EIR-229.txt

EIR-Bericht Nr. 229

" inig

EIR-Bericht Nr. 229

Eidg. Institut flir Reaktorforschung Wirenlingen
Schweiz

MOLTEN CHLORIDES FAST BREEDER REACTOR
Reactor Physics Calculations

J. Ligou

Wiirenlingen, November 1972

EIR Report No 229

MOLTEN CHLORIDES FAST BREEDER REACTOR

Reactor Physics Calculations

J. Ligou

November 1972
Contents

10.

Introduction

Definition of the Proposed Reactor

Cross-sections and Calculational Methods

Reference Calculations for Spherical Geometry

Parasitic Absorbtions

5.1. Chlorine

5.2. Molybdenum

5.3. Vessel

Void and Temperature Coefficients

Buckling Search and Blanket Savings

Transport Calculations in Cylindrical Geometry -
Final Results

Fast Flux Test Facility Using Molten Chlorides

Conclusions

Acknowledgement

References

Appendix 1
Appendix 2
Appendix 3

Page

15

18

19

24

27

29

29

31

32
34
l. Introduction

In an earlier report (l) the possibilities of a Molten Chlo-
rides Fast Breeder Reactor (MCFBR) were analysed, based on
thermohydraulic and neutronic studies. Although reactor phy-
sics calculations have been made from the beginning when

the reactor characteristics were not frozen they can only
be fixed later during the main phases of the studies when
thermohydraulic, chemical and economic aspects are taken
into account. The sensitivity of fast reactor performance

to the neutron spectrum is well known and the spectrum de-
pends strongly on the core composition i.e. on the results
of thermohydraulic, mechanical and optimization studies.
This feedback has therefore led to new reactor physics

calculations.

In addition the earlier studies used a rather old cross-
section set and omitted dilution factors. The new calcula-
tions are more sophisticated based on.-a more recent library

with detailed information on

chloride cross—-sections and fine spectrum
- neutron balance and breeding ratios

- void and temperature reactivity coefficients

specific power distributions etc.

As usual (2) most calculations are made for a spherical geo-
metry; this approximation is very good, only‘the critical
mass and the radial distributions of specific power have

been recalculated for the correct geomefiry;

As was expected, the conclusions of ref. 1 remain valid,

only the coolant tube diameters have to be adjusted
slightly together with an admissible increase in coolant
velocity. All core temperatures remain unchanged in the

core and therefore the atomic densities.

A final section gives some results concerning HIGH FLUX

FAST TEST FACILITY using molten chlorides as proposed in (3).

2. Definition of the Proposed Reactor

The coolant, forming the fertile material is pumped through
the reactor through a lattice of tubes, and the fuel mate-
rial circulates between these tubes in a forced convection
circuit. The reference characteristics of the core cell

are based on a tube pitch of 1.38 cm (1):

Fuel - area Vf = 0.7354 cm?
- volumetric fraction 38.6 %
- mean temperature 12570 K
- mean density 2.344

- molecular composition 16 % PuClsy, 84 % NaCl

Coolant - area Vc = 1.05683 cm2
(inner diameter 2a =1.16 cm)

- volumetric fraction 55.5 %

- mean temperature 10429KK
- mean density 4.010
- molecular composition 65 % UC13, 35 % NacCl
Tubes - area 0.11215 cm2 (thickness 0.3 mm)

- volumetric fraction 5.9 %
— density 10

- welight composition 20 % Mo, 80 % Fe
Only the tube diameter has been changed (l.16 cm instead of
1.20 cm) which has no effect on the temperature, density
etc. provided a new coolant velocity is chosen accordingly
(12 m/s instead of 9 m/s (4)). The composition of the struc-
tural material was also changed (20 % Mo instead of 80 %)

because the reactivity cost of the tubes was too high.

Finally the core atomic densities are (A/cm3°1024):
Pu239 6.6796-10 2
Pu240 1.6699-10"2
U238 3.5629.10°
c1 1.9495-10 2
Na 6.3017-10 °
Mo 7.386 10”2
Fe 5.078 +10 >

which gives 5.584 for the Fertile/Fissile ratio for materials
in the core.
It is assumed in this table that the isotopic composition

of the plutonium is

80 & (Pu239 + Pu24l)
20 % Pu240

and the nuclear properties of Pu239 and Pu24l are the same.
This composition is somewhat arbitrary and fuel cycle calcu-
lations should really be carried out. These calculations are
too long for the preliminary studies laid down here.
Nevertheless the composition chosen is very similar to that

of a solid fuel fast reactor.

For the blanket the coolant characteristics (composition,
density) adopted give:

U238 6.4203-10 °
cl 2.2718-10" 2
Na 3.457- 103

The natural isotopic composition is assumed for the Chlorine.
The dimensions and number of coolant tubes are fixed by the

critical mass calculations.

