energies
Article
Spent Nuclear Fuel Management: Levelized Cost of
Electricity Generation and Analysis of Various
Production Scenarios
Laura Rodriguez-Penalonga † , Beatriz Yolanda Moratilla Soria *,† , Paula Ocaña-Pastor,
Paula Martín-Cañas, Borja Belda-Sánchez, Natalia Cortes-Sanz, Mathilde Estadieu,
José Ignacio Linares-Hurtado, José Manuel Vidal-Bernardez and Marta Niño-Serrano
Cátedra Rafael Mariño, Universidad Pontificia de Comillas, Madrid 28015, Spain;
[email protected] (L.R.-P.); [email protected] (P.O.-P.); [email protected] (P.M.-C.);
[email protected] (B.B.-S.); [email protected] (N.C.-S.); [email protected] (M.E.);
[email protected] (J.I.L.-H.); [email protected] (J.M.V.-B.); [email protected] (M.N.-S.)
* Correspondence: [email protected]; Tel.: +34-91-542-28-00
† These authors contributed equally to this work.
Academic Editor: Hiroshi Sekimoto
Received: 13 November 2015; Accepted: 24 February 2016; Published: 10 March 2016
Abstract: This article aims to analyze the results of an economic study carried out to compare the
influence of nuclear production capacity in different countries. The analysis is based on LCOEs
(levelized cost of electricity) for three back-end strategies: open cycle, closed cycle and advanced
closed cycle. The results show that costs are not a relevant criteria in order to select an energy policy
for the spent nuclear fuel management.
Keywords: nuclear material; used fuel; back-end strategies; levelized costs
1. Introduction
The current world energy scenario is the result of various socio-economic trends leading to an
increasing demand of resources and energy consumption per capita.
Due to the above, it is necessary to develop a global energy restructuration that significantly changes
the current patterns of energy generation and consumption, encouraging sustainable development.
Since the beginning of the century, there has been a discussion about the current energy mix
model, based on fossil fuels, such as oil, coal and natural gas. Nowadays, the limitations of this model
are unquestionable from the economic (high energy price), the social (inequality and energy poor) and
the environmental (adverse implications for the environment) point of view.
In order to achieve a sustainable solution for the energy future, it is especially important to take
into account renewable energies, but nuclear energy is also very important to help us satisfy the recent
increase of electricity demand and, at the same time, reduce the carbon dioxide emissions.
Regarding nuclear energy, it is necessary to take into account other aspects, such as technology and
nuclear proliferation, and to assess all of the nuclear fuel cycle options in order to develop a national
strategy that will be economically, environmentally and socially sustainable.
Waste management has always been the key point in all discussions about nuclear energy.
Therefore, it is absolutely essential to make a suitable long-term plan about how to manage the
used fuel assemblies. Nowadays, there are two possible options: the open cycle, which consists of
directly disposing the used nuclear fuel assemblies in a deep geological repository (DGR), and the
closed cycle, in which the spent nuclear fuel is reprocessed to recover fissile and fertile materials that
are recycled in order to reduce fresh fuel consumption. Both options imply that, prior to the final
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management of the waste product, the used fuel assemblies need to be treated and stored in an interim
management of the waste product, the used fuel assemblies need to be treated and stored in an
storage facility, and also, both of them require a deep geological repository (DGR).
interim storage facility, and also, both of them require a deep geological repository (DGR).
Even
though
technologies,there
thereisisa afuture
futurepossibility
possibility
that
Even
thoughthese
theseare
arethe
thecurrently
currently available
available technologies,
that
is is
being
researched:
the
advanced
closed
cycle,
in
which
fast
reactors
are
introduced,
whereas,
at
being researched: the advanced closed cycle, in which fast reactors are introduced, whereas, at thethe
same
time,
the
also allows
allows the
themulti-recycling
multi-recyclingofoffissile
fissile
and
fertile
same
time,
thereprocessing
reprocessingisisimproved.
improved. This
This also
and
fertile
materials
and
thethe
fullfull
closure
of the
fuelfuel
cycle.
However,
a DGR
is stillis required
to manage
and dispose
materials
and
closure
of the
cycle.
However,
a DGR
still required
to manage
and
of dispose
the residual
actinides
and
fission
products.
of the residual actinides and fission products.
AllAll
ofof
the
the fuel
fuel cycle
cyclefinal
finalstage.
stage.However,
However,
there
theback-end
back-endstrategies
strategiesrequire
require aa DGR
DGR at the
there
areare
significant
differences
strategy, derived
derivedfrom
fromtwo
twomain
main
influences:
significant
differencesininthe
theassociated
associatedcosts
costs for
for each strategy,
influences:
thethe
reduction
volume
needed
and
the
energydensity.
density.For
Forthe
theclosed
closedcycle,
cycle,the
thevolume
volumerequired
requiredfor
reduction
in in
thethe
volume
needed
and
the
energy
the is
DGR
is about
1/5
of open
the open
cycle
DGR
volume,
taking
into
account
theenergy
energydensity,
density,the
thefor
DGR
about
1/5 of
the
cycle
DGR
volume,
butbut
taking
into
account
the
the costs
DGR for
costs
forclosed
the closed
represent
approximately
25%
theDGR
DGRcosts
costs for
for the open
DGR
the
cyclecycle
represent
approximately
25%
ofofthe
opencycle
cycle[1].
[1].
it well-known
is well-known
[1–5],
one
of the
most
important
back-end
costs
in the
closed
cycle
comes
AsAs
it is
[1–5],
one
of the
most
important
back-end
costs
in the
closed
cycle
comes
from
from reprocessing,
in the
caseopen
of the
open
cycle,
it is the
DGR;
bothhave
of them
have
reprocessing,
while inwhile
the case
of the
cycle,
it is
the DGR;
ergo,
bothergo,
of them
advantages
advantages
and
disadvantages.
