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Economic power from fast breeder reactors
J. Nuclear Energy, 1954, Vol. 1. pp, 39 to 46. Pergamon Press Ltd.• London
ECONOMIC POWER FROM FAST BREEDER REACTORS By C. A.
RENNIE
Atomic Energy Research Establishment, Harwell, Berks (Received 5 April 1954)
Abstract-The role of fast breeder reactors in a nuclear power programme is discussed. It is concluded that a balanced scheme of fast reactors which produce more fissilematerial than they consume and thermal reactors which are not quite self-sustaining in fissile material offer an attractive line of development for a country without large reserves of uranium as in this way it should be possible to utilize an appreciable fraction of the source material for power generation. The influence of reactor costs and processing costs on the price of electrical power is discussed and some estimate made of the allowable costs in such a system. A value can be assigned to the fissile material once the other costs are known and this would enable comparisons to be made with other schemes for generating electrical power from nuclear fuels. 1. PROSPECTS
NUCLEAR power stations are attractive as they offer the possibility of using natural uranium or thorium as a new source of fuel for producing electrical power. The scale of this source of power is large as the fission of one gram of uranium or thorium would produce about 800 kilowatt days of heat, and assuming a thermal efficiency of 25 per cent to 30 per cent, that is about 5,000 kilowatt hours of electrical power. The present consumption of electricity in the United Kingdom is about 6'1010 kilowatt hours per year, which could therefore in principle be supplied by the complete utilization of about 12 tonnes of uranium or thorium each year. The problem is to develop this vast potential source of power at a cost which is acceptable for general use. The chief systems for utilizing uranium and thorium are tabulated in Table I, together with their most important features, and the following comments can be made. (a) It has been announced that it is possible to produce more than one atom of plutonium for each atom of uranium 235 consumed with system (8), and it is likely from the published information that system (7) would produce more plutonium than it consumes. (b) No information is available on system (6), but one can hope it would be at least self-maintaining in fissile material. (c) From the information published on systems (1), (2), (3), and (5) one would expect the conversion factor to be less than unity giving a net loss in fissile material. (d) For system (4) no information is available, so it has been assumed that at best it would be self-maintaining in fissile material. All the types of reactor considered involve recycling of the fuel except the first system. Although the first system may at present be the least expensive, it means a continuous feed of natural uranium as it seems doubtful if more than about one per cent .of the uranium can be utilized. In the long run this first system could onlybe of interest to a country with very large reserves of uranium ore which can be extracted cheaply, as any increase in the price of uranium would favour the other systems. 39
40
C. A.
RENNIE
Any country which has to import uranium must of necessity try and use a much larger fraction of the uranium, by adopting one of the other systems involving recycling of the fuel. TABLE I-SOME POSSIBLE TYPES OF POWER REACTORS
System
(I)
I
Fissile Material Source Material
I
I U's~ I
I
Type
I
Overall
Gain Factor
Tbennal
I
Recycling I Product of fuel
Remarks
1
Negative
Converter
Feed Material Natural U
I
Larg:
No
I
uranium re-
quirement
(2)1~1--=-I----I----I------I---I----[--=:---U·ss separation plant Thermal Pu Negative Converter
Natural or Enriched U
Yes
to save uranium
o)~Tborium Thennal
Negative
U'SS and Thorium
Yes
~ ~ Thorium Thennal
Negative or
Thorium and U·s. (1)
Yes
Converter
needed for recycling
u'SS
Separation plan t needed for U,ss with feed of natural uran10m
Breeder
zero (1)
May be self maintaining. not feed of U·s required from (3). (6) or (8)
If
- - - - - - ----::::--I----I'----I-------,-----j--(5)
I
Pu
~ ~ Thorium (7)
(8)
Pu U 28a
Fast Breeder Fast Breeder
U·ss or Fast Thorium Converter
Pu and
Negative
Depleted V
Positive (1)
I
or zero
Pu could be supplied by (2) or (7) or (8)
Yes
Thorium
Yes
DepJetect V
Yes
May breed U·SSwhich COUld be used to supply (3)
I I
Positive
I
Pu
Could produce U28S material
If blanket
was thorium
Positive
Yes
Pu or U·SS
Separation plant needed for U,ss with feed of natural uranium
2. POSSIBILITIES
Until reactors of the various types have been built and operated any estimates of the costs are at the best intelligent guesswork. However, it is possible to examine the principles of the different schemes and to obtain some idea of the allowable costs. The fact that fast reactors can breed more fissile material than they consume means that, providing there is a market for the fissile material, the sale of this fissile material can be put as a credit against the cost of generating electricity. The three possible uses of the extra fissile material produced are for further fast reactors, for mobile reactors, or for feeding into thermal reactors which are not quite self-sustaining in fissile material. The first alternative is limited as the process is divergent in the sense that more and more reactors would be required to provide a market for all the fissile material produced. The second alternative of mobile reactors is also limited, and cannot be a basis for any programme until more information is available. This leaves the third alternative of combining fast reactors which breed more fissile material with thermal reactors which do not as one reasonable approach on which to base a large scale nuclear power programme. In a balanced scheme of this type in which the gain of fissile material from fast reactors is used to make up for the losses of fissile material in thermal reactors, the only nuclear feed material required is the source material, uranium or thorium. The initial investment of fissile material could be supplied either by converter reactors or by a uranium isotope separation plant or from a stockpile of fissile material.
