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UNCLASSIFIED
ORNL




365


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ORN-P-365
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----- LEGAL NOTICE ----
The report *. preure'n. In occnunt of Choirinment in mrh. Sellder the t'nline
uales, wr Who (saamisol. mar ens porta acuta in De best of the Commission
A. Nahra M ITANTS 1m . rutinnipivo . Impiind, 1 routky the ACOM
mocy, completene... O upelulae.. nie informarlon inul in Wale renurt, wat in
of any informalina omaretur, melon, os ponen. dikloord in woremri mos mi latring
frivolely on Inte, or
. Asworo any lenitive eich cranito Ho v ol, no frie danners renvills from the
WAR :any talismotiv, arrily., meu , no pixe11mlnenin ibla repisi
A. und in the white, "perm M 113 on bail ont de l'ammin.lum" in Iwwe kny mo
Noin or crairarlor of the tor 1ro. amples 1 own controlit, to the riteni waal
à prova di camere door of the Inmminok, or more if sua printre les perre..
dinkonate, or ppasigro ancone, ant informatii urouni Roy Alu rafinonruf or rexeral
ILA U tommi . 1941. minneal *111. rontruint
THE FUELING OF NUCLEAR POWER COMPLEXES
Gale Young
Oak Ridge Nationai uboratory
August 24, 1964
do de presented at tlie Gütiinburg Conierence on "Nuclear Education in
the len ära of luclear Power".
*opezuicà by Union Carbide Corporation, Nuclear Division, for the U. S.
tomic Energy Commission.
WABLE OF CONTENTS
Page to
Oyster Creek and Sait water
Thirty Years to Bowie re
Breeders, Breeders Everywhere
Professor Turner's Million Dollar Theorem
FIGURES ADD TABLES
Figu.', 1
Artist's Conception of a large Desalination Plant in the
Desert
Figure 2.
Artist's Conception oî the Oyster Creek Nuclear Electric
Station
Capital Cost of Yuciear Steam Generating Facilities
Figure 3
Table i
Table 2
Capital Costs of Nuclear Electric Stations
Fuel Cycle Costs
Power Cost Estimates
Table 3
Figure 4
Table
Installca Nuclear Generating capacity
U. S. Uranium Ore Resources
Table 5
Natural Urunium Requirements for H20 Reactors
Figure 5
Ore Costs for i120 and D20 Reactors
8
Fast Brecker
Ficure 6
Figure 7
Table é
Slow Breeder
Fuel Purchase Equutions
Shield Materials
:: 7
Table 8
Reactor Parameters
Equations of Problem
Table 2
Figure 8
Optimum Reactor Power Variation
Table 10
Reactor Parameters
Ovster Creek and Salt Water
Luist December marked the 21st anniversary of the neutron ciiain
se
reaction
is in that were a signal for something, atomic power has
come promptly to life and gonc charving off with a glint in its eye,
much ałter the manner of a new voter in an election rear on his way
co resolve the probiems of the nation.
Symbols prominent in this resurgence are desalination and Oyster
Creek. The former has opened our eyes to the future, and the latter
has usiiered in the present.
Like the reverse of Colwidus cicliting a new supply of land, the
worla has now sichtca ü new sumiy oi iresii water, and the hitherto
guici cumlet or desalination is taken on the ceneral aspect of Cape
Canaveral on stamp day. For several years part Pnil Hammond nad
trouble setting anyone to listen to him about nuclear desalination -
now lie is having trouble keeping out of the way of the construction
tricks.
Figure 1 depicts a large desalination plant. This plant is duai
purpose - it produces a billion gallons of iresh water per day und five
million iilowatts of electricity. These outputs are sufficient for a
good size city, such (6 Chicago. The sea water lagoon stretches for
ü thousand feet along the occun shore, with nine water pipes extending
up to ine large building behind it. This building houses a multilevel
riasi evaporator plant, seven workine stories high. Behind the evapo-
rutor is a long turbogenerator building and behind this you can see the
tos of three dores, cach inousing a nutural urunium heavy water reactor
or 83.
ermal megawatt capacity. In the left distance you see an
Figure 1.
Artist's Conception of a large Desalination
Plant in the Desert (Photo 61012)
(Change title as indicated)
irrigated area blooming in the desert.
