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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS -1963
ORNA 2532
NOV 2 9 1966
HC.E. /.002.50
Conf-660934-1
MASTER

Calculating Fuel Cycle Costs for Light Water Reactors*
by
J. A. Lane
For Presentation at the IAEA International Survey Course
On Economic and Technical Aspects of Nuclear Power
Vienna, Austria, September 5-16, 1966
LEGAL NOTICE

· RELEASED FOR ANNOUNCEMENT
-
-
-
IN NUCLEAR SCIENCE ABSTRACTS
Tus report was prepared as an account of Government sponsored work. Neither the United
States, nor the Commission, nor any person acting on behalf of the Commission:
A. Makes any warranty or representation, expressed or implied, with respect to the accu-
racy, completeness, or usefulness of the information contained in this report, or that the use
of any information, apparatus, method, or process disclosed in this report may not infringe
privately owned rights; or
B. Assumes any liabilities with respect to the use of, or for damages resulting from the
use of any information, apparatus, method, or process disclosed in this report.
As used in the above, "'perkon acting on behalf of the Commission” includes any em-
ployee or cc .tractor of the Commission, or employee of such co'Itractor, to the extent that
such employee or contractor of the Commission, or employee of such contractor prepares,
disseminates, or provides access to any information purnuant to bio employment or contract
with the Commission, or le employment with such contrattor.
Y
"
.
"
Research supported by the U. S. Atomic Energy Commission under
contract with the Union Carbide Corporation.
f
17
tu
2.
-
Introduction
Unlike conventional plants in which fuel costs are determined merely
plant, nuclear fuel costs involve a series of fuel cycle operations, the
costs for which have to be added to obtain total costs. Figure 1 shows
what these operations are for light water reactors fueled with slightly
enriched uranium dioxide, Superimposed on the costs for these individual
fuel handling steps are the interest charges on any outstanding capital
investments associated with the fuel cycle. These latter costs are
called the working capital component of fuel cycle costs.
As seen in Figure 1, uranium as mined is processed into a form of
natural uranium ore concentrate (U308) and is subsequentiy converted to
natural uranium hexafluoride (UF) and enriched in the isotope U-235 in
AEC facilities. The enriched uranium hexafluoride gas is converted to a
uranium dioxide (UO2). pellet or powder form and contained in zirconium
tubing suitable for reactor use. After irradiation for production of
power, fuel is reprocessed to recover uranium and plutonium and to remove
fission products as wastes. The depleted uranium iş then converted into
UF. and returned to the U-235 enrichment plant.
Total fuel-cycle cost to electric utilities therefore includes
several component costs which are: depletion cost, fuel fabrication
price, recovery cost, including spent-fuel transportation and reprocess-
ing, and fuel-cycle carrying charges. Plutonium, which is produced will
be used for future fuel, and its value should therefore be subtracted
from the above costs to determine the total fuel-cycle costo
...
The recovered f'issionable inaterial (üranium and plutonium) may,
under AEC leased fuel arrangements, be returned to the
or, under pri-
vate ownership, may be sold by the owner to fuel processors or retained by
the owner for use in the manufacture of future fuel for its plants. In
the case of privately owned plutonium, it may also be sold under certain
conditions to the AEC for development programs. , The U, S: Atonic Energy
Commission controls the price of enrichment services, as well as the re-
purchase price for plutonium for development programs. Optional private
ownership with toll enrichment services becomes available in 1969. with
mandatory private ownership in 1971 (mid-1973 for fuel leased prior to
1971). Fuel cycle costs after 1969 are based on private ownership Ex-
ercise of ownership rights remains. subject to AEC licensing authority.
Utilities purchasing light water reactors from U. S. suppliers can
usually obtain a number of guarantees relative to the performance and
costs of the nuclear fuel for the first 3 to 12 years operation of the
plant. The General Electric Company catalogue, for example, lists costs
of fabricated fuel (enriched to approximately 2.5% J-235) for reactor
cores ranging in size from 50 MWE to 1000 MWE as shown in Table 1.
.
1
1
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V
UNCLASSIFIED
ORNL-LA-DWG 36163

REACTOR
S pent Puel
FUEL
FABRICATION
STORAGE
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SHIPPING
Tolle
Plutonium
RE.