However,
looking
through
various
comparative
studies
of
these
and disadvantages. However, looking through various comparative studies of these strategies, where
where
thehas
economical
aspect has
been
analyzed, that
theythe
all cost
conclude
that the
cost variation
thestrategies,
economical
aspect
been analyzed,
they
all conclude
variation
between
the closed
between the closed and open cycle is nearly 10%, as shown in the last economic analysis carried out
and open cycle is nearly 10%, as shown in the last economic analysis carried out by Moratilla [6].
by Moratilla [6].
In order to make a long-term sustainable decision adopting one or another cycle, it is also
In order to make a long-term sustainable decision adopting one or another cycle, it is also
important to determine the tendency of the costs involved. According to some international studies,
important to determine the tendency of the costs involved. According to some international studies,
the cost of creating a DGR for the open cycle is estimated to be increasing, as shown in Figure 1. This is
the cost of creating a DGR for the open cycle is estimated to be increasing, as shown in Figure 1. This
mainly
due to the newly-identified requirements about the DGR, as it was concluded in the article
is mainly due to the newly-identified requirements about the DGR, as it was concluded in the article
published
byby
Moratilla
published
Moratilla[7].
[7].
Figure 1. Deep geological repository (DGR) evolution cost.
Figure 1. Deep geological repository (DGR) evolution cost.
On the other hand, the costs of the closed cycle are estimated to be decreasing, as it can be found
the 2.
other
theof
costs
of the closed
cycle
areitsestimated
to be decreasing,
as key
it can
be found
in On
Figure
The hand,
maturity
the technology
used
and
constant optimization
are the
points
of
in this
Figure
2. The maturity of the technology used and its constant optimization are the key points of
evolution.
this evolution.
Therefore, in order to make a suitable decision concerning the nuclear cycle, it is necessary to
take into account some other factors, such as the intangible asset or the current energy regulations of
each country. For example, P. Högselius [8] explains that military ambitions and non-proliferation,
technological culture, political culture and civil society, geological conditions and energy policy are
the five main broad explanatory factors that are needed in order to analyze the differences in spent
nuclear fuel policies between each country. Moreover, another important factor to consider is the tax
policy of each country, as it has been explained for the Spanish scenario in different articles [6,9].
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Figure 2. Closed cycle evolution cost.
Figure 2. Closed cycle evolution cost.
Therefore, in order to make a suitable decision concerning the nuclear cycle, it is necessary to
Analyzing
the energy
strategies
ofsuch
different
of them,
suchregulations
as Swedenof
and
take
into account
some other
factors,
as thecountries,
intangiblethere
assetare
or some
the current
energy
Finland,
that have
cycle[8]
strategy,
having
to construct
deepand
geological
repositories,
each country.
Forassumed
example,an
P. open
Högselius
explains
that military
ambitions
non-proliferation,
technological
culture,
culture
andto
civil
society,
geological
conditions
energy policy
whereas
there are
otherspolitical
that have
decided
adopt
the closed
cycle,
having toand
reprocess,
recycleare
and,
the
five
main
broad
explanatory
factors
that
are
needed
in
order
to
analyze
the
differences
in
spent
afterwards, vitrify and compact non-usable residue materials to be stored in the DGR. Some of the
nuclear that
fuel policies
between
each
country.
Moreover,
important
consider Russia
is the tax
countries
have adopted
the
latter
alternative,
suchanother
as France,
India, factor
Japan,toPakistan,
and,
policy
of
each
country,
as
it
has
been
explained
for
the
Spanish
scenario
in
different
articles
[6,9].
more recently, China, have reprocessing facilities. However, there are other countries, such as the
Analyzing
thereprocesses
energy strategies
of different
countries,
arehave
some
ofrequired
them, such
as Sweden
Netherlands,
which
all of the
used fuel,
but theythere
do not
the
facilities,
which
and
Finland,
that
have
assumed
an
open
cycle
strategy,
having
to
construct
deep
geological
is possible by recycling abroad and storing the reprocessed vitrified waste.
repositories,
there are others
decided
adopt theEconomic
closed cycle,
to reprocess,
In Europe,whereas
the communication
aboutthat
thehave
opinion
of thetoEuropean
andhaving
Social Committee
[10],
recycle and, afterwards, vitrify and compact non-usable residue materials to be stored in the DGR.
which was requested and published by the European Commission, is expected to decrease the number
Some of the countries that have adopted the latter alternative, such as France, India, Japan, Pakistan,
of European countries that lack a definitive decision. This communication recommends a European
Russia and, more recently, China, have reprocessing facilities. However, there are other countries,
Energy Dialogue (EED) that will contribute to the implementation of the Energy Union.
such as the Netherlands, which reprocesses all of the used fuel, but they do not have the required
Nevertheless, there are countries, such as Spain, which have still not made a decision about which
facilities, which is possible by recycling abroad and storing the reprocessed vitrified waste.
strategyIntoEurope,
adopt. Hence,
for these countries, there are many factors and methods that have to be taken
the communication about the opinion of the European Economic and Social
into
consideration
when
different
strategies.
the Commission,
most frequently-used
tool
Committee [10], which comparing
was requested
and published
by Currently,
the European
is expected
to to
compare
various
technologies
or
processes
is
the
levelized
cost
of
electricity
(LCOE).
G.
De
Roo
and
decrease the number of European countries that lack a definitive decision. This communication
J.E.recommends
Parsons [1] have
developed
theDialogue
first methodology
order
to calculate
the
LCOE extended
a European
Energy
(EED) thatinwill
contribute
to the
implementation
of to
thethe
reprocessing
strategy.
Energy Union.
Nevertheless, there are countries, such as Spain, which have still not made a decision about
2. which
Methodology
strategy to adopt. Hence, for these countries, there are many factors and methods that have to
be As
taken
into consideration
strategies.
Currently,
the most
frequently-used
described
before, in when
ordercomparing
to make a different
comparison
between
the different
back-end
strategies,
tool
to
compare
various
technologies
or
processes
is
the
levelized
cost
of
electricity
(LCOE).
