EIR-270.txt

EIR-Bericht Nr. 270

EIR-Bericht Nr. 270

Eidg. Institut far Reaktorforschung Wirenlingen
Schweiz

The transmutation of fission products (Cs-137, Sr-90) in
a liquid fuelled fast fission reactor with thermal column

M. Taube, J. Ligou, K.H. Bucher

l I

B

Wilrenlingen, Februar 1975

EIR-Bericht Nr. 270

The transmutation of fission products (Cs-137, Sr-90) in

a liquld fuelled fast fission reactor with thermal column

M. Taube, J. Ligou, K.H. Bucher

February 1975
sSummary

The possibilities for the transmutation of caesium—-137
and strontium-90 in high-flux fast reactor with molten
plutonium chlorides and with thermal column 1s discussed.
The effecitve half 1life of Cs-137 could be decreased from

%0 years to 4-5 years, and for Sr-90 to 2-3 years.
Introduction

The problem of management of highly radiocactive fission product
waste has been intensely and extensively discussed in the recent

paper WASH - 1297 and especially in BNWL 1900 (Fig. 1).

Here only tne transmutation of Fission Products (F.P.) without the
recycling of the actinides 1s discussed, making use of neutron

irradiation by means of a fission reactor (Fig. 2).

A short outline of this paper 1s as follows

1) Why, contrary to many assertions, is neutron transmutation in

a fusion reactor not feasible.

2) Why recent discussions concerning transmutation in fission

reactors are rather pessimistic.

%3) Could the transmutation in a fission reactor be possible

taking into account the neutron balance in a breeding system?

1)y Which are the F.P. candidates for irradiation in a fission

reactor?

5) Is the rate of transmutation sufficiently high in a fission

reactor?

6) In what type of fission reactor is the transmutation physically

possible?

7) What are the limiting parameters for transmutation in a solid

fuelled fission reactor?

8) Is a very high flux fission reactor possible if the fuel is

in the liquid state instead of the solid state?

9) How could such a high flux fast reactor with circulating liquid
fuel and a thermal column operate as a 'burner' for some F.P.

(Cs-137 Sr~90 etc) transmutation.’

10) What engineering problems must be solved for this to be realised?
Radiocactive

Waste
— .

nigh active

low active

waste vaste

/N

any management
A

(ferbiaden

direct

controlled
storage on
tihe surface

litosphere

inydrosphere
{underground)

salt

rocks water ice
mines (deep sheet
see (polar)
floor
stable geologic
conditions nonstable
conditiocns

c

norn controlled
storage

solar deep
impact ¢

management dissipation

transnutation

without witn
cnanging changing
L and 4 A

{but no Z)

coculomb
exitation

(r,v) {(n,2n)

continously

with
cnanging

-

(p,Y)

periodical

fission

.
underground
xplosion

csmic
escape
neutrons neutrons
(primary) (secondary)
fusion fission accelerator
reactor reactor
A /\
fast thermal thermal fast
neutron reutron
with without
thermal tnermail
column column

(p,spallation)

thermonuclear
urcerground
slosion

Fig. 2

10

10

Transmutations of fission products

gquasi stable
F.P,.

Half-1ife, years

1074

stable
nuclides [Living

\E.P. . D,

r__\
\Gpontaneouse
beta decay

\
\

sShort

10

long 1L

i
10~

/
/

10

Cransmuta

iving

10
1. Why the transmutation of F.P., is not feasible in a controlled

thermonuclear reactor (CTR):

The recent studies of the use of a C.T.R. as a transmutation
machine for at least the conversion of Cs-137 have been to some
extent optimistic. Table 1 gives a summary of the most important

data and results from BNWL 1900.

Comments 1

Wolkenhauer (BNWL 4232) calculated the values with a nominal

one energy group cross sectlon and fast neutron {lux

5 X lOl5n cmdgs—l. (The primary flux of 14 MeV neutrons for
10 MW/m2 wall loading equals 5 x 101un cm—zs_l, but such a high

loading 1s very optimistic!)

Cs-137 Sr-90
o{barns) 2 O(S—l) o(barns) 7+ o(s H
(ngY) 0.44 2.0 loulo 0.0188 0.94 - 10-10
(n,2n) 0.147 7.3 - 1070 0.148 7.40 - 107 %Y
(g~-decay) - 8 25. 10 %Y _ 763 1710

The results obtalned are rather pessimistic since the values of
the reduction of the steady state amount due to the trans-

formations are given Dby:

. ~-10

for Cs-137 Atofal 17.76°10 - 2.15
Adecay g 06, 10—10
Atotal 15 97.10‘1O

for Sr-90 —_— = - = 2.09
rdecay 7.63'10—10

rtotal = Adecay + g« 9
Table 1 Transmutation possibilities for different devices (from BNWL-1900, WASH=-1297)
r

