FFR_chap14.txt

CHAPTER 14
NUCLEAR ASPECTS OF MOLTEN-SALT REACTORS*

The ability of certain molten salts to dissolve uranium and thorium salts
in quantities of reactor interest made possible the consideration of fluid-
fueled reactors with thorium in the fuel, without the danger of nuclear ac-
cidents as a result of the settling of a slurry. This additional degree -of
freedom has been exploited in the study of molten-salt reactors.

Mixtures of the fluorides of alkali metals and zirconium or beryllium, as
discussed in Chapter 12, possess the most desirable combination of low
neutron absorption, high solubility of uranium and thorium compounds,
chemical inertness at high temperatures, and thermal and radiation sta-
bility. The following comparison of the capture cross sections of the alkali
metals reveals that Li? containing 0.019, Li% has a cross section at 0.0795 ev
and 1150°F that is a factor of 4 lower than that of sodium, which also has
a relatively low cross section:

Element Cross section, barns
Li7 (containing 0.019; Li®) 0.073
Sodium 0.290
Potassium 1.13
Rubidium 0.401
Cesium 29

The capture cross section of beryllium is also satisfactorily low at all
neutron energies, and therefore mixtures of Lil' and BeFg, which have
satisfactory melting points, viscosities, and solubilities for UF4 and ThF4,
were selected for investigation in the reactor physics study.

Mixtures of NaF, ZrF4, and UF4 were studied previously, and such a
fuel was successfully used in the Aircraft Reactor Iixperiment (see Chap-
ters 12 and 16). Inconel was shown to be reasonably resistant to corrosion
by this mixture at- 1500°F, and there is reason to expect that Inconel
equipment would have a life of at least several years at 1200°F. As a fuel
for a central-station power reactor, however, the Nal'-ZrF4 system has
several serious disadvantages. The sodium capture cross section is less
favorable than that of Li?. More important, recent data [1] indicate that
the capture cross section of zirconium is quite high in the epithermal and
intermediate neutron energy ranges. In comparison with the Lil'-BeFs
system, the Nal'-Zrl, system has inferior heat-transfer characteristics.

*By L. G. Alexander.
626
NUCLEAR ASPECTS OF MOLTEN-SALT REACTORS 627

Finally, the INOR alloys (see Chapter 13) show promise of being as resistant
to the beryllium salts as to the zirconium salts, and therefore there is no
compelling reason for selecting the Nal-ZrF4 system.

Reactor calculations were performed by means of the Univac* program
Ocusol [2], a modification of the Eyewash program [3], and the Oracle?t
program Sorghum. Ocusol is a 31-group, multiregion, spherically symmet-
ric, age-diffusion code. The greoup-averaged cross sections for the various
elements of interest that were used were based on the latest available data
[4]. Where data were lacking, reasonable interpolations based on resonance
theory were made. The estimated cross sections were made to agree with
measured resonance integrals where available. Saturation and Doppler
broadening of the resonances in thorium as a function of concentration
were estimated. Inelastie scattering in thorium and fluorine was taken
into account crudely by adjusting the value of £¢:; however, the Ocusol
code does not provide for group skipping or anisotropy of scattering,

Sorghum is a 31-group, two-region, zero-dimensional, burnout code.
The group-diffusion equations were integrated over the core to remove
the spatial dependency. The spectrum was computed, in terms of a
space-averaged group flux, from group scattering and leakage parameters
taken from an Ocusol caleulation. A critical calculation requires about
1 min on the Oracle; changes in concentration of 14 elements during a
specified time can then be computed in about 1 sec. The major assumption
imvolved 18 that the group scattering and leakage probabilities do not
change appreciably with changes in core composition as burnup progresses.
This assumption has been verified to a satisfactory degree of approximation.

The molten salts may be used as homogeneous moderators or simply as
fuel carriers in heterogeneous reactors. Although, as discussed below,
graphite-moderated heterogeneous reactors have certain potential advan-
tages, their technical feasibility depends upon the compatibility of fuel,
graphite, and metal, which has not as yet been established. For this rea-
son, the homogeneous reactors, although inferior in nuclear performance,
have been given greatest attention.

A preliminary study indicated that if the integrity of the core vessel
could be guaranteed, the nuclear economy of two-region reactors would
probably be superior to that of bare and reflected one-region reactors. The
two-region reactors were, accordingly, studied in detail. Although entrance
and exit conditions dictate other than a spherical shape, it was necessary,
for the calculations, to use a model comprising the following concentric

*Universal Automatic Computer at New York University, Institute of Mathe-
matics.

70ak Ridge Automatic Computer and Logical Engine at Qak Ridge National
Laboratory.
628 NUCLEAR ASPECTS OF MOLTEN-SALT REACTORS [cHAP. 14

spherical regions: (1) the core, (2) an INOR-8 core vessel 1/3 in. thick,
(3) a blanket approximately 2 ft thick, and (4) an INOR-8 reactor vessel
2/3 in, thick. The diameter of the core and the concentration of thorium
in the core were selected as independent variables. The primary dependent
variables were the critical concentration of the fuel (U235 U233 or Pu?39),
and the distribution of the neutron absorptions among the various atomic
species in the reactor. Irom these, the critical mass, critical inventory,
regeneration ratio, burnup rate, ete. can be readily calculated, as described
in the following section.

14-1. HomogENEOUS REACTORS FUBLED wiTH U235

While the isotope U232 would be a superior fuel in molten fluoride-salt
reactors (see Section 14-2), it is unfortunately not available in quantity.
Any realistic appraisal of the immediate capabilities of these reactors must
be based on the use of U235,

The study of homogeneous reactors was divided into two phases: (1) the
mapping of the nuclear characteristies of the initial (i.e., “clean’) states
as a function of core diameter and thorium concentration, and (2) the
analysis of the subsequent performance of selected initial states with
various processing schemes and rates. The detailed results of these studies
are given in the following paragraphs. Briefly, it was found that regenera-
tion ratios of up to 0.65 can be obtained with moderate investment in U235
(less than 1000 kg) and that, if the fission products are removed (Article
14-1.2) at a rate such that the equilibrium inventory is equal to one year’s
production, the regeneration ratio can be maintained above 0.5 for at
least 20 years.

14-1.1 Initial states. A complete parametric study of molten fluoride-
salt reactors having diameters in the range of 4 to 10 ft and thorium con-
centrations in the fuel ranging from 0 to 1 mole 9, ThF4 was performed.
In these reactors, the basic fuel salt (fuel salt No. 1) was a mixture of
31 mole 9, Bel's and 69 mole 9 LiI", which has a density of about 2.0 g/cc
at 1150°F. The core vessel was composed of INOR-8. The blanket fluid
(blanket salt No. 1) was a mixture of 25 mole 9, ThI'4 and 75 mole 95 L1k,
which has a density of about 4.3 g/ce at 1150°F. In order to shorten the
calculations in this series, the reactor vessel was neglected, since the re-
sultant error was small. These reactors contained no fission products or
nonfissionable isotopes of uranium other than U#38,

A summary of the results is presented in Table 14-1, in which the neutron
balance is presented in terms of neutrons absorbed in a given element per
neutron absorbed in U235 (both by fission and the n—y reaction). The
sum of the absorptions is therefore equal to n, the number of neutrons
produced by fission per neutron absorbed in fuel. Further, the sum of the
14-1] HOMOGENEOUS REACTORS FUELED WITH U235 629
(X10'9)

40 ‘

30 |-

AN
4

® Calculated
Values

 

mole % ThF4 In
uel Salt

7

& »

U235 concentration atomsfem3
o
| T T

»

2 — Interpolations
of Data

No ThFA in Fuel Salt \
9

1 | l |
2 4 6 8 10
Core Diameter, f

 

 

 

 

Fic. 14-1. Initial critical concentration of U?3% in two-region, homogeneous,
molten fluoride-salt reactors.

absorptions in U and thorium in the fuel, and in thorium in the blanket
salt gives directly the regeneration ratio. The losses to other elements are
penalties imposed on the regeneration ratio by these poisons; i.e., if the core
vessel could be constructed of some material with a negligible cross seec-
tion, the regeneration ratio could be increased by the amount listed for
capture in the core vessel.

The Inventories in these reactors depend in part on the volume of the
fuel in the pipes, pumps, and heat exchangers in the external portion of
the fuel circuit. The inventories listed in Table 14-1 are for systems having
a volume of 339 ft? external to the core, which corresponds approximately
to a power level of 600 Mw of heat. In these calculations it was assumed
that the heat was transferred to an intermediate coolant composed of the
fluorides of Li, Be, and Na before being transferred to sodium metal. In
more recent designs (see Chapter 17), this intermediate salt loop has been
replaced by a sodium loop, and the external volumes are somewhat less
because of the improved equipment design and layout.

