inventory in the model of Phénix differ
quite a lot from the values obtained from references. However, this is most probably a consequence of having different compositions of plutonium, wrapper materials and depleted uranium
than used in Phénix when the measured values were obtained.
In the results of the simulations it can be obtained that the reactivity and the neutron flux
clearly decrease when the core expands, which was the initial guess of the study. Small increase
of the core radius leads to a significant change in the kef f , which confirms the core-flowering
experiments made in Phénix. The relation between kef f and core expansion does not seem to
be linear in the results obtained from the simulations, which was unexpected. Hence, the relation between kef f and core expansion might be of a higher order, though there is not enough
simulation data to tell. However, in the interval [0, 6] mm the relation is almost linear and the
core, in the core-flowering experiments of Phénix, was only extended up to 5 mm. The results of
the simulations correspond remarkably well to the experimental data, which indicates that the
simulations were a success. It is however hard to validate how significant impact the uncertainties have on the results. Hence, it might be dangerous to make any more conclusions about the
core’s behavior from these simulations (especially about the sudden increase in the neutron flux
at λ = 1.6mm), when suffering from core-flowering.
6.2
A.U.R.N.
The strange events of A.U.R.N. that occurred in Phénix are an important issue in SFR-technology.
It is strange that the phenomenon only occurred in Phénix, especially since there are over 400
years of operating experience of SFRs in the world. Hence, the origin of the negative reactivity
transients is most probably related to some specific parameter of Phénix. This makes the scenario
where an experimental sub-assembly, DAC-assembly, is responsible for provoking core-flowering
most probable.
No negative reactivity transients have been registered since the the fourth event of A.U.R.N.
After that event, the power of Phénix was decreased. This leads to the possible conclusion that
the events could somehow be related to the power of the reactor. Regardless, it is not possible to
make this conclusion without first comparing other parameters such as the sub-assembly set-up
38
A.U.R.N.
DISCUSSION
of the core before and after the power of the facility was reduced.
Radial movement of the core due to core-flowering, is the current most plausible explanation.
It can cause similar patterns in the signals of the neutron chambers to those registered during
the A.U.R.N. events. The free standing core concept that Phénix used, allows radial bowing of
the assemblies, which makes core-flowering possible to occur. However, this should leave some
trace inside the core, especially since it requires strong induced stresses of the sub-assemblies.
The remarkable thing is that no trace has so far been found, which speaks against this scenario
[15]. Although simulations of core-flowering have been made, the results from these cannot give
any further explanation nor conclusion of how core-flowering is related to the negative reactivity
transients.
What makes A.U.R.N. so difficult to understand are the high amplitudes of the signals, the
speed of the phenomenon and the amount of energy required in order to cause such change.
These unsolved issues make some researchers to still believe that failure or noise in the electronic
equipment is responsible for the abnormality in the signals of the neutrons chambers. However,
in the tests the equipment proves its consistency. Furthermore, no physical phenomenon has
been proven to be able to induce similar signals in the neutron chambers, which is not related
to the thermal power of the core. On the other hand, no mechanical phenomenon can provide a
satisfying scenario. Hence, it is possible that the abnormalities were induced by a combination
of a mechanical phenomenon and some failure in the electrical equipment [15].
Although there are some possible scenarios for the A.U.R.N. events, its true origin has to be
found in order to increase the understanding of the SFR concept and for the future development towards commercialization. Phénix is no longer available for neutronic experiments,
though hopefully enough data have been gathered to solve this mystery. Hopefully, some kind
of trace of A.U.R.N. or core-flowering can be found during the decommissioning of Phénix and
the dismantling of the core. It is therefore important that crucial parts of the reactor, during
the dismantling process, are examined thoroughly. Finally, in order to exclude A.U.R.N. from
occurring in current LWRs, the origin of the phenomenon must be found.
39
7
Conclusions
7.1
Conclusions
In this thesis a study of the A.U.R.N. events that occurred in the French reactor Phénix has
been carried out. Furthermore, a model of the Phénix core was created and simulations of how
core-flowering affects the kef f have been made.
The simplified model of the core of Phénix was successfully created and validated, though unfortunately the model’s neutron flux and the amount of fissile isotopes differed from measured
values of Phénix. This model can be used for further simulations, such as burnup calculations.
Regardless of the validation of the Phénix model, the simulations gave satisfying results with the
same value as was measured during the experiments of core-flowering made in the final year of
Phénix. Thus, it was concluded that the relation between kef f and the core extension could be
of higher order (>1), though it is linear in the realistic intervals of the core-extension. However,
these results cannot provide any essential conclusion about the origin of core-flowering nor if
core-flowering is the single answer to the A.U.R.N. events. Though core-flowering as explanation
is not inconsistent with the results of this study.
The most reasonable explanation of A.U.R.N. seems to be core-flowering, since it can recreate similar patterns in the signals of the neutron chambers. The absence of any kind of trace of
this movement is remarkable though, which implies the uncertainties in this scenario. Due to the
high amplitude of the signals, it is possible that there was interference or failure in the electrical equipment. However, the origin of the core-flowering and why it occurred remain unsolved.
Furthermore, if core-flowering is the single reason for A.U.R.N., the high amplitude of the signals would require a core extension of around 5 mm, assuming that the signal from the neutron
chambers directly corresponds to the thermal power of the core. If core-flowering is the sought
answer, then future A.U.R.N. events can be avoided by design. By limiting the fuel elements’
movement the phenomenon can be reduced significantly, for example through strengthening of
the fuel elements.