Machine Flux/ Reactions, and remarks of authors See

Energy of original reports. Comments
Accelerator of Protons Reaction (p,xn.) Not promising. Ruled out _
medium and high 100 MeV on basis of energy balance criteria
energy protons

Protons Spalation (p,xn) and (n,2n) {(n,vy)

1-10 GeV with secondary neutron flux

Cs=137 as Not feasible within limits of current -

target and/or technology. The capital cost 1is

thermalised prohibitive.

fflux of

neutrons

Fusion

(thermonuclear)
reactor in all
cases with wall

Fast flux of

Neutron reactions (n 2n) and &n,y)

Fast Flux of 5 x 10 5n cm~ s

14 MeV neutrons 2
from. (D-T) @ =
5x107 'n cm'ZS_l
Thermalised Practically only (n,y)
flux in Thermal flux 6.7 x 1015n em— 2t 2
beryllium trap
Attractive transmutation rate has not been
demonstrated but possible to transmutate 3

all Cs-137 and Sr-90 created by fission
reactors

Nuclear Fissile Technically not feasible. No. of explosions
explosions explosive or per year very high. Appr. 3900 p.a. each of
thermonuclear 100 k ton. (For USA in year 2000 Cs-137 and| —
explosive Sr-90) Probably not acceptable to public!
Fission See table 2

reactor

and are clearly too small for justifying such a complicated
technology as transmutation in a CTR. In spite of this Wolken-
hauer writes: "the flux level is somewhat higher than that
usually associated with CTR power plants. This value was selec-
ted based upon the hope that by the time transmutation 1s applied
in a CTR that technology will have advanced far enough to allow
for the implied vacuum wall lcocading. If this high a value proves
to be unrealistic longer irradiation times will be required"
"attractive transmutation rates have not been demon-

strated up to this point".

Also all these calculations were done on the basis of isotopically
pure Cs-137 and Sr-90. Later Wolkenhauer writes, "any practical
scheme would probably involve elemental rather than isotopic

loadings"

Comment 2

In BNWL-1900 it was noted that the calculation (in a moderating

blanket of the CTR) represents a more realistic blanket configu-

ration with a neutron wall loading of 10 MW/mz. (This is still

a very optimistic value. M.T.)

In this case the following date have been obtalned for a therma-

lised neutron flux from a CTR w1th a 10 MW/m wall locading.

¢ thermal ¢.0 .o total
n.cm_2s_l (n,vy) (n,2n) tl1/2 eff.
for 807% 6.71-1015 I ):0.117 (n.2n) 20,104 {a=22.2°10 ts7t
fraction > (barn) (barn)
- -10
~291 kg 7.91-10 U 7.0-10 1 9.9 years
Cs/yr

The conclusions of fthis study are that useful quantities of
Cs=137 could be transmuted under the projected CTR blanket
loading conditions. The reduction in Cs-137 "toxdicity" 1s still
expected to be at most a factor 3 down. In addition a study

of the bulld-up of fission product nuclei in order to establish
the requirements of periodic chemical processing and associated

costs has not been carried out.

Comment 3

H.W. Lefevre (appendix to BNWL-1900) makes an interesting comment

on the study of the transmutation of Cs-137 and Sr-90 in CTR:

'Everyone knows that a CTR will be "clean". Don't spoil that
illusion. I think that I would worry some about a CTR loaded
with 50 kg of Cs-13%7"'.
2. Why recent remarks about transmutations in a fission reactor

are rather pessimistic

A recent and most intensive study of the use of a fission reactor
for the transmutation of fission products has been published by
Claiborne (1972). He writes:

"The problem fission products cannot be eliminated by any system
of fission power reactors operating in elther a stagnant or
expanding nuclear power economy since the production rate exceeds
the elimination rate by burnout and decay. Only a equilibrium
will the production and removal rates be equal, a condition

that 1s never attalned in power reactors. Equilibrium can be
obtained, however, for a system that includes the stockpile of
fission products as part of the system inventory since the stock-
pile will grow until its decay rate equals the net production rate
of the system. For the projected nuclear power economy, however,
this will require a very large stockpile with 1ts associated
potential for release of large quantitites of hazardous radio-
isotopes to the environment. It is this stockpile that must

be greatly reduced or eliminated from the blosphere. A method
suggested by Steinberg et al. is transmutation in "burner reactors”,
which are designed to maximize neutron absorption in separated
fission products charged to a reactor. If sufficlent numberes of
these burners are used, the fisslon products inventory of a
nuclear power system can then reach equilibrium and be maintained
at an irreducible minimum, which is the quantity contained 1in the
reactors, the chemical processing plants, the transportation

system, and in some industrial plants.

If the assumption is made that burner reactors are a desirable
adjunct to a nuclear economy, what are the design requirements
and limitations: It 1s obvious that they must maximize (with

due regard to economics) the ratio of burnout of a particular
fission product to 1its production rate in fission reactors, and
the neutron flux must be high enocugh to cause a significant
decrease in its effective half-life. Of the fission types, the
breeder reactor has the most efficient neutron economy and in
principle would make the most efficient burner if all or

part of the fertile material can be replaced by a Sr-Cs mixture
without'causing chemical processing problems or too large a
perturbation in the flux spectrum because of the different
characteristics of these fission products. The cost accounting
in such a system would set the value of neutrons absorbed in
the fission product feed at an accounting cost equal to the value

of the fuel bred from those neutrons.

