ORNL-TM-1810.txt

 

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e B
5 v

CESTI PRICES

 

Contract No. W-7405-eng-26 H.C 32_5:,}’7 . MN - 65

 

\*_-
T Reactor Division

 

] A MODEL FOR COMPUTING THE MIGRATION OF VFRY SHORT-
= LIVED NOBEL GASES INTO MSRE GRAPHITE

 

- R. J. Kedl

|
|

> | JULY 1967

 

OAK RIDGE NATIONAL LABORATORY
Ozk Ridge, Tennessee
: operated by
" UNION CARBIDE CORPORATION
for the
U.S. ATOMIC ENERGY COMMISSION

 

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CONTENTS

AbstraCt @ 8 &8 8 P 88080 SE PRI e e

INETOAUCEION vvvvrreceoernoncncscsaensanss
Diffusion in Salt " 0 ¢ b 8 8 OO A SN BRSSO E S
Diffusion in Graphite ..cveveveeerecncansn

Daughter Concentrations in Graphite .......

Results for MSRE Graphite Samples ........
ConCluSionS 0‘.‘.l.a..Q..!O.‘.O.Q..D.......

References ...“....'.'..7..... .... e . e 00 80

Appendix A. Derivation of Equation Describing Diffusion

in Sgalt Flowing Between Parallel Plates ..

oooooooooooooo - e . .
ooooo . . . ¢ 8 8 s es
ooooooo + a0 - "o e 2000200
-0 «a o000 ¢ s P e 208000
» ¢ e s e s P e ¢ e e 0w e
ooooooooooooooooooooooo
..... . s s s 0 s 090 . .
2 2 % 2P B O IERL LTSS BSOS .

 

0 ~1 v W

17

19

20

 

 
 

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A MODEL FOR COMPUTING THE MIGRATION OF VERY SHORT-LIVED
NOBLE GASES INTO MSRE GRAPHITE

R. J. Kedl

ABSTRACT

A model describing the migration of very short-lived noble
gases from the fuel salt to the graphite in the MSRE core has
been developed. From the migration rate, the model computes
(with certain limitations) the daughter-product distribution in
graphite as a function of reactor operational history. Noble-
gas daughter-product concentrations (*%%Ba, '4lCe, 898r, and 91y)
were measured in graphite samples removed from the MSRE core
after 7800 Mwhr of power operation. Concentrations of these
isotopes computed with this model compare favorably with the
measured values,

 

INTRODUCTION

On July 17, 1966, some graphite samples were removed from the MSRE
core after 7800 Mwhr of power operation. While in the reactor, these sam-
Ples were exposed to flowing fuel salt, and as a result they absorbed some
fission products. After removal from the reactor, the concentrations of
several of these'fission?proauct"isotopes were measured as a function of
depth in the samples. Details of"the samples, their geometry, analytical
methods, and results are presented in Refs. 1 and 2. Briefly, the graphite
samples'were rectangnlar in_crosssection (0.47 X 0.66 in.) and from 4 1/2
to 9-in. long. All samples were"loCated near the center line of the core.
Axially, ‘the samples were located at the top, middle, and bottom of the

core. The top and middle samples were grade CGB graphite and were taken

from the stock from which the core blocks were made. The bottom sample

was: a modified grade of CGB graphite ‘that is structurally stronger and has

t“a higher diffusiv1ty than regular CGB. (This graphite was used to make the
,lower grid bars of the core ) The analytical technique was to mill off

successive layers of- graphite from the surfaces and determine the mean iso-

tropic concentration in each layer by radiochemical means.

 

 
 

 

2

A model was formulated that predicts quantitatively the amount of
certain of these isotopes in the grfiphite as a function of the reactor ,
operational parameters. Specifically the model is applicable only to very
short-lived noble gases and their daughters. This diffusional model may
be described as follows: As fission takes place, the noble gases (xenon
and krypton) are generated in the salt either directly or as daughters of
very short-lived precursors, so they can be considered as generated di-
rectly. These noble gases diffuse thrbugh the salt and into the graphite
according to conventional diffusion laws. As they diffuse through the
graphite they decay and form metal atoms. These metal atoms are active,
and it is assumed that they are‘adsorbed very shortly after their forma-
tion by the graphite. It is also assumed that once they are adsorbed,
they (and their daughters) remain attached and migrate nb,more, dr at
- least very slowly compared with the time scales involved. |

The derivations of the formulas involved in working with this model
are given in the next few sections of this report. The first section con-
siders diffusion through fuel salt, where the noble-gas flux leaving the
salt and migrating to the graphite is determined. In this section the
"very short half-life" restriction is placed on the model. The next sec-
tion takes this flux and determines the noble-gas concentration in the
graphite. The following section determines the noble-gas decay-product
concentration in the graphite as a function of reactor operating history.
The last section compares computed and measured concentrations of four iso-
topes 14%Ba (from 14%e), 141Ce (from 141Xe), 895r (from 8%Kr), and °'y
(from °Kr) in the MSRE graphite samples.