3. Cross—-sections and Calculational Methods

Usually the number of energy groups required for a good defi-
nition of neutron spectrum is at least 12 for fast critical
assembly studies and 22 can be considered desirable (5).
Therefore, a 22 group cross—-section set has been prepared;
the code GGC3 (6) which allows 99 group calculations for a
rather simple geometry has been used for this condensation.
The cross-sections were produced separately for core and
blanket and the scattering anisotropy was limited to P1
which is sufficient for this reactor type. Most of the

GGC3 library data were evaluated by GGA before 1967 but
some are more recent:

- Iron:
Evaluated from ENDF/BI data (Feb. 1968)

~ Molybdenum:
Evaluated from isotopes of ENDF/B data (July 1968)

-~ Plutonium 239:
Evaluated from KFK 750 Resonance Nuclide (Feb. 1969)
New data concerning Chlorine absorbtion cross-sections are
now available at EIR (fig. 1); they are obtained from
ENDF/B-III (Jan. 1972) which is the best nuclear library
at present. Unfortunately this information came too late
to be used for the transport calculations. Fig. 2 (curves

5 and 6) shows that the GGC3 wvalues were underestimated
above 0.6 MeV and overestimated between 10 keV and 0.6 MeV.
The effect of this on the reactivity is not great (Sect.5).
Taking also the Molybdenum cross-section from ENDF/B-IIT
one can see that the GGC3 values are too high (experiments
made with Molybdenum control rods in fast critical assem-
blies could not be reproduced with ENDF/B-I which makes a

new evaluation of data necessary).

Fission product data are from (7). The absorbtion cross-sec-
tions for resonant nuclides are obviously shielded. The
NORDHEIM theory (8) is included in the GGC3 code, it requires

some special data as shown in table 1.

Table 1

4 o) — R

R
Resonant NR(102 ) T K agr Cgr om, 1 omRz om

Nuclide R

U238 6.42:10 °|1042)t0.58]0.925 2.18 7.10| 20.3

(coolant)

Pu239 1.725°10 > 1257] 0.40l0.83 | 26.3 | 23.0 |178.3

(fuel)
4

Pu240 4.32-10 11257/ 0.40(0.83 [105.0 111.7 |731.7
(fuel)

where NR is the lumped nuclear density of absorber R.
4V

The mean chord of the lump 2 ap is given by E?g-where VR is

the coolant or fuel area and 2a the coolant tube dia. For

the coolant one has obviously 3; = a and for the fuel E; =
Vfyel
Ta

The Dancoff coefficient is calculated with a simple formula

(9)

C ¥ 1 - fuel with Z = 0.10 cm-l
cool S N 1 fuel
fuel 2a (fuel total cross—section
fuel
for the resonance energy
of U).
C =1 - cool with I = 0.18 cm T
fuel 5 N 1 cool .

tion for the resonance

energy of Pu).
The cross-sections of the two "inner moderators" (6) per
resonant atom om1 and om2 are defined in the following way.
For U238 the diluents are Na and Cl; for Pu239 - Na and

(C1l+Pu240), for Pu240 - Na and (Cl+Pu239).

. . : R | .
Finally the total diluent cross-section Um is written.

where the "geometrical cross—-section™ OeR is given by (9),

(coolant total cross-sec-
a(1—CR)
o, = — ‘ with o = 1.35
2a_N 1+ (a=-1)Cq

It is not necessary to determine the parameters of Table 1
to a high accuracy because the Doppler coefficients are of
less importance in this reactor compared with thermal

expansion effects (Sect.6).

The GGC3 is currently in use for GCFR studies and a good
agreement with experimental results has been obtained using
the ZPR-3-48 assembly which is representative of an LMFBER
(10) . |

All whole reactor calculations have been made with the one
dimensional transport code SHADOK, using the 22 group cross-
section set in spherical and cylindrical geometry (10). Com-
parison with the more usual SN methods have proved the re-
liability of this code. The transport methods chosen were
aimed at getting a better accuracy for some reactivity coef-
ficients. For the criticality calculations a more simple

approach such as diffusion theory might have been sufficient.

4. Reference Calculations for Spherical Geometry

The 22 group transport calculation gives 125 cm (8.18 m3)
for the critical radius of the core with a blanket thickness
of 95 cm (36.42 m3). The detailed neutron balance is given

below in Table II.
_lO—.