Critical concentration, mass, inventory, and regeneration ratio. The data
in Table 14-1 are more easily comprehended in the form of graphs, such as
Fig. 14-1, which presents the critical concentration in these reactors as a
function of core diameter and thorium concentration in the fuel salt. The
data points represent caleulated values, and the lines are reasonable
interpolations. The maximum concentration caleulated, about 35 x 101°
Total power: 600 Mw (heat).

TasLE 14-1

INtrIaL-STATE NUCLEAR CHARACTERISTICS OF Two-REcioN, HoMoGENEOUS,
MowvteEN FLuoripE-SaLT REAcTORS FUELED wiTH U235

Fuel salt No. 1: 31 mole 9, BeFs + 69 mole 9 1aF + UF4+ ThF4.
Blanket salt No. 1: 25 mole 9, ThF4+ 75 mole 9}, LiF.

External fuel volume: 339 {t3.

 

 

 

 

 

Case number 1 2 3 4 5 6 7
Core diameter, ft 4 5 5 5 5 5 6
Th¥4 in fuel salt, mole 9 0 0 0.25 0.5 0.75 1 0
U235 in fuel salt, mole % 0.952 0.318 0.561 0.721 0.845 0.938 0.107
U235 atom density* 33.8 11.3 20.1 25.6 30.0 33.3 3.80
Critical mass, kg of U235 124 81.0 144 183 215 239 47.0
Critical inventory, kg of U235 | 1380 501 891 1130 1330 1480 188
Neutron absorption ratiost
U235 (fissions) 0.7023 0.7185 0.7004 0.6996 0.7015 0.7041 0.7771
U235 (n— 0.2977 0.2815 0.2996 0.3004 0.2985 0.2959 0.2229
Be-Li-F in fuel salt 0.0551 0.0871 0.0657 0.0604 0.0581 0.0568 0.1981
Core vessel 0.0560 0.0848 0.0577 0.0485 0.0436 0.0402 0.1353
Li-F in blanket salt 0.0128 0.0138 0.0108 0.0098 0.0093 0.0090 0.0164
Leakage 0.0229 0.0156 0.0147 0.0143 0.0141 0.0140 0.0137
U238 in fuel salt 0.0430 0.0426 0.0463 0.0451 0.0431 0.0412 0.0245
Th in fuel salt 0.0832 0.1289 0.1614 0.1873
Th in blanket salt 0.5448 0.5309 0.4516 0.4211 0.4031 0.3905 0.5312
Neutron yield, 7 1.73 1.77 1.73 1.73 1.73 1.74 1.92
Median fission energy, ev 270 15.7 105 158 270 425 0.18
Thermal fissions, 9, 0.052 6.2 0.87 0.22 0.87 0.040 35
n—y capture-to-fission ratio, a 0.42 0.39 0.43 0.43 0.43 0.4203 0.28
Regeneration ratio 0.59 0.57 0.58 0.60 0.61 0.62 0.56

 

 

 

 

 

 

 

 

 

continued

0€9

SLOUJISV UVHATIOAN

Jd0

SHOLOVHY LIVS-NAHLTON

F1 "dVHD]
 

 

 

 

 

 

 

 

 

 

 

 

Tapre 11 1 (continued)
("ase number ~ 9 [0 11 12 13 14
Core diameter, ft {h 6 (s 6 7 8 8
ThI4 in fuel salt, mole 9, 0.25 0.5 0.75 1 0.25 ) 0.25
U235 in fuel salt, mole 9 0.229 0.408 (.552 0. 662 0.114 0.047 0.078
U235 atom density* 8.13 14.5 19.6 23.5 4.0 1.66 2.77
Critical mass, kg of U235 101 179 243 291 79.6 48.7 &1.3
Critical inventory, kg of U233 404 716 972 1160 230 110 184
Neutron absorption ratiost
U235 (figgions) 0.7343 0.7082 0.7000 0.7004 0. 7748 0. 8007 0.7930
U233 (n—y) 0.2657 0.2918 0. 3000 0.2996 0.2252 (. 1993 0.2070
Be--Li-F in fuel salt 0.1082 00770 0.0669 0.0631 0. 1880 0.4130 0.2616
Core vessel 0.0795 0.0542 0 0435 0.0388 0.0951 (. 1491 0.1032
Li—F in blanket salt 0.0116 0.0091 0.0081 0.0074 0.0123 (.0143 0.0112
Leakage ‘ 0.0129 0.0122 0.0119 0.0116 0.0068 0.0084 0.0082
U238 in fuel salt 0.0375 0.0477 0.0467 (. 0452 0.0254 0.0143 00196
Th in fuel salt 0.1321 0. 1841 0.2142 0.2438 0.1761 0.2045
Th in blanket salt 0 4318 0.3683 | 0.3378 03202 | 0.4008 0.4073 03503
Neutron yield, 7 1.82 1.75 1.73 1.73 1.91 2.00 1.96
Median fission energy, ev 5.6 38 100 120 0.16 Thermal 0.10
Thermal fissions, 9% 13 3 0.56 0.48 33 59 45
n -y capture-to-fission ratio, « 0.36 0.41 0.42 0. 42 0.29 0.25 0 26
Regencration ratio .61 .60 0.60 0.61 0.61 0.42 0.57
¥Atoms (X 10719) /ec. $Neutrons absorbed per neutron absorped in U233, continued

[1-51

ezl HLLAW QETEOI SHOLOVAM SOOMNEDOKOIL

1€
TABLE 14-1 (continued)

 

 

 

 

 

Case number 15 16 17 18 19 20 21 22
Core diameter, ft 8 8 8 10 10 10 10 10
ThF4 in fuel salt, mole 0.5 0.75 1 0 0.25 0.5 0.75 1
U235 in fuel salt, mole 9 0.132 0.226 0.349 0.033 0.052 0.081 0.127 0.205
U235 atom density* 4 .67 8.03 12.4 1.175 1.86 2.88 4 .50 7.28
Critical mass, kg of U235 137 236 364 67.3 107 165 258 417
Critical inventory, kg of U235 310 535 824 111 176 272 425 687
Neutron absorption ratiost
U235 (fissions) 0.7671 0.7362 0.7146 0.8229 0.7428 0.7902 0.7693 0.7428
U235 (n 0.2329 0.2638 0.2854 0.1771 0.2572 0.2098 0.2307 0.2572
Be-Li-F in fuel salt 0.1682 0.1107 0.0846 0.5713 0.3726 0.2486 0.1735 0.1206
Core vessel 0.0722 0.0500 0.0373 0.1291 0.0915 0.0669 0.0497 0.0363
Li-F in blanket salt 0.0089 0.0071 0.0057 0.0114 0.0089 0.0073 0.0060 0.0049
Leakage 0.0080 0.0077 0.0074 0.0061 0.0060 0.0059 0.0057 0.0055
U288 in fuel salt 0.0272 0.0368 0.0428 0.0120 0.0153 0.0209 0.0266 0.0343
Th in fuel salt (0.3048 0.3397 0.3515 0.2409 0.3691 0.4324 0.4506
Th in blanket salt 0.3056 0.2664 0.2356 0.3031 0.2617 0.2332 0.2063 0.1825
Neutron yield, n 1.89 1.82 1.76 2.03 2.00 1.95 1.90 1.83
Median fission energy, ev 0.17 5.3 27 Thermal | Thermal 0.100 0.156 1.36
Thermal fissions, 9 29 13 5 66 56 43 30 16
n—y capture-to-fission ratio, « 0.30 0.36 0.40 0.21 0.24 0.26 0.30 0.35
Regeneration ratio 0.64 0.64 0.63 0.32 0.52 0.62 0.67 0.67

 

 

 

 

 

 

 

 

 

 

*Atoms (X 10719)/ce.

tNeutrons absorbed per neutron absorbed in U235,

43y

SHOLOVHAY LIVS-NALTOW 40 SLOAASV dVATIAN

¥1 'dVHD]
14-1} HOMOGENEOUS REACTORS FUELED WITH U235 633

 

T T T ] T

mole % ThF4 In Fuel Salt

1 .
400 — e Calculated volues /
— Interpolations of .

o Data

o 4

=]

® 300+ —
> °

-

2 / . 075 {v
a o -—-—-—..____._____.—-—-—‘—"'—_—
= /./

o 200 I/ -]
= o

S

...
~———No ThF 4 In Fuel Sait

 

 

 

04 5 6 7 8 g 10

Core Diameter,

Fic. 14-2. Initial critical masses of U235 in two-region, homogeneous, molten
fluoride-salt reactors.

atoms of U35 per cubic centimeter of fuel salt, or about 1 mole 9, UF,, is
an order of magnitude smaller than the maximum permissible concentra-
tion (about 10 mole 7).