41
CONCLUSIONS
Suggestions for further work
The irradiation experiments of the sub-assemblies with high burnup of fuel might be one answer to the origin of A.U.R.N., especially since it was one of the major differences between
Phénix and Superphénix, which did not experience any similar transients. A moderated experimental sub-assembly and its possible involvement in inducing a core-flowering in Phénix is being
investigated. Regardless of the origin of the negative reactivity transients, the safety of Phénix
was not affected, such as support structures of the core. Furthermore, the automatic emergency shutdown of the reactor proved its efficiency during these events by shutting down the
operation after a few hundreds of milliseconds. This type of event should therefore not be able
to cause a severe accident, though it is still an issue for the commercialization of the SFR concept.
Further research is needed for finding the explanation behind A.U.R.N.s. It is important to
find the explanation since the origin is unknown and therefore cannot be excluded from occurring in LWRs, even though it is not likely. The importance of finding the answer can be seen
as CEA is still investigating the phenomenon and is going to recruit Ph.D. students for the
investigation.
7.2
Suggestions for further work
In the study a simplified model of Phénix was created, however there are still some parameters in
the model that can be improved. For instance, no reference for the wrapper material was found
for the model and it was therefore set to the same material as the cladding of the fuel pins. It
would also be intriguing to find a design of and more information about the DAC-assemblies and
make further simulations of how these can affect the reactivity and neutron flux of the core.
The simulations of core-flowering using the Phénix model indicated that the change in kef f
is not linear. In order to confirm this, more simulation data should be gathered using the same
models, but with other values of λ. It would also be of great interest to investigate how the
neutron flux in- and outside the core is affected in this model.
Some very crude simulations of how core-flowering affects a LWR core showed an increase in
reactivity instead of a decrease. This is not strange since an increase of the gap between the
sub-assemblies increases the moderation effect. However, better and more simulations should be
carried out before making any conclusions about this.
In order to gain more understanding of core-flowering, more simulations should be carried out
using other codes than Serpent to obtain a better model of the phenomenon. Deterministic
codes, such as CAST3x, could be used for making more complex calculations.
Since the A.U.R.N. events have only occurred in Phénix, the origin of the events should be
bound to some parameters that are specific for Phénix. Thus, it would be convenient to investigate different set-ups of sub-assemblies of Phénix used before and after the events. Furthermore,
an investigation of the differences between Superphénix and Phénix might give some answers to
A.U.R.N.s since the design of Superénix is based on data gathered from the operation of Phénix.
42
References
[1] J. Wallenius. Transmutation of nuclear waste, 2008. Not yet published.
[2] Issued by the U.S. DOE Nuclear Energy Research Advisory Committee and the Generation
IV International Forum. A technology Roadmap for Generation IV Nuclear Energy System.
Generation IV International Forum http: // www. gen-4. org/ , December 2002.
[3] A. E. Waltar and A. B. Reynolds. Fast Breeder Reactors. Pergamon Press, 1980.
[4] World Nuclear Association. Fast neutron reactors. http: // www. world-nuclear. org/ ,
December 2010.
[5] Y. Orechwa and S. F. Su. Homogeneous-Heterogeneous Core Evaluation and StructuralMaterial Selection. Information Bridge - http: // www. osti. gov/ bridge , 1982.
[6] K. E. Holbert. Four factor formula. http: // holbert. faculty. asu. edu/ , December
2010. Handout.
[7] B. Rouben. Introduction to reactor physics. Atomic Energy of Canada Ltd., September
2002.
[8] R. Nakai. Design and Assessment Approach on Advanced SFR Safety with Emphasis on
CDA Issue. http://www-pub.iaea.org/, December 2009.
[9] N. N. Oshkanov, O. M. Saraev, M. V. Bakanov, P. P. Govorov, O. A. Potapov, Yu. M.
Ashurko, V. M. Poplavskii, B. A. Vasilev, Yu. L. Kamaninand, and V. N. Ershov. 30 years
of experience in operating the BN-600 soidum-cooled fast reactor. Atomic Energy, 108, 2010.
[10] Website of The Generation IV International Forum. http://www.gen-4.org/. 2010-11-24.
[11] Ph. Dafour.
Cadarache.
Sodium Fast Reactors Descriptions.
ESFR Seminar, November 2010.
[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. Tenchine, L. Martin, J.F. Sauvage, D. Verwaerde, R. Dupraz, and A. Woaye-Hune. The PHÉNIX
final tests. Abstract ICAPP 2011, 2010.
[17] A. Vasile, B. Fontaine, M. Vanier, D. Tenchine, P. Gauthé, V. Pascal., G. Prulhière,
P. Jaecki, L. Martin., J-F. Sauvage, and R. Dupraz. IAEA TecDoc: Status of liquid metal
cooled fast reactor technology: The Phénix end of life tests. IAEA, 2010. Not yet published.
43
REFERENCES
REFERENCES
[18] F. Gauché, J. Rouault, JC. Garnier, Guedeney, L. Martin, F. Baqué, Verwaerde, J.F.
Sauvage, and J.P. Serpantié. The status of Fast Reactors program in France in 2010. IAEA
TWG-F, November 2010. Prepared by A. Vasile.
[19] P. Le Coz. The ASTRID project. ESFR Seminar, November 2010. Cadarache.
[20] A. MacLachlan. CEA finalizing design options for Gen IV sodium reactor. Platts Nucleonics
Week, March 2010.
[21] F. Brown, W. Martin, J. Leppänen, Wim H., and B. Cochet. Reactor Physics Analysis with
Monte Carlo. ANS PHYSOR-2010 Conference Workshop, 2010.