Table II: Neutron Balance % (MCFBR)
B . .
Region ~Absorbtion Leakage | Production
(n,y) 22.51
U238 25.50 {(n,f) 5.99 U238 8.23
(n,y) 5.58
Pu239 34.56 {(n,f) 98.98 Pu239 85.55
(n,y) 2.24
Pu240 3.78 {(n,f) 1.54 Pu240 4.72
&
o) fuel 1.10
&) cl 3.16 {cool 2.06
Fe 1.30 -
Mo 2,04 -
F.P. 0.50 -
Total 71.10 27.40 98.50
(n,y) 23.15
U238 23.70 {(n'f) 0.5t U238 1.50
49
@
e
—
M
Cl 2.22 -
Total 26.00 2.9 1.50

-11-

The relative fluxes in each group are given in Appendix 1
for core centre and core boundary. The corresponding one
group cross-sections are given in Appendix 2. In figure 2
the neutron spectra (flux per lethargy unit) are compared
to that of the fast critical facility ZPR-3-48. This last
spectrum is slightly harder but the spectrum of the MCFBR
compares favourably with that of a power LMFBR.

From Table II one can deduce the following parameters

koo = 1.3850
! core = ©-716
Breeding ratio < Cblanket = 0.670
[ Ctotal  ~ 1.386

For the given core (125 cm radius) the blanket thickness

was varied between 75 cm and 115 cm. Fig. 3 shows the va-
riation of breeding ratios obtained from the new transport
calculations. The reactivity and the core breeding ratio
remain practically constant in this range making the adjust-
ment of core volume unnecessary. Above 100 cm improvement.
of the breeding ratio by increasing blanket thickness gives
a poor return. For example to increase the breeding rétio
from 1.40 to 1.45 requires a thickness increase of 20 cm

f

or a blanket volume increase of 32 %.

On the other hand, it is clear that the reactivity depends
on the core radius.‘Fig. 4 shows the reactivity variation
with core volume increase. Such a curve is very useful when
it is required to translate the cost in reactivity of a sup-
plementary parésitic absorbtion into an increase in core

volume (or Plutonium inventory). The transport calculations
-12-

which gave figure 4 have not provided the corresponding va-
riation of breeding ratio, rather they have been calculated
from the information in Table II (assuming small core volume
variations < 10 % and no important changes in spectra). This

gives

(1) C, .., - 1-386 - 2.45 6k  (breeding in core unchanged).
By the same method the effect of a modification of core com-
position can be evaluated. The only way of doing that with-
out changing the properties of coolant ana fuel is to vary
the coolant tube diameter. The reactivity is very sensitive
to this parameter. If € and n are respectively the relative
increases of coolant and fuel volume for a constant pitch
one has (§ 2)

n = - l.44¢

From Table II
L v L 8.23+10 %c + 0.90.277

1 + 0.2756¢ + 0,.,3944n

which gives
ny
(2) dk - - 0.924 ¢
or n = 1.56 d&k

The corresponding behaviour of the breeding ratios are

[ ¢ Y 0.716 - 1.72 sk

CcCOrxre
(3) ¢ Crianket 2 0.670 - 1.05 8k
L Ceoe ¥ 1.386 - 2.77 sk
Compared to (1) it can be seen that the penalty on the total
breeding ratio for the same dk is only slightly greater
while the penalty on the increase of Plutonium inventory

is five times less (Eg. 2 and Fig. 4). Therefore, a reduc-
tion in the diameter of coolant tubes is better than an in-
crease of core diameter, provided of course that an increase
in coclant velocity is admissible. This last assumption is
implicit in these calculations since the coolant density

was kept constant.

5. Parasitic Absorbtions

5.1. Chlorine

In the whole system the Chlorine absorbtion represents 5.38 3.
We have seen in Sect.3 that the GGC3 values are different

from the more up to date ones (ENDF/B-III). On the basis of
these new cross-sections given in fig. II (curve 6), and
assuming that the reference spectrum is unchanged, a compu-
tation of the one group cross-sections gives 8.64 mb instead
of 6.38 in the core and 9.11 mb instead of 8.83 mb in the
blanket. In this last region the spectrum is softer and the
increase of cross?sections in the high energy range (E>0.6 MeV)
is almost compensated for by the decrease at the lower ener=-

gies (10 keV - 0.6 MeV).

The total absorbtion by Chlorine for the whole system is
6.57 % instead of 5.38 % giving a loss of reactivity of 1.2 %.
This loss could be replaced by a 1.9 % increase in Pu inven-

tory (see Sect.4 Eq. 2) if a very small decrease (0.65 %)
_14_

of the coolant tube diameter is accepted; otherwise by
changing only the core radius a greater increase of Pu in-

ventory (10 %) is required (Fig. 4).

All these modifications lead to a reduction of the breeding
ratio, 1.353 instead of 1.386 but an increase of the blanket

thickness could compensate for this loss (Fig. 3).