It is of interest to point out the difference between this model and
a previously derived model used to compute nuclear poiséning from !33Xe
(Ref. 3). 1In the !2°Xe-migration model, all the xenon that migrates to
the graphite comes from the bulk of the salt and is transmitted through
the boundary layer. The xenon generated within the boundary layer is con-
sidered negligible. In this noble-gas model, all the xenon (or krypton)
that migrates to the graphite is generated in the boundary layer and that
which comes from the bulk of the salt is negligible. This is a direct -

consequence of the very short half-life restriction placed on the noble-gas

wontil
h’.‘.

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model in contrast to 12 Xe-migration model, which specifies a long half-

life (9.2 hr).

DIFFUSION IN SALT

The equation that describes the concentration distribution of a dif-
fusing material in a flowing stream between two parallel plates and includes

a mass generation and decay term is (see derivation in Appendix A)

Pc, o%¢C

+
2 2

or az Dg Dy Dy oz

Q AC v &C

s

 

 

where

Cg = noble-gas concentration in salt (atoms/ft3),
Q = noble-gas generation rate (atoms/hr per ft3 of salt),
A = noble-gas decay constant (hr-l),

Dg = noble-gas diffusion coefficient in salt (£ft2 /nr),

v = salt velocity (ft/nr), | Salt Flow
z = axial distance (ft),
r = traverse distance (ft), = |  Parallel
Plates
ro, = helf the distance between the plates.
In the case of laminar flow,
z
o 2 I T
v = g-v 1 - ’ 2o
\ Tl

 

 

where‘v is the mean fluid velocity.
CIf we restrict the formulation to very short-lived isotopes of noble
gases, ‘Wwe can say
X,
’-—— =O ;
that is, as the fuel salt is moving through the core the noble-gas genera-

tion and decay rates are balanced and the noble-gas concentration is close

 
 

 

 

 

to steady state. Even though the mean salt velocity past the samples is
in the order of 1 or 2 ft/sec, this analysis is restricted to a salt layer
next to the graphite only a few thousandths of an inch thick. At this

position the salt velocity is very low, and this aessumption is quite ade-

quate. The original differential equation then reducés to

 

The result of this assumption ié that all velocity terms disappear, and
the model of flowing salt reduces to that of a solid.  Integrating once
with the boundary conditions that at r = O, dCs/dr = 0 and Cy = Csé,.where

C.. = steady-state isotope concentration at r = 0, we find that

55
dCg [ 1/2
— == (C., — C.) —=— (C5_ —C%) .
dr Dy ‘88 5 D, ‘'s8 5

In the analysis of 13°Xe poisoning in the MSRE (Ref. 3), it was seen that
the xenon concentration in salt at the interface was very small compared
with the concentration in bulk salt, If a similar situation 1s assumed

in this case, the analysis can be simplified considerably. The assumption
is therefore made that

(Cs)r=ro << Cgg 5

and later it will be seen that this is true. The above equation can now

be evaluated at r = r.:

0

1l/2
(dcs) _ .ZQCss MC3g /
dr r=r, Dg Dg ’

. where the negative root gives the proper sign to (dCS/dr)r=r0. The noble

gas flux leaving the salt at r = rs is related to the concentration

o3

e
 

 

.& \/“V‘i)

&

v}

&

-

o

gradient as

CPFPlux, . =-D_ {-— . -
r=rg - B ‘dr r=r,
By substituting,
Flwteoy = (2ADgCoq ADC2, )12 .

With the very short half-life restriction on this model, the isotope
concentration in the bulk salt is always at steady state, and it can be

evaluated by equating the generation and decay terms as follows:
Q! = )\‘CSS .

Substituting this value of C,, into the above equation, gives
: _ DS 1/2
“Flux = Qf— . 1
o Q(x ) )
DIFFUSION IN GRAPHITE

In. the previous sectioh'we'@etermined the noble-gas flux leaving the
salt and going into the graphite;»‘It is now necessary to relate this noble-
gas flux to the noble-gas concentration in graphite.