The corresponding eritical masses are graphed in IFig. 14-2. As may be
=een, the eritical mass 1s a rather complex function of the diameter and the
thorium concentration. The calculated points are shown here also, and the
sulid lines represent, 1t is felt, reliable interpolations. The dashed lines
were drawn where insufficient numbers of points were calculated to define
the curves precisely; however, they are thought to be qualitatively correct.
Sinee reactors having diameters less than 6 ft are not economically attrac-
tive, only one case with a 4-ft-diameter core was computed.

The critical masses obtained in this study ranged from 40 to 400 kg of
U= However, the ecritical inventory in the entire fuel circuit is of more
interest to the reactor designer than is the critical mass. The critical in-
ventories corresponding to an external fuel volume of 339 ft3 are therefore
<hown in Fig. 14-3. Inventories for other external volumes may be com-
puted from the relation

 

6V,
D)
where D is the core diameter in feet, M is the critical mass taken from

I'ig. 142, V. is the volume of the external system in cubic feet, and I is
the inventory in kilograms of U235, The inventories plotted in Fig. 14-3

I=M(1+
634

NUCLEAR ASPECTS OF MOLTEN-SALT REACTORS

2000

 

l T

mole % ThF4 In Fuel Salt

   

1000

FTTT

Critical Inventory, kg of U233
tn
jo
O
|

N
<
o
T

 

 

 

Core Diameter, ft

[cHaAP. 14

Fig. 14-3. Initial critical inventories of U233 in two-region, homogeneous, molten
fluoride-salt reactors. External fuel volume, 339 ft3.

0.8

 

07 -

o
o~

Regeneration Ratio

o
tn
1

0.4 }—

 

0.3

1 \
Numbers On Data Points

Are Core Diameters In Feet { )} mole % ThFA In Fuel Salt

16
.

8

AN

@
.f \'—-__.___5_ 0 ®

(0.25) @6

8,. 6_‘______.——.—.
!

®
/\‘*\No ThF4 In Fuel Sals
10

1Ce ; |

 

| | l

 

200 400 400 800 1000 1200
Critical Inventory, kg u235

F1e. 14-4. Initial fuel regeneration in two-region, homogeneous, molten fluoride-

salt reactors fueled with U225, Total power, 600 Mw (heat); external fuel volume,
339 ft3; core and blanket salts No. 1.
14-1] HOMOGENEOUS REACTORS FUELED WITH U235 635

 

 

 

 

0.8
{ ) mole % ThF4 In Fuel Salt
0.7 ne N
10 e ———
o« j
1 !
. " 1075) f J
5 s (0.50)
& © 9(0.25)
c 0.6 — - ]
.0
B
D
5 7®
& *No ThF 4 In Fuel Salt
g 0.5 — -
Numbers On Data Points
0.4 ’_ Are Core Diameters In Feet o
| [ |
0.3 L I __J
0 200 400 400 800

Critical inventory, kg of u23s

Fic. 14-5. Maximum initial regeneration ratios in two-region, homogeneous,
molten fluoride-salt reactors fueled with U235, Total power, 600 Mw (heat); ex-
ternal fuel volume, 339 {t3,

range from slightly above 100 kg in an 8-ft-diameter core with no thorium
present to 1500 kg in a 5-ft-diameter core with 1 mole 9, ThF4 present.

The optimum combination of core diameter and thorium concentration
1=, qualitatively, that which minimizes the sum of inventory charges (in-
cluding charges on Li7, Be, and Th) and fuel reprocessing costs. The fuel
cost= are directly related to the regeneration ratio, and this varies in a
complex manner with inventory of U233 and thorium coneentration, as
shown in Vig. 14-4. It may be seen that at a given thorium concentration,
the regeneration ratio (with one exception) passes through a maximum as
the core diameter 1s varied between 5 and 10 ft. These maxima increase
with increasing thorium concentration, but the inventory values at which
they occur alzo increase.

Plotting the maximum regeneration ratio versus ecritical inventory
generates the curve shown in Iig. 14-5. It may be seen that a small in-
vestment in U235 (200 kg) will give a regeneration ratio of 0.58, that 400 kg
will give a ratio of 0.66, and that further increases in fuel inventory have
little effect.

The effects of changes in the compositions of the fuel and blanket salts
are indicated in the following description of the results of a sertes of calcu-
lations for which salts with more favorable melting points and viscosities
were assumed. The BelF'z content was raised to 37 mole % in the fuel salt
636 NUCLEAR ASPECTS OF MOLTEN-SALT REACTORS [cHaP, 14

2000

 

‘ T

mole % ThF4 In Fuel Salt

1000

i —]

Inventory , kg of U233

 

 

 

 

Core Diameter, ft

F1g. 14-6. Initial critical inventories of U235 in two-region, homogeneous, molten

fluoride-salt reactors. Total power, 600 Mw (heat); external fuel volume, 339 {t3;
core and blanket salts No. 2.

 

 

 

 

0.7
r | |
Numbers On Data Points are
Core Diameters In Feet
8.
v 8

.% ; \. o\
o 3 .r.\. \.7 .
c I
S \ e )
T 06 }— * 1 g ]
E 6 \ 6 \ \o
@ - . b e
o @ -
@ 7o (0.50) (0.75)
o ®

/

[

8e (0.25)
{) mole % ThFA in Fuel Salt
0.5 | f \ i |
0 200 400 600 800 1000 1200

Critical Inventory, U235, kg

F16. 14-7. Initial fuel regeneration in two-region, homogeneous, molten fluoride-

salt reactors fueled with U5, Total power, 600 Mw (heat); external fuel volume,
339 ft3; core and blanket salts No. 2.
14-1] HOMOGENEOUS REACTORS FUELED WITH U239 637

(fuel salt No. 2), and the blanket composition (blanket salt No. 2) was
fixed at 13 mole % ThF4, 16 mole % BeF3, and 71 mole % LiF. Blanket
salt No. 2 is a somewhat better reflector than No. 1, and fuel salt No. 2 a
somewhat better moderator. As a result, at a given core diameter and
thorium concentration in the fuel salt, both the critical concentration and
the regeneration ratio are somewhat lower for the No. 2 salts,

Reservations concerning the feasibility of constructing and guaranteeing
the integrity of core vessels in large sizes (10 ft and over), together with
preliminary consideration of inventory charges for large systems, led to
the conclusion that a feasible reactor would probably have a core diameter
lying in the range between 6 and 8 ft. Accordingly, a parametric study in
this range with the No. 2 fuel and blanket salts was performed. In this
study the presence of an outer reactor vessel consisting of 2/3 in. of
INOR-8 was taken into account. The results are presented in Table 14-2
and Figs. 14-6 and 14-7. In general, the nuclear performance is somewhat
better with the No. 2 salt than with the No. 1 salt.

Neutron balances and maiscellaneous details. The distributions of the
neutron captures are given in Tables 14-1 and 14-2, where the relative
hardness of the neutron spectrum is indicated by the median fission energies
and the percentages of thermal fissions. It may be seen that losses to Li,
Be, and F in the fuel salt and to the core vessel are substantial, especially
in the more thermal reactors (e.g., Case No. 18). However, in the thermal
reactors, losses by radiative capture in U235 are relatively low. Increasing
the hardness decreases losses to salt and core vessel sharply (Case No. 5),
but increases the loss to the n—y reaction. It is these opposing trends
which account for the complicated relation between regeneration ratio and
critical inventory exhibited in Figs. 144 and 14-7. The numbers given
for capture in the Li and F in the blanket show that these elements are well
shielded by the thorium in the blanket, and the leakage values show that
leakage from the reactor is less than 0.01 neutron per neutron absorbed in
U235 in reactors over 6 ft in diameter. The blanket contributes sub-
stantially to the regeneration of fuel, accounting for not less than one-third
of the total even in the 10-ft-diameter core containing 1 mole % ThFs.

Effect of substitution of sodium for Li7. In the event that Li? should prove
not to be available in quantity, it would be possible to operate the reactor
with mixtures of sodium and beryllium fluorides as the basic fuel salt. The
penalty imposed by sodium in terms of critical inventory and regeneration
ratio is shown in Fig. 14-8, where typical Na-Be systems are compared
with the corresponding Li-Be systems. With no thorium in the core, the
use of sodium increases the critical inventory by a factor of 1.5 (to about
300 kg) and lowers the regeneration ratio by a factor of 2. The regeneration
penalty is less severe, percentagewise, with 1 mole 9, ThF4 in the fuel
salt; in an 8-ft-diameter core, the inventory rises from 800 kg to 1100 kg
 

TaABLE 14-2

INITIAL-STATE NUCLEAR CHARACTERISTICS OF Two-REcion, HoMmoGENEOUS,

MorLtEN FrLvorine-SaLt Reacrors FueLep wita U235

Fuel salt No. 2: 37 mole 9, BeFs + 63 mole ¢, Lil' 4+ UF4 + ThF4.