The maximum possible burnout of fission products would occur when
the excess neutrons per fission that would be absorbed in a
fertile material are absorbed instead in the fission product feed.
The largest possible burnout ratio would then be the breeding
ratio (or conversion ratio for non-breeders) divided by the
fisslon product yield. The estimated breeding ratio for the
Molten Salt Breeder Reactor (MSBR), a thermal breeder, is 1.05

and for the Liquid Metal Fuelled Fast Breeder Reactor (LMFBR),
1.38. The yield of 13705 + 9OSr is 0.12 atom/fission, but a number
of other isotopes of these elements are produced which would also
absorb neutrons. However, 1f the fission product waste is aged

two years before separation of the cesium and strontium, the
mixture will essentially be composed of about 80% 137Cs + 908r

and 207% 155 136Cs that
decays with a 13-day half-1ife (M.T. see Comment 4): consequently
137CS 950

+ Sr will be decreased by

Cs (which will capture neutrons to form

the maximum burnout ratioc for
20%. This leads to a maximum possible burnout ratio of about 7

for the MSBR and about 9 for the LMFBR. Unfortunately, however,
the neutron fluxes 1n these designs are well below lOl6n cm_zs_l.
Any modiflications of these designs to create high neutron fluxes
will increase the neutron leakage and decrease the burnout ratios

significantly." (Claiborne 1972)
10

Comment 4

It is not clear why Claiborne claimed that after 2 years ageing
and separation of strontium and caesium the isotope composition

will be

Cs=1357

807 Sr-90

20% Cs-13%5
From Crouch (1973%) the fission products of U-23%% have the following

composition (2 years ageing) (in at % per fissioned nucleous)

(see Table 3).

Sr-88 (stable) 3,63
Sr-90 (28 years) 4,39
Cs-1%% (stable) 6.57
Cs-134 (2 years) 3.5 (7.09+0.5 from independent yield)
Cs-135 6.26
Cs-137 5.99
Subtotal 30, 34

"he realistic data are unfortunately more than twice those cited

by Clalborne.

The same negative opinions concerning the use of Fission Reactors

for F.P.-transmutation are given by the following authors:

- A.S. Kubo (BNWL - 1900):
"Fission products are not conductive to nuclear transformation
as a general solution to long term waste management'.

- BNWL - 1900, itself:

"In summary it is improbable that transmutation of fission
products in fission reactors could meet any of the technical
feasibility requirements for the production of stable daughters'.

- Claliborne (1972):

"Developing special burner reactors with the required neutron
flux of the order of 1017n em™¢s™1 is beyond the limits of
current technology'.
5.

11

Is the transmutation in a fissilon reactor possible taking into

account the neutron balance in a breeding system?

In spite of all these pessimiétic opinions on the transmutation of

F.P. (especilally Cs-13%7 and Sr-90) in a fissilon reactor the dis-

cussion below points to a more optimistic conclusion.

The calculation of the transmutations of F.P. nuclides 18 made on

the basis of the following more or less arbitrary assumptions:

1)

The total number of fission power reactors installed must form
a self sustaining system (a breeding system) with a compound
doubling time TS of about 30 years (at a later date in the

development of cur civilization this may be satisfied).

T . 2.75 - M - (1L + ) . 1y D

5 (BR-1) + (1 + a) C
TS = compound doubling time (years)
M = 1initial fuel loading (kg/MW th)
C = fraction of time that reactor is at full power
F = ratio of the fertile isotope fission rate
o = capture to fission ratio for the fissile material
BR = breeding ratio
From this BR = 1 + exf2 * M (L + F) r 1In?2

We have postulated:
TS = 30 years

and we know that the mean values for 'our reactor' are

I3 = 0.20 (instead of 0.3, see Beynon 1974)
a = 0.24

M = 1 kg Pu/MWth

C = 0.8

and we obtain
2)

if

12

We know that the breeding ratio can be defined as

(v=1-a) + (F(v'-1)) - (A+L+T)

BR =
(L + a)
v and v' = number of neutrons per fission
A = ratio of parasitic capture rate in structural material

to fission 1n fissile material

T = ratio of parasitic capture rate in transmutated F.P.

