# A Critical Review of the Recent Improvements in Minimizing Nuclear Waste by

Authors: E. Bomboni; N. Cerullo; G. Lomonaco; V. Romanello
Journal: Science and Technology of Nuclear Installations
 (2008)

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## Abstract

This paper presents a critical review of the recent improvements in minimizing nuclear waste
in terms of quantities, long-term activities, and radiotoxicities by innovative GCRs, with particular
emphasis to the results obtained at the University of Pisa. Regarding these last
items, in the frame of some EU projects (GCFR, PUMA, and RAPHAEL), we analyzed
symbiotic fuel cycles coupling current LWRs with HTRs, finally closing the cycle by GCFRs. Particularly,
we analyzed fertile-free and Pu-Th-based fuel in HTR: we improved plutonium exploitation also by
optimizing Pu/Th ratios in the fuel loaded in an HTR. Then, we chose GCFRs to burn residual MA.
We have started the calculations on simplified models, but we ended them using more “realistic" models of the reactors. In addition, we have added the GCFR multiple recycling option usingkeff calculations for all the reactors. As a conclusion, we can state that, coupling HTR with GCFR, the geological disposal issues concerning high-level radiotoxicity of MA can be considerably reduced.


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## Body

## 1. Introduction

Nowadays nuclear power is the only greenhouse-free
source that can face the always increasing worldwide energy demand. The LWR
technology (at present the most widespread technology) is secure and
well-proven: its major “real” drawback is probably the scarce exploitation of
uranium resource and the consequently “large” production of waste. In fact,
annually a 1000-MWe PWR produces about 30 tons of spent nuclear fuel (burnup around 30 GWD/tU) with the following average composition:(i)
94%
U238;(ii)
1% U235 (please remember that natural uranium contains 0.7% of U235);(iii)
1% Pu;(iv)
0.1% MA
(Np, Am and Cm);(v)
3÷4%
FP.
Considering the actual reprocessing technology, this
quantity of SNF contains about 1200 kg of  “waste” (i.e., FP + MA): such
a vitrified waste occupies about 20 m3, which correspond to the
0.002% of the total amount of domestic waste in UK, for instance [1].On the other hand, it is a relatively small quantity
of waste if  compared with the conventional energy sources: a 1000-MWe  coal-fired power plant discharges annually 6⋅106 tons of CO2, 2⋅105 tons of ashes, and 2⋅105 tons of SO2 [2],
that means a volume
which
is roughly 1⋅6⋅108 times
higher than that of vitrified nuclear  waste.
(In fact, at STP, 6⋅106 tons of CO2
occupies 3⋅109 m3, 2⋅105 tons of SO2
occupies 7⋅107 m3, and 2⋅105 tons of ashes
(with a mean density of 1500 kg/m3) occupies 1.33⋅105 m3.) The main issue for the
nuclear power opponents  is that the spent fuel
radiotoxicity takes more than 100000 years to reach the same amount of radiotoxicity as that  of the uranium ore from which it descends. This long
time is mainly due to Pu, but also if all the Pu would be transmuted, the time
to reach the level of mine (LOM) would still be around some tens of thousand
years because of the presence of the MAs.However, if all
the actinides were fissioned directly or indirectly (by conversion
fertile-to-fissile), the “real” remaining waste should be constituted
by FP, that have a relatively short lifetime (not more than hundreds of years).
Today Pu from SNF is partially recovered: France,
UK, Japan, Russia,
China, and India reprocess their spent fuel in order to
fabricate new MOX fuel elements, while other countries, as USA and Sweden, adopt the OTTO cycle.From a global point of view [3], 16% of the world
energy demand is covered by nuclear power that supplies 350 GWe,
roughly equally subdivided under USA,
Europe, and the rest of the world. These
plants produce 10500 tHM/year of spent fuel, of which 3900 tHM/year are
reprocessed. As already remembered, reprocessing plants recover U and Pu only,
while MA are treated with FP as waste. Of this Pu (recovered form LWRs), only
25% is consumed in thermal reactors, while 10% is converted in MA. MOX fuel can
be reprocessed not more than 2 times in order to manufacture new LWR MOX fuel
(Pu isotopic vector becomes more and more poor in fissile nuclides, while many
higher Pu isotopes and MA are poisons in the thermal spectrum) and its
radiotoxicity increases because of Cm244 buildup [3].Thus, it was clear since the beginning of nuclear age
that different kind of reactor would be necessary in order to increase the
availability of nuclear fuel. Researches on fast reactor technology started in
the past in order to multiply by 50 the availability of nuclear fuel resources.
According to the goals of sustainability, economics, and proliferation
resistance of the Generation IV Initiative [4],
all the HMs have to be seen as resource. To realize the so-called
full
actinide recycle or integral fuel cycle (i.e., a self-sustaining
fuel cycle in which the feed is constituted by fertile material only), one improves 180 times the
uranium resources
exploitation than a once-through LWR cycle [5]. Please remember that using a closed fuel cycle, the
uranium resources would be sufficient for around 2500 years at the actual
consumption rate (considering only the “identified resources,” that are only a
fraction of the total worldwide uranium availability) [6].The activity performed at the University of Pisa  fits into this frame. From many years, the DIMNP group is studying gas-cooled
reactors, which have been largely recovered by Gen-IV both thermal and fast
(two of the six concepts proposed are gas-cooled reactors). They seem to have
the capability to reach the Gen-IV goals thanks to their unique
characteristics.In this frame, it appears useful to analyze the impact
on the entire fuel cycle of the symbiosis of LWR, HTR, and GCFR.


## 2. Transmutation Physics

### 2.1. Theory

The term “transmutation” is applied to all the nuclear reactions
which transform a nuclide into another nuclide. In nuclear reactors,
transmutation happens by way of(n,c), (n,f), and (n,2n) reactions typically.
It is clear that the probability of transmutation for a nuclide is strictly
linked to its effective cross-sections for (n,c), (n,f), (n,2n) reactions in
the considered core. Moreover, the transmutation rate depends obviously also
from the neutron flux intensity. Let us call to mind some useful parameters in
transmutation studies [7]. The neutron spectrum is defined as(1)χ(r→,E,t)=φ(r→,E,t)φ(r→,t), where φ is the neutron flux, while the effective
cross-section of the nuclide n for the reaction x is expressed by(2)σ¯n,x(r→,t)=∫0.001eV10MeVσn,x(E)χ(r→,E,t)dE. The upper integration limit depends from the fission spectrum
(typical of a given nuclide); while the lower limit considers that at the
reactor temperature, the neutron energy is higher than 0.001 eV (in an LWR the
mean energy of the thermal neutrons is about 0.04 eV, e.g.).The transmutation rate for a nuclidei is determined  by Bateman’s equations:(3)ddtNi(r→,t)=−λiNi(r→,t)−(σ¯i,a+σ¯i,(n,2n)+⋯)Ni(r→,t)φ(r→,t)+σ¯i−1,cNi−1(r→,t)φ(r→,t)+σ¯i+1,(n,2n)Ni+1(r→,t)φ(r→,t)+∑kNk(r→,t)λk→i. Let us name σ¯i,a+σ¯i,(n,2n)+σ¯i,(n,3n)+⋯ as σ¯i,t,
effective transmutation cross-section of the nuclide
i. The previous
equations show that destruction rate is as high as follows.(1)
The effective
transmutation cross-section of the nuclidei is high.(2)
The effective
transmutation cross-sections of the precursory nuclides is small or, if it is
high, its most important term is the fission cross-section.(3)
The fluence is
high (i.e., the intensity of the neutron flux is high or the irradiation time
is long).(4)
The decay
constant of the nuclidei is high while the ones of the precursors are
small.
The (n,xn) cross-sections of the actinides are not so important if
compared with the capture or fission cross-sections, so we can neglect them in
transmutation analysis. Similarly, the decay constants are small if compared
with the transmutation rates. Then, we can use the following simplified
equations:(4)ddtNi(r→,t)=−σ¯i,aNi(r→,t)φ(r→,t)+σ¯i−1,cNi−1(r→,t)φ(r→,t). In order to reduce the long-term radiotoxicity of the SNF, the best
transmutation way is fission (direct, if the nuclide is fissile, or indirect,
by way of conversion from fertile to fissile). In fact, capture reactions (also
followed by decay) cause the buildup of other very radiotoxic actinides, while
fissions produce elements
with shorter (except few cases) half-lives. Please note that the effective
cross-sections are obtained by weighting over the neutron spectrum.


### 2.2. Thermal versus Fast Spectrum

As showed by
the previous equations, the energy distribution of the neutrons is a very
important parameter from the transmutation point of view. Regarding HM, their
typical absorption cross-section, as known, can be subdivided into three main
regions as follows:(1)
thermal
range, with an approximately1/v
trend (roughly up to 0.625 eV); in this
region, the fission cross-section is larger than the capture cross-section only
for the fissile nuclides;(2)
resonance
region (between 0.625 eV and 100 keV);(3)
fast
region (above 100 keV), where the fission and capture cross-section are
similar, around 1 barn; particularly, all the HM nuclides are fissile above 1 MeV (threshold).
Although the
fission spectrum is fast (the mean energy is around 2 MeV, while the most
probably energy is about 1 MeV), interactions between neutrons and the
materials of a fast reactor (i.e., inelastic and elastic scatterings) cut off the
mean energy to about 100÷200 keV. So, the fission of fertile nuclides by
neutrons above the threshold is rare (ε≈1.15÷1.20 in fast
reactors [8]).Nevertheless, in order to transmute the HM, a fast
spectrum is better than a thermal one because of the following.(i)
The
higher fluence due to the higher neutron flux intensity (in fast spectrum the
effective fission cross-section is lower, so that an higher flux intensity is
requested to produce the same fission power) increases the HM consumption.(ii)
In
fast spectrum, theα=σc/σf ratio is smaller than in thermal for many
actinides.(iii)
The
neutron productionvσf is higher, so that there is an excess of
neutrons which are available to transmute nuclides.
These considerations can be summarized by a
“reactivity parameter” (RP) defined [8] as(5)RP=σf(v−1−α). RP represents the
(v−1−α) neutrons provided by the
fuel multiplied by σf. (The used cross-sections are obviously one-group homogenized
over the reactor spectrum.)
Higher RP means that transmutation probability increases. (Let us remember that in
the past RP was used in order to evaluate the potential of breeding of a core
concept. According to the Gen-IV goals [4], the
innovative reactors must have a
BG = 0 (self-sustaining from the fissile material point of view); so, the neutron
excess that in the past was useful in order to breed a fertile blanket is now
available for other purposes, mainly transmutation.) Moreover, a positive RP means that
the considered material or nuclide produces more neutrons than it consumes and
vice versa. As we will see in the next paragraph, RP is a useful parameter to
compare the transmutation performance of different kind of core.Theoretically, it has been proposed [9] also to
convert by neutron capture the MA in nuclides with a spontaneous fission
probability of 100% (i.e., some isotopes of Bk and Cf), in order to obtain a
complete transmutation but it is very challenging from the technological
viewpoint.


### 2.3. Innovative Gas-Cooled Thermal and
Fast Reactors

HTRs are
helium-cooled, graphite-moderated high-temperature reactors. These peculiar
characteristics have many positive consequences also from the neutronic point
of view as follows.(i)
The use of helium
as coolant and of graphite as moderator and structural material entails reduced
parasitic captures and then a very good neutron economy.(ii)
Moderator
separated from a neutronically inert coolant allows to change the lattice
parameters without changing dramatically the cooling conditions. This implies a
very large flexibility in the choice of the fuel and of the fuel cycle (e.g.,
HTR can be loaded by Pu without fertile material). (If a loss of coolant occur, the spectral shift
is less important than in an LWR and the void coefficient remains negative [1].
Moreover, the spectrum of GCFR is harder than that of an SFR.)
HTRs allow obtaining
a very high burnup (up to 750 GWD/tHM when fuelled by PuO2) thanks
to the irradiation endurance of the coated particles. This fact implies higher
fluence than in LWR, with a beneficial effect on the transmutation capability. Moreover,
HTR has a slightly epithermal spectrum if compared with LWR
(Figure 1).Figure 1
Comparison between LWR and HTR neutron spectrum [10].The neutron
density in the slowing down range is higher in HTR than in LWR, because the mean lethargic increase of the neutrons is higher with
hydrogen than with carbon. Nevertheless, the thermal peak in LWR is smaller because
of capture by hydrogen nuclei. Thus, HTR seems to have a better transmutation
capability than LWR.The aim of the
GCFR concept is coupling the positive characteristics of the helium-cooled
reactors (high temperature, chemical and neutronic inertia of the coolant) with
those of the fast reactors (better neutron economy and great possibility to
choice structural and fuel materials). (Due to He, GCFR has, e.g., a lower (positive)
void coefficient than that of a typical sodium-cooled fast reactor.)It is useful to
show the RP for some relevant actinides, calculated over the spectrum of a
pebble-bed HTR and a plate-type GCFR, Table1.Table 1
Reactivity parameter for some actinides in a different kind of high
temperature gas reactor [11].
Np237Pu238Pu239Pu240Pu241Pu242Am243Cm244RP HTR−27.0−53.1+181.1−143.3+212.6-46.0−82.5−25.5RP
GCFR+1.40−1.40+3.17+0.01+5.40−0.07−1.50+0.21It is clear
that almost all the actinide nuclide in the fast spectrum of GCFR produce more
neutron than those they consume. Nevertheless, in order to obtain an efficient
transmutation to fulfil the  previous conditions, the use of GCFR is necessary but not enough, as we will
illustrate in the next paragraph.


### 2.4. The Dedicated Assembly Concept: A Way
to Increase Advantages Minimizing Drawbacks

As already  mentioned,
thermal  reactors are
characterized by very large cross-sections but low fluence; while in fast
reactor, the fluence is higher but the cross-sections of the nuclides are low,
especially these ones of some MA. Because both high fluence and high
cross-sections are requested in order to obtain a good transmutation rate, it
seems to be useful to adopt some different moderated assemblies in the core of
a fast reactor, in order to couple high fluence with high cross-sections. At
present, many concepts of dedicated assembly have been designed for LMFBR but
also for GCFR (see, e.g., [12]). However, while a moderated dedicated assembly
enhances greatly the transmutation efficiency for nuclide like Np237 and Am241, it has no effect or a negative one in the case of MA with
low cross-section for all energy ranges as Cm244 or Cm246.
Of course, many researches are still to be performed on this topic.


### 2.5. Challenges

TRU loading is challenging from the safety point of
view. In fact, TRUs
are material characterized by a low delayed neutron fraction and are composed
by lots of nuclides with different behavior in the resonance region. (In fact, the
fission-yield of the precursor nuclei varies with both the type of
fissioned-nuclide and the energy of the neutrons inducing fission.) Moreover, concerning
thermal reactors, if a Pu+MA fuel is used, a higher enrichment in fissile
nuclides is requested than in UOx  fuel, because TRU nuclides have generally a higher capture-to-fission ratio.Fertile material like U238 or Th232 has a positive effect both on delayed neutron fraction and Doppler feedback, so
it can “counterbalance” the effect of the TRU load. The spectrum of HTRs makes
the Doppler coefficient strong negative, so that HTRs can be loaded with
fertile-free fuel [1]. In GCFR, the high mass of DU in the core has a
beneficial effect on the safety parameters; nevertheless further studies are
still needed.The following Table2 shows the effect of fertile
material in the fuel on the total delayed neutron fraction.Table 2(a)
Delayed neutron fraction (vD is the number of delayed neutrons per fission, vtotal is the
total number of neutrons per fission) [13].
IsotopevD/vtotalU2380.0151Th2320.0209U2350.00673Pu2390.00187Pu2410.00462Pu2420.00573Np2370.00334Am2410.00114Am2430.00198Cm2420.00033(b)
Example of delayed neutrons fraction [13].
Example⇒10% fertile fission raises β in fertile
containingfast reactor fuel to:β(U235)β(Pu239)0.10⋅0.0151+0.90⋅0.00187= 0.00151+0.00168= 0.00319(Nearly doubleβ vis-à-vis fertile-free fuel


## 2.1. Theory

The term “transmutation” is applied to all the nuclear reactions
which transform a nuclide into another nuclide. In nuclear reactors,
transmutation happens by way of(n,c), (n,f), and (n,2n) reactions typically.
It is clear that the probability of transmutation for a nuclide is strictly
linked to its effective cross-sections for (n,c), (n,f), (n,2n) reactions in
the considered core. Moreover, the transmutation rate depends obviously also
from the neutron flux intensity. Let us call to mind some useful parameters in
transmutation studies [7]. The neutron spectrum is defined as(1)χ(r→,E,t)=φ(r→,E,t)φ(r→,t), where φ is the neutron flux, while the effective
cross-section of the nuclide n for the reaction x is expressed by(2)σ¯n,x(r→,t)=∫0.001eV10MeVσn,x(E)χ(r→,E,t)dE. The upper integration limit depends from the fission spectrum
(typical of a given nuclide); while the lower limit considers that at the
reactor temperature, the neutron energy is higher than 0.001 eV (in an LWR the
mean energy of the thermal neutrons is about 0.04 eV, e.g.).The transmutation rate for a nuclidei is determined  by Bateman’s equations:(3)ddtNi(r→,t)=−λiNi(r→,t)−(σ¯i,a+σ¯i,(n,2n)+⋯)Ni(r→,t)φ(r→,t)+σ¯i−1,cNi−1(r→,t)φ(r→,t)+σ¯i+1,(n,2n)Ni+1(r→,t)φ(r→,t)+∑kNk(r→,t)λk→i. Let us name σ¯i,a+σ¯i,(n,2n)+σ¯i,(n,3n)+⋯ as σ¯i,t,
effective transmutation cross-section of the nuclide
i. The previous
equations show that destruction rate is as high as follows.(1)
The effective
transmutation cross-section of the nuclidei is high.(2)
The effective
transmutation cross-sections of the precursory nuclides is small or, if it is
high, its most important term is the fission cross-section.(3)
The fluence is
high (i.e., the intensity of the neutron flux is high or the irradiation time
is long).(4)
The decay
constant of the nuclidei is high while the ones of the precursors are
small.
The (n,xn) cross-sections of the actinides are not so important if
compared with the capture or fission cross-sections, so we can neglect them in
transmutation analysis. Similarly, the decay constants are small if compared
with the transmutation rates. Then, we can use the following simplified
equations:(4)ddtNi(r→,t)=−σ¯i,aNi(r→,t)φ(r→,t)+σ¯i−1,cNi−1(r→,t)φ(r→,t). In order to reduce the long-term radiotoxicity of the SNF, the best
transmutation way is fission (direct, if the nuclide is fissile, or indirect,
by way of conversion from fertile to fissile). In fact, capture reactions (also
followed by decay) cause the buildup of other very radiotoxic actinides, while
fissions produce elements
with shorter (except few cases) half-lives. Please note that the effective
cross-sections are obtained by weighting over the neutron spectrum.