De
a tool that allows us to analyze various technologies is the LCOE, which is defined as
the netG.
present
Rooofand
J.E. Parsons
[1] have over
developed
the first
in order
to calculate
LCOEthe
value
the unit-cost
of electricity
the lifetime
of a methodology
generating asset.
This tool
is able to the
compare
extended
to
the
reprocessing
strategy.
lifecycle cost of electricity generation with different technologies or within the same technology class.
In this article, the front-end and the back-end costs of the nuclear fuel cycle are analyzed using
2. Methodology
the LCOE. The front-end costs correspond to the nuclear fuel cycle expenditures incurred prior to the
Asthe
described
order
to make
a comparison
between the
different back-end
strategies,
arrival at
nuclearbefore,
power in
plant
(NPP):
natural
uranium extraction,
conversion
and enrichment
costs,
a tool that
allows
us to
analyze
various
technologies
is the
LCOE,oxide
which(REPUOX)
is defined as
thefabrication
net presentfor
uranium
oxide
(UOX)
fuel
fabrication
and
reprocessed
uranium
fuel
of cycle.
the unit-cost
of electricity
lifetime
of to
a generating
asset. This
tool
is able to compare
thevalue
closed
The back-end
costsover
are the
those
related
the spent nuclear
fuel
management:
interim
the
lifecycle
cost
of
electricity
generation
with
different
technologies
or
within
the
same
technology class.
storage, encapsulation, DGR, reprocessing (for the closed cycle), etc.
Energies 2016, 9, 178
4 of 13
For this study, data have been gathered from the Nuclear Energy Agency (NEA) of the
Organisation for Economic Co-operation and Development (OECD) [11], where costs are analyzed for
different back-end strategies. Therefore, first, in order to analyze the LCOE for the back-end of the
nuclear fuel cycle, there are four main costs that have to be taken into account for each facility implied
in the process:
Investment cost: for each facility, it corresponds to the initial investment cost; the units are in $.
Closure cost: the closure cost of the facility once it reaches the end of its life cycle; the units are in $.
Operations and Maintenance (O&M) cost: the costs related to the operation and maintenance of
the facility during its operational years; as it depends on the years the facility is running (its operational
lifetime), this cost is given in $/year.
Transport cost: The cost related to the shipment of the spent nuclear fuel amongst facilities; as in
the previous case, this cost depends on the number of years in which transportation is required (which
correspond to some of the facilities operational lifetime), so this cost is also given in $/year.
In order to calculate the back-end levelized cost of electricity, there are three economic factors that
have to be applied:
-
Capital recovery factor ( f CRF ): This factor is used to convert each cost into a stream of equal
payments over the NPP operational lifetime, as it is the period of time when the profits are
produced. The f CRF is calculated in Equation (1).
f CRF “
-
p1 ` iq N ´ 1
(1)
where i is the discount rate and N is the NPP operational lifetime.
Discount factor (fd ): This is the factor by which the investment and closure costs must be multiplied
in order to obtain the present value. The fd can be obtained as shown in Equation (2).
fd “
-
i pi ` 1q N
1
p1 ` iqt0
(2)
where t0 is the ∆ t between the time the nuclear power plant starts to be operational (Year 0) and
the time the back-end facility starts to operate.
Conversion factor ( fř ): This factor is applied to the costs that, instead of being a one-time
expenditure, depend on the time the facility is operating. It calculates the total O&M and
transportation costs during the facility operational lifetime.
fř “
p1 ` iq N ´ 1
i p1 ` iq N
(3)
where i is the discount rate and N is the facility operational lifetime.
The LCOEBack´ End can be obtained as the sum of the partial costs applying the
previously-exposed factors, as is shown in Equation (4).
LCOEBack´End “
ÿ
pInvestmentk ` Closurek q ¨ f CRF ¨ f d ` pO&Mk ` Transportk q ¨ f CRF ¨ fř k
(4)
k
where k corresponds to each facility implied in the process.
Once the LCOE for the back-end has been calculated, in order to obtain a more realistic vision
of the global cost of the nuclear fuel cycle, the LCOE is also obtained for the front-end. The costs
affecting the LCOEFront´End , obtained from the data gathered in the OECD/NEA report [7], are:
natural uranium cost, natural uranium conversion cost, UOX enrichment cost, UOX fuel fabrication
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cost and, for the closed cycle back-end strategies, also the REPUOX enrichment cost and the REPUOX
fuel
fabrication
cost.
cost
and, for the
closed cycle back-end strategies, also the REPUOX enrichment cost and the REPUOX
All
of these costs
fuel
fabrication
cost. are in $/kg, so in order to obtain the LCOE, it is necessary to multiply them
by the All
kg/TWh
fuelarerequired
forineach
strategy
of the
front-end
process.
of theseof
costs
in $/kg, so
orderback-end
to obtain the
LCOE,and
it is stage
necessary
to multiply
them
by
The
LCOE
is
shown
in
Equation
(5).
the kg/TWh
ofEnd
fuel required for each back-end strategy and stage of the front-end process. The
Front´
𝐿𝐶𝑂𝐸𝐹𝑟𝑜𝑛𝑡−𝐸𝑛𝑑 is shown in Equation (5).