Figure 2 shows how the famous Oyster Creek station of the Jersey
Central Power and Light Company will appear. This is the atomic power
plant that has gotten the coal people into such a tizzy.
The significance of Oyster Creek lies in one thing - canita.l cost.
Figure 3 reproduces a plot made a couple of years ago of the unit capital
costs of water reactors.
The Oyster Creek reactor would fall approxi-
mately at the point marked "coal". It is seen that this is substantially
lower than the earlier lignt water reactors, and nearly as low as the
projected costs for the larger heavy water reactors intended for desai-
ination.
Table 1 compares capital costs for complete power stations.
The psychological and business import of the capital cost improve-
ment is very great. For many years nuclear electric capital costs have
118 0
re
been substantially higher than for fossil electric plants, until it had
almost come to be accepted as a matter of course that this was fact and
would remain fact. Presumably this was for reasons connected with radi-
ation, mysteries of the atom, etc.
m'he dispelling of this foc ius veen the great contribution of
Oyster Creek. Actually the gain comes from standardization, quantity
production, scaling up of plants and processes, and design simplification
una compaction. If the automobiles you drive were made only on an experi-
mental basis in lots of a few, they would cost their weight in cold, and
60 also would many other of the products of our industrial civilization.
It 16 a different story, however, when we come to fuel cycle costs,
as given in Table 2. The Oyster Creek fuel costs are rather high, and
would not be attractive for large-scale desalination purposes. This is,

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ARTIST'S CONCEPTION OF THE OYSTER CREEK NUCLEAR ELECTRIC STATION
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UNCLASSIFIED
ORNILR-OVIG 73000R

O GE BOILING H2O
A WESTINGHOUSE PRESSURIZED H2O
U DO MODERATED
COAL
BIG ROCK POINT IT
-
DOLLARS PER THERMAL KILOWATT
OHUMBOLDT BAY
abDRESDENİ-
-- \PATHFINDER -
BODEGA BAY -- -
YANKEE
IVOTA MALIBU BEACH |
Dopo i
DU PONT T TITTTTT
l mSARGENT & LUNDY. ORNI
COALA-A
- - --
SARGENT & LUNDY, ORNL
DU PONT
O SARGENT &
LUNDY, ORNL
-
100
100,000
1000
10,000
THERMAL CAPACITY (megawatts)
Capital Cost of Nuclear Steam Generating Facilities.
5.nst.c.. Süüdies
CS::--, ceragercy3, +
Ĉister Creek
720 Feuctor
cicü cüzde, Low
accroicüs Output, Xw
25, ücü*
7,500
Domains ögo
svo
25,000*
8,300
organic
~2,000
620
30mins ago
تتتتت
Sicerisinde system, $/ioni
Sieraisirs system, $/iwe
Baserricas generating system
Vine
Scica, $/itwe
*೧೦ಟ ಏ he re&cors,
TE. CYCLE COSTS
la nislawa oi electricity)
Pü
Pu Sola
CV
Oyster Creek
Deo ܚܐ܇
Interagency Dzo
c: course, the reason for the heavy wüte: moderator in tre desalinataon
rcüciors: irc kiga reutron economy permits tre use of low-cost rütürül
instinto de idea, urid gives a četter yiciä oi' siew pictoriale dei wicii :s
ürü üürisus operation.
One day orier's epicom ze tiie bio desazinatior. reactors as jour
cards Oyster Creer in size, inc site ús Oyster Creck in wit cüpita:
cosi, are employing the low-cost natürisi uranium. fuel cycle or the i
piutorile production reactors ut fani ori and Savannah River. The cool-
wit in the ORYX design is borziriü pict water, the same as Oyster Creek.
Wat
Tire cost o: power from a reactor is a complex subject involving
ixei-crarse rates on capilisi investment, úccomiting practices, inc
Vädüi oz by product püüicnimi, cüc. 2. Fren will be discussion
these ünings with you quier ünů i wiad roi roure to get into suca
müüters here. I wish orije io illustrate ire rather dramatic change in
the past iew years in the cost aigurus people tack about for ruciear
power.