[22] J. Leppänen. Standard comparison between Serpent 1.1.13 and MCNP5.
montecarlo. vtt. fi/ , 2010.
http: //
[23] J. Leppänen. Progress Report 2009. http: // montecarlo. vtt. fi/ , 2010.
[24] PSG / Serpent - a Continuous-energi Monte Carlo Reactor Physics Burnup Calculation
Code. http://montecarlo.vtt.fi/. 2010-10-20.
[25] J. Leppänen. Performance of Woodcock delta-tracking in lattice physics applications using
the Serpent Monte Carlo reactor physics burnup calculation code. Annals of Nuclear Energy,
2010.
[26] F. Varaine. Core specifications and design. ESFR Seminar, November 2010. Cadarache.
[27] F. Delage, A. Courcelle, Y. Guerin, M. Pelletier, and M. Zabiego. Fuel pin & fuel assembly
design: Fuel manufacturing, behaviour and requirements. ESFR Seminar, November 2010.
Cadarache.
[28] World Nuclear Association.
Uranium and depleted uranium.
world-nuclear. org/ , December 2009.
http: // www.
[29] M. Teradaa, R. A. Antunesb, A. F. Padilhab, H. Gomes de Meloc, and I. Costaa. Comparison
of the Corrosion Resistance of DIN W. Nr. 1.4970 (15%Cr-15%Ni-1.2%Mo-Ti) and ASTM F138 (17%Cr-13%Ni-2.5%Mo) Austenitic Stainless Steels for Biomedical Applications, 2005.
[30] JEFF 3.1.1 - Nuclear Data Library. http://www.oecd-nea.org/janis/, December 2010.
44
List of Figures
2.1
2.2
2.3
3.1
3.2
3.3
3.4
3.5
3.6
4.1
4.2
4.3
4.4
5.1
The presence evolution of transuranium elements in spent nuclear fuel. [1] . . . .
This figure shows the fuel pin and the sub-assembly/fuel-assembly arrangements of
FRs and LWRs. Note the LWR fuel-assemblies have more space between the fuel
pins than those of FRs. a) Sub-assembly arrangement of FRs. b) Fuel-assembly
arrangement of LWRs. c) Fuel pin arrangement of FRs. d) Fuel pin arrangements
of LWRs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Overview of the internal and external configuration of a FBR. . . . . . . . . . . .
Overview of the SFR pool design. The system has a primary circuit integrated in
the main vessel and the heat is transferred from the primary circuit to the steam
generators by intermediate circuits. [2] . . . . . . . . . . . . . . . . . . . . . . . .
Chart of downtime at Phénix due to accidents and maintenance. Note the percentage of negative reactivity transients, which is the fourth time-wasting issue, if
scheduled work is not taken into account. [14] . . . . . . . . . . . . . . . . . . .
Two separate registered signals obtained from the neutron chambers during the
last two A.U.R.N. events in Phénix in 1990. Note the oscillating behavior and the
secondary peak, which in both cases slightly exceed the initial power. [14] . . . .
Sub-assemblies under normal operation in a). Sub-assemblies suffering from coreflowering at top b) and in the centre c). . . . . . . . . . . . . . . . . . . . . . . .
Schematic of the Eddy current flow meter used for measuring the mass flow of
sodium in the moderated experimental sub-assembly DAC. [17] . . . . . . . . . .
A picture of the mechanical device, which was used for testing how core-flowering
is affecting the reactivity of the core. [17] . . . . . . . . . . . . . . . . . . . . . .
Two-dimensional view of the core model of Phénix seen from the z-axis/above,
with zoom at the active core and the fuel-assemblies. The red assemblies are
dedicated cells for the control rods, which are withdrawn in this model. The blue
sub-assemblies are blankets and the green and white ones are fuel-assemblies. . .
Plan view of how the sub-assemblies are affected by core-flowering in the simulations.
Side view of how the sub-assemblies are affected by core-flowering in the simulations. Each block corresponds to a block with hexagonal geometry. . . . . . . . .
The gap between the sub-assemblies increases symmetrically in the model of coreflowering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
This figure displays how the kef f of the Phénix model is affected by core extension
due to core-flowering. A linear approximation gives ∆kef f /core extension = -60
pcm/mm, though it does not seem to be a good approximation due to the fact that
three points lie outside the line. However, in the interval [0 6] mm, the relation is
in principle linear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
9
10
16
17
18
21
23
23
30
31
32
32
35
45
LIST OF FIGURES
5.2
LIST OF FIGURES
The figure displays how the neutron flux in the center of the Phénix core model is
affected by core-flowering. It can be seen that the relation between core extension
and neutron flux is not linear. Note the peak at 11.2 mm, which shows a sudden
increase in neutron-flux. This is probably a result of the statistical noise, which
is noticeable in the large error bars. Note that thermal power of the core has the
same value in all simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
D.1 This figure shows how the kef f of the model of PFBR is affected by core extension.
A linear approximation gives ∆kef f /Core extension = -47.6 pcm/mm. . . . . . . D-2
46
List of Tables
3.1
3.2
4.1
4.2
4.3
4.4
4.5
5.1
5.2
Table of some SFRs in world. Note that BN-600 and Superphénix are the only
two reactors of commercial size. [11] . . . . . . . . . . . . . . . . . . . . . . . . .
A summary of the design parameters for the SFR concept of Generation IV. [2] .
A comparison of k∞ between MCNP and Serpent. [22] . . . . . . . . . . . . . . .
A comparison of computation time (in minutes) between MCNP and Serpent. [22]
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. .
Composition of fuel and blanket. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Composition of of the cladding and wrapper steel. [29] . . . . . . . . . . . . . . .
The results of kef f from the simulations of core-flowering. The model of the
Phénix-core was used for these simulations. . . . . . . . . . . . . . . . . . . . . .
