J. Nuclear Energy, 1954, Vol. 1. pp, 39 to 46. Pergamon Press Ltd.• London

ECONOMIC POWER FROM FAST BREEDERREACTORS

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 consumeand thermal reactors which are not quite self-sustaining in fissile material offer an attractive lineof development for a country without large reserves of uranium as in this way it should be possibleto 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 discussedand some estimate made of the allowable costs in such a system. A value can be assigned to thefissile material once the other costs are known and this would enable comparisons to be made withother schemes for generating electrical power from nuclear fuels.

1. PROSPECTS

NUCLEAR power stations are attractive as they offer the possibility of using naturaluranium or thorium as a new source of fuel for producing electrical power. The scaleof this source of power is large as the fission of one gram ofuranium or thorium wouldproduce about 800 kilowatt days of heat, and assuming a thermal efficiency of 25per cent to 30 per cent, that is about 5,000 kilowatt hours of electrical power. Thepresent consumption of electricity in the United Kingdom is about 6'1010 kilowatthours per year, which could therefore in principle be supplied by the completeutilization of about 12 tonnes of uranium or thorium each year. The problemis to develop this vast potential source of power at a cost which is acceptablefor general use.

The chief systems for utilizing uranium and thorium are tabulated in Table I,together with their most important features, and the following commentscan bemade.

(a) It has been announced that it is possible to produce more than one atom ofplutonium for each atom of uranium 235 consumed with system (8), and it is likelyfrom the published information that system (7) would produce more plutonium thanit consumes.

(b) No information is available on system (6), but one can hope it would be atleast self-maintaining in fissile material.

(c) From the information published on systems (1), (2), (3), and (5) one wouldexpect 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 bestit would be self-maintaining in fissile material.

All the types of reactor considered involve recycling of the fuel except the firstsystem. Although the first system may at present be the least expensive, it means acontinuous feed of natural uranium as it seems doubtful if more than about one percent .of the uranium can be utilized. In the long run this first system could onlybe ofinterest to a country with very large reserves of uranium ore which can be extractedcheaply, 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 ofnecessity try and use a much largerfraction of the uranium, by adopting one of the other systems involving recycling ofthe fuel.

TABLE I-SOME POSSIBLE TYPES OF POWER REACTORS

Remarks

Separation plantneeded for U,ss withfeed of natural uran­10m

ILarg: uranium re­quirement

U·ss separation plantneeded for recyclingto save uranium

Pu

u'SS

No

Yes

Yes

1

Recycling I Productof fuel

FeedMaterial

Natural U

Natural orEnriched U

U'SS and Thorium

Negative

Negative

Negative

IOverall I

Gain FactorType

ThermalConverter

ThennalConverter

TbennalConverter

IFissile I Source ISystem Material Material

(I) I U's~ I I(2)1~1--=-I----I----I------I---I----[--=:----

o)~Tborium

May be self main­taining. If not feedof U·s requiredfrom (3). (6) or (8)

Pu could be suppliedby (2) or (7) or (8)

Separation plantneeded for U,ss withfeed of natural uran­ium

IMay breed U·SSwhichCOUld be used tosupply (3)

I

Could produce U28SIf blanket materialwas thorium

Pu orU·SS

Pu

Yes

Yes

Yes

Yes

Yes

Thorium

DepJetectV

Pu andDepleted V

Thorium andU·s. (1)

Positive

Positive II

Positive (1)or zero

I Negative

FastBreeder

Pu

Pu

(7)

(8) U 28a U·ss or FastThorium Converter

(5)

~~ Thorium FastBreeder

~~ Thorium Thennal Negative orBreeder zero (1)

----------::::--I----I'----I-------,-----j---

2. POSSIBILITIES

Until reactors of the various types have been built and operated any estimates ofthe costs are at the best intelligent guesswork. However, it is possible to examine theprinciples 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 meansthat, providing there is a market for the fissile material, the sale of this fissile materialcan be put as a credit against the cost of generating electricity. The three possible usesof 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 fissilematerial.

The first alternative is limited as the process is divergent in the sense that more andmore reactors would be required to provide a market for all the fissile materialproduced. The second alternative of mobile reactors is also limited, and cannot be abasis for any programme until more information is available. This leaves the thirdalternative of combining fast reactors which breed more fissile material with thermalreactors which do not as one reasonable approach on which to base a large scalenuclear power programme. In a balanced scheme of this type in which the gain offissile material from fast reactors is used to make up for the losses of fissile materialin thermal reactors, the only nuclear feed material required is the source material,uranium or thorium. The initial investment of fissile material could be supplied eitherby converter reactors or by a uranium isotope separation plant or from a stockpile offissile 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 inFig. 1, and discussed in more detail. The other possible combined scheme using theuranium 233-thorium system, i.e., systems (4) and (6) in Table I, is not discussed indetail here but the same arguments would apply to this scheme.

Fissionpr-oducts

Uranium

FIG. 1

3. PRINCIPLES

The basic principles of fast and thermal reactors have been described elsewhere andonly 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 factorL, and the fraction of the fissile material which can be consumed before processing isnecessary 1/N.

