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Contract No. W-7405-eng-26

CFSTI EUCES

Hie. S J b ;

Reactor Division

A MODEL FOR COMPUTING THE MIGRATION OF VERY SHORTLIVED NOBEL GASES INTO WR'E GRAPHITE R . J. Ked1

JULY 1967

OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee operated by UNION CARBIDE CORPORATION for t h e U.S.

ATOMIC ENE3GY COMMlSSION

&--

iii CONTENTS

........................................................ Introduction .................................................... Diffusion in Salt ............................................... Diffusion in Graphite ........................................... Daughter Concentrations in Graphite ............................. Results for MSRE Graphite Samples ............................... Conclusions ..................................................... References ...................................................... Appendix A. Derivation of Equation Describing Diffusion in Salt Flowing Between Parallel Plates ........................

Abstract

t ,

1 1

5 7 8 17 19

A MODEL FOR COMPUTING THE MIGRATION OF VERY SHORT-LIVE3 N O B U GASES I N T O MSRE GRAPHITE R. J. Ked1

ABSTRACT i

A model describing t h e migration of very short-lived noble gases from t h e f u e l salt t o the graphite i n t h e MSRE core has been developed. From t h e migration r a t e , t h e model computes ( w i t h c e r t a i n l i m i t a t i o n s ) the daughter-product d i s t r i b u t i o n i n graphite as a function of reactor operational history. Noblegas daughter-product concentrations (l4%a, "%e, "Sr, and 91Y) were measured i n graphite samples removed from t h e MSRE core a f t e r 7800 Mwhr of power operation. Concentrations of these isotopes computed w i t h t h i s model compare favorably w i t h t h e measured values.

INTRODUCTION

On July 17, 1966, some graphite samples were removed f r o m t h e MSRE core a f t e r 7800 Mwhr of power operation.

While i n t h e reactor, these sam-

ples were exposed t o flowing f u e l salt, and as a r e s u l t they absorbed some f i s s i o n products.

After removal from t h e reactor, t h e concentrations of

several of these fission-product isotopes were measured as a function of depth i n t h e samples.

Details of t h e samples, t h e i r geometry, a n a l y t i c a l

methods, and r e s u l t s a r e presented i n Refs. 1 and 2.

Briefly, t h e graphite

samples were rectangular i n cross section (0.47 X 0.66 i n . ) and from 4 1/2

All samples were located near t h e center l i n e of t h e core. ed at t h e top, middle, and bottom of t h e Axially, t h e samples were 1 t o 9 i n . long. core.

The t o p and middle

les were grade CGB graphite and were taken

stock from which core blocks were made. The bottom sample d i f i e d grade of CGB graphite t h a t i s s t r u c t u r a l l y stronger and has

a higher d i f f u s i v i t y than regular CGB. (This graphite was used t o make t h e The a n a l y t i c a l technique w a s t o mill off successive layers

rom t h e surfaces and determine t h e mean iso-

t r o p i c concentration i n each l a y e r by radiochemical means.

A model w a s formulated t h a t predicts quantitatively the amount of

I,'

certain of these isotopes i n t h e graphite as a function of the reactor Specifically t h e model i s applicable only t o very

operational parameters.

short-lived noble gases and t h e i r daughters.

This diffusional model may

be described as follows:

As f i s s i o n takes place, the noble gases (xenon and krypton) a r e generated i n t h e salt e i t h e r d i r e c t l y or as daughters of very short-lived precursors, s o they can be considered as generated d i rectly.

These noble gases diffuse through t h e salt and i n t o the graphite

according t o conventional diffusion laws.

As they diffuse through t h e

graphite they decay and form metal atoms.

These metal atoms a r e active,

and it i s assumed that they a r e adsorbed very shortly a f t e r t h e i r format i o n by t h e graphite.

It i s a l s o assumed t h a t once they a r e adsorbed,

they (and t h e i r daughters) remain attached and migrate no more, or a t l e a s t very slowly compared with t h e time scales involved. The derivations of t h e formulas involved i n working w i t h t h i s model a r e given i n the next few sections of t h i s report.

The f i r s t section con-

siders diffusion through f u e l salt, where t h e noble-gas f l u x leaving t h e

salt and migrating t o t h e graphite i s determined.

In t h i s section t h e

"very short half-life" r e s t r i c t i o n is placed on the model.

The next sec-

t i o n takes t h i s f l u x and determines t h e noble-gas concentration i n t h e graphite.

