Progress in Nuclear Energy 83 (2015) 135e143
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Progress in Nuclear Energy
journal homepage: www.elsevier.com/locate/pnucene
A 232Th closed fuel cycle utilizing both a thermal and hybrid nuclear
systems
M. Perez-Gamboa a, b, M. Nieto-Perez a, *, S. Mahajan c, P. Valanju c, M. Kotschenreuther c,
J.L. François d
a
CICATA Queretaro e IPN, Cerro Blanco 141, Queretaro, QRO 76090, Mexico
GEIQ, Campo Real 1692, Quer
etaro, QRO 76146, Mexico
Institute for Fusion Studies, U of Texas at Austin, 1 University Station C1500, Austin, TX 78712, USA
d
Facultad de Ingeniería e UNAM, Ciudad Universitaria, M
exico 04510, Mexico
b
c
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 23 October 2014
Received in revised form
21 February 2015
Accepted 28 February 2015
Available online 3 April 2015
Nuclear fuel cycles based on thorium are gaining close attention due to its higher availability and more
homogenous geographical distribution. Thorium cycles, likely to be less problematic with regard to waste
generation and weapons proliferation, will extend the availability of nuclear fuel by hundreds/thousands
of years. The principal Th cycle involves the transmutation of the fertile 232Th isotope into the fissile
isotope 233U by means of neutron capture. In the present study, the coupled operation of a hybrid fission/
fusion system and a standard thermal reactor is analyzed. Using the MCNP neutronic transport code, the
behavior for 233U consumption/generation in both systems as a function of Th/U feed ratio to each reactor
is analyzed. The useful composition range for the feed to the thermal reactor was found to be between
1.7% and 2.25%; within these range, breeder input enrichment can be found which causes the rate of
consumption and generation of 233U to be identical. Under this condition, from the point of view of the
fissile isotope, the cycle is closed, with no net generation or consumption. The cycle requires a 232Th
input to compensate the amount spent on breeding the fissile material; for the range of interest, this
varies between 0 and 35% of the total mass flow in the breeder leg of the cycle.
© 2015 Elsevier Ltd. All rights reserved.
Keywords:
Thorium
Closed fuel cycle
Fusion breeders
1. Introduction
One of the key objections invoked against a more aggressive
pursuit of nuclear power as an alternative energy source (to coal
and natural gas, for example), is the “limited” availability of nuclear
fuel. Critics cite that the fissile material contained in the approximately 5 million tons of “cheap uranium” available in the world
(Nuclear Energy Agency, 2011) will last only about 50 years feeding
the 440 commercial reactors in operation. Any significant increase
in the operational reactor fleet will deplete the reserves' lifetime,
and in fact, fuel reserves may get severely depleted even before the
useful life-time of new plants (Mayumi and Polimeni, 2012).
Amongst possible strategies aimed at extending the availability of
nuclear fuel, the following four may be important:
utilization of the nuclear material in nuclear weapons for mixed
oxide (MOX) fuel fabrication,
* Corresponding author. Tel.: þ52 55 57296000x81030.
E-mail address: [email protected] (M. Nieto-Perez).
http://dx.doi.org/10.1016/j.pnucene.2015.02.013
0149-1970/© 2015 Elsevier Ltd. All rights reserved.
the utilization of fast reactor to breed fissile material from natural uranium,
spent fuel reprocessing,
breeding of fissile fuel from the fertile isotopes 238U and 232Th;
the latter will constitute the implementation of a thorium fuel
cycle.