The overall heat rating R is the total heat output times the utilization or load factordivided by the total fissile material investment in the system. The overall heat ratingtherefore depends appreciably 011 the hold up of fissile material in any processingplants, 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 obtainedexpressed as a fraction of the fissilematerial consumed after allowance has been madefor the processing losses which arise because the fuel has to be recycled. For a thermalreactor which is not self-maintaining, the overall gain factor isnegative, i.e., an overallloss factor L, but it can be defined in the same way as the loss in fissile materialexpressed as a fraction of the fissilematerial consumed after making allowance for theprocessing losses.

The fraction of fissile material which can be consumed before processing is necessaryl/Nwill be limited either by nuclear considerations or by structural changes occurringin 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 andreduce the amount of processing required to a minimum as each processing cycle willinvolve a loss of material. It is true that at the expense of time and money theprocessing losses could be reduced to a negligible proportion, but in practice somebalance 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 thatrequired 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 afast reactor will be very similar to the fuel processing plant for a thermal reactor, asthe concentration of fissilematerial is much the same, and here the costs of these twoplants have been assumed to be equal. It should be noted that the processing plantsfor these reactors may be different, and one hopes less expensive, than a plant forextracting and purifying fissile material. For instance, in a system in which the fuelis recycled it would not be necessary to obtain a very high decontamination factor forfission 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 reactorsystems has been taken rather arbitrarily as two hundred times the amount of fissilematerial in the system.

4. PROGRAMME

Since the gain or loss of fissile material is proportional to the heat output times thegain 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 mustbe in the ratio of the overall gain factor of the fast reactors to the overall loss factor ofthe thermal reactors. The average cost of generating electricity in the balanced schemewill then be a weighted average of the costs in the two systems.

TABLE II-NOTATION AND ASSUMPTIONS

Item Fastsystem

Thermalsystem

---~---..~~~--~~~~~~~~-~~~--+~-

Cost of reactor and generating plant per kilowatt installed capacityCost of processing fast reactor blanket or thermal reactor fuel per

gram of PuCost of processing fast reactor core per gram of PuCost of Pu per gramCost of U per kilogramCost per unit generated in penceOverall heat rating in kilowatts per gram of PuOverall gain or loss factorFraction of Pu consumed before processing is necessaryThermal efficiency of generating plantInterest rates charged on U or PuDepreciation interest and operating charges on reactor and generating

plantLoad factor of reactor and generating plant (assumed to be a base load

station)Heat equivalent of Pu in kilowatt days per gram

sr,£Pf£F£UCfR!GlIN!

2705%4%

15%

80%800

£F£uCtR t

-Lu«,

27'5%4%

15%

80%800

Average overall heat rating in kilowatts per gram of Pu

Average cost per unit generated in pence

R = R,Rt(L -I- G)"""R;:-tL~-I-:--:R;:-!-:=G:--

- LC,+ GCtC=-L-+-O-'

The notation used and the assumptions made about the fast and thermal reactorsare given in Table II. Using these figures the contributions to the cost per unit ofelectricity generated can be obtained and are tabulated in Table III. The total costper 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

Thermalsystem.__, _ s~~~~ _--';- _

Due to

Fixed charges on reactor and generating plant

Processing of fast reactor core or thermal reactor fuel

Processing of fast reactor blanket

Profit or loss on fissile material

Interest charges on fissile material

0·005 X,

0'045 NIP,

0·45 GP/

-0,045 OF

O·OO4F----.n;--

0-005 K/

0'045N/P/

0·045 LF

0-004F

~

Interest charges and losses of source material0·001 U

~

0-002 UR;-

In one year's operation a fraction 0.45R of the fissile material is consumed and the electrical powergenerated is 2400 R kilowatt hours (or units) per gram of fissile material in the system.

For the fast reactors:0·004 F 0-001 Uc, = 0·005 x, + 0-045 NiP! - 0·045 G (F - Pt) +-R~ + R-

t tFor the thermal reactors:

0-004 F 0·002 Uc,= a-ODS x, + 0-045 NtPt + 0-045 LF +~ +~

For the combined system:

In the expressions for C, and C, the first term corresponds to the fixed charges, thesecond to the fuel processing costs, the third to the profit or loss of fissilematerial, thefourth to the interest charges on the plutonium investment, and the last term tothe interest charges on and the losses of the uranium.

It can be seen that as the price of plutonium decreases the cost of generatingelectricitywill increase for the fast reactor system, willdecrease for the thermal reactorsystem, and will decrease for the combined system. Therefore, at someparticular priceof plutonium the cost of generating electricity from the fast and thermal systemswillbe 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 unitfrom each system are equal, will be determined by the reactor characteristics, theprocessing costs, and the price of uranium, and some estimates of this value are madelater. However, before discussing this question, some general remarks can be madeabout the way in which a combined fast and thermal reactor system should beoperated.