The last time I mentioned ü number for the cost om atomic power
in a public talk was four years ago.O di that time I remarked as iol-
Ows:
"For those of you who are numero ogists, I have an observation to
report. Since it involves 7 three cimes, it may have some special inner
sisnižicance.
"milie first 7 is the 7 mais per is nour oi electricity that all
wowe central station reactor types wili jead to as trieir eventual power
cost, wäen the fac cas adequate. y supported ineir development - way inis
is so is not known, but it is amply substantiated by mary careilid cost
C::.ico. Second, raido io induoli.c current Coul of power room (
voi conventionally fucecai lililily Owe'r'
inic.
Wird, wiren you drive
kvito it illinis ointion and bliy burcioni Cruaic) gasoline for your cur',
di Costu you ? milis ;cr silowite oi' livist."
Trés, you scc, wils in the good old dayü o: 7 mil power. Wouny
verbuy centri computer le code of lower i'rən the Oyster Creek runc-
Corvot leto linn te maillo, Wirile lar: municipiil
10 rructors lonave veen
estimice velow 2 millo.1,6.," bor ivc liwe government rencloru in jiwa
C
D
iüid rucior service (ouch to 6pmiy ric power 10 gieous vilnici iuri plicitoi),
istie' votimates costo below ios mundos ior the Oyster Creek vyjc inu iwwii
i for the D20 type. caliiki tinizi incit reactor to lurer ulica (Topo
the cost below 1 mill. These varioli cütimates are collected in 0.0 3.
23
fiilid /wiir)
reactor
Pü Sonia
divi sono
ricom
Oyster Creeks
3.3
Pixe'di chiuso
10.
riste!
Lirge 3.202,2, +
1.6-1.3
2.0-2.1
:'Ixes ciradovi,
dilly scale iliel
pianis
ܝܐ
1.5)
1000 libie Oyster Creex?
2000 Xwe do?
1.0
1.4)
lirecciale iuc
into, reduced in-
richant cosi, 95%
load i'uctor
Dibi, in four years we have come i'ron talking about 7 mili power to
die wiris de mill planta starli.. constriction and, under the rost favorable
cubiction, can even onviwillie piercirii the I vil barrior. This is pruity
Licionary wilie und I hacten to iniu tic coberiring absurunce that these coule can
lovici, in fnet, tiny turn around and 60 riolit buck up upain in the not too
visine. luture.
peor the near-icon l'utile', I venturu only the moiicut prediction thut
Cod Critud cost couimtes :or nucleur vlectric ötutions will now - 18 un
Ervutilzy valute to Oyster Creer - bucome about $100/xwc for all known re-
uctox' types.
? MV cars to powder
coountind weinirleri in the otherwisie slowing picture or low-cost
istinc power to the limited wavuni vi' low-cost uraniwn ore known to be
davidcowie.
I trust Mr. Slibur will bring us up to date on the resource
piciure this siternoon - ior ay purjusie's here I wall simply accept at
ii.ce villie ile cinta 0:' ciie
902 ABC Rezort to the Presidente
migure 4 reproduced it risentiscion by linn on the wc forecas. For
ile ürünth 0: the United Sintes nuciuir elcctric syöten. I have extrap-
oliieri che lincar portion o:' live graph back to the baseline at 1989. The
struivit line can also be extrapolated forward and continues to closely
represent tlie sic projection to the year 2000, which is as far as tlie fore-
cist etiended. This simple limur i'it to the power growth curve will be
convenient for subscqucrit illüllysis.
Dei'one louvind ris. do let us time li joou look at the numbers 17-
volved. You have all ovserved the wount of controversy regarding pres-
ervüüion of wildlife and park areas, etc., which has been generated by
UNCLASSIFIED
ORNL-DWG 64-6832

-
---
.
INSTALLED NUCLEAR ELECTRIC CAPACITY (THOUSANDS OF Mvi(e)]
1960 1980 2000 2020 2040
YEAR
Installed Nucleor Generating capacity.
tric Bodega Bay reactor in California. Now the projected nuclear capacity
at the right side of the figure (the year 2030) 16 about equal to 13 times
the present total gonerating capacity of the country. It is also equal to
that of 8500 Bodega Bay reactors. About 10% or the United States' electri-
cal generation is in the southwest region, mainly in California. A simple
calculation will show you that ir 850 power stations are distributed along
the 600 miles of coast from Bodega to San Diego, there would be one station
cvery 3700 feet! Whether they be rucied with uranium or coal or corncová,
this is a lot of power stations. If the stations are made larger, they
can be iartner apart.