The equation th&t‘déSdribéS'diffusion of & gas in graphite at steady

state and includeé a decay té?fiJie‘_.

s, o,

 

| z . g'-’-'a2Cg ) E_.lcg ’
ox%. Jdy?  d7P Dy
vhere _ o . _
Cg = noble-gas'éoncentrétiofifin graphite (atoms per ft3 of graphite),
- € = graphite vold fraction available to gas,
Dg = ndble-gagldiffusion coefficient in graphité (£t3 void/hr per ft

of graphite),

 
 

 

A = noble-gas decay constant (hr-!),
X,¥,2 = coordinates (ft).

There is no generation term in this expression because these gases

are generated only in the salt. It will also be assumed that the cross
sections are suffidiently low that burnup can be neglected. - Sinée we:have
restricted the formulation to very short-lived isotopes, we need consider
only the one-dimensional case because the isotopes are present only near

the surface of the graphite. The above equation then reduces to

 

) o
d Cg €A
=_08 -
2
dx Dg

Solving with the boundary conditions that Cg =0as x — ® andTCg = Cgi

at x = 0, we obtain

- 1/2 .
Cg _ cgi . x(ek/Dg) ] (2)

Differentiating and evaluating at x = 0, we obtain

dac 1/2
g fex\2/
(_) e — C gi(D_ .

The noble-gas flux into the graphite is represented by

D, [aC
g g
ax X=0

and by substituting we obtain

Dg) 1/2
m&:o gi c
 

 

e A AP gt

P —k

0N .

&

w3

=)

or

< \1/2
Coi = Flux, . (@ s (3)

which is the equation that relates the noble-gas concentration at the
graphite surface to the noble-gas flux. By combining Egs. (2) and (3),

we can relate the flux to concentration anywhere in the graphite,

1/2 1l/2 |

and by combining this equation with Eq. (1), we can relate Cg to known

reactor operational parameters.

Ce =X \D,

1/2
Q(Dse) e X(eMDg)/E (5)
g

DAUGHTER CONCENTRATIONS IN GRAPHITE

As an example consider the 4%Xe chain for whlch data from the MSRE

graphite samples are available (specifically 14°Ba) .The decay chain is

a8 follows:

(16 sec)*%e — (66 sec)t400s — (12 8 day)l4%Ba
Yield - 3.8% | Yield - 6.35%

— (40. 2 hr)14°La — (stable)14°Ce

From.Eq (5) we can compute the 14°Xe ‘concentration in the graphlte

' Neglecting the short-lived 14°Cs the 140pg generation rate is given by

-14°Ba generation rate = xxecxe

and
140y decay rate = xgacga .

When the reactor is at power, the change in '4%Ba concentration in the

 
 

 

bt e S L o 0 o -

 

 

graphite as a function of time is

 

acBa
g _ xXecge‘_ kBana )
dt

If we specify that the equation is applicable only for intervals of
time when the reactor power level is constant, and recognize that Cée will

approach equilibrium very shortly after the reactor is brought to power,

Xe Xe

the term M\ Cg is a constant and the equation can be integrated. With

the boundary condition that at zero time, Cga = Cgi, the solution is
Xe Xe :
cBa ~ A Cg (l _ e-)hBat) . CB& e-lBat (6)
€ = ,Ba €y .

Then, when the reactor isshut down, the 140Ba concentration will decay as

Ba ,
Ba Ba -AT7t
C =C_~ e .
g go | (7)
With these equations, the 140Bs concentration in the graphite can be
determined as a function of time and can be taken through the "reactor on"
and "reactor off" cycles by solving the equations the appropriate number

of times.

RESULTS FOR MSRE GRAPHITE SAMPLES

The concentrations of four isotopes from noble-gas precursors were
measured in the MSRE graphite samples in order to determine the applica-’
bility of the model to the MSRE. The decay chains involved are the follow-
ing: '

(16-5)14%%e — (66-5)1%0Cs — (12.84)1%0Ba — (40.2-h)1%%La — (stable)!“CCe ,
3.8 6.0 6.35 6.35 6.44

(1.7-8)1%Xe — (25-s)1%1Cs — (18-m)'%1Bs -
1.33 4.6 6.3

— £3.8-h)141La — (33-4)'%¥Ce — (stable) flPr ,
6.4 6.0

i

—p

 
 

 

 

 

—¥)

w)

L]