Blanket salt No. 2: 13 mole 9, ThF4+ 16 mole §; BeFs 4+ 71 mole 9 LiF.
Total power: 600 Mw (heat).

External fuel volume: 339 {t3.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Case number 23 24 25 26 27 28
Core diameter, ft 0 6 6 6 7 7
ThF, in fuel salt, mole ¢ 0.25 0.5 0.75 1 0.25 0.5
U235 in fuel salt, mole 9 0.169 0.310 0.423 0.580 0.084 0.155
U235 atom density* 5. 87 100. 91 15.95 20.49 3.13 5H.38
Critical mass, kg of U235 727 135 198 254 61.5 106
Critical inventory, kg of U235 291 540 790 1010 178 306
Neutron absorption ratiost
U232 (fisgions) 0.7516 0.7174 0.7044 0.6958 0.7888 0.7572
U233 (n—y) (.2484 0.2826 0.2956 0.3042 0.2112 0.2428
Be—Li-F in fuel salt 0.1307 0. 0900 (0.0763 0.0692 0.2147 0.1397
Core vessel 0 1098 0.0726 0.0575 0.0473 0.1328 0.0905
Li-F in blanket salt 0.0214 0.0159 0.0132 0.0117 0.0215 0.0167
Outer vessel 0.0024 0.0021 0.0021 0.0019 0.0019 0.0018
Leakage 0.0070 0.0065 0.0064 0.0061 0.0052 0.00350
U2 1n fuel salt 0.0325 0.06426 0.0452 0.0477 0.0214 0.0307
Th in fuel salt 0.1360 0.1902 0.2212 0. 2357 0.1739 0.2565
Th in blanket salt 0.4165 0.3521 0.3178 0.2962 0.3770 (.3294
Neutron vield, n 1.86 1.77 1.74 1.72 1.95 1.87
Median fission energy, cv ().480 10.47 58.10 76.1 0.1223 0.415
Thermal fissions, 9 21 7 2.8 .84 43 24
n—y capture-to-fission ratio, « 0.33 0.39 0. 42 (.44 0.37 0.32
Regeneration ratio (.59 .58 {).58 (.58 0.57 0.62
continued

SIOAASY UVATINN Qe9

Jd0

SHOLOVIY ITVS-NHLTOW

FI "dVHD]
 

 

(ase number

(‘ore diameter, ft

ThIy in fuel salt, mole %
U232 1n fuel salt, mole 9
U235 atom density™®

Critical mass, kg of U232
Critical inventory, kg of U235

Neutron absorption ratiost
U235 (figsions)
T'#33 (n-)
Be-Li-F in fuel salt
Core vessel
Li-F in blanket salt
Outer vessel
Teakage
U238 in fucl salt
Th in fuel salt
Th in blanket salt

Neutron yield, n

Median fission energy, ev
Thermal fissions, 9

n—y capture-to-fission ratio, «
Regeneration ratio

TasLe 14-2 (continued)

 

 

 

 

20 30 31 32 33 34
7 7 8 8 8 8
0.75 1 0.25 0.5 0.75 1
0.254 0.366 0.064 0.099 0.163 0.254
8.70 13.79 2.24 3.51 5.62 9 09
171 271 65.7 103 165 267
494 783 149 233 374 604
0.7282 0.7094 0.8014 0.7814 0.7536 0.7288
0.2718 0.2906 0.1986 0.2186 0.2464 0.2712
0.1010 0.0824 0.2769 0.1945 0.1354 0.1016
0.0644 0.0497 0.1308 0.0967 0.0696 0.0518
0.0131 0.0108 0.0198 0.0162 (0.0130 0.0105
0.0016 0.0015 0.0017 0.0016 0.0014 0.0013
0.0048 0.0045 (0.0045 0.0043 0.0042 0.0040
0.0392 0.0447 0.0177 0.0233 0.0315 0.0392
0.2880 0.3022 0.1978 0.3043 0.3501 0.3637
0.2866 0.2566 0.3240 0.2892 0.2561 0.2280
1.80 1.75 1.97 1.93 1.86 1.80
7.61 25.65 519, thermal 0.136 0.518 7.75
11 4.3 51 38 23 11
0.37 0.41 0.25 0.28 0.33 0.37
0.61 0.60 0.54 0.62 0.64 0.63

 

 

 

 

 

 

 

 

*Atoms (X 10719)/cc.

tNeutrons absorbed per neutron absorbed in U233,

[1-¥1

cpz(l HIIM JHTING SHOLOVHY SNOHANHDOWOH

669
640 NUCLEAR ASPECTS OF MOLTEN-SALT REACTORS [cHAP. 14

 

 

 

 

 

ti—Be Salt with 1 mole
® % ThF4
10 -
06— ¢ FuelSalta 8"""“-—2— ]
*
o
2 tmo ThF 4 8e-—e—_
o
Fuel Salt A 108,

o
‘.2. 0.4 _.8. Fuel Salt B/ ~ ]
g ’ Na-Be Salt
o &7
s 108 &No ThFy4 With 1 male <% ThFy4
o
o ge —Fuel Salt B

0.2 — IOL

\
Numbers On Data Points Are
Core Diameters in Feet
1 ! |
0 400 800 1200 1600

Critical Inventory, Kg of y23s

Fta. 14-8. Comparison of regeneration ratio and critical inventory in two-region,
homogeneous, molten fluoride-salt reactors fueled with U235, Fuel salt A: 37 mole
9% BeF 2 plus 63 mole 9, Li"F. Fuel salt B: 46 mole 9, BeF2 plus 54 mole 9, NaF.

and the regeneration ratio falls from 0.62 to 0.50. Details of the neutron
balances are given in Table 14-3.

Reactivity coefficients. By means of a series of calculations in which the
thermal base, the core radius, and the density of the fuel salt are varied
independently, the components of the temperature coeflicient of reactivity
of a reactor can be estimated as illustrated below for a core 8 ft in diam-
eter and a thorium concentration of 0.75 mole 9 in the fuel salt at 1150°F.
From the expression

k=T, p, R),

where & is the multiplication constant, T is the mean temperature in the
core, p 1s the mean density of the fuel salt in the core, and E is the core
radius, it follows that

Ldk _1{0k 1/0k\ dR , 1/3k\ dp
m“—%(fi)p.R+fc(a—ze)p.m+z(a_p)&m—r (14-1)

where the term (1/k)(0k/0T),, r represents the fractional change in & due
to a change in the thermal base for slowing down of neutrons, the term
(1/k)(0k/0p)r, T represents the change due to expulsion of fuel from the
core by thermal expansion of the fluid, and the term (1/k)(0k/0OR), r
represents the change due to an increase in core volume and fuel holding
TaBLE 14-3

INiTIAL NucLrear Cnaractreristics oF Two-RecroN, HoMOGENEQUS,
MorteEN Soprum-BeryLuivm FruoripE Reacrors FugLep wita U238

Fuel salt: 53 mole 9}, NaF + 46 mole 9, BeFz2 + 1 mole 9, (ThF4+ UF4).

Blanket salt: 58 mole 9, NaF + 35 mole 9; BeF2 + 7 mole 9, ThF,.
Total power: 600 Mw (heat).

External fuel volume: 339 ft3.

 

 

Case number

Core diameter, ft

ThF4 in fuel salt, mole %
U235 in fuel salt, mole 9
U?3% atom density*

Critical mass, kg of U235
Critical inventory, kg of U235

Neutron absorption ratiost
U235 (fissions)
U235 (n-
Na-Be-F in fuel salt
Core vessel
Na-Be-F in blanket salt
Leakage
U238 in fuel salt
Th in fuel salt
Th in blanket salt

Neutron yield, 5

Median fission energy, ev
Thermal fissions, 9

n—y capture-to-fission ratio, a
Regeneration ratio

 

 

35 36 37 38 39 40

6 6 8 8 10 10
0 1 0 1 0 1
0.174 0.7014 0.091 0.465 0.070 0.282
6.17 24.9 3.24 16.5 2.47 124.0
76.4 308 95.1 484 142 710

306 1230 215 1100 234 1170
0.7417 0.6986 0.7737 0.7011 0.7862 0.7081
0.2583 0.3014 0.2263 0.2989 0.2138 0.2919
0.2731 0.1153 0.4755 0.1411 0.6119 0.2306
0.1181 0.0476 0.1125 0.0392 0.0917 0.2306
0.0821 0.0431 0.0660 0.0315 0.0495 0.2306
0.0222 0.0182 0.0145 0.0116 0.0105 0.2306
0.0360 0.0477 0.0263 0.0434 0.0232 0.0467

0.2418 0.3150 0.3670

0.3004 0.2120 0.2163 0.1450 0.1550 0.1048
1.83 1.73 1.91 1.73 1.94 1.75
1.3 190 0.20 36 0.087
17 0.42 34 1.4 4.1
0.25 0.43 0.29 0.43 0.27 0.41
0.54 0.50 0.24 0.51 0.18 0.52

 

 

 

 

 

 

 

*Atoms (X 10719) /cc.

tNeutrons absorbed per neutron absorbed in U235,

(11

gzl HLIM CATINA SHOLOVIY SNOUENIHDONWOH

¥9
(12 NUCLEAR ASPECTS OF MOLTEN-SALT REACTORS [cHAP. 14

capacity. The coeflicient dR/dT may be related to the coefficient for linear
expansion, ¢, of INOR-8, viz:

dR
d_T = Ra.
Likewise the term dp/d7T may be related to the coefficient of cubical ex-
pansion, 3, of the fuel salt:

dp _
AT 8.