to fission in fissile material

L = leakage ratio

In this paper the following rather For illustration only

conservative data are postulated (ref. Beynon, 1974)
GCFR LMFBR MSBR

L = 0.06 0.05 0.04 0.0244
A = 0.30 (instead of 0.23) 0.0067 0.09 0.163%
v = 2.96 2.95 2.93

vi = 2.70 2.92 2.77

F = 0.20 (instead of 0.30) 0.25 0.19

o = 0.24 0.22 0.28

we obtain

T = v-1-x-BR (1+x)-A-L + F (v'-1)
T = 0.364
T = 0 T=0 T =0 T = 0

then BR max. = 1.371 1.47 1.21 1.06

Table 2

Possibility for transmutation of F.P. - particularly

Sr-90 in a fission reactor according to BNWL - 1900

Cs=-13%7 and

Reactor

Reference

Flux

Remarks

thermal

power reactor

Steinberg
Wotzak

Manowitz,l1964

The authors use a wrong value:
Kr-85 with large 83 = 15 Dbarns
instead of 65 = 1.7 barns.
Isotopic separation of Kr-
isotopes

13

310 thermal

Only I-129 can be transmuted.

high flux (trap)

Steinberg, 1964

1016 in the trap

smaller 1n the
presence of the
F.P. target

An equal or greater no., of F.P.
would be formed in the fission
process per transmutation
event.

Claiborne, 1972

15

2+10 thermal

This reactor does not meet the
criteria of overall waste ba-
lance and of total transmuta-
tion rate.

ffast

ligquid metal
fast breeder

Claiborne, 1972

15

1-10 fast

Neutron excess 0.15 - 0.3 at
the expense of being no longer
a viable breeder of fissile
material. Also this flux does
not allow the attainment of a
sufficiently high transmutation
rate and is, therefore, not a
feasible concept.

fast with
thermal

Liguid fuel
fast reactor
with thermal
column

this paper.

¢T
14

The result can be checked as focllows:

In a mixed breeder/burner system let the ratio of the power be X

Breeder reactors power

Burner reactors power

From this

X-BR = (X + 1) BR
max in
also
BR = BR . + i
max min 1l + a
T
£ (Blen 1l + a) B Blen
_ 1+ a
X = BRmin T = 3,607
Conclusions

BR_ .
min

Tt is clear that a breeding-self transmutating system with

T >>0 1is possible only for a fast reactor in which the value of

breeding ratio BR is >1.3 and not for a thermal reactor in which

BR <1.06 (see Fig. 3).
15

Fig. 3 Burning of F.P. 1in steady state
Sr—=90 Cs-137
beta decay only
1
B tnermal
1074
Q) —
¢,
O
)
©
C
per ic recharging, 1 year
5 ,
0 10 ™
2
o
3
Q0 -
=
@
Q
o
43
s -
—
O
£ -3 . .
10 74 contlnouse reprocessing
i dwelling time: 10 days

16

4. Which fission products are candidates for transmutation?

In our case the amount of transmutatable nuclide can equal

T = 0.307

The tables of (BNWL-1900) provide the data for Fig. 4 in which
the radiloactivity of a I'.P. after a very short 'cooling' time
is seen, from which it is clear that the main hazard arises from

only a few radionuclides.

But these radionuclides nevertheless constitute the global
hazard even taking the amounts produced during the next period

of nuclear energy development.

The crucilal nuclides are characterised in Table 3 together with
other 1isctopes. All this data now makes i1t possible to estimate
the number of candidates for transmutation in our breeder/

burner system. The criterilia are as follows

- the total amount of all transmutated nuclides cannot be
bigger than the estimated value of T = 0.367, that is
~3%6 atoms of F.P. nuclides for each 100 fissioned

nuclides.

- fthe priority of transmutation is given as follows

Cs>Sr>I>Te>Kr Total equals: T = 0.3318

- in the first instance no isotopic separation process is

postulated.

Table % shows the F.P. nuclides selected for transmutation.

(see also Fig. 4).
Table 3 The priority for the transmutation of fissioned products

Selected Yield for fission of Atom/100 atom Pu-239 Assuming isotopic
100 atoms of Pu-239 Subtotal separation

atoms/100 atoms
Pu-239

Cs=-13%3% (stable) 6.91 6.91 0.14

Cs=-13%5 7.54 21.140 14.450 7.54 14,37

Cs-137 6.69 ' 21.140 6.69

Sr-90 2.18 25.32 2.18

Sr-88 (stable) 1.44x0.02 = 0.029 2.203 23,349 0.029 2.209

(2% isotopic

separation

efficiency)

I-129 1.17 } 24,519 1.17
I-127 (stable) 0.38 1.55 24,899 0.01 J 1-1°
Te-99 5,81 5.81 30.709 5.81 5.81
Kr-83% (stable) 0.36 h
Kr-84 (stable) 0.56
Kr-85 0.672 2. 14Th 0.67

0.
Krf86 (stable) 0.882 ) 3%.183 0.04 rt

Total 3%.18% 24,28

LT

curie/watt

Aectivity

18

1 day
]

10 days

100 days 1 year 10 years 100 years 1000 y.

