Transmutation of Americium in Fast Neutron
Facilities
YOUPENG ZHANG
Licentiate Thesis, Stockholm, Sweden, 2011
TRITA-FYS 2011:07
iii
Abstract
In this thesis, the feasibility to use a medium sized sodium cooled fast reactor fully loaded with MOX fuel for efficient transmutation of americium is
investigated by simulating the safety performance of a BN600-type fast reactor loaded with different fractions of americium in the fuel, using the safety
parameters obtained with the SERPENT Monte Carlo code. The focus is
on americium mainly due to its long-term contribution to the radiotoxicity of
spent nuclear fuel and its deterioration on core’s safety parameters. Applying the SAS4A/SASSYS transient analysis code, it is demonstrated that the
power rating needs to be reduced by 6% for each percent additional americium
introduction into the reference MOX fuel, maintaining 100 K margin to fuel
melting, which is the most limiting failure mechanism.
Safety analysis of a new Accelerator Driven System design with a smaller
pin pitch-to-diameter ratio comparing to the reference EFIT-400 design, aiming at improving neutron source efficiency, was also performed by simulating performance for unprotected loss of flow, unprotected transient overpower,
and protected loss-of-heat-sink transients, using neutronic parameters obatined
from MCNP calculations. Thanks to the introduction of the austenitic 15/15Ti
stainless steel with enhanced creep rupture resistance and acceptable irradiation swelling rate, the suggested ADS design loaded with nitride fuel and cooled
by lead-bismuth eutectic could survive the full set of transients, preserving a
margin of 130 K to cladding rupture during the most limiting transient.
The thesis concludes that efficient transmutation of americium in a medium
sized sodium cooled fast reactor loaded with MOX fuel is possible but leads
to a severe power penalty. Instead, preserving transmutation rates of minor
actinides up to 42 kg/TWhth , the suggested ADS design with enhanced proton
source efficiency appears like a better option for americium transmutation.
Acknowledgements
First of all, I want to express my sincerest appreciation to my supervisor, Prof.
Janne Wallenius, who has supported me throughout my licentiate thesis with his
patience and knowledge. I attribute to his encouragements and efforts on this thesis’
writing procedure.
In my daily work I have been blessed with my friendly colleagues: Calle and
Andrei as my old roomates sharing wonderful talks and discussions on both physics
and life tips; Dr. Michael Jolkkonen as an encyclopedia-type consultant for almost
everything; Dr. Nils Sandberg for excellent comments on influences of irradiation
damage and also as the best ski instructor; Dr. Vasily Arzhanov for cooperations
during the lab teaching and also instructive stories; Dr. Torbjörn Bäck for excellent
instructions on lab teaching and Linux usage.
I also want to express my gratitude to Dr. Daniel Westlén and Dr. Marcus
Eriksson who aroused my passion on reactor physics before I started my PhD career
three years ago.
To Odd Runevall and Jan Dufek, thanks for your comments on my first journal
paper, which is really an important milestone.
To Sideeg, thanks for helping me to sketch out SERPENT models.
I want to thank the wonderful working circumstance created by Milan, Jitka,
Pertti, Han Song, Merja, Farnaz, Qi Chong and Xu Zhenxiang.
This research was financially supported by Svensk Kärnbränslehantering AB
(SKB).
The Department of Physics has provided the support and equipment I have
needed to accomplish my studies.
Finally, I want to show my thanks to my parents for encouraging on my PhD
study and also my girlfriend for taking care of my life in Sweden.
v
List of Papers
Publications
1. Youpeng Zhang, Janne Wallenius and Andrei Fokau, Transmutation of Americium in a Medium Size Sodium Cooled Fast Reactor Design, Annals of Nuclear
Energy, 37(5):629-638, 2010.
2. Youpeng Zhang, Andrei Fokau, Shinya Ishida and Janne Wallenius, Physics
and safety studies of a compact ADS design loaded with nitride fuel, Annals
of Nuclear Energy, Submitted, 2010.
Author’s Contribution
In Paper I and II, reactor performance parameters and reactivity coefficients
were calculated with the SERPENT Monte Carlo code by the author. In addition, the core safety performance for various transients were simulated with the
SAS4A/SASSYS code by the author.
Papers Not Included
1. Andrei Fokau, Youpeng Zhang, Shinya Ishida, Janne Wallenius, A source efficient ADS for minor actinides burning, Annals of Nuclear Energy, 37(4):540545, 2010.
2. W. Maschek, C. Artioli, X. Chen, F. Delage, A. Fernandez-Carretero, M.
Flad, A. Fokau, F. Gabrielli, G. Glinatsis, P. Liu, L. Mansani, C. Matzerath
Boccaccini, C. Petrovich, A. Rineiski, M. Sarotto, M. Schikorr, V. Sobolev,
S. Wang, Y. Zhang, Design, Safety and Fuel Developments for the EFIT Accelerator Driven System with CERCER and CERMET Cores, Actinide and
Fission Product Partitioning and Transmutation, 10th OECD/NEA Information Exchange Meeting, Mito, Japan, 2008.
3. Youpeng Zhang and Janne Wallenius, Upper Limits to Americium Concentration in Medium Size Sodium Cooled Fast Reactors, Global 2009, Paris, France,
2009.
vii
ix
x
NOMENCLATURE
Nomenclature
ADS
Accelerator Driven System
BOC
Beginning of Cycle
CW
Cold Worked, a work hardening process to enhance metal’s
mechanical properties
DHR
Decay Heat Removal
EBR-II SHRT
Shutdown Heat Removal Test on Experimental Breeder
Reactor, metallic fuel loaded and sodium cooled
EFIT
European Facility for Industrial
Transmutation
EOC
End of Cycle
EOEC
End of Equilibrium Cycle
FBR
Fast Breeder Reactor, conversion ratio higher than 1.0
FIMA
Fission of Initial Metal Atom
FP
Fission Products
GEMs
Gas Expansion Modules
GeV
Giga electron Volts
GFR
Gas-cooled Fast Reactor
HLM
Heavy Liquid Metal
HLW
High Level Waste
HTR
High Temperature gas-cooled Reactor
xi
LBE
Lead-bismuth Eutectic
LFR
Liquid-metal-cooled Fast Reactor
LINAC
LINear ACcelerator
LLW
Low Level Waste
MA
Minor Actinides, actinides except U and Pu , e.g., Np
Am, Cm
MeV
Mega electron Volts
MLW
Medium Level Waste
MOX
Mixed OXide, a compound of PuO2 and UO2
MWe
Megawatt electrical
MWth
Megawatt thermal
PDS-XADS
Preliminary Design Studies of an Experimental
Accelerator Driven System
PLOHS
Protected Loss-of-Heat-Sink
ULOF
Unprotected Loss-of-Flow
UTOP
Unprotected Transient-over-Power
RF
Radio Frequency
SFR
Sodium-cooled Fast Reactor
TREAT M-series
Transient REActor Test facility, series
tests for Metallic fuel in Mark-III sodium loop
UOX
Uranium OXide
XTADS
eXperimental facility demonstrating
the technical feasibility of Transmutation in an
Accelerator Driven System
Contents
Acknowledgements
v
List of Papers
vii
Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
Author’s Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
Papers Not Included . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
Nomenclature
x
Contents
xii
1 Introduction
1.1 Nuclear waste . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Transmutation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Candidate fast-neutron facilities
2.1 Fast neutron reactor . . . . . . . . . . . .
2.1.1 Sodium-cooled fast reactor (SFR) .
2.1.2 Lead-cooled fast reactor (LFR) . .
2.1.3 Gas-cooled fast reactor (GFR) . .
2.2 Accelerator driven system . . . . . . . . .
2.2.1 The accelerator . . . . . . . . . . .
2.2.2 The spallation target . . . . . . . .
2.2.3 The subcritical core . . . . . . . .
1
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3 Simulation tools
3.1 SERPENT Monte Carlo code . . . . . . . . . . . . . . . . . . . . . .
3.2 SAS4A/SASSYS transient analysis code . . . . . . . . . . . . . . . .
19
19
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4 SERPENT and SAS4A/SASSYS models
4.1 SERPENT models . . . . . . . . . . . . .
4.1.1 For BN600 . . . . . . . . . . . . .
4.1.2 For the nitride fuelled ADS design
4.2 SAS4A/SASSYS models . . . . . . . . . .
23
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CONTENTS
5 Effects from the introduction of americium
5.1 Effects on safety parameters . . . . . . . . . . . . . . . .
5.1.1 The effective delayed neutron fraction . . . . . .
5.1.2 The Doppler constant . . . . . . . . . . . . . . .
5.1.3 The void worth . . . . . . . . . . . . . . . . . . .
5.1.4 Radial and axial expansion reactivity coefficients
5.1.5 The effective multiplication factor . . . . . . . .
5.1.6 Safety parameters of the suggested ADS design .
5.2 Effects on thermophysical properties . . . . . . . . . . .
5.2.1 Thermal conductivity . . . . . . . . . . . . . . .
5.2.2 Fuel melting point . . . . . . . . . . . . . . . . .
5.2.3 Heat capacity . . . . . . . . . . . . . . . . . . . .
xiii
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6 Transient simulation results and discussion
6.1 Summary of transient simulation results . . . . . . . . . . . . . . . .
6.2 Am transmutation capabilities . . . . . . . . . . . . . . . . . . . . .
43
43
45
7 Conclusions
47
Bibliography
49
A SERPENT inputs
A.1 BN600 type sodium cooled fast reactor . . . . . . . . . . . . . . . . .
A.2 The compact ADS loaded with nitride fuel . . . . . . . . . . . . . . .
57
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Chapter 1
Introduction
1.1
Nuclear waste
Nuclear waste can be divided into three main groups based on their corresponding radioactivity as listed in Table 1.1. Among them, the spent fuel, containing
long-lived transuranic actinides, e.g. 239 Pu, 240 Pu, 241 Am, 243 Am, and also fission products [1], has several orders of magnitude higher radioactivity than waste
generated from other steps in nuclear fuel cycle [2].
Table 1.1. Nuclear waste categories [3] [4]
Type
LLW
Radioactivity (Bq/g)
∼ 5×105
MLW
5×105 ∼5×108
HLW
5×108 ∼
Content
Stuff contaminated by
radioactive materials
Irradiated structure material
and milling waste
Irradiated or used
nuclear fuel
Fission products can be divided into long-lived and short-lived types. The shortlived nuclides dominating the fission product (FP) inventory, e.g. 137 Cs and 90 Sr,
are major decay heat contributors during the short-term disposal or cooling period.
Comparing to other long-lived fission products (LLFP), such as 93 Zr or 135 Cs, 99 Tc is
more harzadous due to its higher radioactivity and higher mobility [5][6]. However,
the decay energy released from LLFP nuclides is still negligible comparing to that
released from radioactive actinides [7].
Although plutonium dominates the transuranic inventory (≈90 wt.%) discharged
from light water reactors, americium and curium isotopes bred from neutron capturing starting from uranium isotopes will bring more difficulties to the spent fuel
handling due to additional neutrons generated by (α,n) reactions and spontaneous
fission, in addition to high levels of decay heat [8].
1
2
CHAPTER 1. INTRODUCTION
Currently, a deep geologically repository is still a well-accepted solution of HLW.
In order to reduce the burden on a geological disposal, the magnitude and the longterm radiotoxicity of HLW inventory needs to be minimized.
1.2
Transmutation
The terminology "transmutation" stands for a conversion process from one nuclide
to another nuclide. When talking about the nuclear waste transmutation, it means
fissioning long-lived transuranic nuclides or converting LLFP nuclides into shortlived ones.
Figure 1.1. Fission probabilities of transuranic nuclides
Since the radiotoxicity of fission products will be lower than that of natrual
uranium after approximately 300 years, the long-term hazard would be considerably reduced if the transuranic elements could be eliminated, which is the major
motivation for spent fuel transmutation.
The long-term radiotoxic inventory in the spent fuel discharged from LWRs can
be reduced by a factor of 200 [9] with the multi-recycling strategy in advanced
PWR, which is mainly due to the reduction of 239 Pu and 241 Pu that can be partly
transmuted in a thermal neutron spectrum as shown in Fig. 1.1. However, fission probabilities of transuranic actinides containing even number of neutrons, e.g.,
241 Am and 243 Am, are almost equal to 0 in thermal neutron spectrum and will in-
1.2. TRANSMUTATION
3
crease with incident neutron energy. Thus, fast neutron facilities are more efficient
to transmute transuranic nuclides especially minor actinides comparing to thermal
neutron reactors, in which actinides with even neutron number will more likely be
bred into heavier nuclides (e.g. 252 Cf) instead of being fissioned. Besides, accumulation of 252 Cf, being a strong neutron source, will arise after several rounds of
recycling processes, which leads to more troubles for spent fuel handling.