ENRICHMENT
CHEMICAL
PROCESSING
30g Makovo
Uronium
Waste
U-NITRATE
TO UP
The u236.4230, slightly enriched Uranium fuel cycle.
Figure 1
N
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- 3.
Table 1
General Electric Fabrication Prices (May 24, 1965)
Net Plant Racing
MWE
Non Reheat Plants
18t Core
2nd Core
3rd Core
Total
Total
Total Core
$/kg $ Thousands $/kg $ Thousands $/kg $ Thousands
145 1,360 145 1,360 145 1,360
99 6,210
5,822 84 5,283
96 10,027
9,358
8,367
94 14,800
13,659 78 12,207
94 19,643 86 18,121 77 16,139
50
300
500
750
1000
93
80
Reheat Plants
Net Plant Rating
MWE
300
500
750
1000
99
93
$/kg $ Thousands $/kg $ Thousands $/kg
6,133
5,752 - 84
96 9,883 89
9,224
80
94 14,586 87 13,462 717
94 19,357
86
17,858 77
Thousands
5,220
8,247
12,030
15,904
These cores are warranted by GE to obtain average exposure levels of
16,500 MWD/MT for the first core and 22,000 MWD/MT for the second and third
cores. The prices for fabrication include, the conversion of UF: to UO2
powder, processing of the powder, fabricating of fuel bundles and the
following services:
(a) A core loading and repositioning schedule or revision as
necessary,
(b) Reactor operating conditions and limits or revision as
necessary,
Physics and fuel exposure calculations,
Safeguard calculations on fuel,
Provision of shipping containers for fresh fuel including
return transportation for GE reuse.
Although not all of the nuclear fuel cycle operations are under the
control of the reactor supplier, guarantees of overall nuclear fuel costs
have been negotiated by nuclear plant purchasers. The Tennessee Valley
Authority, for example, was able to obtain from GE a warranted cost or
heat supplied by the reactor for the first 12 years operation of their
Brown's Ferry Plant (consisting of two 1100 MWE boiling water reactors).
This ranged from 14.9€/million Btu (1.57 mills per Kwhr) in 1970 to 10.34/
million Btu (1.09 mills per Kwhr) in 1982. In most cases, however,
nuclear plant owners have negotiated separate contracts for the Individual
fuel cycle operations.
Estimated fuel cycle costs for boiling water reactors based on GE'S
fabrication costs and warranted performance are given in Table 2. Similar
ཟླ
Cost Items
Table 2
Estimated Fuel Cycle Costs Based on General Mectric Guarantees
Het Plant Rating (WB)
Ist Core (1970-7lond
- aa em szes 1c4)
n ་ o 70_ im_ o_ ༧n, o_ 750_ m_
/
o_
p_
Ind Core (1977-81 lond)
n_ o 70_ im_
-
(MBTU)
U Depletin
Pa Creilles
Recovery
Fabrication
Fuel Cycle Financing Cost
4.5
13Ass
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Kon-Reheat Plants
U Depletion .
Pa Credit
Recovery
Fabrication
Fuel Cycle Pinancing Cout
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ཟླཙུནྟི ནྟི
ཊྛིཏྟཱ སྒྱུ $ ཡུ ཚུ ཤཱ ཉྙོ 11 | }} {།
བྱམནྟི བྷཱུ ཙྩོ }} { }} |
༦ ཙྪཱ བྷྱཱ EQWEཧཱུཾ་
།
ཙྩ བྷཱུ བྷྱཱ
ཨཱུ ༔ ༅ WW ཨཱ ༔ {{ }}} ༑
བྷཱུཏྟཱ བྷྱཱ ཙུ ཝུ ཨཱ བྷྱཱ ཙ ་ཙ ནཱ ཉྙོ ཙྩོམ།
ཚུཉྩནྟུཏྟཱ བྷྱཱ ཙསུ ཤུ ༔ ༔ ༔ ཤུ ཤྩ
མ ཤཱཥཱ ཉྙོ ཙW ཉྙ
༩ཙུག %
ཨཱི ཨཱི ཨུ བྷཱུ
ཆུབློབུ ཝུ བྷྱཱ
ཨུ་ཝེ ཨཱི
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Total
( མ) -
Bebeat Plants
U Depletion
Pe Credit
Recovery
Fabrication
Fuel Cycle Pinancing ini
，
}}}}}
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Total
1ss 1s1.