Economic power from fast breeder reactors
41
One possible combined scheme of fast and thermal reactors using the plutoniumuranium 238 systems, i.e., systems (5) and (7) in Table I, is shown diagrammatically in Fig. 1, and discussed in more detail. The other possible combined scheme using the uranium 233-thorium system, i.e., systems (4) and (6) in Table I, is not discussed in detail here but the same arguments would apply to this scheme.
Fission pr-oduct s
Uranium FIG. 1
3.
PRINCIPLES
The basic principles of fast and thermal reactors have been described elsewhere and only the points relevant to the subsequent analysis are discussed here. In any reactor in which the fuel is recycled there are three very important factors, the overall heat rating of the fissile material R, the overall gain factor G or loss factor L, and the fraction of the fissile material which can be consumed before processing is necessary 1/N. The overall heat rating R is the total heat output times the utilization or load factor divided by the total fissile material investment in the system. The overall heat rating therefore depends appreciably 011 the hold up of fissile material in any processing plants, and this hold up must be reduced to a minimum. The overall gain factor G for a fast reactor is the increase in fissile materal obtained expressed as a fraction of the fissile material consumed after allowance has been made for the processing losses which arise because the fuel has to be recycled. For a thermal reactor which is not self-maintaining, the overall gain factor is negative, i.e., an overall loss factor L, but it can be defined in the same way as the loss in fissile material expressed as a fraction of the fissile material consumed after making allowance for the processing losses. The fraction of fissile material which can be consumed before processing is necessary l/Nwill be limited either by nuclear considerations or by structural changes occurring in the fuel due to the fission products produced, and this will be true whether a continuous or an intermittent recycling process is used. It is clearly essential to try and reduce the amount of processing required to a minimum as each processing cycle will involve a loss of material. It is true that at the expense of time and money the processing losses could be reduced to a negligible proportion, but in practice some balance will have to be drawn between the cost and the efficiencyof a processing plant. The processing plant for the core of the fast reactor is likely to be different from that required for the blanket of source material surrounding the core as the concentration
42
C. A.
RENNIE
of fissile material will be very different. However, the blanket processing plant for a fast reactor will be very similar to the fuel processing plant for a thermal reactor, as the concentration of fissilematerial is much the same, and here the costs of these two plants have been assumed to be equal. It should be noted that the processing plants for these reactors may be different, and one hopes less expensive, than a plant for extracting and purifying fissile material. For instance, in a system in which the fuel is recycled it would not be necessary to obtain a very high decontamination factor for fission products, if all the operations on the fuel were carried out by remote control. The amount of source material required for both the fast and thermal reactor systems has been taken rather arbitrarily as two hundred times the amount of fissile material in the system. 4. PROGRAMME
Since the gain or loss of fissile material is proportional to the heat output times the gain or loss factor, this means, assuming both systems have the same thermal efficiency, that in a balanced scheme the power outputs from the thermal and fast reactors must be in the ratio of the overall gain factor of the fast reactors to the overall loss factor of the thermal reactors. The average cost of generating electricity in the balanced scheme will then be a weighted average of the costs in the two systems. TABLE II-NOTATION AND ASSUMPTIONS
Item ---~---
..