Chapter 2
Candidate fast-neutron facilities
2.1
Fast neutron reactor
Fast neutron reactors, or fast reactors in short, are reactors using fast neutrons to
sustain chain reactions. As can be observed in Fig. 2.1, more fission neutrons could
be released per neutron absorption in fuel in a fast neutron spectrum comparing
to cases in a thermal neutron spectrum [10] , besides the ones used to maintain
the chain reaction, there may be more neutrons available to breed fertile 238 U into
fissile 239 Pu, through neutron capture followed by β decay reactions as shown in Eq.
2.1. Although the fission neutron yield per fissile nuclide absorption higher than
2.0, including one fission neutron needed to sustain chain reactions and the other
fission neutron used to breed new fissile nuclide, is adequate to provide a conversion
ratio equal to unity ideally, there are still possibilities for neutrons to leak out core
active zone or to be captured by fission products, coolant, inner structure material,
control rods in reactor core, which explains why U-Pu cycle in a well thermalized
spectrum is hardly feasible for achieving a conversion ratio ≥1.0.
n +238 U ⇒239 U + γ ⇒239 Np + β − ⇒239 Pu + β −
(2.1)
Fast neutron reactors were initially promoted to make a better usage of U resources by breeding fissile 239 Pu nuclides from fertile 238 U nuclides. Some countries
even raised extensive research on fast breeder reactors aiming at producing more
fissile materials, concerning the fissile material shortage. However, by 1970s, geological exploration showed that the uranium shortage will not become a problem in
the near future, limiting the necessity for comissioning more fast reactors in the following years. Recently, thanks to the higher transmutation capability of long-lived
transuranic isotopes comparing to light water reactors, fast reactors were promoted
again, aiming at reducing the HLW stockpile and shorten the time needed for geological storage.
Besides, as can be noticed from Fig. 2.2, transuranic nuclides with even neutron
numbers, e.g., 238 Pu, 240 Pu, 242 Pu, 241 Am, 243 Am, 244 Cm and 246 Cm, have much
higher probabilities to undergo fission in a fast neutron spectrum than in a ther5
CHAPTER 2. CANDIDATE FAST-NEUTRON FACILITIES
Fission Neutron Yield per Neutron Absorption
6
3.5
Thermal
3.0
Fast
2.5
2.0
1.5
1.0
239
Pu
235
U
0.5
0.0
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
Incident Neutron Energy (eV)
Figure 2.1. Fission neutron yields per neutron absorption in fuel
mal neutron spectrum, leading to a much lower accumulation of highly radioactive
252 Cf. Therefore, when recycling transuranic isotopes in a fast neutron spectrum,
the neutron activity of transuranic inventory was reported to drop by a factor of
two comparing to recycling transuranic inventory in a thermal neutron spectrum
[11].
In order to get a fast neutron spectrum, coolant moderation power and absorption should be minimized. Water and organic materials, are then excluded due to
large scattering cross sections of C and H nuclides and also large energy losses for
neutrons during collisions. Thus, liquid Na, liquid Pb and chemically inert gases
(e.g. He) are recommended for Gen-IV reactors as shown in Fig. 2.3.
2.1.1
Sodium-cooled fast reactor (SFR)
As the most mature fast reactor technology, not only prototype but also half commercial SFR units have been commissioned. Actually, except for the first few experimental reactors operated in 1940s and 1950s, e.g. CLEMENTINE (US), BR-I
(USSR) and EBR-I (US), liquid Na was implemented as primary coolant for all fast
neutron reactors, especially fast breeder reactors, thanks to: first, the maximum
allowable Na velocity through pin bundles, having been reported to be 8.0 m/s
[14][15], is not determined by concerns for corrosion on stainless steel surface but
by concerns for the flow-induced vibration, which is highly sensitive to cylindrical
structures. Since the maximum allowable velocity of liquid Na flow passing through
2.1. FAST NEUTRON REACTOR
7
246Cm
245Cm
Transuranic Isotopes
244Cm
Fast Spectrum
Thermal Spectrum
243Am
241Am
242Pu
241Pu
240Pu
239Pu
238Pu
0.0
0.1
0.2
0.3
0.4
0.5
Fission Probability,
0.6
f
/ (
0.7
f
+
0.8
0.9
1.0
)
c
Figure 2.2. Spectrum-averaged fission probabilities of transuranic isotopes in a
sodium cooled core and a PWR, loaded with oxide fuel
fuel bundles is quite high, as well as the heat capacity, the minimum allowed coolant
flow area for liquid Na could be quite small, preserving a specific heat removal rate
(defined in Eq. 2.2) and temperature increase from core inlet to outlet (∆T). Thus,
a small pitch-to-diameter ratio could be permitted for fuel pin bundles cooled by
liquid Na, leading to less neutron leakage and less neutron absorption in coolant
incurred by small coolant volumetric fraction. A good neutron economy and excellent breeding performance could then be expected; second, as can be observed from
Fig 2.4, in a fast spectrum, capture cross sections of Na are small, permitting small
neutron losses in coolant inventory; third, the thermal conductivity of liquid Na [17]
is around 3 orders of magnitude higher than that of light water [19], leading to a
high heat transfer coefficient and thus low temperature difference between cladding
and coolant for a specific linear power rating.
Q = ṁ × Cp × ∆Tcoolant
= ρ × vcoolant × Acoolant × Cp × ∆Tcoolant
(2.2)
As a commercialized SFR that has been commissioned since 1980 with the power
rating of 1470 MWth (600 MWe) [20], BN600 has excellent operational performance
during the last 30 years, permitting proposals to be raised on new fuel loading
plans (e.g., UOX/MOX hybrid and full MOX) apart from the reference UOX fuel
and new pin configurations (e.g., introducing upper sodium plenum, inner breeding
zone) [21] [22]. Moreover, after achieving reliability improvement of primary pump
impellers and applying the 20%CW ChS68 stainless steel [23] as cladding material
8
CHAPTER 2. CANDIDATE FAST-NEUTRON FACILITIES
Figure 2.3. Different types of fast reactors
instead of SS316, the lifetime of primary pumps was extended to 35000 ∼ 50000
hours and the maximum irradiation damage that the pin cladding can withstand
was increased up to 94 dpa [20]. Therefore, the geometrical model of the fully
UOX fuelled core specified in the BN600 benchmark, being representative for the
medium-sized sodium cooled fast reactors considered in Gen-IV context, was chosen
for the studies in Paper I.
Although BN600 has a wonderful operational history and more other SFR designs have been promoted by several countries consecutively from 1960s to 1980s
[24], SFR technology has not been fully commercialized as LWR technology. On
one hand, except a small rebound during 1975-1980, uranium price stayed at a
low level in the past 50 years [25][26], reducing the urgency to widely commission
fast reactors aiming at a better usage of uranium resources. On the other hand,
there are still several drawbacks to use liquid Na as primary coolant in FRs: first,
physical contact between chemical reactive Na and oxide fuel, steam or moisture in
air, incurred by cladding rupture, steam pipe break or Na leakage, leads to violent
chemical reactions, in the form of fire or explosion, which may turn a small failure to
a severe accident as happened in MONJU SFR [27]; second, the boiling point of liquid Na is only 1156 K at 1 atm, leading to a small margin to coolant voiding, which
2.1. FAST NEUTRON REACTOR
9
1
10
Pb
Na
Capture Cross-section (barn)
0
10
-1
10
-2
10
-3
10
-4
10
-5
10
-6
10
1000
10000
100000
1000000
Neutron Energy (eV)
Figure 2.4. Capture cross sections of Na and Pb
can generate noticeable reactivity response, especially after coolant void worth was
enhanced by the introduction of Am. Cladding rupture could also be expected after
coolant boils out; third, in order to prevent the leakage of radioactive 24 Na bred
from neutron capturing, an intermediate sodium loop is required for a SFR, leading
to a more complicated system and higher capital cost; fourth, maintaining 100 K
temperature increase from core inlet to outlet, only ≈200 Pa gravity head per meter elevation difference between thermal centers of core and heat exchanger can be
generated due to the small thermal expansion coefficient of liquid Na. Thus only a
small natural convection flow rate could be expected after the total loss of primary
pump head.
2.1.2
Lead-cooled fast reactor (LFR)
Comparing to liquid Na, liquid Pb has three major merits: much higher boiling
point, larger density change with temperature and inert chemical property with
respect to water.
At 1 atm, the boiling point of liquid Pb is equal to 2038 K, which is about 800
K higher than that of liquid Na. Actually, this boiling point is even much higher
than creep rupture limits of most cladding materials, which makes liquid Pb boiling
no longer an issue during accidental situations.
Correlations to express densities of liquid Pb [18] and liquid Na [17] as a function
of temperature are:
10
CHAPTER 2. CANDIDATE FAST-NEUTRON FACILITIES
ρN a = 1012 − 0.2205T − 1.923 × 10−5 T 2 + 5.637 × 10−9 T 3
ρP b = 10587 − 1.2220(T − 600.6)
(2.3)
From Eq. 2.3, it can be noticed that the density of liquid Pb has a higher
decrease than liquid Na for a unit temperature increase, leading to a higher natural
convection driven by a unit elevation change between thermal centers in core and
heat exchanger. Based on simulations performed by Maschek [59] and Zhang [66],
approximately 40% residual flow could be expected for a liquid Pb cooled core, but
only less than 5% residue flow could be generated in BN600 type SFR after a total
loss of primary pump head.
Unlike chemically reactive Na, liquid Pb is chemically inert to H2 O and steam.
Thus, the steam generator could be installed inside the primary loop for LFRs,
leading to a compact system and less capital cost for power plant construction.
Thanks to the lower boiling point comparing to liquid Pb, permitting reactors to
work at a lower temperature level and thus leaving a bigger margin to clad failure,
LBE alloy was first promoted. In Russia, the frst full-scaled prototype LBE cooled
reactor (27/VT facility) was commissioned by 1959 based on research and design
works started from the early 1950s. The 27/VT facility was in operation for only two
runs due to accidents incurred by accumulation of impurity slags in the core inlet
[33]. Later, two types of LBE-cooled primary circuit systems (OK-550 and BM40/A) have been recommended for submarines by 1970s [29]. More recently, pure
liquid Pb cooled BREST reactor and compact STAR-LM reactors were proposed by
Russia and US, concerning accumulation of highly radioactive 210 Po from neutron
capture of 209 Bi. In the 6th Framework program, design work was performed on a
400 MWth grade ADS design (known as EFIT-400) and a 600 MWe (1500 MWth)
grade ADS design (known as ELSY), which are also cooled by liquid Pb [30] [31].
However, until now, no civilian LFRs have been commissioned. A major problem when operating continuously at full power is corrosions on cladding and inner
structure materials incurred by inter-grannular penetration and mass transfer [32],
especially for austenitic stainless steels with high concentrations of Ni, which has
the highest solubility into liquid Pb comparing to other elements in stainless steel
matrix. The mass transfer from stainless steel to liquid Pb may lead to changes of
the microstructure, composition, and surface morphology of the structural materials, affecting physical and mechanical properties of the structural materials, e.g.,
embrittlement and drop of rupture strength. However, it has also been reported
that this corrosion attack can be minimized if a thin protective oxide layer (2-3
µm) could be formed on the steel surface [30]. In liquid Pb, the minimum oxygen
concentration required for the formation of protective oxide layer on surfaces of
Fe-based alloys, equivalent to the oxygen potential ensuring the conditions to form
the least stable oxide (Fe3 O4 ), can be calculated from Eq. 2.4, which is valid in the
temperature region from 603 to 1183 K [33][34].
logCF e,wt.% =
0.34 − 3450
T
logCO,min,wt.% = −0.75logCF e,wt.% + 2.355 −
10600
T
(2.4)
2.1. FAST NEUTRON REACTOR
11
The upper limit of oxygen concentration in liquid Pb could be defined by Eq.
2.5, concerning coolant contamination by PbO, which is the most stable lead oxide
in solid phase. The accumulation of PbO may clog the coolant flow channel or
deposit on heat exchanger surfaces, leading to a loss of cooling capacity. [33].
logCO,max,wt.% = 3.2 −
5000
T
(2.5)
Another factor that needs to be considered is that the temperature at the interface between cladding and Pb coolant is not equivalent to the bulk temperature of
liquid Pb in order to permit heat transfer from fuel pin to coolant and from coolant
to pipes in heat exchanger. If we assume the core inlet temperature, core outlet
temperature, cladding temperature at hot spot and pipe wall temperature at the
cold spot in heat exchanger are equal to 673 K, 773 K, 823 K and 573 K respectively, the allowable oxygen concentration can then be determined as the shaded
area in Fig. 2.5. It can be noticed that this area is fairly small, leading to the
requirement of a precise oxygen control. Even with oxygen control, stability of the
protective oxide layer was reported to be deteriorated if it was exposed HLM flow
with a velocity higher than 1.9 m/s [16], which sets the upper limit of liquid Pb
flow velocity in LFRs.