1
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Pued cost Asgatalans
(11 Values Are Based on Deivate Ownership of fuel)
Core Lond
Betective Date
༠༠
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s:
Basis for Us Vanes:
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Couversion to W6, $/100
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Seperative cost, fait
at
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Recovery, $/kg U
. 1.༠
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Fuel Cycle Piomacing Rate
hai da cart
Irradiation and post-trradiation
inventory rate :
Notes:
che Betective Date" indicates year that valves are assumed to be in effect.
pissile platonium in form of nirate (13).
Includes spent fuel aansportation to reactor to reprocessing plant and reprocessing wraniu to Ws toms and plutonium to ritrate taxi.
•
，
，
•
• 5.
guarantees and similar fuel cycle costs, of course, are available from
other suppliers of light water reactors such as Babcock and Wilcox,...
Combustion Engineering and Westinghouse Electric Corporation. The GE
data given here are only for illustrative purposes.
Guarantees obtainable from nuclear plant suppliers; however, are
apt to cover only the first several years of operation of a nuclear
plant. Even though these first years cperation are very important from
the standpoint of nuclear versus conventional power economics, in order
to decide between these two types of plants, prospective buyers should
look beyond these first years and evaluate the influence of subsequent
years fuel cycle costs. The following peragraphs will illustrate the
techniques and principles involved in such an evaluation.
Cost of Natural Uranium (as U208)
The present free world price of natural uranium ranges from $10 to
$13 per kg UzOg. It is anticipated that this price might be maintained
during the next decade; however, after that time increased demands will
probably push the price toward per kg. 'The discovery of extensive
bodies of low cost uranium ore, of course, can alter this situation. In
view of treee uncertainties it may be prudent to evaluate fuel costs in
the 1980 to 1990 period on the basis of natural uranium at $19/kg U30g.
Preparation of Diffusior. Plant Feed
The current V.S. AEC cost of converting U30g to Ufo is about $2.50
per kg 4,0g. By 1970 this price may drop to $2.00 per kg and by 1980
to $1.00 per kg, This would make the total cost of natural uranium fed
AEC base price of $23.50/kg U as UFG.
Uranium Enrichment Coste
The cost of enriched uranium is given by the equation,
%-¢¢ (5)+ < (1)
where, C = cost of reactor feed material, $/kg U
Ce = cost of natural U as UF6, $/kg U
C = cost of separative work, $/kg S.W.
F/P = kg natural U/kg reactor feed
A/P = kg S.W./kg reactor feed.
F/P (fourd from uranium material balance equations). 1s given by
517
W
hy
'
.6.
where, Xo = reactor feed enrichment, 8 U-235,
X, * diffusion plant tails (waste) enrichment % U-235
Xp = U-235 enrichment in naturai. U = 0.71% U-235.
AP (found from diffusion plant material balance equations) is given by
4/8 = (V- V)- (V - Vio
. .
where, V., = 2-2)
ve
(1-
Vp = (1-2),
)
en = natural logarithm
The optimum diffusion plant waste concentration, Xw, depends on
the ratio of feed costs to separative work, costs as shown in Figure 2.
At the present time, U.S. AEC charges for U-235 enrichment are $30/kg
S.W., and according to the U.S. AEC proposed toll enrichment criteria
(for enriching privately owned natural uranium in government owned
plants) this price will be maintained as a ceiling subject only to
escalation based on power and labor costs. Using the $30 kg S.W. & 8 .
a basis and assuming that natural uranium will amount to $23.50/kg U,
the value of CF/CA 18 0.79. From Figure 2, the optimum diffusion
plant tails assay 18 found to be 0.2534 U-235. Use of this value of
Xow in the above equations would give the minimum cost of enriched
uranium for CF = $23.50/kg and CA = $30/kg.