Two of these strategies, breeder (fast) reactors and fuel
reprocessing, pose very high proliferation risks (access to weaponsgrade Pu). This is due to the fact that both technologies can be used
to refine plutonium; reprocessing does this by recovering the
plutonium present in the spent fuel from power reactors, and fast
breeders generate plutonium from natural uranium. Supporters of
the fast breeder path have argued that without enrichment and
reprocessing capability, a breeder does not represent a proliferation
danger (Simnad, 1998; Chirayath et al., 2009; Dautray, 2011). Their
contention is that because the plutonium generated is mixed with
the rest of the fuel, it cannot be used to build an efficient nuclear
explosive in that state (Dautray, 2011). Regarding reprocessing,
about 1.5% of spent fuel is fissile material (235U, 239Pu and 241Pu),
136
M. Perez-Gamboa et al. / Progress in Nuclear Energy 83 (2015) 135e143
Nomenclature
mi,j
xi,j
mi
DmB,j
DmT,j
ri,j
E
Tn
h
molar flow, in mol/s, of species j in current i of the
cycle
mole fraction of species j in current i of the cycle
total molar flow, in mol/s, in current i of the cycle
mass change, in mol/s, of species j in the fusion
breeder block of the cycle
mass change, in mol/s, of species j in the thermal
fission reactor block of the cycle
rate of production/destruction of component i due
to process j
neutron energy in the fusion breeder block of the
cycle
neutron temperature in the thermal fission reactor
block of the cycle
thorium conversion efficiency
which can be reused directly in the fuel cycle. Reprocessing is
coupled to the fast breeder technology because the recovered 238U
can be used as fertile material in a breeder reactor. A fuel cycle
incorporating uranium enrichment, conventional reactors, fast
breeders and reprocessing is depicted in Fig. 1.
The conversion of nuclear material from weapons into fuel for
nuclear power plant has been demonstrated by the Megatons to
Megawatts program, an industryegovernment partnership started
in 1995 focused on converting nuclear materials from Russian
intercontinental ballistic missile (ICBM) warheads to fuel for
civilian nuclear reactors (USEC Megatons for Megawatts Program).
This program, before it expired in 2013, accounted for roughly 10%
of the electricity generated in the US, transforming roughly 500
tons of weapons grade uranium into enriched fuel for civilian usage
(Bunn, 2011).
Perhaps the largest untapped source of nuclear energy lies in the
enormous Th deposits with a natural abundance similar to that of
lead but higher than that of uranium (Jayaram, 1987). Though
recent estimates put the reserves to the tune of 10 million tons,
resource prospecting has not been as intense as in the case of
uranium due to the lack of a well-defined market; India, the United
States and Australia are the countries with the most known reserves of thorium (Schaffer, 2013). In the thorium cycle, the naturally abundant 232Th isotope is transmuted into the fissile 233U
isotope by neutron capture. Depending on the reactor design and
fuel cycle scheme, the 233U generated either undergoes fission in
the same reactor or is separated and formed into fresh nuclear fuel.
In addition to the advantage of being an alternate abundant
nuclear fuel, thorium is part of a proliferation resistance fuel cycle
that produces smaller quantities of plutonium and minor actinides
(Schaffer, 2013; Ünak, 2000). It should also be considered that in a
thorium fuel cycle, the produced 233U is inevitably contaminated
with 232U, and isotope with several decay products that emit energetic gamma radiation. 232U is very difficult to separate from 233U
and represents a radiological barrier and makes the handling
difficult. In addition, the high radiation field may damage the
warhead electronics if 233U contaminated with 232U is used for
weapons manufacture (Schaffer, 2013).
The fissile isotope 233U can be bred in either a thermal or a fast
reactor from 232Th. If bred in a thermal reactor (a unique feature for
Th fuel cycles), the fissile material is consumed within the reactor
and it can generate power. However, breeding on a thermal reactor
is difficult because the capture competes with fission from the
neutron economy point of view (Kumar et al., 2009). Hence, a 233U
breeder with a very small amount of fission when compared to a
thermal reactor might be advantageous, and for this purpose fusion
neutron sources might be a very good choice, since the bred fissile
Fig. 1. Four-tier nuclear fuel cycle incorporating thermal and fast reactors.
M. Perez-Gamboa et al. / Progress in Nuclear Energy 83 (2015) 135e143
material can be used in a thermal reactor for the sole purpose of
power generation, with very limited breeding (Moir, 1982). The use
of fusion reactors as thorium-based breeders has been proposed in
the past with promising results (Şahin and Yapıcı, 1999; Ma et al.,
2010). In fact, a completely reprocessing-free (ReFree) nuclear
fuel cycle with a fusion neutron source at its heart has been proposed (Kotschenreuther et al., 2012). This reported study clearly
outlines the feasibility and advantages of using a fusion neutron
source for the purpose of breeding fissile 233U from fertile 232Th
minimizing the production of the undesirable 232U due to the fast
neutron spectrum.