## 2.2. Thermal versus Fast Spectrum

As showed by
the previous equations, the energy distribution of the neutrons is a very
important parameter from the transmutation point of view. Regarding HM, their
typical absorption cross-section, as known, can be subdivided into three main
regions as follows:(1)
thermal
range, with an approximately1/v
trend (roughly up to 0.625 eV); in this
region, the fission cross-section is larger than the capture cross-section only
for the fissile nuclides;(2)
resonance
region (between 0.625 eV and 100 keV);(3)
fast
region (above 100 keV), where the fission and capture cross-section are
similar, around 1 barn; particularly, all the HM nuclides are fissile above 1 MeV (threshold).
Although the
fission spectrum is fast (the mean energy is around 2 MeV, while the most
probably energy is about 1 MeV), interactions between neutrons and the
materials of a fast reactor (i.e., inelastic and elastic scatterings) cut off the
mean energy to about 100÷200 keV. So, the fission of fertile nuclides by
neutrons above the threshold is rare (ε≈1.15÷1.20 in fast
reactors [8]).Nevertheless, in order to transmute the HM, a fast
spectrum is better than a thermal one because of the following.(i)
The
higher fluence due to the higher neutron flux intensity (in fast spectrum the
effective fission cross-section is lower, so that an higher flux intensity is
requested to produce the same fission power) increases the HM consumption.(ii)
In
fast spectrum, theα=σc/σf ratio is smaller than in thermal for many
actinides.(iii)
The
neutron productionvσf is higher, so that there is an excess of
neutrons which are available to transmute nuclides.
These considerations can be summarized by a
“reactivity parameter” (RP) defined [8] as(5)RP=σf(v−1−α). RP represents the
(v−1−α) neutrons provided by the
fuel multiplied by σf. (The used cross-sections are obviously one-group homogenized
over the reactor spectrum.)
Higher RP means that transmutation probability increases. (Let us remember that in
the past RP was used in order to evaluate the potential of breeding of a core
concept. According to the Gen-IV goals [4], the
innovative reactors must have a
BG = 0 (self-sustaining from the fissile material point of view); so, the neutron
excess that in the past was useful in order to breed a fertile blanket is now
available for other purposes, mainly transmutation.) Moreover, a positive RP means that
the considered material or nuclide produces more neutrons than it consumes and
vice versa. As we will see in the next paragraph, RP is a useful parameter to
compare the transmutation performance of different kind of core.Theoretically, it has been proposed [9] also to
convert by neutron capture the MA in nuclides with a spontaneous fission
probability of 100% (i.e., some isotopes of Bk and Cf), in order to obtain a
complete transmutation but it is very challenging from the technological
viewpoint.


## 2.3. Innovative Gas-Cooled Thermal and
Fast Reactors

HTRs are
helium-cooled, graphite-moderated high-temperature reactors. These peculiar
characteristics have many positive consequences also from the neutronic point
of view as follows.(i)
The use of helium
as coolant and of graphite as moderator and structural material entails reduced
parasitic captures and then a very good neutron economy.(ii)
Moderator
separated from a neutronically inert coolant allows to change the lattice
parameters without changing dramatically the cooling conditions. This implies a
very large flexibility in the choice of the fuel and of the fuel cycle (e.g.,
HTR can be loaded by Pu without fertile material). (If a loss of coolant occur, the spectral shift
is less important than in an LWR and the void coefficient remains negative [1].
Moreover, the spectrum of GCFR is harder than that of an SFR.)
HTRs allow obtaining
a very high burnup (up to 750 GWD/tHM when fuelled by PuO2) thanks
to the irradiation endurance of the coated particles. This fact implies higher
fluence than in LWR, with a beneficial effect on the transmutation capability. Moreover,
HTR has a slightly epithermal spectrum if compared with LWR
(Figure 1).Figure 1
Comparison between LWR and HTR neutron spectrum [10].The neutron
density in the slowing down range is higher in HTR than in LWR, because the mean lethargic increase of the neutrons is higher with
hydrogen than with carbon. Nevertheless, the thermal peak in LWR is smaller because
of capture by hydrogen nuclei. Thus, HTR seems to have a better transmutation
capability than LWR.The aim of the
GCFR concept is coupling the positive characteristics of the helium-cooled
reactors (high temperature, chemical and neutronic inertia of the coolant) with
those of the fast reactors (better neutron economy and great possibility to
choice structural and fuel materials). (Due to He, GCFR has, e.g., a lower (positive)
void coefficient than that of a typical sodium-cooled fast reactor.)It is useful to
show the RP for some relevant actinides, calculated over the spectrum of a
pebble-bed HTR and a plate-type GCFR, Table1.Table 1
Reactivity parameter for some actinides in a different kind of high
temperature gas reactor [11].
Np237Pu238Pu239Pu240Pu241Pu242Am243Cm244RP HTR−27.0−53.1+181.1−143.3+212.6-46.0−82.5−25.5RP
GCFR+1.40−1.40+3.17+0.01+5.40−0.07−1.50+0.21It is clear
that almost all the actinide nuclide in the fast spectrum of GCFR produce more
neutron than those they consume. Nevertheless, in order to obtain an efficient
transmutation to fulfil the  previous conditions, the use of GCFR is necessary but not enough, as we will
illustrate in the next paragraph.


## 2.4. The Dedicated Assembly Concept: A Way
to Increase Advantages Minimizing Drawbacks

As already  mentioned,
thermal  reactors are
characterized by very large cross-sections but low fluence; while in fast
reactor, the fluence is higher but the cross-sections of the nuclides are low,
especially these ones of some MA. Because both high fluence and high
cross-sections are requested in order to obtain a good transmutation rate, it
seems to be useful to adopt some different moderated assemblies in the core of
a fast reactor, in order to couple high fluence with high cross-sections. At
present, many concepts of dedicated assembly have been designed for LMFBR but
also for GCFR (see, e.g., [12]). However, while a moderated dedicated assembly
enhances greatly the transmutation efficiency for nuclide like Np237 and Am241, it has no effect or a negative one in the case of MA with
low cross-section for all energy ranges as Cm244 or Cm246.
Of course, many researches are still to be performed on this topic.


## 2.5. Challenges

TRU loading is challenging from the safety point of
view. In fact, TRUs
are material characterized by a low delayed neutron fraction and are composed
by lots of nuclides with different behavior in the resonance region. (In fact, the
fission-yield of the precursor nuclei varies with both the type of
fissioned-nuclide and the energy of the neutrons inducing fission.) Moreover, concerning
thermal reactors, if a Pu+MA fuel is used, a higher enrichment in fissile
nuclides is requested than in UOx  fuel, because TRU nuclides have generally a higher capture-to-fission ratio.Fertile material like U238 or Th232 has a positive effect both on delayed neutron fraction and Doppler feedback, so
it can “counterbalance” the effect of the TRU load. The spectrum of HTRs makes
the Doppler coefficient strong negative, so that HTRs can be loaded with
fertile-free fuel [1]. In GCFR, the high mass of DU in the core has a
beneficial effect on the safety parameters; nevertheless further studies are
still needed.The following Table2 shows the effect of fertile
material in the fuel on the total delayed neutron fraction.Table 2(a)
Delayed neutron fraction (vD is the number of delayed neutrons per fission, vtotal is the
total number of neutrons per fission) [13].
IsotopevD/vtotalU2380.0151Th2320.0209U2350.00673Pu2390.00187Pu2410.00462Pu2420.00573Np2370.00334Am2410.00114Am2430.00198Cm2420.00033(b)
Example of delayed neutrons fraction [13].
Example⇒10% fertile fission raises β in fertile
containingfast reactor fuel to:β(U235)β(Pu239)0.10⋅0.0151+0.90⋅0.00187= 0.00151+0.00168= 0.00319(Nearly doubleβ vis-à-vis fertile-free fuel


## 3. The Level of Mine (LOM) Concept as Reference Parameter: Definition and Discussion

### 3.1. Radiotoxicity

Radiotoxicity is a measure for the dose that a human suffers
when a certain amount of radioactive nuclides enters the body [1]. The activity
of the material, the half-life of its constituent nuclides, the type of
radiation, the energy of the emitted particles, the way the radionuclides enter
the human body (inhalation/ingestion), the organs that are exposed to the
radiation, and the time that the nuclides stay in different organs (biological half-lives)
determine the value of this parameter. However, we should not forget that
radiotoxicity indicates a potential hazard upon ingestion and/or inhalation,
thus if the radionuclides are sufficiently separated from the biosphere, no
dose is suffered [1].


### 3.2. Level-of-Mine Balancing Time

Nevertheless, it is difficult to guarantee the perfect
integrity  of a human-made confinement beyond 10·000 years [3], then in
international context the LOM is used as reference parameter. A reactor or fuel
cycle has a positive impact on long-term spent fuel management if it reduces
the time that the spent fuel takes to reach the radiotoxicity level of the
original uranium ore from which is extracted (see [14], level of mine balancing
time (LOMBT)). Because the level of mine is the radiotoxicity of a quantity of
natural uranium, it is expressed in Sv. The LOMBT dimension is a time usually
expressed in years.In order to find the LOMBT of the spent fuel from the
irradiation cycles showed in the following paragraphs, we have had to calculate
the corresponding LOM. We assumed 20 mSv/gU as radiotoxicity of natural uranium
[15], while we have neglected the radiotoxicity of thorium, if present. Consider,
for instance, a quantity of natural uranium that is enriched and then used as
fuel in a chain of reactors (Figure 2).Figure 2
Sketch for LOM calculation.The
radiotoxicity of SNF will depend by the initial fuel composition, the kind of
reactor, and the burnup. The corresponding level of mine is obtained
calculating the mass of natural uranium that generated the considered quantity
of SNF.This equivalent
natural uranium is given by going backward in the following recursive system:(6)Ii=Qi−1⋅fi,Qi=(Ii+Fi)⋅bi, where(1)
Ri
is the ith reactor;(2)
Ii is the fuel loaded in the nth reactor (then let us assume
I0=Unat);(3)
fi
is the ratio between the input HM mass for the ith reactor
and the output HM mass of the (i−1)th reactor;(4)
Fi
is the natural uranium quantity equivalent to be added to the spent
fuel from the (n−1)th in order to manufacture the fuel of the nth reactor;(5)
bi is the ith reactor burnup expressed as mass of HM
discharged/mass of HM loaded (of course b0=1);(6)
Qi
is the fuel discharged from the nth reactor.
After having
found the I0=Unat  mass (expressed in grams), the LOM is
obtained as follows:
(7)LOM=Unat⋅20mSv/gUnat.


## 3.1. Radiotoxicity

Radiotoxicity is a measure for the dose that a human suffers
when a certain amount of radioactive nuclides enters the body [1]. The activity
of the material, the half-life of its constituent nuclides, the type of
radiation, the energy of the emitted particles, the way the radionuclides enter
the human body (inhalation/ingestion), the organs that are exposed to the
radiation, and the time that the nuclides stay in different organs (biological half-lives)
determine the value of this parameter. However, we should not forget that
radiotoxicity indicates a potential hazard upon ingestion and/or inhalation,
thus if the radionuclides are sufficiently separated from the biosphere, no
dose is suffered [1].


## 3.2. Level-of-Mine Balancing Time

Nevertheless, it is difficult to guarantee the perfect
integrity  of a human-made confinement beyond 10·000 years [3], then in
international context the LOM is used as reference parameter. A reactor or fuel
cycle has a positive impact on long-term spent fuel management if it reduces
the time that the spent fuel takes to reach the radiotoxicity level of the
original uranium ore from which is extracted (see [14], level of mine balancing
time (LOMBT)). Because the level of mine is the radiotoxicity of a quantity of
natural uranium, it is expressed in Sv. The LOMBT dimension is a time usually
expressed in years.In order to find the LOMBT of the spent fuel from the
irradiation cycles showed in the following paragraphs, we have had to calculate
the corresponding LOM. We assumed 20 mSv/gU as radiotoxicity of natural uranium
[15], while we have neglected the radiotoxicity of thorium, if present. Consider,
for instance, a quantity of natural uranium that is enriched and then used as
fuel in a chain of reactors (Figure 2).Figure 2
Sketch for LOM calculation.The
radiotoxicity of SNF will depend by the initial fuel composition, the kind of
reactor, and the burnup. The corresponding level of mine is obtained
calculating the mass of natural uranium that generated the considered quantity
of SNF.This equivalent
natural uranium is given by going backward in the following recursive system:(6)Ii=Qi−1⋅fi,Qi=(Ii+Fi)⋅bi, where(1)
Ri
is the ith reactor;(2)
Ii is the fuel loaded in the nth reactor (then let us assume
I0=Unat);(3)
fi
is the ratio between the input HM mass for the ith reactor
and the output HM mass of the (i−1)th reactor;(4)
Fi
is the natural uranium quantity equivalent to be added to the spent
fuel from the (n−1)th in order to manufacture the fuel of the nth reactor;(5)
bi is the ith reactor burnup expressed as mass of HM
discharged/mass of HM loaded (of course b0=1);(6)
Qi
is the fuel discharged from the nth reactor.
After having
found the I0=Unat  mass (expressed in grams), the LOM is
obtained as follows:
(7)LOM=Unat⋅20mSv/gUnat.


## 4. Computer Codes Used

### 4.1. MCNP-4B

We used MCNP mainly as a part of
MONTEBURNS or MCB codes but also  to perform some preliminary evaluations on
initialkeff values. MCNP [16] is a general-purpose Monte Carlo
N-Particle code that can be used for neutron, photon, electron, or coupled
neutron/photon/electron transport, including the capability to calculate
eigenvalues for critical systems.The code treats an arbitrary
three-dimensional configuration of materials in geometric cells bounded by
first- and second-degree surfaces and fourth-degree elliptical tori.Pointwise cross-section data
are used. For neutrons, all reactions given in a particular cross-section file
(such as ENDF/B-VI) are accounted for. Thermal neutrons are described by both
the free gas andS(α,β) models. For photons, the code takes account of
incoherent and coherent scattering, the possibility of fluorescent emission
after photoelectric absorption, pair production, and bremsstrahlung. A
continuous slowing down model is used for electron transport that includes
positrons, x-rays, and bremsstrahlung but does not include external or
self-induced fields.Important standard features
that make MCNP very versatile and easy to use include a powerful general
source, criticality source, and surface source; both geometry and output tally
plotters; a rich collection of variance reduction techniques; a flexible tally
structure; and an extensive collection of cross-section data.