Fast system
Thermal system
~~~--~~~~~~~~-~~~--+~-
Cost of reactor and generating plant per kilowatt installed capacity Cost of processing fast reactor blanket or thermal reactor fuel per gram of Pu Cost of processing fast reactor core per gram of Pu Cost of Pu per gram Cost of U per kilogram Cost per unit generated in pence Overall heat rating in kilowatts per gram of Pu Overall gain or loss factor Fraction of Pu consumed before processing is necessary Thermal efficiency of generating plant Interest rates charged on U or Pu Depreciation interest and operating charges on reactor and generating plant Load factor of reactor and generating plant (assumed to be a base load station) Heat equivalent of Pu in kilowatt days per gram
Average overall heat rating in kilowatts per gram of Pu Average cost per unit generated in pence
sr, £Pf
£F £U Cf R! G
lIN! 2705%
4%
£F
£u Ct
Rt -L
u«,
27'5%
4%
15%
15%
80%
80% 800
800
R = R,Rt(L -I- G)
"""R;:-tL~-I-:--:R;:-!-:=G:--
LC,+ GC t C=-L-+-O-'
The notation used and the assumptions made about the fast and thermal reactors are given in Table II. Using these figures the contributions to the cost per unit of electricity generated can be obtained and are tabulated in Table III. The total cost per unit in pence of the electrical power generated can then be written down.
Economic power from fast breeder reactors
43
TABLE III-CONTRIBUTIONS TO COST PER UNIT OF ELECTRICITY 'IN PENCE
Due to
._ _, _
s~~~~ _--';-
Thermal system _
Fixed charges on reactor and generating plant
0·005 X,
0-005 K/
Processing of fast reactor core or thermal reactor fuel
0'045 NIP,
0'045N/P/
Processing of fast reactor blanket
0·45 GP/
Profit or loss on fissile material
-0,045 OF
O·OO4F
Interest charges on fissile material
0-004F
----.n;--
Interest charges and losses of source material
0·045 LF
~
0·001 U
0-002 U
~
R;-
In one year's operation a fraction 0.45R of the fissile material is consumed and the electrical power generated is 2400 R kilowatt hours (or units) per gram of fissile material in the system.
For the fast reactors:
c, =
0·005
x, + 0-045 NiP! -
0·045 G (F - Pt)
F 0-001 U + 0·004 -R~ + R t t
For the thermal reactors:
c, =
a-ODS
0-004 F
0·002 U
x, + 0-045 NtP t + 0-045 LF + ~ + ~
For the combined system:
In the expressions for C, and C, the first term corresponds to the fixed charges, the second to the fuel processing costs, the third to the profit or loss of fissilematerial, the fourth to the interest charges on the plutonium investment, and the last term to the interest charges on and the losses of the uranium. It can be seen that as the price of plutonium decreases the cost of generating electricity will increase for the fast reactor system, will decrease for the thermal reactor system, and will decrease for the combined system. Therefore, at some particular price of plutonium the cost of generating electricity from the fast and thermal systems will be equal to each other and of course equal to the cost for the combined system. This "equilibrium" value of plutonium, that is the value at which the costs per unit from each system are equal, will be determined by the reactor characteristics, the processing costs, and the price of uranium, and some estimates of this value are made later. However, before discussing this question, some general remarks can be made about the way in which a combined fast and thermal reactor system should be operated. In order to start such a programme there must be either an initial supply of plutonium from convertor reactors or the system must be started on uranium 235 from a uranium isotope separation plant. If this initial price of fissile material is higher than the "equilibrium" value, then it would not be the best policy to operate a balanced
44
C. A.
RENNIE
scheme. In practice one would increase the ratio of fast reactors to thermal reactors so that the cost of electricity was reduced to the "equilibrium" value and a surplus of plutonium was produced. This surplus of plutonium could then be used to start up further systems, and the value of the plutonium would gradually fall to the "equilibrium" value as the programme progressed. This picture of the method of operating a combined fast and thermal reactor system is greatly over simplified as improvements in processing plants, and in reactor design, will alter the "equilibrium" value of plutonium as the programme proceeds, but these developments will not alter the main line of argument. If on the other hand the price of fissile material either from convertor reactors or from a uranium isotope separation plant was less than the "equilibrium" value for a balanced fast and thermal reactor scheme, there would be no point in starting such a scheme. It would, however, become economic either when the cost of fissile material from other schemes had become higher due to an increase in the price of uranium, or when the "equilibrium" value had been reduced, by improvements in processing plants and reactor design, to the point where it was less than the price of fissile material from other systems. In equating values of different fissile materials, allowance must of course be made for the different nuclear properties. 5. OPERATING COSTS