Table live shows the estimated total United States uranium resources,
and Table 5 gives the uranium requirements for meeting the postulated
power generation using Oyster Creek type reactors with plutoniun recycle.
It is seen that the reactors built by the year 2000 suffice to drive the
orc cost above 30 $/10. At this price the ore consumed (with plutonium
recycle) costs 1 nill/kwa of electricity, and the ore cost of the fuel
Inventory in the reactor and fuel cycle is about 70 $/kwe.
TABLE 4
V. S. URANIUM ORE RESOURCES
$/10 of U308
5 to 10
Millions
of Short Tons of U308
0.8*
10 to 30
0.7+
30 to 50
50 to 100
100 to 500
2000
* Including geologic estimate of future discoveries.
*Incomplete estimate because of lack of data.
TABLE 5
NATURAL URAVIUM REQUIREMENTS FOR H20 REACTORS
Short tons of U303, cumulative
Committed for
remainder of
Mined plus
plant livest
committed
Year ending
Mined*
1965
1970
3,000
10,000
30,000
1975
3,000
11,000
30,000
70,000
160,000
330,000
1980
1985
1990
70,000
140,000
300,000)
560,000
1,000,000
6,000
21,000
60,000
140,000
300,000
630,000
1,200,000
2,100,000
1995
640,000
1,100,000
2000
*Uranium mined to provide initial inventory and makeup requirements
through the year stated.
The additional amount of uranium that would be required to sustain
operation of reactors built through the year stated. New plants
are all based on a 30-year life.
Assuming the ore cost to rise linearly within each price interval
in Table 4, Dietrich has computed the ore cost per unit electrical out-
put as a function of time. 10 His results are shown in Fig 5. With
H20 reactors the situation blows up in our face in about the year 2000,
the great age of atomic power has come and gone, and we go back to using
coal. As the song goes, "It was great fun, but it was just one of those
things".
UNCLASSIFIED
ORNL-DWG 64-6834

ORE COST (mills/kwh!!
DO
2030
1970
1990
2010
YEAR
Ore Costs for H2O and D20 Reactors.
In this connection Zinn has remarked, 9 "The H20 converter system
18 at best a temporary solution to the question of electricity genera-
tion from fibile material and, at worst, could use up all resources of
cheap uranium with the result that nuclear power as a principal source
of electrical energy would be delayed until exhaustion of fossil fuels
creates a substantial increase in power costs. I believe the scheme
that was followed perhaps accidentally in this country of developing
the H20 converters was perfectly all right because it brought us at a
fairly early date to the realization that nuclear power could be com-
petitive now. But it wasn't the best scheme for protecting our long-
range utilization."
W28
"I believe to make these reactors which protect our resources 18
a hard technical job. It was a hard technical job in 1945 when I started
in on one such project. It didn't go along very fast because no one was
interested in the subject of resources. It didn't seem to be important.
Then we got into the business of trying to make nuclear power competitive
as soon as possible. Now that it may have happened, we are faced with
the problem of how far does that take us. As the AEC report correctly
pointed out, if you generate electricity in amounts anything like the
projection you run out of uranium in 20 to 30 years and it was not worth
all the trouble. You have to give real attention to making it worth
while."
And along the same lines from Commissioner Hayworth, ?1 "It would
be fatal 11 we someway managed it so that the kinds of reactors that
made the highest profits were those that used up our supplies the most
rapidly. It would not matter how good technically a breeder reactor
was; it just wouldn't be used as long as there was uranium to burn in
the others.
"I think this is one of the most important responsibilities that
the Atomic Energy Commission has in this area, that 16, to be sure that
the economics, the kind of reactors that will make the best use of our
resources over the long pull, are reactors that will naturally be used
because they are economically attractive reactors.
"It has been said that if the Government steps out of the reactor
promotion, the power promotion field, that business will take over when
the time comes that we really need power. I submit 1f the question had
been asked in the last century - should we maybe do something about what
was happening to the forests and maybe think about replanting and things
of that sort - the answer might have been given, 'Well, when lumber gets
SCOTC
scarce the industry will take care of it.'