### 4.2. ORIGEN2.1

We used ORIGEN mainly as
a part of MONTEBURNS code. ORIGEN [17, 18]
is a computer code system for calculating the buildup, decay, and processing of
radioactive materials. ORIGEN2 is a revised version of the original ORIGEN and
incorporates updates of the reactor models, cross-sections, fission product
yields, decay data, and decay photon data, as well as the source code. ORIGEN2.1
replaces ORIGEN and includes additional libraries for standard and
extended-burnup PWR and BWR calculations, which are documented in
ORNL/TM-11018. ORIGEN2.1 was first released in August 1991.ORIGEN uses a matrix exponential method to solve a
large system of coupled, linear, first-order ordinary differential equations
with constant coefficients.
ORIGEN2 has been variably dimensioned to allow the user to tailor the size of
the executable module to the problem size and/or the available computer space.
Dimensioned arrays have been set large enough to handle almost any size
problem, using virtual memory capabilities. The user is provided with much of
the framework necessary to put some of the arrays to several different uses,
call for the subroutines that perform the desired operations, and provide a
mechanism to execute multiple ORIGEN2 problems with a single job.ORIGEN2 solves Bateman's equations by matrix
exponential method. The system of differential equations can be written as
follows:(8)X˙(t)=AX(t), where(1)
X is the
column vector of the nuclide concentration;(2)
A is the
transition matrix containing the transformation rates.
This equation has the solution(9)X(t)=X(0)⋅eAt, where X(0) is the vector of initial nuclide
concentrations.The matrix exponential method generatesX(t) expanding
in series the exponential function (incorporating enough terms in order to
obtain the desired accuracy):(10)X(t)=X(0)[I+At+12(At)2+⋯].


### 4.3. MONTEBURNS1.0

We used MONTEBURNS in order to perform all the burnup
calculations except for those ones referred to [19, 20].MONTEBURNS [21] couples MCNP [16] and ORIGEN [17]
codes through MONTEB utility and a PERL [22] procedure. MONTEBURNS produces a
large number of criticality and burnup results based on various material
feed/removal specifications, power(s), and time intervals.MONTEBURNS [18] processes input from the user that
specifies the system geometry, initial material compositions, feed/removal
specifications, and other code-specific parameters. Various results from MCNP,
ORIGEN2, and other calculations are then output successively as the code runs.
The principle function of MONTEBURNS is to transfer one-group cross-section and
flux values from MCNP to ORIGEN2, and then transfer the resulting material
compositions (after irradiation and/or decay) from ORIGEN2 back to MCNP in a
repeated, cyclic fashion (a simple predictor-corrector method is used during
this process).The depletion equations use fluxes, nuclide number
densities and cross-sections to determine the time-dependent nuclide inventory.
The simplified one-group depletion equation is [23](11)dN(r,t)dt=−φ(r,t)⋅σ(r)⋅N(r,t). The solution for nuclide density is(12)N(r,t)=N0(r)e−σ(r)∫t1t2φ(r,t)dt. Thus, the change in nuclide concentration is dependent
on the fluence. However, the time-dependent flux depends on the nuclide
density, then the previous equation is not linear. In order to make the
equation linear, it is necessary to assume the flux constant throughout the
burn step equal to the average flux over the entire burn step:(13)N(r,t)=N0(r)e−σ(r)φ(r)average. MONTEBURNS, as already anticipated, makes an
approximation of the average flux behavior by using a predictor-corrector
method as follows.(1)
Firstly, MCNP runs in order to calculate the initial
macroscopic one-group cross-sections and flux over the core.(2)
Then, ORIGEN is executed in order to perform a burnup
calculation over the half time step[t(i)→t(i+1/2)]: this is the
“Predictor-step.”(3)
Fluxes and collision densities are recalculated by
MCNP at the half-time step (based on the nuclide inventory found by ORIGEN
during the predictor step).(4)
These fluxes and collision densities are used by
ORIGEN to perform the burnup calculation over the full time step[t(i)→t(i+1)]:
this is the “Corrector-step.”
Obviously, the time steps cannot be too long, in order
to avoid unacceptable changes of the flux shape.


### 4.4. MCB

We used MCB in order to perform the burnup
calculations referred to [19, 20].MCB [24] is a
general-purpose MC code used to calculate the evolution in time of nuclide
density and composition, taking burnup, and decay into  account. It was
developed by  Cetnar,  Gudowski, and
Wallenius and can perform both
eigenvalue calculations for critical and subcritical systems as well and neutron
transport calculations in fixed source mode or k-code mode, to obtain reaction
rates and energy deposition that are necessary for burnup calculations. This
code integrates the well-known code MCNP [16], version 4C, which is used for
neutron transport calculation, and a novel TTA code [25], which serves for
density evolution calculation, including formation and analysis of the
transmutation chain. MCB is compatible with MCNP and preserves its structure,
so that a complete burnup calculation can be performed in one single run,
requiring just slight modification of an MCNP input file. The code was
extensively tested by the authors in benchmark calculations and reactor core
designing. The general conclusion from practical application shows that MCB version
1C produces valuable results that are physically consistent, and the
correctness of physical model applied has been proved. This version of MCB can
also simulate material processing including continuous feeding of materials
that is the most important for our purpose. Development of the code was
addressed towards improving calculation effectiveness, system diagnostic, and
physical model for rigorous treatment but also providing simplified model
option for quick design studies or benchmarks. The TTA code [25] implements a new technique of Bateman
equation solutions which adequately represents the physics of the transmutation
process, and thus it is capable of delivering additional information of the
transmutation process when compared to the matrix method. This approach allows
the user to obtain qualitative and quantitative trajectories of transmutations
additionally to densities of transmuted nuclides.


### 4.5. WIMSD5B.12

We have used
WIMS code in order to perform some preliminary parametric evaluations on HTR and
GCFR cores. Winfrith improved multigroup scheme (WIMSD) [26] is a deterministic
code that sets out to calculate neutron flux  distribution and values
of k-infinity or k-effective. To do
this it has to solve a mathematical form of the neutron transport equation.
WIMSD is a very useful tool to perform quickly calculation for analysis of
experiments, criticality and power reactor design, assessment and operation.
There are currently three versions of WIMS, namely WIMSD, WIMS-E (now up to version
WIMS-8), and LWRWIMS. All versions use a WIMS library, initially in 69 energy
groups and containing equivalent data. WIMSD (originally WIMS, followed by
versions A to D) was developed from 1963÷5, with some later improvements. It is
a single code with a limited number of options, is fast in execution, and is
recommended for straightforward “pin-cell” and cluster calculations. In the
late 1960s, development on WIMS-E began to provide a modular code scheme giving
the user much more flexibility in choosing his options. Execution time may be
much longer than those for WIMSD so that WIMS-E is used for problems that WIMSD
cannot calculate adequately. LWRWIMS has a structure which is based on that of
WIMS-E although the modules are bound together in a single program. Development
started in the early 1970s and has continued at a low level since then. LWRWIMS
was written specifically for light water reactor geometries. In summary, WIMSD
is useful for homogeneous slab, pin-cell or cylindrical cluster geometries. It
has been developed substantially for GCR, AGR, CANDU, and RBMK, although it can
be used with caution also for other kinds of reactor.


### 4.6. XSDRNPM

We have used
XSDRNPM code in order to perform some preliminary parametric evaluations on
GCFR cores. XSDRNPM [27] is a discrete-ordinates code that solves
the one-dimensional Boltzmann equation in slab, cylindrical, or spherical
coordinates. Alternatively, the user can select  p1
diffusion
theory, infinite medium theory, or Bn theory.
A variety of calculational types is available, including fixed source,
eigenvalue, or “search” calculations. In SCALE, XSDRNPM is used for
several purposes: eigenvalue (keff) determination, cross-section
collapsing, shielding analysis, and for producing bias factors for use in Monte Carlo  shielding calculations.


### 4.7. CARL

We have
developed CARL code in order to perform in a quick but reliable way all the
radiotoxicity evaluations for the spent fuel (outside the reactors). Calculation of radiotoxicities lifetime
(CARL) code was originally (in 2003) developed for master degree thesis
purposes [19] in MATHCAD environment.
It originally calculated the radiotoxic (ingestion) inventory evolution versus
time of a given radionuclide composition. It was developed in order to perform
the complex calculations regarding the nuclear spent fuel hazard versus time
(it was supposed, prudentially, that water could, in a remote future, corrode
casks, and transport radionuclides to biosphere). It is well known in fact that
the danger coming from nuclear waste over time decreases continuously due to
radioactive decay. Version 2 of the code was developed in MATLAB environment (MATLAB 6.5, release 13 or higher required), and
was strongly enhanced: it performs in addition to radiotoxicity, also activity,
dose and decay power calculations; it displays also the “Gamma Spectrum,” a 3D plot indicating the activity of gamma rays versus
time and radiation energy. Code’s input can be given manually (in grams for
every nuclide), or by file (by using MCB-1C, MONTEBURNS-1.0 output file, or
CARL input file).The present
version of the code (2.2) presents the following additional features: it
includes U232 isotope (very useful in thorium fuel cycles
calculations) and common nuclear reactors activation materials (Cr51,
Mn56, Fe59, Co60, Ni65, Cu64,
Zn65, Zn69, Zr95, Mo99, Ta182,
W187) [28], and displays also two additional plots indicating the equivalent gamma dose rate (in mSv/h) versus
time (the distance considered, in meters, is assigned in input), both in air
and in concrete/rock; moreover it displays the masses (in grams) in the text
output file of all the radionuclides at the various logarithmically spaced time
points.The
calculation procedure implemented by CARL 2.2 solves theBateman equations for radioactive decay chains. If we have chain radioactive
decays, and we refer to the initial nucleus as 1, to the succeeding generations
(daughter) as 2, granddaughter as 3, and so forth, that is, (14)1→2→3→4→⋯, it
will be [28](15)dNi=λi−1Ni−1dt−λiNidt, (every
nuclide will decay and will be produced from its parent decay).IfN0 is the number of initial nuclei of type 1 and none of the other
types are present, the activity of the nth nuclide will be(16)An=N0∑i=1ncie−λit=N0(c1e−λ1t+c2e−λ2t+⋯+cne−λnt),cm=∏i=1nλi∏i=1,i≠mn(λi−λm)=λ1λ2λ3⋅⋅⋅λn(λ1−λm)(λ2−λm)⋅⋅⋅(λn−λm). The
code divides the time interval in 50 logarithmically spaced points (by default, which obviously may be changed
by the user). Activities are then multiplied for the dose factors (Sv/Bq) [28] to obtain the
(ingestion) radiotoxicities. Partial activities and radiotoxicities are summed up
to obtain totals.Then
code multiplies the calculated activities for the respective decay energies
(expressed in MeV [28]) and for 1.6⋅10−13 to obtain watts from
MeV/sec (1 eV = 1.6⋅10−19 J).To
obtain the integrated dose to materials from time 0 tot, we have to integrate the activity,
multiply the result for the energy of disintegration (in MeV) and divide for
the number of grams to obtain MeV/g; we will multiply the result by 1.6⋅10−10 to express the integrated dose versus time in
Grays (1 Gray
= 1 J/Kg = 100 rad):(17)D=(∫0tAdt)⋅E⋅1.6⋅10−10g=(∫0tλN0e−λtdt)⋅E⋅1.6⋅10−10g=N0(1−e−λt)⋅E⋅1.6⋅10−10g(Grays).
Volumes
of water are calculated assuming a daily assumption of 2.5 litres of water by
ingestion, that is, 913 litres/year; dividing this value for the input annual limit (in Sv/year), we obtain the
number of  litres/Sv to maintain the
water potable. Divided by total nuclides mass and multiplying by 106 to obtain m3/ton, we have(18)Volume_Water=Total_Radiotoxicity⋅(913/limit)Total_Mass⋅106(m3/ton). The
Gamma Spectrum represents only the
gamma energy of the radiations (which may be dangerous due to their penetration
power), interesting in case of isotopes handling (e.g., nuclear spent fuel).
Only principal energy decays are considered.Equivalent Dose Rate could be calculated as follows: if we consider a gamma-ray intensity of
Iγ photons/m2· s with an energy of Eγ MeV,
the energy flux will be IγEγ
MeV/m2 s. The rate of energy deposition per unit volume
(in a small volume) will be IγEγμa
MeV/m3s, with μa as the
linear
absorption coefficient (m−1). If ρ is the density of the
material, then IγEγμa/ρ will be the rate of energy deposition
(MeV/Kg s), and remembering that 1MeV=1.60×10−13J and 1rad=10−2J/Kg, it will be(19)Dγ=1.60⋅10−11IγEγμaρ[rad/s]=5.76⋅10−5IγEγμaρ[mrad/h]. Considering
that at a distance R from the source the photons are distributed uniformly over
a sphere of area 4πR2, and that travelling trough a medium (e.g.:
air or concrete) will be attenuated by the factor e−μR, it is(20)Iγ=A4πR2e−μR. Substituting
(20) in (19), it will be(21)AdsorbedDoseRate=5.76⋅10−54π⋅AEγμaR2ρe−μR=4.58⋅10−6⋅AEγμaR2ρe−μR[mrad/h]=4.58⋅10−8⋅AEγμaR2ρe−μR[mSv/h]. The
air density considered is 1.225 Kg/m3 (at room temperature),
concrete/rock density 2500 Kg/m3. The value of μa_air is 5×10−3m−1 for air (an
average value in the range 0.1–2.0 MeV, [2]); for concrete, it was considered
an HVT (Half Value Thickness) of 5 cm, so μa_concrete=ln(2)/(5⋅10−2)=13.863m−1. Total dose rate is
calculated as the sum of every single radionuclide chain contribution.
Obviously it is an approximate value.Radionuclides
masses (in grams) in the text output file are calculated from the following
equations [28]:(22)A(t)=λN(t),N(t)=A(t)λ=m(t)AM⋅NA,m(t)=A(t)⋅AMλ⋅NA,
where AM is the atomic mass of the
radionuclide, NA the Avogadro’s
number, and N(t),
and m(t), respectively, the number of
decaying nuclei and the radionuclide mass at time t.


## 4.1. MCNP-4B

We used MCNP mainly as a part of
MONTEBURNS or MCB codes but also  to perform some preliminary evaluations on
initialkeff values. MCNP [16] is a general-purpose Monte Carlo
N-Particle code that can be used for neutron, photon, electron, or coupled
neutron/photon/electron transport, including the capability to calculate
eigenvalues for critical systems.The code treats an arbitrary
three-dimensional configuration of materials in geometric cells bounded by
first- and second-degree surfaces and fourth-degree elliptical tori.Pointwise cross-section data
are used. For neutrons, all reactions given in a particular cross-section file
(such as ENDF/B-VI) are accounted for. Thermal neutrons are described by both
the free gas andS(α,β) models. For photons, the code takes account of
incoherent and coherent scattering, the possibility of fluorescent emission
after photoelectric absorption, pair production, and bremsstrahlung. A
continuous slowing down model is used for electron transport that includes
positrons, x-rays, and bremsstrahlung but does not include external or
self-induced fields.Important standard features
that make MCNP very versatile and easy to use include a powerful general
source, criticality source, and surface source; both geometry and output tally
plotters; a rich collection of variance reduction techniques; a flexible tally
structure; and an extensive collection of cross-section data.


## 4.2. ORIGEN2.1

We used ORIGEN mainly as
a part of MONTEBURNS code. ORIGEN [17, 18]
is a computer code system for calculating the buildup, decay, and processing of
radioactive materials. ORIGEN2 is a revised version of the original ORIGEN and
incorporates updates of the reactor models, cross-sections, fission product
yields, decay data, and decay photon data, as well as the source code. ORIGEN2.1
replaces ORIGEN and includes additional libraries for standard and
extended-burnup PWR and BWR calculations, which are documented in
ORNL/TM-11018. ORIGEN2.1 was first released in August 1991.ORIGEN uses a matrix exponential method to solve a
large system of coupled, linear, first-order ordinary differential equations
with constant coefficients.
ORIGEN2 has been variably dimensioned to allow the user to tailor the size of
the executable module to the problem size and/or the available computer space.
Dimensioned arrays have been set large enough to handle almost any size
problem, using virtual memory capabilities. The user is provided with much of
the framework necessary to put some of the arrays to several different uses,
call for the subroutines that perform the desired operations, and provide a
mechanism to execute multiple ORIGEN2 problems with a single job.ORIGEN2 solves Bateman's equations by matrix
exponential method. The system of differential equations can be written as
follows:(8)X˙(t)=AX(t), where(1)
X is the
column vector of the nuclide concentration;(2)
A is the
transition matrix containing the transformation rates.
This equation has the solution(9)X(t)=X(0)⋅eAt, where X(0) is the vector of initial nuclide
concentrations.The matrix exponential method generatesX(t) expanding
in series the exponential function (incorporating enough terms in order to
obtain the desired accuracy):(10)X(t)=X(0)[I+At+12(At)2+⋯].