For illustration let us take some rather arbitrary values for the quantities involved and see what the cost per unit of electricity generated would be. For instance, if in the fast reactor system G = 0-5 and R, = 0·5 (which would give a doubling period for the fissile material of about 9 years), and in the thermal reactor system L = 0·2 (that is, an overall conversion factor of 0'8), R, = 1'0, and N, = 1·0 corresponding to 0'5 per cent burn up of the fuel if the ratio of U to Pu is 200 to 1, then:
+ 0·045 NfP + 0·0225 P, - 0·0145 F + 0·002 U c, = 0·005 x, + 0'045 r, + 0,013 F + 0·002 U
C, = 0'005 K,
f
Assuming that the cost per kilowatt installed capacity is the same for both systems, i.e., K, = K t , then the cost per unit for each system will be the same if 0·045 NfPf = 0-0225 P,
+ 0·0275 F. or F =
2NP -P f f 2 t 1·2
In Fig. 2 the contribution to the cost per unit, due to the fuel and processing cost only, is plotted against the value of the fissile material for various assumed values of Pt and NfP,. The price of uranium has been taken as £20 per kilogram. The values of F obtained lie in the region of £5 to £15 per gram and the fuel and the processing cost per unit between 0·2 and 0·5 pence. In the United Kingdom the cost per unit of electricity generated is at present about 0<75 pence. So with the figures taken here one would need to have a value of K of about £100 or £120 to obtain power at a comparable price. This value of K is about twice that for a conventional coal fired power station in the United Kingdom at the present day, and is in line with estimates of the cost of nuclear power stations made elsewhere. The figures taken indicate an allowable blanket or thermal reactor fuel processing
Economic power from fast breeder reactors
45
cost of between £2 and £6 per gram of plutonium, and an allowable total core processing cost for the fast reactor of between £4 and £12 per gram of plutonium. The core processing cost allowable for each cycle will depend on the value of N, the number of times each gram of plutonium has to be processed before it is all consumed. tal
a.
0'61---+-+--+--:::b-'F-~oc----+::
.... III o
0'5p-~:---f-~=""""",""""k---t---:e_
<)
t7I
c 'iii III
gIII 3• 0·31--1"..---j----::::lo~"'F--.p.,._I_=~~..L-----' li; 8 10 'tJ
Q.0·21--I--+"o-t""""'c.;-,.+--!
~:: 0.1
Nf PfTotal core processing £/ gram of Pu.
cost in
$.-
:J
c:
lJ..:I
0 o.......-=--"':-~:-----=--~-:-':---:"-:-~-:-'::--::'=-------\
2
4
f'IG. 2
6. CAPITAL COSTS
The average overall heat rating of the plutonium for the combined fast and thermal reactor system is given by R = RtRtCL G) RtL +RtG
+
which is equal to 0'77 kilowatts per gram using the figures taken above. That would mean an investment of about 5 grams of plutonium and 1 kilogram of uranium per kilowatt installed capacity. In practice, the thermal reactor systems could be started on natural or slightly enriched uranium which would reduce the plutonium investment required by about one half, i.e., to about 2·5 gm of plutonium per kilowatt installed capacity. Taking an average value of £10 per gram for the plutonium this would mean a capital investment of about £50 per kilowatt on account of fuel, but this capital investment would not depreciate. The investment on reactor and generating plant would be about £120, per kilowatt installed. The capital investment on processingplant is difficultto assess, as no published information is available on processing costs. The total capital investment per kilowatt installed capacity is however likely at first to be three or four times that for a coal fired station. However, as the development of nuclear power proceeds the capital investment on reactor, generating plant, and processing plant should be reduced, and the figures given here indicate the target at which one has to aim. With the figures assumed for a combined fast and thermal reactor scheme about 35 per cent of the plutonium invested is consumed and replaced each year, so that the plutonium is used and replaced on the average about once every three years. The amount of uranium used for power generation would be about 0·5 per cent of the uranium processed, so that if the processing losses for uranium were 5 per cent then about 10 per cent of the uranium fed into the system would be used for power
46
C.
A. RENNIE:
Economic power from fast breeder reactors
generation. If the uranium processing losses were only 1 per cent then about one third uranium fed in could be used for power generation. 7. CONCLUSIONS
The generation of electrical power by a balanced fast and thermal reactor scheme is a promising line of development for a country without large resources of homeproduced uranium. In such a scheme it is possible to use a comparatively large fraction of the uranium 238, the actual fraction depending on the economic aspects of the processing losses in recycling the uranium. In a scheme of this kind a value can be assigned to the fissile material, once the other costs are known, so that a comparison can be made with schemes using uranium 235 produced by a separation plant and with schemes using the thorium-uranium 233 system. In general, the use of a combined scheme of fast reactors which breed more fissile material with thermal reactors gives much more flexibility in design, so that it is not necessary to push either type of reactor to its limit, and this may have important economic results. Finally, it is clear that the processing costs for the fuel and blanket playa vital part in the economic assessment of the scheme. They are of about the same importance as the costs of the reactor and generating plant.