"There is just a time log and it doesn't happen. It didn't happen.
We used up our forests long before reforestation was begun. The same
thins might be said about the exploitation of the western lands, that
when contour plowing became necessary, the farmers would do it, and so
forth; but they didn't. Sure, we have lots of land. We have no trouble
about having enough wheat and so forth, but I submit that the human misery
of the dust bowl days was something that there just is not any recompense
for.
It is a responsibility of the Government to think of these things
long in advance."
Several years ago McKinney warned, 12 "In the long term - beyond the
year 2000 - vast populations and worldwide industrialization presage vast
energy demands which miót tax the finite limits of conventional energy
resources. Science and technology must be put to work now seeking the
solutions to these ultimate energy problems .........., even though
promising avenues toward commercialization are not yet evident. In the
meantime, conscious conservation must take the place of unconscious
waste. Both fossil and atomic fuels must be used efficiently to give
the time needed for the achievement of longer term solutions."
"Assuring the availability and the most effective utilization of
energy resources is the responsibility of Government because it affects
the national welfare and security. Where antitrust regulations, con-
servation laws, and import-export controls have been adequate to dis-
charge this responsibility in the past, direct Government research ....
er
will in the future also be required."
"Present principal avenues of atomic power development aim at
utilizing jess than 1 percent of the potential energy content of ura-
nium. Yet truly low-cost atomic power could make available the full
energy content of world atomic resources, which exceed by many times
over the world's fossil fuel resources. Research directed to this goal
couln, if successful, provide the vast, low-cost, noninterruptible
energy resources necessary to support expanding world populations, both
in developed and underdeveloped regions."
But, "The United States did not orient its own peaceful domestic
atomic activities to support the ....... objectives to which it had
assigned such great importance....... Advanced reactor experiments and
the imaginative ...... research facilities and equipment needed for
successful attack at the frontiers of atomic knowledge were too conser-
vative, too few in numbers, and inadequate to the task.
Instead,
20
activities of the Atomic Energy Commission were primarily directed to
the development of hardware in support of demonstrations of current tech-
nology."
Around the winter fires in a far away land 18 whispered a logond:
of the tribe which got so hungry toward the end of one winter that it
broke the taboo and ate the seed com - and perished from the earth the
next year. Just 10, atomic power has a lot of fertile soil (thorium and
U-238) in which to grow new fuel. But it is now busily consuming its
seed corn (U-235) in the H20 reactors - may it not thereby vanish from
the earth.
Breeders, Breeders Everywhere
If the ladies in the audience will forgive me, I should like to
come to my next topic by way of a story. There were two charming ladies
who were the recognized social leaders in their respective small and very
exclusive communities. One was young and sophisticated and very smooth,
and the other was more the old toughened battle axe type. One day their
paths crossed at a large reception and mutual acquaintances settled back
to watch the fur fly. There was wary circling and parrying for a time,
and the charge in the air built up. Then the younger woman spotted a
slight weakress in the other's defense and like a dagger she leaped to
pour steel through the gap. "Why really, my dean," she purred, "now
very quaint. Now in Nanchuckett we think that breeding is everything."
"Well now, dearie," replied the other, "I wouldn't go so far as to say
that. But even in Scratchassit we agree that it's a hell of a lot of
fran."
OSE
Con is in the atomic power business these days. After being a
2003 reiüiion ia the cioset for many years, suägeniy breeding is every-
whitje te hac is for it, the GAC is for it, the Congress is for it,
the Presideni is cor ii -- even the coal magnates are for ii.