\fi (2 8-n)88Kr + neutron

(4. 4- )39Br ~0. 85 22, (3.2-m)8%r — (l5.4-m)89Rb
4.59 |
| Sy (16-8) 87y

By l
— (50.5-d)%%r ”0'99_8'(stab1e)39y ,
T 4.79

foo (5l-m)91mY\

' o,
\8 .
(10-8)92Kr — (72- s)glR'b — (9.7-n)%18r 2:40, .40 (58-0)°'Y ¥ (stavle)dlzr .
3.45 5,43 5.81 ~5.4 5.84

The underlined element is the particular isotope whose concentration

was measured. The measured concentration profiles are shown in Figs. 1
through 4. The three curves shown on each plot are for the top, middle,
and bottom graphite samples.. Although data are available from three sides
of the rectangular sample that was exposed to salt, for the sake of clarity,
only date from the wide face are shown. Concentrations from the other
faces exposed to salt are‘ih'good‘agréement with these.

~The noble-gas diffusion coefficient in graphite that was used in
these calculationS'fias determinéd fromjthejdaughterhproduct concentration
profiles. The assumption was mede earlier that as a noble gas in graphite
decays, its metal daughter is immediately adsorbed and migrates no more.
If this is-true, it_can,be‘sthnjthat the deughter distribution in graphite
will folldfi the same exponential as the ndble-gas'distribution. - Equation

(2) represents theffidble#gas'distributionvfor the one-dimensionael case,
and this equation can be evaluated for the "half thickness" case as follows:

C 1 - o
& __ 'xllz(ex/Dg 1/2 0-0:693
Cgi "2
;VThefefore
.- e\ 2. '
Dy = —L2 (8)
(0.693)2

 
 

08, CONCENTRATION IN GRAPHITE (dpm per gram of graphite)

10

ORNL-DWG &7-3516

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5 O SAMPLE FROM TOP OF CORE - WIDE FACE
| ® SAMPLE FROM MIDDLE OF CORE — WIDE FACE
® A SAMPLE FROM BOTTOM OF CORE - WIDE FACE
> CIRCLED POINTS AT DEPTH=0 INDICATE COMPUTED VALUES
° - _
5 \\ N
A N
N[O\
; NN
NG 0 N \WMIODLE
®
BOTTO
2 O,
o K
10 \\\\ AN
10 \\ \.\\
5 \\ <
\ N\
2 ‘\\\\ ‘\\\\
N\ o\
10°
o 0.010 0.020 0.030 0.040 0.050
DEPTH IN GRAPHITE (in.)
Fig. 1. 140Ba Distribution in MSRE Graphite Samples at 1100 hr on

July 17, 1966.

]

C

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—;

o

v}

-§ .

10”
5
2
@ 10'°
£
Q.
S
o
‘S
E 5
5
5
a
£
o
=
w2
=
I
o
<
& .9
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=
o
-
<l
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-
1
o
=
o
O
3
e 2
108
5
2

0

 

0.010

11

ORNL-DWG 67-3517
O SAMPLE FROM TOP OF CORE - WIDE FACE

® SAMPLE FROM MIDDLE OF CORE - WIDE FACE
A  SAMPLE FROM BOTTOM OF CORE — WIDE FACE
CIRCLED POINTS AT DEPTH = O INDICATE COMPUTED VALUES

0020  0.030 0.040  0.050 0.060
DEPTH IN GRAPHITE (in)

Fig. 2. '%Ce Distribution in MSRE Graphite Samples at 1100 hr on

July 17, 1966.

 

 

 
 

 

 

12

ORNL-DWG 67-3518

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.0€0

3 (5 O SAMPLE FROM TOP OF CORE - WIDE FACE
- ®
é ® SAMPLE FROM MIDDLE OF CORE — WIDE FACE
o 2 A SAMPLE FROM BOTTOM OF CORE — WIDE FACE
‘s CIRCLED POINTS AT DEPTH=0 INDICATE COMPUTED VALUES
E N
e @\o
o o\
g 10! N\ e
: S~
s ~~
w ™~
% 0O \ o T~
£ N\ s
5 -------....___A _Em @ ®
z —a o
= 5 *AA\
S A
[
< N
'—
= \
g 2
2 \
8 o
& N\
©
0 0.010 0020 0.030 0.040 0050
DEPTH IN GRAPHITE (in.)
Fig. 3. 89Sr Distribution in MSRE Graphite Samples at 1100 hr on

July 17, 1966.

ey,

r=e
 

 

kg

o

4‘)

-

 

13

ORNL-DWG 67-3519

DATA NOT AVAILABLE FOR TOP AND BOTTOM SAMPLES
CIRCLED POINT AT DEPTH = O INDICATES COMPUTED VALUE

 

2
1011

5

®

|a 2

o

on

S

§ 10/°

o

©

Q.

