Int. J. Global Energy Issues, Vol. 35, No. 1, 2011
The costs of power: plutonium and the economics of
India’s prototype fast breeder reactor
J.Y. Suchitra
Centre for Public Policy, Faculty Block A, P-101,
Indian Institute of Management,
Bangalore, Bannerghatta Road, Bangalore 560076, India
E-mail: [email protected]
M.V. Ramana*
Programme on Science and Global Security and
Nuclear Futures Laboratory,
Woodrow Wilson School of Public and International Affairs,
Princeton University,
Princeton, NJ 08540, USA
Fax: +1-609-258-3661
E-mail: [email protected]
*Corresponding author
Abstract: The Indian Department of Atomic Energy plans to expand nuclear
power in the country by constructing a large fleet of plutonium fuelled breeder
reactors, seen as necessary because of perceived shortage of uranium resources.
We analyse the economics of generating electricity at the first such reactor in
India, the prototype fast breeder reactor. We find that such electricity will be
80% more expensive than the corresponding cost at pressurised heavy water
reactors with our base case assumptions. The economics of breeder electricity
is primarily determined by the cost of reprocessing spent fuel to produce
plutonium and fabricating it into fuel. Breeder reactors become more
competitive as the cost of fuelling heavy water reactors with uranium goes up,
but only very slowly. The crossover cost is $1,375 per kilogram of uranium for
our base case. At such a high cost, poorer quality ores can be economically
mined. We perform an extensive sensitivity analysis to show that the broad
conclusions hold even under assumptions that are far more favourable to
breeder economics.
Keywords: breeder reactors; prototype fast breeder reactor; PFBR; plutonium
breeder economics; electricity costs; India energy; Department of Atomic
Energy; DAE; DAE breeder programme; uranium availability; reprocessing
costs; India nuclear power.
Reference to this paper should be made as follows: Suchitra, J.Y. and
Ramana, M.V. (2011) ‘The costs of power: plutonium and the economics of
India’s prototype fast breeder reactor’, Int. J. Global Energy Issues, Vol. 35,
No. 1, pp.1–23.
Copyright © 2011 Inderscience Enterprises Ltd.
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J.Y. Suchitra and M.V. Ramana
Biographical notes: J.Y. Suchitra received her Master’s in Economics from
the University of Hyderabad. She is currently with the Centre for Public Policy
at the Indian Institute of Management, Bangalore. She has been working on the
economics of nuclear energy for the past five years, and has published
academic papers and popular articles in this area.
M.V. Ramana is an Associate Research Scholar at the Woodrow Wilson School
of Public and International Affairs, Princeton University. He received his PhD
in Physics from the Boston University and is the author of a forthcoming book
on the Indian nuclear programme.
1
Introduction
India plans a major expansion of nuclear energy over the next few decades.
Currently installed nuclear capacity in the country is 4,120 MW (megawatts),1 which
constitutes 3% of all power generation. The Indian Department of Atomic Energy (DAE)
envisions nuclear power growing to 275,000 MW by 2052 (Srinivasan et al., 2005).
There have been even higher projections recently. Much of this planned expansion is
based on fast breeder reactors.2 For example, out of the 275,000 MW, breeders constitute
262,500 MW (Grover and Chandra, 2006). The DAE has long been interested in breeder
reactors.
This interest in breeders is not exceptional. Since the 1950s, several countries around
the world spent large quantities of money on research and development related to
breeders; about half a dozen countries constructed pilot scale or demonstration breeder
reactors (IPFM, 2010). However, over the decades, most have suspended their
programmes. Even France, the country that has actually gone on from the demonstration
level to building and operating the commercial scale superphénix reactor, has not planned
for construction of any future breeders. In part, the disenchantment with breeders is due
to economic reasons. Several studies have shown that electricity from breeder reactors is
expensive in comparison to that from light water reactors that dominate the world’s
nuclear capacity (Bunn et al., 2005; Chow, 1995; Cochran, 1974; Feiveson et al., 1979).
In contrast, the DAE claims that electricity from breeder reactors is comparable in
cost to that from a pressurised heavy water reactor (PHWR), the reactor type that
accounts for the largest share of nuclear generation in the country (Bhoje, 2003; Paranjpe,
1991). The DAE, however, has not demonstrated this assessment with rigorous economic
analysis. To address this lacuna, we calculate the cost of generating electricity at the
500 MW prototype fast breeder reactor (PFBR) that the DAE is currently constructing.
The DAE argues that breeders are important for India because the country has limited
uranium reserves, insufficient for a large nuclear programme. To test the argument about
uranium scarcity, we perform our cost comparison as a function of the cost of fuelling the
PHWR with uranium.
This paper is structured as follows. We start with a historical overview followed by
a description of the methodology used for economic evaluation. The next section
lays out the cost and other assumptions. The results of our analysis and a discussion of
their sensitivity to various parameters constitute the subsequent two sections, before
we go on to the conclusions.
The costs of power
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3
Historical background
Breeder reactors in India were originally conceived of as part of a three phase nuclear
programme proposed in the 1950s as a way to expand nuclear power despite the
relatively small amounts of uranium ore, and those too of very poor quality, discovered in
the country (Bhabha and Prasad, 1958). The first phase involves the use of uranium fuel
in PHWRs, followed by reprocessing the spent fuel to extract plutonium. In the second
phase, the accumulated plutonium stockpile is used in the nuclear cores of fast breeder
reactors. These nuclear cores could be surrounded by a blanket of either depleted uranium
or natural uranium, to produce more plutonium; if the blanket were to contain thorium, it
would produce Uranium-233. So as to ensure that there is adequate plutonium to fuel
these second phase breeder reactors, a sufficiently large fleet of such breeder reactors
with uranium blankets would have to be commissioned before thorium blankets are
introduced. The third phase involves breeder reactors using Uranium-233 in their cores
and thorium in their blankets.
The DAE started planning for the PFBR in 1983 when it requested the government
for budgetary support (Bidwai, 1983). The first expenditures on the PFBR started in
1987–1988 (DAE, 1991). In 1990, it was reported that the government had “recently
approved the reactor’s preliminary design and… awarded construction permits”; at that
time, the reactor was supposed to come on line by 2000 (Hibbs, 1990). The reactor is
now expected to be commissioned in 2012 (Subramanian, 2010). A public sector
company called BHAVINI has been set up to construct and operate the PFBR and future
breeder reactors.
The PFBR is to be the first of many breeder reactors that the DAE envisions building.
Its ‘primary objective’ is said to be “to demonstrate techno-economic viability of fast
breeder reactors on an industrial scale” (Chetal et al., 2006). The DAE claims that the
“cost of power from PFBR will be comparable to that from…PHWRs” (Bhoje, 2003).
This claim should be evaluated rigorously and transparently before large scale
construction of breeder reactors begins.