De coas peopie curther wow just how it should be done. They
una ima avor ou sast üreeders as opposed to siom breeders, preswombay
Om
care te crows that to be quick is better than to be taray. Figure ó
SH015 in eariy prototype casc breeder. I believe our Australian irienas
Cüte vouche cor the authenticity oë this modei. Figure 7 depicts a slow
Creeder. mais one takes a bit conser bui bais there just the same.
so zár ús i wow, Oviy xr. Lewis of Canada is not for it. Vr.
mazowice beaty water reucitrs. You will note in Fig. 5 thai the
Punce stays in business much better than the üzü reactors, and
nas beiieves inai its stayino power is good enough that breeders
mään ravi ve teeded. 3 zile change üe rici - the ore suppiy estimates
her i carde up or doing significaniiy, the picture might become clearer
Como respecî. However, r enis eventübiy szeaks thorium into his
CSS
Q
Owe
Srei
S
.
zinciors trà, since his reactors are so gooi in neutron economy, i süs-
cei cani de üsçüüricies manse a rom being a wember in good sianäine
cä iness
me wii-öredér society. In any case, i agree with him in
woroculacij suturas (cr teariy tatürúi) uranium heavy water reactors zor
tin cui inüüse. From ine work on such reactors in large sizes for üe-
süaniinia can we bezieve thai they represent the caeapest source că power
cione pancora non avainagie, una they give a good account of themselves in
conserito ine ore suppiy.
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SLOW BREEDER
26
But I digress. Let us get back to breeders. When Columbus cance
BUL
over he told the Indians about breeders. He told them how there are
rast neutron breeders which have a high breeding gain, but they are
rather concentrated and it is hard to get much heat out so that the
power per unit of fuel inventory is low. And he told them about thermal
neutron breeders which do not have muca breeding gain, but they can be
much more dilute and so give higher specific power. At this point
Coluous wandered oil, leaving the Indians busily arguing as to which
is tre best.
As remarked earlier, the coal people already know the answer to
the problem that is troubling the Indians. Another bit of folklore in
S
.
tre öreeder business can be traced as follows: What red blooded Ameri-
can boy doesn't like a nice juicy profit on a deal - and the bigger and
faster the better? This undoubtedly underlies the popularity of the
chain letter game, whereby you receive a letter for which you pay, say,
& donar, and then you send out five copies for which the recipients
are to send you a dollar each, and so on. You are admonished that it
is very bad luck if you break the chain.
This leads one to wiat might be called the great chain letter
theory of breeding, according to which it doesn't matter how much fuel
re
ve
you have to buy or what you have to pay for it, if only you can make a
iot o: additional fuel in tre turnover. This point of view seems to
reiniorce that o# the coal people in favoring the fast reactor, which
has the highest breeding gain.
However, the serious reason for having breeder reactors is not 60
that we can all get rich selling fuel to each other (have you ever been
25
around a neighborhood where everybody has a garden, when the bumper to-
mato crop comes in?), but rather to conserve the uraniwa ore supply. Let
us therefore consider the matter from that point of view.
We are dealing here with two different figures of merit. High spe-
ci:1. power is good since it reduces the amount of fuel needed to install
a specified generating capacity. High breeding gain is good since it in-
creases the amount of fuel wnich is produced within the power system it-
seli. To consider the interplay of these parameters we assure a prescribed
power growth curve Plt) for the entire nuclear electric system of the
country, and study the effect of the parameters upon the amount of ore
needed to fiel the system.
Let the specific power of the reactor together with its fuel cycle
de p; the specific mass is then m = 1/2, and the total fuel content of
the system is M(+) = m P(t). The net rate of fuel production by breeding
is B(+) = b Plt) where, apart from certain constants, b is the excess of
the usual breeding ratio over unity. With the linear approximation to
the system growth curve shown in Fig. lk, we obtain the results given in .
Table 6.
Fuel is added to the system inventory at a constant rate ma, ile
the rate at which it 16 supplied by breeding is bat. The difference has
at first to be made up by external fuel purchase, but by the time ri/b
breeding takes over the entire job of fuel supply and no more need de
purchased. It is seen that the amount of external fuel (and cre) needed
varies directly with the system growth rate a, and inversely with the
square of the specific power multiplied by the breeding gain. For ex-
ample, doubling the specific power does as much good as increasing the
breeding gain by a factor of four.
26
TABLE 6
FUEL PURCHASE EQUATIONS
Quantity
Power
Fuel inventory
Formula
Plt) - at
m = m = mat
B - OP = bat
am - B -
Breeding rate
Fuel purchase rate
ma - bat
Total fuel purchase
a (ambt Date - Part
Professor murer's Villion Dollar teorem
mere is surely no more popular question in the atomic business,
and no more enthusiastic subject for devate, than "What is the best re-
actox?".