The results of the neutron flux in the core center obtained from the simulations
of core-flowering, where λ is the increase in the gap between the sub-assemblies.
The model of the Phénix-core was used for these simulations. . . . . . . . . . . .
14
15
26
27
28
29
29
34
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 negative reactivity), page 2
CEA Commissariat à l’énergie atomique et aux énergies alternatives (French Alternative Energies and Atomic Energy Commission), page 19
EFR
European Fast Reactor, page 13
FBR Fast Breeder Reactor, page 8
FR
Fast Reactor, page 5
GFR Gas-cooled Fast Reactor, page 1
IHX
Intermediate Heat Exchangers, page 14
LFR
Lead-cooled Fast Reactor, page 1
LWR Light-Water Reactor, page 5
MOX-fuel Mixed Oxide fuel, page 15
MSR Molten Salt Reactor, page 1
PFBR Prototype Fast Breeder Reactor. A sodium-cooled fast reactor under construction in
India., page 3
PWR Pressurized Water Reactor, page 14
S/A
Sub-assembly, page 28
SCWR Super-Critical Water Reactor, page 1
SFR
Sodium-cooled Fast Reactor, page 1
TRU Transuranium Elements, page 8
VHTR Very High Temperature Reactor, page 1
49
Appendices
51
A
Definitions of the units in the Four Factor
Formula
In this section the definitions of the different units of the four factor formula are presented
� = F ast f ission f actor
f = T hermal ultilization
p = Resonance escape probability
P = N on − leakage probabilities
total f ission neutrons f rom thermal and f ast f ission
�=
f ission neutrons f rom thermal f ission
thermal neutrons absorbed by f uel
f=
total thermal neutrons absorbed
absorption
P =
production
N umber of neutrons slowing to thermal energy
p=
total number of f ast neutrons available f or slowing
k∞ = kef f without any leakage of neutrons, a reactor with no boundaries.
A-1
B
Code of the Phénix Model
The code used to create the model of Phenix in Serpent:
s e t t i t l e " Phenix "
% −−−−−−−−−−−−−−−−− Fuel / Pins −−−−−−−−−−−−−−−−−
% −−− Low e n r i c h e d f u e l
pin 1
lowfuel
void
cladding
sodium
0.275
0.2825
0.3275
%
%
%
%
%
low−f u e l p i n
f u e l p e l l e t outer radius
cladding inner radius
cladding outer radius
coolant outside of clad
%
%
%
%
%
high−f u e l p i n
f u e l p e l l e t outer radius
cladding inner radius
cladding outer radius
coolant outside of clad
% −−− High e n r i c h e d f u e l
pin 2
highfuel
void
cladding
sodium
0.275
0.2825
0.3275
% −−− B la n ke t p i n
pin 3
blanket
0.625
% blanket pin
B-1
CODE OF THE PHÉNIX MODEL
cladding
sodium
0.67
% coolant outside of clad
% −−− Coolant
pin 9
sodium
% dummy p i n f o r f i l l i n g t h e l a t t i c e
% −−−−−−−−−−−−−−−−− L a t t i c e s −−−−−−−−−−−−−−−−−
% −−− Fuel Sub−assembly , low−e n r i c h e d
l a t 10 2
0 0 19 19 0 . 7 8
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 9
9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 9
9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 1 9
9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 1 1 9
9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 1 1 1 9
9 9 9 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9
9 9 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9
9 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9
9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9
9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9 9
9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9 9 9
9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9 9 9 9
9 1 1 1 1 1 1 1 1 1 1 1 1 1 9 9 9 9 9
9 1 1 1 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9
9 1 1 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9
9 1 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9
9 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
% −−− Fuel Sub−assembly , high−e n r i c h e d
l a t 20 2
0 0 19 19 0 . 7 8
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 2 2 2 2 2 2 2 2 2 9
9 9 9 9 9 9 9 9 2 2 2 2 2 2 2 2 2 2 9
9 9 9 9 9 9 9 2 2 2 2 2 2 2 2 2 2 2 9
9 9 9 9 9 9 2 2 2 2 2 2 2 2 2 2 2 2 9