In the present paper, a complementary study of the ReFree fuel
cycle, assuming a closed fuel cycle, is presented. The goal is to
explore the synergy between a fusion-based 233U breeder from a
232
Th feed and a thermal PWR reactor that burns the fuel bred in
the fusion device, but allowing the spent fuel from the thermal
reactor to be injected back into the fusion breeder. Although the
closing of the fuel loop may involve certain reprocessing, the
operation does not involve extraction of fissile material from the
fuel cycle, only addition or removal of thorium. An overall mass
balance for the cycle is described; such balance requires knowledge
of the transmutation (in the case of the hybrid) and burning (in the
case of the thermal) efficiencies of the two systems. To estimate
these efficiencies, the neutronic behavior of both the thermal and
fast reactor is modeled using the MCNPX code (MCNP6.1) with the
ENDL92 cross section database from Lawrence Livermore National
Laboratory.
2. Description of the cycle
The proposed Th fuel cycle has the following four stages:
A fusion-based breeder fed with a 232Th/233U mixture that is
exposed to a 14 MeV neutron flux from a tokamak fusion
reaction.
A Th separator that increases the mole fraction of 233U in the
stream in order to feed it to the thermal reactor by removing
thorium; the removed Th is fed into the diluter unit.
A thermal reactor where some of the 233U is burned to generate
power.
A diluter that incorporates fresh 232Th to the cycle and prepares
the feed to the fusion breeder.
Although this paper discusses the cycle as a whole, the main
focus of the present article will be the two reactive blocks: the
fusion breeder and the thermal reactor; of the two remaining
blocks, the concentrator (which involves the separation of 233U and
232
Th) needs to perform a separation of Th and U elements by
extracting the Th. will make use of existing technology for the
separation of the two elements. Ion exchange separation of these
two elements has been documented from the early days of nuclear
industry (Poirier et al., 1958), and current research on these topic is
focused on finding solvents that can selectively absorb thorium,
with recovery efficiencies greater than 95% reported in the literature even for the case of coexisting Th and U ions in solution
(Hosseini and Hosseini-Bandegharaei, 2010; Demirel et al., 2003).
For the case of the diluter, it should be mentioned that its input
needs to be preconditioned, an operation that implies the removal
of any unwanted material produced in the thermal reactor, such as
minor actinides and fission products. The effect in the cycle performance of having uranium isotopes other than 233 (which will be
difficult to separate) falls beyond the scope of the present study, but
will be addressed in future work.
The cycle is depicted in Fig. 2, with the different mass flows
labeled; a description of these currents is presented in Table 1. Each
137
Fig. 2. Block diagram of the proposed closed Th cycle, showing the four units
comprising it and the labeled mass flows.
current considers only three components: 232Th, 233U and 16O
isotopes, since it is assumed that the fuel is in the form of metal
oxides. The total mass is adjusted in the currents such that the fuel
masses processed in both the hybrid and the thermal reactor are
the same. Since for the case of 233U there is both a source and a sink,
an equilibrium can be found where the fissile material produced by
the breeder equals the amount of this material burned in the
thermal reactor; for the 232Th on the other hand, since there is only
consumption, the cycle requires a steady stream of this isotope,
which is added in the diluter unit. Currents 5 and 6 are handled
separately in the mass balance, but it is assumed that the removed
Th from the enricher (current 5) can be readily added to the diluter
thorium input (current 6); the difference of current 6 minus current
5 is the net amount of fresh thorium required from outside the
cycle.
3. Mass balance
For the purpose of the mass balance, metal basis is considered,
meaning the only relevant species in the balance are 232Th and 233U.