Even taking into account this latest data the problem of
parasitic absorbtion of the Chlorine is not dramatic so
there appears to be no need to enrich the Chlorine (Cl137),
which is consistent with the conclusions of Nelson (2). Fi-
gure 2 clearly shows the importance of spectrum shape since
the peak of the spectrum corresponds to the Chlorine cross-
section minimum (65 %2 of neutrons are in an energy range
where GCl z 5 mb). This fact was not perhaps recognised 15
years ago when fine spectrum calculations were not possible,

it would perhaps explain the pessimistic conclusions of se-

veral eminent physicists (11).

5.2. Molybdenum

For the chosen alloy (20 % Mo) the reactivity cost 2 % (see
Table II) is gquite acceptable. However, the cost could ra-
pidly become prohibitive if the volume of the structural ma-
terial and/or the Molybdenum content should increase due to
technological reasons. In the context of detailed studies
this point may well be more important than the definition of
the proper Chlorine cross—sections, although it does seem
that the Molybdenum cross-sections taken from GGC3 were

overestimated.
-15-

5.3. Vessel

In the previous calculations no core vessel was allowed for
at the core/blanket boundary but all the required information
is available - fluxes, one group cross-sections etc. {(Appen-
dix 2) at this point. Using the 'same alloy for the vessel

(20 %3 Mo) the one group macroscopic absorbtion cross=-section

is 2.56'10_3 cm—l giving a loss of reactivity:

Sk(g) = 0.721e
where e is the thickness of the vessel in cm.

For 19 mm thickness as in {2) one gets 1.37 % for the loss

of reactivity, which would be compensated by an increase of
core volume of about 10 % i.e. about 9 m3 instead of 8.18 m3
(10 m3 in Ref. 2). A better solution would be an increase in
the Plutonium inventory of about 2.1 % in the reference core

volume (loss in breeding ratio 1.386 > 1.350).

6. Void and Temperature Coefficients

Five complete transport calculations (GGC3 + SHADOK) have
been made for different coolant or fuel densities, different
temperatures (in this case with the density constant to
determine only the Doppler effect). The reactivity changes

with respect to the reference core are diven in Table III.
_16_

Table III: Reactivity Changes with Density and Temperature

Type of Modification Reactivity Changes
Fuel density -3.0 2 { -1.9 (onky)
(-5 %) U0 -1.1 (leakage)
Coolant density . +2.0 (onkg).
(-5 %) +0.77 & | -1.23 (leakage)
Fuel temperature < o
(+300°C) .01 %
Coolant temperature _ o
(+300°C) .14 %
Full loss of coolant +12.0 % {Yery high on k_ (70 %)

Note:

The partial changes on k_ or leakage are only approximate but

the total reactivity changes are evaluated directly and are

therefore more precise.

The Doppler effect in the fuel is quite negligible due to

compensation between the capture and the fission process.

The effect of full loss of coolant is large and positive but
considerably lower than might be expected from crude calcula-

tions (k_, changes in the reference spectrum).
From Table IITI one can deduce the "feedback effect" which is

very important for kinetics studies:

oy Y op -4
(%) — 60(— - 15 (— - 4,810 ST :
P fuel P coolant (coolant)
-17-

The void coefficient of the fuel (lst term) is strongly ne-

: : -2 ,
gative; 1 % woid (-‘S—Q = =10 ) gives a 0.6 % loss in reactivi-
ty. If boiling occurs in the fuel it will be rapidly arrested

by a decrease in reactor power.

If one considers that all density modifications come from
thermal expansion (liguid phase only), one can define general
temperature coefficients.

The thermal expansion coefficients are (see Apprendix 3).

S _ _
(—%5) = -0.63.107> °c7t
P fuel
(Q%E) = -0.89-1073 Y"1
P coolant

Replacing these values in Egq. (4) lead to the following
expression:

8Kiay ¥ _q ge1n”2 .10" 2
(5) (%) -3.8°10 (5T)fue + 1.29.10 (8§T)

k 1

coolant

In the second term the part played by the Dopplexr coefficient
(4.8-10_4) is quite negligible. For +100°C in the fuel, the
loss of reactivity is -3.8 % which is very important from

the safety point of view. Compared to any kind of power
reactor (even the BWR) the advantage of this kind of reactor

is quite evident.

For the Nelson value of the thermal expansion —3.10-4 in-

stead of --6.3-'10-4 one gets -1.8 % .which is very close to

\Q

the Nelson result -1.5 % (2).
~18-

If we postulate an accident condition and assume that the
same increase of coolant temperature immediately follows the
fuel temperature rise, the overall change in reactivity is

defined by:

%5(%) Y _2.51-107% sT

This important isothermal and pessimistic coefficient is
still negative. Nevertheless during a detailed study of this
reactor concept it would be necessary to check the values of
the thermal expansion coefficient for fuel and coolant more
carefully. The relative value of the coolant term (Eg. 5)
which is positive might prove to be too high if the differ-
ences between fuel and coolant became too marked. This pro-

blem did not arise with the present data.