In the remaining moments I would like to indicate for you an
approach to this question that has recently been taken at Oak Riase.
Sometimes the difiiculty wiin a troublesome question is that it is the
wrono question - it is asking the wrong thing. Let me illustrate with
an ex:wile from another subject. Suppose I want to put a lightweight
neutron shield around a point source and I have two materials available,
as indicated in Table 7.
OWN
TABLE I
SHIELD MTERIALS
Removal Cross-Section
Naterial
Density
The second material is something like water, the first is more like
a metal or metal hydride. Material #1 is better in removal cross-section,
buü +2 is better in density. Which one is better? Let us try them out
and see. I make a spherical shield of #2 and it has, say, radius R and
weight W. I then do the same thing with #1; its radius needs be only
hali as great, which gives it one-eighth the volume, but because of the
higher density the weight comes out the same as before.
At this point I might conclude that it is a matter of indifference
how I choose materials. But a wiser man would see more deeply into the
situation and would make a shield with #1 material on the inside and a
layer of #2 on the outside. Then, after adjusting the relative thick-
nesses of the two materials to give the best result, which is a simple
calculus problem, he would have a shield which weighs only 0.53 W.
Evidently the correct question to asis was not "Which material is
best?" but rather, "What is the best arrangement of the materials?".
In
the case of shielding, the simple example cited above has been developed
by Kalos and Troubetzkoy into a powerful method for taking many materials
in a multidimensional property space and determining the right ones to
use and the best way to arrange them.14
This suggests that perhaps Columbus, being a sly rascal, was really
posing for the Indians a more subtle problem than the "which is best" argu-
ment noted above. Table 8, giving relative parameters for two reactors, is
analogous to Table 7 which displayed two shielding materials. According to
the results in Table 6, these two reactors are equivalent in fuel purchase
IS
requirea* when used separately. What happens if we use both of them together?
For present purposes we are limiting attention to the two dimensions -
breeding gain and specific power - that affect fuel requirements; and
shall not go into the many other indiferences between reactors such as
capital cost, operating cost, development time and cost, etc.
MO
w
o
met Fl
....
28
-..
-
-
TABLE 8
REACTOR PARAMETERS
Relative
Breeding Gain
Reactor
Relative
Specific Power
.men
.
#1
......
.
.
.
Into my office at Oak Ridge about two months ago walked Professor
.
.
.
L. H. Turner of the University of Tennessee Mathematics Department. We
talked for awhile about some mathematical questions and when he left he
took the above problem with him. I would like to present his solution
to you now, in its first time on the air, so to speak.
When both reactors are used the total power output is divided be-
tween them in some manner, and we have the relations shown in Table 9.
2
OM
TABLE 2
EQUATIONS OF PROBLEM
Quantity
Total power
Fuel inventory
Formula
Plt) - Bz(t) + Ba(t) = at
M(t) = myP1 + mapa
B(t) = 67P2 + bapa
0 % BZ(t) = P(t)
M'(t) = B(t)
Breeding rate
Boundary conditions
Hinton interior arc equation
It 16 seen that, with Plt) given, the system operating history is speci-
fied by a single function, say Pz(t). It is desired to determine this
tampons
sono
s
oro
29
.
.
function so as to minimize the amount of fuel that has to be purchased
..
.
from the outside. The function being sought must satisfy the boundary
--
-.
condition shown, and may consist in whole or in part of arcs along these
boundaries. In solving the problem Professor Turner made use of a result
inolvit..:*
due to Hinton which states that if the solution has any interior arcs
,
(i.e., arcs not on the boundary), then the relation shown must be satis-
i
fied along these arcs.
.- .-*-:iice
-
re..
"**
-
..
-.
--
.
Figure 8 displays Professor Turner's solution.15 In this diagram
t2 = m2/02 is the time at which fuel purchase ceases for the #2 reactor
used alone, and ty 16 the corresponding quantity for the #1 reactor. In
Turner's solution 72 = P out to t#, and then decreases along a Hinton arc
to zero at üz.
With the data of Table 8, ta = 3t2 = 12t* and the amount of fuel
purchased in Turner's case is 41% of that for either reactor used alone.
se
-**...-
-
..