i

| | | 1 1

time, seconds
19

5. Is the rate of transmutation good enough?

1t 1s clear that the rate of radiocactive nuclide removal in a

field of particles is given by:

ln 2

eff Adecay ¥ Atransmutation (s l) =

t 1/2 (eff)

where

A = g @
trans trans
. 2 ) .
o = c¢ross section (ecm ) for a given reaction

¢ = flux of the reacting particles (cmngs_l)

Let us assume that the energy production 1s based on a set of n
burners and nX breeders (see §3). At time tn (see Fig. 5) when
1t 1s declded to stop fission energy production in favour of

other sources the total amount of a selected fission product is

(1) (k) = (X + Ln<
el
with K = YP/E
Y = yield of the selected F.P.
P = power per burner (or breeder) (watt)
E = energy per fission (Joule)

This amount of F.P. 1s located only in the burners, therefore,
each burner can receive (X + 1)%eff although their own produc-

tion should represent only T in the steady state.
elfl

At time tn the nX breeders are shut down and only n burners are
in operation. Later on (time tn_l) the nuclide removal 1s

such that a rearrangement 1is possible and one burner can be
stopped, 1ts F.P. content will be loaded in the remaining burners

etc. At the beginning of each time step, tp, the p burners which
0c

A Fig. 5
(X + 1) V- . K - ,
\\ oo = 75 amount of F.P. produced by one burner
(n,1)(X+1) \\ eff in steady state
N\
N
\\
AN

X+1 \

p( ) \
N
N\
3(X+1)
\
N\
\\

2(X+1 '

( ) N

N
I N
N
(X+1) N
\\
1.2 T~
1.0 4 — 4+ e 5 — e e —
11 D DL 5 o N 0

Burner
number n n.l? P 3 2 = O
%EESS;P X-n 0 0 0 0 0 0

21

are stl1ll working contain the max. possible amount of F.P.:

where N(t) represents the total amount of the selected F.P.

One could imagine other schemes: for example one could make the re-
arrangement only when 2 burners can be shutdown. From the reacti-
vity point of view this solution is worse than the proposed one.

Coming back to the original proposal one has still to solve at

each time step (tp, tp_l) the burn up equation.
(3) ai Keff N = K.p where the right hand side is the F.P.
at production

Then the solution is

(4) N(t) = 22+ (e ) -

using (2) one deduces the time needed to go from p burners to
(p-1).

(5) Agrp (tp—l ~ tp) = 1ln

with a summation one gets the time t, after which one burner only

1
is 1in operation

(6) A

(b = &)

eff 1

I
Ho™H
}._I

3

22

A more direct evaluation can be obtained if n is so large that
the number of operating burners changes continuously with time

(p = n(t)) then by a single elimination of p between (2) and (3)

one gets
dN .
gt T rere N7 NApp or
X+ 1
A (t -t )
!
(4 ) N(t) = N(t ) e erf =171
1 _ X + 1 N(tn) _ L+ 1
(6 ) )\eff(tl tl’l) = < 1In N‘(t ) = ——'X—'— 1n ( 1’1)

The two approaches give similar results except at the end when
few burners are in operation (see Fig. 5)

For times longer than £, only one burner is operated and the

1
amount of F.P. would decrease from (X + 1) % to % the
el f

We shall postulate that it has no sense to operate this last

burner when the amount of F.P. is only 1.2 times longer than the

asymptotic wvalue which requires a new time interval (eq. 4 p =1)

A (to - tl) = 1In b X

The total time to - tn will be the sum (6) + (7) which corres-
n{x + 1)
1.2
only be obtained by natural decay (t>to).

ponds to the reduction factor Further reductions can

Numerlcal application:

With x = 4,n = 100 which means the economy was based before tn

on 400 breeders, the initial F.P. amount is reduced 415 times

when the last burner is shutdown. Then the required time is defined
_ : . 1

by Aorr (tO tn) = 8.9% (8.76 with the approx expression (67 ).

It this time is to be less than say 60 years (2 reactor generations)
23

then Aeff

Since the most hazardous F.P. nuclides are those which apart from

> 4.7-10"95_l(t 1/2 eff = 4,7 years).

their high metabolic activity and high retention in living organisms
also have a half life of the same order as a human life span of
60-70 years we arrive at the following list of hazardous isotopes

which are the most important for transmutation.

Kr-85 t 1/2 = 10 years Adec = 20.9 ].O“los_l
-10 -1

Sr-90 6 1/2 = 28.2 years Adec _ 7.76 - 10 S
Cs-137 t 1/2 = 30 years Mo = T-32 ¢ 10”0571
. : -9 -1

1 1 - = . =
desired 'half 1life L.7 years Adesired b7 10 S
= A

+
dec Ktrans

The most important problem arises from the fact that the two nuc-
lides Sr-90 and Cs=137 have very small cross sections for neutron

absorption in both the thermal and fast regions.