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 auranium isotope separation plant. If this initial price of fissile material is higher thanthe "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 reactorsso that the cost of electricity was reduced to the "equilibrium" value and a surplus ofplutonium was produced. This surplus of plutonium could then be used to start upfurther systems, and the value of the plutonium would gradually fall to the "equi­librium" value as the programme progressed. This picture of the method of operatinga combined fast and thermal reactor system is greatly over simplified as improvementsin processing plants, and in reactor design, will alter the "equilibrium" value ofplutonium as the programme proceeds, but these developments will not alter the mainline of argument.

If on the other hand the price of fissile material either from convertor reactors orfrom a uranium isotope separation plant was less than the "equilibrium" value for abalanced fast and thermal reactor scheme, there would be no point in starting such ascheme. It would, however, become economic either when the cost of fissile materialfrom other schemes had become higher due to an increase in the price of uranium, orwhen the "equilibrium" value had been reduced, by improvements in processingplants and reactor design, to the point where it was less than the price of fissilematerial 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 involvedand see what the cost per unit of electricity generated would be. For instance, if in thefast reactor system G = 0-5 and R, = 0·5 (which would give a doubling period for thefissile material of about 9 years), and in the thermal reactor system L = 0·2 (that is, anoverall conversion factor of 0'8), R, = 1'0, and N, = 1·0 corresponding to 0'5 per centburn up of the fuel if the ratio of U to Pu is 200 to 1, then:

C, = 0'005 K, + 0·045 NfPf + 0·0225 P, - 0·0145 F + 0·002 U

c,= 0·005 x, + 0'045 r, + 0,013 F + 0·002 U

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

2NP -P0·045 NfPf = 0-0225 P, + 0·0275 F. or F = f f 2 t

1·2

In Fig. 2 the contribution to the cost per unit, due to the fuel and processing costonly, is plotted against the value of the fissile material for various assumed values ofPt and NfP,. The price of uranium has been taken as £20 per kilogram. The values ofF obtained lie in the region of £5 to £15 per gram and the fuel and the processing costper unit between 0·2 and 0·5 pence. In the United Kingdom the cost per unit ofelectricity generated is at present about 0<75 pence. So with the figures taken here onewould 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 powerstation in the United Kingdom at the present day, and is in line with estimates of thecost 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 coreprocessing 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, thenumber of times each gram of plutonium has to be processed before it is all consumed.

2 4

t­ala.

.... 0'61---+-+--+--:::b-'F-~oc----+::IIIo<) 0'5p-~:---f-~=""""",""""k---t---:e_t7Ic'iiiIIIIII •g 3 0·31--1"..---j----::::lo~"'F--.p.,._I_=~~..L-----'

li; 8 10'tJ Q.0·21--I--+"o-t""""'c.;-,.+--! Nf PfTotal core processing~:: 0.1 cost in £/gram of Pu.$.-:J c:lJ..:I 0o.......-=--"':-~:-----=--~-:-':---:"-:-~-:-'::--::'=-------\

f'IG. 2

6. CAPITAL COSTS

The average overall heat rating of the plutonium for the combined fast and thermalreactor system is given by

R= RtRtCL + G)RtL +RtG

which is equal to 0'77 kilowatts per gram using the figures taken above. That wouldmean an investment of about 5 grams of plutonium and 1 kilogram of uranium perkilowatt installed capacity. In practice, the thermal reactor systems could be startedon natural or slightly enriched uranium which would reduce the plutonium investmentrequired by about one half, i.e., to about 2·5 gm of plutonium per kilowatt installedcapacity. Taking an average value of £10 per gram for the plutonium this wouldmean a capital investment of about £50 per kilowatt on account of fuel, but thiscapital investment would not depreciate. The investment on reactor and generatingplant 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 howeverlikely at first to be three or four times that for a coal fired station. However, as thedevelopment of nuclear power proceeds the capital investment on reactor, generatingplant, and processing plant should be reduced, and the figures given here indicate thetarget at which one has to aim.

With the figures assumed for a combined fast and thermal reactor scheme about35per cent of the plutonium invested is consumed and replaced each year, so that theplutonium is used and replaced on the average about once every three years. Theamount of uranium used for power generation would be about 0·5 per cent of theuranium processed, so that if the processing losses for uranium were 5 per cent thenabout 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 thirduranium fed in could be used for power generation.

7. CONCLUSIONS

The generation of electrical power by a balanced fast and thermal reactor scheme isa promising line of development for a country without large resources of home­produced uranium. In such a scheme it is possible to use a comparatively largefraction of the uranium 238, the actual fraction depending on the economic aspects ofthe processing losses in recycling the uranium.

In a scheme of this kind a value can be assigned to the fissile material, once the othercosts are known, so that a comparison can be made with schemes using uranium 235produced by a separation plant and with schemes using the thorium-uranium 233system.

In general, the use of a combined scheme of fast reactors which breed more fissilematerial with thermal reactors gives much more flexibility in design, so that it is notnecessary to push either type of reactor to its limit, and this may have importanteconomic results.

Finally, it is clear that the processing costs for the fuel and blanket playa vital partin the economic assessment of the scheme. They are of about the same importance asthe costs of the reactor and generating plant.