3
Methodology
We use the standard discounted cash flow (DCF) methodology to calculate the life cycle
cost of producing electricity at the PFBR and a PHWR (Brealey and Myers, 2000). In this
approach, all costs are discounted to some arbitrary but fixed reference date; the total cost
is the sum of the present values (PV) or future values (FV) of costs discounted to this
date. In addition, the benefits, i.e., the electricity generated in different years, are also
discounted to the same reference date.
Our calculations are all performed in 2004 Rupees, the year when construction of the
PFBR started. To convert costs from one year to another, we use the ratio of GDP
deflators for the respective years as specified by the World Bank. For future costs, we
follow the Indian Nuclear Power Corporation and use a 5% rate of escalation (Thakur and
Chaurasia, 2005). We convert all Rupee figures to US $ figures using the conversion rate
of $1 = Rs. 44, which was the prevalent rate in 2004.
India’s Central Electricity Regulatory Commission has recommended a nominal
discount rate of 10.6% for costing power (CERC, 2006). This translates to a real discount
rate of about 5%. However, nuclear power plants are financially more risky
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J.Y. Suchitra and M.V. Ramana
(Farber, 1991). This is primarily because these have higher fixed costs as compared to,
say, coal plants, which have higher operating costs. For plants with higher fixed costs, the
systematic risk is higher (Hamada, 1972; Lev, 1974; Mandlekar and Rhee, 1984). This
necessitates the use of a higher discount rate.3 We therefore, use a real discount
rate of 6%.4
Our analysis is based on cost figures from Government of India and DAE budget
documents as far as possible. Unfortunately, many cost elements were not publicly
available. An attempt to acquire some of the information using India’s Right to
Information Act succeeded in obtaining annual construction cost estimates and the
allocations for waste management, but BHAVINI denied all fuel chain costs, including
that of fuel fabrication and reprocessing (Suchitra and Ramana, 2007).5 Therefore, we
have extrapolated from international cost figures or made our own calculations based on
other Indian data.
4
Cost components and other assumptions
We consider the same set of cost components for both the PFBR and a PHWR, namely
construction of the reactor (capital cost), fuelling, operations and maintenance,
decommissioning, refurbishment, working capital, and management of low level
radioactive wastes.6 For the PHWR, the fuelling cost includes those of uranium and fuel
fabrication. Also included are the costs of the initial heavy water inventory and of
replacing the heavy water that is lost during routine operations. For the PFBR, the
fuelling cost includes that of producing plutonium through reprocessing and fabricating it
into MOX fuel. We assume that the cost of uranium for the MOX fuel and the blankets is
free. This is because there are no strong isotopic requirements for the PFBR fuel, and
therefore depleted uranium, which is available in copious quantities from reprocessing as
well as uranium enrichment, could be used for this purpose (Ramana and Suchitra, 2007).
The plutonium for the initial core as well as for the first few reloads has to come from
reprocessing PHWR spent fuel at the DAE’s Kalpakkam Reprocessing Plant (KARP)
(Hibbs, 2003). Because the PFBR has a relatively low breeding ratio, it will not be
producing excess plutonium in significant quantities.7 Therefore, future breeder reactors
with the same design will also have to adopt the same practice of using plutonium from
reprocessing PHWR spent fuel for the initial cores and the first few reloads, at least for a
couple of decades. Once the breeder reactor is shut down, the value of the plutonium
recovered is accounted for at the same cost at which it is assumed to be obtained from
KARP. Similarly, the heavy water for the initial loading of the PHWR is assumed to be
obtained from DAE and returned when the reactor is shut down.
4.1 Prototype fast breeder reactor
4.1.1 Construction cost
The DAE has estimated the total construction cost of the PFBR to be Rs. 34.92 billion,
which translates to Rs. 28.41 billion in 2004 Rupees.8 This converts to $645.75 million
(in 2004 dollars). As a unit cost, this is $1292/kW. This is roughly half of corresponding
estimates of breeder reactor construction costs elsewhere; the Nuclear Energy Agency
The costs of power
5
(NEA) gives a range of $2,000–2,800/kW (in 2004 dollars) for MOX fuelled fast reactors
[NEA, (2002), p.216].
When compared to these estimates, breeder reactors already constructed have been
more expensive. Construction costs for the French phénix reactor totalled FF 800 million
(1974 French francs), which translates to $800 million in 2004 dollars or $3,200/kW
(IPFM, 2010). The 1,240 MW Superphénix was far more expensive with an initial
investment of FF 28 billion (1985 figure, which translates to $4.9 billion in 2004 dollars)
[NUKEM, (1997), p.15]. The 300 MW Kalkar reactor in Germany cost DM 7 billion
(1985 Deutsche Marks), which translates to $3.6 billion in 2004 dollars (Neffe, 1985).
The projected cost of the PFBR falls well below both the NEA’s estimates and actual
costs. There are also historical and technical reasons to expect that the PFBR’s cost will
turn out to be higher than the DAE’s estimate. The initial cost estimates of all reactors
constructed in India have been much lower than the final cost figures (DAE, 1996, 2002).
This may be the case with the PFBR too; reports suggest that construction costs have
been higher than anticipated because of rising prices of steel, cement, and other raw
materials (TOI, 2009).9
Technically, breeder reactors can be expected to be more expensive than PHWRs for
two reasons. First, the use of molten sodium as coolant brings with it several operational
requirements, such as heating systems to keep the sodium molten at all times, and
safety-related requirements, such as extensive fire fighting equipment (Farmer, 1984).
Second, accidents at breeder reactors could lead to the release of large quantities of
explosive energies (Bethe and Tate, 1956). Therefore, they have to include extensive
safety features which are a significant component of the total capital cost of a breeder
reactor.
Despite these many reasons to expect cost escalation, we use the DAE’s estimate for
PFBR’s cost and, as we discuss later on, for the PHWR’s cost as well.
4.1.2 Plutonium-related costs
In economic terms, the primary material requirement for the PFBR is plutonium. The
PFBR design requires an initial inventory of 1.9 tons of plutonium in its core
(IGCAR, 2003).10 It has been estimated that at 75% capacity factor (CF),11 the PFBR
requires 1012 kg of plutonium every year for refuelling (Glaser and Ramana, 2007).
Taking into account losses at the fuel fabrication stage, usually estimated to be 1%
[Benedict et al., (1981), p.150], the total plutonium requirement is 1,022 kg per year.
This plutonium is converted to MOX (mixed oxide) fuel by mixing with uranium.
Initially, the PFBR requires 6,549 kg of MOX fuel for the core of the reactor and the
axial blanket; the radial blankets require an additional 2,622 kg of uranium fuel (Glaser
and Ramana, 2007). The fuel fabrication is being done at the Advanced Fuel fabrication
facility at Tarapur (Balu et al., 1998). Later on, the fabrication will be done at the fast
reactor fuel cycle facility at Kalpakkam once it is constructed (AERB, 2006). No cost
estimates are available for either of these. Therefore, we follow the NEA and assume that
the cost of fabricating driver fuel is $1,400/kgHM and the cost of fabricating (radial)
blanket fuel is $500/kgHM (both in 2000 dollars), or $1,512/kgHM and $540/kgHM
(in 2004 dollars) (NEA, 2002). In our sensitivity analysis, we also consider lower values.