## 4.3. MONTEBURNS1.0

We used MONTEBURNS in order to perform all the burnup
calculations except for those ones referred to [19, 20].MONTEBURNS [21] couples MCNP [16] and ORIGEN [17]
codes through MONTEB utility and a PERL [22] procedure. MONTEBURNS produces a
large number of criticality and burnup results based on various material
feed/removal specifications, power(s), and time intervals.MONTEBURNS [18] processes input from the user that
specifies the system geometry, initial material compositions, feed/removal
specifications, and other code-specific parameters. Various results from MCNP,
ORIGEN2, and other calculations are then output successively as the code runs.
The principle function of MONTEBURNS is to transfer one-group cross-section and
flux values from MCNP to ORIGEN2, and then transfer the resulting material
compositions (after irradiation and/or decay) from ORIGEN2 back to MCNP in a
repeated, cyclic fashion (a simple predictor-corrector method is used during
this process).The depletion equations use fluxes, nuclide number
densities and cross-sections to determine the time-dependent nuclide inventory.
The simplified one-group depletion equation is [23](11)dN(r,t)dt=−φ(r,t)⋅σ(r)⋅N(r,t). The solution for nuclide density is(12)N(r,t)=N0(r)e−σ(r)∫t1t2φ(r,t)dt. Thus, the change in nuclide concentration is dependent
on the fluence. However, the time-dependent flux depends on the nuclide
density, then the previous equation is not linear. In order to make the
equation linear, it is necessary to assume the flux constant throughout the
burn step equal to the average flux over the entire burn step:(13)N(r,t)=N0(r)e−σ(r)φ(r)average. MONTEBURNS, as already anticipated, makes an
approximation of the average flux behavior by using a predictor-corrector
method as follows.(1)
Firstly, MCNP runs in order to calculate the initial
macroscopic one-group cross-sections and flux over the core.(2)
Then, ORIGEN is executed in order to perform a burnup
calculation over the half time step[t(i)→t(i+1/2)]: this is the
“Predictor-step.”(3)
Fluxes and collision densities are recalculated by
MCNP at the half-time step (based on the nuclide inventory found by ORIGEN
during the predictor step).(4)
These fluxes and collision densities are used by
ORIGEN to perform the burnup calculation over the full time step[t(i)→t(i+1)]:
this is the “Corrector-step.”
Obviously, the time steps cannot be too long, in order
to avoid unacceptable changes of the flux shape.


## 4.4. MCB

We used MCB in order to perform the burnup
calculations referred to [19, 20].MCB [24] is a
general-purpose MC code used to calculate the evolution in time of nuclide
density and composition, taking burnup, and decay into  account. It was
developed by  Cetnar,  Gudowski, and
Wallenius and can perform both
eigenvalue calculations for critical and subcritical systems as well and neutron
transport calculations in fixed source mode or k-code mode, to obtain reaction
rates and energy deposition that are necessary for burnup calculations. This
code integrates the well-known code MCNP [16], version 4C, which is used for
neutron transport calculation, and a novel TTA code [25], which serves for
density evolution calculation, including formation and analysis of the
transmutation chain. MCB is compatible with MCNP and preserves its structure,
so that a complete burnup calculation can be performed in one single run,
requiring just slight modification of an MCNP input file. The code was
extensively tested by the authors in benchmark calculations and reactor core
designing. The general conclusion from practical application shows that MCB version
1C produces valuable results that are physically consistent, and the
correctness of physical model applied has been proved. This version of MCB can
also simulate material processing including continuous feeding of materials
that is the most important for our purpose. Development of the code was
addressed towards improving calculation effectiveness, system diagnostic, and
physical model for rigorous treatment but also providing simplified model
option for quick design studies or benchmarks. The TTA code [25] implements a new technique of Bateman
equation solutions which adequately represents the physics of the transmutation
process, and thus it is capable of delivering additional information of the
transmutation process when compared to the matrix method. This approach allows
the user to obtain qualitative and quantitative trajectories of transmutations
additionally to densities of transmuted nuclides.


## 4.5. WIMSD5B.12

We have used
WIMS code in order to perform some preliminary parametric evaluations on HTR and
GCFR cores. Winfrith improved multigroup scheme (WIMSD) [26] is a deterministic
code that sets out to calculate neutron flux  distribution and values
of k-infinity or k-effective. To do
this it has to solve a mathematical form of the neutron transport equation.
WIMSD is a very useful tool to perform quickly calculation for analysis of
experiments, criticality and power reactor design, assessment and operation.
There are currently three versions of WIMS, namely WIMSD, WIMS-E (now up to version
WIMS-8), and LWRWIMS. All versions use a WIMS library, initially in 69 energy
groups and containing equivalent data. WIMSD (originally WIMS, followed by
versions A to D) was developed from 1963÷5, with some later improvements. It is
a single code with a limited number of options, is fast in execution, and is
recommended for straightforward “pin-cell” and cluster calculations. In the
late 1960s, development on WIMS-E began to provide a modular code scheme giving
the user much more flexibility in choosing his options. Execution time may be
much longer than those for WIMSD so that WIMS-E is used for problems that WIMSD
cannot calculate adequately. LWRWIMS has a structure which is based on that of
WIMS-E although the modules are bound together in a single program. Development
started in the early 1970s and has continued at a low level since then. LWRWIMS
was written specifically for light water reactor geometries. In summary, WIMSD
is useful for homogeneous slab, pin-cell or cylindrical cluster geometries. It
has been developed substantially for GCR, AGR, CANDU, and RBMK, although it can
be used with caution also for other kinds of reactor.


## 4.6. XSDRNPM

We have used
XSDRNPM code in order to perform some preliminary parametric evaluations on
GCFR cores. XSDRNPM [27] is a discrete-ordinates code that solves
the one-dimensional Boltzmann equation in slab, cylindrical, or spherical
coordinates. Alternatively, the user can select  p1
diffusion
theory, infinite medium theory, or Bn theory.
A variety of calculational types is available, including fixed source,
eigenvalue, or “search” calculations. In SCALE, XSDRNPM is used for
several purposes: eigenvalue (keff) determination, cross-section
collapsing, shielding analysis, and for producing bias factors for use in Monte Carlo  shielding calculations.


## 4.7. CARL

We have
developed CARL code in order to perform in a quick but reliable way all the
radiotoxicity evaluations for the spent fuel (outside the reactors). Calculation of radiotoxicities lifetime
(CARL) code was originally (in 2003) developed for master degree thesis
purposes [19] in MATHCAD environment.
It originally calculated the radiotoxic (ingestion) inventory evolution versus
time of a given radionuclide composition. It was developed in order to perform
the complex calculations regarding the nuclear spent fuel hazard versus time
(it was supposed, prudentially, that water could, in a remote future, corrode
casks, and transport radionuclides to biosphere). It is well known in fact that
the danger coming from nuclear waste over time decreases continuously due to
radioactive decay. Version 2 of the code was developed in MATLAB environment (MATLAB 6.5, release 13 or higher required), and
was strongly enhanced: it performs in addition to radiotoxicity, also activity,
dose and decay power calculations; it displays also the “Gamma Spectrum,” a 3D plot indicating the activity of gamma rays versus
time and radiation energy. Code’s input can be given manually (in grams for
every nuclide), or by file (by using MCB-1C, MONTEBURNS-1.0 output file, or
CARL input file).The present
version of the code (2.2) presents the following additional features: it
includes U232 isotope (very useful in thorium fuel cycles
calculations) and common nuclear reactors activation materials (Cr51,
Mn56, Fe59, Co60, Ni65, Cu64,
Zn65, Zn69, Zr95, Mo99, Ta182,
W187) [28], and displays also two additional plots indicating the equivalent gamma dose rate (in mSv/h) versus
time (the distance considered, in meters, is assigned in input), both in air
and in concrete/rock; moreover it displays the masses (in grams) in the text
output file of all the radionuclides at the various logarithmically spaced time
points.The
calculation procedure implemented by CARL 2.2 solves theBateman equations for radioactive decay chains. If we have chain radioactive
decays, and we refer to the initial nucleus as 1, to the succeeding generations
(daughter) as 2, granddaughter as 3, and so forth, that is, (14)1→2→3→4→⋯, it
will be [28](15)dNi=λi−1Ni−1dt−λiNidt, (every
nuclide will decay and will be produced from its parent decay).IfN0 is the number of initial nuclei of type 1 and none of the other
types are present, the activity of the nth nuclide will be(16)An=N0∑i=1ncie−λit=N0(c1e−λ1t+c2e−λ2t+⋯+cne−λnt),cm=∏i=1nλi∏i=1,i≠mn(λi−λm)=λ1λ2λ3⋅⋅⋅λn(λ1−λm)(λ2−λm)⋅⋅⋅(λn−λm). The
code divides the time interval in 50 logarithmically spaced points (by default, which obviously may be changed
by the user). Activities are then multiplied for the dose factors (Sv/Bq) [28] to obtain the
(ingestion) radiotoxicities. Partial activities and radiotoxicities are summed up
to obtain totals.Then
code multiplies the calculated activities for the respective decay energies
(expressed in MeV [28]) and for 1.6⋅10−13 to obtain watts from
MeV/sec (1 eV = 1.6⋅10−19 J).To
obtain the integrated dose to materials from time 0 tot, we have to integrate the activity,
multiply the result for the energy of disintegration (in MeV) and divide for
the number of grams to obtain MeV/g; we will multiply the result by 1.6⋅10−10 to express the integrated dose versus time in
Grays (1 Gray
= 1 J/Kg = 100 rad):(17)D=(∫0tAdt)⋅E⋅1.6⋅10−10g=(∫0tλN0e−λtdt)⋅E⋅1.6⋅10−10g=N0(1−e−λt)⋅E⋅1.6⋅10−10g(Grays).
Volumes
of water are calculated assuming a daily assumption of 2.5 litres of water by
ingestion, that is, 913 litres/year; dividing this value for the input annual limit (in Sv/year), we obtain the
number of  litres/Sv to maintain the
water potable. Divided by total nuclides mass and multiplying by 106 to obtain m3/ton, we have(18)Volume_Water=Total_Radiotoxicity⋅(913/limit)Total_Mass⋅106(m3/ton). The
Gamma Spectrum represents only the
gamma energy of the radiations (which may be dangerous due to their penetration
power), interesting in case of isotopes handling (e.g., nuclear spent fuel).
Only principal energy decays are considered.Equivalent Dose Rate could be calculated as follows: if we consider a gamma-ray intensity of
Iγ photons/m2· s with an energy of Eγ MeV,
the energy flux will be IγEγ
MeV/m2 s. The rate of energy deposition per unit volume
(in a small volume) will be IγEγμa
MeV/m3s, with μa as the
linear
absorption coefficient (m−1). If ρ is the density of the
material, then IγEγμa/ρ will be the rate of energy deposition
(MeV/Kg s), and remembering that 1MeV=1.60×10−13J and 1rad=10−2J/Kg, it will be(19)Dγ=1.60⋅10−11IγEγμaρ[rad/s]=5.76⋅10−5IγEγμaρ[mrad/h]. Considering
that at a distance R from the source the photons are distributed uniformly over
a sphere of area 4πR2, and that travelling trough a medium (e.g.:
air or concrete) will be attenuated by the factor e−μR, it is(20)Iγ=A4πR2e−μR. Substituting
(20) in (19), it will be(21)AdsorbedDoseRate=5.76⋅10−54π⋅AEγμaR2ρe−μR=4.58⋅10−6⋅AEγμaR2ρe−μR[mrad/h]=4.58⋅10−8⋅AEγμaR2ρe−μR[mSv/h]. The
air density considered is 1.225 Kg/m3 (at room temperature),
concrete/rock density 2500 Kg/m3. The value of μa_air is 5×10−3m−1 for air (an
average value in the range 0.1–2.0 MeV, [2]); for concrete, it was considered
an HVT (Half Value Thickness) of 5 cm, so μa_concrete=ln(2)/(5⋅10−2)=13.863m−1. Total dose rate is
calculated as the sum of every single radionuclide chain contribution.
Obviously it is an approximate value.Radionuclides
masses (in grams) in the text output file are calculated from the following
equations [28]:(22)A(t)=λN(t),N(t)=A(t)λ=m(t)AM⋅NA,m(t)=A(t)⋅AMλ⋅NA,
where AM is the atomic mass of the
radionuclide, NA the Avogadro’s
number, and N(t),
and m(t), respectively, the number of
decaying nuclei and the radionuclide mass at time t.


## 5. Activity Performed at the University of Pisa

### 5.1. The HTR as Plutonium Burner

In order to demonstrate
the capability of HTRs to contribute in reducing nuclear waste (actinides in
particular), it was decided to analyze Pu-based fuel [14]. In order to validate
the used code (namely MONTEBURNS), an international code-to-code benchmark was
performed. The obtained results have shown a good agreement between the codes
adopted by the different participants, as reported in [29].Particularly, 1st generation Pu [20] (i.e., Pu deriving from reprocessing typical LWR spent fuel)
and 2nd generation Pu [20] (i.e., Pu deriving from the reprocessing
of typical MOX spent fuel) were considered.Therefore the following
calculations were performed:(i)
HTR loaded
with 1 g/pebble 1st generation Pu, 600 GWd/ton (600 EFPD);(ii)
HTR loaded with 1.5 g/pebble 2nd generation
Pu, 430 GWd/ton (645 EFPD).
To check the advantages in using different fuel cycles, the
radiotoxicity evolution of spent fuel versus time was evaluated. As reference
for radiotoxicity, we, as described above, originally defined [14] the
LOMBT
(level of mine balancing time), that is, the interval of time necessary for
the radiotoxicity of the exhausted fuel to return to the values of the mineral
extracted from the mine (in this case of uranium) from which the fuel was generated.The
results show that 1st-generation Pu behaves (in terms of LOMBT)
better than 2nd-generation Pu.In another article [30],
we considered the possibility of adopting Th-Pu fuel cycle and, for the first
time, the use of a (relatively) simplified LWR-HTR-GCFR symbiotic fuel cycle
(Figure 3).Figure 3
Symbiotic fuel cycles (without or with using MOX in LWR).It should be noted that,
in the case of HTR, we considered a once-through fuel cycle. Consequently, we assumed that the waste
contains Pu, MA, and FP. Instead in the case of GCFR, we considered that all
the Pu will be recycled at the end of (each) GCFR step. Consequently, we
assumed that the final waste contains only MA and FP.In Table3, the obtained
results are summarized. In column 7, the ratio between inlet and outlet
transuranic elements (Pu+MA) and in column 8 the ratio between inlet and outlet
actinides (Th+U+Pu+MA) is shown.Table 3
Summary of the obtained results.
CaseReactorFuelLOMBT [y]EnergygPuPuoutPuinTRUoutTRUinActoutActin12345678aHTR1st g-Pu/Th (1/1)37982∗60.16 GJ24.14%31.75%63.88%bHTR1st g-Pu/Th (1/2)37547*59.40 GJ27.75%33.88%76.25%cHTR1st g-Pu/Th (1/3)37117*58.89 GJ29.06%34.37%81.94%dGCFR1st g-Pu∗∗/MA/U238 (10/1/40)9204∗∗∗154.44 GJ85.66%86.77%57.78%eGCFR2nd g-Pu†/MA/U238 (10/1/40)9310***155.26 GJ85.85%87.77%57.57%fGCFR‡2nd g-Pu†/MA/U238 (10/1/40)11860***105.57 GJ98.02%98.95%70.64%∗ In the case of HTR,
we assumed a once-through fuel cycle. Consequently, the waste contains Pu, MA,
and FP.∗∗ 1st-generation Pu is
added to Pu which is
already present in the spent fuel of HTR loaded with 1st-generation
Pu.∗∗∗ In the case of
GCFR, we assumed that all the Pu is recycled. Consequently, the waste contains
only MA and FP.† 2nd-generation Pu is
added to Pu which is
already present in the spent fuel of HTR loaded with  2nd-generation
Pu.‡ In this case, we assumed that
thickness of the external layer of the CP is 0.003 mm instead of 0.005 mm (like
cases d and e). Therefore the spectrum is not so hard as in case e.In the case
of LWRs spent fuel, the LOMBT is about 250000 years [15]. From
Table 3, we can
see that this figure of merit (the most important in terms of safety) is
significantly reduced (an order of magnitude) using HTR and further (recycling
Pu as fuel) by using GCFR to close the cycle.


### 5.2. The GCFR as Actinide Burner

In the first calculations (see previous paragraph) on GCFRs
concepts, we adopted a simplified model for the GCFR core. In the further
calculations, we refined this model, as showed in the following paragraphs.