ECONOMIC POWER FROM FAST BREEDER REACTORS By C. A.
RENNIE
Atomic Energy Research Establishment, Harwell, Berks (Received 5 April 1954)
Abstract-The role of fast breeder reactors in a nuclear power programme is discussed. It is concluded that a balanced scheme of fast reactors which produce more fissilematerial than they consume and thermal reactors which are not quite self-sustaining in fissile material offer an attractive line of development for a country without large reserves of uranium as in this way it should be possible to utilize an appreciable fraction of the source material for power generation. The influence of reactor costs and processing costs on the price of electrical power is discussed and some estimate made of the allowable costs in such a system. A value can be assigned to the fissile material once the other costs are known and this would enable comparisons to be made with other schemes for generating electrical power from nuclear fuels. 1. PROSPECTS
NUCLEAR power stations are attractive as they offer the possibility of using natural uranium or thorium as a new source of fuel for producing electrical power. The scale of this source of power is large as the fission of one gram of uranium or thorium would produce about 800 kilowatt days of heat, and assuming a thermal efficiency of 25 per cent to 30 per cent, that is about 5,000 kilowatt hours of electrical power. The present consumption of electricity in the United Kingdom is about 6'1010 kilowatt hours per year, which could therefore in principle be supplied by the complete utilization of about 12 tonnes of uranium or thorium each year. The problem is to develop this vast potential source of power at a cost which is acceptable for general use. The chief systems for utilizing uranium and thorium are tabulated in Table I, together with their most important features, and the following comments can be made. (a) It has been announced that it is possible to produce more than one atom of plutonium for each atom of uranium 235 consumed with system (8), and it is likely from the published information that system (7) would produce more plutonium than it consumes. (b) No information is available on system (6), but one can hope it would be at least self-maintaining in fissile material. (c) From the information published on systems (1), (2), (3), and (5) one would expect the conversion factor to be less than unity giving a net loss in fissile material. (d) For system (4) no information is available, so it has been assumed that at best it would be self-maintaining in fissile material. All the types of reactor considered involve recycling of the fuel except the first system. Although the first system may at present be the least expensive, it means a continuous feed of natural uranium as it seems doubtful if more than about one per cent .of the uranium can be utilized. In the long run this first system could onlybe of interest to a country with very large reserves of uranium ore which can be extracted cheaply, as any increase in the price of uranium would favour the other systems. 39
40
C. A.
RENNIE
Any country which has to import uranium must of necessity try and use a much larger fraction of the uranium, by adopting one of the other systems involving recycling of the fuel. TABLE I-SOME POSSIBLE TYPES OF POWER REACTORS
System
(I)
I
Fissile Material Source Material
I
I U's~ I
I
Type
I
Overall
Gain Factor
Tbennal
I
Recycling I Product of fuel
Remarks
1
Negative
Converter
Feed Material Natural U
I
Larg:
No
I
uranium re-
quirement
(2)1~1--=-I----I----I------I---I----[--=:---U·ss separation plant Thermal Pu Negative Converter
Natural or Enriched U
Yes
to save uranium
o)~Tborium Thennal
Negative
U'SS and Thorium
Yes
~ ~ Thorium Thennal
Negative or
Thorium and U·s. (1)
Yes
Converter
needed for recycling
u'SS
Separation plan t needed for U,ss with feed of natural uran10m
Breeder
zero (1)
May be self maintaining. not feed of U·s required from (3). (6) or (8)
If
- - - - - - ----::::--I----I'----I-------,-----j--(5)
I
Pu
~ ~ Thorium (7)
(8)
Pu U 28a
Fast Breeder Fast Breeder
U·ss or Fast Thorium Converter
Pu and
Negative
Depleted V
Positive (1)
I
or zero
Pu could be supplied by (2) or (7) or (8)
Yes
Thorium
Yes
DepJetect V
Yes
May breed U·SSwhich COUld be used to supply (3)
I I
Positive
I
Pu
Could produce U28S material
If blanket
was thorium
Positive
Yes
Pu or U·SS
Separation plant needed for U,ss with feed of natural uranium
2. POSSIBILITIES
Until reactors of the various types have been built and operated any estimates of the costs are at the best intelligent guesswork. However, it is possible to examine the principles of the different schemes and to obtain some idea of the allowable costs. The fact that fast reactors can breed more fissile material than they consume means that, providing there is a market for the fissile material, the sale of this fissile material can be put as a credit against the cost of generating electricity. The three possible uses of the extra fissile material produced are for further fast reactors, for mobile reactors, or for feeding into thermal reactors which are not quite self-sustaining in fissile material. The first alternative is limited as the process is divergent in the sense that more and more reactors would be required to provide a market for all the fissile material produced. The second alternative of mobile reactors is also limited, and cannot be a basis for any programme until more information is available. This leaves the third alternative of combining fast reactors which breed more fissile material with thermal reactors which do not as one reasonable approach on which to base a large scale nuclear power programme. In a balanced scheme of this type in which the gain of fissile material from fast reactors is used to make up for the losses of fissile material in thermal reactors, the only nuclear feed material required is the source material, uranium or thorium. The initial investment of fissile material could be supplied either by converter reactors or by a uranium isotope separation plant or from a stockpile of fissile material.