As mentioned, the plutonium for the initial core as well as for the first few reloads has
to come from reprocessing PHWR spent fuel at KARP. In order for it to be ready in time
to fabricate the core, this plutonium would have been required in 2007, three years ahead
6
J.Y. Suchitra and M.V. Ramana
of starting reactor operations (Hibbs, 1997a).12 The lifecycle cost of reprocessing at
KARP has been estimated at about Rs. 29,010/kgHM at a 6% discount rate (Ramana and
Suchitra, 2007).13 Assuming losses of 1% of the plutonium in the spent fuel, this
translates to a plutonium cost of Rs. 7,814/g or $178/g. This assumption may be
optimistic and experience at DAE run reprocessing plants appears to indicate a higher
rate of losses, closer to 3% [Tongia and Arunachalam, (1998), p.552]. Subsequently, the
plutonium for the PFBR is obtained from reprocessing its own spent fuel. Because of the
higher plutonium content of the PFBR spent fuel, the cost of such plutonium would be
lower; we estimate it to be $43/g (see Appendix 1).
KARP does not have adequate reprocessing capacity to produce enough plutonium in
any given year to fuel the PFBR.14 Therefore, much of the plutonium that is used in the
PFBR’s initial loading would have been separated several years before it is fabricated
into MOX fuel. As the plutonium ages, one of its isotopes, Plutonium-241, decays into
Americium-241, another radioactive material that absorbs neutrons and lowers the
amount of energy produced by the reactor. This would have to be chemically separated
before the plutonium is fabricated into MOX. The americium removal cost would have to
be incurred only in the case of plutonium coming from KARP.15 This has been estimated
to cost ‘$18 per gram of plutonium’ in 1987 Dollars, which translates to $26.75 per gram
in 2004 dollars [NEA, (1989), p.64]. Table 1 summarises the quantities of materials used
to fuel the reactor and their costs.
Table 1
Quantities and costs related to PFBR fuel chain
Plutonium required for initial core (tons)
1.9
Assumed loss at fuel fabrication plant
1%
Amount of plutonium required for core per year (mg/kWh)
0.35
Fabrication requirement for core + axial fuel (mg/kWh)
2.24
Fabrication requirement for radial blanket fuel (mg/kWh)
0.89
Cost of plutonium from KARP ($/g) (in 2004 dollars)
178
Cost of plutonium from PFBR spent fuel ($/g) (in 2004 dollars)
43
Cost of fabricating fuel for core ($/kgHM) (in 2004 dollars)
Cost of fabricating fuel for blanket ($/kgHM) (in 2004 dollars)
Cost of removing americium from KARP plutonium ($/gPu) (in 2004 dollars)
1,512
540
26.75
According to the PFBR design, the reactor has to be refuelled after ‘180 effective full
power days’ of operation (Sodhi et al., 1995). For a CF of 75%, this translates to about
eight months. As per design, the spent fuel is stored within the reactor for a further eight
months. We assume that it is stored under water for an additional 16 months outside the
reactor to give a total storage time of two years.16 During this period, the spent fuel
becomes cooler and some of the short lived radioactive substances decay. We assume that
reprocessing, fuel fabrication, and the necessary transport operations together take an
additional year. In all, the total time between when the fuel is removed from the reactor
core and when it reappears as a fresh fuel rod is three years. This means that for at least
the first three years of operation, PFBR will require plutonium from KARP. This is in
addition to the initial loading of fuel.
The costs of power
7
However, if the facility to reprocess the spent fuel from the PFBR is not ready by
2015, then plutonium for further loadings would also have to be obtained from KARP.
In September 2007, the chairman of the Atomic Energy Commission announced that a
reprocessing plant to deal with the PFBR spent fuel has been planned and that its
construction was to commence in 2008 (Kakodkar, 2007). As of June 2008, no budgetary
allocations seem to have been made (MoSPI, 2008). Even in 2010, an article by three
senior officials closely involved with the breeder programme in the trade journal Nuclear
Engineering International only says “a dedicated commercial scale reprocessing plant is
proposed to be constructed”. Given the complicated nature of reprocessing plants,
the DAE’s very limited experience with reprocessing fast breeder spent fuel,17
and the experience of persistent delays in constructing reprocessing plants in India
and elsewhere,18 it is quite likely that reprocessing of PFBR spent fuel will not
commence in 2015.
4.2 Pressurised heavy water reactor
The bulk of operating reactors in India are PHWRs, of either 220 MW or 540 MW
capacity. But, “future PHWRs… are planned to be only of 700 MW unit size” [DAE,
(2005), p.26]. Four such 700 MW reactors are at an advanced state of planning and
early procurement of equipment has started [DAE, (2008), pp.19–21]. We assume that
construction of the first of such reactors is completed by 2015.
We use the Indian Nuclear Power Corporation’s estimates of Rs. 52 million/MW in
2005 prices for 700 MW PHWRs (Thakur and Chaurasia, 2005).19 Thus, a twin
power station with two 700 MW PHWRs will cost Rs. 69.88 billion in 2004 Rs
($1.58 billion). The corresponding unit cost is Rs. 49,914/kW or $1,134/kW (2004
figures). This is comparable to though slightly lower than estimated costs for the PHWRs
that were completed after 2005 or are under construction; these have unit costs ranging
from $1,154/kW to $1,204/kW [Bohra and Sharma, (2006), Table 5, p.849]. When
compared to the lowest of these, the decreased cost for the 2 × 700 MW power station is
less than 2%. We emphasise that the cost data and assumptions are those of the DAE.
Assuming the distribution of costs across the years used by Thakur and Chaurasia (2005),
we estimate a total construction cost of Rs. 103.93 billion (mixed year figure) for a plant
which is constructed by 2015.
In addition, the costs of the initial loading of heavy water and uranium, which will be
incurred a year before commissioning, have to be included. As our base case, we assume
that the uranium is purchased at a cost of $200/kg and fabricating it into fuel costs
$200/kgHM.20 This is comparable to reported costs of fabricated uranium fuel in India
(Subramanian, 2002).
The initial requirement for each 1,400 MW station is about 194 tons of uranium
metal (Grover and Chandra, 2006). As with MOX fuel fabrication, we assume 1% losses
at the fuel fabrication stage. In all, the initial loading costs Rs. 3.44 billion or $78.2
million (in 2004 figures). Once the reactor commences operation, uranium will be
consumed at the rate of 20.7 mg/kWh, which corresponds to an average burnup of 7,000
MWtd/tU (megawatt thermal day per ton of Uranium) (Changrani et al., 1998; Hibbs,
1997b).21
The heavy water cost has been estimated to be Rs. 26,466 or $601 per kilogram
(in 2004 figures) (Ramana, 2007). The initial loading of heavy water is 850 tons
8
J.Y. Suchitra and M.V. Ramana
[Bhardwaj, (2006), p.862], which would cost Rs. 22.49 billion or $511 million. Some of
the heavy water is also lost every year due to evaporation and leaks. In 220 MW PHWRs,
this amounts to 7 tons/year [Kati, (2003), p.39]. We scale this by the ratio of power
outputs to obtain the corresponding figure of 44.5 tons/y for a 1,400 MW plant.22 All fuel
quantities and costs are shown in Table 2.