-1
10
-2
Oxygen Concentration, wt.%
10
Contamination
-3
10
PbO
-4
10
Oxidation
-5
10
-6
10
Cold Spot
-7
10
++++++++++
++++++++++
++++++++++
++++++++++
++++++++++
++++++++++
++++++++++
Fe O
3
4
-8
10
Hot Spot
-9
10
Core Outlet
-10
10
Core Inlet
-11
Dissolution
10
-12
10
500
600
700
800
900
1000
1100
Temperature, K
Figure 2.5. Oxygen Specifications in liquid Pb
1200
12
2.1.3
CHAPTER 2. CANDIDATE FAST-NEUTRON FACILITIES
Gas-cooled fast reactor (GFR)
The typical coolant used in a GFR is He. Unlike liquid Na or liquid Pb, He, being a
non-active gas, is chemically and physically compatible with air, moisture and Febased alloys, permitting the usage of a direct Brayton gas turbine cycle, by which a
higher thermal efficiency could be expected [35]. Besides, since He is already in gas
phase at normal operating temperature, coolant boiling or reactivity response from
coolant voiding may not be issues any more, providing a better safety performance
and also permitting more than 3 times bigger temperature increase from core inlet
to outlet comparing to SFRs and LFRs.
Current GFR researches are mainly based on design processes and operational
experiences of several graphite-moderated thermal spectrum gas-cooled reactors,
e.g., AVR (Germany), HTTR (Japan), HTR-10 (China), and design studies of fast
spectrum gas-cooled reactors, e.g., GCFR (US & EU) and the Allegro reactor. These
researches are mainly on selecting a proper fuel form, material for cladding and core
configuration to provide efficient conversion of fertile U and a better management
of transuranic inventories, preserving system integrity and compatibility [36]. The
conceptual design of a prototype Allegro reactor with a capacity of 50-80 MWth is
planned to be accomplished by 2019 and commissioned by 2025 according to R&D
plans [37].
Before achieving these targets, there are still some technical challenges need to
be faced. First, the radiation resiliency of candidate fuel forms, e.g., actinide-carbide
and ceramic-ceramic, for GFR operating conditions (1673 K, 20%h.a. burnup and
150 dpa irradiation dose) should be further investigated [36]. Second, although
advanced ceramic materials have been promoted for in-vessel structure usage, their
capabilities to withstand temperatures up to 1873 K and fast neutron damage still
need to be validated. Third, as can be noticed from Eq. 2.2, the heat removal
rate is linearly related to coolant temperature increase (∆T), cross-sectional area
of coolant flow channel (A), coolant velocity (v), coolant heat capacity (Cp) and
coolant density (ρ). Since ∆T is limited by material reliability, A is restricted by
the concern of neutron leakage and neutron economy, v is limited by the concern
of erosion on in-vessel structure with the existence of impurities and Cp of He was
reported to be constant in a wide temperature range [38], He density should be
increased by enhancing coolant pressure in GFR system (normally ≥4 MPa [39])
in order to achieve a higher cooling capability. Since He density will intensively
decrease according to Eq. 2.6 during depressurization [38], a passive system to
provide back-up pressure is then required in order to maintain sufficient cooling
capability for decay heat removing.
ρHe (kg/m3 ) = 48.14 ×
P (atm) −1
P (atm)
× [1 + 0.4446 ×
]
T (K)
T (K)1.2
(2.6)
2.2. ACCELERATOR DRIVEN SYSTEM
2.2
13
Accelerator driven system
Since the consumption rate of MA will increase with the fraction of MA in fuel
for fast reactors, the maximum allowable content of MA should be determined
in order to maximize the transmutation capability of fast reactors. However, it
has been reported that loading FRs with only MA inventory, may lead to safetyrelated problems due to degradations of safety parameters incurred by the absence
of fertile U. Besides, higher content of MA, especially Am, may lead to further
degradations of safety parameters, such as a reduction of effective delayed neutron
fraction, a reduction of the Doppler constant and an increase in coolant void worth
[40]. Therefore, the maximum allowable fraction of Am homogeneously loaded into
SFRs has been investigated and first quoted as 2.5% [41]. Recently, this limit has
been uplifted to 5% for SFRs loaded with metallic fuels [42]. If target sub-assemblies
were introduced, this limit for target sub-assemblies may be higher [43]. LFRs are
more robust systems than SFRs, regarding core safety during transients, thanks to
its high boiling point and excellent natural convection behavior. Thus, up to 10%
MA, equivalent to 7% Am, was claimed to be acceptable for a medium LFR with
600 MWe power rating without considering core performances during transients
[44]. For a 2400 MWth grade GFR, only 1.1% of MA was proposed to be loaded,
corresponding to self-recycling [45]. Hence, in order to host higher fraction of minor
actinides aiming at higher MA transmutation rates, FRs should be designed to
operate in a sub-critical mode, which can provide improved flexibility and safety
characteristics, concerning degradation of core safety performance incurred by minor
actinides introduction. The sub-critical core needs to be driven by an external
neutron source. In order to generate sufficient neutrons from spallation reactions,
the proton beam should be accelerated before bombarding an heavy metal target,
giving rise to the term the terminology "Accelerator Driven System (ADS)".
Before further investigations, a terminology named "the energy gain (G)", equalling
the ratio of the total power of system (Ptot ) to the proton beam power (Pacc ), should
be introduced in order to parameterize the influence from changes of target and core
designs on power amplification of system. The energy gain of ADS can be calculated by Eq. 2.7, in which kef f is the multiplication factor of system, Ef is the
averaged energy released per fission reaction, ν is the fission yield, Ep is the proton
beam energy and ψ ∗ is the proton source efficiency [50]. Thus, in order to maximize
the energy gain aiming at a better system economy, kef f , ν, Ef and ψ ∗ should be
maximized and Ep should be minimized. Since kef f is limited by safety concerns,
Ep affects the spallation neutron yield, ν and Ef are assumed to be constant for
a specific fuel composition, the energy gain could be increased by optimising the
system design aiming at a higher ψ ∗ .
G=
kef f Ef ∗
Ptot
=
ψ
Pacc
1 − kef f νEp
(2.7)
14
CHAPTER 2. CANDIDATE FAST-NEUTRON FACILITIES
30
25
Neutron Yield
20
15
10
5
0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Proton Energy (GeV)
Figure 2.6. Neutron yield per proton for a liquid Pb target with 20 cm radius and
60 cm length
2.2.1
The accelerator
Spallation neutrons are produced by (p,xn) reactions in spallation target. Fig. 2.6
shows the neutron yield per proton as a function of incident proton energy for a
liquid Pb target with 20 cm radius and 60 cm length [46]. It can be noticed that the
neutron yield from (p,xn) and (n,xn) reactions in spallation target increases with
incident proton energy up to 1.0 GeV. However, the capital cost for construction
and maintenance of proton accelerator may continue to increase with proton energy.
Moreover, the region where source neutrons release may be wider than the core
height in the axial direction if higher proton beam energy was applied, leading to
higher neutron leakage and thus lower neutron economy. Hence, 1.0 GeV may be
considered as the upper limit of proton beam energy.
Current proton accelerators can be categorized into circular accelerators (e.g.,
cyclotrons, synchrocyclotrons) and linear accelerators (LINAC). For simple cyclotrons, the energy of particle beam is limited under 15 MeV due to a mismatch
between the increase of circulation radius and particle speed or the preset radio frequency. For synchrocyclotrons, due to the variation of frequency and the oscillation
of voltage supply, only limited number of particles owning the maximum energy at
the outermost region of magnetic field can be captured, which sets the upper limit
to the intensity of output beam. Comparing to circular type accelerators, a linear
accelerator was reported to be able to deliver a 10 mA/1.0 GeV ion beam with a
high reliability, being able to run an EFIT-400 type ADS along [47].
2.2. ACCELERATOR DRIVEN SYSTEM
15
Figure 2.7. Window and windowless targets
2.2.2
The spallation target
Target material
Until now, LBE, Hg and liquid Pb have been proposed for high power spallation
targets thanks to their excellent performance for source neutron production (high
neutron yield per incident proton) and high heat removal capacity (ρCP ). Concerning evaporation of target materials and volatilization of spallation products
when connecting to a vacuum cavity required by accelerators, a window was once
recommended for spallation target to separate the vacuum cavity and the spallation zone. However, harsh working conditions, including high working temperature,
HLM corrosion and irradiation defects, may lead to a target window failure due
to accumulations of thermal, irradiation and mechanical loads [48]. A windowless
target without a physical separation between the vacuum cavity and the liquid target material was then proposed as shown in Fig. 2.7. However, adequate pumping
capacity is required to maintain the high vacuum condition above target surface
and prevent impurities invasion from target zone into proton beam line. LBE and
Pb are then more suitable for a windowless target usage rather than Hg, thanks
to their four orders of magnitude lower vapour pressure at the normal operating
temperature [49].
16
CHAPTER 2. CANDIDATE FAST-NEUTRON FACILITIES
In Paper II, the nitride fuelled ADS employs a windowless spallation target,
which is cooled by liquid Pb instead of LBE in order to prevent the accumulation
of highly radioactive 210 Po from 209 Bi through (n,γ) reactions followed by β decay
reactions.
Target size
Since the fast fission threshold of Am and other fertile nuclides is in the region
0.5-1.0 MeV as shown in Fig. 1.1, higher moderation on liquid Pb in target block
permits less spallation neutrons to enter into the most effective energy region for
fissioning fertile nuclides, leading to smaller proton source efficiency [50]. Thus,
the spallation target size should be minimized, preserving sufficient heat removal
capability. In the suggested ADS design, thanks to the employment of nitride fuel,
smaller pin pitch and compact spallation target, the proton source efficiency could
be enhanced by 80% comparing to the reference EFIT-400 design. Thus, the proton
current and proton beam power required for the system could be reduced by 67%
[51], leading to less deposit heat into spallation target, which permits the reduction
of spallation target size.
2.2.3
The subcritical core
Similar to critical reactors, the sub-critical core in ADS also consists of sub-assemblies,
which is in hexagonal geometry in order to achieve better radial power profile and
enable a better fit of the spallation target. However, since the safety of sub-critical
core can be enhanced due to the bigger margin to prompt criticality than critical
facilities, higher minor actinides concentration, leading to further deterioration of
inherent safety, can be permitted. In the reference EFIT-400 design, U-free oxide
fuel containing 54.3 at.% minor actinides was proved to be allowable, providing a
MA consumption rate of ≈42 kg/TWhth [52].
Since the melting point of LBE (44.5%Pb-55.5%Bi) (397 K, at 1 atm) is around
200 K lower than that of Pb, it is used as the primary coolant instead of liquid
Pb for the nitride fuelled ADS investigated in Paper II aiming at a lower coolant
temperature at core inlet, which limits thermal loading and corrosion effect on
cladding and in-vessel structures. However, severe inter-grannular penetration and
mass transfer have also been reported for stainless steel in LBE, leading to the
requirement of oxide protective layer as the case for liquid Pb. The minimum oxygen
concentration required for the formation of protective oxide layer on surfaces of Febased alloys can be calculated from Eq. 2.8, which is valid in the region from 823
to 1053 K. Concerning coolant contamination incurred by PbO accumulation, the
upper limit of oxygen concentration in liquid Pb could be defined by using Eq.
2.9, which is valid in 673 - 973 K. Therefore, oxygen control is also required for a
LBE-cooled system.
logCF e,wt.% = 2.01 − 4380
T
logCO,min,wt.% = −0.75logCF e,wt.% + 1.2375 −
9757
T
(2.8)
2.2. ACCELERATOR DRIVEN SYSTEM
logCO,max,wt.% = 1.2 −
17
3400
T
(2.9)
In the nitride fuelled ADS, the pin pitch is reduced from 1.35 cm (for the reference EFIT-400 design) to 1.20 cm in order to reduce the coolant volumetric fraction
in system, aiming at a better neutron economy in the sub-critical core. However,
since the velocity of LBE flow washing stainless steel bundles is restricted under
1.9 m/s as discussed above, the reduction of pin pitch may lead to reduction of
coolant flowrate per pin not only during the normal operating condition but also
during transients. In order to maintain an adequate margin to cladding rupture,
the austenitic 15/15Ti stainless steel with enhanced thermal and irradiation creep
resistance, instead of the ferritic-martensitic T91 stainless steel inplemented in the
reference EFIT-400 design, is used for the suggested ADS design.