9 9 9 9 9 2 2 2 2 2 2 2 2 2 2 2 2 2 9
9 9 9 9 2 2 2 2 2 2 2 2 2 2 2 2 2 2 9
9 9 9 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 9
9 9 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 9
9 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 9
9 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 9 9
B-2
CODE OF THE PHÉNIX MODEL
9 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 9 9 9
9 2 2 2 2 2 2 2 2 2 2 2 2 2 2 9 9 9 9
9 2 2 2 2 2 2 2 2 2 2 2 2 2 9 9 9 9 9
9 2 2 2 2 2 2 2 2 2 2 2 2 9 9 9 9 9 9
9 2 2 2 2 2 2 2 2 2 2 2 9 9 9 9 9 9 9
9 2 2 2 2 2 2 2 2 2 2 9 9 9 9 9 9 9 9
9 2 2 2 2 2 2 2 2 2 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
% Dummy assembly with sodium
l a t 110 2
0 0 19 19 0 . 7 8
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
% −− Blanket−assembly
l a t 30 2 0 0 11 11 1 . 4 5
9 9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 3 3 3 3 3 9
9 9 9 9 3 3 3 3 3 3 9
9 9 9 3 3 3 3 3 3 3 9
9 9 3 3 3 3 3 3 3 3 9
9 3 3 3 3 3 3 3 3 3 9
9 3 3 3 3 3 3 3 3 9 9
9 3 3 3 3 3 3 3 9 9 9
9 3 3 3 3 3 3 9 9 9 9
9 3 3 3 3 3 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9 9
B-3
CODE OF THE PHÉNIX MODEL
%Core l a t t i c e
l a t 200 3
0 0 21 21 1 2 . 7
22 22 22 22 22 22 22 22 22
22 22 22 22 22 22 22 22 22
22 22 22 22 22 22 22 22 22
22 22 22 22 22 22 22 22 22
22 22 22 22 22 22 22 22 33
22 22 22 22 22 22 22 33 33
22 22 22 22 22 22 33 33 51
22 22 22 22 22 33 33 51 51
22 22 22 22 33 33 51 51 50
22 22 22 33 33 33 51 50 50
22 22 22 33 33 51 50 50 50
22 22 33 33 33 51 50 80 50
22 22 33 33 51 51 50 50 50
22 22 33 33 51 51 50 50 80
22 22 33 33 51 51 50 50 50
22 22 33 33 33 51 51 51 51
22 22 33 33 33 33 51 51 51
22 22 33 33 33 33 33 33 33
22 22 22 33 33 33 33 33 33
22 22 22 22 22 22 22 22 22
22 22 22 22 22 22 22 22 22
% P i t c h 1 2 . 7 cm
22 22 22 22 22 22
22 22 22 22 22 22
22 22 33 33 33 33
33 33 33 33 33 33
33 33 33 51 51 51
33 51 51 51 51 51
51 50 50 50 50 50
50 50 50 80 50 50
80 50 50 50 50 50
50 50 50 50 80 50
50 50 50 50 50 50
50 50 50 50 50 51
50 50 80 50 51 51
50 50 50 51 51 33
50 50 51 51 33 33
51 51 33 33 33 22
33 33 33 33 22 22
33 33 33 22 22 22
33 22 22 22 22 22
22 22 22 22 22 22
22 22 22 22 22 22
22
22
33
33
33
51
51
51
51
51
51
33
33
33
22
22
22
22
22
22
22
22
22
33
33
33
33
51
51
51
33
33
33
33
22
22
22
22
22
22
22
22
22
22
33
33
33
33
33
33
33
33
33
33
22
22
22
22
22
22
22
22
22
22
22
22
33
33
33
33
33
33
33
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
% −−−−−−−−−−−−−−−−− S u r f a c e s −−−−−−−−−−−−−−−−−
s u r f 1 hexyprism 0 0 5 . 8 5
s u r f 2 hexyprism 0 0 6 . 2
−42.5
−42.5
42.5
42.5
% i n n e r sub−a s s s t r u c t
% o u t e r sub−a s s s t r u c t
s u r f 3 hexyprism 0 0 5 . 8 5
s u r f 4 hexyprism 0 0 6 . 2
−83.4
−83.4
83.4
83.4
% i n n e r sub−a s s s t r u c t
% o u t e r sub−a s s s t r u c t
s u r f 5 hexyprism 0 0 5 . 8 5
s u r f 6 hexyprism 0 0 5 . 8 5
42.5 68.5
−72.5 −42.5
% i n n e r sub−a s s s t r u c t
% i n n e r sub−a s s s t r u c t
s u r f 7 hexyprism 0 0 6 . 2
s u r f 8 hexyprism 0 0 6 . 2
42.5 68.5
−72.5 −42.5
% o u t e r sub−a s s s t r u c t
% o u t e r sub−a s s s t r u c t
s u r f 100 sph 0 0 0 300
s u r f 200 sph 0 0 0 400
s u r f 500 c y l 0 0
105
% Region o f Neutrons
% Sphere o f i n t e r e s t
% Re acto r tank
% −−−−−−−−−−−−−−−−− C e l l s −−−−−−−−−−−−−−−−−
c e l l 1000 80 sodium
c e l l 1001 80 sodium
B-4
−4
4
CODE OF THE PHÉNIX MODEL
% −−− U n i v e r s e 1 0 0 , low−e n r i c h e d sub−assembly
cell
cell
cell
cell
cell
cell
cell
1
2
56
53
54
55
5
50
50
50
50
50
50
50
cladding
cladding
cladding
sodium
f i l l 10
f i l l 15
f i l l 15
−1
1
−6
6
−5
5
2
−2
−2
−8
−8
−7
−7
5
1
1
1
1
6
2
2
2
2
7 8
−1
1
−6
6
−5
5
2
−2
−2
−8
−8
−7
−7
6
1
1
1
1
5
2
2
2
2
8 7
% −−− U n i v e r s e 2 0 0 , high−e n r i c h e d sub−assembly
cell
cell
cell
cell
cell
cell
cell
6
7
8
50
51
52
10
51
51
51
51
51
51
51
cladding
cladding
cladding
sodium
f i l l 20
f i l l 15
f i l l 15
% −−− U n i v e r s e 3 0 0 , b l a n k e t −assembly