Economic power from fast breeder reactors
41
One possible combined scheme of fast and thermal reactors using the plutoniumuranium 238 systems, i.e., systems (5) and (7) in Table I, is shown diagrammatically in Fig. 1, and discussed in more detail. The other possible combined scheme using the uranium 233-thorium system, i.e., systems (4) and (6) in Table I, is not discussed in detail here but the same arguments would apply to this scheme.
Fission pr-oduct s
Uranium FIG. 1
3.
PRINCIPLES
The basic principles of fast and thermal reactors have been described elsewhere and only the points relevant to the subsequent analysis are discussed here. In any reactor in which the fuel is recycled there are three very important factors, the overall heat rating of the fissile material R, the overall gain factor G or loss factor L, and the fraction of the fissile material which can be consumed before processing is necessary 1/N. The overall heat rating R is the total heat output times the utilization or load factor divided by the total fissile material investment in the system. The overall heat rating therefore depends appreciably 011 the hold up of fissile material in any processing plants, and this hold up must be reduced to a minimum. The overall gain factor G for a fast reactor is the increase in fissile materal obtained expressed as a fraction of the fissile material consumed after allowance has been made for the processing losses which arise because the fuel has to be recycled. For a thermal reactor which is not self-maintaining, the overall gain factor is negative, i.e., an overall loss factor L, but it can be defined in the same way as the loss in fissile material expressed as a fraction of the fissile material consumed after making allowance for the processing losses. The fraction of fissile material which can be consumed before processing is necessary l/Nwill be limited either by nuclear considerations or by structural changes occurring in the fuel due to the fission products produced, and this will be true whether a continuous or an intermittent recycling process is used. It is clearly essential to try and reduce the amount of processing required to a minimum as each processing cycle will involve a loss of material. It is true that at the expense of time and money the processing losses could be reduced to a negligible proportion, but in practice some balance will have to be drawn between the cost and the efficiencyof a processing plant. The processing plant for the core of the fast reactor is likely to be different from that required for the blanket of source material surrounding the core as the concentration
42
C. A.
RENNIE
of fissile material will be very different. However, the blanket processing plant for a fast reactor will be very similar to the fuel processing plant for a thermal reactor, as the concentration of fissilematerial is much the same, and here the costs of these two plants have been assumed to be equal. It should be noted that the processing plants for these reactors may be different, and one hopes less expensive, than a plant for extracting and purifying fissile material. For instance, in a system in which the fuel is recycled it would not be necessary to obtain a very high decontamination factor for fission products, if all the operations on the fuel were carried out by remote control. The amount of source material required for both the fast and thermal reactor systems has been taken rather arbitrarily as two hundred times the amount of fissile material in the system. 4. PROGRAMME
Since the gain or loss of fissile material is proportional to the heat output times the gain or loss factor, this means, assuming both systems have the same thermal efficiency, that in a balanced scheme the power outputs from the thermal and fast reactors must be in the ratio of the overall gain factor of the fast reactors to the overall loss factor of the thermal reactors. The average cost of generating electricity in the balanced scheme will then be a weighted average of the costs in the two systems. TABLE II-NOTATION AND ASSUMPTIONS
Item ---~---
..