˙
ˆ ˙ ˆ
ˆ
𝑇𝑊ℎ ˙
ř
kg ( 𝑘𝑔 ) ∙ 𝐶𝑜𝑠𝑡$ ( $ ) ∙ ( 11TWh
𝐿𝐶𝑂𝐸
= ∑ 𝐹𝑢𝑒𝑙
)
¨
Cost
¨
LCOEFront´End
“𝐹𝑟𝑜𝑛𝑡−𝐸𝑛𝑑
Fuel
𝑇𝑊ℎ 𝑘
𝑘𝑔
1000 𝑀𝑊ℎ
𝑘,𝑖 TWh
kg ki 𝑘𝑖 1000 MWh
k,i
k
1 𝑇𝑊ℎ
1 TWh
=
“
1000 𝑀𝑊ℎ
ˆ1000 MWh
ˆ
˙
kg 𝑘𝑔
· (𝑁𝑎𝑡𝑢𝑟𝑎𝑙
𝑢𝑟𝑎𝑛𝑖𝑢𝑚 (
)
¨ Natural
uranium
𝑇𝑊ℎ
TWh
ˆ
ˆ
˙
ˆ
˙˙
ˆ
˙
$ $
$
kg
$
𝑘𝑔
¨ Natural
uranium
cost
`
Conversion
cost
`
UOX
· (𝑁𝑎𝑡𝑢𝑟𝑎𝑙 𝑢𝑟𝑎𝑛𝑖𝑢𝑚 𝑐𝑜𝑠𝑡
(
) + 𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑐𝑜𝑠𝑡 ( kg U
)) + 𝑈𝑂𝑋 (
) TWh
ˆ
ˆkg U𝑘𝑔 𝑈 ˙
ˆ
𝑘𝑔 𝑈
𝑇𝑊ℎ ˙˙
(5)
$
$
(5)
¨ UOX Enrichment cost
` UOX Fabrication cost $
$
· (𝑈𝑂𝑋
) + 𝑈𝑂𝑋 𝐹𝑎𝑏𝑟𝑖𝑐𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑠𝑡 (
kg ))
UOX
ˆ𝐸𝑛𝑟𝑖𝑐ℎ𝑚𝑒𝑛𝑡
˙ 𝑐𝑜𝑠𝑡kg(UOX
𝑘𝑔 𝑈𝑂𝑋
𝑘𝑔 𝑈𝑂𝑋
kg
𝑘𝑔
`REPUOX
+ 𝑅𝐸𝑃𝑈𝑂𝑋
(
)
TWh
ˆ
ˆ
˙
𝑇𝑊ℎ
$$
¨ REPUOX
Enrichment
cost
· (𝑅𝐸𝑃𝑈𝑂𝑋 𝐸𝑛𝑟𝑖𝑐ℎ𝑚𝑒𝑛𝑡 𝑐𝑜𝑠𝑡kg
( REPUOX)
ˆ
𝑘𝑔 𝑅𝐸𝑃𝑈𝑂𝑋 ˙˙˙
$
`REPUOX Fabrication cost
$
kg
REPUOX
+ 𝑅𝐸𝑃𝑈𝑂𝑋 𝑓𝑎𝑏𝑟𝑖𝑐𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑠𝑡 (
)))
𝑘𝑔 𝑅𝐸𝑃𝑈𝑂𝑋
where the costs of REPUOX are only applied for the closed cycle back-end strategies
where the costs of REPUOX are only applied for the closed cycle back-end strategies
Finally, the LCOE is obtained as the addition of LCOEFront´End and LCOEBack´End .
Finally, the LCOE is obtained as the addition of 𝐿𝐶𝑂𝐸𝐹𝑟𝑜𝑛𝑡−𝐸𝑛𝑑 and 𝐿𝐶𝑂𝐸𝐵𝑎𝑐𝑘−𝐸𝑛𝑑 .
3. Results
3. Results
The purpose of this paper is to analyze the costs of the back-end of the nuclear fuel cycle for
The purpose of this paper is to analyze the costs of the back-end of the nuclear fuel cycle for
different production scenarios and for three NPP operational lifetime situations.
different production scenarios and for three NPP operational lifetime situations.
For the analysis, three back-end strategies have been considered according to the OECD/NEA
For the analysis, three back-end strategies have been considered according to the OECD/NEA
report [11]:
report [11]:
- - OFC
(once-through
the SNF
SNF(spent
(spentnuclear
nuclearfuel)
fuel)
stored,
OFC
(once-throughfuel
fuelcycle)
cycle)orordirect
direct disposal:
disposal: the
is is
stored,
encapsulated
and,
finally,
disposed
in in
the
DGR,
encapsulated
and,
finally,
disposed
the
DGR,asasshown
shownininFigure
Figure3.3.
Figure
3. Once-through
Once-throughfuel
fuelcycle.
cycle.UOX,
UOX,
uraniumoxide.
oxide.
Figure 1.
uranium
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-
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Partial recycling: the SNF is reprocessed, and the recovered fissile materials are recycled in the form
Partial recycling: the SNF is reprocessed, and the recovered fissile materials are recycled in the
Partial
recycling:
the
SNF
is reprocessed,
and the
recovered
fissile
materials
are
recycled
in the
of- MOX
(mixed
oxide)
and
REPUOX
Then,
the
irradiated
bundles
are
stored,
encapsulated
form
of MOX
(mixed
oxide)
andfuel.
REPUOX
fuel.
Then, the irradiated
bundles
are
stored,
form
of
MOX
(mixed
oxide)
and
REPUOX
fuel.
Then,
the
irradiated
bundles
are
stored,
and disposed
in a DGR.
This cycle
shown
Figure
4. in Figure 4.
encapsulated
and disposed
in a is
DGR.
Thisin
cycle
is shown
encapsulated and disposed in a DGR. This cycle is shown in Figure 4.
Figure
2. Partial
recycling
cycle.
AFC
(advanced
cycle):
LWRs
(Light-water
reactors)
and (Fast
Figure
4. Partial
recycling
cycle.
AFC
(advanced
fuelfuel
cycle):
LWRs
(Light-water
reactors)
and FRs
Figure 2. Partial recycling cycle. AFC (advanced fuel cycle): LWRs (Light-water reactors) and
FRs
(Fast
reactors)
are
used
in
this
strategy,
so
MOX
and
REPUOX
fuels
can
be
reprocessed
reactors)
used
in this are
strategy,
so this
MOX
and REPUOX
fuels
be reprocessed
recycled again as
FRs are
(Fast
reactors)
used in
strategy,
so MOX
andcan
REPUOX
fuels canand
be reprocessed
and
recycled
again
as fuel
in A
FRs,
closing
the fuel
cycle. A DGR
willthe
also
be necessary
to
fuel in
FRs,
closing
the
fuel
cycle.