Chapter 3
Simulation tools
3.1
SERPENT Monte Carlo code
In this thesis, the reactor operating parameters and reactivity coefficients were evaluated by the SERPENT Monte Carlo code based on the JEFF-3.1 data library. The
SERPENT Monte Carlo code was initiated as the program "Probalistic Scattering
Game" starting from 2004 in VTT Technical Research Centre in Finland [53]. Similar to the MCNP and MCB Monte Carlo codes, a universe based geometry model
is applied to describe the configuration of fuel pins and sub-assemblies. The burnup
calculation is realized by solving the Bateman equations with the Transmutation
Trajectory Method (TTA) and expressed with time or burn rate steps. The JEFF3.1.1 decay data library and the JEFF-3.1 fission yield data library have been used
for the burnup calculation.
Comparing to existing most-used Monte Carlo codes, e.g. MCNP, the SERPENT Monte Carlo code has two merits. First, Monte Carlo calculation is accelerated by 5 to 15 times faster thanks to: 1. evenly subdividing the energy grid
in cross section spectrums, which reduces the time consumption for iteration process when generating cross section data; 2. combining conventional ray-tracing and
delta-tracking methods enhances neutron transport calculation efficiency. Second,
homogenized few-group constants, e.g. diffusion rates, effective delayed neutron
fractions, and statistical error estimation can be obtained directly by including
some newly developed scripts.
The SERPENT Monte Carlo code has been preliminarily validated with respect
to MCNP and the deviation between these two codes is reported to be less than 2%
[54].
3.2
SAS4A/SASSYS transient analysis code
The Safety Analysis System (SAS) was initially written by D. R. MacFarlane as
a PhD thesis at the middle of 1960s and upgraded by the staff at safety analysis
section at Argonne national laboratory in the following years, aiming at licencing
19
20
CHAPTER 3. SIMULATION TOOLS
governmental sponsored research facilities by accomplishing safety analysis.
In this thesis, all transient analysis were performed by applying the SAS4A/SASSYS
code (version 3.1), which has been extensively validated based on experimental data
obtained from the TREAT M-series, EBR-II SHRT and GEMS tests. This version
code is then qualified for licensing liquid metal (e.g., liquid Na, liquid Pb and Pb/Bi
eutectic alloy) cooled reactor cores loaded with oxide or metallic fuels, by means of
transient accident simulations, such as Loss-of-Flow (LOF), Transient-over-Power
(TOP) and Beam Trip (BT).
In the SAS4A code, one or more sub-assemblies sharing similar thermophysical properties and thermal hydraulic structure are represented by one thermalhydraulic channel. A whole-core model is formed by several channels. Heat transfer
between fuel, cladding and structure is modeled with a two-dimensional (r/z) heat
conduction equation. Heat transfer between cladding and coolant is evaluated by
simulating single and two-phase coolant thermal-hydraulics with a one-dimensional
non-equilibrium, homogenous coolant flow model in axial direction. Introduction of
models for ex-reactor coolant systems enables the SAS4A/SASSYS code to analyze
LOHS-involved transients.
The neutronic behavior of reactor core during transients is evaluated by applying
the point kinetic model as shown in Eq. 3.1, in which p(t), ρ(t), β(t), Λ(t), λk ,
ck (t) and s(t) stand for the power, the reactivity, the delayed neutron fraction, the
prompt neutron life time, the group-wise decay constants, the group-wise decay
precursor fractions and the source term of core as a function of time [55].
X
ρ(t) − β(t)
dp(t)
λk ck (t) + s(t)
=
× p(t) +
dt
Λ(t)
k
(3.1)
The point kinetic model is an appoximation to the time-dependent continuous
energy diffusion equation. It has been reported that deviations from the usage of
point kinetic approximation in sub-critical systems is fairly small (≤5.0%). However,
it has also been indicated that the precision of the point kinetic model decreases remarkably when approaching criticality, especially in the case of local perturbations,
such as single control rod withdrawal [56], due to slower migration of spatial perturbations. However, if non-local perturbation is assumed to be introduced during
LOF and TOP transients, simulation results obtained from the point kinetic model
are still considered to be reliable [57].
The net reactivity change during transients dρ(t) could be calculated by summing up reactivity feedbacks from six components as listed in Eq. 3.2, standing
for programmed/user-defined, the Doppler effect, fuel pin axial expansion, coolant
density change, core radial expansion and control rod drive expansion respectively.
For ADS, since reactivity swing and reactor shutdown could be managed by adjusting spallation neutron source, control rods are not required. Thus, expansion
of control rod drive, contributing reactivity feedback, is not considered in transient
simulation for the nitride fuelled ADS.
3.2. SAS4A/SASSYS TRANSIENT ANALYSIS CODE
dρ(t) = dρp (t) + dρD (t) + dρd (ax) + dρcoolant (t) + dρre (t) + dρcr (t)
21
(3.2)
Chapter 4
SERPENT and SAS4A/SASSYS models
4.1
4.1.1
SERPENT models
For BN600
The geometry of fuel pin, sub-assembly and other core inner structures was adopted
from the reference BN600 design fully loaded with UOX as sketched in Fig. 4.1.
This core consists of 369 driver sub-assemblies. Each fuel sub-assembly is loaded
with 127 fuel pins and one stainless steel rod in center. Pin pitch and sub-assembly
pitch is equal to 8 mm and 99 mm respectively [24][58].
In order to maintain the multiplication factor above unity during burnup, 20
at.% Pu was introduced into the MOX fuel for present core design. In order to
parameterize the impact from Am introduction on core safety parameters seperately
from Np and Cm, Am content in fuel was varied from 0.0 wt.% to 10.0 wt.%. The
isotopic composition of Pu and Am were obtained from spent fuel discharged from
LWR with 50 MWd/kgHM burnup after 5 years of cooling. The isotopic vectors of
Pu are listed in Table 4.1
Table 4.1. Plutonium vectors
Isotope
238 Pu
240 Pu
242 Pu
Atomic Fraction
3.50
23.82
7.90
Isotope
239 Pu
241 Pu
Atomic Fraction
52.88
12.90
The Am inventory consists of 241 Am (57.58 at.%) and 243 Am (42.42 at.%). The
cladding material adopted for BN600 was ChS68, containing 0.06 wt.% C, 15.9 wt.%
Cr, 0.013 wt.% N, 1.6 wt.% Mn, 1.4 wt.% Si, 14.5 wt.% Ni, 0.3 wt.% Ti, 0.03 wt.%
Cu, 0.15 wt.% V and 2.2 wt.% Mo. As stated in Paper I, depleted uranium in axial
blankets is replaced by stainless steel, to address the non-proliferation requirement
23
24
CHAPTER 4. SERPENT AND SAS4A/SASSYS MODELS
Figure 4.1. Geometrical layouts of pin (left), sub-assembly (middle) and core (right)
for BN600 [15]
for Gen-IV system. Steel shielding assemblies (SSA) are filled with the ChS68 stainless steel. Boron reflector assemblies consist of pins loaded with B4 C, containing
80.0 at% 10 B.
Based on geometrical and compositional details stated above, a 3-D SERPENT
model was constructed as shown in Fig. 4.2.
4.1.2
For the nitride fuelled ADS design
The geometry of fuel pins and sub-assemblies loaded into the suggested ADS design was mainly adopted from the reference EFIT-400 design loaded with ceramicceramic fuel, except some modifications aiming at a higher neutron source efficiency
4.3 [51]:
1. The spallation target size was reduced from 19 sub-assemblies to 7 subassemblies.
2. The number of driver sub-assemblies was reduced from 432 to 78, including 12,
42 and 24 fuel assemblies in inner, intermediate and outer zones respectively.
4.1. SERPENT MODELS
Figure 4.2. SERPENT model for BN600, top view (above) and side view (below)
25
26
CHAPTER 4. SERPENT AND SAS4A/SASSYS MODELS
3. The pin pitch was reduced from 1.35 cm to 1.20 cm, permiting 217 pins
(including 216 fuel pins + 1 stainless steel pin in center) instead of 169 pins
(including 168 fuel pins + 1 stainless steel pin in center) to be settled in each
sub-assembly.
In order to minimize the radial power peaking factor, inert matrix nitride fuel,
containing 78.1 vol.%, 73.9 vol.% and 66.1 vol.% ZrN, was loaded into the inner,
intermediate and outer zones respectively. The atomic fraction of Pu in HM was
fixed to 43.5%. The MA inventory consists of Np (4.0 at.%), Am (91.8 at.%) and
Cm (4.2 at.%).
Figure 4.3. Geometrical layouts of pin (Left), sub-assembly (middle) and core
(right) for the suggested ADS design [59]
Based on geometrical and compositional information stated above, a SERPENT
model for the suggested ADS design was constructed as shown in Fig. 4.4.
4.2
SAS4A/SASSYS models
As shown in Fig. 4.5, in the primary loop of BN600, coolant moves from the core to
an outlet plenum and then passes through an intermediate heat exchanger (IHX).
The primary pump is located at the cold leg. In the primary loop of the suggested
ADS design, coolant moves from the core to an outlet plenum and then passes
4.2. SAS4A/SASSYS MODELS
Figure 4.4. SERPENT model for the suggested ADS design, top view (above) and
side view (below)
27
28
CHAPTER 4. SERPENT AND SAS4A/SASSYS MODELS
Figure 4.5. SAS4A/SASSYS models of BN600 (a) and ADS (b)
4.2. SAS4A/SASSYS MODELS
29
through the primary pump and an IHX. The primary pump is located at the hot
leg.
The core region in BN600 was subdivided into six different channels loaded with
fuel sub-assemblies (including low, intermediate and high enriched zones), steel
shielding assemblies, boron shielding asseblies and control rods respectively, which
were categorized by different thermophysical properties, neutronic characteristics
and power densities. The suggested ADS core was represented by 5 channels, including 3 fuel channels stand for three fuel zones loaded with nitride fuels containing
different fractions of matrix, 1 bypass channel stands for the spallation target and
1 reflector channel.
The foot and exit section of sub-assemblies are significant components contributing pressure drops, and thus represented by liquid segments called pipes at core inlet
and outlet separately as shown in Fig. 4.5. Pressure drops from different parts of
assembly foot and exit could then be added to the primary circuit by simply adjusting orifice coefficients of these two pipe segments. Since geometrical details of
BN600 inner structures required for pressure drop estimation is not available for
our department, pressure drops through the foot, the core region and the exit of
fuel sub-assemblies are simply assumed to be in the ratio of 0.35:0.50:0.15, which is
equal to the one recommended for the EFIT-400 design [60]. Pressure drop through
the core region at steady state was set at 0.5 MPa [15] for BN600 and 0.032 MPa
for the suggested ADS design. Total pressure drop through the primary loop of
BN600 will then be 2.00 MPa for a coolant flowrate set at 0.14 kg/s (equivalent to
8.0 m/s coolant velocity) per fuel pin, including ∆Pcore (1.00 MPa), ∆PIHX (0.80
MPa) and ∆Ppump (0.20 MPa). Total pressure drop through the primary circuit of
the suggested ADS design is equal to 0.141 MPa, including ∆ Pcore (0.064 MPa),
∆ PIHX (0.034 MPa) and ∆ Ppump+accessories (0.043 MPa), if the coolant velocity
was set at 0.80 m/s as recommended for the reference EFIT-400 design [61]. Accessories are components like core diagrids, decay heat removal heat exchangers, fuel
handling machines and so on.
Chapter 5
Effects from the introduction of
americium
Fresh Am is a white lustrous metal. The melting point and density of pure Am
are 1267 K and 13.67 g/cm3 (293 K) respectively [62]. In dry atmosphere, Am
metal will be tarnished by heat generated from spontaneous fission reactions and α
irradiation.
Figure 5.1. Relations of the most important actinides, via α-decay, β-decay and
neutron capture reactions
31
32
CHAPTER 5. EFFECTS FROM THE INTRODUCTION OF AMERICIUM
The first identified Am isotope is 241 Am, which was synthesized from successive
neutron capture reactions of Pu by Seaborg et al. at 1944 [63]. Apart from 241 Am,
at least 10 Am isotopes with atomic mass ranging from 237 to 247 have been
synthesized, in which 237 Am has the longest half-life time equaling 7400 years.
Like other transuranic nuclides with atomic numbers higher than 95, all Am
isotopes can undergo α decay and spontaneous fission reactions. α particles released
from α decay reactions of 241 Am has the average energy of 5.48 MeV, which is
three times higher than those released from α decay reactions of 226 Ra. γ particles
discharged during α decay and spontaneous fission reactions have the average energy
of around 59 keV and 7 MeV [64] respectively. Thus, accumulation of Am nuclides
leads to difficulties for fuel handling.