7. Buckling Search and Blanket Savings

In a spherical assembly the fluxes in the core are given to

a good approximation by (6) ¢aé(r,E) = S;gBr f(E) where the

space function is called the "fundamental mode" (solution of

VZW + BZ? = 0 in spherical geometry). The critical buckling

B? is obtained from homogeneous calculations based only on

the cross-section data of the core, £(E) is the asymptotic
spectrum which is space independent far from the core boun-
dary. For the same 22 energy groups one gets

B2 = 4.08.10_4 cm_2
-]19-

Using this value Eg.6 gives a good fit of the "exact fluxes"
obtained from the complete transport calculations (Fig. 5).

The asymptotic fluxes cancel for

r = R = % = 155.5 cm
where Re is the extrapolated radius.
By definition the blanket saving is given by
§ = R_ - RC = 30.5 cm

where Rc is the core critiqal radius defined in Section 4.
The blanket saving depends mainly on the nuclear properties
of core and blanket and on blanket thickness. However, for
thicknesses greater than 60 cm this last effect is very
weak. Finally the shape and size of the core have almost

no influence on this saving. This parameter, for this reason
so important in reactor physics, will be used in the next

section for the one dimensional cylindrical calculations.

8. Transport Calculations in Cylindrical Geometry -
Final Results

The axial blanket thickness is taken to be equal to the ra-
dial thickness (95 cm), and the core height as H, = 200 cm.
The critical radius of this cylindrical core has to be de-
termined. The two dimensional transport calculations are too
expansive (and unsafe) and only one dimensional calculatlons.

have been made, which is suff1c1ently accurate. Axial trans-
-.20._.

port calculations are not required since the blanket saving o
is known from the spherical geometry calculations. One can

therefore assume the following flux shape.
v
(7) ¢ (r,z,E) - cosBz¥(r,E)

for any r value (including the radial blanket) and

< < C

z >

- <
2

—52 is the axial buckling computed from the extrapolated
height He = HC + 26 = 261 cm which gives

g = %— = 1.204:10 % cn *

1.450-10 % cm” %)

—
™w
i

The computation of core radius and spatial distribution
have been made with the SHADOK code (cylindrical version)
by introducing axial leakage defined by 62. Before that a
first approximation is obtained by introducing the radial
buckling uz, that is to say assuming for the core only,

v
the shape ?(r,E)—Jo(ur)f(E) where JO is the usual Bessel

function. One obtains u2=B2-82 where the critical total
buckling is 4.08-10-4 cm“2 (see Sect.7) which gives
o¢2=2.63°lo_4 cm_2 and a=1.625-10"2 cm_l. Then the extra-

polated radius of the cylindrical reactor is
2.405

R = = 148.0 cm.
e o

Finally with the previous blanket saving we get a core ra-
dius proper of RC = 117.5 cm. The direct transport calcula-

tions with SHADOK gives Rc = 118 cm: This clearly indicates
-2] -

the value of the blanket saving concept. Nevertheless these
transport calculations are still necessary because they give
the radial distribution of fluxes and specific power over

the whole system and more detailed informations. Fig. 6 shows
some of the radial distributions of flux and specific power.
The energy production in the blanket is quite small (1.7 %

of the core power) because no fissile materials are present
(and only fast fissions occur in U238). In practice it would
be higher (say 5 %) since the reprocessing process would not
be able to remove all the fissile nuclides produced even with

continuous fuel (coolant) reprocessing.

The radial form factor for specific power distribution is,

for this core

mean power
a = . p - O.6O
R maximum powerx

It would be possible to improve this coefficient by choice

of different latfibes particularly the most reactive at

peripheralHregion.

The axial distribution of specific power is given with a good
approximation by Eg.7. If the axial mean value is unity then

this distribution is:

B Hc
(8) P(z) = T cos Bz
2sin3—9
. _m _ (il _ 1Aam2 -1
with B = o ~ H 4238 1.2-10 cIn
and HC = 200 cm giving

-22—

P(z) = 1.285 cospZicm) -100=22100
261
and az = 0.78 for the axial form factor.

This axial distribution is very close to that used in Ref. 1.

The critical volume is higher for cylindrical geometry 8.75 m

compared to 8.18 m3 (Sect.

critical size corresponds
19,941 in ref. 1. For the

and from the form factors

3

4) ; this increase was expected. This
to 23,000 coolant tubes instead of
total power given in (1) 1936 MW

and one group fission cross-—sections

(Appendix 2) one can determine the absolute level of the to-
tal fast flux in the median plane:

7-10:"5 n.cmfl2 5"l (1.18'1016 in the centre).