From the nuclear ealculations, the components of the temperature co-
efficient were estimated, as follows:

1(8k

. JT)p, L =—(0134£0.02) X 107%/°F,

R{Ok .
A_-(?R)p, =+ 04123 0.0005,

=5

|

D

%( J ) — —0.405 + 0.0005.
pP/R. T

The Iinear coefficient of expansion, ¢, of INOR~-8 was estimated to be
(8.0+0.5) X 1076/°F [5], and the coefficient of cubical expansion, 83, of
the fuel was estimated to be (9.889 4 0.005) X 10~ 3/°F from a correlation
of the density given by Powers [6]. Substitution of these values in
Eq. (14-1) gives

= == —(3.804: 0.04) X 107 3/°F

for the temperature coefficient of reactivity of the fuel. In this calculation,
the effects of changes with temperature in Doppler broadening and satura-
tion of the resonances in Th and U?3? were not taken into account. Since
the effective widths of the resonances would be increased at higher tem-
peratures, the thorium would contribute a reactivity decrease and the
U235 an increase. These effects are thought to be small, and they tend to
cancel each other.
14-1] HOMOGENEOUS REACTORS FUELED WITH U230 643

Additional coefficients of interest are those for U235 and thorium. For
the 8-ft-diameter cores,

 

 

N(U235) ( ok ) T4 [0.17N(U285) X 10717]
k 6N(U235) N(Th)-——- 247N (U235 x 1019
and
N(Th) ( ok ) __ N(Th) ( dk ) dN (U?33)
k. \ON(Th)/wvw=s k& \ON(UZ?)/yrm dN(Th)
where
w — 0.0595N (Th) x 10~1%
JNTH) = 0.0805 ¢ :

In these equations, N (U235) represents the atomic density of U235 in atoms
per cubic centimeter, N.(U?35) is the critical density of U?3%, and N(Th)
is the density of thorium atoms.

Heat release in core vessel and blanket. The core vessel of a molten-salt
reactor is heated by gamma radiation emanating from the core and blanket
and from within the core vessel itself. Estimates of the gamma heating can
be obtained by detailed analyses of the type illustrated by Alexander and
Mann [7]. The gamma-ray heating in the core vessel of a reactor with an
8-ft-diameter core and 0.5 mole % ThF4 in the fuel salt has been estimated
to be the following:

Source Heat release rate, w/cm3
Radioactive decay in core 1.4
Fission, n—y capture, and inelastic 5.2

scattering in core
n—y capture in core vessel 4.
n—y capture in blanket 0.

Total 11.4

W On

Estimates of gamma-ray source strengths can be used to provide a crude
estimate of the gamma-ray current entering the blanket. For the 8-ft-
diameter core, the core contributes 45.3 w of gamma energy per square
centimeter to the blanket, and the core vessel contributes 6.8 w/cm?, which,
multiplied by the surface area of the core vessel, gives a total energy
escape into the blanket of 9.7 Mw. Some of this energy will be reflected
into the core, of course, and some will escape from the reactor vessel, and
644 NUCLEAR ASPECTS OF MOLTEN-SALT REACTORS [cHaP. 14

therefore the value of 9.7 Mw is an upper limit. To this may be added the
heat released by capture of neutrons in the blanket. From the Ocusol-A
calculation for the 8-ft-diameter core and a fuel salt containing 0.5 mole %
ThF4 it was found that 0.176 of the neutrons would be captured in the
blanket. If an energy release of 7 Mev/capture is assumed, the heat release
at a power level of 600 Mw (heat) is estimated to be 8.6 Mw. The total is
thus 18.3 Mw or, say, 204+ 5 Mw, to allow for errors.

No allowance was made for fissions in the blanket. These would add 6
Mw for each 1% of the fissions occurring in the blanket. Thus it appears
that the heat release rate in the blanket might range up to 50 Mw.

14~1.2 Intermediate states. Without reprocessing of fuel salt. The nu-
clear performance of a homogeneous molten-salt reactor changes during
operation at power because of the accumulation of fission produects and
nonfissionable isotopes of uranium. It is necessary to add U235 to the fuel
salt to overcome these poisons and, as a result, the neutron spectrum is
hardened and the regeneration ratio decreases because of the accompanying
decrease in 7 for U233 and the increased competition for neutrons by the
poisons relative to thorium. The accumulation of the superior fuel U233
compensates for these effects only in part. The decline in the regeneration
ratio and the increase in the critical inventory during the first year of
operation of three reactors having 8-ft-diameter cores charged, respectively,
with 0.25, 0.75, and 1 mole %, ThF'4 are illustrated in Fig. 14-9. The criti-
cal inventory increases by about 300 kg, and the regeneration ratio falls
about 16%,. The gross burnup of fuel in the reactor charged with 1 mole 7,
ThF4 and operated at 600 Mw with a load factor of 0.809 amounts to
about 0.73 kg/day. The U235 burnup falls from this value as U233 assumes
part of the load. During the first month of operation, the U235 burnup
averages 0.69 kg/day. Overcoming the poisons requires 1.53 kg more and
brings the feed rate to 2.22 kg/day. The initial rate is high because of the
holdup of bred fuel in the form of Pa233. As the concentration of this iso-
tope approaches equilibrium, the U235 feed rate falls rapidly. At the end
of the first year the burnup rate has fallen to 0.62 kg/day and the feed rate
to 1.28 kg/day. At this time U233 contributes about 129, of the fissions.
The reactor contains 893 kg of U235 70 kg of U233, 7 kg of Pu23?, 62 kg
of U236 and 181 kg of fission products. The U236 and the fission products
capture 1.8 and 3.89, of all neutrons and impair the regeneration ratio
by 0.10 units. Details of the inventories and concentrations are given in
Table 14-4.

With reprocessing of fuel salt. If the fission products were allowed to ac-
cumulate indefinitely, the fuel inventory would become prohibitively large
and the neutron economy would become very poor. However, if the fission
products are removed, as described in Chapter 12, at a rate such that the
14-1] HOMOGENEOUS REACTORS FUELEP WITH U230 645

0.7

 

1 mole °4 Th¥4 in Fuel Salt
0.75

 

Regeneration Ratio

 

1 0.50
|
}+— Processing Begins

0.4 i i

 

 

 

Inventory, Kg

 

 

 

 

200 No Processing ——wjw— Processing Begins U233
100 |- | mote % ThE4 _
0.75
0.50
0 I |
1 2 3

Time of Operation, years

I'ta. 14-9. Operating performance of two-region, homogeneous, molten flyoride-
salt reactors fueled with U235, Core diameter, 8 ft; total power, 600 Mw (heat);
load factor, 0.80.

equilibrium inventory is, for example, equal to the first year’s production,
then the increase in U235 inventory and the decrease in regeneration ratio
are effectively arrested, as shown in Fig. 14-10. The fuel-addition rate
drops immediately from 1.28 to 0.73 kg/day when processing is started.
At the end of two years, the addition rate is down to 0.50 kg/day, and 1t
continues to decline slowly to 0.39 kg/day after 20 years of operation.
The nonfissionable isotopes of uranium continue to accumulate, of course,
but these are nearly compensated by the ingrowth of U233, As shown in
Fig. 14-10, the inventory of U235 actually decreases for several years in a
typical case, and then increases only moderately during a lifetime of
20 vears,

The rapid increase in critical inventory of U235 during the first year can
be avoided by partial withdrawl of thorium. In Fig. 14-10 the dashed
lines indicate the course of events when thorium is removed at the rate of
1/900 per day. Burnup reduces the thorium concentration by another
(46 NUCLEAR ASPECTS OF MOLTEN-SALT REACTORS [cuaPp. 14

 

 

 

 

 

 

 

 

 

 

0.7 T 1 ‘
2 : I .
T
o
c 06 _ |
.0
*é 1 mole % ThFy4 In Fuel Salt
a T —
0.5 —~—— _ ]
E.’_’ ‘‘‘‘‘‘‘ Decreasing ThF4
x ; L
o4 ] T
1200 T T T
: | ! |
™ /

g}: 1000 +— // —
5 1 mole % ThF4 In Fuel Salt
o 800 ” — - .

o~ y235 _—— x
= | B . ——— Decreasing ThF4
5 400 - ]
o
x
52.; oo 1 mole % ThFg In Fuel Salt |
< —>
2 233
£ 200 e ——— v
= {Accumulated)
J ! | i | | | [ i
G 10 20

Time of Operation, years

F1g. 14-10. Long-term nuclear performance of typical two-region, homogeneous,
molten fluoride-salt reactors fueled with U235, Core diameter, 8 ft; total power,
600 Mw (heat); load factor, 0.80.