#### 5.2.1. Comparison among Core Concepts

Three main core concepts exist for GCFR:(1)
particle-bed
core;(2)
pebble-bed
core;(3)
plate-type
core.
The particle-bed core consists of a lattice of annular
cylinders filled by CPs. The coated particles are characterized by a larger oxide
fuel kernel and few coating layers than those designed for HTGRs [30].The pebble-bed core is like that proposed in [31],
with pebbles filled by a matrix of graphite and CPs with carbide kernels.The new plate-type concept, proposed recently by CEA [32],
is a lattice of hexagonal assemblies. Every assembly contains 21 fuel plates
coated by SiC and cooled by He. The fuel is a matrix of (U,Pu)C and SiC [32].At the begin, we have investigated on these three core
concepts to evaluate the actinide-burning capability of these different kinds
of GCFR, particularly in order to check that the plate type has really the best
waste-transmutation characteristics if compared with the others (as already
stated on the basis of some preliminary calculations performed in the frame of
GCFR project). In fact, all our successive work is focused on this kind of
core, in the frame of the EU GCFR project.  Figures4,
5, and 6 show the core we modelled
by MCNP4B code.Figure 4
Particle-bed core. The FA is constituted by two walls of porous SiC (in
light blue); the CPs (in dark color); an outer wall of SiC (in blue). The
purple region is He.Figure 5
Pebble-bed core: details of a pebble (in the
inner part of the sphere there are the CPs, the green shell is the fuel-free
zone in C, the yellow region is the coolant He).Figure 6
Plate-type core: details of corexy-cross-section
(fuel matrix is in red colour, SiC in yellow, and He in green).In all three cases, the HM part of the fuel is
composed by DU and Pu+MA with the isotopic vector of LWR spent fuel. The
relative percentages of DU and (Pu+MA) are adjusted in order to obtain
criticality.The main  results we found are summarized in Table4.Table 4
Summary of the comparison of the GCFR core
concepts.
Plate-type GCFRCP-bed GCFRPB-GCFRPower [MWth]6002400300Power Density [W/cc]1005050Irradiation time length [days]294419381138Pu+MA charge (atomic fraction)20%20%25%DU initial mass[kg]12531.517543.85894.049DU final mass [kg]11012.117034.65610.23Pu initial mass [kg]2842.439661776.04Pu final mass [kg]269938981708.45MA initial mass [kg]299.1417.7186.615MA final mass [kg]248.49458.11180.979ΔmDU/Energy [kg⋅100/GWD]86.0210.9583.17ΔmPu/Energy [kg⋅100/GWD]8.121.4619.81ΔmMA/Energy [kg⋅100/GWD]2.87−0.871.64Please note that we used as figure of merit the following ratio:(23)Δmi100/Energy[kg/GWD], where(a)
Δmi  is the difference
between the loaded mass and the discharged mass in the core for the ith group of nuclides [Kg];(b)
“Energy” indicates the
energy produced by the core during irradiation [GWD].
The higher this figure of merit, the better the
performance of the core in burning the ith group of nuclide.As we  can see from Table4, the plate-type core has
three main advantages:(1)
a longer fuel cycle thanks to the
better conversion fertile-to-fissile of DU;(2)
a smaller initial enrichment in Pu+MA
than the pebble-bed type (Pu and MA have a quite different dynamic behaviour
than traditional fuel);(3)
a higher consumption of DU. The Pu
net consumption is not too high because of the conversion and the subsequent
high-fission probability of Pu239 and also of the conversion of Np237;(4)
a higher consumption of the higher
isotopes of Pu and of the MA due to the harder neutron spectrum
(Table5 and Figure 7).
The harder neutron spectrum of the plate-type core is
due to the higher volumetric fraction of the fuel than that of structural
material (in fact, the structural material is composed by Si and C, which are
relatively light nuclei), Table 6.Table 5
(Δm⋅100/GWD) of the
different core concepts for the main nuclides.
NuclidePlate-typeCP-bedPebble-bedU23884.9210.7581.88Np2374.400.807.30Pu238−2.58−0.71−5.62Pu2393.40020.04Pu240−3.96−1.10−11.06Pu24111.103.4017.84Pu2420.17−0.13−1.38Am2410.31−1.33−2.00Am2430.360.040.17Cm244−1.29−0.18−2.04Table 6
Volumetric percentages of the materials in
the core concepts analyzed.
Plate-typeCP-bedPebble-bedFuel (HM oxide or carbide) % vol.24.59.515Coolant % vol.557439Structural mat. % vol.20.516.546Figure 7
Comparison of the mean neutron spectra: the
plate-type core has the harder spectrum (groups over 100 keV).Please note that the CP-bed core reaches the
criticality also with a very low fraction of fuel, thanks to its large size
(2400 MWth  with a power density of 50 W/cm3), that
minimizes the neutron losses.These positive characteristics justify a deeper
analysis of this kind of core that will be performed in the following
paragraphs.


#### 5.2.2. Benchmarks and Codes Validation

GCFR is a new concept of core that has not already
been studied with the standard computer codes for neutronic analyses. Then, in
the frame of the EU GCFR project, we have participated to a code-to-code
benchmark using the reference core configuration (plate-type GCFR), proposed by
CEA [32]. This comparison supplied very interesting results, because the core
has been modelled both with an MC code (MCNP) and with a 1D deterministic code
(XSDRNPM). The differences in keff and in the isotopic evolution of
the fuel during burnup are very small, mainly due to the different set of
cross-sections used. In fact, the agreement has been very good for U, Pu239,
and Pu240, while the biggest difference has been found regarding the MA and the
higher isotopes of Pu. That is not surprising, because the cross-sections of
these nuclides are those with the higher uncertainties and the higher
differences among the different sets [33].The good agreement between the 3D heterogeneous model
and the 1D homogeneous model is probably due to the presence of a fast
spectrum: the mean free path of the neutrons is comparable with the typical
dimensions of the core, so that the collision densities in both configurations
are similar. This is a very promising result, because the deterministic codes (XSDRNPM,
WIMS, etc.) allow to perform preliminary evaluations in a quicker way: we can
so use those tools with confidence.


#### 5.2.3. Multiple Recycling on GCFR: A Preliminary Evaluation

As already explained, an important aim of the GCFR
core design is to obtain a self-sustaining core fed with fertile material. The
batches discharged from GCFR would be reprocessed, recovering all the HMs, and
eliminating the FPs as waste. Then the HMs would be reused in order to
fabricate new fuel, adding DU to replace the material consumed by fission. We
have performed some calculations in order to evaluate the fuel behavior during
multiple recycling, starting with an initial composition with 80% DU and 20%
(Pu+MA) from LWR. Moreover, we have neglected the cooling time between an
irradiation cycle and the fact that matter will be deepened in the frame of the
optimization of the entire fuel cycle, as future work. Here it is sufficient to
remember that few years of decay causes mainly the buildup of Am241 from Pu241 (half-life 14.4 years) and Pu238 from Cm242 (half-life 163 days). We have performed three complete irradiation cycles, the
main results are summarized in Table 7.Table 7
Out/in ratio (%) for the main nuclides in
multiple recycling.
1st cycle2nd cycle3rd cycleTotalLength [days]2944186317386545(Pu+MA)C   atomic fract. (%)2018.418.3—U238out/U238in (%)88919273.7Np237out/Np237in (%)46616618.5Pu238out/Pu238in (%)1639789140.7Pu239out/Pu239in (%)9610110197.9Pu240out/Pu240in (%)110105104120Pu241out/Pu241in (%)45859837.5Pu242out/Pu242in (%)98939384.8Am241out/Am241in (%)94808563.9Am243out/Am243in (%)87949476.9Cm244out/Cm244in (%)245118106306.4This core shows a very good conversion capability that
can be described as follows (Table7):(a)
the added DU initial fraction increases from a cycle to the other
because the reduced destruction of Pu fissile isotopes (i.e., Pu239 and Pu241) and the increased burnup of those fertile (i.e., Pu240 and Pu242) allow to obtain criticality in the successive cycles also
with lower percentages of (Pu+MA);(b)
the lower initial content of Pu+MA causes a decrease of the single cycle
step length;(c)
except the fissile Pu nuclides, all the isotopes show a progressive
decrease either of their quantity or, at least, of their growing rate (i.e., Pu240 and Cm244) from a cycle to the other.
This will not be a real problem. In fact we are not
sure that it will be possible to reach a so long irradiation cycle length (due to
radiation damage of the core materials). These trends are encouraging: optimizing the
parameters of the fuel and the cycle; and using some dedicated assemblies,
there are good possibilities of further actinide reduction by GCFR.


### 5.3. Symbiotic Fuel Cycles

Although [34]
water-cooled thermal reactors have reached a high stage of development and can
(economically) give a significant contribution to the world energy supply, the
efficient utilization of U or Th resources and the long-term management of the
waste are still a challenge. As stated before, in the short term, even
if U availability seems to be adequate to fuel the continuing installation of
thermal reactors, this cannot be sustained for the next centuries. Future
improvements in the performance of thermal reactors can be reached particularly
in terms of increased efficiency through higher temperatures of the HTR system.
Furthermore, by using the fast reactors features and multiple symbiotic cycles,
the utilization of uranium resources could be highly enhanced in addition to a
further waste reduction.A symbiotic
fuel cycle is a strategically planned chain, where the output of a reactor is
the input of the following. Each link of such a chain is a different kind of
reactor (e.g., LWR, HTR, or FR, etc.), because each one is able to do a
different task. Of course, between two different steps, the fuel has to be
cooled and reprocessed. Further data on chemical aspects of these reprocess
steps are available in the international literature (e.g., documents from EU
projects on HTR).In this
way, the waste radiotoxicity growth can be reduced by recycling both Pu and MA,
producing, at the same time, energy.


#### 5.3.1. A symbiotic LWR-HTR-GCFR Fuel Cycle

As shown,
in the past, our group has already performed similar calculations using LWR-HTR-GCFR
fuel cycles [30]. In Figure 8, a flowchart of our proposed symbiotic cycle is
shown.Figure 8
Symbiotic fuel cycle
LWR-HTR-GCFR [34].We have modeled the core of a pebble-bed HTR (like a 233 MWth  PBMR) [34], whose CPs are loaded by Pu+MA coming from LWR (the considered
burnup is the typical value of 33 GWD/tU). The chemical form of the fuel kernel
is (Pu, MA)O2. Thus, we performed for this HTR core the burnup
calculation until keff  became less than 1 (about 500 GWD/tHM). The
isotopic composition we obtained constitutes the fissile material to be added
to depleted uranium in the GCFR fuel. Finally, we have performed the burnup
calculation of the GCFR core until keff became less than 1 (about
188 GWD/tHM) and evaluated the radiotoxicity of the final waste (i.e., only the
FPs in the frame of the full actinides recycle strategy). For
criticality reasons, we chose for GCFR a fuel composition constituted by 30% as
atomic fraction of Pu+MA (TRU) and 70% of DU (DU contains 0.25% in U235).
Please note that DU represents a material not more useful in order to produce
energy in a “classical” way. Therefore, it has a very low cost. The
isotopic vectors of TRU resulting, respectively, from LWR and HTR that we used
are shown in Table 8.Table 8
TRU isotopic vectors.
Mass fractionSpent LWRSpent HTRNp2370.0460.056Pu2380.0230.073Pu2390.4900.074Pu2400.2150.313Pu2410.1140.18Pu2420.0620.20Am2410.0280.0001Am2430.0160.04Cm242—0.013Cm2440.0050.043Cm245—0.0079Please note
that the burnup calculation on GCFR here shown is only the first of a series
performed in the frame of the Generation IV Initiative. This strategy
represents the so calledfull actinide recycle strategy, proposed by CEA
for this kind of reactor. A preliminary study of this strategy in GCFR is shown
in the previous paragraphs and summarized in Table 7.As already
described, this concept consists in adding all the actinides coming from GCFR
spent fuel to DU that substitutes the mass of fuel lost as fission products. If
the efficiency of the separation process were 1, the waste would be (ideally)
composed by FP only, while the actinides would always be reused in the reactor
as new fuel.


#### 5.3.2. LOMBT Evaluations for LWR-HTR-GCFR Fuel Cycles

To check the advantages of the chosen fuel cycles, we mainly took into
account the radiotoxicity evolution of the spent fuel versus time. As already
anticipated, please remember that as reference for radiotoxicity, we defined [14]
the level-of-mine balancing time (LOMBT). This value is linked to the LOM definition, value
characteristic
of the type of fuel cycle and it is not easily defined (due to its oscillation
range). However, in this paper, we adopt the LOM only as a conceptual reference
level.At the end of the single steps we consider as waste the following:(1)
Pu+MA+FP in
the case of HTR, because HTR has a “single-step” fuel cycle (i.e., a
given quantity of material spends only a burnup cycle in this kind of reactor);(2)
FP in the
case of GCFR; in fact, in GCFR, thefull actinide recycle is foreseen
(i.e., all the actinides from an irradiation step will be mixed to new DU in
the “fresh” fuel for cycle continuation).However, in this paper, we have limited the analyses to the first
irradiation cycle in GCFR without considering what happens with the multiple
recycles of the fuel. The evaluations of the successive irradiation cycles are
in progress.Table9 gathers the results we found; while in Figures
9 and 10, two
typical CARL output graphs are showed.Table 9
Summary of the obtained results.
HTR (513 EFPD)GCFR (4950 EFPD)Symbiotic cycle∗LOMBT [years]63·682
(waste = FP+HM)159 (waste = FP∗∗)159 (waste = FP∗∗)Np237out/Np237in66%27%18%Pu238out/Pu238in165%75%123%Pu239out/Pu239in81%306%248%Pu240out/Pu240in77%73%56%Pu241out/Pu241in80%26%20%Pu242out/Pu242in170%72%122%Am241out/Am241in21%243%51%Am243out/Am243in126%83%104%Cm244out/Cm244in412%102%420%∗ In this case, there is no indication about EFPD because the real cycle
is made of burnup days inside the reactors plus days out-of-pile (mainly due to
recycling times).∗∗ The fission products
considered here are the following: Rb87, Sr90, Zr93,
Nb94, Tc99, Pd107, Sn126, I129,
Cs135, Cs137, Sm147, Sm151, and Eu154.Figure 9
Spent fuel radiotoxicity versus time for HTR, intermediate
step (“waste”  =  Pu+MA+FP): LOMBT = 63682 years.Figure 10
Spent fuel radiotoxicity versus time for GCFR,
“final” step (“waste” = FP): LOMBT = 159 years. (The fission products considered here are the following: Rb87,
Sr90, Zr93, Nb94, Tc99, Pd107,
Sn126, I129, Cs135, Cs137, Sm147,
Sm151, and Eu154.) (If we
would consider as waste FP and MA, the LOMBT would become equal to 20491 years.)This strategy couples the advantages of both the HTR neutron spectrum
(good performance in Pu, Np237 and Am241 burning) and the
GCFR spectrum (capability of burning the higher Pu isotopes and of decreasing
the Cm244 growing rate).