DGR
will
also
be
necessary
to
store
vitrified
waste. to
This is
and recycled again as fuel in FRs, closing the fuel cycle. A DGR will also be necessary
store the vitrified waste. This is shown in Figure 5.
shown
in
Figure
5.
store the vitrified waste. This is shown in Figure 5.
Figure 3. Advanced fuel cycle.
Figure 3. Advanced fuel cycle.
Figure 5. Advanced fuel cycle.
Some assumptions and considerations have been made in order to proceed with the calculations,
Some assumptions and considerations have been made in order to proceed with the calculations,
some of which derive from the OECD/NEA report [11]:
some of which derive from the OECD/NEA report [11]:
Some
assumptions and considerations have been made in order to proceed with the calculations,
All of the back-end facilities are assumed to be ready and operational exactly at the time when
All of the
back-end
are assumed
to be[11]:
ready and operational exactly at the time when
some- of which
derive
from facilities
the OECD/NEA
report
they are
needed.
they are needed.
All facilities’ investment costs are considered overnight capital costs.
- All
the facilities’
back-endinvestment
facilities are
assumed
to be ready
and capital
operational
- of All
costs
are considered
overnight
costs. exactly at the time when they
SNF is cooled down at the reactor site for seven years.
are
- needed.
SNF is cooled down at the reactor site for seven years.
For the OFC and partial recycling strategies, SNF or MOX and REPUOX irradiated bundles are
- facilities’
For the OFC
and partial
recycling
strategies,overnight
SNF or MOX
and REPUOX irradiated bundles are
- All
investment
costs
are considered
then transported
to the
interim
storage facility
where capital
they arecosts.
stored for 50 years before the
then
transported
to
the
interim
storage
facility
where
they
are stored for 50 years before the
- SNF isfinal
cooled
down at the reactor site for seven years.
disposal.
final disposal.
-
For the OFC and partial recycling strategies, SNF or MOX and REPUOX irradiated bundles are then
transported to the interim storage facility where they are stored for 50 years before the final disposal.
Energies 2016, 9, 178
-
-
7 of 13
For the partial recycling and AFC strategies, an integral reprocessing facility is considered, including
Energies 2016, 9, 178
7 of 13
a reprocessing plant, an FP (fission products)/MA (minor actinides) vitrification plant and a recycling
plant
(MOX
fabrication).
For thefuel
partial
recycling and AFC strategies, an integral reprocessing facility is considered,
For theincluding
AFC strategy,
the shareplant,
of FRs
fleet is
assumed to be
17.5%,
with a cost
premium
of 20%.
a reprocessing
anin
FPthe
(fission
products)/MA
(minor
actinides)
vitrification
plant
and a recycling
plant (MOX
fuel fabrication).
Four electricity
production
scenarios
are considered: 25 TWh/year, 75 TWh/year, 400 TWh/year
- 800
ForTWh/year.
the AFC strategy, the share of FRs in the fleet is assumed to be 17.5%, with a cost premium
and
of 20%.
The calculations
are made for 40, 60 and 80 years NPP operational lifetime and discount rates of 0% and 3%.
Four electricity production scenarios are considered: 25 TWh/year, 75 TWh/year, 400 TWh/year
The results are obtained in 2010 USD.
and 800 TWh/year.
The
are made
for 40, 60
and 80 years
operational
lifetime
andOECD-NEA
discount rates[11],
of the
Using
thecalculations
methodology
previously
explained
andNPP
the data
provided
by the
0%
and
3%.
LCOE can be obtained for all of the different scenarios considered.
-
The results are obtained in 2010 USD.
3.1. Analysis
forthe
Different
NPP Operational
Lifetime Scenarios
Using
methodology
previously explained
and the data provided by the OECD-NEA [11], the
LCOE
canto
be visualize
obtained for
alleffects
of the different
scenarios
considered.
In
order
the
of the NPP
operational
lifetime in the costs of the back-end
of the nuclear fuel cycle, an analysis of the different strategies has been made for a 40-, 60- and
3.1. Analysis for Different NPP Operational Lifetime Scenarios
80-year lifetime.
In order to visualize the effects of the NPP operational lifetime in the costs of the back-end of the
â
OFC
Strategy
nuclear
fuel cycle, an analysis of the different strategies has been made for a 40-, 60- and 80-year lifetime.
 OFC
The results
of Strategy
the LCOE for the direct disposal strategy are presented in Table 1.
The results of the LCOE for the direct disposal strategy are presented in Table 1.
Table 1. Levelized cost of electricity (LCOE) for once-through fuel cycle (OFC) in different scenarios in
$(2010)/MWh.
Table 1. Levelized cost of electricity (LCOE) for once-through fuel cycle (OFC) in different scenarios
in $(2010)/MWh.
0% Discount Rate
0% Discount Rate
40 Years
60 Years
80 Years
40 Years
60 Years
80 Years
25 TWh/year
11.83
10.65
10.09
25 TWh/year
11.83
10.65
10.09
75 TWh/year
7.34
6.86
6.65
75 400
TWh/year
6.86
6.65
TWh/year 7.34
5.51
5.33
5.26
400800
TWh/year
5.33
5.26
TWh/year 5.51
5.31
5.15
5.10
800 TWh/year
5.31
5.15
5.10
3% Discount Rate
3% Discount Rate
60 Years
80 Years
40 Years
60 Years
80 Years
7.05
6.70
6.56
7.05
6.70
6.56
5.40
5.25
5.20
5.40
5.25
5.20
4.74
4.66
4.64
4.74
4.66
4.64
4.66
4.59
4.58
4.66
4.59
4.58
40 Years
Figure
6 represents
these
results
for
of 0%
0%and
and3%.