1/4300 per day. The U2% inventory rises to 826 kg and then falls, at the
end of eight months, to 587 kg. At this time, the processing rate is in-
creased to 1/240 per day (eight-month cycle), but the thorium is returned
to the core and the thorium concentration falls thereafter only by burnup.
It may be seen that the U235 inventory creeps up slowly and that the re-
generation ratio falls slowly. The increase in U235 inventory could have
been prevented by withdrawing thorium at a small rate; however, the re-
generation ratio would have fallen somewhat more rapidly, and more U235
feed would have been required to compensate for burnup.

14-2. HomoGENEQOUs REACTORS FUELED wrTH [J233

Uranium—233 is a superior fuel for use in molten fluoride-salt reactors in
almost every respect. The fission cross section in the intermediate range of
neutron energies is greater than the fission cross sections of U235 and
Pu23?, Thus initial critical inventories are less, and less additional fuel is
required to override poisons. Also, the parasitic cross section is sub-
stantially less, and fewer neutrons are lost to radiative capture. Further,
the radiative captures result in the immediate formation of a fertile iso-
C'ore diameter: 8 ft.

TanLe 11-4

Fxternal fuel volume: 339 ft3.

NucLeak Perrormasce or A Two-Redion, HoMocENEOUS,
MovrreN FLuoribe-Saur Reactor Frenep wita U232
AND Coxrtaining 1 mour 9 Tuly 1x THE Furn Sart

Total power: 600 Mw (heat).
Load factor: 0.8.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Initial state After 1 year
Inventory, Absorptions, Fissions, Inventory, Absorptions, Fissions,
kg % o kg % %
Core elements
Th232 2,100 20.3 2,100 16.7
[*a233 8.2 0.3
17233 61.0 5.9 12.5
234 1.9 0.0
235 604 55.4 100 &893 49 .3 86.3
U236 62.2 1.8
Np237 4.2 0.2
1238 45.3 2.2 57.9 2.0
Pu2ss 6.8 0.8 1.2
Fission fragments 181 3.8
L7 3,920 1.9 3,920 0.9
Be? 3,008 0.6 3,008 0.5
Ir9 24,000 3.2 24,000 3.0
Rlanket element
238 8 7
Total fuel 604 963
1225 burnup rate, kg/day 0.69 0.62
U235 feed rate, kg/day 2.22 1.28-0.73
Regeneration ratio 0.64 0.53
continued

[g-%1

pez(l HLIM UETINA SUOLOVAY SNOANTADOWOH

L¥9
TaBLE 14-4 (continued)

 

 

 

 

 

 

 

 

 

 

 

 

 

After 2 years After 5 years
Inventory, Absorptions, Fissions, Inventory, Absorptions, Fissions,
kg % %o kg %% %
Core elements
Th232 2,100 16 .3 2,100 15.4
Pg233 7.9 02 7.5 0.2
Uzss 110 9 7 20.8 201 15.3 33.0
234 6.5 0.1 27.1 04
235 863 44 .3 77.4 818 36.9 64.1
U236 115 31 222 5.2
Np237 0.8 0.4 1.8 0.8
[j238 69.7 23 9.0 2.7
Py239 12.0 13 1.8 24 .3 2.0 2.9
Fission fragments 181 36 181 3.1
Li? 3,920 08 3,920 0.6
Be? 3,008 0.5 3,008 0.5
Fo 24,000 3.0 24,000 3.0
Blanket element
233 16 24
Total fuel 990 1,045
U235 burnup rate, kg/day 0.58 0.47
U235 feed rate, kg/day 0.50 0.45
Regeneration ratio 0.53 0.54
continued

8+9

SIOUdSY UVHTOON

SHOLOVHY LIVS-NEHLIOK J0

F1 dVHD)
TaBLE 14-4 (continued)

 

After 10 years

After 20 years

 

 

 

 

Inventory, Absorptions, Fissions, Inventory, Absorptions, Fissions,
kg Yo % kg %o %
Core elements
Th232 2,100 14.6 2,100 13.7
Pa?33 7.1 0.2 6.7 0.2
233 266 17.6 38.38 322 18.8 41.0
U234 64.4 0.8 124 1.4
U235 831 33.5 58.2 R72 31.7 54.9
U236 328 6.7 450 7.9
Np237 2.6 0.9 3.2 1.0
U238 10.8 2.9 12.9 3.0
Pu?239 37.3 2.4 3.5 52.6 2.8 4.1
Fission fragments 181 2.7 181 2.4
Li7 3,920 0.5 3,920 0.4
Be? 3,008 0.5 3,008 0.5
Ie 24,000 3.0 24,000 3.0
Blanket element
233 28 33
Total fuel 1,129 1,232
U235 burnup rate, kg/day 0.41 0.38
U235 feed rate, kg/day 0.44 0.39
Regeneration ratio 0.533 0.530

 

 

 

 

 

 

 

 

[Z-%1

cpz{l HIIM JATINA SHOLOVHY SNO0ANITDONOH

6%9
650 NUCLEAR ASPECTS OF MOLTEN-SALT REACTORS [cHAP. 14

tope, U234, The rate of accumulation of U?3% is orders of magnitude smaller
than with U235 as a fuel, and buildup of Np?37 and Pu?3? is negligible.

The mean neutron energy is rather nearer to thermal m these reactors
than it is in the corresponding U235 cases. Consequently, losses to core
vessel and to core salt tend to be higher. Both losses will be reduced sub-
stantially at higher thorium concentrations.

14-2.1 Initial states. Results from a parametric study of the nuclear
characteristics of two-region, homogeneous, molten fluoride-salt reactors
fueled with U23? are given in Table 14-5. The core diameters considered
range from 3 to 10 ft, and the thorium concentrations range from 0.25 to 1
mole 9. Although the regeneration ratios are less than unity, they are very
good compared with those obtained with U235, With 1 mole 9, ThF4 in
an 8-ft-diameter core, the U23? inventory was only 196 kg, and the re-
generation ratio was 0.91.

The regeneration ratios and fuel inventories of reactors of various diam-
eters containing 0.25 mole 9} thorium and fueled with U235 or U233 gre
compared in Fig. 14-11. The superiority of U233 is obvious.

 

 

 

 

1.0 | |
U233
.0
5 08[ —
=
9
3
g U235
o \
0.4 | |
0 200 400 600

Critical Inventory, kg of U

F1a. 14-11. Comparison of regeneration ratios in molten-salt reactors containing
0.25 mole 9, ThF, and U?35- or U?33.enriched fuel.

14-2.2 Intermediate states. Calculaticns of the long-term performance
of one reactor (Case 51, Table 14-5) with U233 as the fuel are described
below. The core diameter used was 8 ft and the thorium concentration
was 0.75 mole 9. The changes in inventory of U233 and regeneration ratio
are listed in Table 14-6. During the first year of operation, the inventory
rises from 129 to 199 kg, and the regeneration ratio falls from 0.82 to 0.71.
If the reprocessing required to hold the concentration of fission products
TasLE 14-5

NucrLear CnaracrerisTics oF Two-Reaion, HoMoGENEOUS,
MoLTEN FLUORIDE-SALT REACTORS FUKLED wiTh U233

Core diameter: 8 ft.

External fuel volume: 339 ft3.