thermal fast
Sr-90 0.6 Dbarns 0.007 barns
Cs=-137 0.06 " 0.010 "
therefore to achieve A . = 4.7 - 10_93"1 the neccessary fluxes
desired

should be

. A e
fast flux Cs-137 @fast = -S&sired decay _ _4.10

2
cCs-137 fast 0.01-10

u =

= 4.0-1017(n cm_gs—l)
24

4+1077 16 —2 -1
thermal flux Cs=-13%7 gth: ...... 5T T 6-10 (n em “s )
0.06+10
4001077
) 15 -2 -1
Sr-90 ) T = 6.6°107"(n cm “s )
th 0.6-10°"

The question then arises, in what device are such fluxes possible -
a fast flux of Ll'lO17 or a thermal flux 6~1016. It is interesting
to point out that during the period of 60 years which provides

the reduction factor of 415 (if the Aeff = H.?-lo_gs_l can be
achieved) the natural decay of Cs=137 would have reduced it only

by a factor 4 which demonstrates the efficiency of the burner.

Also the burning which cccurs during the first period (t € tn)

reduces the amount of

F.P. R times = 6.7 times for Cs-137

6. In what reactors are the transmutations possible?

From the point of view of this paper the most important process
is the transmutation of some of these nuclides by neutrons in a
fission reactor. The criteria given in chapter 2 1limit the choilce

of system. That is

a) the number of F.P. nuclei cannot be too large in relation to
the number of fissioned atoms in the burner reactor (reactor
for transmutation) because the latter process also produces

new fission products.

b) the fission reactor should be self-sustaining - that is a

breeding system.
25h

c) the specific power of the reactor is proportional to the
neutron flux. High neutron flux means high specific power

which 1s controlled by the erfectiveness of the core cooling.

d) the specific power P and the neutron flux ¢ are coupled by the
fission cross section and the concentration of fissile nuclide
(Nf)

For thermal neutrons Of is approx. 700 barns and for fast

neutrons only 1.0 barns, that is 400 times smaller.

Yor the gilven total power and the same specific power the

product N Y for the thermal reactor must be approx. 400

times smailer than for a fast reactor. Since the critical

concentration of fissile nuclides in a thermal reactor can
only be 10 times smaller than for a fast reactor then for a
given specific power the neutron flux in a fast reactor can

be about 40 times higher than that of a thermal reactor.

The cross section for thermal neutrons for the nuclides con-
sidered here 1s from 3 to 10 times larger than in a fast

flux and this must be taken into account.

All these factors bring us to the following solution of the

problems under discussion.

a) The highest specific power and hence the highest neutron flux
is possible if the cooling process is carried out by the fuel

itself and not by a separate cooling agent only.

This directs our interest towards a reactor with molten fuel

in spite of the exotic nature of this solution.
26

b) The high flux reactor must be a fast reactor (small o for fast
fission)

¢) Because Oth >Gfast the fthermalisation of the high flux 1n a

thermal (column) 1s postulated, then 1t 1is possible that

@column core
therm. ffast

d) The first approximation is made for an isotopically pure radio-
nuclide e.g. Cs-137 without Cs-133% (stable) and Cs-135 and
also Sr-90 without Sr-88 (stable)

The discussion then results in:

- transmubtation of Cs-137 (and some other nuclides) in a therma-
lised trap of high flux neutrons: @ thermal = 5'1Ol6n cmmzs_l

§ -1

- production of a high flux of fast neutrons >5-lOl n cm_gs

5

and the high specific power of 15 KW cm ° is achieved by

means of liquid fuel circulating through an external cooler.

- transmutation of other selected fission products in an
external thermalised region with a thermal flux of
5 -2 -1
5-1()1b or 1-1015n cm 28 .
- coupling of one burner - high flux fast burner reactor with

a system of 'nmormal' power breeder reactors,
27

7. What are the limits of specific power Iin a solid fuelled

reactor?

Is the specific power of 15 KWcm_3 achievable in a solld fuel
reactor? These are the self-evident limits in solid fuelled

reactors:

a) rate of burning of fissile nuclides limited due to depletion

of fissile or an increase of F.P. nuclides.
b) heat transfer limitation of fuel/clad to coolant

c) temperature and temperature gradients in the fuel and

cladding (melting, mechanical properties)
d) bolling of coolant

e) limitation of coolant velocity, pumping power, stabllity

Now we discuss these limitations in more detail

a) the dwell time in a solid fuelled reactor in core for the

fissile nuclides must not be too short.

concentration of fissile nuclide * maximum burn-up

£
dwell fission rate

We could write:

28

where N = concentration of fissile nuclide
N = g : g and £ = 3.1 X lOlO fissions/joule
s

= power (watts)

R = fission rate (fission s l)
R =P " 7f

from this:

tdwell ) T G 0
o .