3%.
Figure
6 represents
these
results
fordiscount
discount rates
rates of
Figure 6. LCOE for OFC.
Figure 6. LCOE for OFC.
Energies 2016, 9, 178
8 of 13
The tendency of the LCOE curves is to decrease when the electricity production increases, which
is an expected result, because, even though the total cost in $ is higher, this cost increment is thoroughly
Energies 2016, 9, 178
8 of 13
compensated
by the increase in MWh.
From The
these
curves,
it can
also
be noted
that the
LCOE
decreases
when the
NPP operational
tendency
of the
LCOE
curves
is to decrease
when
the electricity
production
increases,
which
lifetime
is
higher.
This
happens
because,
when
the
NPP
lifetime
is
higher,
more
years
of generating
is an expected result, because, even though the total cost in $ is higher, this cost increment
is
profitsthoroughly
are taken into
account,by
which
compensates
compensated
the increase
in MWh.the costs of the back-end facilities’ operational years.
From the
these
curves, it
be noted
the LCOE decreases
when the
NPP operational
However,
decrease
ofcan
thealso
LCOE
is notthat
proportional
to the number
of years
the operational
lifetime
is
higher.
This
happens
because,
when
the
NPP
lifetime
is
higher,
more
years
of
generating
lifetime is increased: from 40 years to 60 years, the reduction is higher than from 60 to 80 years.
profits are
taken into
compensates
thethe
costs
of the back-end
facilities’
operational
years. so the
This happens
because
theaccount,
factorswhich
that are
applied to
different
costs have
exponential
values,
However, the decrease of the LCOE is not proportional to the number of years the operational
LCOE decreases rapidly for low capacities and slower when the capacity increases.
lifetime is increased: from 40 years to 60 years, the reduction is higher than from 60 to 80 years. This
Furthermore,
when the discount rate is increased, both the effect of the variation in the NPP
happens because the factors that are applied to the different costs have exponential values, so the
operational
lifetime
thefor
total
areand
reduced.
another
observation that can be
LCOE decreases and
rapidly
lowLCOE
capacities
slower Additionally,
when the capacity
increases.
made is that,
for
capacities
higher
than
400
TWh/year,
the
curve
becomes
almost
flat,inwhich
is due to
Furthermore, when the discount rate is increased, both the effect of the variation
the NPP
operational
lifetime and
the cost
totalis
LCOE
arelow
reduced.
Additionally,
another observation
the fact
that the increase
in the
really
compared
to the increase
of capacity.that can be
â
made is that, for capacities higher than 400 TWh/year, the curve becomes almost flat, which is due to
Partial
Strategy
the factRecycling
that the increase
in the cost is really low compared to the increase of capacity.
The results
of theRecycling
LCOE for
the partial recycling strategy are presented in Table 2.
 Partial
Strategy
The results
of2.the
LCOE
for
the partial
recycling
strategy
are presented
in Table 2.
Table
LCOE
for
partial
recycling
in different
scenarios
in $(2010)/MWh.
Table 2. LCOE for partial recycling in different scenarios in $(2010)/MWh.
0% Discount Rate
0% Discount
Rate 80 Years
40 Years
60 Years
40 Years
60 Years
80 Years
25 TWh/year
11.87
10.23
9.39
25 TWh/year
11.87
10.23
9.39
75 TWh/year
7.00
6.21
5.78
75 TWh/year
6.21
5.78
400 TWh/year 7.00 5.87
5.55
5.39
400 TWh/year
5.55
5.39
800 TWh/year 5.87 5.02
4.77
4.65
800 TWh/year
5.02
4.77
4.65
3% Discount Rate
Discount
40 Years 3%60
Years Rate
80 Years
40 Years
60 Years
80 Years
7.12
6.71
6.54
7.12
6.71
6.54
5.62
5.41
5.31
5.62
5.41
5.31
5.16
5.105.31
5.31
5.16
4.64
4.52
4.475.10
4.64
4.52
4.47
FigureFigure
7 represents
these
results
forfordiscount
of0%
0%and
and3%.
3%.
7 represents
these
results
discount rates
rates of
Figure 7. LCOE for partial recycling.
Figure 7. LCOE for partial recycling.
As it can be observed in Figure 7, the tendency of these curves is very similar to the previous
case:
the be
LCOE
decreases
when 7,
thethe
electricity
production
increases,
and the
effecttofrom
NPP case:
As
it can
observed
in Figure
tendency
of these curves
is very
similar
the the
previous
operational
lifetime
is the
as observed
before. increases, and the effect from the NPP operational
the LCOE
decreases
when
thesame
electricity
production
lifetime is the same as observed before.
Energies 2016, 9, 178
9 of 13
Nevertheless, the discount rate has a minor effect on the costs compared to the previous case, and
Energies 2016, 9, 178
9 of 13
a change in the slope of around 400 TWh/year is observed. This is due to the fact that the model used
to calculate
the reprocessing
facility
a piecewise
of the
UOX heavy
production:
Nevertheless,
the discount
ratecosts
has is
a minor
effect function
on the costs
compared
to themetal
previous
case,
forand
capacities
lower
than
400
TWh/year,
the
sub-function
is
linear,
and
for
higher
capacities,
a change in the slope of around 400 TWh/year is observed. This is due to the fact that the modelthe
sub-function
followsthe
a scaling
law. This
way, costs
the change
from a steeper
slope
less pronounced
used to calculate
reprocessing
facility
is a piecewise
function
of to
thea UOX
heavy metalone
in production:
400 TWh/year
a downturn
in the
function.
for entails
capacities
lower than
400LCOE
TWh/year,
the sub-function is linear, and for higher
capacities, the sub-function follows a scaling law. This way, the change from a steeper slope to a less
â pronounced
AFC Strategy
one in 400 TWh/year entails a downturn in the LCOE function.