Total power: 600 Mw (heat).
Load factor: 0.8,

 

 

 

 

 

 

 

 

 

 

 

 

 

Case number 41 42 43 44 45 46
Fuel and blanket salts* 1 1 1 1 1 1
Core diameter, ft 3 4 4 5 6 6
Th¥, in fuel salt, mole 9 0 0 0.25 0 0.25 0.25
U233 in fuel salt, mole 9 0.592 0.158 0.233 0.106 0.048 0.066
U233 atom density 21.0 6.09 8.26 3.75 1.66 2.36
Critical mass, kg of U233 64.9 22.3 30.3 26.9 20.5 29.2
Critical inventory, kg of U233 1620 248 337 166 82.0 117
Neutron absorption ratios?
U232 (figsions) 0.8754 0.8706 0.8665 0.8725 0.8814 0.8779
U283 (n—y) 0.1246 0.1294 0.1335 0.1275 0.1186 0.1221
Be-Li-F in fuel salt 0.0639 0.1061 0.0860 0.1472 0.3180 0.2297
Core vessel 0.0902 0.1401 0.1093 0.1380 0.1983 0.1508
Li-Be-F in blanket salt 0.0233 0.0234 0.0203 0.0196 0.0215 0.0179
Leakage 0.0477 0.0310 0.0306 0.0193 0.0160 0.0157
Th in fuel salt 0.1095 0.1593 0.1973
Th in blanket salt 0.9722 0.8857 0.8193 0.7066 0.6586 0.5922
Neutron yield, 7 2.20 2.19 2.18 2.19 2.21 2.20
Median fission energy, ev 174 14 19 2.9 0.33 1.2
Thermal fissions, % 0.053 8.0 2.3 16 38 29
n—y capture-to-fission ratio, « 0.14 0.15 0.15 0.15 0.13 0.14
Regeneration ratio 0.97 0.89 0.93 0.87 0.66 0.79
continued

[z¥1

ezl HLIM QHTENd SHOLOVAYM SNOINADOWOH

169
TaBLE 14-5 (continued)

 

 

 

 

 

 

 

 

 

 

Case number 47 48 49 50 51
Fuel and blanket salts* 1 1 1 1 2
Core diameter, ft 8 8 10 10 8
ThF, in fuel salt, mole 9 0.25 1 0.25 1 0.75
U233 in fuel salt, mole %, 0.039 0.078 0.031 0.063 0.0597
U233 atom densityt 1.40 2.95 1.10 2.29 1.97
Critical mass, kg of U233 41.1 86.6 63.0 131 58.8
Critical inventory, kg of U233 93.1 196 104 216 129
Neutron absorption ratiosi
U233 (figsions) 0.8850 0.8755 0.8881 0.8781 0.8809
U233 (n—y) 0.1150 0.1245 0.1119 0.1219 0.1191
Be-Li-F in fuel salt 0.3847 0.1899 0.5037 0.2360 0.2458
Core vessel 0.1406 0.0778 0.1168 0.0629 0.1168
Li-Be-F in blanket salt 0.0141 0.0095 0.0108 0.0071 0.0187
Leakage 0.0095 0.0090 0.0068 0.0065 0.0050
Th in fuel salt 0.2513 0.5768 0.2852 0.6507 0.4903
Th in blanket salt 0.4211 0.3344 0.3058 0.2408 0.3325
Neutron yield, n 2.22 2.20 2.23 2.20 2.21
Median fission energy, ev 0.20 1.1 509, Th 3.2 0.68
Thermal fissions, 9 43 24 50 30 34
n—y ecapture-to-fission ratio, « 0.13 0.14 0.13 0.14 0.14
Regeneration ratio 0.67 0.91 0.59 0.89 0.82

 

 

649

SLOHISY UVHATIAN

SUOLOVHEY LIVS-NALIOW 40

*Fuel salt No. 1: 31 mole 9, BeFs + 69 mole 9, LiF + UF4+ ThF.
Blanket salt No. 1: 25 mole 9%, ThF4+ 75 mole 9, LiF
Fuel salt No. 2: 37 mole 9, BeFs + 63 mole 9, LiF' + UF4+4 ThF,
Blanket salt No. 2: 13 mole 9, ThF4 + 16 mole 9, BeF3 4+ 71 mole 9, LiF

TAtoms (X 10719) /ce. tNeutrons absorbed per absorption in U233,

$1 "dVHD]
NucLear PerrormaNck or A Two-RecioN, HoMoGuNEOUS,
Moty Frroripe-Sart Reacror Fuernep wita U233 Anxp

TaBLE 14-6

Conrtaining 0.75 moLE 97 TuF4 IN THE FUEL SavT

Total power: 600 Mw (heat).
Load factor: 0.8.

Core diameter: 8 ft.

External fuel volume: 339 ft3.

 

 

 

 

 

 

 

 

 

 

 

 

 

Initial state After 1 year
Inventory, Absorptions, Fissions, Inventory, Absorptions, Fissions,
kg % % kg % o
Core elements
Th2s2 1,572 22.2 1,572 19.1
Pa23 9. 0.5
1233 129 45.2 100 199 45.3 99 .5
234 23.3 0.9
235 1.9 0.3 0.5
;236 01 0.1
Np237
1238
P39
IFission fragments 181 7.9
Li6 3,920 6.5 3,920 3.4
Bef 3,004 0.8 3,008 6.7
e 24,000 40 24,000 3.5
Blanket element
{233 8.6
Total fuel 129 210
1233 feed rate, kg/day 0.790 (. 370-0.189
Regeneration ratio 0.82 0.71
continued

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TaBLE 14-6 (continued)

 

 

 

 

 

 

 

 

 

 

 

 

 

After 2 years After 5 years
Inventory, Absorptions, Fissions, Inventory, Absorptions, Fissions,
kg Yo Yo kg % T
Core elements
Th232 1,572 18.9 1,572 18.3
Pa233 9.0 0.5 8.9 0.4
U233 204 44 .9 98.5 216 43.7 95.6
234 44 0 1.7 89 3.1
=235 5.4 0.8 1.5 17.7 2.3 4.4
236 0.6 0.3 4.2 0.2
Np27 0.1 0.1 0.5 0.1
=38 0.3
Pu239
Fission fragments 1381 7.7 181 7.2
L1 3,920 3.3 3,920 2.8
Be? 3,008 0.6 3,008 0.6
Ir19 24,000 3.4 24,000 3.3
Blanket clement,
1J233 10.7 16.2
Total fuel 220 250
U233 feed rate, kg/day 0. 188 0.181
Regeneration ratio 0.72 0.73
continued

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SHOLOVHY LIVS-NALIONW JO SLOAdSY HVHTOAN

$1 "dVHD]
TasrLe L1 6 (continued)

After 10 years

 

After 20 vears

 

 

 

 

 

Inventory, Absorptions, Fissions, Inventory, Absorptions, Fissions,
kg Yo To kg T %o
Core elements
Th232 1,572 17.8 1,572 17.2
Pa233 8.6 0.4 8.4 0.4
17233 231 425 92.8 247 41.5 90.5
1234 132 4.2 172 5.0
U235 32.5 3.7 7.1 47 4.8 9.0
236 12.5 0.6 24 1.1
Np237 1.7 0.2 3.4 0.3
238 1.7 0.1 5.1 0.3
Py 239 0.2 0.1 0.1 0.8 0.3 0.5
Figsion fragments 181 6.7 181 6.3
1.8 3,920 2.5 3,920 2.1
Be? 3,008 0.6 3,008 0.6
F1o 24,000 3.3 24,000 3.3
Blanket element
y23s 22 .2 31.6
Total fuel 282 295
U233 feed rate, kg/day 0.171 0.168
Regeneration ratio 0.73 0.73

 

 

 

 

 

 

 

 

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656 NUCLEAR ASPECTS OF MOLTEN-SALT REACTORS fchar. 14

and Np237 constant is begun at this time, the inventory of U?33 increases
slowly to 247 kg and the regeneration ratio rises slightly to 0.73 during the
next 19 years. This constitutes a substantial improvement over the per-
formance with U235,

14-3. HomoGENEOUS REACTORS FUELED WiTH PLUTONIUM

It may be feasible to burn plutonium in molten fluoride-salt reactors.
The solubility of PuF3 in mixtures of LiF and BeFs is considerably less
than that of UF4, but is reported to be over 0.2 mole % [8], which may be
sufficient for criticality even in the presence of fission fragments and non-
fissionable isotopes of plutonium but probably limits severely the amount
of ThF4 that can be added to the fuel salt. This limitation, coupled with
the condition that Pu?3? is an inferior fuel in intermediate reactors, will
result in a poor neutron economy in comparison with that of U233-fueled
reactors. However, the advantages of handling plutonium in a fluid fuel
system may make the plutonium-fueled molten-salt reactor more desirable
than other possible plutonium-burning systems.

14-3.1 Initial states. Critical concentralion, mass, tnventory, and regen-
eration ratto. The results of calculations of a plutonium-fueled reactor
having a core diameter of 8 ft and no thorium in the fuel salt are described
below. The critical concentration was 0.013 mole % PuF3, which is an
order of magnitude smaller than the solubility limits in the fluoride salts
of interest. The critical mass was 13.7 kg and the critical inventory in a
600-Mw system (339 ft3 of external fuel volume) was only 31.2 kg.

The core was surrounded by the Li-Be-Th fluoride blanket mixture
No. 2 (13% ThF4). Slightly more than 19% of all neutrons were captured
in the thorium to give a regeneration ratio of 0.35. By employing smaller
cores and larger investments in Pu?3® however, it should be possible to
increase the regeneration ratio substantially.