For a thermal reactor (some arbitrary values)

D = 0.03

6§h = 700 - 10‘2Ll em®

Y = 5 1016 n cm_zs_l

tdwell = 850 s = 14.3% minutes

but also for b = 0.10 we achieve ¢t = 47.6 minutes
dwell

For a fast reactor (some arbitrary values)

D = 0.10
6£a5t - 1.8 x 102" en?
@ = 5 1016 n cm—gs—l
_ 6 -
tdwell = 1.1 10" sec = 12.9 days
Conclusion:

- the dwell time in a thermal reactor i1s prohibitive short;

- in a fast reactor it 1s more reasonable but still very short,

especially in the case a of solid fuel reactor
29

b) The limitation of specific power by heat transfer 1s the

following:

a o . . .
Speciflc power PspeC in a 'good!' 3 thh power reactor and

with the appropriate flux can be taken from literature is:

.05 kW/cmB; 2

spec th
5

fast Pspec =1 kW/cm™; @f

15

5 x 10

t

thermal P

5

b X lOl

In a high flux reactor: (see LANE 1969, FEINBERG 1970)

(see also Fig. 6)

thermal
thermal: P = 2.0 kW/cmB; 2z = 3 x 1015n cm S
spec th
5 16 -2 -1
= [N . =
Popee © 1e0 kW/cm” ; ¢, = 3 x 107'n
fast: P = 1.0 KW/cmB; @ = 1.5 x 1016n cm—gs_l
spec f

With the same geometfry the very high flux reactor desired here
would have the following flux for Cs-137 transmutation:
16 5

5.0 x 10 the specific power Pth = 22.5 kW/cm

for @th

.0 x 1017 the specific power P, = 20 kW/cm3

f

for @th
30

Eifi;_é Fuel cycle
o
Feinberg's C
calculation Fast reactor
for 2 GW with thermal
column
1016-
@ HFIR
ATR @
15
w10 e !FBR
5 ® ETR
= ®
; MSBR
3 14 (continuous)
— WR
a
7 "
S
()
e
=
1013 T T 1 T T
0.01 0.1 1 10 100 500
Fuel cycle, days
1004 Specific power einberg's
calculation
1 GW(th)
4o M/s
20
M Thermal
E 10 column in
; 1 fast reactor
X
L.fl
0]
=
O
2 5 HFIR
3 CM-2 (Feinberg)
h
O
) 1 -
o
|92]
0.5 FFTFEF
4hoo MW
0.2 -
0.1 .
1ot R 1010 1017

Thermal flux,lq/cmzs
For a solid fuel we

Jlmension

Cell: D.9x0.9x1.0 cm
Fuel: f = 0.6 cm
Cladding: 2. = 0.6 cm

i

s = 0.03% cm

2 = 0.6 cm

ol
Coolant:

0

-

31

volume

.81 cm5
Z
.283% em”

.568-10H20m5
.5

e

1

cim

5

postulate the following "unit-cell"

cCross-—= surface-

section area

area

0.81 cm2 3.60 cm2
9!

0.28% cm2 1.885 em”

0.568-10h2 cm2 1.904 cma

0.521 Cm2

In this specified cell of a "desired" high-flux-reactor, we would

achieve a heat-flux, per unit fuel element surface area:

(for both types of reactors, thermal and fast)
b

z
21 kW/cem”
}{ — = Fasn 2]

, A
0.51 cm”

f's

D)
- j— Fan
1.685 cm

)

9 kW/em ©
52

Using now a simplified model for the first guess of the tempera-
ture gradlent we can say: the amount of heat generated in the
fuel must be the same as leaving the surface of the cladding-

material.

' - . 5
Alclad - Hfs i\

Where s = wall thickness and A = heat conductivity (w-cm_l-K_l)

an optimistic value for stainless steel is A = 0.4 W-cm_l'K"l.

ATclad = 9000 - —;T— = 0675 “C

It is evident that this result 1is not realistilc.

The solution of this problem may be the thermalisation of neutrons
in a high flux fast core and the irradiation of Cs-137 in a thermal

trap (see Fig. 7).

In such a thermal trap we postulate (which must be based later

on core calculation)

@th = 1.2~ Qjfast

_ 16 . _ 16 -2 -1
to reach @th = 6.0-10 we reguire ®fast = 5.0-10 n cm S

For this fast flux the specific power can be assumed, 1f we
take into account the effective increase of the fisslon cross
section because of the influence of the thermal trap. The simpli-

30

fied calculation results in a specific power of ~10 KW/cm

The corresponding heat-flux 1s therefore reduced to

P B
H _ _Spec cell <UL % KW/ em 2

Pig., 7 ast molten chlorides

thermal column

reactor witn

NN ~ N
NN N NN
‘uel O
\\\
Pumyp
Cooling ol
the c\\l urr
Thnermal
e fflectq column
AN
/// N
O
AN
N \\
N \

Heat
exchanger
34

and the temperature gradient to

AT = 4300 (W-em ©) 0.05 E;mzl = 323 °C
0.4 (Weem K 7)

clad

This value 1s still rather high. A rough estimate of the thermal

stress 1n the wall can be takes as

B = coefficient of linear
expansion (K1)

E = modolus of elasticity
(Kprem™2)

and the corresponding values for stainless steel (19-9 DL)

o, =1

g = % - 15-10 (K ©) - 323 (XK) ° 1.5-106(Kp-cm—2) = 5500 Kp-cm"2

It is also evident that thils result 1s not realistic!