When Turner's results came in we were not too surprised by the
factor of 2 saving in ore requirement - we had been suspecting something
like this from earlier considerations - but the time scale of the reactor
use pattem was to me slightly astonishing. If we say the #1 (high gain
or fast) reactor has a doubling time ty of 12 years, then that of the #2
(nigh specific power or thermal) reactor is 36 years, and t* comes out to
be only three years. Thus we would build fast reactors for three years
only, and then start shutting them down! Since there might be some objec-
tions of a non-ore nature to tearing down brand new plants, the problem
was changed slightly to specify that a plant once built is to be kept in
operation for 30 years. With this change, the Turner fuel requirement
rises to 50% of that for either reactor alone.
UNCLASSIFIED
ORNL - DWG 64-6833. i
> Plt)

POWER
1
P.17)
k
e***02> TIME
L
ys
?
Optimum Reactor Power Variation.
32
low is the ricü iliustration, the first two ore classes in babies
cca. 1.2 ä сoc retric tor.s ci ürüninAt 3.3 grams of tiel per inte
vi con un risc ürwie wieg * this amourt of cre wouia provide 4 x 200 kg of shiel.
o con cucior and sunt power conversion erficiency, the reactors of
Dubovic wound buco requiere
X kg of thel purchase when used sop-
.تنام ما
19 20
FEACTOR PARTES
Specific power
Kontlic
Breedins
Gain
770
.18
..02
2300
MO
C. civi che idris muca ore, 606wing with Dietrich a linear variation of
wie cui minn euch cre cilss, is jū x 80% dollars. If we use both
rucivis de ü Dürer puiiem, tie imoürii oi ore is cut in huis and its
cini in reduce to x ius comúrs. Thus, the reduction in ore require-
to 29 Dei coniurs. I consequently trust you will agree
whüü have rated Professor Trimer's theorem conservatively in the section
este
d
Onse
.ته: نثم نامه
.you مفتذة :
*mas üpproximates the yield of thermally fissionable plutonium from
Conü randen beavy water reactors. The yield of fuel from gaseous
diri usion. plants is about 50% greater.
32
REZERCES
i. Á M. Weinberg and Gale Youns, "Scale, Nuclear Economics and Salt
Water," Vucicar Xews, p. 3, May 1963.
2. I. Spicwas, "A Lurce Desalinization Reactor Based on Current Pech-
noiocy," Nucleonics, p. 6lt, Jul: 1góź.
writeracercy Task Group, "An A6sessment or large fucicar Powerco Sec
hüter Distillation Plants," orrice of Science and Technolocy Report,
March 1964.
4.
ucitel Corp., "iarce Reactor Study for Sea Water Distillation,"
wc Report TID-19267, July 1963.
Jersey Central Power and Light Company, "Report on Economic maiysis
for Oyster Creek Nuclear Electric Generatira Station," Nucleur rews,
April 1964.
6. Gale Youns, "Frontiers Require rindamentals," Nuclear Congress,
April 6, 1960.
7. J. A. Lane, "The Economics oz & Reactor-Diriusion Pleunt Complex,"
(ORL internal memo), July 1964.
8. ABC, "Civilian Nuclear Power - A Report to the President - 1962,"
and Apendices.
licurings on "Developmenü, Growth, and State of the Atomic Enercy
Industry," Part 2, p. 681, April 1963.
10. J. R. Dietrich, "Eificicnt Utilization of Nuclear fuels," Ponur ius
ictor Technology, p. i, Puli 1963.
L. j. Haworth, liearings before the JCtz on "Developent, Growin, and
Stute of the Atomic Enercy industry," Part 2, p. 819, April 1903.
12. Report to the JCAE, "Review of the International Atomic Policies and
Programs of the United States," Vil. 2, pp. 48, 77, 78B, 78), October
1960.
13. W. B. Lewis, "How Much of the rocks and the Oceans for power? -
Exploiting the Uranium-Thorium Fission Cycle," DM-72 (AECL-1916)
April 1964.
iht. E. S. Troubetzkoy, "Minimum Weight Shield Synthesis," UNC-5017, Part
ds, October 1962.
25. L. H. Turner, (work in progress), 1964.
DATE FILMED
12/ 9 / 64



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.
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