c
OAK RIDGE NATIONAL LABORATORY Operoted by
UNION CARBIDE NUCLEAR COMPANY
ees
Division of Union Corbide Corporation
Post Office Box X
COPY NO.
DATE:
October 17, 1958
SUBJECT:
Survey of LQW Enriehment Molten-Salt Reactors
External !Transmittal Authorized
U st e d Distribution
H s t r i b u t i o n Limited t o Recfpients Indicated
TO: FROM:
Ti
158-10-
H. G. MacPherson
Abstract 0
.
-
A rough survey of t h e nuclear c h a r a c t e r i s t i c s of graphite-moderated molten-salt reactors u t i l i z i n g an i n i t i a l complement of low enrichment uranium f u e l has been made. Reactors can be constructed with i n i t i a l enrichments as low as l.Pj$ U-235; i n i t i a l eonversfon r a t i o s of as high as 0.8 can be obtained with enrichment o f less than 2%$ Eghly enriched uranium would be added as make-up f u e l , and such Peaetors could probably be operated f o r burnups as high as 60,000 Mwd/ton before buildup of f i s sion products would make replacement of t h e f u e l desirable. A t y p i c a l c i r c u l a t i n g f u e l r e a c t o r of t h f s class mlght contain an i n i t i a l inventory of 3600 tons o f 1.8% enriched waafm, operated a t 640 Mw (theMnal), and generate a net of 260 Mw ( e l e c t r i c a l ) . The t o t a l f i e 1 cycle c o s t would be approximately 1.3 m i l l s / k w h s , of which 1,O m i l l is burnup of enrlched U-235,
NOTICE This document contains informotion o f a preliminary nature and was prepored primarily far internal use a t the Oak Ridge National Laboratory. It i s subject to revision or correction and therefore does not represent a final report.
Errata f o r CF
58-io-&
Please maice the following changes in your copy of CF 58-io-&: Page 1 (Cover Sheet)
W e change
i n line LO of a b s t r a c t
From:
3600 tons of 1.8$
To:
36 tons of
1.w
Page 2 Make change in next to l a s t l i n e
20
From:
8.94 x 10
To :
8.54 x 10
22
Page 3 Make change ia line 18
/:
I-----
From:
-..
A-
,+-
-2-
SURVEY OF LOW ENRICEMENT MOLTEN-SALT Rj3ACToRs To s u r v e y t h e field of low enrichment graphite-moderated reactors
a number of calculations have been made with the four-factor formula k&= qaf. The following fuel salt was considered: mole $ 20
uF4 Id7,
-
BeF2
70 10
It is probably more corrosive
%ais s a l t has a melting point of about 900’F.
than one mole $ fuel, but i s probably satisfactory for use w i t h atomic concentrations were its follows at 600 L;f
- 175.7
x LOm
- 25.12 x loxf u - 50022 x F - 426.8 x lo2’ Be
-
65OoF, per L.
A. Wnn:
atoms/ce
atoms/cc
atomslec
Fluorine
.0149
Be
.0028
composed of contribution
.0051
The concentration of UF is 2,62 g / c c ; that of urmium is 1.98 g/cc.
4
was assumed to be of density
power of 0.0631 an-’.
The
aloms/@c
The slawfng down power of the salt is 0,0228 cm-’,
L;1
IN OR-^^
Graphite
1.7, with 8.54 x 1020 atoms/cc, and a ‘slowingdown
The graphite was assumed to have a cra = 0.0045 barns*
-3I n the four-factor formula, 7 is taken f o r convenience t o be t h a t f o r U-235, while the thermal u t i l i z a t i o n f a c t o r f i s defined as t h e proport i o n of thermal absorption i n U-235. L
Thus, using cross sections derived
from Fig. 2.3, page 2,20, of ORNL-2500, Part 2, 7 f o r U-235 is taken as
528 o r 7 2.47 x 650
= 2 - 0 0 . Effective % h e m a l f i s s i o n cross sections and absorp-
t i o n cross sections a r e assumed t o be 528 barns and 650 barns, respectively, corresponding t o neutron temperatures of GOO C. 0
The fast f i s s i o n f a c t o r was assumed t o be 1.02, since the values calculated f o r graphite l a t t i c e s vary from 1,02 t o
1.04, This
assumption
i s s u f f i c i e n t l y accurate f o r survey purposes. For t h e c a l c u l a t i o n of t h e resonance escape probability, t h e reson-
.
ance i n t e g r a l was calculated from,
I n t h i s formula,
53
I s t h e m a t t e r i n g cross section
i n barns per uranim
S i s t h e surface area of t h e fuel channel atom within t h e fuel channel, and per gram of U-238 i n the channel.