To simplify notation, 233U is labeled as component 1 and 232Th is
component 2. Currents are labeled with the numbers shown in
Fig. 2, and a reference to a current without a component specified
refers to total current; hence, molar flows and atomic fractions for
components are represented by mi,j and xi,j, respectively, where i is
the current label and j is the component label, and total molar flows
are represented by mi.
3.1. Mass balance in the breeder block
The component and total mass balance in the breeder reads:
m1 ¼ m4
(1a)
m1;j ¼ m4;j þ DmB;j x4;1
(1b)
Table 1
Description of currents shown in Fig. 2.
Current ID
Description
1
2
3
4
5
6
Breeder reactor output, fuel concentrator input
Fuel concentrator output, thermal reactor input
Thermal reactor output, feed to fuel dilutor
Fuel dilutor output, hybrid reactor input
Th removal on concentrator
Th make-up current
138
M. Perez-Gamboa et al. / Progress in Nuclear Energy 83 (2015) 135e143
where DmB,j represents the mass change rate of component j in the
breeder, a strong function of the 233U fraction in the breeder feed,
x4,1. Since the main transformation that occurs in the breeder is
from 232Th to 233U, the change in total mass in the unit is zero. The
atomic fractions at the exit of the breeder are given by:
m4;j þ DmB;j x4;1
DmB;j x4;1
x1;j z
¼ x4;j þ
m4
m1
(2)
x2;i ¼
m2;i m1;i m5;i
¼
m2
m1 m5
(7)
For the purposes of this study, it will be assumed that the
enricher is perfect and does not remove any fissile material,
meaning that m5,2 ¼ m5 and m5,1 ¼ 0. This assumption is valid
considering reports regarding ion exchange separation efficiencies
(Hosseini and Hosseini-Bandegharaei, 2010).
3.4. Mass balance in the dilutor unit
3.2. Mass balance in the thermal reactor block
Similar total and component mass balances are obtained for the
thermal reactor:
m3 ¼ m2 þ
X
DmT;j x2;1
(3a)
j
m3;j ¼ m2;j þ DmT;j x2;1
(3b)
This time, DmT,j represents the mass change rate of component j
in the thermal nuclear reactor, which again depends on the 233U
fraction in the thermal reactor feed, x2,1. The mass fractions obtained at the exit of the thermal reactor are given by an expression
similar to eq. (2):
x3;j
m3;j m2;j þ DmT;j x2;1
m
¼
¼
¼ 2
m3
m3
m3
!
DmT;j x2;1
x2;j þ
m2
(4)
Notice that if m2/m3 ¼ 1 (no net change in total mass in the
thermal reactor), eq. (4) would simplify and be equivalent to eq. (2).
The MCNP simulations performed in this study show that this ratio
is equal to 0.94, and this numerical value is used for the mass
balance. The rate of species i generation/consumption in the
breeder and in the thermal reactor are formally given by:
DmB;i ¼
Z X
ri;j E; x4;1 dV
(5a)
ri;j Tn ; x4;1 dV
(5b)
j
DmT;i ¼
Z X
j
where ri,j is the reaction rate of component i due to process j. Since
the fusion neutrons are monoenergetic, all rates depend on a single
energy E, whereas for the case of the thermal reactor the rate depends on the neutron energy distribution characterized by a
neutron temperature Tn. To evaluate eqs. (5a) and (5b), the MCNPX
code was used, which takes into account neutron energy spectrum,
geometry, neutron flux strength and initial isotopic composition to
calculate the mass changes in the hybrid and in the thermal reactor.
3.3. Mas balance in the enricher unit
The enricher has the purpose of increasing the mole fraction of
U on the thermal reactor input by removing 232Th on the stream.
The mass balances for this unit read:
As implied by the name, the dilutor unit adds thorium to the
current in order to reduce the mole fraction of fissile material in the
current and operate the breeder with low enrichment. In the
dilutor the mass balances are:
m4 ¼ m3 þ m5 þ m6
(8a)
m4;i ¼ m3;i þ m5;i þ m6;i
(8b)
And the corresponding atomic fractions at the output are given
by:
x4;i ¼
m4;i m3;i þ m6;i þ m5;i
¼
m4
m3 þ m6 þ m5
(9)
It will be assumed that the makeup material does not contain
the fissile isotope, meaning that m6,2 ¼ m6 and m6,1 ¼ 0.