c e l l 11 33
c e l l 12 33 c l a d d i n g
c e l l 13 33 sodium
f i l l 30
−3 −4
3 −4
4
% −−− U n i v e r s e 2 2 , dummy−assembly with sodium f o r l a t t i c e
c e l l 1111 22
c e l l 1311 22 sodium
f i l l 110
−4
4
% −−− U n i v e r s e 0 , t h e c o r e
c e l l 101 0
f i l l 200
c e l l 102 0 v o i d
c e l l 103 0 o u t s i d e
−500 −100
500 −100
100
% −−−−−−−−−−−−−−−−− P l o t t i n g −−−−−−−−−−−−−−−−−
%
%
%
%
plot
plot
plot
plot
3
2
2
3
800
800
800
800
800
800
800 0 −3.1 3 . 1 −150 150
800 0 −69.5 6 9 . 5 −69.5 6 9 . 5
%
%
%
%
P l o t t i n g t h e whole geometry
P l o t t i n g s i d e −view
Plotting f u e l pins
Plot of inner core
% −−−−−−−−−−−−−−−−− M a t e r i a l s −−−−−−−−−−−−−−−−−
% −−− High e n r i c h e d f u e l
B-5
CODE OF THE PHÉNIX MODEL
mat h i g h f u e l −10.98 rgb 255 255 255
92238.12 c
0.7646
92235.12 c
0.0054
94238.12 c
0.0081
94239.12 c
0.1194
94240.12 c
0.0547
94241.12 c
0.0297
94242.12 c
0.0182
8016.12 c
2
%
%
%
%
%
%
%
%
%
−10.9777
U−238 99.3%
U−235 0.07%
Pu−238 3.5%
Pu−239 51.9%
Pu−240 23.8%
Pu−241 12.9%
Pu−242 7.9%
O2
%
%
%
%
%
%
%
%
%
−10.9683
U−238
U−235
Pu−238
Pu−239
Pu−240
Pu−241
Pu−242
O2
% −−− Low e n r i c h e d f u e l
mat l o w f u e l −10.97 rgb 0 255 0
92238.12 c
0.8143
92235.12 c
0.0057
94238.12 c
0.0063
94239.12 c
0.0934
94240.12 c
0.0428
94241.12 c
0.0232
94242.12 c
0.0142
8016.12 c
2
% −−− Cladding , SS 316
% SS 316
%mat c l a d d i n g
%26000.06 c 0 . 6 6
%28000.06 c 0 . 1 3
%24000.06 c 0 . 1 7
%42000.06 c 0 . 0 2 5
%25055.06 c 0 . 0 1 5
−7.9402
% 15−15 Ti
mat c l a d d i n g
−7.8974
6000.06 c 0.0009
24000.06 c 0.146
28000.06 c 0.150
42000.06 c 0.0125
14000.06 c 0.0046
25055.06 c 0.0170
22000.06 c 0.0046
26000.06 c 0.6644
% −−− Sodium , c o o l a n t
mat sodium −0.968 rgb 255 0 0
11023.06 c 1
B-6
rgb 255 255 0
% N a t u r a l Fe
%
rgb 255 255 0
CODE OF THE PHÉNIX MODEL
% −−− Blanket , U−238
mat b l a n k e t −10.5 rgb 0 0 255
92238.06 c 0.997
92235.06 c 0.003
8016.06 c 2
% d e p l e t e d Uranium , U−238
% d e p l e t e d Uranium , U−238
% O2
% −−−−−−−−−−−−−−−−− D e t e c t o r s −−−−−−−−−−−−−−−−−
d e t 1 % D e t e c t o r f o r measuring t h e a v e r a g e f l u x o f t h e c o r e
dz −42.5 4 2 . 5 20
d l 200
dv 1 . 2 9 E6
det 3
dx −1
dy −1
dz −1
du 0
dv 8
%
1
1
1
D e t e c t o r f o r measuring t h e n e u t r o n f l u x a t t h e c o r e ’ s c e n t e r
1
1
1
% −−−−−−−−−−−−−−−−− 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 1 u . x s d a t a "
% −−−−−−−−−−−−−−−−− Values f o r n o r m a l i z a t i o n −−−−−−−−−−−−−−−−−
s e t power 5 . 6 3 E8
% t h e r m a l power o f t h e c o r e
% −−−−−−−−−−−−−−−−− S t a r t −v a l u e s −−−−−−−−−−−−−−−−−
s e t pop 10000 3000 50 1 . 0 0 1
B-7
C
Output data from a test run of the Phénix model
Here is a test run of the core model of Phénix used for the report. Note that only two active
cycles are presented since there is no value in displaying them all.
_
.−=−.
.−==−.
{ }
__
. ’ O o ’.
/ −<’ )−−<
{ }
. ’ O’ .
/ o . −. O \
/ .−−−‘
{ }
/ . −. o\
/O /
\ o\
/O /
\ ‘−‘ /
\ O‘ − ’ o /
\ O‘ − ‘ o /
‘ −. − ‘
’ .____. ’
‘ .____. ’
PSG2 / S e r p e n t
A Continuous−e n e r g y Monte C a r l o R eac tor P h y s i c s Burnup C a l c u l a t i o n Code
− V e r s i o n 1 . 1 . 1 3 ( August 2 5 , 2 0 1 0 ) −− Contact : Jaakko . Leppanen@vtt . f i
− P a 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 1 3 : 3 0 : 4 4 2011
Reading i n p u t f i l e " Phenix " . . .
P r o c e s s i n g 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.
Calculating isotope fractions . . .
OK.
Reading data from ACE f i l e s :
Isotope
6 0 0 0 . 0 6 c (C−nat ) . . .
Isotope
8 0 1 6 . 0 6 c (O− 1 6 ) . . .
Isotope
8 0 1 6 . 1 2 c (O− 1 6 ) . . .
I s o t o p e 1 1 0 2 3 . 0 6 c (Na − 2 3 ) . . .
I s o t o p e 1 4 0 0 0 . 0 6 c ( Si−nat ) . . .
I s o t o p e 2 2 0 0 0 . 0 6 c ( Ti−nat ) . . .
I s o t o p e 2 4 0 0 0 . 0 6 c ( Cr−nat ) . . .
I s o t o p e 2 5 0 5 5 . 0 6 c (Mn− 5 5 ) . . .
I s o t o p e 2 6 0 0 0 . 0 6 c ( Fe−nat ) . . .