Nevertheless, since fission probabilities of the major Am isotopes are close to
zero in a thermal neutron spectrum as can be noticed from Fig. 1.1, Am nuclides are
more likely to be bred to 252 Cf, which is a strong neutron source and heat emitter,
instead of being fissioned if they are recycled in a thermal spectrum as shown in Fig.
5.1. It has been reported that the equilibrium concentration in a fast spectrum of Cf
and the corresponding neutron reactivity will be 2-3 orders of magnitude lower than
in a thermal spectrum. Thus, fast neutron facilities are better suited to implement
transmutation of Am [65].
For the suggested ADS design, isotopic composition of fuel and core design parameters have been adjusted to achieve a higher proton source efficiency comparing
to the reference EFIT-400 design, preserving the same minor actinide transmutation
rate equalling 42 kg/TWh. Thus, in Paper II, the major task is to confirm the suggested ADS design by investigating core safety performances during the postulated
transients.
For fast critical reactors, the consumption rate of Am is highly dependent on the
ratio between Am and Pu in the fresh fuel. A larger Am/Pu ratio permits a higher
Am burning rate, in terms of kilogram Am consumed per TWh power produced.
However, since Am has a detrimental effect on essential safety parameters of reactor
core, e.g. the effective delayed neutron fraction, the Doppler constant, the coolant
void worth and the axial/radial expansion reactivity coefficient, a careful analysis
of transient performance as a function of Am concentration in the fuel must be
performed, also taking the degradation of thermophysical properties into account.
5.1
Effects on safety parameters
Effects from the introduction of Am on reactivity coefficients and core performance
parameters were evaluated by modifying MOX fuel with different fractions of Am
and then loaded into a SERPENT model derived from the geometrical design of
BN600 [66]. Calculation results are summarized into Fig. 5.2.
5.1. EFFECTS ON SAFETY PARAMETERS
33
34
5.1.1
CHAPTER 5. EFFECTS FROM THE INTRODUCTION OF AMERICIUM
The effective delayed neutron fraction
Neutrons released from fission reactions can be divided into prompt and delayed
neutrons. A prompt neutron is a neutron emitted immediately from fission reactions. A delayed neutron is a neutron emitted from fission products decay anytime
from several milliseconds (ms) to about 55 seconds (such as 87 Br) [67]. The delayed
neutron fraction (β) is then defined as the number of delayed neutrons divided by
the number of total fission neutrons. The effective delayed neutron fraction (βef f )
is defined as the fraction of fission inducing neutrons that were born as delayed
neutrons.
Since capture cross section of 241 Am is 5 times higher than that of 238 U for
the average energy of delayed neutrons (≈0.5 MeV), the effectiveness of delayed
neutrons will decrease in proportion to Am content as can be noticed from Fig.
5.2. Smaller βef f may lead to: first, shorter mean generation time (Λ) of fission
neutrons, limiting the time for non-malignant responses from either the manual
operation or inherent safety characteristics; second, higher sensitivity of core power
to reactivity fluctuations according to Eq. 3.1. The increase of βef f during burnup
is mainly due to the consumption of Am nuclides.
5.1.2
The Doppler constant
The Doppler effect of fertile nuclides is mainly from the Doppler broadening of
capture resonances of 238 U and 240 Pu, permitting more neutrons distributed in a
wider energy spectrum to be captured, which leads to a lower effective multiplication
factor. The Doppler constant is then used to correlate the reactivity change with
fuel temperature change as shown in Eq. 5.1, in which ρ(T1 ) and ρ(T2 ) stand for
core reactivities at fuel temperatures T1 and T2 .
KD = −
ρ(T2 ) − ρ(T1 )
ln(T2 /T1 )
(5.1)
As can be observed from Fig. 5.2, the Doppler effect will be weakened by a
factor of two when Am content was increased from 1.0 wt.% to 10.0 wt.% because
the introduction of Am permits less fission neutrons to enter the energy region where
the Doppler effect is most efficient and also weakens the Doppler broading effects of
238 U and 240 Pu by covering their resonance capture regions with that of 241 Am as
shown in Fig. 5.3, whose Doppler broadening effect is weaker as shown in Fig. 5.4.
The increase of the Doppler constant shown in Fig. 5.2 is the consequence of
Am consumption during burnup and also accumulations of fission products, which
function as extra moderators in fuel matrix, permitting more fission neutrons to
enter the most effective energy region for the Doppler effect as discussed in Paper
I.
5.1. EFFECTS ON SAFETY PARAMETERS
35
c),
barn
20
238
15
241
Am
240
Capture Cross-section (
U
Pu
10
5
0
-3
-3
10
-3
2x10
-3
3x10
4x10
-3
5x10
Incident Neutron Energy (MeV)
Figure 5.3. Capture cross-section spectrums of
238
U,
241
Am and
240
Pu
238U
1.006
241Am
1.004
1.002
1.000
(
c/
a,
1800) / (
c/
a,
600)
1.008
0.998
0.0011
0.00115
0.0012
0.00125
0.0013
Incident neutron Energy (MeV)
Figure 5.4. The increase of capture rate by Doppler broadening
36
5.1.3
CHAPTER 5. EFFECTS FROM THE INTRODUCTION OF AMERICIUM
The void worth
The coolant void worth is a safety parameter that describes the reactivity change
after coolant in core boils out. It can then be calculated by subtracting the reactivity
of the voided core from the reactivity during normal operating conditions. Since
liquid metal is the primary coolant, also functions as neutron reflector, two major
impacts may arise from the coolant voiding on core performance: first, neutron flux
will be hardened due to less neutron moderation; second, core leakage will be higher
due to less neutron reflection.
Since fission probabilities of Am nuclides are much higher than that of 238 U and
increase intensively with incident neutron energy in the energy region around 500
keV, introduction of Am will lead to a higher sensitivity to the spectral shift of
incident neutrons. Thus, an almost linear increase of the coolant void worth with
Am concentration could be noticed from Fig. 5.2 due to the negligible change of
core leakage after coolant voiding for BN600 fully loaded with MOX fuel.
5.1.4
Radial and axial expansion reactivity coefficients
The radial expansion reactivity coefficient (αR ) is a safety parameter that correlates
the reactivity change with the radial expansion of sub-assembly diagrids. It can be
calculated as αR =∆ρ/∆T, in which ∆ρ stands for the reactivity change due to
a specific diagrid expansion and ∆T stands for the temperature change required
to realize this specific diagrid expansion. Similarly, the axial expansion reactivity
coefficient, calculated as αA =∆ρ/∆T, is used to correlate the reactivity change with
the thermal elongation of fuel pin in axial direction.
It can be noticed from Fig. 5.2 that the radial expansion of sub-assembly diagrid
leads to a decrease of core reactivity for BN600, which is mainly due to enhanced
neutron leakage in axial direction. Moreover, since the introduction of Am hardens
the neutron spectrum, the radial expansion reactivity coefficients decreases by a
factor of two when Am content is increased from 0.0 wt.% to 10.0 wt.% at BOL due
to higher neutron leakage in axial direction and lower fission probabilities of Am
nuclides for incident neutrons with lower energy incurred by more moderation.
Since more fissile material moves up and downwards into regions where neutrons
are further moderated by coolant in hot pool and cold pool, the axial expansion
may reduce the multiplication factor as shown in Fig. 5.2. The introduction of 10.0
wt.% Am reduces the axial expansion reactivity coefficient by a factor of two due
to a higher sensitivity to the spectral shift of incident neutrons for Am nuclides.
5.1.5
The effective multiplication factor
The effective multiplication factor (kef f ) is equal to the average number of neutrons
emitted from one fission reaction that can cause another fission reaction. Except
these "effective" neutrons, other fission neutrons will either be consumed by nonfission reactions or leak out from the active region.
5.2. EFFECTS ON THERMOPHYSICAL PROPERTIES
37
Table 5.1. Reactivity coefficients and core performance parameters
ADS
Types
kef f , BOC
kef f swing, pcm
βef f (pcm)
Wcoolant (pcm), BOC
Wcoolant (pcm), EOC
KD (¢)
αR (¢/K)
Nitride ADS
SERPENT
0.97
1780
164±2
3322±10
3026±10
22±6
-0.56±0.03
Nitride ADS
MCNP
0.97
234
142±13
3504±18
2877±18
31±5
-0.50±0.05
EFIT-Pb
(cermet)
0.97
165
168
7335
6325
68
-0.64
EFIT-Pb
(cercer)
0.97
709
148
7077
6037
31
-0.54
It can be observed from Fig. 5.2 that: 1. negative kef f swing could be noticed
due to consumption of fissile materials and generation of fission products, which
leads to lower concentration of fissile material in fuel matrix and also more moderations on fission neutrons; 2. kef f remains higher than unity at EOEC state for all
cases thanks to 20% Pu concentration in fuel matrix in order to achieve the selfsustainability required for Gen-IV systems as stated above; 3. kef f swing for cases
with higher Am content are smaller than cases with lower Am content thanks to the
transmutation of 241 Am via 242 Cm to 238 Pu and breeding of 244 Cm from 243 Am.
5.1.6
Safety parameters of the suggested ADS design
Comparing to the reference EFIT-400 designs, the most important impact incurred
by the pin pitch reduction from 1.35 cm to 1.20 cm is reported to be a ≈50% decrease
for coolant void worth as shown in Table 5.1, thanks to the smaller volumetric
fraction of coolant. Since Am is the major contributor to positive coolant void
worth, the coolant void worth decreases by around 10% during burnup due to the
consumption of Am.
5.2
5.2.1
Effects on thermophysical properties
Thermal conductivity
Oxides Fuel
AmO2 and Am2 O3 are the most stable americium oxides, having Face Centered
Cubic (FCC) and Hexagonal Closed Packing (HCP)/Body Centered Cubic (BCC)
crystal structures respectively [68]. The molar ratio between these two oxides is
affected by temperature and oxygen potential, determining the stoichiometry deviation of oxygen (x) in AmO2−x .
38
CHAPTER 5. EFFECTS FROM THE INTRODUCTION OF AMERICIUM
8
UOX
Thermal Conductivity (W/m/K)
MOX, 1.95 O/M
MOX, 2.00 O/M
7
MOX, 28 at% Pu
MOX, 3 at% Am
6
AmO
2
5
4
3
2
1
0
500
1000
1500
2000
2500
3000
Temperature (K)
Figure 5.5. Thermal conductivities of actinide oxides
Thermal conductivities of different oxides are compared in Fig. 5.5, from which
it can be noticed that:
• Thermal conductivity of AmO2 [70] is more than 50% lower than that of UO2
[72].
• If the stoichiometry deviation of oxygen was set at 0, the introduction of less
than 28 at.% Pu or less than 3 at% Am gives negligible impact on thermal
conductivity of UO2 [74] [75] [76] [72] [77].
• Thermal conductivities of actinide oxides are more sensitive to the stoichiometry deviation of oxygen. This effect can be expressed using correlation 5.2,
in which x stands for the stoichiometry deviation of oxygen, being set at 0.05
for the MOX fuel investigated in Paper I, and t is equal to T/1000 [74].
kM OX
A = 2.85x + 0.035
C = −0.715x + 0.286
−16.35/t
= 1.158(A + Ct)−1 + 6400 e t5/2
(5.2)
Four phenomena were suggested to be considered in order to estimate the burnup
effects on thermal conductivity of UO2 [73], which were assumed to be valid for fuels
in this thesis study:
• Dissolution and precipitation of solid fission products (κd )
5.2. EFFECTS ON THERMOPHYSICAL PROPERTIES
39
• Fission gas bubbles and pores (κp )
• Stoichiometric deviation (κx )
• Radiation damage induced circumferential cracks (κr )
κd and κp are dependent on the burnup and could be expressed into Eq. 5.3
and Eq. 5.4, in which T is in Kelvin and B is in at%.