4. MCNPX model description
4.1. Fusion breeder model
The base model is a 2D model with rotational symmetry representing a proposed fission/fusion hybrid already described in
detail previously (Kotschenreuther et al., 2009). The following regions are included in the model: copper for coils and center stack,
tungsten first wall on the fusion reactor, stainless steel for the
vacuum vessel and a region where the thorium/uranium oxide fuel
is located (fission blanket). The blanket is assumed to be homogenous in nature, and the coolant in this region is lithium. The
neutron source is a point at the center of the vacuum region. Fig. 3
depicts such model, while the corresponding dimensions are
included in Table 2.
4.2. Thermal reactor model
The thermal reactor MCNPX model chosen is based on a watercooled Westinghouse AP1000 PWR fuel assembly, an arrangement
of 17 17 rods, with the composition and dimensions specified in
Table 3. The geometrical model for the thermal reactor fuel assembly is shown in Fig. 4.
233
m1 ¼ m2 þ m5
(6a)
m1;i ¼ m2;i þ m5;i
(6b)
So the atomic fraction for each component in the concentrator
output is:
5. Results
The MCNPX code was used to model the breeding rate and the
consumption rate as a function of 233U input fraction in both the
fusion breeder and the thermal reactors described above. Both reactors were fed with varying amounts of 233U and 232Th and the
makeup oxygen, keeping the total mass constant for all the calculated cases.
M. Perez-Gamboa et al. / Progress in Nuclear Energy 83 (2015) 135e143
139
Fig. 3. Hybrid system geometry, the dimensions are given in Table 2.
Table 2
Fusion breeder dimensions.
Parameter
Radius [m]
Copper center stack
Plasma chamber (vacuum)
Tungsten armor
Steel vessel
Fission blanket
Copper coil
1.0
3.974
3.994
4.0
6.0
7.0
5.1. Correlation between input and output in the breeder ant the
thermal reactor
Once the mass change values for each component, both in the
breeder and in the thermal reactor, were calculated for different
uranium fractions in the feed, eqs. (2) and (4) are used to generate
Figs. 5 and 6, respectively. Fig. 5 shows the dependence of x1,1 as a
function of x4,1. In the figure, the dots indicate the values obtained
from MCNP simulations, and the solid line is the condition
x1,1 ¼ x4,1. The closer the dots are to the solid line, the worse is the
performance of the breeder. It is clear that the breeder performance
is best as the input enrichment decreases, having a maximum
breeding equivalent to 0.7% 233U enrichment output for a pure
thorium feed. Hence, the breeder feed should have the lowest
enrichment possible to achieve the maximum breeding. Since this
fuel cycle is designed with no 233U extraction out of the cycle, the
input fraction of 233U to the breeder cannot be set to exactly zero,
but should be kept below 1% in order to obtain a significant
breeding rate.
The equivalent behavior for the thermal reactor is shown in
Fig. 6. Here, it can be clearly seen that for input enrichments below
Table 3
Thermal fuel assembly parameters.
Parameter
Value
Fuel assembly height (cm)
Fuel assembly width (cm)
Fuel Stack Height (cm)
Fuel rods (per assembly)
Fuel rods on assembly side (per side)
Fuel rod pitch (cm)
Mass of uranium (kg)
Percent of theoretical density
Guide tubes (per assembly)
Instrumentation tubes (per assembly)
Fuel pellet radius (cm)
Fuel clad inner radius (cm)
Fuel clad outer radius (cm)
Clad thickness (cm)
Guide tube inner radius (cm)
Guide tube outer radius (cm)
Guide tube thickness
Burnable poison rod outer radius (cm)
BPR clad inner radius (cm)
BPR clad outer radius (cm)
Clad/guide/instr. tube material
406.65
21.44
365.8
264
17
1.27
464
94.85
24
1
0.41
0.42
0.475
0.055
0.57
0.61
0.04
0.34
0.44
0.48
ZIRC-4
Fig. 4. Westinghouse AP1000 fuel assembly MCNPX model.