I s o t o p e 2 8 0 0 0 . 0 6 c ( Ni−nat ) . . .
I s o t o p e 4 2 0 0 0 . 0 6 c (Mo−nat ) . . .
I s o t o p e 9 2 2 3 5 . 0 6 c (U− 2 3 5 ) . . .
I s o t o p e 9 2 2 3 5 . 1 2 c (U− 2 3 5 ) . . .
I s o t o p e 9 2 2 3 8 . 0 6 c (U− 2 3 8 ) . . .
I s o t o p e 9 2 2 3 8 . 1 2 c (U− 2 3 8 ) . . .
I s o t o p e 9 4 2 3 8 . 1 2 c (Pu − 2 3 8 ) . . .
I s o t o p e 9 4 2 3 9 . 1 2 c (Pu − 2 3 9 ) . . .
I s o t o p e 9 4 2 4 0 . 1 2 c (Pu − 2 4 0 ) . . .
I s o t o p e 9 4 2 4 1 . 1 2 c (Pu − 2 4 1 ) . . .
I s o t o p e 9 4 2 4 2 . 1 2 c (Pu − 2 4 2 ) . . .
OK.
Reading e n e r g y a r r a y s :
Isotope
6 0 0 0 . 0 6 c (C−nat ) . . .
Isotope
8 0 1 6 . 0 6 c (O− 1 6 ) . . .
Isotope
8 0 1 6 . 1 2 c (O− 1 6 ) . . .
I s o t o p e 1 1 0 2 3 . 0 6 c (Na − 2 3 ) . . .
I s o t o p e 1 4 0 0 0 . 0 6 c ( Si−nat ) . . .
I s o t o p e 2 2 0 0 0 . 0 6 c ( Ti−nat ) . . .
I s o t o p e 2 4 0 0 0 . 0 6 c ( Cr−nat ) . . .
I s o t o p e 2 5 0 5 5 . 0 6 c (Mn− 5 5 ) . . .
I s o t o p e 2 6 0 0 0 . 0 6 c ( Fe−nat ) . . .
I s o t o p e 2 8 0 0 0 . 0 6 c ( Ni−nat ) . . .
I s o t o p e 4 2 0 0 0 . 0 6 c (Mo−nat ) . . .
I s o t o p e 9 2 2 3 5 . 0 6 c (U− 2 3 5 ) . . .
I s o t o p e 9 2 2 3 5 . 1 2 c (U− 2 3 5 ) . . .
I s o t o p e 9 2 2 3 8 . 0 6 c (U− 2 3 8 ) . . .
I s o t o p e 9 2 2 3 8 . 1 2 c (U− 2 3 8 ) . . .
I s o t o p e 9 4 2 3 8 . 1 2 c (Pu − 2 3 8 ) . . .
I s o t o p e 9 4 2 3 9 . 1 2 c (Pu − 2 3 9 ) . . .
I s o t o p e 9 4 2 4 0 . 1 2 c (Pu − 2 4 0 ) . . .
I s o t o p e 9 4 2 4 1 . 1 2 c (Pu − 2 4 1 ) . . .
I s o t o p e 9 4 2 4 2 . 1 2 c (Pu − 2 4 2 ) . . .
C-2
OUTPUT DATA FROM A TEST RUN OF THE PHÉNIX MODEL
OK.
− Main g r i d t h i n n e d from 198270 t o 198270 p o i n t s u s i n g t o l e r a n c e 0 . 0 0E+00.
− 34737 i m p or t a n t p o i n t s added r e s u l t i n g i n a t o t a l o f 198270 p o i n t s .
− F i n a l g r i d s i z e 198046 p o i n t s ( 1 . 0 0 E−11 < E < 2 0 . 0 ) .
− T o t a l 2387 p o i n t s i n nubar g r i d .
− 2 e n e r g y gr ou ps i n few−group s t r u c t u r e .
P r o c e s s i n g XS data :
Isotope
6 0 0 0 . 0 6 c (C−nat ) . . .
Isotope
8 0 1 6 . 0 6 c (O− 1 6 ) . . .
Isotope
8 0 1 6 . 1 2 c (O− 1 6 ) . . .
I s o t o p e 1 1 0 2 3 . 0 6 c (Na − 2 3 ) . . .
I s o t o p e 1 4 0 0 0 . 0 6 c ( Si−nat ) . . .
I s o t o p e 2 2 0 0 0 . 0 6 c ( Ti−nat ) . . .
I s o t o p e 2 4 0 0 0 . 0 6 c ( Cr−nat ) . . .
I s o t o p e 2 5 0 5 5 . 0 6 c (Mn− 5 5 ) . . .
I s o t o p e 2 6 0 0 0 . 0 6 c ( Fe−nat ) . . .
I s o t o p e 2 8 0 0 0 . 0 6 c ( Ni−nat ) . . .
I s o t o p e 4 2 0 0 0 . 0 6 c (Mo−nat ) . . .
I s o t o p e 9 2 2 3 5 . 0 6 c (U− 2 3 5 ) . . .
I s o t o p e 9 2 2 3 5 . 1 2 c (U− 2 3 5 ) . . .
I s o t o p e 9 2 2 3 8 . 0 6 c (U− 2 3 8 ) . . .
I s o t o p e 9 2 2 3 8 . 1 2 c (U− 2 3 8 ) . . .
I s o t o p e 9 4 2 3 8 . 1 2 c (Pu − 2 3 8 ) . . .
I s o t o p e 9 4 2 3 9 . 1 2 c (Pu − 2 3 9 ) . . .
I s o t o p e 9 4 2 4 0 . 1 2 c (Pu − 2 4 0 ) . . .