M
The f i r s t term is t h e same as t h e reson-
F,
ance i n t e g r a l f o r an i n f i n i t e medfum of the f u e l salt composition, formula, involving t h e f i r s t power of -Si n s t e a d of
M
This
w a s used because
i t i s more l o g i c a l l y extrapolated t o t h e case of d i l u t i o n of uranium with f u e l salt.
S For uranium metal this reduces t o t h e f a m i l i a r ur = 9.25 x 2407 -
I n the f u e l considered here, 's = 43.3 NO
, and
ur = 18.5 +
M
24,7 S
M
-4A s e r i e s of r e a c t o r s having tubular f u e l channels on a square
a r r a y I s considered. as
. 1
The spacing of these channels w a s a r b i t r a r i l y taken
8 i n . center t o center, and t h e calculations are made for various volume
f r a c t i o n s of f u e l in t h e graphite from 0.05 t o 0.25.
The following t a b l e
gives t h e f u e l channel diameter, the value of
value of as
E ’ the
, and
the
value of the resonance escape p r o b a b i l i t y p for the d i f f e r e n t volume f r a c p i s calculated from p = e
tions.
where
A =
where A Its given by,
i s the u-238 atom d e n s i t y i n the f u e l channel and F i s the volume
u fractian of f u e l i n t h e core. jY
-A
Numerically,
x lo2’ or F x 10 -24 0,0631 (-1-F)+ 0.0228 F 50.22
%ble I
-F *05
-D
*075
.10 15
.20
-25
2.08 i n .
.382
2.54 2.94 3.60 4.15 4.65
313 .271 9
.221 192
.171
27.95 barns 26.25 25.20
-
23 97 23*25 22.73
The thermal u t i l i z a t i o n f a c t o r i s given by,
f =
F e Nu h
F e Nu oa
U
-I-F
Nu
ba 238 -k
A U ba
salt F Ca
i
(1 - F) Zag 7;’
0.891 0.848 0.807
0.733 0 065-3 0.584
1.82
1.73 1.65 1 495 1.332 1.191
-5 A U where e i s t h e enrichment, oa i s t h e e f f e c t i v e absorption cross s e c t i o n f o r
U-235, and y i s t h e thermal flux disadvantage f a c t o r .
For t h i s survey, y i s
assumed t o be 2.0, which seems a reasonable value based on ORNL-2500.
!phis
simplifying assumption w a s made t o avoid c a l c u l a t i n g t h e flux d i s t r i b u t i o n , and probably i s the roughest approximation made i n t h i s survey,
Numerically
the above equation reduces t o ,
\
f =
3.22 F e
+ 0.0137
F
3.22 F e
-t 0.0028
F
+
0.000768 (1
-
F)
An easy computational form i s ,
-f1 = I + 0.0157
+ 0.00077
3.22 e
W
To c a l c u l a t e the enrichment necessary t o achieve a given k-, transformations a r e made,
and
The conversion f a c t o r i s c a l c u l a t e d as follows, Rc 9
-
(1 - p ) + p x(proportion of thermal absorptions i n u-238) px(proport5on of thermal absorptions i n U-235)
From k&,
2 2 k@B i s obtained from B =
3
1
t h e following
-6 and
I
8 i s taken as,
18= T g 1r a p- hFi t e
+
2
Lwphite
x (proportion of thermal absorptions occurring i n graphite)
The correction for Tgaphitei s an approximate one, but not too
c
important numerically. 2
From B
yGaphite i s taken
as 324 em
2
2
and LPaphite
t h e dimensionsof a minimum volume c y l i n d r i c a l core were e a l -
culated using a r e f l e c t o r savings of 2 f t .
This i s less than used i n ORNL-2500,
but may s t i l l be optimistic because some fuel must be used i n t h e r e f l e c t o r t o cool it. Table I I g i v e s t h e r e s u l t s of calculations f o r six values of t h e volume f r a c t i o n of f u e l i n t h e core and for two values of I-$The +,volume of t
f u e l i n t h e core should be evaluated i n terms of the e x t e r n a l volume f o r a c i r c u l a t i n g f u e l reactor, which i s about 0.56
360 cu f t for a 260 Mw ( e l e c t r i c a l ) plant.
CU
f t per thermal megawatt!, o r
It i s evident t h a t one m u s t pay
f o r conversion r a t i o s above 0,8 with enrichments of over 2%. The s e l e c t i o n of an economically optimum r e a c t o r of t h i s type requires a knowledge of t h e method of chemical reprocessing and i t s c o s t , and a way of c a l c u l a t i n g t h e e f f e c t of poisoning by buildup of f i s s i o n products.
The l a t t e r problem w a s looked at b r i e f l y , using as a b a s i s t h e calcu-
l a t i o n s of Blomeke and Todd (ORNL-2127), and assuming a buildup of PU sub i n f i n i t y as defined i n t h e Brookhaven Geneva Paper
461. For
the very long
exposures i t i s probable that the one-group calculations can not give a 9
2
i s 2950 cm
good answer because of t h e l a r g e buildup of absorbing
Pu isoto?es* However,
it might be possible t o operate a r e a c t o r such as Case 8 of Table I1 for as
' .