In the proposed toll enrichment criteria, the AEC has taken the
stand that it has to be in a position to select the tails assay--in
other words, determine quantities of feed material to be furnished in
relation to the quantities of enrichment to be delivered--in the interest
of ansuring optimum plant operation. This means that the amount of
separative work to be performed will be determined "in accordance with
the then-current standards table of enriching services published by the
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- 8.
AEC". The possibility of later customer selection, presumably if ex-
perience shows that only a small range of enrichment generally will be
l'equired after all, was held out in the following note in the criteria:
"The initial table, as presently contemplated, will not provide to the
customer the flexibility to select a quantity of feed and an amount of
separative work other than those specified in the AEC table. However,
the AFC is giving further study to the question of providing, at some
date in the future, a form of contract under which flexibility would
be available."
For any given tails assay xi., the amount of natural uranium feed
per kg U-235 in the reactor feed" (F') may be found from Figure 3. This
value of F' may be converted to F/P by multiplying by the U-235 concen-
::tration in the reactor fuel. For example, at Xw = 30025 and Xp = 0.02
(2% enrichment) F' = 192 kg U per kg U-235 and F/P := 3.84 kg natural U
per kg enriched U.
by the initial fuel enrichment.
Thus A/P = A'(x):
Value of Depleted Uranium
The credit for depleted uranium can be found from the same equations
given previously by substituting for the reactor initial, enrichment, 3
the reactor fuel discharge enrichment (or from Figures 2-4). When the
discharge enrichment is below that of natural uranium, the value of the
depleted material can be conveniently found from Table 3 for the given
costs of natural uranium and separative work:
Table 3
Value of Depleted Uranium
(Basis $30/kg S.W., $23.50/kg nat. U as UF6)
wt % U-235 $/kg U
3.00
3.00
3.70
4.60
5.60
6.65
7.75
8.90
10.10
11.35
12.65
13.95
15.35
18.90
22.60
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A. WASTE CONCENTRATION
Fig. 4.
-
.
-
. - 11 -
Credit for Plutonium Recovered from Depleted Fuel
Normally, the anticipated concentration of plutonium isotopes in
depleted reactor fuel is obtainable from the fuel supplier and based
on detailed physics calculations for the given core loading. When such
data are unavailable, the credit for plutonium from spent fuel can be .
estimated from the data in Table 4, based on representative light water
reactors. ii .
!
.. : ::: . .. ...
Table 4
:
- Fissile Plutonion Concentration in Spent ::
Fuel for Representative Light Water Reactors
Average Exposure,
MWD/MT
Fissile Plutonium (Pu-239, Pu-241).
Concentration, grs/kg U
m
.
..
.
.
....
.3.5 H
4.2 .is
... 4.8. :
:
D
10,000 . ...
15,000 .. ..
20,000 ..
25,000
30 000..
.
35,000 .i.
.
.
;
;
..
..
.
.. 15.4
. 5.6
..
!
The credit for plutonium in $/kg U is found by multiplying the Pu
concentration by the value of fissile plutonium in $/gram (as nitrate).
This value depends on whether the plutonium is subsequently used in the
same or other light water reactors (in which case it is worth about: 75%
to 80% of the cost of highly enriched U-235) or in plutonium fueled fast
breeders (in which case it is worth up to 1.5 times the cost of highly
enriched U-235. For the given economic conditions ($23:50/kg U, $30/kg A)
the cost of fully enriched U-235 i /gram. Thus, the value of fissile
Pu might range from $9.00 per gram to $18 per gram in the 1980-1990 period.
Fuel Element Fabrication Costs
Fuel element fabrication costs in oxide fueled light water reactors
depend not only on the characteristics of the fuel bundle (rod diameter,
rod number, method of spacing, etc.) but also on the method of inserting
the oxide in the rods (pelletizing, swaging, vibratory compaction) and
the size of the fabrication plant (kg y daily or annual throughput).
Thus, it is very difficult to predict what future fabrication costs might
be in the 1980-1990 period. Some indications of possible fabrication
cost reductions are as follows:
a) Process Improvement - The use of vibratory compaction of
VO2 powder should reduce fabrication costs by 10-15% ac-
cording to ORNL studies (ORNL-3686).
(7) Rod Diameter - Experience may indicate that it is possible
to operate with slightly higher centerline temperatures than
- 12 -
in current designs resulting in permissible increases :
in rod diameter. A 100 increase in diameter would re-
sult in approximately a 20% reduction in fabrication costs.