ω = 1.09 B 3.265 + 0.0643(T /B)1/2
κd = ω[arctan(1/ω)]
κp = 1 +
0.019B
(3 − 0.019B)[1 + e−(T −1200)/100 ]
(5.3)
(5.4)
Nitride fuel
Correlations for thermal conductivities of different actinide nitrides were provided by
Arai [78] [79], Basini [83] and Nishi [81] as shown in Fig. 5.6. It can be noticed that
thermal conductivities of UN, NpN and PuN are around 150%, 60% and 30% higher
than that of AmN. Besides, as a chemical stablizer with high thermal conductivity,
the introduction of 75 at% ZrN may increase the thermal conductivity of (Pu,Zr)N
by more than 80%. Thus, thermal conductivity of (Ac,Zr)N can be simply calculated
based on Eq. 5.5, in which c and k stand for atomic fractions of actinides in fuel
and thermal conductivities of different actinide nitrides.
k(N p, P u, Am, Zr)N
= c(N p)k(N pN ) + c(P u)k(P uN )
+ c(Am)k(AmN ) + c(Zr)k(ZrN )
(5.5)
In order to estimate the burn up effect on thermal conductivity of nitride fuel,
porosity build up was considered [82] by introducing Maxwell-Eucken correction
as expressed in Eq. 5.6, in which P is porosity and β equals 2.00 for (Pu,Zr)N
[83]. Irradiation swelling rate of UN can be calculated based on Eq. 5.7, in which
Tf uel,ave , Bu and ρ stand for the average fuel temperature in Kelvin, the fuel burnup
in at.% and the as-fabricated fuel density in % theoritical density (TD) respectively
[84]. This correlation is proved to be valid for (U,Pu)N based on results obtained
from irradiation experiments performed in JOYO [85]. Thus, it is also assumed to
be valid for fuel discussed in Paper II.
k = k0
1−P
1 + Pβ
0.83 0.5
∆V /V (%) = 4.7 × 10−11 Tf3.12
ρ
uel,ave Bu
(5.6)
(5.7)
40
CHAPTER 5. EFFECTS FROM THE INTRODUCTION OF AMERICIUM
40
Thermal Conductivity (W/m/K)
35
30
25
20
UN
PuN
15
ZrN
(Pu0.25Zr0.75)N
AmN
10
NpN
400
800
1200
1600
2000
2400
2800
Temperature (K)
Figure 5.6. Thermal conductivity of actinide nitrides
5.2.2
Fuel melting point
Oxide fuel
For simulations performed in Paper I, fuel failure starts when solidus temperature
of fuel was offset. Solidus and liquidus temperatures of oxide fuel can be calculated
by applying Vegard’s law [86] as:
Tsol = TU O2 cU + TP uO2 cP u + TAmO2 cAm + Csol
Tliq = TU O2 cU + TP uO2 cP u + TAmO2 cAm + Cliq
(5.8)
, in which c stands for atomic fractions of different elements. TU O2 , TP uO2 and
TAmO2 stand for melting points of UO2 , PuO2 and AmO2 , equalling 3120 K, 2663
K and 2783 K respectively [87]. Csol and Cliq are the corrections for solidus and
liquidus temperatures, which can be obtained with:
Csol = −121cU cP u − 340b − 1000|x|
Cliq = 129cU cP u − 340b − 300|x|
(5.9)
, in which cU , cP u , b, |x| stand for atomic fraction of U, atomic fraction of Pu,
fuel burnup, absolute value of the stoichiometric deviation respectively.
Nitride fuel
Since dissociation temperatures of UN, PuN, NpN and AmN are much lower than
their corresponding congruent melting temperatures if partial pressure of nitrogen is
5.2. EFFECTS ON THERMOPHYSICAL PROPERTIES
41
130
UO
2
120
(U
Pu
0.75
)O
0.25
1.98
PuO
Heat Capacity (J/mol/K)
2
110
AmO
2
100
90
80
70
600
800
1000 1200 1400 1600 1800 2000 2200 2400
Temperature (K)
Figure 5.7. Heat capacities of actinide oxides, [72], [88], [89]
less than 0.15 MPa, failure point of (Pu,Am,Zr)N is assumed to be the temperature
when 0.01% AmN dissociates into metallic Am and nitrogen gas, concerning the relocation of Am in liquid phase. Based on the calculation results from the Thermo-Calc
code applying ALCHYMY database, failure point of (Pu0.2 Am0.3 Zr0.5 )N compound
in a small volume, such as an intact fuel cladding, is equal to 2400 K [71]. Burn up
effect on failure point of nitride fuel was neglected.
5.2.3
Heat capacity
Since differences between heat capacities of different actinide oxides, as well as
actinide nitrides, are negligibly small up to 2500 K as shown in Fig. 5.8 and 5.7,
heat capacities of the modified MOX fuel loaded into BN600 and the U-free nitride
fuel loaded into the suggested ADS can simply be represented by heat capacities of
MOX fuel containing 25 at.% Pu and PuN respectively.
CHAPTER 5. EFFECTS FROM THE INTRODUCTION OF AMERICIUM
70
65
Heat Capacity (J/mol/K)
42
60
55
UN
50
(U
,Pu
0.80
)N
0.20
PuN
45
200
AmN
400
600
800
1000
1200
1400
1600
1800
Temperature (K)
Figure 5.8. Heat capacities of actinide nitrides, [90], [91], [70]
Chapter 6
Transient simulation results and
discussion
6.1
Summary of transient simulation results
In Paper I and II, safety analysis was performed for BN600 loaded with MOX fuel
modified by different fractions of Am, as well as for the suggested ADS design loaded
with nitride fuel, by applying the SAS4A/SASSYS code. Coolant boiling, cladding
rupture and fuel melting were considered as design limits to terminate transient
simulations.
Figure 6.1. Cladding inner surface temperature for ULOF (left) and UTOP (right)
transients, Pmax =37 kW/m
As shown in Fig. 6.1 and 6.2, for a BN600 type fast reactor, the highest cladding
and coolant temperatures that can be reached during, UTOP, the most limiting
transient, are 50 K and 60 K lower than the working limit of 15-15Ti stainless steel
43
44
CHAPTER 6. TRANSIENT SIMULATION RESULTS AND DISCUSSION
Figure 6.2. Coolant temperature at core outlet for ULOF (left) and UTOP (right)
transients, Pmax =37 kW/m
Figure 6.3. Fuel hot spot temperature at BOL (L) and EOEC (R) states, Pmax =37
kW/m
(1200 K for a Hoop stress loading of 120 MPa) and the boiling point of sodium
(1160 K at 1 atm) respectively, thanks to negative reactivity mainly incurred by
structure radial expansion.
As can be noticed from Fig. 6.4, the Doppler effect is the major contributor of
nagative reactivity feedbacks during the UTOP transient. Since the increase of Am
content from 1.0 wt.% (equivalent to the reference MOX fuel) to 5.0 wt.% leads to
an around 50 % decrease in the Doppler constant as shown in Fig. 5.2, asymptotic
temperatures at fuel column hot spot increase by approximately 300 K as shown
6.2. AM TRANSMUTATION CAPABILITIES
45
Figure 6.4. Reactivity feedbacks of BN600 with 5.0 wt.% Am at BOL during ULOF
(right) and UTOP (left) transients
in Fig. 6.3, providing an adequate negative reactivity response to counterbalance
the positive reactivity insertion. Preserving a 100 K margin to fuel melting, the
maximum allowable linear power rating of a fast reactor of the present design is 37
kW/m. If Am concentration is increased from 1.0 wt.% to 2.0 wt.%, the core power
should be reduced by 6%, in order to maintain the same margin to fuel failure.
In Paper II, safety analysis of the suggested ADS design with 1.20 cm pin pitch
was performed. Maximum fuel and coolant temperatures that were reached during
the postulated transients are 1727 K and 1122 K, preserving around 700 K margin
to fuel failure and 900 K margin to coolant boiling respectively. The cladding’s
asymptotic temperature during transients is limited to less than 1070 K, preserving
more than 130 K margin to pin cladding burst. Thus, this ADS design could be
confirmed to survive the full transients.
The cladding hot spot temperature during normal operating condition is equal
to 789 K, preserving approximately 40 K margin to rupture limit in terms of thermal
creep, irradiation damage and HLM corrosion.
The reactor vessel’s asymptotic temperature during transients is limited to less
than 690 K, which is approximately 30 K lower than the reported creep limit of the
reactor vessel, under which the reactor vessel integrity can be assured [92].
6.2
Am transmutation capabilities
As discussed in Paper I, for a medium sized BN600 type fast reactor, 6.0 wt.% Am
content could be permitted, giving a 8.4 kg/TWhth consumption rate of Am, at
46
CHAPTER 6. TRANSIENT SIMULATION RESULTS AND DISCUSSION
Table 6.1. Transient simulation results for the suggested ADS design
Transient
BOC
max
Tfuel [K]
Tmax
clad [K]
Tfinal
clad [K]
max
TLBE [K]
Normalized Pfinal
∆ρmax
net [$]
Normalized ṁfinal
EOC
max
Tfuel [K]
Tmax
clad [K]
final
Tclad [K]
Tmax
LBE [K]
Normalized Pfinal
∆ρmax
net [$]
Normalized ṁfinal
ULOF
UTOP
PLOHS
1727
1145
1068
1118
0.97
-0.83
0.44
1507
900
900
859
1.42
6.29
1.02
1109
851
823
850
0.06
0.75
0.09
1497
1149
1069
1122
0.98
-0.75
0.44
1121
898
898
857
1.41
6.00
1.02
864
856
823
856
0.06
1.02
0.09
the cost of a power penalty of 30%. The 30% power penalty may lead to a 40%
increase of the capital cost per unit power rating. For the suggested ADS having 43
kg/TWhth consumption rate of Am, the capital cost per unit power rating will also
be increased by approximately 40% due to the implementation of the proton beam
[93]. Thus, for comparable cost penalties, the consumption rate of Am in this ADS
is still around five times higher than in a sodium cooled BN600 type fast reactor.
Since the Am generation rate of one 1000 MWe (3400 MWth ) grade LWR was
reported to be 0.55 kg/TWhth after 60 MWd/kgHM burnup and 10-year cooling
[94], one BN600 type SFR operating with the power rating of 1000 MWth , providing a consumption rate of Am equalling 1.7 kg/TWhth , is sufficient to transmute
the Am inventory generated by one 1000 MWe grade LWRs in the same time
period. If the core power rating was reduced by 30%, permitting 6.0 wt.% Am
content, one BN600 type SFR is sufficient to transmute the Am inventory generated by three 1000 MWe grade LWRs in the same time period. In comparison,
one nitride fuelled ADS in the suggested design is sufficient to transmute the
Am inventory generated by five 1000 MWe grade LWRs in the same time period.
Chapter 7
Conclusions
The upper limit to the amount of Am that can be loaded into a medium sized sodium
cooled fast reactor was once reported as 2-3%. However, after performing transient
analysis with the SAS4A/SASSYS code for BN600 fully loaded with MOX fuel, no
solid limit was found. Instead, we could show that a 6% power penalty is required
when Am content was raised from 1% to 2%. If linear power rating could be further
reduced, it is feasible introduce more Am, permitting a higher Am transmutation
rate.
Based on safety performance evaluations made with the SAS4A/SASSYS code,
the suggested ADS design with 1.20 cm pin pitch, providing a MA transmutation
rate of 42 kg/TWhth , could survive the full set of transients, thanks to switching the
cladding material from the reference T91 stainless steel to the austenitic 15/15Ti
stainless steel.
One nitride fuelled ADS with the power rating of 201 MWth and the consumption rate of Am equalling 43 kg/TWhth is sufficient to transmute the Am inventory
generated by five 1000 MWe grade LWRs within the same operating time. In
comparison with the suggested ADS design, the BN600 type SFR with the same
cost penalty can only transmute the Am inventory generated by three 1000 MWe
grade LWRs within the same operating time. Therefore, it can be demostrated that
the suggested ADS design is still more efficient for transmuting Am comparing to
medium sized sodium-cooled fast reactors fully loaded with MOX fuel.
47
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1970.
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Carlo Method, In Proc. XII Meeting on Reactor Physics in the Nordic Countries, Halden, 2005.
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accelerator driven transmuter and considerations for further developments, Energy Conversion and Management, Article in Press, 2010.
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[61] W. Maschek et al., Accelerator driven systems for transmutation: Fuel development, design and safety, Progress in Nuclear Energy, 50(2-6): 333-340, 2008.
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Proc. Int. Conf. GLOBAL 2005.
[66] Youpeng Zhang and Janne Wallenius, Transmutation of americium in a
medium size sodium cooled fast reactor design, Annals of Nuclear Energy, 2010.
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Tables, 6(2): 141-151, 1969.
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Materials, 279(1): 1-18, 2000.
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(U,Pu)O2−x mixed oxide, Journal of Nuclear Materials, 277(2-3): 143-158,
2000.
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light water reactors, 37: 924-933, 2000.