4
-7long as 30 years a t 640 Mw (thermal) wjithout a need f o r the U-235 inventory t o increase by more than a f a c t o r of two, and wfth a breeding r a t i o averaging g r e a t e r t h a n 5O$> Wsthout any reprocessing, m
For purposes of estimating t h e f u e l cycle cost, a l i f e of LO years without, reprocessing was assumed,
For this period, t h e U-235 concentration
would probably not have to be increased aver i t s i n i t i a l value, and t h e breedi.ng r a t i o should average a t Least
6 ~ $ ~
Applying t h e formula of ORNL-2500, but using t h e thermal cycle of t h e reference design molten-salt r e a c t o r
(CF-58-5-3) the
chemSeal reprocessing
charges and fuel inventory charges a r e 0.034 millllrwhr and 0.14 mill/kwhr, Ten-year depreciation and c a p i t a l charges on t h e base salt
respectively.
. 6
mount t o 0.093 mill/kwhro conversion r a t i o of 0.6.
1 . 3 mills/kwhr
.
Burnup of U-235 would b e w l . 0 milllkwhr a t a
Thus, t o t a l f u e l cycle c o s t s would be approximately
This r e a c t o r was based on Case 8 of Table 11, using a t o t a l f u e l
volume of 600 ft3 and an inventory o f
%
tons of uranium of 1.8% enrichment*
The ten-year reprocessing cycle represents a fuel l i f e of approximately 60,000 Mwd/ton.
More accurate c a l e u h t i o n s a r e needed t o eonfirm t h e above conclusions.
-8Table 91 Vol f r a c t i o n Cas e
F
1
0.05
3
0 *075
2 I
.
4 5
a a
L
0.10
in core cu ft
Critical I n i t i a l in core mass of conversion u-245 Ratio k@;
Vf
Mu
5235
Rc
1.30 1.45
395 143
22,100
298
.546
116
.492
~ 0 5 1.10
1.25
427 167
23,900
298
9635
1.05
1 275 1.46
445 179
1.525
474
1.05
1.10
1.39
1.80
0-20
1.05
1.10
2.24 2.88
11
0.25
1.05 2.10
4- 36 7.05
10
Vol of fuel U r a n i u m
1.05
1-10 0.15
e
9
12
k
kc+
1.10
6 7
Percent
Enrichment of uranium
of f u e l in core
197
520
206
8,000 9,340
24,900
10,000
19
,600
318
707 668
146
26,600
405
29,100
652
ii,ooo
11,540
5 75
32,200
240
13,430
198 332
1400 952
e
Q
7P6 780
865 .865 e
*goo .865
-9D i s t r i b u t ion
.
1. L. G. Alexander 2. C. J. Barton 3 . E. SI B e t t i s 4. J. P. Blakely 5. F. F. Blankenship 6 . A. L. Boch 7 . W. F. Boudreau 8. E. J. Breeding 9 . W. E . Browning 10. D. 0 . Ca,nipbeZl 11. W. H. Carr 12. Go I. Cathers 13. R . A. Charpie 14. D, A. Douglas 15. W. K. Ergen 16. E. L. Falkenberry . 17. 4. P. Fraas 18. W. R. Grimes 19. R. W. Hoff'man 20. W. H. Jordan 21. G. We Keilholtz 22. F. Kertesz 23. B. W. Kinyon 24. 81. E. Iackey 25. J. A. h n e 26. W. J, Iarkin, AEX, ORO
. 2 7 * H. G o MacPherson 28. 29 *
30
31
0
32
33 34 * 35 36 * 37 * 38 39 40.
9
0
41. 42
e
43 44 45 * 4.647 * e
48.
49
8
50 *
51. 52
R. E. BhcPherson
W. D. Manly
E. R. Mann L. A. &UUI W* Be !&Donald H. 6. Metz R. PI Milford F. C. Moesel, AEC, Washington G. J. Nessle W. R. Osborn J. T. Roberts H. W. Savage A. W. Savolainen M. J. Skinner E. S t o r t o J. A. S w a p Z ; ~ ~ t AI %boa& R * E; T ~ O W D. B. "auger Fo C. Vonderikge G. M a Watson A. M. Weinberg G. Do Whftman J. Zasler Iaboratory Records, R.C.
Errata f o r CP 58-10-60
Please &e
the following changes in your copy of CF 58-10-60:
Page 1 (Cover Sheet) i
Make change i n l i n e 10 of abstract
From:
36aO tons of
To:
36 tons of
1.q
Page 2 W e change in next to P a s t l i n e
20
From:
8,54
To :
8.54 x 10
Page 3 Make change Ln l i n e 18
From:
1.w
x 10
22