140
M. Perez-Gamboa et al. / Progress in Nuclear Energy 83 (2015) 135e143
DmB;j x4;1
¼ x1;j x4;j
m4
(10b)
5.2. Equilibrium in fissile material consumption and production
Fig. 5.
233
U enrichment on the breeder output as a function of input enrichment.
1.5% the thermal reactor is performing like a breeder, since the
output enrichment is higher than the input (i.e. the points are
above the solid line in the figure); moreover, the reactor is breeding
enough fuel to compensate the burn and keep the output enrichment constant; arguments related to fuel burnup and reactivity also
hinder the operation of the reactor at such low enrichments. If the
consumption of 233U is an indication of efficient fuel utilization in
the thermal reactor, its operation would require input enrichments
above 3%.
The relative change in masses for both the thermal reactor and
the breeder need to be known as well. Those quantities can be
obtained from eqs. (2) and (4), since Figs. 5 and 6 give the functional
relationship between input and output fractions:
DmT;j x2;1
¼ 1:064x3;j x2;j
m2
(10a)
Fig. 6. 233U enrichment on the thermal reactor output as a function of input
enrichment.
If a self-sustained cycle is desired (that is, a cycle that produces
as much fissile material as it consumes), once the enrichment at the
entrance or exit of either reactor is specified, all other enrichments
can be calculated using eqs. (2) and (4). This is because the system
would be restricted by requiring equal rates of consumption in the
thermal reactor and production in the breeder, so no need for 233U
removal from or addition to the cycle would be necessary.
A plot of eqs. (10a) and (10b) using input enrichment (x2,1 and
x4,1) as the parameter is shown in Fig. 7. The uranium enrichment
on the thermal reactor input is capped by the maximum production
rate of 233U in the breeder: for an input enrichment of 2.25%, the
thermal reactor consumes as much 233U as can be generated in a
breeder with zero enrichment on the input, which is the maximum
rate of production of the fissile isotope in the breeder; operation of
the thermal reactor above this input enrichment would necessarily
require external addition of 233U. The lower end of the thermal
reactor input enrichment is also capped by not allowing the thermal reactor to breed 233U (since its main function should be
burning fissile material), so according to Fig. 6 the lowest enrichment possible is 1.5%. Another interesting point occurs for an
enrichment of 1.7%, where the two curves in Fig. 7 intersect. This
point represents the scenario of the two systems in consumption/
production equilibrium with identical enrichment on their inputs.
This cross over point defines two regions of operation: a region of
high 233U utilization going from 1.7 to 2.25% enrichment in the
thermal reactor input, and a low 233U utilization going from 1.5 to
1.7%. The discussion in the present work will concentrate on the
high utilization region, which requires lower concentration in the
breeder input and hence produces more fissile material.
Although the equilibrium states can be visualized in Fig. 7 by
drawing horizontal lines and noting the values for x4,1 (breeder
input) and x2,1 (thermal input) corresponding to the intersection
points with the two curves, it is convenient to see the pairs that
Fig. 7. Production and consumption rate behavior as a function of input enrichment,
for the thermal (solid) and breeder (dashed) reactors. Dotted lines indicate relevant
features.
M. Perez-Gamboa et al. / Progress in Nuclear Energy 83 (2015) 135e143
generate the equilibrium in production/consumption of 233U. Fig. 8
presents this information, which will be used later in the paper to
explore the Th utilization efficiency for different cycle operation
scenarios; it should be noted that the mass changes in 233U increase
with increasing thermal input enrichment, as can be seen in Fig. 7.
Table 4 summarizes some combinations of 233U atomic fractions in
the different currents of the cycle that generate the production/
consumption equilibrium condition for operation on the high power regime.
141
Table 4
233
U enrichment percentages that generate production/consumption equilibrium
for fissile material in the cycle.