Appendix A
SERPENT inputs
A.1
BN600 type sodium cooled fast reactor
pin 1
fuel 0.295 % fuel pellet outer radius
void 0.305 % cladding inner radius
clad 0.345 % cladding outer radius
sodium % coolant outside of clad
%void
pin 2 % gas plenum
void 0.305
clad 0.345
sodium
%void
pin 12
clad 0.345
sodium
pin 5
clad 0.600
sodium
surf
surf
surf
surf
surf
surf
surf
4000 hexyc 0.0 0.0 0.40365
401 pz -226 % lower nozzel
402 pz -152 % gas plenum
403 pz -86.5 % lower blanket
404 pz -51.5 % lower active zone
405 pz 51.5 % upper active zone
406 pz 81.5 % upper blanket
57
58
APPENDIX A. SERPENT INPUTS
surf 407 pz 124 % head
cell
cell
cell
cell
cell
cell
400
401
402
403
405
406
400
400
400
400
400
400
fill 1 -4000 404 -405 % hexagonal lattice
sodium -4000 401 -402 % nozzel
fill 2 -4000 402 -403 % gas plenum
fill 12 -4000 403 -404 % lower blanket
fill 12 -4000 405 -406 % upper blanket
sodium -4000 406 -407 % head
%cell 407 400 void 4000 404 -405
cell 407 400 sodium 4000 404 -405
cell 408 400 sodium -401
cell 409 400 sodium 407
cell 410 400 sodium 4000 -404 401
cell 411 400 sodium 4000 405 -407
lat 110 3 0.0 0.0 15 15 0.8073
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 5 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 % Fuel
% Geometry
surf
surf
surf
surf
surf
surf
1000 hexxc 0.0 0.0 4.544425 % hexagonal lattice surface ( P/D = 1.17 )
1001 hexxc 0.0 0.0 4.800000
2 pz -226
3 pz -51.5
4 pz 51.5
7 pz 124
cell 100 100 fill 110 -1000 2 -7 % hexagonal lattice
A.1. BN600 TYPE SODIUM COOLED FAST REACTOR
59
cell 101 100 clad 1000 -1001 2 -7
%cell 102 100 void 1001 3 -4
cell 102 100 sodium 1001 3 -4
cell 103 100 sodium 1001 4 -7
cell 104 100 sodium 1001 2 -3
cell 105 100 sodium -2
cell 106 100 sodium 7
surf 2000 hexxc 0.0 0.0 4.80000
cell 200 200 clad -1001 2 -7
cell 201 200 sodium 1001 2 -7
cell 202 200 sodium -2
cell 203 200 sodium 7
cell
cell
cell
cell
901
902
903
904
900
900
900
900
sodium
sodium
sodium
sodium
-1001 2 -7
1001 2 -7
-2
7
lat 300 2 0.0 0.0 27 27 9.9
200 200 200 200 200 200 200 200 200
200 200 200 200 200 200 200
200 200 200 200 200 200 200 200 200
200 200 200 200 200 200 200
200 200 200 200 200 200 200 200 200
100 100 100 100 200 200 200 200 200
100 100 100 100 100 100 100 100 100
200 200 200 200 200 100 100 100 100
200 200 200 200 200 200 200 200 200
900 100 100 100 100 100 200 200 200
100 100 100 100 100 100 100 100 100
200 200 200 100 100 100 900 100 100
200 200 200 200 200 200 200 200 200
100 100 100 100 100 100 100 200 200
100 100 900 100 100 100 900 100 100
200 100 100 100 100 100 900 100 100
100 200 200 200 200 200 200 100 100
100 100 100 100 900 100 100 100 200
100 100 100 100 100 100 100 100 100
100 100 100 100 100 100 900 100 100
100 200 200 200 % hex mid
200 200 100 100 100 100 100 100 100
100 100 100 100 200 200 200 % 11
200 200 100 100 100 900 100 100 100
200 200 200 200 200 200 200 200 200 200 200
200 200 200 200 200 200 200 200 200 200 200
200
200
100
100
200
200
100
100
100
200
100
100
100
200
100
100
200
200
100
100
200
200
100
100
100
200
100
100
900
200
100
900
200
200
100
100
100
200
100
900
100
200
100
100
100
200
100
100
200
200
200
100
100
200
100
100
100
200
100
100
100
200
100
100
200
200
200
100
100
200
200
100
100
200
100
100
100
100
100
100
100
200
200
100
100
200
200
100
100
200
200
100
100
100
100
900
100
200
200
100
100
200
200
100
100
100
200
900
100
100
200
100
100
200
200
100
900
200
200
900
100
100
200
100
100
100
200
100
100
200
200
100
100
100
200
100
100
100
200
100
100
100
200
100
100
200
200
100
100
100
200
100
100
100
200
100
100
100
200
100
100
100
200
200
100
100
200
100
100
100
200
100
100
100
200
100
100 100 100 100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100 100 100 900
60
APPENDIX A. SERPENT INPUTS
100
200
100
200
100
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
100
200
100
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
100
100
200
100
200
100
200
100
200
100
200
100
200
100
200
100
200
200
200
200
200
200
200
surf
surf
surf
surf
surf
surf
surf
surf
surf
3000
3001
3010
3002
3003
3004
3005
3008
3009
hexyc 0.0 0.0 98.59699
hexyc 0.0 0.0 148.09699
hexyc 0.0 0.0 157.99699
cyl 0.0 0.0 207.0000
cyl 0.0 0.0 210.0000
pz -226
pz 124
pz -426
pz 324
cell
cell
cell
cell
cell
cell
cell
cell
cell
cell
300
301
302
303
304
305
306
308
309
310
fill 300 -3000 3004 -3005
clad 3000 -3001 3004 -3005
BC4 3001 -3010 3004 -3005
sodium 3010 -3002 3004 -3005
clad 3002 -3003 3004 -3005
clad -3003 -3004 3008
clad -3003 3005 -3009
outside -3008
outside 3009
outside 3003 3008 -3009
0
0
0
0
0
0
0
0
0
0
200
100
200
100
200
100
200
100
200
100
200
100
200
100
200
100
200
100
200
200
200
200
200
200
100
200
100
200
100
200
100
200
100
200
100
200
100
200
100
200
100
200
200
200
200
200
200 200 % 10
100 100 900 100
200 200 % 9
100 100 100 100
200 200 % 8
100 100 100 100
200 200 % 7
900 100 100 100
200 200 % 6
100 100 100 100
200 200 % 5
100 100 900 100
200 200 % 4
100 100 100 100
200 200 % 3
100 100 100 100
200 200 % 2
100 100 100 100
200 200 % 1
200 200 200 200
200 200 %
200 200 200 200
200 200 %
100 100 100 100 100 100 100 900 100 100 100
900 100 100 100 900 100 100 100 100 100 100
100 100 100 100 100 100 100 100 100 100 100
100 900 100 100 100 100 900 100 100 100 200
100 100 100 100 100 100 100 100 100 200 200
100 100 900 100 100 100 100 100 200 200 200
100 100 100 100 100 100 100 200 200 200 200
100 100 100 100 100 100 200 200 200 200 200
100 100 100 100 200 200 200 200 200 200 200
200 200 200 200 200 200 200 200 200 200 200
200 200 200 200 200 200 200 200 200 200 200
A.1. BN600 TYPE SODIUM COOLED FAST REACTOR
mat fuel -9.8500 % Oxide fuel with 10 percent porosity
92238.15c 0.8000 % 80 percent U-238
94238.15c 0.0070 %
94239.15c 0.1038 %
94240.15c 0.0476 % Pu vector from spent LWR fuel
94241.15c 0.0258 %
94242.15c 0.0158 %
95241.15c 0.0000 % 0.0 precent Am vector
95243.15c 0.0000 %
8016.15c 2.0000 % Two oxygen atoms per metal atom
mat clad -7.76 % Steel cladding density
6012.09c -0.060e-2
7014.09c -1.300e-4
14028.09c -1.300e-2
14029.09c -0.060e-2
14030.09c -0.036e-2
22046.09c -0.024e-2
22047.09c -0.022e-2
22048.09c -0.221e-2
22049.09c -0.016e-2
22050.09c -0.015e-2
23051.09c -0.150e-2
24050.09c -0.691e-2
24052.09c -13.32e-2
24053.09c -1.511e-2
24054.09c -0.376e-2
25055.09c -1.600e-2
26056.09c -63.85e-2
28058.09c -9.871e-2
28060.09c -3.802e-2
28061.09c -0.165e-2
28062.09c -0.527e-2
28064.09c -0.134e-2
29063.09c -0.021e-2
29065.09c -0.009e-2
42092.09c -0.326e-2
42094.09c -0.204e-2
42095.09c -0.350e-2
42096.09c -0.367e-2
42097.09c -0.210e-2
42098.09c -0.531e-2
42100.09c -0.212e-2
61
62
APPENDIX A. SERPENT INPUTS
% Coolant
mat sodium -0.74
11023.09c 1.0
% Gas
mat He -5e-5
2004.09c 1.0
%BC4, reflector
mat BC4 -2.52
5010.09c 0.20
5011.09c 0.80
6012.09c 2.00
set acelib "jeff31.xsdata"
set bc 1
set pop 4000 4000 30
set powdens 80.352E-3 %
set egrid 1e-4 % Cross section grid thinning (to reduce memory requirement)
set declib "../Documents/Serpent1.1.0/xsdata/jeff31/JEFF311RDD"
set nfylib "../Documents/Serpent1.1.0/xsdata/jeff31/JEFF31NFY"
set fpcut 1E-6
set stabcut 1E-12
set ttacut 1E-18
set xsfcut 1E-6
% — Options for burnup calculation:
set bumode 1 % TTA method
set pcc 1 % Predictor-corrector calculation on
set xscalc 2 % Cross sections from spectrum
A.2. THE COMPACT ADS LOADED WITH NITRIDE FUEL
set printm 1 % No mater
plot 1 10000 10000
plot 3 10000 10000
A.2
The compact ADS loaded with nitride fuel
pin 1
fuel1 0.400 % fuel pellet outer radius
gas 0.416 % cladding inner radius
clad 0.476 % cladding outer radius
LBE % coolant outside of clad
%void
pin 21
fuel2 0.400 % fuel pellet outer radius
gas 0.416 % cladding inner radius
clad 0.476 % cladding outer radius
LBE % coolant outside of clad
pin 31
fuel3 0.400 % fuel pellet outer radius
gas 0.416 % cladding inner radius
clad 0.476 % cladding outer radius
LBE % coolant outside of clad
pin 2 % gas plenum
gas 0.416
clad 0.476
LBE
%void
pin 12
clad 0.476
LBE
pin 3 % LBE below and above core
LBE
%void
pin 6
63
64
APPENDIX A. SERPENT INPUTS
clad 0.600
LBE
surf
surf
surf
surf
surf
surf
surf
surf
surf
surf
surf
4000 hexyc 0.0 0.0 0.6000
401 pz -257 % lower plenum
402 pz -135 % lower plug
403 pz -131 % gas plenum
404 pz -46.5 % insulator
405 pz -45.0 % lower active zone
406 pz 45.0 % upper active zone
407 pz 46.5 % insulator
408 pz 73.0 % spring chamber
409 pz 75.0 % top plug
410 pz 151 % upper plenum
cell
cell
cell
cell
cell
cell
cell
cell
cell
400
401
402
403
405
406
407
408
410
400
400
400
400
400
400
400
400
400
fill 1 -4000 405 -406 % hexagonal lattice
fill 12 -4000 404 -405 % insulator
fill 2 -4000 403 -404 % gas plenum
fill 12 -4000 402 -403 % lower plug
dum -4000 401 -402 % lower plenum
fill 12 -4000 406 -407 % insulator
fill 2 -4000 407 -408 % spring chamber
fill 12 -4000 408 -409 % top plug
dum -4000 409 -410 % upper plenum
cell
cell
cell
cell
cell
411
412
413
414
415
400
400
400
400
400
dum
dum
dum
dum
dum
cell
cell
cell
cell
cell
cell
cell
cell
cell
420
421
422
423
425
426
427
428
430
410
410
410
410
410
410
410
410
410
fill 21 -4000 405 -406 % hexagonal lattice
fill 12 -4000 404 -405 % insulator
fill 2 -4000 403 -404 % gas plenum
fill 12 -4000 402 -403 % lower plug
dum -4000 401 -402 % lower plenum
fill 12 -4000 406 -407 % insulator
fill 2 -4000 407 -408 % spring chamber
fill 12 -4000 408 -409 % top plug
dum -4000 409 -410 % upper plenum
4000 405 -406
4000 401 -405
4000 406 -410
-401
410
cell 431 410 dum 4000 405 -406
cell 432 410 dum 4000 401 -405
cell 433 410 dum 4000 406 -410
A.2. THE COMPACT ADS LOADED WITH NITRIDE FUEL
65
cell 434 410 dum -401
cell 435 410 dum 410
cell
cell
cell
cell
cell
cell
cell
cell
cell
440
441
442
443
445
446
447
448
450
420
420
420
420
420
420
420
420
420
fill 31 -4000 405 -406 % hexagonal lattice
fill 12 -4000 404 -405 % insulator
fill 2 -4000 403 -404 % gas plenum
fill 12 -4000 402 -403 % lower plug
dum -4000 401 -402 % lower plenum
fill 12 -4000 406 -407 % insulator
fill 2 -4000 407 -408 % spring chamber
fill 12 -4000 408 -409 % top plug
dum -4000 409 -410 % upper plenum
%cell 451 420 void 4000 405 -406
cell 451 420 dum 4000 405 -406
cell 452 420 dum 4000 401 -405
cell 453 420 dum 4000 406 -410
cell 454 420 dum -401
cell 455 420 dum 410
lat 110 3 0.0 0.0 19 19 1.20
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 6 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 %Fuel 1
lat 120 3 0.0 0.0 19 19 1.20
410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410