Fast system
Thermal system
~~~--~~~~~~~~-~~~--+~-
Cost of reactor and generating plant per kilowatt installed capacity Cost of processing fast reactor blanket or thermal reactor fuel per gram of Pu Cost of processing fast reactor core per gram of Pu Cost of Pu per gram Cost of U per kilogram Cost per unit generated in pence Overall heat rating in kilowatts per gram of Pu Overall gain or loss factor Fraction of Pu consumed before processing is necessary Thermal efficiency of generating plant Interest rates charged on U or Pu Depreciation interest and operating charges on reactor and generating plant Load factor of reactor and generating plant (assumed to be a base load station) Heat equivalent of Pu in kilowatt days per gram
Average overall heat rating in kilowatts per gram of Pu Average cost per unit generated in pence
sr, £Pf
£F £U Cf R! G
lIN! 2705%
4%
£F
£u Ct
Rt -L
u«,
27'5%
4%
15%
15%
80%
80% 800
800
R = R,Rt(L -I- G)
"""R;:-tL~-I-:--:R;:-!-:=G:--
LC,+ GC t C=-L-+-O-'
The notation used and the assumptions made about the fast and thermal reactors are given in Table II. Using these figures the contributions to the cost per unit of electricity generated can be obtained and are tabulated in Table III. The total cost per unit in pence of the electrical power generated can then be written down.
Economic power from fast breeder reactors
43
TABLE III-CONTRIBUTIONS TO COST PER UNIT OF ELECTRICITY 'IN PENCE
Due to
._ _, _
s~~~~ _--';-
Thermal system _
Fixed charges on reactor and generating plant
0·005 X,
0-005 K/
Processing of fast reactor core or thermal reactor fuel
0'045 NIP,
0'045N/P/
Processing of fast reactor blanket
0·45 GP/
Profit or loss on fissile material
-0,045 OF
O·OO4F
Interest charges on fissile material
0-004F
----.n;--
Interest charges and losses of source material
0·045 LF
~
0·001 U
0-002 U
~
R;-
In one year's operation a fraction 0.45R of the fissile material is consumed and the electrical power generated is 2400 R kilowatt hours (or units) per gram of fissile material in the system.
For the fast reactors:
c, =
0·005
x, + 0-045 NiP! -
0·045 G (F - Pt)
F 0-001 U + 0·004 -R~ + R t t
For the thermal reactors:
c, =
a-ODS
0-004 F
0·002 U
x, + 0-045 NtP t + 0-045 LF + ~ + ~
For the combined system:
In the expressions for C, and C, the first term corresponds to the fixed charges, the second to the fuel processing costs, the third to the profit or loss of fissilematerial, the fourth to the interest charges on the plutonium investment, and the last term to the interest charges on and the losses of the uranium. It can be seen that as the price of plutonium decreases the cost of generating electricity will increase for the fast reactor system, will decrease for the thermal reactor system, and will decrease for the combined system. Therefore, at some particular price of plutonium the cost of generating electricity from the fast and thermal systems will be equal to each other and of course equal to the cost for the combined system. This "equilibrium" value of plutonium, that is the value at which the costs per unit from each system are equal, will be determined by the reactor characteristics, the processing costs, and the price of uranium, and some estimates of this value are made later. However, before discussing this question, some general remarks can be made about the way in which a combined fast and thermal reactor system should be operated. In order to start such a programme there must be either an initial supply of plutonium from convertor reactors or the system must be started on uranium 235 from a uranium isotope separation plant. If this initial price of fissile material is higher than the "equilibrium" value, then it would not be the best policy to operate a balanced
44
C. A.
RENNIE
scheme. In practice one would increase the ratio of fast reactors to thermal reactors so that the cost of electricity was reduced to the "equilibrium" value and a surplus of plutonium was produced. This surplus of plutonium could then be used to start up further systems, and the value of the plutonium would gradually fall to the "equilibrium" value as the programme progressed. This picture of the method of operating a combined fast and thermal reactor system is greatly over simplified as improvements in processing plants, and in reactor design, will alter the "equilibrium" value of plutonium as the programme proceeds, but these developments will not alter the main line of argument. If on the other hand the price of fissile material either from convertor reactors or from a uranium isotope separation plant was less than the "equilibrium" value for a balanced fast and thermal reactor scheme, there would be no point in starting such a scheme. It would, however, become economic either when the cost of fissile material from other schemes had become higher due to an increase in the price of uranium, or when the "equilibrium" value had been reduced, by improvements in processing plants and reactor design, to the point where it was less than the price of fissile material from other systems. In equating values of different fissile materials, allowance must of course be made for the different nuclear properties. 5. OPERATING COSTS