"he following section determines t h e noble-gas decay-product

concentration i n t h e graphite as a function of reactor operating history. The l a s t section compares computed and measured concentrations of four isotopes 140Ba (from 14%e), l4lCe (from 141Xe), 89Sr (from 89Kr), and 91Y

(froin 'lKr)

i n t h e MSRE graphite samples.

It i s of i n t e r e s t t o point out t h e difference between t h i s model and

a previously derived model used t o compute nuclear poisoning from 135Xe (Ref. 3 ) .

In t h e 135Xe-migration model, all the xenon t h a t migrates t o

t h e graphite comes from t h e bulk of t h e salt and i s transmitted through t h e boundary layer.

The xenon generated within t h e boundary layer i s con-

sidered negligible.

In t h i s noble-gas model, all t h e xenon (or krypton)

t h a t migrates t o the graphite i s generated i n the boundary layer and t h a t

which comes f r o m t h e bulk of t h e s a l t i s negligible.

This i s a d i r e c t

consequence of the very short h a l f - l i f e r e s t r i c t i o n placed on t h e noble-gas

3 model i n contrast t o l3 ’Xe-migration model, which specifies a long halfl i f e (9.2 h r ) .

DIFFUSION IN SALT The equation that describes t h e concentration d i s t r i b u t i o n of a d i f fusing material i n a flowing stream between two p a r a l l e l p l a t e s and includes

a mass generation and decay term i s (see derivation i n Appendix A )

ar2

az2

where

Cs = nohe-gas concentration sa t (atoms/ft3 ), Q = noble-gas generation r a t e (atoms/hr per f t 3 ’ o f s a l t ) ,

X Ds

= noblk-gas decay‘ constant (hr” ), = noble-gas diffusion coefficient i n =

salt ( f t 2 / h r ) ,

s a l t velocity ( f t / h r ) ,

S a l t Flow

z = a x i a l distance ( f t ) ,

r = traverse distance (ft), ro = half t h e distance between t h e p l a t e s . I n t h e case of laminar flow,

v=--yl--

where

7 is

1;)

LParallel Plates

the mean f l u i d velocity.

If we r e s t r i c t t h e formulation t o very short-lived isotopes of noble gases, w e can say

LJ c

-c P

that is, as t h e f u e l salt i s moving through t h e core t h e noble-gas genera-

t i o n and decay r a t e s a r e balanced and t h e noble-gas concentration i s close

4 1

t o steady s t a t e .

Even though t h e mean salt velocity past t h e samples i s

i n t h e order of 1 o r 2 ft/sec, t h i s analysis i s restrdcted t o a salt layer

, '

At this position t h e salt velocity is very low, and t h i s assumption i s quite ade-

next t o t h e graphite only a f e w thousandths of an inch thick. quate.

The o r i g i n a l d i f f e r e n t i a l equation then reduces t o d2Cs

ICs

dr2

The r e s u l t of t h i s assumption is that a l l velocity terms disappear, and t h e model of flowing salt reduces t o that of a solid.

Integrating once

with t h e boundary conditions that a t r = 0, dCs/dr = 0 and Cs = Css,

where

Css = steady-state isotope concentration a t r = 0, we f i n d that

dCS = dr

(css

- cs) - x (Cis - c:)lI/2 . DS

I n t h e analysis of 135Xe poisoning i n the MSRE (Ref. 3 ) , it w a s seen t h a t t h e xenon concentration i n salt a t t h e interface w a s very small compared w i t h t h e concentration i n bulk s a l t ,

If a similar s i t u a t i o n i s assumed

i n this case, t h e analysis can be simplified considerably.

The assumption

i s therefore made that

and later it w i l l be seen that t h i s is t r u e .

The above equation can now

be e v a l u t a d a t r = r,,:

where t h e negative root gives t h e proper sign t o (dCs/dr)r=ro. gas f l u x leaving t h e salt at r = r

The noble

i s r e l a t e d t o t h e concentration

gradient as

By substituting,

With t h e very short h a l f - l i f e r e s t r i c t i o n on t h i s model, the isotope concentration i n t h e bulk salt i s always a t steady s t a t e , and it can be evaluated by equating t h e generation and decay terms as follows:

= XCss

Substituting t h i s value of Css i n t o the above equation, gives

DIFFUSION I N GRAPHITE

I n . t h e previous section we determined t h e noble-gas f l u x leaving t h e salt and going i n t o the graphite.