The resulting thermal stress in the cladding wall coupled with the

high flux 1s prohibitive.

¢) Impact of the thermal flux tall in the fast neutron solid fuel core

Here, the most important problem 1s the local overheating by the
thermal flux present at the interface of the thermal column and
the solid fuel core. If, in the fast region near to the interface
approx. 20% of the energy comes from the thermal neutrons, the

following ratio of fluxes must be achileved:

th ] gth i(Ofast ' Qjfast) 0.2
o)
fast . 1.8
tn Dogse = 02 Zopp 0 0e20 0.0
tn
@ <5.10—M )
th — flast
55

That the thermal flux must be 2000 times lower than the fast,
would seem very difficult to realise. It is feasible in a liquid

fuel core, externally cooled.

d) The liquid-fuelled fast reactor with thermal trap

A much better solution is using a liquid-fuel. The %transfer of

the neal generated 1s done, by pumping and cooling the liquid

fuel out of core.

5

For a unit cell of 1 cm”, which in this case consists of fuel only,

we can write the following heat-balance.

= . -é_’I.l. . — 3 . _3_ -1
Pspec = (prc) W T (pre) = Heat capacity (J-em K ™)
W = Veloclity of fuel (cm/s)
AT/ 1 = Temperature lincrease per
unit cell (K-cm—l)
_ . o =5
spec Speclfic power (We.cm 7)

I we allow in the core a temperature increase of AT/l ~3 deg-cm_l

B 21+10° (w-cm'B) .
W= B 7T 55 m.s
2.0 (Jrem 7K 7)) - % (Krem 7))

This velocity appears to be within the limits of LANE who in 1969
proposed a fuel-velocity of 40 m.sec_1 for a reactor with 10 kW.cm
specific power. This point however has to be seriously investigated,

as erosion due to high velocities is a problem,
For a 7000 MW(th) core with a specific power of 21 XW-cm

36

5 the

fuel volume is about %30 liters.

The target volume, that is the volume of irradiated (transmuted)

fission products e.g. Cs-137, 1s postulated as 1300 liters. The

diameter of a spherical core is therefore 146 cm. The temperature

increase of the unit cell of fuel, in one pass through the core,

equals approximately

AT = 3 (deg-cm_l) - 146 (cm) = 4738 e

fuel

and for an fuel inlet temperature of 550 OC we reach an outlet

)

temperature of approx. 988 “C.

The idea of a ligquid fuel high flux reactor has been discussed

for some years. LANE (1971) for example writes about high flux

fast reactors:

"As an alternative
to the possibility
test facility. The
ability to achieve

time eliminate the

some consideration has been given at Oak Ridge
of using a molten salt reactor as a fast [lux

primary virtue of this approach includes the
very high power densitilies and at the same

down time associated with refuelling the

reactor. A fast spectrum molten salt reactor however requlres a

high fissile concentration (i.e. 300 to 500 g

235U/litre) in

order to get mean neutron energies in the range of 10 to 50 keV.

Switching from an NaF - UFM salt (on which the energy range Jjust

mentioned is based) to a chloride-salt reactor would permit a

higher mean energy

for the same fuel concentration but would

require the development of a new technology assoclated with the

use of chlorides.
57

Since the fast flux level is largely determined by the power
density a flux of the order of 1016 Oor more corresponds to a
peak power density in the fuel salt in a range of 5 to 10 MW/
litre and to a power level of about 1000 MW(th). This means
that there will be only 100 to 200 litres in the core: however

the external volume would be about 10,000 litres™.

. How could such a high flux fast reactor with circulating

liquid fuel and thermal column operate as burner?

The details will be given in the second part of this report

(see also Fig. 7 and 8).

9. What engineering problems must be solved for this to be

realised

Short life of the structure materials because of nuclear trans-
formation in these materials, due to the extremely high neutron

flux. The details will be given in the second part of this report.

Acknowledgment

We express out thanks to R. Stratton for preparing the text.
50

Fig. © Selfsustalining slow-breeding and steady

state transmutation power system

/utilities § power units™\

power
reactor

ectrical
—— crergy

el

(breeder)

// fufl irtadiated \\\

fue
U naturaj fuel __2@+U+actinides fuel -
preparatid reprocessing L
u;\\ Tor sale
Tugl ///’—“_
/"— TN
/] . H. \

// V I'.P. reprpcégsing

uasi stable
uclides

V l%table e

reprocessing

ower
and P _
) . reactor
transmutation (burner) dlectrical
central — iy
energy

wflit \ }/
\\\ \\\‘\h_ 1 power un%;::::£>

SN———

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Hegedis F., Chakraborty S.

Gregory M.V., Steinberg M.

59

The nuclear physics of fast reactors

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4o

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b1

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