For illustration let us take some rather arbitrary values for the quantities involved and see what the cost per unit of electricity generated would be. For instance, if in the fast reactor system G = 0-5 and R, = 0·5 (which would give a doubling period for the fissile material of about 9 years), and in the thermal reactor system L = 0·2 (that is, an overall conversion factor of 0'8), R, = 1'0, and N, = 1·0 corresponding to 0'5 per cent burn up of the fuel if the ratio of U to Pu is 200 to 1, then:
+ 0·045 NfP + 0·0225 P, - 0·0145 F + 0·002 U c, = 0·005 x, + 0'045 r, + 0,013 F + 0·002 U
C, = 0'005 K,
f
Assuming that the cost per kilowatt installed capacity is the same for both systems, i.e., K, = K t , then the cost per unit for each system will be the same if 0·045 NfPf = 0-0225 P,
+ 0·0275 F. or F =
2NP -P f f 2 t 1·2
In Fig. 2 the contribution to the cost per unit, due to the fuel and processing cost only, is plotted against the value of the fissile material for various assumed values of Pt and NfP,. The price of uranium has been taken as £20 per kilogram. The values of F obtained lie in the region of £5 to £15 per gram and the fuel and the processing cost per unit between 0·2 and 0·5 pence. In the United Kingdom the cost per unit of electricity generated is at present about 0<75 pence. So with the figures taken here one would need to have a value of K of about £100 or £120 to obtain power at a comparable price. This value of K is about twice that for a conventional coal fired power station in the United Kingdom at the present day, and is in line with estimates of the cost of nuclear power stations made elsewhere. The figures taken indicate an allowable blanket or thermal reactor fuel processing
Economic power from fast breeder reactors
45
cost of between £2 and £6 per gram of plutonium, and an allowable total core processing cost for the fast reactor of between £4 and £12 per gram of plutonium. The core processing cost allowable for each cycle will depend on the value of N, the number of times each gram of plutonium has to be processed before it is all consumed. tal
a.
0'61---+-+--+--:::b-'F-~oc----+::
.... III o
0'5p-~:---f-~=""""",""""k---t---:e_
<)
t7I
c 'iii III
gIII 3• 0·31--1"..---j----::::lo~"'F--.p.,._I_=~~..L-----' li; 8 10 'tJ
Q.0·21--I--+"o-t""""'c.;-,.+--!
~:: 0.1
Nf PfTotal core processing £/ gram of Pu.
cost in
$.-
:J
c:
lJ..:I
0 o.......-=--"':-~:-----=--~-:-':---:"-:-~-:-'::--::'=-------\
2
4
f'IG. 2
6. CAPITAL COSTS
The average overall heat rating of the plutonium for the combined fast and thermal reactor system is given by R = RtRtCL G) RtL +RtG
+
which is equal to 0'77 kilowatts per gram using the figures taken above. That would mean an investment of about 5 grams of plutonium and 1 kilogram of uranium per kilowatt installed capacity. In practice, the thermal reactor systems could be started on natural or slightly enriched uranium which would reduce the plutonium investment required by about one half, i.e., to about 2·5 gm of plutonium per kilowatt installed capacity. Taking an average value of £10 per gram for the plutonium this would mean a capital investment of about £50 per kilowatt on account of fuel, but this capital investment would not depreciate. The investment on reactor and generating plant would be about £120, per kilowatt installed. The capital investment on processingplant is difficultto assess, as no published information is available on processing costs. The total capital investment per kilowatt installed capacity is however likely at first to be three or four times that for a coal fired station. However, as the development of nuclear power proceeds the capital investment on reactor, generating plant, and processing plant should be reduced, and the figures given here indicate the target at which one has to aim. With the figures assumed for a combined fast and thermal reactor scheme about 35 per cent of the plutonium invested is consumed and replaced each year, so that the plutonium is used and replaced on the average about once every three years. The amount of uranium used for power generation would be about 0·5 per cent of the uranium processed, so that if the processing losses for uranium were 5 per cent then about 10 per cent of the uranium fed into the system would be used for power
46
C.
A. RENNIE:
Economic power from fast breeder reactors
generation. If the uranium processing losses were only 1 per cent then about one third uranium fed in could be used for power generation. 7. CONCLUSIONS
The generation of electrical power by a balanced fast and thermal reactor scheme is a promising line of development for a country without large resources of homeproduced uranium. In such a scheme it is possible to use a comparatively large fraction of the uranium 238, the actual fraction depending on the economic aspects of the processing losses in recycling the uranium. In a scheme of this kind a value can be assigned to the fissile material, once the other costs are known, so that a comparison can be made with schemes using uranium 235 produced by a separation plant and with schemes using the thorium-uranium 233 system. In general, the use of a combined scheme of fast reactors which breed more fissile material with thermal reactors gives much more flexibility in design, so that it is not necessary to push either type of reactor to its limit, and this may have important economic results. Finally, it is clear that the processing costs for the fuel and blanket playa vital part in the economic assessment of the scheme. They are of about the same importance as the costs of the reactor and generating plant.