Table 2
Quantities and costs related to 1,400 MW of PHWR capacity
Uranium required for initial core (tons)
194
Uranium cost ($/kg)
200
Uranium fabrication cost ($/kgHM)
200
Heavy water required for initial core (tons)
850
Heavy water cost ($/kg)
601
Heavy water losses (tons/y)
44.5
Uranium fuel fabrication losses
1%
Uranium fuel requirement (mg/kWh)
20.7
4.3 Other cost elements
Some amount of power generated by the reactors is consumed on the site itself. This
auxiliary consumption is assumed to be 10% for both reactors. We also assume that both
the PFBR and the PHWR store a year’s worth of fabricated fuel and heavy water to
account for potential supply disruptions, which is equivalent to the working capital
component included in standard electricity cost calculations. This will be returned, and
the lifecycle cost adjusted accordingly, at the end of the lifetime of the reactor. Both
reactors are expected to undergo refurbishments some time during their operating life. In
line with Thakur and Chaurasia (2005), we assume that this will cost 5% of the capital
cost and is incurred after 15 years of operation.
4.3.1 Annual non-fuel costs
Every year, there will be costs incurred towards operations and maintenance (O&M) of
the reactor and waste management at the reactor site itself.23 BHAVINI estimates
that the annual O&M cost for the PFBR will be Rs. 690 million ($15.7 million),
which translates to 2% of the capital cost; it also assumes that a Rs. 0.05/kWh
(or 0.01 mills/kWh) charge will suffice for waste management. This is likely to be an
underestimate. Because of the use of liquid sodium, actual O&M costs for breeder
reactors are typically much higher. For example, the O&M costs for the French
superphénix reactor were FF 1.7 billion per year (1994 figure), which translates to about
$320/kW (in 2004 dollars), which is about 8% of the capital cost (IPFM, 2010).
Nevertheless, in line with our methodology, we adopt the official figure of 2%. For the
PHWR, we assume the same fraction of the capital cost (2%) for O&M costs, which
amounts to Rs. 1,397.6 million or $31.8 million (in 2004 figures), and a waste
management charge of Rs. 0.05/kWh.
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9
4.3.2 Decommissioning
In line with estimates made by the World Nuclear Association, we assume that
decommissioning would cost 10% of the initial capital cost (WNA, 2008). This amount is
assumed to be spent in the ratios 40:20:40 at the end of the reactor operations, 20 years,
and 40 years after end of reactor operations respectively. Decommissioning might be
much more expensive. For example, decommissioning the 60 MWt (megawatt thermal)
demonstration fast reactor (DFR) that operated from the late 1950s to 1977 in the UK has
been estimated to cost £760 million (1.4 billion in 2004 Dollars) (UKAEA, 2007). This is
nearly 20 times the decommissioning cost assumed for the PFBR, a reactor that is about
20 times larger in power capacity.
5
Results
Based on the methodology described above and the cost figures listed in the earlier
section, the key cost components have been calculated and are presented in Table 3.
Table 3
Base case comparison of electricity generation cost
PFBR
PHWR
646
1,588
6
6
Capital cost (present value) ($million 2004)
504
987
Capacity factors (percent)
80
80
Lifetime plutonium or uranium cost (present value) ($million 2004)
1,480
697
Total lifecycle cost ($million 2004 $)
2,212
2,550
Levelised cost (Rs/kWh)
2.77
1.54
Levelised cost (cents/kWh)
6.30
3.49
Capital cost (overnight construction cost) ($million 2004)
Real discount rate (percent)
Percentage difference (PFBR-PHWR)
80%
Even in our ‘base case’, electricity from the PFBR is 80% more expensive than the
corresponding cost from PHWR. The main cost component of the PHWR is the capital
cost of the reactor, which constitutes 39% of the total lifecycle cost. The corresponding
figure for the PFBR is 23%. The main component of the total lifecycle cost at the PFBR
turns out to be that of the plutonium used in the reactor (67%). In comparison, the
corresponding uranium cost for the PHWR is only 27%.24 This is primarily because of
the much higher costs associated with the production and fabrication of plutonium.25
The higher costs relating to plutonium reflect two factors. First, there are substantial
costs associated with simply extracting the metal from the spent fuel, because
reprocessing plants are very capital intensive. Second, the fabrications of MOX fuel costs
much more than the fabrication of uranium fuel. This in turn is related to two
characteristics, one of plutonium itself and one of the fuel for fast breeder reactors.
Plutonium being more radioactive and toxic than uranium, fabricating it into fuel requires
special facilities so that all possible contact with the material is avoided [Farmer, (1983),
p.36]. Fuels for fast breeder reactors produce much more heat per unit volume which has
10
J.Y. Suchitra and M.V. Ramana
to be efficiently conducted away. Therefore, they have to be far thinner and structured
more intricately than uranium fuel rods for PHWRs.26
5.1 Uranium cost
Like breeder advocates elsewhere, the DAE’s argument in favour of the breeder
programme in India is that uranium supply is limited. The current estimates are of about
60,000 tons of uranium (Kakodkar, 2006). While widely articulated, this formulation is
misleading. India’s uranium resource base cannot be represented by a single number. The
resource base increases with continued exploration for new deposits as well as
technological improvements in uranium extraction.26 In addition, as with any other
mineral, at higher prices it becomes economic to mine lower grade and less accessible
ores. In other words, if the PHWR operator is willing to bear a higher cost for fuelling the
reactor, the amount of uranium available will be much larger.
We therefore address the DAE’s argument about limited uranium resources by
considering a range of uranium costs in our comparison of electricity generation costs at
breeder reactors and heavy water reactors (see Figure 1). The difference in the generation
costs decreases because of the increased cost of fuelling the PHWR. Only when the
uranium cost goes up to $1,375/kg, nearly seven times the base case of $200/kg, does the
difference become zero.
Figure 1
Sensitivity to uranium cost (see online version for colours)
100%
Percentage
80%
60%
Difference in
levelised costs of
generation
40%
20%
0%
0
200
400
600
800
1000
1200
-20%
1400
1600
Fraction of
uranium cost in
PHWR
generation cost
Uranium cost ($/kg)
Figure 1 also shows the fraction that the cost of uranium (including that of fuel
fabrication) contributes to the PHWR generation cost. While the plutonium-related costs
constitute about 67% of the PFBR generation cost in the base case, uranium-related costs
exceed 50% of the PHWR generation cost only at around $800/kg. In other words, one
can pay a lot more for uranium without affecting the price of electricity from PHWRs
significantly.