.
c) Size of Industry - During the early 1970's, the capacity
of fuel fabrication plants will be of the order of several
tons per day each. By 1980, the average size of fabrication
plants will be about 5-10 tons per day resulting in a 30%
decrease in fabrication costs compared to 1-2 ton per day
plants.
--
-
-
.
.
· If all of the above benefits materialize, fabrication costs will
drop from $80-90/kg in the 1970's to $50-60/kg in the 1980's.
Reprocessing Costs
Processing of spent fuel during the early 1970's will be mostly
carried out by Nuclear Fuel Services, Inc., in a plant which has a
nominal capacity of 1 MIU per day. The cost of processing is based on
a daily charge of $23,500 per revenué day (processing days plus turn
around days) subject to escalation. Fuel enrichments up to 3% and
burnup up to 30,000 MWD/MT can be handled by the plant; however, through-
puts decrease with higher initial enrichments than 30% (880 kg U/day at
4%) and the number of processing days for a given batch of fuel increase
correspondingly.
Tlne standard MFS turnaround time requirement is 8 days or one-third
of the processing days, whichever is greater. For batches requiring
less than 8 days to process, the turnaround time can be reduced to equal
the process time down to 2 days) provided that these small batches can
be combined with other small batches by NES. Thus the minimum processing
cost in the NFS plant is
: (1.33) 23,500 - $31.4/kg U
1,000 kg
and the maximum processing cost of "standard fuel" is $47/kg U. Anti..
cipated increases in the size of chemical processing plants may reduce
these costs a factor of two by 1980.
Interim Waste Disposal Costs
The NFS charges include interim storage of radioactive wastes and
eventual perpetual maintenance of storage tanks for light water reactor
fuels.
Spent Fuel Shipping
Computer codes have been developed at ORNL for calculating the
dimensions and optimum loading of spent fuel shipping casks for any
given type of spent fuel (ORNL-3586). Table 5 shows the results for
light water reactors as a function of exposure level.
- 13 -
Table 5
Exposure,
MWD/MT
Cooling Time,
· (From Reactor ..
to Shipper) days
Delivery: Tiré,- Shipping cost,(2)
Days (1)
kg US
20,000
25.000
:
:. .::.
....
.
150
150
150
150
00.000
.:
.
..
:
.2.41 :,
2.923
3.39 11.
4.21
35,000
.
.
.
Basis: (i) 1,000 miles between reactor and process' plant
(2) Costs include cask handling, insurance round trip
freight by rail, all fixed charges on shipping cask
.. investment: : ..
..
;
Conversion of UNH to UF6
The AEC currently charges $5.60 per kg U for carrying out this con-
version step. It is anticipated that this cost might be reduced to $3.50
per kg by 1980 based on the availability of privately owned facilities
for carrying out this step.
The Relation of Unit Fuel Costs to Power Costs
by,
24(Burnup, MID/MT) (Thermal efficiency, /100)
a) The economic parameter of importance here is the price (and
Talue) of fissile (and fertile) materials as a function
The fuel processing or "handling" costs, including any chemical
conversion steps, fuel fabrication, shipping, recovery of spent fuel
and losses are given by,
1000 Etc. + Cp + C + Cm + C) $/kg
24(Burnup, MWD/MT) (Thermal Efficiency, %/100)
a) The economic parameters of importance are the unit processing
costs themselves and the magnitude of assumed losses in each step.;
Sw
- 14 -
Working Capital and Special Nuclear Materials
tch
Nin..
..
Normal working capital (cash on hand for salaries, materials,
supplies and other out-of-pocket expenses) is a non-depreciating asset
and not subject to all of the charges applied to the "book" value of
the investment. For example, Pixed charges on capital invested in
stocks of coal or oil are often based only on the cost of money depend-
ing on local laws, etc.
.
In the case of a nuclear plant, a certain amount of working
capital is required to support the fuel cycle because certain fuel cycle
expenses lead the fuel cycle revenue in time. At the present time these
include fabrication investment charges and other Fuel handling charges
however, the charges for fuel inventory are not included since this is
presently leased from the AEC. Under private ownersh2p, investment in
nuclear fuel would become part of working capital.