Neutron balance and miscellaneous details. Details of the neutron economy
of a reactor fueled with plutonium are given in Table 14-7. Parasitic cap-
tures in Pu?39 are relatively high; n is 1.84, compared with a » of 2.9. The
neutron spectrum is relatively soft; almost 60% of all fissions are caused
by thermal neutrons and, as a result, absorptions in lithium are high.

14-3.2 Intermediate states. On the basis of the average value of @ of
Pu239 it is estimated that Pu?40 will accumulate in the system until it cap-
tures, at equilibrium, about half as many neutrons as Pu?®. While these
captures are not wholly parasitic, inasmuch as the product, Pu?%!, is
fissionable, the added competition for neutrons will necessitate an increase
in the concentration of the Pu?3?. Likewise, the ingrowth of fission products
14--4] HETEROGENEOUS GRAPHITE-MODERATED REACTORS 657

will necessitate the addition of more Pu?3”. Further, the rare earths among
the fission products may exert a common-ion influence on the plutonium
and reduce its solubility. On the credit side, however, is the U233 produced
in the blanket. If this is added to the core it may compensate for the in-
growth of Pu?® and reduce the Pu?*" requirement to below the solubility
limit, and it may be possible to operate indefinitely, as with the U23>-
fueled reactors.

14—4. HETEROGENEOUS GRAPHITE-MODERATED RREACTORS

The use of a moderator in a heterogencous lattice with molten-salt
fuels is potentially advantageous. First, the approach to a thermal neutron
spectrum 1mproves the neutron yield, 5, attainable, especially with U235

TaBLE 14-7
INITIAL-STATE NUCLEAR CHARACTERISTICS OF A
TypicaL MoLTEN FLUoriDE-SarT REACTOR
FueLenp wrtn Pu239

 

 

 

 

Core diameter: 8 ft.
External fuel volume: 339 ft3.
Total power: 600 Mw (heat).
Load factor: 0.8.
Critical inventory: 31.2 kg of Pu?3Y,
Critical concentration: 0.013 mole 9 Pu239,
Neutrons absorbed per
neutrons absorbed in Pu??*®
Neutron absorbers
Pu?*9 (fissions) 0.630
Pu# (n—y) 0.372
Li% and Li7 in fuel salt 0.202
Be® in fuel salt 0.022
F191n fuel salt 0. 086
Core vessel 0.145
Th in blanket salt - 0.352
Li-Be-F 1n blanket salt 0.024
Reactor vessel 0.004
Leakage 0.003
Neutron yield, 1.84
Thermal fissions, % 59
Regeneration ratio 0.352

 

 

 

 
(58

NUCLEAR ASPECTS

TaBLE 14-8

OF MOLTEN-SALT REACTORS

[cHAP. 14

CoMPARISON OF GRAPHITE-MODERATED MOLTEN-SALT
AND Liguip-MEeTAL-FUELED *REACTORS

 

 

 

 

LMFR MSFR-1 MSFR-2
Total power, Mw (heat) 580 600 600
Over-all radius, in. 75 75 72
Critical mass, kg of U233 9.9 9.6 27.7
Critical inventory, kg of U233* 467 77.8 213
Regeneration ratio 1.107 0.83 1.07
Core
Radius, 1n. 33 33 34.8
Graphite, vol 9 45 45 45
Tuel fluid, vol % 55 DD HH
TFuel components, mole %
Bi ~100
Lil 69 61
Bels 31 36.5
T}1F4 2 . 5
Unmoderated blanket
Thickness, in. 6 6 13.2
Composition, mole 9
Bi 90
Th 10 (Th) | 10 (ThF4) 13 (ThFy)
LiF 70 71
Bel's 20 16
233 0.015 0.014
Moderated blanket
Thickness, in. 36 36 24
Composition, vol 9%
Graphite 66.6 66.6 100
Bianket fluidt 33.4 33.4
Neutron absorption ratiol
Th in fuel fluid 0.566
U233 in fuel fluld 0.918 0.925 1.000
Other components of fuel fluid 0.081 0.324 0.106
Th in blanket fluid 1.110 0.825 0.490
1233 in blanket fluid 0.083 0.071
Other compenents of blanket fluid 0.040 0.092 0.038
Leakage 0.012 0.004 0.014
Neutron yield, 9 2.24 2.24 2.21

 

 

 

 

 

*With bismuth, the external volume indicated in Ref. 10 was used. The molten-

salt systems are calculated for 339 ft* external volumes.
tSame as unmoderated blanket fluid.
tNeutrons absorbed per neutron absorbed in 17233,
14-4] HETEROGENEOUS GRAPHITE-MODERATED REACTORS 659

and Pu®?”. Second, in a heterogeneous system, the fuel i partially shielded
from neutrons of intermediate energy, and a further improvement in ef-
fective neutron yield, n, results. Further, the optimum systems may prove
to have smaller volumes of fuel in the core than the corresponding fluorine-
moderated, homogeneous reactors and, consequently, higher concentrations
of fuel and thorium in the melt. This may substantially reduce parasitic
losses to components of the carrier salt. On the other hand, these higher
concentrations tend to increase the inventory in the circulating-fucl
system external to the core. The same considerations apply to fission prod-
ucts and to nonfissionable isotopes of uranium.

Possible moderators for molten-salt reactors include beryllium, BeO),
and graphite. The design and performauce of the Aircraft Reactor Experi-
ment, a beryllium-oxide moderated, sodium-zirconium fuoride salt, one-
region, U*7-fueled burner reactor has been reported (see Chapter 16).
Since beryvllium and BeO and molten salts are not chemically compatible,
1t wax necessary to line the fuel circuit with Inconel. Tt is easily estimated
that the presence of Inconel, or any other prospective containment metal
in a heterogeneous thermal reactor would seriously impair the regeneration
ratio of a converter-breeder. Consequently, beryllium and BeO are elimi-
nated from consideration.

Preliminary evidence indicates that uranium-bearing molten salts may
be compatible with some grades of graphite and that the presence of the
graphite will not carburize metallic portions of the fuel circuit seriously [9].
It therefore becomes of interest to explore the capabilities of the graphite-
moderated systems. The principal independent variables of interest are
the core diameter, fuel channel diameter, lattice spacing, and thorium
concentration,

14—4.1 Initial states. Two cases of graphite-moderated molten-salt re-
actors have been caleulated for the same geometry and graphite-to-fluid
volume ratio as those for the reference-design LMFR [10]. The results for
these two cases, together with those for the Hquid bismuth case, are sum-
marized in Table 14-8. Only the initial states arc considered, and a metallie
shell to separate core and blanket fluids has not been included. With no
thorium in the core fluid, the molten-salt-fucled reactor has a significantly
lower regeneration ratio than that of the liquid-metal-fueled reactor, with
only a slightly lower eritical mass, Adding 2.5 mole ¢ ThF, to the core
fluid increases the initial regeneration ratio to about 1.07, with a critical
mass and a corresponding total fuel inventory that are acceptably low.
660 NUCLEAR ASPECTS OF MOLTEN-SALT REACTORS [cuap. 14

REFERENCES

1. R. L. MackuiN, Neutron Activation Cross Sections with Sb-Be Neutrons,
Phys. Rev. 107, 504-508 (1957).

2. L. G. Avexaxper et al.,, Operating Instructions for the Univac Program
Ocusol-1, A Modification of the Eyewash Program, USAEC Report CF-57-6-4,
Oak Ridge National Laboratory, 1957.

3. J. H. Avexanper and N. D. Given, 4 Machine Multigroup Calculation.
The Eyewash Program for Univac, USAKC Report ORNIL-1925, Oak Ridge
National Laboratory, 1955.

4, J. T. Roserts and L. G. AvLeExanprr, Cross Sections for the Ocusol-A
Program, USAEC Report CF-57-6-5, Oak Ridge National Laboratory, 1957.

5. B. W. Kinvon, Oak Ridge National Laboratory, 1958, personal communi-
cation.

6. W. D. Powgrs, Oak Ridge National Laboratory, 1958, personal communi-
cation.

7. L. G. ALExanDpER and L. A. MaNN, First Estimate of the Gamma Heating
in the Core Vessel of a Molten Fluoride Converter, USAEC Report CF-57-12-77,
Oak Ridge National Laboratory, 1957.

8. C. I. Barton, Solubtility and Stability of PuFg tn Fused Alkali Fluoride-
Beryllium Fluoride, USAEC Report ORNL-2530, Oak Ridge National Labora-
tory, 1958.

9. F. Kurresz, Oak Ridge National Laboratory, 1958, personal communica-
tion.

10. Bascock anp Wincox Co., Liguid Metal Fuel Reactor, Technical Feast-
bility Report, USAEC Report BAW-2(Del.), 1955.