It i s now necessary t o r e l a t e t h i s noble-

gas f l u x t o t h e noble-gas concentration i n graphite. The equation that describes diffusion of a gas i n graphite a t steady state and includes a decay term is4

where

Cg = noble-gas concentration i n graphite (atoms per f t 3 of graphite), E = graphite void f r a c t i o n available t o gas,

Dg = noble-gas diffusion coefficient i n graphite (ft3 void/hr per f t of graphite),

6 X = noble-gas decay constant (hr-’),

x,y,z = coordinates ( f t ) , There i s no generation term i n t h l s expression because these gases

It w i l l also be assumed that t h e cros6 sections a r e s u f f i c i e n t l y low that burnup can be neglected. Since we have

a r e generated only i n t h e salt.

r e s t r i c t e d t h e formulation t o very short-lived isotopes, we need consider only t h e one-dimensional case because t h e isotopes a r e present only near The above equation then reduces t o

t h e surface of t h e graphite.

d2Cg

ax2

-=-

Solving with t h e boundary conditions t h a t Cg = 0 a s x

and’CQ =

Cg,

a t x = 0, w e obtain

Cg = Cgi

Differentiating and evaluating a t

-x(EX/Dg )’ I2

X =

0, we obtaili

The noble-gas f l u x i n t o t h e graphite i s represented by

Fl-=,

=--(--) De E

x=o

and by substituting we obtain

which i s t h e equation that r e l a t e s the noble-gas concentration a t t h e graphite surface t o t h e noble-gas flux.

By combining Eqs. (2) and (31, w e can r e l a t e t h e f l u x t o concentration anywhere i n t h e graphite,

and by combining t h i s equation w i t h Eq. (l), we can r e l a t e C

t o known

reactor operational parameters.

DAUCHTER CONCENTRATIONS IN GRAPHITE

As an example consider t h e 140Xe chain f o r which data from the MSRE

graphite samples a r e available ( s p e c i f i c a l l y '"Ba)

as follows: (16 sec)14%e 3.8$ Yield

The decay chain i s

(66 s e ~ ) l ~ ~ 4C(12.8 s day)14%a Yield 6.35s

(40.2 hr)140La

(stable)l4OCe

FromEq. (5) w e can compute t h e 140Xe concentration i n t h e graphite. Neglecting t h e short-lived 140Cs,

t h e l 4 O I 3 a generation r a t e i s given by

14%a generation rate =

xXecgX e

and OBa decay rate = X B % P

When t h e reactor i s a t power, the change i n "%a

. concentration i n t h e

graphite as a function of time i s dCF

- x XecgXe - - x

Bacg Ba

If we specify t h a t t h e equation i s applicable only f o r i n t e r v a l s of

time when t h e reactor power l e v e l i s constant, and recognize t h a t C g e w i l l approach equilibrium very shortly a f t e r t h e reactor i s brought t o power, t h e term A.xeCze

i s a c m s t a n t and t h e equation can be integrated.

t h e boundary condition that a t zero time,

= CBa

go'

With

the solution i s t

i I

Then, when t h e reactor i s s h u t down, t h e 140Ba concentration w i l l decay as CBa f3

CBa e-X go

(7)

With these equations, the 140Ba concentration i n t h e graphite can be

determined as a function of time and can be taken through t h e 1

reactor on''

and "reactor off" cycles by solving t h e equations t h e appropriate number of times. RESULTS FOR MSRE GRAPHITE SAMPLES

The concentrations of four isotopes from noble-gas precyrsors were measured i n t h e %RE

graphite samples i n order t o determine t h e applica--:.

b i l i t y of the model t o t h e MSRE. ing :

( 1 6 - ~ ) ' ~ ~ X e (66-s)140Cs 3.8 6.0 (1.743)' 41Xe 1.33

(2%

)' 41C s

4.6 +

The decay chains involved a r e t h e follow-

(12.8d)14'Ba 6.35

(18-m)' 41Ba 6.3

(40.2-h)l4'La 6.35

(stab1e)'"Ce 6.44

43.8-h)"'La

6.4

(33-d)14?!Ce 6.0

(stab1e)'f'Pr

5 (2.8-h)88Kr + neutron J 3 Y . rH4.85 (15. 4-m)89Rb (4.4-s ) 89Br 3( ‘ .2-m)89Kr 4.59 ( 16-s 89mY

P 1 (50.5-d)89Sr -0.99913, ( ~ t a b l e ) ~ ’ Y , 4.79

(10-s)’lKr 3.45

(72-s)’lRb 5.43

5.81

-5.4

The underlined element i s t h e p a r t i c u l a r isotope whose concentration

w a s measured. through 4 .