As explained in Appendix 2, when the uranium cost goes up to $1,375/kg, the
availability of uranium increases by a factor of at least about 60 and possibly about
120. It is likely that even these factors underestimate the actual availability in the longer
term because of technological improvements. In any case, lack of uranium reserves is
unlikely to be a limiting factor for the expansion of nuclear power based on PHWRs for
decades.27
The costs of power
11
Around 2005–2008, there were numerous reports that stated that the Nuclear Power
Corporation was facing a severe shortage of uranium and even the existing PHWRs (with
a capacity of approximately 4,000 MW) could not be fuelled adequately (for example
Subramanian, 2006). This does not contradict our estimates of increased uranium
availability. The shortage was cause not by a lack of uranium deposits under the ground
but due to a mismatch between mining capacity and reactor requirements.
5.2 Sensitivity analysis
There are a number of variables that affect the cost of electricity from the PFBR. The
most important of these relate to the performance of the reactor, the capital cost, and the
costs related to the recovery of plutonium. In our base case, we have used values that are
favourable to the economics of the PFBR.
5.2.1 Capacity factor
Breeder reactors across the world have been plagued with small accidents and other
problems, in part due to the use of liquid sodium as coolant.28 It is not surprising,
therefore, that they have had relatively low lifetime CFs (Table 4). Of particular
importance is the low capacity factor of the superphenix, which was supposed to be
France’s first commercial breeder reactor. In India, the fast breeder test reactor (FBTR)
has operated for only 36,000 hours over the first 20 years of its life, or 75 days a year,
implying that it functioned for only about 20% of the time [DAE, (2006), p.16].
Table 4
Performance of breeder reactors
Date of grid connection
Cumulative load factor (percent)
Phenix
PFR
BN-600
Superphenix
13-Dec.-73
10-Jan.-75
08-Apr.-80
14-Jan.-86
41.34
23.87
73.48
6.6
Source: Power Reactor Information System Database, International Atomic
Energy Agency, Downloaded 22 March 2009
If the PFBR experience were to be similar, a CF of 50% or less might be more plausible.
At 50%, the levelised cost of generation at the PFBR would be Rs. 3.67 per unit
(8.35 cents per kWh), 139% more expensive than PHWRs (assuming that the PHWR
operates at the same 80% CF). The uranium crossover cost for this case is $2,235/kg.
5.2.2 Capital cost
The next parameter that we vary is the capital cost of the PFBR, since there are good
reasons for it to escalate. We assume that this is on account of delayed construction, and
that the PFBR starts functioning two years later than the projected schedule. An
additional 10% of the total cost is assumed to be incurred in each of those years.
Therefore, the overnight construction cost increases from $1,292/kW to $1,503/kW.
Assuming all the other costs are the same as our base case, the levelised cost of
generation at the PFBR would be Rs. 2.88 per unit (6.55 cents per kWh), 88% more
expensive than the PHWR.
Breeder enthusiasts might claim that future reactors would be cheaper to construct
because of learning. Historically, however, nuclear construction costs have not reduced
12
J.Y. Suchitra and M.V. Ramana
significantly with time. In the USA, the country with the most nuclear reactors,
construction costs grew steadily from $1,279/kW (in 2006 dollars) for reactors
commissioned between 1966–1967 to $4,377/kW (in 2006 dollars) for reactors
commissioned a decade later (CBO, 2008). The steady growth in costs persisted even in
later reactors (Hultman et al., 2007). Similarly, during the late 1970s and 1980s, the
period when France brought on line most of its current nuclear power plants, the capital
costs (measured in constant francs) actually increased with time, roughly at the same rate
as construction costs in general (Grubler, 2009). Increases in cost have also been reported
in the series of reactors, with somewhat standardised design, that were commissioned in
India in the 1990s [Bohra and Sharma, (2006), p.849].
Nevertheless, in order to account for the possibility of future reduction in costs, we
also considered the case where the capital cost of the PFBR is lower by 15%. Assuming
all the other costs are the same as our base case, the levelised cost of generation at the
PFBR would be Rs. 2.67 per unit (6.08 cents per kWh), 74% more expensive than the
PHWR. The reason – the expensive nature of dealing with plutonium – has been
elaborated earlier.
A variable that is related closely to the capital cost is the discount rate. If we hold all
fuelling costs (cost of plutonium, uranium, heavy water, and fuel fabrication) fixed, then
at a discount rate of 8%, the levelised costs of electricity generation at the PFBR and
PHWR increase to 7.55 cents/kWh and 4.06 cents/kWh, up by 20 and 16% respectively
from the base case. This shows that the levelised cost depends sensitively on the discount
rate, as expected for a capital intensive technology. The difference between the two
levelised costs increases to 86%, as compared to the base case of 80%.
5.2.3 Plutonium cost
Since the major share of the PFBR levelised cost comes from the charges for plutonium,
we now look at different possibilities for the cost of plutonium recovery. There are two
separate elements: the cost of plutonium for the initial core and the first few reloads, and
the cost of plutonium from reprocessing PFBR spent fuel. Therefore, there are a number
of different combinations possible. Finally, there is also the possibility of a lower cost of
fuel fabrication compared to what we have assumed. We illustrate the kinds of variations
(see Table 5).
The first set of possibilities is related to the cost of plutonium for the initial core and
the first few reload. At one extreme is the DAE’s methodology, where KARP plutonium,
including the americium removal cost, is assumed to be free. The lifecycle cost of all
plutonium from KARP, including the discounted cost of plutonium debited after the
PFBR stops operating, is Rs. 39.8 billion ($0.9 billion), 1.8 times the lifecycle capital cost
of the PFBR itself. As a strategy for a large expansion of breeder reactors, this is
unsustainable. It is also methodologically flawed to assume such a large subsidy while
evaluating the economics of the PFBR.
At the other extreme, it is possible that the PFBR requires the use of KARP
plutonium for a much longer period than we have assumed in our base case, ten loadings
instead of five. A third and intermediate possibility, which might be applicable to future
breeder reactors, is that all plutonium used is derived from reprocessing the spent fuel of
other breeder reactors. Therefore, the plutonium for the entire lifetime of the reactor,
including the initial loading, is available at $43/g.
The costs of power
13
The next set of possibilities corresponds to the cost of recovering plutonium from the
PFBR. There is no official cost figure for reprocessing PFBR spent fuel. As an alternative
to our estimate of $43/g, we also consider the lower and higher cases of plutonium
costing $21/g and $74/g (see Appendix 1 for details).
Yet another scenario that we consider is that PFBR spent fuel is used to make weapon
grade plutonium for the nuclear arsenal (Glaser and Ramana, 2007).29 In this case, some
of the plutonium recovered by reprocessing the blankets of the PFBR will be diverted for
military purposes. To compensate, some plutonium from KARP would have to be
acquired. This quantity has been estimated at 345 kg/year at 75% CF. We assume that
this varies in proportion to the operational CF.