I s o t o p e 9 4 2 4 1 . 1 2 c (Pu − 2 4 1 ) . . .
I s o t o p e 9 4 2 4 2 . 1 2 c (Pu − 2 4 2 ) . . .
OK.
F i n a l i z i n g XS data . . .
OK.
Preparing s t a t i s t i c s . . .
OK.
Setting partial reaction l i s t s for material cross sections . . .
OK.
Calculating material total cross sections :
material highfuel . . .
material lowfuel . . .
material cladding . . .
m a t e r i a l sodium . . .
C-3
OUTPUT DATA FROM A TEST RUN OF THE PHÉNIX MODEL
material blanket . . .
OK.
S t a r t i n g the tran s p o rt c a l c u l a t i o n c y c l e . . .
Sampling i n i t i a l s o u r c e . . .
OK.
Inactive
Inactive
Inactive
Inactive
Inactive
Inactive
Inactive
Inactive
Inactive
Inactive
cycle
cycle
cycle
cycle
cycle
cycle
cycle
cycle
cycle
cycle
1
2
3
4
5
6
7
8
9
10
/
/
/
/
/
/
/
/
/
/
10:
10:
10:
10:
10:
10:
10:
10:
10:
10:
k−e f f
k−e f f
k−e f f
k−e f f
k−e f f
k−e f f
k−e f f
k−e f f
k−e f f
k−e f f
=
=
=
=
=
=
=
=
=
=
0.45696
0.78370
0.93937
0.96630
1.00147
1.00093
1.00404
1.00514
0.98590
1.00188
(DT
(DT
(DT
(DT
(DT
(DT
(DT
(DT
(DT
(DT
thresh
thresh
thresh
thresh
thresh
thresh
thresh
thresh
thresh
thresh
=
=
=
=
=
=
=
=
=
=
0.9000)
0.9000)
0.9000)
0.9000)
0.9000)
0.9000)
0.9000)
0.9000)
0.9000)
0.9000)
−−−−− Begin a c t i v e c y c l e s −−−−−
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
S e r p e n t 1 . 1 . 1 3 −− C r i t i c a l i t y s o u r c e s i m u l a t i o n
T i t l e : " Phenix "
Active c y c l e
1 / 100 ( 5 0 0 0 s o u r c e n e u t r o n s )
Delta−t r a c k i n g on : t h r e s h = 0 . 9 0 , e f f = 0 . 5 3 , f r a c = 0 . 8 5
Running time :
Estimated r u n n i n g time :
Estimated r u n n i n g time l e f t :
0:00:21
0:05:40
0:05:19
k−e f f ( a n a l o g )
= 0 . 9 9 9 8 8 +/− 0 . 0 0 0 0 0
k−e f f ( i m p l i c i t ) = 0 . 9 9 7 8 0 +/− 0 . 0 0 0 0 0
[0.99988
[0.99780
0.99988]
0.99780]
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
(...)
S e r p e n t 1 . 1 . 1 3 −− C r i t i c a l i t y s o u r c e s i m u l a t i o n
T i t l e : " Phenix "
Active c y c l e
C-4
100 / 100 ( 5 0 0 0 s o u r c e n e u t r o n s )
OUTPUT DATA FROM A TEST RUN OF THE PHÉNIX MODEL
Delta−t r a c k i n g on : t h r e s h = 0 . 9 0 , e f f = 0 . 5 3 , f r a c = 0 . 8 7
Running time :
Estimated r u n n i n g time :
Estimated r u n n i n g time l e f t :
0:03:13
0:03:13
0:00:00
k−e f f ( a n a l o g )
= 1 . 0 0 2 6 7 +/− 0 . 0 0 1 8 6
k−e f f ( i m p l i c i t ) = 1 . 0 0 2 7 1 +/− 0 . 0 0 1 0 9
[0.99903
[1.00056
1.00632]
1.00485]
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
F i n i s h e d a f t e r 100 a c t i v e c y c l e s o f 5000 s o u r c e n e u t r o n s .
T o t a l c a l c u l a t i o n time 3 . 2 2 minutes .
Notes :
− Unable t o r e a d a v a i l a b l e memory from / p r o c / meminfo .
C o n s i d e r manual o v e r r i d e .
− U n r e s o l v e d r e s o n a n c e p r o b a b i l i t y t a b l e s a v a i l a b l e f o r 10
n u c l i d e s but s a m p l i n g NOT i n u s e .
− 2 n e u t r o n s e m i t t e d above maximum e n e r g y 2 0 . 0 0 MeV.
C-5
D
Results of the PFBR-model
The parameters and the results of the kef f , obtained from the simulation of the PFBR model
can be seen in Table D.1. The result is displayed in figure Figure D.1. The linear approximation
of the result gives the relation ∆kef f /Core extension = -47.6 pcm/mm.
Table D.1: The results from the simulations of the PFBR-core
Increase in
the
S/A
gap, λ(mm)
0
0.2
0.4
0.8
1.2
1.6
2.0
Extension
of the core
(mm)
0.0
1.8
3.6
7.2
10.8
14.4
18.0
Neutron
population
Number of
cycles
kef f
500000
300000
300000
300000
300000
300000
250000
2356
1000
1300
1300
1300
1300
5000
1.16338
1.16240
1.16166
1.15987
1.15829
1.15653
1.15472
Standard
deviation,
σ(10−5 )
4
7
7
7
7
7
4
D-1
RESULTS OF THE PFBR-MODEL
Figure D.1: This figure shows how the kef f of the model of PFBR is affected by core extension.
A linear approximation gives ∆kef f /Core extension = -47.6 pcm/mm.
D-2