The measured concentration p r o f i l e s a r e shown i n Figs. 1

The t h r e e curves shown on each plot a r e f o r t h e top, middle,

and bottom graphite samples.

Although data a r e available from t h r e e sides

of t h e rectangular sample that w a s exposed t o salt, f o r t h e sake of c l a r i t y , only d a t a from t h e wide face a r e shown.

Concentrations from t h e other

faces exposed t o salt are i n good agreement w i t h these. The noble-gas diffusion coefficient i n graphite that w a s used i n

these calculations w a s determined from t h e daughter-product concentration profiles.

The assumption w a s made e a r l i e r that as a noble gas i n graphite

decays, i t s metal daughter i s immediately adsorbed and migrates no more. If t h i s i s true, it can be shown t h a t t h e daughter d i s t r i b u t i o n i n graphite w i l l follow t h e same exponential as t h e noble-gas d i s t r i b u t i o n .

Equation

(2) represents t h e noble-gas d i s t r i b u t i o n f o r t h e one-dimensional case, and t h i s equation can be evaluated f o r t h e “half thickness” case as follows:

Theref ore Dg =

E%,, 9

(0.693)

,- 5I u

ORNL-DWG

SAMPLE FROM TOP OF CORE - WIDE FACE

SAMPLE

SAMPLE FROM BOTTOM OF CORE - WIDE FACE

CIRCLED

67-35t6

FROM MIDDLE OF CORE - WIDE FACE

POINTS AT DEPTH =0 INDICATE

COMPUTED

VALUE:

\MIDDLE

0.020

0.030

DEPTH IN GRAPHITE

Fig. 1. ""E& July 17, 1%6.

Distribution

(in.)

in MSRE Graphite

Samples at 1100 hr on

I U

lo"

ORNL-DWG 67-35f7

OF CORE - WIDE FACE

SAMPLE FROM MIDDLE OF CORE -WIDE FACE

SAMPLE FROM TOP

SAMPLE FROM BOTTOM OF CORE -WIDE FACE

: 4 L Q)

a a a

z to9 z 0 k E

0.010

0.020

0.030

0.040

0.050

0.060

DEPTH IN GRAPHITE (in.)

Fig. 2. 141Ce Distribution i n MSFiE Graphite Samples a t 1100 hr on July 17, 1966.

a I

ab ORNL-DWG 6 7 - 3 ~ ~

- WIDE FACE

SAMPLE FROM TOP OF CORE

SAMPLE FROM MIDDLE OF CORE

- WIDE FACE SAMPLE FROM BOTTOM OF CORE - WIDE FACE

CIRCLED POINTS AT DEPTH = 0 INDICATE COMPUTED VALUES

0.010

0.020

0.030

0.040

0.050

0.060

DEPTH IN GRAPHITE (in.)

Fig. 3.

"Sr

July 17, 1966.

Distribution in MSRE Graphite Samples at 1100 hr on

13 ORNL-DWG 67-3519

DATA NOT AVAILABLE FOR TOP AND BOTTOM SAMPLES CIRCLED POINT AT DEPTH = 0 INDICATES COMPUTED VALUE

z 109

Ea U

t - 5

0.0IO

0.020

0.030

0.040

0.050

DEPTH IN GRAPHITE (in.)

W f

Fig. 4 . ’lY Distribution i n MSFC3 Graphite Samples a t 1100 hr on July 17, 1966

tj'

where x1 /2

= graphite thickness where daughter isotope concentration i s re-

duced by 1/2, E =

graphite void available t o noble gas (taken t o be lo$),

X = appropriate noble-gas decay constant.

Since the distributions of the noble gas and i t s daughters follow the same exponential, the value of x

112

w i l l be the same f o r both.

Half-thick-

ness data can therefore be obtained from Figs. 1 through 4 and Eq. (8) evaluated f o r D i n graphite. The diffusion coefficient i n graphite i s g

not constant throughout but, rather, i s a function of depth.