410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410
66
APPENDIX A. SERPENT INPUTS
410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410
410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410
410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410
410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410
410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410
410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410
410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410
410 410 410 410 410 410 410 410 410 6 410 410 410 410 410 410 410 410 410
410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410
410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410
410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410
410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410
410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410
410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410
410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410
410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410
410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 410 %Fuel 2
lat 130 3 0.0 0.0 19 19 1.20
420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420
420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420
420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420
420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420
420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420
420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420
420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420
420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420
420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420
420 420 420 420 420 420 420 420 420 6 420 420 420 420 420 420 420 420 420
420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420
420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420
420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420
420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420
420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420
420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420
420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420
420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420
420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 420 %Fuel 3
% Geometry
surf 2100 hexxc 0.0 0.0 8.900 % hexagonal lattice surface
surf 2103 hexxc 0.0 0.0 9.300
surf 2101 pz -257
A.2. THE COMPACT ADS LOADED WITH NITRIDE FUEL
surf 2102 pz 151
cell
cell
cell
cell
cell
100
106
103
104
105
170
170
170
170
170
surf
surf
surf
surf
2200
2203
2201
2202
cell
cell
cell
cell
cell
120
126
123
124
125
surf
surf
surf
surf
2300
2303
2301
2302
cell
cell
cell
cell
cell
130
136
133
134
135
fill 110 -2100 2101 -2102
clad 2100 -2103 2101 -2102
dum 2103 2101 -2102
dum -2101
dum 2102
hexxc 0.0 0.0 8.900 % hexagonal lattice surface
hexxc 0.0 0.0 9.300
pz -257
pz 151
180
180
180
180
180
fill 120 -2200 2201 -2202
clad 2200 -2203 2201 -2202
dum 2203 2201 -2202
dum -2201
dum 2202
hexxc 0.0 0.0 8.900 % hexagonal lattice surface
hexxc 0.0 0.0 9.300
pz -257
pz 151
190
190
190
190
190
fill 130 -2300 2301 -2302
clad 2300 -2303 2301 -2302
dum 2303 2301 -2302
dum -2301
dum 2302
surf 2000 hexxc 0.0 0.0 9.300
cell 201 200 dum -2000
cell 202 200 dum 2000
surf 1000 hexxc 0.0 0.0 9.300
cell 901 900 Pb -1000
cell 902 900 Pb 1000
lat 300 2 0.0 0.0 13 13 19.1
200 200 200 200 200 200 200
200 200 200 200 200 200 200
200 200 200 200 200 190 180
200 200 200 200 190 180 180
200
190
180
180
200
190
180
180
200
190
180
180
200
190
180
180
200
200
190
190
200
200 % 1
200 % 2
200 % 3
67
68
APPENDIX A. SERPENT INPUTS
200
200
200
200
200
200
200
200
200
200
200
200
190
190
190
190
200
200
200
190
180
180
180
180
180
190
200
surf
surf
surf
surf
surf
surf
surf
surf
3000
3001
3002
3003
3004
3007
3005
3006
hexyc 0.0 0.0 90.976
hexyc 0.0 0.0 145.0
hexyc 0.0 0.0 198.0
hexyc 0.0 0.0 230.4
cyl 0.0 0.0 250.0000
cyl 0.0 0.0 280.0000
pz -257
pz 151
cell
cell
cell
cell
cell
cell
cell
cell
cell
300
301
302
303
304
305
308
309
310
fill 300 -3000 3005 -3006
dum 3000 -3001 3005 -3006
dum 3001 -3002 3005 -3006
dum 3002 -3003 3005 -3006
dum 3003 -3004 3005 -3006
dum 3004 -3007 3005 -3006
outside 3007 3005 -3006
outside -3005
outside 3006
0
0
0
0
0
0
0
0
0
190
180
180
180
180
180
180
190
200
180
180
170
170
170
180
180
190
200
180
170
900
900
170
180
180
190
200
170
900
900
900
170
180
180
200
200
170
900
900
170
180
180
190
200
200
170
170
170
180
180
190
200
200
200
mat fuel1 -7.7574802237749 % zone 1
94238.12c 0.0017820249237
94239.12c 0.0221474927079
94240.12c 0.0162706395411
94241.12c 0.0018333336609
94242.12c 0.00565063695
94244.12c 5.722164E-7
93237.12c 0.0024058147932
95241.12c 0.0467674689006
95342.12c 0.0001571298561
95243.12c 0.0099434027385
96243.12c 4.10011686E-5
96244.12c 0.0018589880295
96245.12c 0.0007055669376
96246.12c 5.48127405E-5
180
180
180
180
190
200
200
200
200
180
180
180
190
200
200
200
200
200
190
190
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
%
%
%
%
%
%
%
%
4
5
6, mid
5
4
3
2
1
A.2. THE COMPACT ADS LOADED WITH NITRIDE FUEL
96247.12c 1.0529001E-6
96248.12c 6.19353E-8
7015.12c 0.5
40090.12c 0.20085051
40091.12c 0.043800636
40092.12c 0.06695017
40094.12c 0.067848044
40096.12c 0.01093064
mat fuel2 -8.0235247898826 % zone 2
94238.12c 0.0021214582425
94239.12c 0.0263660627475
94240.12c 0.0193698089775
94241.12c 0.0021825400725
94242.12c 0.00672694875
94244.12c 6.8121E-7
93237.12c 0.00286406523
95241.12c 0.055675558215
95342.12c 0.0001870593525
95243.12c 0.0118373842125
96243.12c 4.8810915E-5
96244.12c 0.0022130809875
96245.12c 0.00083996064
96246.12c 6.52532625E-5
96247.12c 1.2534525E-6
96248.12c 7.37325E-8
7015.12c 0.5
40090.12c 0.19010775
40091.12c 0.0414579
40092.12c 0.06336925
40094.12c 0.0642191
40096.12c 0.010346
mat IHX -10.19
5010.09c 2.5456014873332E-7
5011.09c 1.0246365785698E-6
6000.09c 0.0023049941029031
14028.09c 0.0054507790547269
14029.09c 0.00027599629389108
14030.09c 0.00018320953127674
15031.09c 0.00026999930923377
22046.09c 0.00019057451243417
22047.09c 0.00017186356030427
22048.09c 0.0017029276432299
69
70
22049.09c
22050.09c
24050.09c
24052.09c
24053.09c
24054.09c
25055.09c
28058.09c
28060.09c
28061.09c
28062.09c
28064.09c
42092.09c
42094.09c
42095.09c
42096.09c
42097.09c
42098.09c
42100.09c
26054.09c
26056.09c
26057.09c
26058.09c
82204.09c
82206.09c
82207.09c
82208.09c
83209.09c
APPENDIX A. SERPENT INPUTS
0.00012497068027501
0.00011965769386776
0.0034668666303684
0.066855072057984
0.0075808285052084
0.0018870286722258
0.0075499806841294
0.048120104339525
0.018535680128316
0.00080580693842353
0.0025686863282729
0.00065454142542122
0.00051346268635706
0.00032004918118617
0.00055083059075502
0.0005771265234795
0.00033042915463005
0.00083489586400242
0.00033319714754842
0.019155184993375
0.30069543950079
0.0069443690335263
0.0009241680356085
0.00312928
0.05386832
0.04939792
0.11712448
0.27648
mat fuel3 -8.506510266008 % zone 3
94238.12c 0.00275789571525
94239.12c 0.03427588157175
94240.12c 0.02518075167075
94241.12c 0.00283730209425
94242.12c 0.008745033375
94244.12c 8.85573E-7
93237.12c 0.003723284799
95241.12c 0.0723782256795
95342.12c 0.00024317715825
95243.12c 0.01538859947625
96243.12c 6.34541895E-5
96244.12c 0.00287700528375
96245.12c 0.001091948832
96246.12c 8.482924125E-5
A.2. THE COMPACT ADS LOADED WITH NITRIDE FUEL
96247.12c 1.62948825E-6
96248.12c 9.585225E-8
7015.12c 0.5
40090.12c 0.169965075
40091.12c 0.03706527
40092.12c 0.056655025
40094.12c 0.05741483
40096.12c 0.0092498
mat clad -7.76 % Steel cladding density
5010.09c 5.0912029746663E-7
5011.09c 2.0492731571396E-6
6000.09c 0.0046099882058062
14028.09c 0.010901558109454
14029.09c 0.00055199258778216
14030.09c 0.00036641906255347
15031.09c 0.00053999861846753
22046.09c 0.00038114902486833
22047.09c 0.00034372712060853
22048.09c 0.0034058552864598
22049.09c 0.00024994136055002
22050.09c 0.00023931538773551
24050.09c 0.0069337332607368
24052.09c 0.13371014411597
24053.09c 0.015161657010417
24054.09c 0.0037740573444517
25055.09c 0.015099961368259
28058.09c 0.09624020867905
28060.09c 0.037071360256632
28061.09c 0.0016116138768471
28062.09c 0.0051373726565458
28064.09c 0.0013090828508424
42092.09c 0.0010269253727141
42094.09c 0.00064009836237235
42095.09c 0.00110166118151
42096.09c 0.001154253046959
42097.09c 0.0006608583092601
42098.09c 0.0016697917280048
42100.09c 0.00066639429509684
26054.09c 0.038310369986749
26056.09c 0.60139087900158
26057.09c 0.013888738067053
26058.09c 0.001848336071217
71
72
% Coolant
%LBE 673K, Pb44.5Bi55.5
mat LBE -10.19
82204.06c 0.00625856
82206.06c 0.10773664
82207.06c 0.09879584
82208.06c 0.23424896
83209.06c 0.55296
%dum, reflector
mat dum -9.50
5010.06c 3.5638420822664E-8
5011.06c 1.4344912099977E-7
15031.06c 3.7799903292727E-5
22046.06c 2.6680431740783E-5
22047.06c 2.4060898442597E-5
22048.06c 0.00023840987005219
22049.06c 1.7495895238502E-5
22050.06c 1.6752077141486E-5
24050.06c 0.00048536132825158
24052.06c 0.0093597100881177
24053.06c 0.0010613159907292
24054.06c 0.00026418401411162
25055.06c 0.0010569972957781
28058.06c 0.0067368146075335
28060.06c 0.0025949952179642
28061.06c 0.00011281297137929
28062.06c 0.00035961608595821
26054.06c 0.0026817258990725
26056.06c 0.04209736153011
26057.06c 0.00097221166469368
26058.06c 0.00012938352498519
28064.06c 9.163579955897E-5
42092.06c 7.1884776089989E-5
42094.06c 4.4806885366064E-5
42095.06c 7.7116282705702E-5
42096.06c 8.079771328713E-5
42097.06c 4.6260081648207E-5
42100.06c 4.6647600656778E-5
82208.06c 0.2178515328
83209.06c 0.5142528
APPENDIX A. SERPENT INPUTS
A.2. THE COMPACT ADS LOADED WITH NITRIDE FUEL
mat gas -5e-5 % He
2004.09c 0.99999863
mat Pb -10.19 % Pb target
82204.09c 0.00625856
82206.09c 0.10773664
82207.09c 0.09879584
82208.09c 0.23424896
83209.09c 0.55296
set acelib "jeff31.xsdata"
set bc 1
set pop 2000 2000 30
set power 2233333.3 % Power normalised to 201e6/90
set egrid 0.6e-3 % Cross section grid thinning (to reduce memory requirement)
set declib "../Documents/Serpent1.1.0/xsdata/jeff31/JEFF311RDD"
set nfylib "../Documents/Serpent1.1.0/xsdata/jeff31/JEFF31NFY"
set fpcut 1E-6
set stabcut 1E-12
set ttacut 1E-18
set xsfcut 1E-6
% — Options for burnup calculation:
set bumode 1 % TTA method
set pcc 1 % Predictor-corrector calculation on
set xscalc 2 % Cross sections from spectrum
set printm 1 % No material compositions
plot 1 10000 10000
plot 3 10000 10000
73