All previous data: breeding ratios, reactivity coefficients,
penalties of parasitic absorbtions etc. remain valid for the
cylindrical geometry (provided that axial and radial blanket
are identical). The main characteristics of the MCFBR are

given by the following table:
_.23....

Table IV

- Core geometry - cylindrical
height : 2.00m
diameter : 2.36 m

fuel 38.6 %
volume : 8.75 m coolant 55.5 %
tubes 5.9 %

- Blanket volume (95 cm thickness) : 47.85 m3

-~ Mean power density in the core : 220 MW m_3 (Thermal power in
core 1940 MW)

- Plutonium in core : 2900 kg (20 % Pu240)
-~ Number of coolant tubes : 23000

Radial : 0.60
- Power form factors

Axial : 0.78
Core : 0.71l6
- Breeding ratio : 1.386
Blanket : 0.670

— Neutron balance : Table ITI (without wvessel)

- Mean fast flux across core : 7'1015 n.cmuzs“l

(for 220 MW/m3) (1.2°1016 in centre)

- Spectrum : Appendix 1 and Figure 2

-~ Temperature reactivity coefficients (§k(%)/8T(°C)):
- fuel -3.80-10:%
- coolant: +1.29°10

~ Reactivity change with core volume: figure 4

~ Loss of reactivity in the vessel: 0.72 % (100 mm thickness)
_24_

9., Fast Flux Test Facility Using Molten Chlorides

Some calculations have been made concerning a high fast
flux facility. In this case the core consists only of the
fuel which is again a PuCl3 - NaCl mixture. No fertile
coolant is used and the fuel itself is circulated outside
the core. Based on the preliminary thermohydraulic calcu-
lations (4) the main data selected for the neutronic cal-

culations were:

Plutonium content (80 % Pu239) 1.22 kg/1 (core)
Fe 1.45 kg/l

M .
olybdenum alloys Mo 0.465 kg/1

1.915 kg/1 {

Molar fuel composition 31 % PuCl3 and 69 % NaCl.

The Molybdenum alloys represent partly the structural mate-
rials and partly the loop materials (since this is a materials
test reactor ) - 25 % of the core volume for an alloy density
of 7.65. The choice of this alloy is rather pessimistic

from the reactivity point of view.

From this the atomic densities (A/cm3'1024) can be deduced.

Pu239 2.457-10 °
PU240 6.143.10
Na 6.837-10 °
cl 1.605°10 2
Mo 2.907-10 >
Fe 1.555-10"2
F.P. 2.457-10""

The 22 group cross-~section set was prepared once mcr.- with
the GGC3 code and a blanket of 84 cm thickness was a.:umed
with the same composition as the blanket of the breeder

power reactor (Sect.2).
The SHADOK calculations give 36 cm for the critical core ra-
dius in spherical geometry (1951 for the core volume and
238 kg of Pu). As in earlier calculations one obtains

- 3.432°10 2 cm~? for the critical buckling

~ 53.61 and 17.61 cm respectively for the extrapolated
core radius and blanket savings

From these last results one can define the critical size for

cylindrical geometry for several active heights HC.

Hc = 48 cm Rc = 36.07 cm Vv, = 195.4 1

H = 62.9 cm R = 31.45 cm \YJ = 195.45 1
Cc C C

etc.

For this small core surrounded by a large blanket all shapes
give the same critical volume. The corresponding neutron ba-

lance is given by the Table V.

The k , for the core is very high: 2.52 and in principle
breeding is possible in the blanket (1.20 for the breeding
ratio). The leakage from the blanket is significant (20 %)
and its thickness could be increased. The spectrum is
harder than for the breeder power reactor (Appendix 1l). The
maximum occurs in the range 0.5 MeV to 0.7 MeV instead

of 10-50 keV with the NaF-UF4 salt concept (3).

Using the previous data and results the main characteristics

of the High Fast Flux test facility are
- Core volume (including loops) : 1951
- Blanket volume (84 cm thickness) : 7.04 3

- Power density in the core : 4.1 MW/1 (total power 800 MW)
_26_

Table V: Neutron Balance % (HFFMCR)

Region Absorbtion (%) Leakage (%)| Production (%)
(n,vy) 2.5
Pu239 31.00 { ol Pu239 86.00
(n,Y) 1.0
Pu240 3.80 { ‘g g Pu240 8.60
Q
& Na 0.06
o)
o c1 0.57
Fe 0.64
Mo 1.23
F.P. Q.20
Total 37.50 57.10 84.60
(n,y) 37.14
o U238 39.14 {(n,f) 5. 09 U238 5.40
<
5 Na 0.12
m
Cl 3.24
Total 42 .50 20,00 5.40