I n drawing

t h e l i n e through the data points i n t h e figures, more weight w a s attached

t o the surface concentration d i s t r i b u t i o n than the i n t e r i o r d i s t r i b u t i o n because the diffusion coefficient a t the surface i s of primary i n t e r e s t . Actually, some of the concentration p r o f i l e s tend t o l e v e l out a t greater depths i n the graphite.

This implies t h a t D

increases with depth. The g diffusion coefficient was computed f o r each sample of each decay chain and the r e s u l t s a r e shown i n column 4 of Table 1. The diffusion coeffic i e n t selected f o r the remainder of these calculations i s shown i n t h e following tabulation, where t h e values of bxe have been averaged f o r each g sample, and t h e values of Dfi from the 89Kr chain were given precedence g

over the ' l K r

chain. Diffusion Coefficient i n Graphite ( f t 2 / h r ) Top Sample

Middle Sample

Bottom Sample

1.6 x 10-5

2.0 x 10-5

6.9 x 10-5

0.3 x 10-5

0.9 x 10-5

14.4 x 10-5

From t h i s tabulation it may be seen t h a t the bottom sample has a higher Dg than e i t h e r of the others.

This w a s expected because it w a s a more per-

Die the top and middle samples agree f a i r l y well whereas i n t h e case of D F the top sample i s about 30$ of t h e middle sample. Probably the greatest inconsistency i n the tabulat i o n i s t h a t Die i s greater than f o r the top and middle samples, whereas g it would be expected t h a t would be greater than Die. The reason f o r g

meable grade of graphite.

In t h e case of

DKr

t h i s i s not known.

There may be some question about the assumption t h a t t h e

f t

Table 1. Computed Values f o r MSRE Graphite Samples ~-

5 c

Precursor

' 4

Sample Position i n Core

14'Ba 'Ba l 4'Ba

Middle Bottom

'4'~e

TOP

'4ke

Bottom

89Sr 89~r 89~r

TOP Middle Bottom

9l Y

Middle

TOP

1 4 1 ~ ~ Middle

cs s

Flux Cs i (atoms/hr pef (atoms per (atoms per f t 3 of s a l t ) d f t 3 of s a l t ) e f t 2 of s a l t )

Flux/(

(atoms/hr per ft3 of s a 1 t ) b

Cgi (atoms per f t 3 of graphite)c

0.9 X 1.2 x 10-5 4.9 x 10-5

0.68 X 1 0 l 8 2.28 x io18 1.22 x io18

2.43 X 7.38 x 1015 2.09 x 1015

5.01 X 10I2 15.4 X 1 0 l 2 4.34 X 1 0 l 2

4.33 X 1015 14.6 X 1015 7.82 X

3.85 X 12.9 X 1014 6.94 X 1014

0.006 0.006 0.006

2.4 x 10-5 2.7 x 10-5 8.9 x 10-5

2.39 x io1? 8.04 x 1017 4.31 x 1017

0.91 x 1014 2.77 x 1014 0.78 x 1014

1.89 X lo1' 5.76 x 1011

1.63 X 5.49 x 1 0 ~ 4

4.41 X 1013 14.8 x 1013

0.002 0.002

0.3 X

0.82 X 10l8 2.75 x io18 1.48 x io18

0.85 X 1017 1.65 x 1017 0.22 x 1017

5.47 X 1014 10.6 X 1014 1.42 X

6.29 X 21.1 X 10I6 11.4 X 1 0 l 6

1.68 X 5.65 X 1015 3.04 X

0.025 0.025 0.025

7.32 X 14.2 X 1.94 X

2.06 X 10l8

6.46 X 1015

4.17 X

8.28 X 1015

9.70 X

0.0058

1.11 x 102l

D (ft27hr)a

0.9 x 10-5

14.4 x 10-5 0.4 X lom5

*'Oms

0.86 X 10l1 2.60 X lo1' 0.74 X lo1'

7.44 x 1019 22.6 x 1019 6.41 x 1019

6.29 2.06 X lo1' lo1'

?Noble-gas generation r a t e a t 7.5 Mw.

fNoble-gas flux from s a l t t o graphite.