 The
AFC
Strategy
results
of the LCOE for the AFC strategy are presented in Table 3.
The results of the LCOE for the AFC strategy are presented in Table 3.
Table 3. LCOE for AFC in different scenarios in $(2010)/MWh.
Table 3. LCOE for AFC in different scenarios in $(2010)/MWh.
0% Discount Rate
3% Discount Rate
0% Discount Rate
40 Years
60 Years
80 Years
40 Years
60 Years
80 Years
25 TWh/year
8.77
7.58
6.96
25 TWh/year
8.77
7.58
6.96
75 TWh/year
5.64
4.93
4.55
75 TWh/year
4.934.95
4.55
400 TWh/year 5.64 5.37
4.73
400 TWh/year
4.954.21
4.73
800 TWh/year 5.37 4.56
4.03
800 TWh/year
4.56
4.21
4.03
40 Years
40 Years
6.20
6.20
5.32
5.32
5.32
5.32
4.66
4.66
3% Discount Rate
60 Years
80 Years
60 Years
80 Years
5.80
5.63
5.80
5.63
5.02
4.89
5.035.02
4.91 4.89
4.425.03
4.31 4.91
4.42
4.31
Figure
8 represents
0% and
and 3%.
3%.
Figure
8 representsthese
theseresults
resultsfor
fordiscount
discount rates
rates of
of 0%
Figure 8. LCOE for AFC.
Figure 8. LCOE for AFC.
In Figure 8, it can be observed that the effect of the NPP operational lifetime is higher than in the
In Figure
8, itstudied.
can be This
observed
thatbecause
the effect
the NPP operational
lifetime
higher
than in the
previous
cases
happens
theofinvestment
costs are higher
for is
the
AFC strategy,
previous
cases
studied.
This
happens
because
the
investment
costs
are
higher
for
the
AFC
strategy,
so
so the number of years the NPP is operating has a stronger impact on the cost.
It canofalso
be noted
thatis there
is thehas
same
tendencyimpact
as in the
recycling strategy, which
the number
years
the NPP
operating
a stronger
on partial
the cost.
happens,
as explained
because
of the
scaling
law applied
from
400 TWh/year
It can also
be notedbefore,
that there
is the
same
tendency
as in the
partial
recyclingonwards.
strategy, which
Finally,
in
order
to
visualize
the
non-linearity
observed
when
the
NPP
operational
lifetime is
happens, as explained before, because of the scaling law applied from 400 TWh/year onwards.
increased (the cost increase is not the same from 40 to 60 years as from 60 to 80 years), Table 4 and
Figure 9 present the capital recovery factor.
Energies 2016, 9, 178
10 of 13
Finally, in order to visualize the non-linearity observed when the NPP operational lifetime is
increased (the cost increase is not the same from 40 to 60 years as from 60 to 80 years), Table 4 and
Figure 9 present the capital recovery factor.
Energies 2016, 9, 178
10 of 13
Table 4. Capital recovery factor for different nuclear power plant (NPP) operational lifetimes.
Table 4. Capital recovery factor for different nuclear power plant (NPP) operational lifetimes.
40 years
40 years
60 years
60 years
80 years
80 years
0%Discount
Discount Rate
0%
Rate
0.0250
0.0250
0.0167
0.0167
0.0125
0.0125
3%3%
Discount
RateRate
Discount
0.0433
0.0433
0.0361
0.0361
0.0331
0.0331
Figure 9. Capital recovery factor.
Figure 9. Capital recovery factor.
As it can be observed, the increase in the capital recovery factor is lower from 60 to 80 years than
be observed,
the increase
inthe
theLCOE
capitalhas
recovery
factor
is lower from 60 to 80 years than
fromAs
40 ittocan
60 years,
which explains
why
a similar
behavior.
from 40 to 60 years, which explains why the LCOE has a similar behavior.
3.2. Comparison of Different Strategies
3.2. Comparison of Different Strategies
After carrying out an analysis to compare the effect of the NPP operational lifetime on the LCOE,
After carrying out an analysis to compare the effect of the NPP operational lifetime on the LCOE,
a comparison amongst the different back-end strategies is realized in order to be able to comprehend
a comparison amongst the different back-end strategies is realized in order to be able to comprehend
the variations in the costs when the electricity production changes.
the variations in the costs when the electricity production changes.
Due to the similarities in the tendencies of the curves within the same strategy for different
Due to the similarities in the tendencies of the curves within the same strategy for different
lifetime scenarios, this analysis is realized only for the 60-year NPP lifetime case.
lifetime scenarios, this analysis is realized only for the 60-year NPP lifetime case.
The results of the LCOE for the different strategies are presented below in Table 5 for discount
The results of the LCOE for the different strategies are presented below in Table 5 for discount
rates of 0% and 3%.
rates of 0% and 3%.
Table5.5. LCOE
LCOE for
for different
differentback-end
back-endstrategies
strategiesin
in$(2010)/MWh.
$(2010)/MWh.
Table
0% Discount Rate
Electricity
0% Discount Rate
Electricity
Production
OFC
Partial Recycling
Production
Partial
Recycling
25 TWh/year
10.65 OFC
10.23
25 TWh/year
10.23
75 TWh/year
6.86 10.65
6.21
75
TWh/year
6.86
6.21
400 TWh/year
5.33
5.55
400 TWh/year
5.33
5.55
800 TWh/year
5.15 5.15
4.77
800 TWh/year
4.77
AFC
AFC
7.58 OFC
7.58
4.93
4.93
4.95
4.95
4.21
4.21
These results are also presented in Figures 10 and 11.
3% Discount Rate
OFC
Partial
AFC
Partial 6.71
AFC
6.70
5.80
6.71
5.80
5.25
5.41
5.02
5.02
4.665.41
5.16
5.03
5.16
5.03
4.594.52
4.52
4.42
4.42
3% Discount Rate
6.70
5.25
4.66
4.59
Energies 2016, 9, 178
11 of 13
These results are also presented in Figures 10 and 11.