E 5

Q.

3

[F1]

-

a 2

<

a

O

=

Z 10

o

—

=

- 5

=<

Ll

Q

=

o

© MIDDLE

> 2

n

- 108

5
2 .

S [+ 4

0 S 0010 0020 0030 0040 0050
-~ . 'DEPTH IN GRAPHITE (in) -

rFig. 4. Oly Distribution in MSRE Graphite Samples af 1100 hr on
July 17, 1966. |

 
 

 

 

14

where

X1/2 = graphite thickness where daughter isotope concentration is re-
duced by 1/2,
graphite void available to noble gas (taken to be 10%),

€

A

appropriate noble-gas decay constant.

Since the distributions of the noble gas and its daughters follow the
same exponential, the value of X1/2 will be the same for both. Half-thick-
ness data can therefore be obtained from Figs. 1 through 4 and Eq. (8)
evaluated for Dg in graphite. The diffusiofi coefficient in graphite is
not constant throughout but, rather, is a function of depth. In drawing
the line through the data points in the figures, more weight was attached
to the surface concentration distribution than the interior distribution
because the diffusion coefficient at the surface is of primary interest.
Actually, some of the concentration profiles tend to level out at greater.
depths in the graphite. This implies that Dg increases with depth. The
diffusion coefficient was computed for each sample of each decay chain
and the results are shown in column 4 of Table 1. The diffusion coeffi-
cient selected for the remainder of these calculations is shown in the
following tabulation, where the values of DXe have been averaged for each

sample, and the values of DKr from the 8°Kr chain were given précedence
over the ?Kr chain.

g

Diffusion Coefficient in Graphite (ft°/nr)

 

Top Sample Middle Sample Bottom Sample
ng 1.6 X 1075 2.0 X 1075 6.9 X 1077
Dg 0.3 X 1077 0.9 X 107° 14.4 X 1072

From this tabulation it may be seen that the bottom sample has a higher
Dg than either of the others. This was expected because it was a more per-
meable grade of graphite. In the case of Dée the top and middle samples
agree fairly well whereas in the case of Dgr the top sample is about 30%

of the middle sample. Probably the greatest inconsistency in the tabula-

tion is that Dge is greater than Dgr for the top and middle samples, whereas
it would be expected that Dgr would be greater than Dge. The reason for

this is not known. There may be some question about the assumption that the

ot Yy
 

 

 

 

 

15

Table 1. Computed Values for MSRE Graphite Samples

 

 

 

 

 

 

 

1 2 -3 4 5 6 7 8 9 10 11 12
| o - Calculated Daughter Concentration®
_~.. Measured Sample | Q Coi Cqi Css Flux
g;ziirgzi Daughter Position (fggfihr)a (atoms/hr per (atomsgper ft®>  (atoms per (atoms per (atoms/hr per ?i;x/é Atoms per ft3 dpm per g of
Isotope in Core ££3 of salt)P of graphite)® ft? of salt)d ft3 of salt)® ft? of salt) ’ per. Graphite at Date
of Graphite .
| of Sampling
140xe 140py  Top 0.9 X 1075  0.68 X 10*® 2,43 x 10%° 5.01 X 10%®  4.33 x 10*3  3.85 x 104 0.006 1.20 X 10?0 0.86 x 10t
140ye ~ 140gg ~  pMiddle 1.2 X 107% 2.28 X 108 7.38 x 10%3 15.4 X 10} 14.6 x 10*° 12,9 x 10*%  0.006 3.65 X 1029 2.60 x 101!
140xe 140 Bottom 4.9 X 1075 1.22 x 10'%®  2.09 x 10'7 4.34 X 1012 7.82 x 10Y°  6.94 x 10'*  0.006 1.04 X 1020 0.74 % 10!
lelye  4lge  Top 2.4 X 1077  2.39 x 107  0.91 x 104 1.89 X 1011 1.63 x 10**  4.41 x 102 0.002 7.44 X 1019 2.06 x 1019
lélye Yaloe Middle 2.7 X 1077 8.04 x 107 2,77 x 10%4 5.76 X 10*1 5,49 x 10%%  14.8 x 10}2  0.002 22.6 x 10%° 6.29 % 100
lalye  14lge Bottom 8.9 X 10"%  4.31 x 107 0.78 X 104 1.62 X 10t 2.94 x 104 7.97 X 10*3  0.002 6.41 X 1019 1.78 x 101°
89kr 895y Top 0.3 X 10~ 0.82 x 10'¢ 0.85 X 1017 5.47 X 104 6.29 X 106  1.68 X 10'°> 0.025 7.32 X 1020 1.32 x 101
89Ky 89y Middle 0.9 X 10™° 2.75 X 1018 1.65 X 107 10.6 X 10%4 21.1 X 1016 5.65 X 105 0.025 14.2 X 1020 2.55 X 1011
89gr 89gy Bottom 1l4.4 X 10-5  1.48 X 10'8 0.22 X 107 1.42 X 1014 11.4 X 10%6 3.04 X 10'5  0.025 1.94 X 1020 0.348 x 101
o1y °ly Middle 0.4 X 107° 2.06 x 1018 .46 x 1013 4.17 X 1012 8,28 x 105  9.70 x 10** 0.0056  1.11 X 102} 1.75 x 1011
®Diffusion coefficient in graphite near surface. ®Noble-gas concentration in bulk salt at 7.5 Mw (Q/A).
bNoble-gas generatlon rate at 7.5 Mw. fNoble-gas flux from salt to graphite. f
i
NOble-gas concentration in graphite at surface at 7.5 Mw. 8Fquivalent film thickness. i
dNoble-gas concentratlon in salt at interface at 7.5 Mw (in equi- hiy graphite at surface at date of sampling. f