_27_

- Plutonium in the core : 238 kg

=~ Structural materials and , Fe 283 kg
content of loops : 374 kg (in roughly 50 l){Mo 91 kg
16 -2 -1
~ Mean fast flux across core _ 4.2°107 n.cm S
(for 4.1 MW/1) " (6.8:101% in centre)

~ Spectrum in centre: Appendix 1

- Reactivity change with the core volume: %E (%) = 31. %E
- Breeding ratio (blanket) : 1.20
- Flux form factor (spherical or cylindrical geometry): 0.618

10. Conclusions

From these reactor physics calculations the main advantages of
Molten Chloride fuels can be seen. For breeder powef reactors
the use of a fertile coolant which removes the need for a
large plutonium inventory outside the core is very attractive.
The total breeding ratio is more than 1.35 (more probably
1.40), lying between the GCFR and the LMFBR values. Against
this it is known that the breeding ratio for thermal reactors
using molten U233, Th232 fluorides is low (1.06 perhaps) so
that molten salt reactors based on chlorides are very inter-

esting.

From the safety point of view the very high void (or tempera-
ture) reactivity coefficients make the molten salt reactor

more stable than any other reactor type considered to date.

The other characteristics - and the most important of these
is obviously the on site (continuous) fuel recycling - are

discussed in (1).
_..28_.

In the last part of this tudy the possibilities of a high
fast flux molten chlorides reactor were discussed. Compared
to the most advanced concept FFTF (3) the H.F.F. MCR gives
a flux at least five times higher with a harder spectrum.
However, a larger amount of fissile material must be

accepted for the primary circuit.

Finally the absorbtion of chlorine atoms is not as dramatic
as was at first feared. The latest data lead to an increase
of chlorine cross—-section in the high energy range which

is quite acceptable; also the o0ld values of molybdenum cross-

section were overestimated.

From the neutronics point of view the main points which should

be checked in the next stages are (for both reactors):

- the total amount of structural materials which are necessary
and the molybdenum content of the proposed allows (cor-
rosion problem). It might be that the total breeding ratio
and the plutonium inventory could change with too large

a variation from our reference case

- the density and the thermal expansion of the fissile and
fertile salts (critical volume and reactivity coefficients
could be affected)

- reactor control

— reactor kinetics
=20

Acknowledgement

The author is indebted to M. Taube who has initiated the

studies on the Molten Chloride Fast Rearctor at EIR, for

many helpful discussions. He would also like to thank

R. Stratton for correcting the manuscript.

References

(1)

(2)

(4)

(3)

M. Taube, J. Ligou:

Molten Chlorides Fast Breeder Reactor,
Problems'and Possibilities

EIR Report No 215 (1972)

P.A. Nelson et al.:

Fuel Properties and Nuclear Performance of Fast
Reactors Fuelled with Molten Chlorides

Nuclear Applications, Vol. 3 (1967) 540

J.A. Lane:
Test-reactors Perspectives
Reactor and Fuel Technology 12 (1968/1969) 1

M. Taube:

Private communication

G.I. Bell, S. Glasstone:
Nuclear Raactor Theory 5
Van Nostrand Reinhold Comp. (1970) 244-247
(6)

_30_

J. Adir et al.:

User's and Programmer's Manual for the GGC3 Multigroup
Cross—Section Code

Part 1, GA 7157 (1967)

I.J. Bodarenko et al.:

Group Constants for Nuclear Reactor Calculations (1964)

L.W. Nordheim:
A Program of Research and Calculations of Resonance
Absorption

GA 2527 (1961)

M.M. Hummel:
Reactor Physics Division Annual Report, July 1, 1964
to June 30, 1965 - ANL 7110, 319

J. Ligou:
Improved Integral Transport Theory by Means of Space
Polynomial Approximations

Accepted for publication in Nucl. Sci. Eng.

A.M. Weinberg, E.P. Wigner:
The Physical Theory of Neutron Chain Reactor VI, 143
Univ. Chic. Press (1958)
-3]1-