Finally, we also consider the possibility that fuel fabrication is less expensive
compared to what we have assumed because of lower labour costs in India. Accordingly
we assume that the costs of fabricating driver fuel and (radial) blanket fuel are
$756/kgHM and $270/kgHM (in 2004 dollars) respectively, 50% of the values suggested
by NEA (2002). This is somewhat extreme because labour is typically only a small
component of the costs of fabrication.
Table 5
Cost differences (percentage) under different assumptions
PFBR capacity factor
80%
50%
Base case (KARP plutonium for five years)
80
139
Base case with KARP plutonium at zero cost
9
45
All plutonium from reprocessing breeder reactor spent fuel (at $43/g)
24
65
Base case with KARP plutonium for ten years
118
177
Base case with PFBR plutonium at $74/g
107
166
Base case with PFBR plutonium at $21/g
62
121
Base case with weapon grade plutonium extracted from PFBR spent fuel
126
185
Lower fuel fabrication costs (reduced by 50%)
74
131
For all cases, we see that the cost of electricity from the PFBR is more expensive than
from the PHWR. In particular, even for the case where the plutonium from KARP is
assumed to be completely free, in other words, the cost is borne by the tax payers, the
cost difference ranges from 9% to 45% depending on the performance of the PFBR.
Likewise, even if several breeder reactors were to be constructed and the excess
plutonium generated by these is sufficient for the initial loading of a new breeder reactor,
electricity from the breeder will be more expensive than from a PHWR by 24% to 65%.
Even at the lowest of these differences, i.e., 9%, the crossover uranium price is $335/kg,
at which price about four times more uranium might be available.
If KARP plutonium is required for a longer period, the cost difference varies from
118% to 177%. For the cases of lower and higher plutonium recovery costs from the
PFBR, we find that the cost difference varies from 62% to 166%. If the PFBR were to be
used to make weapon grade plutonium throughout its lifetime, then the cost difference in
electricity goes up from between 126% and 185%, reflecting the higher cost of plutonium
from KARP. Finally, if the fuel fabrication costs are only 50% of what we have assumed
14
J.Y. Suchitra and M.V. Ramana
in our base case, the cost difference goes down to 74% and 131% for the two assumed
CFs.
6
Conclusions
The Indian DAE has been constructing PHWRs for close to 40 years and these reactors
have dominated the nuclear generation capacity in India thus far. However, the DAE’s
plans for expanding nuclear power in the country over the next few decades are based
primarily on breeder reactors, which are expected to take over from PHWRs by 2025.
The first such reactor, the PFBR, is currently under construction. The DAE has claimed
that breeder reactors will be economically competitive with PHWRs. This is despite the
fact that the PFBR is the first of its kind while the PHWRs are a relatively mature
technology.30
Our results show that this claim is not valid and the cost of generating electricity from
the PFBR is much higher than the corresponding cost at PHWRs. In our base case, even
with optimistic assumptions for the PFBR’s operating parameters, its electricity cost is
80% more expensive than that from PHWRs. Our sensitivity analysis demonstrates that,
even though this percentage might decrease or increase with different assumptions about
specific cost items, fuel chain assumptions (for example, whether the plutonium comes
from other breeder reactors or from PHWRs), and performance, the conclusion about the
higher cost of electricity generation at the PFBR is robust. The high cost of breeder
electricity is primarily because producing plutonium and fabricating it into fuel for the
PFBR are expensive. This in turn is related to both the inherent properties of
plutonium – its greater radioactivity and toxicity as compared to uranium – and the
stringent design requirements for breeder reactor fuel. Therefore, the cost differences in
the fuel chain will persist.
The only way that breeder reactors could become competitive is if the cost of uranium
goes up. We have therefore compared the generating costs at the two reactor systems as a
function of uranium cost and demonstrate that the crossover uranium cost is $1,,375/kg,
nearly seven times the uranium cost of $200/kg used in our base case. This is because the
cost of generating electricity at PHWRs is only weakly dependent on the uranium cost. A
reactor operator willing to incur such high costs for uranium would have access to much
larger quantities of uranium than currently considered economically recoverable. The
DAE’s assertion about limited uranium in the country assumes a fixed and static figure
for the mineral’s reserves. Once the increased availability as the cost increases is taken
into account, the argument that breeder reactors make economic sense in the Indian
context can be seen to be flawed.
The assumption that breeder electricity will be economical is also the basis for the
DAE’s pursuit of reprocessing. As we have shown earlier, reprocessing is expensive as a
way of dealing with radioactive spent fuel (Ramana and Suchitra, 2007). Our analysis
here shows reprocessing is not economically justified even if the value of the recovered
plutonium as fuel is taken into account.
We also find that the significant cost difference between electricity from the PFBR
and PHWRs persists even if breeder reactor construction were to become significantly
cheaper. Lowering construction costs might, however, compromise safety. As it is, the
PFBR design reflects cost reduction efforts made in the 1990s (Bhoje, 2001). This design
makes it more susceptible to catastrophic accidents (Kumar and Ramana, 2008).
The costs of power
15
A non-economic argument that the DAE advances is that breeder reactors are the only
option for meeting India’s future power needs (Subramanian, 2004). This claim assumes
very rapid growth of breeder reactor capacity to keep pace with demand; however, these
projections are based on faulty methodology and unrealistic assumptions (Ramana and
Suchitra, 2009). In addition, the DAE’s projections do not take economic considerations
into account. The high cost of breeder electricity makes it even less likely that there will
be large scale construction of breeder reactors; therefore, they are unlikely to be a
significant component of India’s electricity sector in the foreseeable future.
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Notes
1
2
3
4
5
Unless otherwise specified, watts refers to electrical power.
Fast breeder reactors are thus termed because they are based on energetic (fast) neutrons and
because they produce (breed) more fissile material than they consume.
The higher discount rate is required because the expected rate of return on an investment is the
sum of return on a risk free instrument and the product of the systematic risk, beta, with the
difference in the expected rate of return of the risky and risk free investments. Beta is the ratio
of the covariance of the investment with the market and the variance of market returns. Since
beta is higher for nuclear plants, it would require a higher rate of return on the equity
component (Farber, 1991).
We thank Professor R. Srinivasan of the Indian Institute of Management, Bangalore for
pointing this out to us and for calculating the increase in discount rate on account of the higher
systematic risk.
Passed in 2005, the Right to information act was intended to enable citizens to access
information from public organisations in order to promote transparency and accountability.
The costs of power
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
19
In line with the DAE’s philosophy of not treating spent fuel as waste, we do not include the
cost of dealing with this highly radioactive material; however, in the case of the PFBR, the
cost of reprocessing its spent fuel is indirectly included in the fuelling cost.
At 75% capacity factor, assuming losses of 1% each at the reprocessing and fuel fabrication
stages, the PFBR will produce about 21 kg of plutonium over and above its own fuel
requirement (Glaser and Ramana, 2007). Thus, it would take about 90 years of operation for it
to produce enough plutonium for the core of a similar reactor.