librium w1th C . Henry's law constant for Xe in molten salt: ;
2.75 X 107° mo%es of Xe per cc of salt per atm; Henry's law constant ]
for Kr in molten salt: 8.5 X 10™° moles of Kr per cc of salt per atm.

 

 
 

 

16

noble-gas daughters do not migrate. This assumption should be good for
all daughters involved, except possibly cesium and rubidium. These ele-
ments have boiling points of 1238°F and 1290°F, respectively, and there-
fore their vapor pressures could be significant at the reactor operating -
temperature of approximately 1200°F, and they may diffuse a little. Never-

theless the above values of D, are in the expected range, and since the

g
following calculations are not strong functions of Dg the values will be
used as listed above.

The diffusion coefficients of noble gases in molten salt were taken

to be (Ref. 3):

DA = 5.0 x 10°% pt2/nr
and
DY = 5.5 x 10°% £t2/hr

and represent an average of coefficients estimated from the Stokes-Einstein
equation, the Wilke-Chang equation, and an indirect measurement based on
analogy between the noble gas-salt system and heavy metal ion-water system.

The noble-gas generation rate (Q) was evaluated for each sample posi-
tion (top, middle, and bottom) from computed thermal-flux distribution
curves (Refs. 5 and 6).

The operational history of the MSRE was taken to be as listed below.
The first significant power operation of appreciable duration started on
April 25, 1966, and the graphite sample concentrations were extrapolated
back to the sampling date (1100 hr on July 17, 1966).

 

Power Level Time at Indicated Power
(Mw) (hr)
5.0 88 Starting date
0 248
5.0 ' 64
0 12
7.0 86
0 by
5.0 28
0 42
5.5 60
7.5 68
0 - 430

 

z’."‘;'.‘
 

 

 

 

gy

_\_."

»}

i

 

 

17
Power Level - Time at Indicated Power
(Mw) | (hr)
7.0 26
o - 12
7.2 292
0 100
7.2 320
0 16
7.2 50 '
0. 1 Sampling date

‘For each isotope involved and for each sampling position, Eq. (5) was
evaluated for the ndble-gas:COncéntration in the graphite. The concentra-
tion of the appropriate daughter isotope was then solved for and carried
through the reactor operational history with Eqs. (6) and (7). The results

‘of these calculations are listed in Table 1 and shown in Figs. 1 through

4, TFor the sake of clarity, the daughter-product concentrstion in the
table and on the figures is given only at the surface of the graphite. On
the figure it is indicated by a circle around the appropriate symbol.