Breeder
233
Thermal
Input
Output
Input
Output
1.63
1.00
0.62
0.33
0.23
0.00
1.82
1.29
1.02
0.85
0.80
0.70
1.69
1.79
1.91
2.03
2.12
2.25
1.49
1.50
1.51
1.51
1.53
1.54
U percent change
0.20
0.30
0.40
0.52
0.60
0.70
5.3. Thorium balance in the cycle
Since the entrance to the thermal reactor requires higher atomic
fractions of 233U and the input current to the fusion breeder requires a fraction as low as possible, the enricher and diluter blocks
in Fig. 2 remove or add 232Th, respectively, in order to adjust the
fissile material input concentration. The removal of the Th isotope
from current 1 will generate the entrance to the thermal reactor, in
order to increase the atomic fraction of 233U. From eq. (7), the
expression for the Th fraction at the exit of the enriching unit can be
written as:
x2;2 ¼ 1 x2;1 ¼
1 x1;1 m1 m5
m1 m5
(11)
Algebraic manipulation of eq. (11) allows writing the percent of
removed Th (that is, the fraction of Th entering the enricher that is
separated) as a function of the atomic fractions at the input and
output:
m5
¼
m1;2
1
1 x1;1
1
x1;1
x2;1
(12)
From Fig. 8, x2,1 can be correlated with x4,1 for equilibrium
operation; and from Fig. 5, x1,1 can be found knowing x4,1. A similar
analysis yields the following expression for the percent of Th
entering the hybrid that is added in the diluting unit. The starting
point is eq. (9) for component 2, rewritten here as:
x4;2 ¼ 1 x4;1 ¼
1 x3;1 ðm4 m6 Þ þ m6
m4
(13)
Fig. 8. Input enrichment values that generate production/consumption equilibrium for
the fissile material within the cycle in the high power regime.
An expression similar to eq. (12) can be obtained from eq. (13)
following the same procedure, this time indicating the fraction of
fresh Th (both from outside the cycle and coming from the
enricher) that enters the breeder reactor:
m6
¼
m4;2
1
1 x4;1
1
x4;1
x3;1
(14)
By using the data from Figs. 6 and 8, x4,1 can be used to find x2,1,
and in turn once x2,1 is known x3,1 is determined. Fig. 9 presents the
fractions of Th removal/addition, given by eqs. (13) and (14)
respectively, as a function of thermal reactor input enrichment. It
is interesting to note the existence of a region where the roles of the
enricher and the dilutor are reversed, indicated by the negative
signs in the fractions; the region where both reach a positive value
is defined by x2,1 > 0.01706.
By use of eq. (1a), the ratio of Th removed in the enriching unit
to Th added in the diluting unit is then given by:
m5 x3;1 x2;1 x1;1
¼
m6 x2;1 x3;1 x4;1
(15)
The closest this ratio is to unity, the more self-sufficient the cycle
is; the cycle, however, cannot reach this state because there is net
consumption of 232Th, which needs to be replenished by the
addition of fresh material from outside the cycle. The equation has a
singularity (m6 ¼ 0) when x3,1 ¼ x4,1, which occurs when
x2,1 ¼ 0.015, corresponding to the point where the enrichment
input to the breeder is equal to the enrichment output of the
Fig. 9. Fraction of Th added/removed on the dilutor (addition) and the concentrator
(removal). The inset shows the region where the zero crossing occurs.
142
M. Perez-Gamboa et al. / Progress in Nuclear Energy 83 (2015) 135e143
thermal reactor. This may seem a contradiction at first, since it is
mandatory to have a thorium input; however, according to Fig. 9,
this point is located in the region where the concentrator is actually
performing a dilution function, so there is a net addition of thorium
to the cycle, but it occurs in the other unit. The zero on this
expression occurs when x2,1 ¼ x1,1, when the enrichment in the
breeder output is equal to the thermal input, which occurs at
x2,1 ¼ 0.01706. This last point may be an attractive operation point
since it is the point where the enriching unit is not necessary;
however, further analysis would be required to determine its
attractiveness from the point of view of the energy balance.