This does not include the expenditures on the PFBR prior to 2004, which amount to
1.24 billion in mixed year Rupees.
Such cost increases could affect the PHWR as well.
The details of the different isotopic fractions have not been mentioned here because they are
not relevant to our economic analysis, but they can be found in (Glaser and Ramana, 2007).
The capacity or load factor is a measure of the efficiency of plant operations and is the ratio of
the actual electricity generated in a given period of time to what it could have generated if the
plant had been working at maximum power continuously for the same period.
In September 2007, it was announced that “production of the mixed oxide fuel for PFBR has
already commenced” (Kakodkar, 2007).
This is a lifecycle cost and thus costs over an assumed lifetime of 15 years.
KARP has a maximum capacity of 100 tons/year. Typical PHWR spent fuel has 3.75 kg of
plutonium in each ton of spent fuel. Assuming 1% losses, KARP produces 371 kg of
plutonium per year. The annual fuel requirement of PFBR at even 50% CF is 681 kg.
The assumption is that the plutonium derived from reprocessing PFBR spent fuel is used
almost immediately; if there are delays in such use, there would be further americium removal
costs. We neglect this possibility.
Reprocessing of the FBTR spent fuel also required a cooling period of two years (Raj, 2005).
Likewise, worldwide experience of reprocessing of MOX fuel from fast breeder reactors is
also sparse and limited only to pilot scale amounts (tens of tons in all) [NEA, (1993), p.234].
According to various DAE performance budgets KARP took 16 years to construct and the
relatively small facility that reprocesses FBTR spent fuel took 13 years to construct.
In comparison, coal plants in India are typically estimated to cost Rs. 40 million/MW; so a 500
MW plant like the PFBR will cost about Rs. 20 billion ($455 million). Similar figures for 500
MW of hydropower, wind, and combined cycle gas plants are Rs. 22.5 billion, 21 billion, and
15 billion respectively.
These refer to long term contract prices, not spot prices that are typically reported. The latter
represent only a small fraction of the total uranium market and tends to have high volatility
due to short term mismatches between supply and demand.
The burnup is the amount of thermal energy produced per unit of fuel. The thermal efficiency
of Indian PHWRs is 0.29.
This may be an overestimate because losses typically grow at a rate slower than power rating
of reactors. Our use of this assumption is favourable to the economics of breeder reactors.
The waste management cost does not include the cost of dealing with highly radioactive spent
fuel, which is reprocessed. It only covers the cost of dealing with the low and intermediate
level radioactive wastes generated during routine reactor operations.
This share of uranium cost is larger than in other countries and studies, for example (CERI,
2004), because we have assumed that uranium is purchased at $200/kg, which is
representative of uranium mining costs in India. This is higher than elsewhere (for example,
(CERI, 2004) assumes uranium costs of about $15 to $35/kg) because of the poor quality of
uranium ore in India. Assuming a lower uranium cost would only make the breeder more
uneconomical. For a more elaborate discussion of PHWR generation costs in India, see
(Ramana et al., 2005). Note also that our definition of uranium costs includes the cost of the
initial fuel loading; other studies, such as (CERI, 2004), include this in the capital cost because
it is spent before the reactor is commissioned.
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25
26
27
28
29
30
31
32
33
34
J.Y. Suchitra and M.V. Ramana
The lower cost assumed for the PFBR when compared to other countries is also a factor.
Similarly, most comparisons of breeder reactors and LWRs assume much larger reprocessing
plants with substantial economies of scale compared to the Indian case. This has been
elaborated in Appendix 1.
This is reflected in the DAE’s estimates of uranium availability over the decades, which has
increased from about 15,000 tons in the early 1950s (Bhabha, 1955), to the current
60,000 tons. In addition to these more definitive resources, there are also resources about
which there is greater uncertainty. Including these will double the availability [NEA, (2008),
p.207]. The DAE typically does not publicise these additional resources, possibly because it
would undermine the rationale for greater emphasis on breeders. This is also borne out by the
fact that in spite the continued increase in uranium estimates, the DAE has continued to
maintain that only 10,000 MW of PHWR can be supported by the available uranium in the
country.
We deliberately restrict ourselves to domestic uranium reserves.
Though breeder enthusiasts claim that sodium reactor technology is robust, experience around
the world has demonstrated that sodium cooled systems often suffer serious disruptions even
in the event of relatively minor failures. Sodium reacts violently with air and water. The
problem is exacerbated because sodium is opaque, which does not allow for visual detection
of faults (unlike reactors that use light or heavy water, which are transparent). These
technological problems strongly suggest that any large scale breeder reactor would be prone to
problems [Lidsky and Miller, (2002), p.140].
The isotopic composition of the plutonium that will be bred in the blankets of the PFBR is
well suited to make nuclear weapons. The DAE has not ruled out this possibility. During the
negotiations on the Indo-US nuclear deal, when the issue of putting the PFBR on the civilian
list under IAEA safeguards was raised, the DAE’s secretary said: “both, from the point of
view of maintaining long-term energy security and for maintaining the minimum credible
deterrent [in other words, increasing the size of the nuclear weapons arsenal], the fast breeder
program just cannot be put on the civilian list” (Bagla, 2006).
However, as argued earlier, there may not be any significant reductions in reactor construction
cost due to learning.
The original design capacity of the FBTR is 42 MWt (thermal). The spent fuel has been
discharged with a burnup of 100,000 MWtd/t or more. Even at a hundred percent capacity
factor, therefore, the reactor will discharge only about 150 kg/y of spent fuel.
This includes the costs of decommissioning the reprocessing and associated servicing plants.
We follow the OECD’s Nuclear Energy Agency and assume that these cost ‘30% of the
original capital cost’, and that the expenditure is assumed to start 20 years after the end of the
operating life of the plant and is spread out over seven years [NEA, (1994), p.114].
In India, for example, though uranium has been mined only in the state of Jharkand, one can
find uranium even in the Himalayan ranges, albeit at concentrations of 1.88 to 28.6 ppm
(Macfarlane and Miller, 2007).
This is true till the ore grade becomes about 1 ppm, beyond which the availability starts
declining.
The costs of power
21
Appendix 1
Reprocessing of PFBR spent fuel
There are no publicly available cost estimates for reprocessing of spent fuel from PFBR
(Suchitra and Ramana, 2007). The only reprocessing plant in India that deals with
breeder reactor spent fuel is the one associated with the FBTR. Its capacity, which is not
mentioned in DAE documents, does not have to be more than 200 kg/y.31 DAE budgets
show that this plant cost Rs. 8.2 billion (28 million in 2004 dollars). To this we have to
add the costs associated with waste management and operations and maintenance. Our
assumption for the capital cost of the waste management plant is based on the cost of the
waste immobilisation plant at Tarapur (Ramana and Suchitra, 2007). The annual
recurring costs are assumed to be Rs. 50 million ($1.1 million). We scale these up to
obtain the corresponding costs for reprocessing spent fuel from the PFBR, using the
standard rule of thumb that costs scale with the plant capacity to the power of 0.6
[National Research Council, (1996), p.421].