CONCLUSTONS

The following observations can be made from studying the table and
the figures.
1. -The model predicts very short-lived noble-gas and daughter-product

concentrations in graphite fairly well. This is especially true when we

‘consider the degree of uncertainty of some of the parameters, such as fis-

sion_yields-of_shortslived;@oble gases -and their half-lives, D, .and D,
and detailed’information on fission density distribution.
2. From comparing columns 7 and & of the table, it can be seen that

‘the assump_tion(CfS.)r=rb <<?ng‘rn thé_section "Diffusion in Salt" is quite

good. o . _
3. Column 10 of the table is the thickness of an imaginary salt film

next to the graphite if all the xenon (or Krypton) generated in this film
- goes into making up the computed noble-gas flux. Specifically, it is

column 9 divided by Golumn 5. .It can be shown that the dissolved gas con-

centration will reach 63% of its steady-state concentration (CSS) at this

 
 

 

 

18

distance from the graphite. The film thickness for 14%Xe, 4lXe, and %'kr
is very thin and the salt velocities this close tbithe graphite are in-
deed very low. It may be recalled that the differential equation for dif-
fusion in a flowing stream in the section "Diffusion in Salt" reduced to
an equation for diffusion in a solid, but since the salt film thickness
involved is small, this is an adequate reduction. |

4. In the case of ®%Kr, the film thickness is substential and it is
probably coincidental that the model fits this decay chain és:well as it

does. Krypton-89 is not a short-lived noble gas in the sense of this de~

velopment. As a matter of fact, its half-life (3.2 min) is equivalent

to almost eight circuit times of fuel salt around the loop (25 sec); -The,

89k r concentration in the external loop will therefore become appreciable,
and effects of the xenon stripper and circulating bubbles as additional
krypton sinks must be considered. - |

oo W

bt

g

 
 

AR e e ke bl i < oy e e e <Py b

1.
2.
3,
4.
7
_ 5,
'Ji
6.
’,?

19

REFERENCES

Oak Ridge National Laboratory, MSRP Semiann. Progr. Rept. Aug. 31, 1965,
USAEC Report QRNL-3872

Oak Rldge National Laboratory, MSRP Semiann. Progr. Rept. Aug. 31, 1966,
USAEC Report ORNL-4037.

R. J. Kedl, Development of a Model for Computing the 135%e Migration
in the MSRE, UBAEC Report ORNL-4069, Qak Ridge National Laboratory
(to be published).

G. M. Watson and R. B. Evans, Xenon Diffusion in Graphite: Effects
of Xenon Absorption in Molten Salt Reactors Containing Graphite, QOak
Ridge National Laboratory, unpublished internal document, Feb. 15, 1961.

P. N. Haubenreich et al., MSRE Design and Operations Report, Part III.
Nuclear Analysis, USAEC Report ORNL-TM-730, Oak Ridge National Labora-

tory, February 1964.

B. E. Prince, Oak Ridge National Laboratory, perSonal communication.

 
 

iv

 

 

 

 

 

 
 
7

 

 

 

7 .

 

8

o

oy

21

APPENDIX A

Derivation of"Equation Describing Diffusion in Salt
Flowing Between Parallel Plates

Consider two parallel plates, as shown below, with flow in the z di-

rection only.

 

 

 

 

Flow

/. Direction Z ;

7
A l 4
S =20 . )
) P r 'y
a8 g
’ HE /
7 . Diff t
7 Az —t T >sion” |
A pad - /
A 1 | %
/ i /
7 /
; —H AT e f
P /

 

 

Let AzAr(l) be an element of volume one unit in width. Consider the

flow to be viscous, that is, no turbulent mixing. Dissolved material may

enter and leave the volume element by diffusion in both the z and r direc-

tions. It may enter and leave the volume element by cohvection only in

the 2z direction.' Mass is 'generat'ed in the volume element at & constant

rate resulting from_fissidn;',_anda 'mass_ is depleted from the volume as a

_rés.ult of decay. - The noblé-gas_‘ deca.y rate ‘iS‘proportidnalrto its concen-

tration. A material 'balapc'e,-aromd the element of volume will yield the

mass:
mass.
mass
‘mass
mass

mass

- following terms injuriits -of e.toins/hi': o

in 'by diffusibh-,rat r
out by diffusion &t r + Ar
in by diffusion at z

‘out by diffusion at z + Az

in by convection at z

out by convection at z + Az

! qr/r Ai(l) o
Dy 22(1)
q-i/z or(l) , -
Az /z+Az rAr(l)
vCgy Ar(l)

Vs (z4nz) ar(1)

 
 

 

 

22
mass generation . Q ArAz(l)
mass decay , ACgy ArAZ(1)
where the terms are defined as follows:
= mass flux in the direction of r and at position r (atoms/hr.ft?)

qr/r
Qr/r+Ar

i

mass flux in the direction of r and at position r + Ar '
(atoms/hr: £t )
2z = axial dimension (ft)
r = traverse dimension (ft)
v = salt velocity (ft/hr)
Cs = noble-gas concentration dissolved in salt (atoms per ft? of
salt)
Q = noble-gas generation rate (atoms/hr per ft> of salt)
A = noble-gas decay constant (hr~?)
Ds = noble-gas diffusion coefficient in salt (£t2/hr)

By equating the input and output terms and dividing by ArAz(l) we obtain

r /r+ar ~ Gr/r s Az /z+0z ~ Qz/z .\ v(Cs(z+az) = Csz) Q. v 2 .
- sz =Y .