#### 5.3.3. Discussion on the Obtained Results

As figure of merit, we have considered theα ratio, α=σc/σf. This ratio
value versus burnup remains substantially constant or suffer limited variations
that can be neglected (e.g., see Figure 11).
This  justifies our choice to
assume the value of α at BOC valid for the whole irradiation time.Figure 11
α versus time in GCFR (fluctuations are due
to the MC method adopted in our calculations).It is possible to highlight the fact that the higher
theα ratio, the higher the probability of capture than fission for the considered
nuclide in the given flux.From Table10, we can analyze the results we have
obtained.Table 10
1-groupα ratio at
BOC.
GCFRPBMRU2385.27—Np2374.73200Pu2380.6214.25Pu2390.320.60Pu2401.49416.67Pu2410.190.36Pu2421.70204.08Am2416.33119.05Am2436.96333.33Cm2441.5730.96The capture-to-fission  ratio comes in fact  from the effective
cross-sections. These last
have  obtained weighting over the neutron spectrum, as we have seen in the first
part of this paper. In fast reactors, the neutron spectrum is less dependent
from variations of the fuel composition than in thermal reactors. In fact,
during burnup FPs and actinides with higher mass number buildup. FPs have
generally a high-capture cross-section in thermal and/or epithermal range,
while the HM with higher mass number has often larger absorption cross-sections
in this same energy range than the actinides more abundant in the fresh fuel
(i.e., U238 and Pu239) [35], Figures
12 and
13, so that
at EOC in thermal reactors the spectrum becomes harder, because its softer tail
is absorbed by these nuclides.Figure 12
σa versus E of some HMs (Pu239 in red
color, Pu240 in green, Pu241 in blue, Pu242 in
purple, Am241 in light green) [35].Figure 13
σa  versus E of some FPs (Xe135 in red
color, Sm149 in green) [35].This effect is negligible in fast spectrum, so that we
obtain the trend shown in Figure11.Concerning the Pu fissile isotopes (i.e., Pu239 and Pu241), they burn better in fast spectrum than in thermal
one. (α in fast spectrum is
lower than in thermal for both, the probability of fission is higher than that
of capture.)
Particularly, in the PBMR the quantity of Pu239 decreases of about
20%, while its daughter Pu240 is also slightly reduced despite its
high α ratio (≈417): this is due
to Pu239 transmutation by capture. Please note also that there is
not a production channel of Pu239 because the fuel is fertile-free. In
PBMR, Pu241 also slightly decreases and transmutes partially in Pu242 that builds up during irradiation. In GCFR, α of these nuclides is smaller than
in PBMR: in fact there is a higher probability to have fission. Their daughters
Pu240 and Pu242 are both decreasing. Nevertheless, the
total amount of Pu239 multiplies in GCFR by a factor three during
burnup because of the behavior of its parent U238. This fact is
positive in order to obtain an effective self-sustaining core with a full-actinide
recycle. In fact,  if the Pu isotopic
vector would be too much degraded, the criticality would be probably not
maintained in the following cycle substituting the FPs only with pure DU.Concerning the  chain Np237→ Pu238,
Np237 has a high α both in thermal and fast spectrum: its transmute
in Pu238 by capture. Obviously, the quantity of Np237 that transmutes in GCFR is higher because in thermal spectrum, it has to
compete with other strong absorbers (Figure 14). In this GCFR core, Pu238 is fissile and its quantity decreases during irradiation.Figure 14
Comparison of the absorption cross-sections
among some nuclides (Np237 in red, Pu239 in purple,
Pu240 in green, Pu241 in light green, Am241 in blue)
[35].Regarding the chain of Cm244 that at the
moment is the most difficult nuclide to be burnt, we can observe the following.(1)
In the thermal spectrum, Cm244 grows a lot. In fact, its precursors (Pu242 and Am243) both
increase and have a large α ratio (resp., 204 and 333).
Moreover, Cm244 has a very low absorption cross-section, if compared
with the other nuclides in the fuel (Figure 15).(2)
In the fast spectrum, Cm244 has a lower growing rate, because Pu242 and Am243 are
both decreasing, and the absorption cross-sections of the HMs are all
comparable in this range. Moreover, α is not too large for all these nuclides.
Finally, there is something more related to Am241: the thermal
spectrum burns it very good thanks to its high capture cross-section (Figures
12 and 14); while in GCFR, the amount of this nuclide has a nonmonotonic trend
(Figure 16). Its main production channel is the β- decay of Pu241 (half-life = 14.4 years). The total irradiation time is comparable (4950 days)
with the Pu241 half-life (14.4 years are about 5250 days). On the
other hand, the most part of Pu241 is transmuted by absorption. The
production of Am241 can be expressed in a simplified manner as(24)dAm241dt=λPu241⋅Pu241−σaAm241⋅φ⋅Am241, where Am241 and Pu241 are the
time-dependent quantities of the considered nuclides. (λPu241) and (σaAm241⋅φ) are, respectively, 1.53⋅10−9s−1 and 3.2⋅10−9s−1.
Now, we can do some qualitative considerations. At beginning and for the most
part of the cycle, the first term of the right hand of this equation makes the
exponential solution increasing because of the relatively high Pu241 initial quantity. The solution of the equation reaches a maximum, and then it
starts to decrease, because the quantity of Am241 is not more
negligible (the product σaAm241⋅φ has no significant changes due to the fast spectrum),
see also Figure 16.Figure 15
Comparison among some absorption
cross-sections (Cm244 in red, Pu242 in green,
Am243 in blue) [35].Figure 16
Quantity versus time of Pu241 and Am241.


## 5.1. The HTR as Plutonium Burner

In order to demonstrate
the capability of HTRs to contribute in reducing nuclear waste (actinides in
particular), it was decided to analyze Pu-based fuel [14]. In order to validate
the used code (namely MONTEBURNS), an international code-to-code benchmark was
performed. The obtained results have shown a good agreement between the codes
adopted by the different participants, as reported in [29].Particularly, 1st generation Pu [20] (i.e., Pu deriving from reprocessing typical LWR spent fuel)
and 2nd generation Pu [20] (i.e., Pu deriving from the reprocessing
of typical MOX spent fuel) were considered.Therefore the following
calculations were performed:(i)
HTR loaded
with 1 g/pebble 1st generation Pu, 600 GWd/ton (600 EFPD);(ii)
HTR loaded with 1.5 g/pebble 2nd generation
Pu, 430 GWd/ton (645 EFPD).
To check the advantages in using different fuel cycles, the
radiotoxicity evolution of spent fuel versus time was evaluated. As reference
for radiotoxicity, we, as described above, originally defined [14] the
LOMBT
(level of mine balancing time), that is, the interval of time necessary for
the radiotoxicity of the exhausted fuel to return to the values of the mineral
extracted from the mine (in this case of uranium) from which the fuel was generated.The
results show that 1st-generation Pu behaves (in terms of LOMBT)
better than 2nd-generation Pu.In another article [30],
we considered the possibility of adopting Th-Pu fuel cycle and, for the first
time, the use of a (relatively) simplified LWR-HTR-GCFR symbiotic fuel cycle
(Figure 3).Figure 3
Symbiotic fuel cycles (without or with using MOX in LWR).It should be noted that,
in the case of HTR, we considered a once-through fuel cycle. Consequently, we assumed that the waste
contains Pu, MA, and FP. Instead in the case of GCFR, we considered that all
the Pu will be recycled at the end of (each) GCFR step. Consequently, we
assumed that the final waste contains only MA and FP.In Table3, the obtained
results are summarized. In column 7, the ratio between inlet and outlet
transuranic elements (Pu+MA) and in column 8 the ratio between inlet and outlet
actinides (Th+U+Pu+MA) is shown.Table 3
Summary of the obtained results.
CaseReactorFuelLOMBT [y]EnergygPuPuoutPuinTRUoutTRUinActoutActin12345678aHTR1st g-Pu/Th (1/1)37982∗60.16 GJ24.14%31.75%63.88%bHTR1st g-Pu/Th (1/2)37547*59.40 GJ27.75%33.88%76.25%cHTR1st g-Pu/Th (1/3)37117*58.89 GJ29.06%34.37%81.94%dGCFR1st g-Pu∗∗/MA/U238 (10/1/40)9204∗∗∗154.44 GJ85.66%86.77%57.78%eGCFR2nd g-Pu†/MA/U238 (10/1/40)9310***155.26 GJ85.85%87.77%57.57%fGCFR‡2nd g-Pu†/MA/U238 (10/1/40)11860***105.57 GJ98.02%98.95%70.64%∗ In the case of HTR,
we assumed a once-through fuel cycle. Consequently, the waste contains Pu, MA,
and FP.∗∗ 1st-generation Pu is
added to Pu which is
already present in the spent fuel of HTR loaded with 1st-generation
Pu.∗∗∗ In the case of
GCFR, we assumed that all the Pu is recycled. Consequently, the waste contains
only MA and FP.† 2nd-generation Pu is
added to Pu which is
already present in the spent fuel of HTR loaded with  2nd-generation
Pu.‡ In this case, we assumed that
thickness of the external layer of the CP is 0.003 mm instead of 0.005 mm (like
cases d and e). Therefore the spectrum is not so hard as in case e.In the case
of LWRs spent fuel, the LOMBT is about 250000 years [15]. From
Table 3, we can
see that this figure of merit (the most important in terms of safety) is
significantly reduced (an order of magnitude) using HTR and further (recycling
Pu as fuel) by using GCFR to close the cycle.


## 5.2. The GCFR as Actinide Burner

In the first calculations (see previous paragraph) on GCFRs
concepts, we adopted a simplified model for the GCFR core. In the further
calculations, we refined this model, as showed in the following paragraphs.


### 5.2.1. Comparison among Core Concepts

Three main core concepts exist for GCFR:(1)
particle-bed
core;(2)
pebble-bed
core;(3)
plate-type
core.
The particle-bed core consists of a lattice of annular
cylinders filled by CPs. The coated particles are characterized by a larger oxide
fuel kernel and few coating layers than those designed for HTGRs [30].The pebble-bed core is like that proposed in [31],
with pebbles filled by a matrix of graphite and CPs with carbide kernels.The new plate-type concept, proposed recently by CEA [32],
is a lattice of hexagonal assemblies. Every assembly contains 21 fuel plates
coated by SiC and cooled by He. The fuel is a matrix of (U,Pu)C and SiC [32].At the begin, we have investigated on these three core
concepts to evaluate the actinide-burning capability of these different kinds
of GCFR, particularly in order to check that the plate type has really the best
waste-transmutation characteristics if compared with the others (as already
stated on the basis of some preliminary calculations performed in the frame of
GCFR project). In fact, all our successive work is focused on this kind of
core, in the frame of the EU GCFR project.  Figures4,
5, and 6 show the core we modelled
by MCNP4B code.Figure 4
Particle-bed core. The FA is constituted by two walls of porous SiC (in
light blue); the CPs (in dark color); an outer wall of SiC (in blue). The
purple region is He.Figure 5
Pebble-bed core: details of a pebble (in the
inner part of the sphere there are the CPs, the green shell is the fuel-free
zone in C, the yellow region is the coolant He).Figure 6
Plate-type core: details of corexy-cross-section
(fuel matrix is in red colour, SiC in yellow, and He in green).In all three cases, the HM part of the fuel is
composed by DU and Pu+MA with the isotopic vector of LWR spent fuel. The
relative percentages of DU and (Pu+MA) are adjusted in order to obtain
criticality.The main  results we found are summarized in Table4.Table 4
Summary of the comparison of the GCFR core
concepts.
Plate-type GCFRCP-bed GCFRPB-GCFRPower [MWth]6002400300Power Density [W/cc]1005050Irradiation time length [days]294419381138Pu+MA charge (atomic fraction)20%20%25%DU initial mass[kg]12531.517543.85894.049DU final mass [kg]11012.117034.65610.23Pu initial mass [kg]2842.439661776.04Pu final mass [kg]269938981708.45MA initial mass [kg]299.1417.7186.615MA final mass [kg]248.49458.11180.979ΔmDU/Energy [kg⋅100/GWD]86.0210.9583.17ΔmPu/Energy [kg⋅100/GWD]8.121.4619.81ΔmMA/Energy [kg⋅100/GWD]2.87−0.871.64Please note that we used as figure of merit the following ratio:(23)Δmi100/Energy[kg/GWD], where(a)
Δmi  is the difference
between the loaded mass and the discharged mass in the core for the ith group of nuclides [Kg];(b)
“Energy” indicates the
energy produced by the core during irradiation [GWD].
The higher this figure of merit, the better the
performance of the core in burning the ith group of nuclide.As we  can see from Table4, the plate-type core has
three main advantages:(1)
a longer fuel cycle thanks to the
better conversion fertile-to-fissile of DU;(2)
a smaller initial enrichment in Pu+MA
than the pebble-bed type (Pu and MA have a quite different dynamic behaviour
than traditional fuel);(3)
a higher consumption of DU. The Pu
net consumption is not too high because of the conversion and the subsequent
high-fission probability of Pu239 and also of the conversion of Np237;(4)
a higher consumption of the higher
isotopes of Pu and of the MA due to the harder neutron spectrum
(Table5 and Figure 7).
The harder neutron spectrum of the plate-type core is
due to the higher volumetric fraction of the fuel than that of structural
material (in fact, the structural material is composed by Si and C, which are
relatively light nuclei), Table 6.Table 5
(Δm⋅100/GWD) of the
different core concepts for the main nuclides.
NuclidePlate-typeCP-bedPebble-bedU23884.9210.7581.88Np2374.400.807.30Pu238−2.58−0.71−5.62Pu2393.40020.04Pu240−3.96−1.10−11.06Pu24111.103.4017.84Pu2420.17−0.13−1.38Am2410.31−1.33−2.00Am2430.360.040.17Cm244−1.29−0.18−2.04Table 6
Volumetric percentages of the materials in
the core concepts analyzed.
Plate-typeCP-bedPebble-bedFuel (HM oxide or carbide) % vol.24.59.515Coolant % vol.557439Structural mat. % vol.20.516.546Figure 7
Comparison of the mean neutron spectra: the
plate-type core has the harder spectrum (groups over 100 keV).Please note that the CP-bed core reaches the
criticality also with a very low fraction of fuel, thanks to its large size
(2400 MWth  with a power density of 50 W/cm3), that
minimizes the neutron losses.These positive characteristics justify a deeper
analysis of this kind of core that will be performed in the following
paragraphs.


### 5.2.2. Benchmarks and Codes Validation

GCFR is a new concept of core that has not already
been studied with the standard computer codes for neutronic analyses. Then, in
the frame of the EU GCFR project, we have participated to a code-to-code
benchmark using the reference core configuration (plate-type GCFR), proposed by
CEA [32]. This comparison supplied very interesting results, because the core
has been modelled both with an MC code (MCNP) and with a 1D deterministic code
(XSDRNPM). The differences in keff and in the isotopic evolution of
the fuel during burnup are very small, mainly due to the different set of
cross-sections used. In fact, the agreement has been very good for U, Pu239,
and Pu240, while the biggest difference has been found regarding the MA and the
higher isotopes of Pu. That is not surprising, because the cross-sections of
these nuclides are those with the higher uncertainties and the higher
differences among the different sets [33].The good agreement between the 3D heterogeneous model
and the 1D homogeneous model is probably due to the presence of a fast
spectrum: the mean free path of the neutrons is comparable with the typical
dimensions of the core, so that the collision densities in both configurations
are similar. This is a very promising result, because the deterministic codes (XSDRNPM,
WIMS, etc.) allow to perform preliminary evaluations in a quicker way: we can
so use those tools with confidence.


### 5.2.3. Multiple Recycling on GCFR: A Preliminary Evaluation

As already explained, an important aim of the GCFR
core design is to obtain a self-sustaining core fed with fertile material. The
batches discharged from GCFR would be reprocessed, recovering all the HMs, and
eliminating the FPs as waste. Then the HMs would be reused in order to
fabricate new fuel, adding DU to replace the material consumed by fission. We
have performed some calculations in order to evaluate the fuel behavior during
multiple recycling, starting with an initial composition with 80% DU and 20%
(Pu+MA) from LWR. Moreover, we have neglected the cooling time between an
irradiation cycle and the fact that matter will be deepened in the frame of the
optimization of the entire fuel cycle, as future work. Here it is sufficient to
remember that few years of decay causes mainly the buildup of Am241 from Pu241 (half-life 14.4 years) and Pu238 from Cm242 (half-life 163 days). We have performed three complete irradiation cycles, the
main results are summarized in Table 7.Table 7
Out/in ratio (%) for the main nuclides in
multiple recycling.
1st cycle2nd cycle3rd cycleTotalLength [days]2944186317386545(Pu+MA)C   atomic fract. (%)2018.418.3—U238out/U238in (%)88919273.7Np237out/Np237in (%)46616618.5Pu238out/Pu238in (%)1639789140.7Pu239out/Pu239in (%)9610110197.9Pu240out/Pu240in (%)110105104120Pu241out/Pu241in (%)45859837.5Pu242out/Pu242in (%)98939384.8Am241out/Am241in (%)94808563.9Am243out/Am243in (%)87949476.9Cm244out/Cm244in (%)245118106306.4This core shows a very good conversion capability that
can be described as follows (Table7):(a)
the added DU initial fraction increases from a cycle to the other
because the reduced destruction of Pu fissile isotopes (i.e., Pu239 and Pu241) and the increased burnup of those fertile (i.e., Pu240 and Pu242) allow to obtain criticality in the successive cycles also
with lower percentages of (Pu+MA);(b)
the lower initial content of Pu+MA causes a decrease of the single cycle
step length;(c)
except the fissile Pu nuclides, all the isotopes show a progressive
decrease either of their quantity or, at least, of their growing rate (i.e., Pu240 and Cm244) from a cycle to the other.
This will not be a real problem. In fact we are not
sure that it will be possible to reach a so long irradiation cycle length (due to
radiation damage of the core materials). These trends are encouraging: optimizing the
parameters of the fuel and the cycle; and using some dedicated assemblies,
there are good possibilities of further actinide reduction by GCFR.