Since the DAE has not even mentioned the size of the reprocessing plant it will build
to deal with PFBR spent fuel, we start by noting that the PFBR produces about
12.2 tons/year of spent fuel even at 100% CF (Glaser and Ramana, 2007). We assume
that this requires a reprocessing plant designed to handle about 17 tons/year. Such a plant
could operate at around 70% CF and yet deal with all the spent fuel of the PFBR. For a
dedicated plant with capacity 17 tonsHM/year, the reprocessing cost, scaled up from that
of the FBTR reprocessing plant, is $5,017 per kgHM (kilogram of heavy metal in spent
fuel).32 Since, the FBTR reprocessing plant is co-located with the reactor, scaling up from
its cost takes into account the savings resulting from this proximity.
Since there are no large reprocessing plants that deal with breeder reactor spent fuel,
all available cost figures are only estimates. The most detailed of these that we have come
across are for a plant that was proposed to deal with the spent fuel of the commercial fast
reactor in the UK, which was ultimately never built. That plant was designed to reprocess
250 tons/y and was to cost £756 million (1979 figures) which translates to about
$3.3 billion (2004 figures) (RNPDA, 1980). Its O&M costs were estimated at
40.2 million pounds (1979 figures) which translates to about $177 million/year (2004
figures). At 70% CF, therefore, reprocessing breeder spent fuel would cost $2973 per
kgHM (in 2004 Dollars). A more recent estimate for a 50 t/y plant is $5,400 per kgHM of
breeder spent fuel (Takata et al., 2004). These two figures are comparable if scaled by a
power of 0.6.If the UK cost figure is scaled down to 17 tons/y, then the corresponding
reprocessing cost would be $8,714/kgHM.
Some have argued on the basis of estimates of costs of reprocessing plants that the
rule of thumb typically used, i.e., scaling by a power of 0.6, is not valid when
extrapolating from very large units to very small units, i.e., over a large range and that
“small plants are disproportionately expensive” (Haire, 2003). This could be avoided by
comparing the costs of reprocessing at the 17 tonsHM/year capacity with the estimated
cost of a 15 tonsHM/year reprocessing plant, “designed to provide reprocessing services
for just one or two demonstration breeder reactors… The cost for such a stand-alone
facility, built for and dedicated to reprocessing, was 0.8 ± 0.2 billion 1982 dollars”
(Haire, 2003). Just accounting for this capital cost without including any of the O&M
costs and decommissioning would result in reprocessing costs of over $11,000/kgHM
22
J.Y. Suchitra and M.V. Ramana
(in 2004 dollars). Thus our estimate of $5,017/kgHM is generous to the economics of the
PFBR.
One could argue that the economies of scale dictate that a much larger reprocessing
plant should be built. This would have two problems. One is that there would be
additional costs for transportation and other infrastructure, which are avoided by having
appropriately sized reprocessing plants at the same site as the reactor. This argument has
historically been the reason for the DAE’s preference for smaller plants co-located with
the reactor (Srinivasan, 1985). The second problem is that such a plant would lie idle for
a significant fraction of its initial years because there is only one breeder reactor under
construction at the present. The low level of use during the initial years will drive up the
costs of reprocessing.
However, to explore the sensitivity to lower costs due to economies of scale, we also
assume a plant that is sufficient for five more reactors the same size as the PFBR.
The spent fuel discharged by the PFBR has about 12% plutonium when both core and
the blanket elements are reprocessed together. At a reprocessing cost of $5,017/kgHM,
therefore, the cost of plutonium is about $43/g, provided 99% of the plutonium is
recovered from the spent fuel. In our sensitivity analyses, we also considered plutonium
costs of $74/g and $21/g, corresponding to reprocessing costs of $8,714/kgHM and
$2,500/kgHM (roughly half of our estimate) respectively. The latter corresponds to the
cost that would be expected if the reprocessing plant is sufficient to service the fuel from
six reactors of the same capacity as the PFBR, the plant operates at the same capacity
factor of 70% as assumed for the smaller plant, and there are no additional costs due to
transportation of spent fuel to this facility.
Appendix 2
Uranium availability and costs
There is a general perception that uranium is a scarce resource. However, uranium has an
average concentration in the earth’s crust of 2.8 parts per million (ppm), and is more
abundant than silver or tungsten [Schneider and Sailor, (2008), p.380]. Uranium deposits
are found in several different kinds of rocks, such as sedimentary, igneous, and
metamorphic rocks, as well as in seawater.33
Geologists have roughly estimated the amount of uranium present as a function of
grade, and find that there is roughly a three hundred fold increase in the estimated amount
of recoverable uranium for every ten fold decrease in the ore grade (Deffeyes and
MacGregor, 1980).34 This means that the availability of uranium is related to the ore
grade by a power law:
n
⎛G ⎞
U 2 = U1 ⎜ 1 ⎟ where U is the quantity of uranium available at a certain ore grade G.
⎝ G2 ⎠
The exponent n is the slope of the uranium availability curve, which is estimated at about
2.5 in the range of ore grades that are being currently mined (Deffeyes and MacGregor,
1980).
There are different possible relationships between the ore grade and the cost of
obtaining uranium from that ore (Schneider and Sailor, 2008). The simplest assumption is
that the cost of uranium mining is inversely proportional to the ore grade, and the price of
The costs of power
23
uranium is directly proportional to the cost of mining. Then, the relationship between
uranium availability and price of uranium becomes:
n
⎛P ⎞
U 2 = U1 ⎜ 2 ⎟ where U is the uranium availability at a certain uranium price P. Since
⎝ P1 ⎠
n is rather large, the amount of uranium available goes up sharply as the price goes up.
Therefore, if the cost of uranium goes up from our base case value of $200/kg to the base
case crossover value of $1,375/kg, then the uranium availability will go up by a factor of:
5
U ($1,375)
⎛ 1,375 ⎞ 2
=
= 124 .
U ($200) ⎜⎝ 200 ⎟⎠
Other models are somewhat more conservative. One model that includes both the costs of
extraction and discovering new resources suggests that
1 ⎛P ⎞
U 2 − U1 = ln ⎜ 2 ⎟
b ⎝ P1 ⎠
where b = 0.00054 and U is the cumulative uranium ore quantity in thousands of tons
(Kroch, 1979). In this model, for the same increase of $200/kg to $1,375/kg in uranium
price, the uranium availability will go up by a factor of 60.5.
The assumption that mining poorer quality ores will necessarily be costlier might not
be justified and the price could come down because of technological improvements. This
has been the case with other minerals. For example, during the period 1900–1998, world
copper production increased by 2,465% while its constant dollar price and the average
ore grade decreased by 75% and seven fold respectively (Wilburn et al., 2005).