 

 

Ar JAVA Az

If Ar and Az are allowed to approach zero,

qu dqg Cg

 

 

—_—t =+t V——=Q + Mg =0
dr oz Az
and, by definition,
D EEE d D EEE
or € 3z
Therefore
2 2
dq,, 0°Cy dq,, o°C,
— = — D4 and —— =-=D .
or dr? oz dz2

Y
 

 

 

Y 1

my—gy Y

Substituting we get

23

 

J2C BZCS Q A v oCg

s

 

+

 

or®  3*® Dy Dy Dy Oz

s

and in the case of fully developed laminar flow between parallel plates

v = vl -

N Jw

) i

r_
2
o

 
 

¥

 

 
 

e memnssema st ot b i bty A b ik e s

-

R

- iy 8

”n v

15.
16.
17.
18.
19.
20.
21.
22.
23.
24 .
25,
2627 .
28.
29.
30.
31.
32.
33.
34.

35..
360'
37.

38.

39.'

40.
41.
42.
43,
b,
45,
46 .
47 .

 

25

ORNT.-TM-1810

Internal Distribution

M. Adamson.
G. Affel

G. Alexander
F. Baes

J. Ball

- P. Barthold

F. Bauman

E. Beall
Bender

S. Bettis

E. Blanco

F. Blankenship
0. Blomeke
G. Bohlmann
J. Borkowski
A. Bredig

B. Briggs

R. Bronstein
D. Brunton
Cantor

. L. Carter

I. Cathers
M. Chandler
L. Compere
H. Cook

F. Cope

B. Cottrell
L. Crowley
L. Culler
J. Ditto

R. Engel -

. P. Epler

B. Evans
E. Ferguson

- M. Ferris_
.P. Freas

A. Friedman
H. Frye, Jr.

. E. Goeller

R. Grimes

‘H. Guymon

H. Harley
G. Harmon
S. Harrill

N. Haubenreich
A. Heddleson

48.
49.
50.
51.
52.
53-57.
58.
59.
60.
61.
62.
63.
64 .
65.
66.
67.
68.
69.
70.
71.
72.
73.
4.
75.
76.
77 «
78.
79.
80.
81.
82.
83 .
84.
85.

86.

87 .

. 88-
89.
90.
91-94,
95,
9.
97,
98.
99,
100.

J. R. Hightower
H. W. Hoffman
R. W. Horton

W. H. Jordan

P. R. Kasten

R. J. Kedl

M. J. Kelley

M. T. Kelley

T. W. Kerlin

H. T. Kerr

5. 5. Kirslis
D. J. Knowles
J. A. Lane

R. B. Lindauer
A. P. Litman

M. I. Lundin

R. N. Lyon

H. G. MacPnherson
R. E. MacPherson
C. L. Matthews
R. W. McClung
H. C. McCurdy
H. F. McDuffie
C. J. McHargue
L. E. McNeese
A. J. Miller

R. L. Moore

J. P. Nichols
E. L. Nicholson
L. C. Oakes '
P, Patriarca

A. M. Perry

H. B. Piper

B. E. Prince

R. C. Robertson
M. W. Rosenthal
H. C. Savage

A. W. Savolainen
C. E. Schilling
Dunlap Scott

H. E. Seagren
W. F. Schaffer
J. H. Shaffer
M. J. Skinner
G. M. Slaughter
A. N. Smith

 
 

 

 

101.
102 »
103.
104.
105 &
106.
107.
108.

109. -

110.
lll *

127.
128,
129.
130.
131-132.
133.
134—148.

F.
0.
P.
W.
I.

Je
R.
D.
Je
S.

A.
T.
H.
W.

26
J. Smith 112.
L. Smith 113.
G. Smith 114.
F. Spencer 115.
Spiewak 116,
. H. Stone 117.
R. Tallackson 118.
E. Thoma 119-120.
B. Trauger 121-122.
S. Watson 123—-125,
S. Watson 126.

C. F. Weaver

A. M. Weinberg

J. R. Weir

K. W. West

M. E. Whatley

G. D. Whitman

H. C. Young

Central Research Library
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P