## 5.2.1. Comparison among Core Concepts

Three main core concepts exist for GCFR:(1)
particle-bed
core;(2)
pebble-bed
core;(3)
plate-type
core.
The particle-bed core consists of a lattice of annular
cylinders filled by CPs. The coated particles are characterized by a larger oxide
fuel kernel and few coating layers than those designed for HTGRs [30].The pebble-bed core is like that proposed in [31],
with pebbles filled by a matrix of graphite and CPs with carbide kernels.The new plate-type concept, proposed recently by CEA [32],
is a lattice of hexagonal assemblies. Every assembly contains 21 fuel plates
coated by SiC and cooled by He. The fuel is a matrix of (U,Pu)C and SiC [32].At the begin, we have investigated on these three core
concepts to evaluate the actinide-burning capability of these different kinds
of GCFR, particularly in order to check that the plate type has really the best
waste-transmutation characteristics if compared with the others (as already
stated on the basis of some preliminary calculations performed in the frame of
GCFR project). In fact, all our successive work is focused on this kind of
core, in the frame of the EU GCFR project.  Figures4,
5, and 6 show the core we modelled
by MCNP4B code.Figure 4
Particle-bed core. The FA is constituted by two walls of porous SiC (in
light blue); the CPs (in dark color); an outer wall of SiC (in blue). The
purple region is He.Figure 5
Pebble-bed core: details of a pebble (in the
inner part of the sphere there are the CPs, the green shell is the fuel-free
zone in C, the yellow region is the coolant He).Figure 6
Plate-type core: details of corexy-cross-section
(fuel matrix is in red colour, SiC in yellow, and He in green).In all three cases, the HM part of the fuel is
composed by DU and Pu+MA with the isotopic vector of LWR spent fuel. The
relative percentages of DU and (Pu+MA) are adjusted in order to obtain
criticality.The main  results we found are summarized in Table4.Table 4
Summary of the comparison of the GCFR core
concepts.
Plate-type GCFRCP-bed GCFRPB-GCFRPower [MWth]6002400300Power Density [W/cc]1005050Irradiation time length [days]294419381138Pu+MA charge (atomic fraction)20%20%25%DU initial mass[kg]12531.517543.85894.049DU final mass [kg]11012.117034.65610.23Pu initial mass [kg]2842.439661776.04Pu final mass [kg]269938981708.45MA initial mass [kg]299.1417.7186.615MA final mass [kg]248.49458.11180.979ΔmDU/Energy [kg⋅100/GWD]86.0210.9583.17ΔmPu/Energy [kg⋅100/GWD]8.121.4619.81ΔmMA/Energy [kg⋅100/GWD]2.87−0.871.64Please note that we used as figure of merit the following ratio:(23)Δmi100/Energy[kg/GWD], where(a)
Δmi  is the difference
between the loaded mass and the discharged mass in the core for the ith group of nuclides [Kg];(b)
“Energy” indicates the
energy produced by the core during irradiation [GWD].
The higher this figure of merit, the better the
performance of the core in burning the ith group of nuclide.As we  can see from Table4, the plate-type core has
three main advantages:(1)
a longer fuel cycle thanks to the
better conversion fertile-to-fissile of DU;(2)
a smaller initial enrichment in Pu+MA
than the pebble-bed type (Pu and MA have a quite different dynamic behaviour
than traditional fuel);(3)
a higher consumption of DU. The Pu
net consumption is not too high because of the conversion and the subsequent
high-fission probability of Pu239 and also of the conversion of Np237;(4)
a higher consumption of the higher
isotopes of Pu and of the MA due to the harder neutron spectrum
(Table5 and Figure 7).
The harder neutron spectrum of the plate-type core is
due to the higher volumetric fraction of the fuel than that of structural
material (in fact, the structural material is composed by Si and C, which are
relatively light nuclei), Table 6.Table 5
(Δm⋅100/GWD) of the
different core concepts for the main nuclides.
NuclidePlate-typeCP-bedPebble-bedU23884.9210.7581.88Np2374.400.807.30Pu238−2.58−0.71−5.62Pu2393.40020.04Pu240−3.96−1.10−11.06Pu24111.103.4017.84Pu2420.17−0.13−1.38Am2410.31−1.33−2.00Am2430.360.040.17Cm244−1.29−0.18−2.04Table 6
Volumetric percentages of the materials in
the core concepts analyzed.
Plate-typeCP-bedPebble-bedFuel (HM oxide or carbide) % vol.24.59.515Coolant % vol.557439Structural mat. % vol.20.516.546Figure 7
Comparison of the mean neutron spectra: the
plate-type core has the harder spectrum (groups over 100 keV).Please note that the CP-bed core reaches the
criticality also with a very low fraction of fuel, thanks to its large size
(2400 MWth  with a power density of 50 W/cm3), that
minimizes the neutron losses.These positive characteristics justify a deeper
analysis of this kind of core that will be performed in the following
paragraphs.


## 5.2.2. Benchmarks and Codes Validation

GCFR is a new concept of core that has not already
been studied with the standard computer codes for neutronic analyses. Then, in
the frame of the EU GCFR project, we have participated to a code-to-code
benchmark using the reference core configuration (plate-type GCFR), proposed by
CEA [32]. This comparison supplied very interesting results, because the core
has been modelled both with an MC code (MCNP) and with a 1D deterministic code
(XSDRNPM). The differences in keff and in the isotopic evolution of
the fuel during burnup are very small, mainly due to the different set of
cross-sections used. In fact, the agreement has been very good for U, Pu239,
and Pu240, while the biggest difference has been found regarding the MA and the
higher isotopes of Pu. That is not surprising, because the cross-sections of
these nuclides are those with the higher uncertainties and the higher
differences among the different sets [33].The good agreement between the 3D heterogeneous model
and the 1D homogeneous model is probably due to the presence of a fast
spectrum: the mean free path of the neutrons is comparable with the typical
dimensions of the core, so that the collision densities in both configurations
are similar. This is a very promising result, because the deterministic codes (XSDRNPM,
WIMS, etc.) allow to perform preliminary evaluations in a quicker way: we can
so use those tools with confidence.


## 5.2.3. Multiple Recycling on GCFR: A Preliminary Evaluation

As already explained, an important aim of the GCFR
core design is to obtain a self-sustaining core fed with fertile material. The
batches discharged from GCFR would be reprocessed, recovering all the HMs, and
eliminating the FPs as waste. Then the HMs would be reused in order to
fabricate new fuel, adding DU to replace the material consumed by fission. We
have performed some calculations in order to evaluate the fuel behavior during
multiple recycling, starting with an initial composition with 80% DU and 20%
(Pu+MA) from LWR. Moreover, we have neglected the cooling time between an
irradiation cycle and the fact that matter will be deepened in the frame of the
optimization of the entire fuel cycle, as future work. Here it is sufficient to
remember that few years of decay causes mainly the buildup of Am241 from Pu241 (half-life 14.4 years) and Pu238 from Cm242 (half-life 163 days). We have performed three complete irradiation cycles, the
main results are summarized in Table 7.Table 7
Out/in ratio (%) for the main nuclides in
multiple recycling.
1st cycle2nd cycle3rd cycleTotalLength [days]2944186317386545(Pu+MA)C   atomic fract. (%)2018.418.3—U238out/U238in (%)88919273.7Np237out/Np237in (%)46616618.5Pu238out/Pu238in (%)1639789140.7Pu239out/Pu239in (%)9610110197.9Pu240out/Pu240in (%)110105104120Pu241out/Pu241in (%)45859837.5Pu242out/Pu242in (%)98939384.8Am241out/Am241in (%)94808563.9Am243out/Am243in (%)87949476.9Cm244out/Cm244in (%)245118106306.4This core shows a very good conversion capability that
can be described as follows (Table7):(a)
the added DU initial fraction increases from a cycle to the other
because the reduced destruction of Pu fissile isotopes (i.e., Pu239 and Pu241) and the increased burnup of those fertile (i.e., Pu240 and Pu242) allow to obtain criticality in the successive cycles also
with lower percentages of (Pu+MA);(b)
the lower initial content of Pu+MA causes a decrease of the single cycle
step length;(c)
except the fissile Pu nuclides, all the isotopes show a progressive
decrease either of their quantity or, at least, of their growing rate (i.e., Pu240 and Cm244) from a cycle to the other.
This will not be a real problem. In fact we are not
sure that it will be possible to reach a so long irradiation cycle length (due to
radiation damage of the core materials). These trends are encouraging: optimizing the
parameters of the fuel and the cycle; and using some dedicated assemblies,
there are good possibilities of further actinide reduction by GCFR.


## 5.3. Symbiotic Fuel Cycles

Although [34]
water-cooled thermal reactors have reached a high stage of development and can
(economically) give a significant contribution to the world energy supply, the
efficient utilization of U or Th resources and the long-term management of the
waste are still a challenge. As stated before, in the short term, even
if U availability seems to be adequate to fuel the continuing installation of
thermal reactors, this cannot be sustained for the next centuries. Future
improvements in the performance of thermal reactors can be reached particularly
in terms of increased efficiency through higher temperatures of the HTR system.
Furthermore, by using the fast reactors features and multiple symbiotic cycles,
the utilization of uranium resources could be highly enhanced in addition to a
further waste reduction.A symbiotic
fuel cycle is a strategically planned chain, where the output of a reactor is
the input of the following. Each link of such a chain is a different kind of
reactor (e.g., LWR, HTR, or FR, etc.), because each one is able to do a
different task. Of course, between two different steps, the fuel has to be
cooled and reprocessed. Further data on chemical aspects of these reprocess
steps are available in the international literature (e.g., documents from EU
projects on HTR).In this
way, the waste radiotoxicity growth can be reduced by recycling both Pu and MA,
producing, at the same time, energy.


### 5.3.1. A symbiotic LWR-HTR-GCFR Fuel Cycle

As shown,
in the past, our group has already performed similar calculations using LWR-HTR-GCFR
fuel cycles [30]. In Figure 8, a flowchart of our proposed symbiotic cycle is
shown.Figure 8
Symbiotic fuel cycle
LWR-HTR-GCFR [34].We have modeled the core of a pebble-bed HTR (like a 233 MWth  PBMR) [34], whose CPs are loaded by Pu+MA coming from LWR (the considered
burnup is the typical value of 33 GWD/tU). The chemical form of the fuel kernel
is (Pu, MA)O2. Thus, we performed for this HTR core the burnup
calculation until keff  became less than 1 (about 500 GWD/tHM). The
isotopic composition we obtained constitutes the fissile material to be added
to depleted uranium in the GCFR fuel. Finally, we have performed the burnup
calculation of the GCFR core until keff became less than 1 (about
188 GWD/tHM) and evaluated the radiotoxicity of the final waste (i.e., only the
FPs in the frame of the full actinides recycle strategy). For
criticality reasons, we chose for GCFR a fuel composition constituted by 30% as
atomic fraction of Pu+MA (TRU) and 70% of DU (DU contains 0.25% in U235).
Please note that DU represents a material not more useful in order to produce
energy in a “classical” way. Therefore, it has a very low cost. The
isotopic vectors of TRU resulting, respectively, from LWR and HTR that we used
are shown in Table 8.Table 8
TRU isotopic vectors.
Mass fractionSpent LWRSpent HTRNp2370.0460.056Pu2380.0230.073Pu2390.4900.074Pu2400.2150.313Pu2410.1140.18Pu2420.0620.20Am2410.0280.0001Am2430.0160.04Cm242—0.013Cm2440.0050.043Cm245—0.0079Please note
that the burnup calculation on GCFR here shown is only the first of a series
performed in the frame of the Generation IV Initiative. This strategy
represents the so calledfull actinide recycle strategy, proposed by CEA
for this kind of reactor. A preliminary study of this strategy in GCFR is shown
in the previous paragraphs and summarized in Table 7.As already
described, this concept consists in adding all the actinides coming from GCFR
spent fuel to DU that substitutes the mass of fuel lost as fission products. If
the efficiency of the separation process were 1, the waste would be (ideally)
composed by FP only, while the actinides would always be reused in the reactor
as new fuel.


### 5.3.2. LOMBT Evaluations for LWR-HTR-GCFR Fuel Cycles

To check the advantages of the chosen fuel cycles, we mainly took into
account the radiotoxicity evolution of the spent fuel versus time. As already
anticipated, please remember that as reference for radiotoxicity, we defined [14]
the level-of-mine balancing time (LOMBT). This value is linked to the LOM definition, value
characteristic
of the type of fuel cycle and it is not easily defined (due to its oscillation
range). However, in this paper, we adopt the LOM only as a conceptual reference
level.At the end of the single steps we consider as waste the following:(1)
Pu+MA+FP in
the case of HTR, because HTR has a “single-step” fuel cycle (i.e., a
given quantity of material spends only a burnup cycle in this kind of reactor);(2)
FP in the
case of GCFR; in fact, in GCFR, thefull actinide recycle is foreseen
(i.e., all the actinides from an irradiation step will be mixed to new DU in
the “fresh” fuel for cycle continuation).However, in this paper, we have limited the analyses to the first
irradiation cycle in GCFR without considering what happens with the multiple
recycles of the fuel. The evaluations of the successive irradiation cycles are
in progress.Table9 gathers the results we found; while in Figures
9 and 10, two
typical CARL output graphs are showed.Table 9
Summary of the obtained results.
HTR (513 EFPD)GCFR (4950 EFPD)Symbiotic cycle∗LOMBT [years]63·682
(waste = FP+HM)159 (waste = FP∗∗)159 (waste = FP∗∗)Np237out/Np237in66%27%18%Pu238out/Pu238in165%75%123%Pu239out/Pu239in81%306%248%Pu240out/Pu240in77%73%56%Pu241out/Pu241in80%26%20%Pu242out/Pu242in170%72%122%Am241out/Am241in21%243%51%Am243out/Am243in126%83%104%Cm244out/Cm244in412%102%420%∗ In this case, there is no indication about EFPD because the real cycle
is made of burnup days inside the reactors plus days out-of-pile (mainly due to
recycling times).∗∗ The fission products
considered here are the following: Rb87, Sr90, Zr93,
Nb94, Tc99, Pd107, Sn126, I129,
Cs135, Cs137, Sm147, Sm151, and Eu154.Figure 9
Spent fuel radiotoxicity versus time for HTR, intermediate
step (“waste”  =  Pu+MA+FP): LOMBT = 63682 years.Figure 10
Spent fuel radiotoxicity versus time for GCFR,
“final” step (“waste” = FP): LOMBT = 159 years. (The fission products considered here are the following: Rb87,
Sr90, Zr93, Nb94, Tc99, Pd107,
Sn126, I129, Cs135, Cs137, Sm147,
Sm151, and Eu154.) (If we
would consider as waste FP and MA, the LOMBT would become equal to 20491 years.)This strategy couples the advantages of both the HTR neutron spectrum
(good performance in Pu, Np237 and Am241 burning) and the
GCFR spectrum (capability of burning the higher Pu isotopes and of decreasing
the Cm244 growing rate).


### 5.3.3. Discussion on the Obtained Results

As figure of merit, we have considered theα ratio, α=σc/σf. This ratio
value versus burnup remains substantially constant or suffer limited variations
that can be neglected (e.g., see Figure 11).
This  justifies our choice to
assume the value of α at BOC valid for the whole irradiation time.Figure 11
α versus time in GCFR (fluctuations are due
to the MC method adopted in our calculations).It is possible to highlight the fact that the higher
theα ratio, the higher the probability of capture than fission for the considered
nuclide in the given flux.From Table10, we can analyze the results we have
obtained.Table 10
1-groupα ratio at
BOC.
GCFRPBMRU2385.27—Np2374.73200Pu2380.6214.25Pu2390.320.60Pu2401.49416.67Pu2410.190.36Pu2421.70204.08Am2416.33119.05Am2436.96333.33Cm2441.5730.96The capture-to-fission  ratio comes in fact  from the effective
cross-sections. These last
have  obtained weighting over the neutron spectrum, as we have seen in the first
part of this paper. In fast reactors, the neutron spectrum is less dependent
from variations of the fuel composition than in thermal reactors. In fact,
during burnup FPs and actinides with higher mass number buildup. FPs have
generally a high-capture cross-section in thermal and/or epithermal range,
while the HM with higher mass number has often larger absorption cross-sections
in this same energy range than the actinides more abundant in the fresh fuel
(i.e., U238 and Pu239) [35], Figures
12 and
13, so that
at EOC in thermal reactors the spectrum becomes harder, because its softer tail
is absorbed by these nuclides.Figure 12
σa versus E of some HMs (Pu239 in red
color, Pu240 in green, Pu241 in blue, Pu242 in
purple, Am241 in light green) [35].Figure 13
σa  versus E of some FPs (Xe135 in red
color, Sm149 in green) [35].This effect is negligible in fast spectrum, so that we
obtain the trend shown in Figure11.Concerning the Pu fissile isotopes (i.e., Pu239 and Pu241), they burn better in fast spectrum than in thermal
one. (α in fast spectrum is
lower than in thermal for both, the probability of fission is higher than that
of capture.)
Particularly, in the PBMR the quantity of Pu239 decreases of about
20%, while its daughter Pu240 is also slightly reduced despite its
high α ratio (≈417): this is due
to Pu239 transmutation by capture. Please note also that there is
not a production channel of Pu239 because the fuel is fertile-free. In
PBMR, Pu241 also slightly decreases and transmutes partially in Pu242 that builds up during irradiation. In GCFR, α of these nuclides is smaller than
in PBMR: in fact there is a higher probability to have fission. Their daughters
Pu240 and Pu242 are both decreasing. Nevertheless, the
total amount of Pu239 multiplies in GCFR by a factor three during
burnup because of the behavior of its parent U238. This fact is
positive in order to obtain an effective self-sustaining core with a full-actinide
recycle. In fact,  if the Pu isotopic
vector would be too much degraded, the criticality would be probably not
maintained in the following cycle substituting the FPs only with pure DU.Concerning the  chain Np237→ Pu238,
Np237 has a high α both in thermal and fast spectrum: its transmute
in Pu238 by capture. Obviously, the quantity of Np237 that transmutes in GCFR is higher because in thermal spectrum, it has to
compete with other strong absorbers (Figure 14). In this GCFR core, Pu238 is fissile and its quantity decreases during irradiation.Figure 14
Comparison of the absorption cross-sections
among some nuclides (Np237 in red, Pu239 in purple,
Pu240 in green, Pu241 in light green, Am241 in blue)
[35].Regarding the chain of Cm244 that at the
moment is the most difficult nuclide to be burnt, we can observe the following.(1)
In the thermal spectrum, Cm244 grows a lot. In fact, its precursors (Pu242 and Am243) both
increase and have a large α ratio (resp., 204 and 333).
Moreover, Cm244 has a very low absorption cross-section, if compared
with the other nuclides in the fuel (Figure 15).(2)
In the fast spectrum, Cm244 has a lower growing rate, because Pu242 and Am243 are
both decreasing, and the absorption cross-sections of the HMs are all
comparable in this range. Moreover, α is not too large for all these nuclides.
Finally, there is something more related to Am241: the thermal
spectrum burns it very good thanks to its high capture cross-section (Figures
12 and 14); while in GCFR, the amount of this nuclide has a nonmonotonic trend
(Figure 16). Its main production channel is the β- decay of Pu241 (half-life = 14.4 years). The total irradiation time is comparable (4950 days)
with the Pu241 half-life (14.4 years are about 5250 days). On the
other hand, the most part of Pu241 is transmuted by absorption. The
production of Am241 can be expressed in a simplified manner as(24)dAm241dt=λPu241⋅Pu241−σaAm241⋅φ⋅Am241, where Am241 and Pu241 are the
time-dependent quantities of the considered nuclides. (λPu241) and (σaAm241⋅φ) are, respectively, 1.53⋅10−9s−1 and 3.2⋅10−9s−1.
Now, we can do some qualitative considerations. At beginning and for the most
part of the cycle, the first term of the right hand of this equation makes the
exponential solution increasing because of the relatively high Pu241 initial quantity. The solution of the equation reaches a maximum, and then it
starts to decrease, because the quantity of Am241 is not more
negligible (the product σaAm241⋅φ has no significant changes due to the fast spectrum),
see also Figure 16.Figure 15
Comparison among some absorption
cross-sections (Cm244 in red, Pu242 in green,
Am243 in blue) [35].Figure 16
Quantity versus time of Pu241 and Am241.