Fuel working capital and charges can be computed from the
following equation::
#jag s [co, + x + v1+ 9 +)+ Cpu - «x3]
Hiere, i = annual carrying charges on working capital, fractional
interest rate per year,
ty = preirradiation holdup, yrs,
= fuel residence time in core, yrs,
Nut
tq = post irradiation holdup, yrs,
Cp - fabrication cost, $/kg U,
V, V. - initial, final U value, $/kg U,
Cru credit for Pu, $/kg U,
C = all recovery costs, $/kg 0.
Costs in $/kg can be converted into mills per Kwh by dividing by exposure
and thermal efficiency as in previous equations. Examples of the break-
down of fuel cycle cote for light water reactors are summarized
Tables 6-9.
. - 15 -
Table 6
Fuel Cost Technical Bases.
Light Water Nuclear Electric Plants
First
Core'
Replacement
Fre!
800
2570
167
880
2820
167
Rating
eMW net
UMW
Uranium Loading, MTU
Uranium Enrichment, % U-235
Initial
Discharge
Kg Uranium Discharged per kgu Charged
Fissile Plutonium Diecharged, Grams per
initial KgU
Fuel Exposure and Energy Equivalence
2.01
0.80
0.976
2.37
0.81
0.970
4.4
106' BTU/KGU
eMWH net/KgV
Fuel Specific Power, tMW/MTU
Fuel Residence Time in core, Full Power
Years
..
16.5
1350
123
15.4
22.0
1800
165
16.9
.
2.9
3.6
Table ?
Fuel Cost Economic and Operational Assumptions
Light Water Nuclear Electric Plant
First
Core
90
30
.2.7
Early ::::.
Replacement
80
:.5 .
301.
2.7.
0.299..
. 8.5 ....:
6 . ,
32
8.5
Fabrication Price
Natural Uranium Price, $/1b U308
Separative Work Price, $/ib kgU
Conversion of Natural U3Og to UK
Cascade Tails Assay, % U-235
Plutoniun Credit $/gram fissile
Post Irradiation Shipping, $/kgU
Chemical Processing,
Conversion of UNH to UF
Ex-Core Inventory Holdup Time, Years
Working Capital Charges,
Plant Capacity Factor, %
Fuel Losses in Spent Fuel Recovery, %
Uranium
Plutonium
.
6
1.5
10
.
.
.....
1.0.
10
80
1.3
1.3
1.0
• 16 -
Table 8
Uranium Prices at Specific Assays
(Pricing Assumptions Given in Table 7)
Weight % U-235
in Uranium
0.80
0.82
2.01
2.37
$/gram U-235 at 90%
$/kg U as UF
21.1
21.8
116.4
148.2 :
10.22 :::
:
:
:
Table 9 :
:
: :
:
:
Fuel Cost Results
Light Water Nuclear Electric Plants
Component
800-880 eMW Net
Specific Costs ..
100
e
. Fuel Cost, M/KWH
.
Direct
Indirect Total
First Core
Fabrication
90.0 18.8
Feed Uranium ... : 116.6 24.2
Discharge Uranium (20.3). 4.2
Spent Fuel Recovery.44.0 *
9.1
Plutonium
(37.0) 7.8
Total :
15.0
19.4.
3.4
.7.3
0.73
0.95
(0.16)
0.36
(0.30)
.1.58
0.19 0.92
0.24 1.19
0.04 (0.12)
(0.09) .0.27
20.08 (0.22)
0.46 2.04
Replacement Fuel
Fabrication
80.0
Feed Uranium
148.2
Discharge Uranium.. (20.9)
Spent Fuel Recovery., 42.0
Plutonium
(40.4)
Total
15.2
28.1
4.0
8.0
7.6
13.4
24.7
3.5 .
.7.0
6.7
0.49
0.90
(0.12)
0.26
(0.25.)
1.28.:. :
0.13 .0.62
0.24. 1.14
0.03. (0.09)
(0.07) 10.19
0.07% (0.18)
0.40 :.1.68
.
F
.
.
Note: Values in parenthesis are negative. ;

END
DATE FILMED
12/ 21 / 66




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