Fig. 10 shows the ratio given by eq. (15) as a function of thermal
reactor input enrichment, ignoring the region with inverted roles
for the dilutor and enricher. Eq. (15) is always less than 1 for
x2,1 ¼ 0.01706, indicating the net consumption of Th in the cycle,
and the value oscillates between 0.70 and 0.84; at 1.75% thermal
input enrichment, the maximum ratio of 0.84 occurs. As the
enrichment at the input of the thermal reactor increases, the ratio
drops. This result is interesting, because the initial expectation was
that a requirement of high enrichment represents more Th
removal, and the contribution of the removed stream of Th to the
injected one was expected to be higher; however, as can be seen
from Fig. 8, higher enrichment requires a higher dilution to achieve
the breeder input enrichment. The net effect is that lower concentrations of 233U at the thermal reactor input leads to lower 232Th
makeup current because the breeder requires more Th (lower
enrichment).
A useful parameter can be obtained by comparing the fertile
material required by the cycle to the fissile material produced/
consumed in it. The conversion efficiency is defined as:
Th fed from the outside of the cycle m6 m5
¼
h¼
Th transformed in the breeder
DmB;2
x1
x2
xx43
x1 x4
Fig. 11. It can be seen that the utilization grows as the thermal
reactor operates with higher enrichment, and the maximum value
is 0.45 which is reached at the cap of thermal reactor input
enrichment. For better Th utilization, the results suggest operation
at higher input enrichment for the thermal reactor.
6. Conclusions
(16)
The numerator of eq. (16) can be evaluated taking the difference
between eqs. (14) and (12), while the denominator is obtained from
eq. (2). The result is given by:
h¼
Fig. 11. External thorium utilization efficiency, as defined by eq. (15), as a function of
thermal reactor input enrichment.
(17)
A plot of Th utilization efficiency given by eq. (17) is shown in
Fig. 10. Ratio of thorium removal to addition as a function of thermal reactor input
enrichment.
A closed fuel cycle involving a fusion-based breeder and a
thermal reactor, both operating with 232Th/233U mixtures, has been
analyzed. Because the breeder operates better with low 233U
enrichment and the thermal reactor gives off more power with high
enrichment, two additional units for adjusting the 233U enrichment
were required: one to concentrate the fissile material and one to
dilute it. The overall and component mass balances for the cycle
were used to calculate composition of all currents. For the case of
the two reacting blocks, MCNPX was used to evaluate the mass
changes for each species; it was found that the overall mass change
in the fusion breeder is almost zero, while for the thermal reactor
the overall mass change is roughly 6% for the range explored.
Equilibrium between the generation of fissile material in the
breeder and its consumption in the thermal reactor was found for
different thermal reactor input compositions, so the cycle can be
operated at different power levels.
The power level for the thermal reactor is capped by the
maximum breeding that can be achieved in the fusion system,
which is obtained for a pure Th feed to the breeder, and corresponds to uranium enrichment at the entrance of the reactor of
2.25%. For low input enrichment, below 1.5%, the thermal reactor
can even work as a breeder itself, but that regime is not explored in
the present work. Between 1.5 and 1.7% input enrichment to the
thermal reactor, the breeder input enrichment required for equilibrium is larger, so the roles of the concentrator and the diluter are
reversed. Hence, the useful range for the thermal input enrichment
is between 1.7% and 2.25%.
The cycle requires a Th makeup feed that varies with thermal
reactor input enrichment, from 0% of the cycle mass flow in the
breeder leg at thermal input enrichment of 1.7%, to 30% when this
enrichment is 2.25%. The utilization factor of the Th fed to the cycle
is nonlinear, but the maximum of 45% Th utilization in the breeder
is reached for the maximum thermal reactor input enrichment.
M. Perez-Gamboa et al. / Progress in Nuclear Energy 83 (2015) 135e143
Some aspects of the closed cycle, such as separation efficiency in
the concentrating unit, the effect of fission products and minor
actinides in the cycle, the presence of other uranium isotopes or the
effect of Th feed purity need to be addressed in further studies.
Acknowledgments
This work was partially supported by SIP-IPN grant 20130337.
MPG acknowledges support from a CONACYT scholarship that
allowed her a closer interaction with coauthors at UT Austin during
an internship.
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