## 5.3.1. A symbiotic LWR-HTR-GCFR Fuel Cycle

As shown,
in the past, our group has already performed similar calculations using LWR-HTR-GCFR
fuel cycles [30]. In Figure 8, a flowchart of our proposed symbiotic cycle is
shown.Figure 8
Symbiotic fuel cycle
LWR-HTR-GCFR [34].We have modeled the core of a pebble-bed HTR (like a 233 MWth  PBMR) [34], whose CPs are loaded by Pu+MA coming from LWR (the considered
burnup is the typical value of 33 GWD/tU). The chemical form of the fuel kernel
is (Pu, MA)O2. Thus, we performed for this HTR core the burnup
calculation until keff  became less than 1 (about 500 GWD/tHM). The
isotopic composition we obtained constitutes the fissile material to be added
to depleted uranium in the GCFR fuel. Finally, we have performed the burnup
calculation of the GCFR core until keff became less than 1 (about
188 GWD/tHM) and evaluated the radiotoxicity of the final waste (i.e., only the
FPs in the frame of the full actinides recycle strategy). For
criticality reasons, we chose for GCFR a fuel composition constituted by 30% as
atomic fraction of Pu+MA (TRU) and 70% of DU (DU contains 0.25% in U235).
Please note that DU represents a material not more useful in order to produce
energy in a “classical” way. Therefore, it has a very low cost. The
isotopic vectors of TRU resulting, respectively, from LWR and HTR that we used
are shown in Table 8.Table 8
TRU isotopic vectors.
Mass fractionSpent LWRSpent HTRNp2370.0460.056Pu2380.0230.073Pu2390.4900.074Pu2400.2150.313Pu2410.1140.18Pu2420.0620.20Am2410.0280.0001Am2430.0160.04Cm242—0.013Cm2440.0050.043Cm245—0.0079Please note
that the burnup calculation on GCFR here shown is only the first of a series
performed in the frame of the Generation IV Initiative. This strategy
represents the so calledfull actinide recycle strategy, proposed by CEA
for this kind of reactor. A preliminary study of this strategy in GCFR is shown
in the previous paragraphs and summarized in Table 7.As already
described, this concept consists in adding all the actinides coming from GCFR
spent fuel to DU that substitutes the mass of fuel lost as fission products. If
the efficiency of the separation process were 1, the waste would be (ideally)
composed by FP only, while the actinides would always be reused in the reactor
as new fuel.


## 5.3.2. LOMBT Evaluations for LWR-HTR-GCFR Fuel Cycles

To check the advantages of the chosen fuel cycles, we mainly took into
account the radiotoxicity evolution of the spent fuel versus time. As already
anticipated, please remember that as reference for radiotoxicity, we defined [14]
the level-of-mine balancing time (LOMBT). This value is linked to the LOM definition, value
characteristic
of the type of fuel cycle and it is not easily defined (due to its oscillation
range). However, in this paper, we adopt the LOM only as a conceptual reference
level.At the end of the single steps we consider as waste the following:(1)
Pu+MA+FP in
the case of HTR, because HTR has a “single-step” fuel cycle (i.e., a
given quantity of material spends only a burnup cycle in this kind of reactor);(2)
FP in the
case of GCFR; in fact, in GCFR, thefull actinide recycle is foreseen
(i.e., all the actinides from an irradiation step will be mixed to new DU in
the “fresh” fuel for cycle continuation).However, in this paper, we have limited the analyses to the first
irradiation cycle in GCFR without considering what happens with the multiple
recycles of the fuel. The evaluations of the successive irradiation cycles are
in progress.Table9 gathers the results we found; while in Figures
9 and 10, two
typical CARL output graphs are showed.Table 9
Summary of the obtained results.
HTR (513 EFPD)GCFR (4950 EFPD)Symbiotic cycle∗LOMBT [years]63·682
(waste = FP+HM)159 (waste = FP∗∗)159 (waste = FP∗∗)Np237out/Np237in66%27%18%Pu238out/Pu238in165%75%123%Pu239out/Pu239in81%306%248%Pu240out/Pu240in77%73%56%Pu241out/Pu241in80%26%20%Pu242out/Pu242in170%72%122%Am241out/Am241in21%243%51%Am243out/Am243in126%83%104%Cm244out/Cm244in412%102%420%∗ In this case, there is no indication about EFPD because the real cycle
is made of burnup days inside the reactors plus days out-of-pile (mainly due to
recycling times).∗∗ The fission products
considered here are the following: Rb87, Sr90, Zr93,
Nb94, Tc99, Pd107, Sn126, I129,
Cs135, Cs137, Sm147, Sm151, and Eu154.Figure 9
Spent fuel radiotoxicity versus time for HTR, intermediate
step (“waste”  =  Pu+MA+FP): LOMBT = 63682 years.Figure 10
Spent fuel radiotoxicity versus time for GCFR,
“final” step (“waste” = FP): LOMBT = 159 years. (The fission products considered here are the following: Rb87,
Sr90, Zr93, Nb94, Tc99, Pd107,
Sn126, I129, Cs135, Cs137, Sm147,
Sm151, and Eu154.) (If we
would consider as waste FP and MA, the LOMBT would become equal to 20491 years.)This strategy couples the advantages of both the HTR neutron spectrum
(good performance in Pu, Np237 and Am241 burning) and the
GCFR spectrum (capability of burning the higher Pu isotopes and of decreasing
the Cm244 growing rate).


## 5.3.3. Discussion on the Obtained Results

As figure of merit, we have considered theα ratio, α=σc/σf. This ratio
value versus burnup remains substantially constant or suffer limited variations
that can be neglected (e.g., see Figure 11).
This  justifies our choice to
assume the value of α at BOC valid for the whole irradiation time.Figure 11
α versus time in GCFR (fluctuations are due
to the MC method adopted in our calculations).It is possible to highlight the fact that the higher
theα ratio, the higher the probability of capture than fission for the considered
nuclide in the given flux.From Table10, we can analyze the results we have
obtained.Table 10
1-groupα ratio at
BOC.
GCFRPBMRU2385.27—Np2374.73200Pu2380.6214.25Pu2390.320.60Pu2401.49416.67Pu2410.190.36Pu2421.70204.08Am2416.33119.05Am2436.96333.33Cm2441.5730.96The capture-to-fission  ratio comes in fact  from the effective
cross-sections. These last
have  obtained weighting over the neutron spectrum, as we have seen in the first
part of this paper. In fast reactors, the neutron spectrum is less dependent
from variations of the fuel composition than in thermal reactors. In fact,
during burnup FPs and actinides with higher mass number buildup. FPs have
generally a high-capture cross-section in thermal and/or epithermal range,
while the HM with higher mass number has often larger absorption cross-sections
in this same energy range than the actinides more abundant in the fresh fuel
(i.e., U238 and Pu239) [35], Figures
12 and
13, so that
at EOC in thermal reactors the spectrum becomes harder, because its softer tail
is absorbed by these nuclides.Figure 12
σa versus E of some HMs (Pu239 in red
color, Pu240 in green, Pu241 in blue, Pu242 in
purple, Am241 in light green) [35].Figure 13
σa  versus E of some FPs (Xe135 in red
color, Sm149 in green) [35].This effect is negligible in fast spectrum, so that we
obtain the trend shown in Figure11.Concerning the Pu fissile isotopes (i.e., Pu239 and Pu241), they burn better in fast spectrum than in thermal
one. (α in fast spectrum is
lower than in thermal for both, the probability of fission is higher than that
of capture.)
Particularly, in the PBMR the quantity of Pu239 decreases of about
20%, while its daughter Pu240 is also slightly reduced despite its
high α ratio (≈417): this is due
to Pu239 transmutation by capture. Please note also that there is
not a production channel of Pu239 because the fuel is fertile-free. In
PBMR, Pu241 also slightly decreases and transmutes partially in Pu242 that builds up during irradiation. In GCFR, α of these nuclides is smaller than
in PBMR: in fact there is a higher probability to have fission. Their daughters
Pu240 and Pu242 are both decreasing. Nevertheless, the
total amount of Pu239 multiplies in GCFR by a factor three during
burnup because of the behavior of its parent U238. This fact is
positive in order to obtain an effective self-sustaining core with a full-actinide
recycle. In fact,  if the Pu isotopic
vector would be too much degraded, the criticality would be probably not
maintained in the following cycle substituting the FPs only with pure DU.Concerning the  chain Np237→ Pu238,
Np237 has a high α both in thermal and fast spectrum: its transmute
in Pu238 by capture. Obviously, the quantity of Np237 that transmutes in GCFR is higher because in thermal spectrum, it has to
compete with other strong absorbers (Figure 14). In this GCFR core, Pu238 is fissile and its quantity decreases during irradiation.Figure 14
Comparison of the absorption cross-sections
among some nuclides (Np237 in red, Pu239 in purple,
Pu240 in green, Pu241 in light green, Am241 in blue)
[35].Regarding the chain of Cm244 that at the
moment is the most difficult nuclide to be burnt, we can observe the following.(1)
In the thermal spectrum, Cm244 grows a lot. In fact, its precursors (Pu242 and Am243) both
increase and have a large α ratio (resp., 204 and 333).
Moreover, Cm244 has a very low absorption cross-section, if compared
with the other nuclides in the fuel (Figure 15).(2)
In the fast spectrum, Cm244 has a lower growing rate, because Pu242 and Am243 are
both decreasing, and the absorption cross-sections of the HMs are all
comparable in this range. Moreover, α is not too large for all these nuclides.
Finally, there is something more related to Am241: the thermal
spectrum burns it very good thanks to its high capture cross-section (Figures
12 and 14); while in GCFR, the amount of this nuclide has a nonmonotonic trend
(Figure 16). Its main production channel is the β- decay of Pu241 (half-life = 14.4 years). The total irradiation time is comparable (4950 days)
with the Pu241 half-life (14.4 years are about 5250 days). On the
other hand, the most part of Pu241 is transmuted by absorption. The
production of Am241 can be expressed in a simplified manner as(24)dAm241dt=λPu241⋅Pu241−σaAm241⋅φ⋅Am241, where Am241 and Pu241 are the
time-dependent quantities of the considered nuclides. (λPu241) and (σaAm241⋅φ) are, respectively, 1.53⋅10−9s−1 and 3.2⋅10−9s−1.
Now, we can do some qualitative considerations. At beginning and for the most
part of the cycle, the first term of the right hand of this equation makes the
exponential solution increasing because of the relatively high Pu241 initial quantity. The solution of the equation reaches a maximum, and then it
starts to decrease, because the quantity of Am241 is not more
negligible (the product σaAm241⋅φ has no significant changes due to the fast spectrum),
see also Figure 16.Figure 15
Comparison among some absorption
cross-sections (Cm244 in red, Pu242 in green,
Am243 in blue) [35].Figure 16
Quantity versus time of Pu241 and Am241.


## 6. Conclusions and Future Perspectives

This work represents a contribute to the researches on
the important topic of waste reduction. In fact, from the results we can see
that HTRs reduce waste radiotoxicity of an order of magnitude burning Pu and
supplying energy. Adopting Th-Pu-based cycle, it appears that the total amount
of produced energy is quite large.The use of GCFR after HTR fuelled with Pu-U (or Pu-Th)
is capable to further reduce radiotoxicity in the waste and gives back (as
expected) almost the same amount of Pu initially loaded and, at the same time,
supplies a lot of energy. It is important to underline that this Pu, used as
fuel, is not a waste but a source of energy, not a problem but a resource [36].
It is important to highlight the
progress in this research performed in the last period. In fact, while in our
first papers [14, 20, 30] on this topic, the calculations were performed on
simplified models (kinf, etc.), the most recent calculations
(reported in the final part of this paper) were performed on a “real”
model of the studied reactors (both PBMR and GCFR). In addition, we have added
the GCFR multiple recycling option using  keff calculations for
all the considered reactors.Regarding the future perspectives, the material
technology is probably the most challenging aspects in innovative reactor and
fuel cycles field. In fact, the fuel has to be stable under high temperature
and high fast fluence, simply to be reprocessed and refabricated. Moreover, it
has also to contain a consistent fraction of MA, which has often a chemical behavior
different not only from U but also from Pu. Moreover, their extensive use as
fuels will require additional shielding respect to the actual reprocessing and
fabrication plants: many MAs are so strongγ and neutrons emitters that it is impossible
to adopt the actual MOX fabrication technology to treat them.Carbide and nitride are very interesting chemical
forms for the new fuel concepts: they have a larger thermal conductivity and a
higher density of HM than oxides (Table11) but many technological studies have
to be still performed on this topic. (The higher HM density allows to obtain criticality also with
higher volumetric fraction of coolant in the core. This fact is very important
for GCFR design [5].)Table 11
Property data of some fuel compound [5].
UPuO2UPuCUPuNDensity [g/cm3]11.013.614.3HM density [g/cm3]9.712.913.5Tmelt[∘C]277524802780Thermal conductivity [W/mK]2.919.619.8Recovering of all the HMs from SNF is another aspect
to be investigated. For instance, for theintegral fuel cycle proposed
for GCFR, all the HMs have to be together extracted during reprocessing and
then used to manufacture new fuel. It is clear that to find an extracting
molecule (or a group of molecules) that allows the selective extraction of all
the actinide together is a complex issue. Other problems are partitioning of
actinides (especially the trivalent ones) from lanthanides and Am from Cm [37, 38].At the end of the proposed symbiotic cycle, the waste results to be
virtually made up only by fission products, that was be separated by the
actinides, whose best repository seems to be the new GCFR core itself, in order to
further reduce the HLW and best exploit the uranium resources.Moreover, the LOMBT is reduced to less than 200 years. Please remember
that in an LWR, using aonce-through cycle (even if a MOX technology is adopted), the LOMBT will be reached after
more than 100000 years.It is important also to highlight that we adopt,
in proposed recycling scheme, only chemical and not isotopic separations: in
this way, it is possible to reduce the costs and to avoid proliferation
concerns linked to the use of plutonium.Finally, we can underline that GCFR
is a “real” reactor not a simple burner that, while burning MA, produces
energy. Furthermore, considering the positive
characteristics of HTR in terms of Pu burning due to their excellent neutronic
economy, and coupling it with GCFR (fast neutronic
spectrum and high fluence) in a symbiotic fuel cycle, we can say that the
geological disposal issues concerning high level radiotoxicity of actinides can
be considerably reduced.



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*Source: 265430-2008-05-27.xml*