Energies 2016, 9, 178
Energies 2016, 9, 178
11 of 13
11 of 13
Figure 10. LCOE for different backend strategies: 0% discount rate.
Figure 10. LCOE for different backend strategies: 0% discount rate.
Figure 10. LCOE for different backend strategies: 0% discount rate.
Figure 11. LCOE for different back-end strategies: 3% discount rate.
Figure 11. LCOE for different back-end strategies: 3% discount rate.
Figure 11. LCOE for different back-end strategies: 3% discount rate.
Figures 10 and 11 show that the most profitable strategy is the AFC. This is due to the fact that,
Figures
andFRs
11 show
that integral
the mostreprocessing
profitable strategy
the AFC.
This isthey
dueare
to the
fact that,
even though10the
and the
plant is
costs
are high,
thoroughly
Figures
10the
andFRs
11 show
that
the
most profitable
strategy
is the
AFC.
This
is due
to the
fact
that, even
even
though
and
the
integral
reprocessing
plant
costs
are
high,
they
are
thoroughly
compensated by the savings in the front-end cost, because of the reduction in the natural
though
the FRsby
andthe
the savings
integral reprocessing
plant costs
high, they
by
compensated
in the front-end
cost,are
because
of are
the thoroughly
reduction compensated
in the natural
uranium requirements.
the
savings
in
the
front-end
cost,
because
of
the
reduction
in
the
natural
uranium
requirements.
uranium
This requirements.
result is clearly observed in Figure 10. However, in Figure 11, with a discount rate of 3%,
This
result is
is clearly
clearlyobserved
observed inFigure
Figure10.
10.However,
However,
Figure
withdiscount
a discount
of
This
in in
Figure
11, 11,
with
rate rate
of
when theresult
electricity
production isin400
TWh/year,
the LCOE
is higher
in athe
AFC than
in 3%,
the
3%,
when
electricity
production
is 400
TWh/year,
LCOE
higherininthe
theAFC
AFC than
than in
in the
when
the the
electricity
production
is 400
TWh/year,
thethe
LCOE
is is
higher
the
OFC strategy.
OFC
strategy.
OFC Concerning
strategy. the partial recycling strategy, the results are more variable. When a discount rate of
thecosts
partial
strategy,
results
more
When aexcept
discount
ratethe
of
0% isConcerning
applied, the
forrecycling
this strategy
are the
lower
thanarefor
the variable.
OFC strategy,
when
0%
is applied,
the costs
for TWh/year.
this strategy
are lower
the OFC
except
when
the
electricity
production
is 400
However,
for than
a 3%for
discount
rate,strategy,
the LCOE
for the
partial
electricity
production
is
400
TWh/year.
However,
for
a
3%
discount
rate,
the
LCOE
for
the
partial
recycling strategy is higher than the OFC LCOE in every case. This is due to the fact that, for the OFC
recycling
strategy
is higher
than the
OFC LCOE
in the
every
case.recycling.
This is due to the fact that, for the OFC
strategy, the
discount
rate effect
is higher
than for
partial
strategy, the discount rate effect is higher than for the partial recycling.
Energies 2016, 9, 178
12 of 13
Concerning the partial recycling strategy, the results are more variable. When a discount rate of
0% is applied, the costs for this strategy are lower than for the OFC strategy, except when the electricity
production is 400 TWh/year. However, for a 3% discount rate, the LCOE for the partial recycling
strategy is higher than the OFC LCOE in every case. This is due to the fact that, for the OFC strategy,
the discount rate effect is higher than for the partial recycling.
4. Conclusions
‚
‚
‚
‚
‚
As seen in the analysis of the results, the capacity has a great influence on the costs for the different
back-end strategies.
According to the LCOE results for the strategies analyzed, the first conclusion can be obtained
regarding the capacity of nuclear energy production in different countries. The variation in the
LCOE between the first and the second points analyzed (25 and 75 TWh per year) implies that
a greater decrease in costs is experienced in countries with a small nuclear energy production
compared to those that have a higher production, whose costs have a much less pronounced fall,
as the electrical production rises.
Nowadays, Spain has a production of 57 TWh per year, which implies that costs are positioned in
a highly decreasing slope. Because of this, an increase in the nuclear energy production should
lead to considerable cost savings.
Currently, the most realistic scenario is to consider a discount rate of 0%. From the different
calculations realized for various NPP operational lifetimes (40, 60 and 80 years), a conclusion that
can be drawn is that the decrease in the LCOE extending the NPP operational lifetime from 40 to
60 years is more significant than from 60 to 80 years.
For the Spanish case, the differences between the open cycle and the closed cycle costs are less
than an 8%, which is not relevant enough to make a decision based only on the economic aspects.
This is the reason why the fuel cycle cost, including the front-end (obtaining fresh nuclear fuel) and
the back-end (SNF management), represent a small fraction of the nuclear electricity generation
cost (about 10% to 16%), the back-end being the less significant one (about 5%).
Acknowledgments: The authors would like to thank the Rafael Mariño Chair of New Energy Technologies of
Universidad Pontificia Comillas, which is the entity that sustains the research activity of the group.
Author Contributions: José Manuel Vidal-Bernardez and Marta Niño-Serrano have analyzed and developed the
DGR cost and closed cycle cost tendency charts for the Introduction. Paula Ocaña-Pastor, Paula Martín-Cañas
and Mathilde Estadieu have gathered information and data for the state of the art (Introduction).
Borja Belda-Sánchez and Natalia Cortes-Sanz have collaborated in the mathematical formulation of the paper.
José Ignacio Linares-Hurtado has developed the methodology and calculations. Laura Rodriguez-Penalonga and
Beatriz Yolanda Moratilla Soria have carried out the calculations, performed the analysis of the results and drawn
the conclusions, as well as carried out the global coordination of the paper.
Conflicts of Interest: The authors declare no conflict of interest.
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