APPENDIX 1

Relative Fluxes in Each Group

g Bogfig:§y $§i2e (Letfigrgy) Centre Boiigiry
1 |15 MeVv 12.2 MeV . <10"% (.0002) <10”%
2 |10 8.18 . .0010 (.0026) 0006
3 6.7 5.49 . .0045 (.0116) 0029
4 4.5 3.67 . .0112 (.0286) .0072
5 3.0 2.46 0.4 .0222 (.0552) .0146
6 2.0 1.65 0.4 .0407 (.0901) 0285
7 1.35 1.23 0.2 .0264 (.0536) 0193
8 1.11 1.00 0.2 .0281 (.0536) .0215
9. | 0.91 0.78 0.3 .0475 (.0837) 0379
10 0.67 0.55 0.4 .0924 (.1373) 0787
11 0. 45 0.37 0.4 .1072 (.1254) 0972
12 0.30 0.25 0.4 <1162 (.1042) .1136
13 0.20 0.165 0.4 .1044 (.0749) 106 4
14 0.135 0.108 0. 45 .1046 (.0662) 1108
15 | 86.5 keV |59.5 keV 0.75 .1061 (.0549) 1208
16 | 40.8 25.0 1.00 .1043 (.0394) 1262
17 | 15.0 8.0 1.25 .0581 (.0145) .0768
18 4.31 2.94 0.75 .0047 (.0011) .0066
19 2.03 1.39 0.75 .0148 (.0025) .0208
20 0. 96 0.67 0.75 .0048 (.0004) 0079
21 | 0.45 0.24 1.25 0008 (<10 %) 0017
22 0.13 <1o-4 (<1o_4) <]_of4
Total | 0.4 eV - 15 MeV | 1. 0000 ;110?¢0

~ (x) values related to the spectrum in the Fast Flux Test Fa-

cility (Sect.9).

_32_

APPENDIX 2

One Group Cross-Sections Based on the Reference 22 Group

Transport Calculation (barns)

Type Core Spectrum Blanket Spectrum
Nuzfide Cc i Of v Oc O ¢ v
U238 0.249 3.30-10 2| 2.746) 0.326 7.71+10 “|2.715
Pu239 |0.329 1.709 2.951} 0.536 1.841 2.917
Pu240 |0.527 0.364 3.052| 0.790 0.174 2.998
Na 1.62-10 ° - - | 2.044:107° - -
c1 6.38:10 ° - - | 8.83-107° - -

(8.64°10 °)* (9.11+10 ) * - -
Fe 1.01-10 2 - - 1.43-10 % - -
Mo 0.109 - - 0.166 - -
FP 0.225 ~ - 0.362 - -

* These values were computed on the basis of ENDF/B.III data.

It is interesting to know the cross-sections of Iron and Mo-
lybdenum for the core blanket boundary spectrum (useful for
the reactivity cost of the vessel); these intermediate va-
lues are:

2 for Iron

for Molbydenum

1.142+10

o]
c (barns) = {0.126
-33=-

In the blanket the spectrum is softer than in the core;
except for the fast fissioning in the fertile isotopes all

cross-sections are therefore higher in the blanket.

The new core spectrum is softer compared to that of (1)
which explains the deviations observed in the one group

cross-sections.
-34~-

APPENDIX 3

If the volume remains constant during the mixing, the densi-
ties of the various liquids are given by (see the composition

in Sect.2):

1 N 1 {

(1) S euer T 93 Blpucrs T 947 Blyac
1 ny 1 1
— - —_ + . —
(D)coolant 0.32 D)UClS ©.08 (D)NaCl

ith 1.5 ~3
wi pNaCl .5 g cm
- Y47 ~3 h d
pPuClB pUCl3 - 4,76 g cm one gets the expecte
values (Sect.2)

P = 2.344 g cm >
fuel ' 9
P - 4.0l g cm >
coolant * 9

By taking the derivatives of both sides of Eq. 1 it follows:

(p )fuel 0.26 )PuClB O.74 (p )NaCl
(2) {
Sp = Sp Sp
_(p ) coolant 0-78 (Fyerz * 0-22 (p ) Nac1

The thermal expansion coefficients are given in (1) Appendix

for pure PUC1l3 and NaCl:
)fuel

coolant

_35_

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1INN A9¥VHL3T d¥3d XN1d
sord Breeding Ratio C and blanket thickness t /
m .
3 -
( Core volume = 8.18 m" ) 145
—
L0 - —
Blanket Volume V - - 1.40
30
Ref. Case .1 1.35
20 -
t (cm)
0 | H 1 i ] 1 "30
720 / 80 90 100 10 120
—~y 4+ 2%
Fig. 4 .
*gk Reactivity change with Core volume -
X (Blanket Thickness=95cm) -
i y
+ 1% — -t + 1%,
i Ref.Case
- v -
) Co
: | (L) core O
0.9 1.0 1 1.2
F -
- 1% }— i '.’.

Fig. 5
4, A Radial distributions of the 16'" and i2'"
flux (Sph. Geom.)
transport calculations

th ~~=-= Asymptotic mode in the core

Fig. 6
Radial distributions of the l2thflux P ‘
and specific power (Cyl. geom.)

3.16° -
1107
210> -
specific __ g
power
0.5-10°
110> -
Asymptotic mode
| { 1

0 - 50 100 150 r (cm)