QEquivalent f i l m thickness.

dNoble-gas concentration i n s a l t a t i n t e r f a c e a t 7.5 Mw ( i n equil i b r i u m with C ). Henry's law constant f o r Xe i n molten s a l t : 2.75 X lom9 mofds of Xe per cc of s a l t per a t m ; Henry's l a w constant f o r Kr i n molten salt: 8.5 X lo" moles of K r per cc of s a l t per a t m .

hIn graphite a t surface a t d a t e of sampling.

i I ~

I I

dpm per g of Graphite a t Date of Sampling

1.20 x 1020 3.65 X lo2' 1.04 X lo2'

eNoble-gas concentration i n bulk s a l t a t 7.5 MI! (Q/X).

concentration i n graphite a t s u r f a c e a t 7.5 Mw.

per ft3

of Graphite

&Diffusion c o e f f i c i e n t i n g r a p h i t e near surface. 'Noble-gas #

Calculated Daughter C onc e n t r a t ionh Measured Daughter Isotope

lo2' lo2' lo2'

1.78 X lo1' 1.32 x loll 2.55 x loll 0.348 X 10l1 1.75 X

16 T h i s assumption should be good f o r

noble-gas daughters do not migrate.

a l l daughters involved, except p o s s i b l y cesium and rubidium.

ments have b o i l i n g p o i n t s of 1238'F

These ele-

and 1290째F, respectively, and there-

f o r e t h e i r vapor pressures could be s i g n i f i c a n t a t t h e r e a c t o r operating and they may d i f f u s e a l i t t l e .

temperature of approximately 1200'F,

Never-

t h e l e s s t h e above values of D63 a r e i n t h e expected range, and s i n c e t h e following c a l c u l a t i o n s a r e not strong functions of D t h e values w i l l be g used as l i s t e d above. The d i f f u s i o n c o e f f i c i e n t s of noble gases i n molten salt were taken

t o be ( R e f . 3 ) : = 5.0 X

ft2/hr

DEr = 5.5 X

ft2/hr

D r and

and represent an average of c o e f f i c i e n t s estimated from t h e Stokes-Einstein equation, t h e Wilke-Chang equation, and an i n d i r e c t measurement based on

analogy between t h e noble g a s - s a l t system and heavy metal ion-water system. The noble-gas generation rate (Q) w a s evaluated f o r each sample posit i o n (top, middle, and bottom) from computed thermal-flux d i s t r i b u t i o n curves (Refs. 5 and 6). The operational h i s t o r y of t h e MSRE w a s taken t o be as l i s t e d below. The f i r s t s i g n i f i c a n t power operation of appreciable duration s t a r t e d on

A p r i l 25, 1966, and t h e graphite sample concentrations were extrapolated back t o t h e sampling d a t e (1100 hr on J u l y 17, 1966). Time a t Indicated Power

Power Level (Mw) .

(hr)

5.0 0 5.0 0 7.0 0 5.0 0 5.5 7.5 0

88 S t a r t i n g d a t e 248 64 12 86

44 28 42 60 68 430

-..

... . .. .. .....

. ..

...

. ..

.. .. ...

Power Level

Time a t Indicated Power

(hd

7.0 0 7.2 0 7.2 0 7.2 0

12 292 100 320 16

50 1 Sampling date

For each isotope involved and f o r each sampling position, Eq. ( 5 ) w a s

evaluated f o r the noble-gas concentration i n t h e graphite.

t i o n of t h e appropriate daughter isotope was then solved f o r and carried

The concentra-

through t h e reactor operational history with E q s . ( 6 ) and (7). The r e s u l t s of these calculations a r e l i s t e d i n Table 1 and shown i n Figs. 1 through

4 . For t h e sake of c l a r i t y , t h e daughter-product concentration i n t h e t a b l e and on t h e figures i s given only a t t h e surface of t h e graphite.

t h e f i g u r e it i s indicated by a c i r c l e around t h e appropriate symbol.

CONCLmIONS The following observations can be made from studying t h e t a b l e and t h e figures. 1. The model predicts very short-lived noble-gas and daughter-product

concentrations i n graphite f a i r l y well. T h i s i s especially t r u e when we consider t h e degree of unceAainty of some of t h e parameters, such as fis-

. . )

sion yields of short-lived noble gases and t h e i r half-lives, Dg and Ds,

and detai1ed:information on f i s s i o n density d i s t r i b u t i o n . 2.

From comparing columns 7 and 8 of t h e table, it can be seen that

t h e assumption

(e$)rqo

ss i n t h e section "Diffusion i n Salt" i s q u i t e

good.

Column 10 of t h e table i s t h e thickness of an imaginary s a l t f i l m

next t o t h e graphite i f a l l t h e xenon (or Krypton) generated i n t h i s f i l m goes i n t o making up t h e computed noble-gas flux. column 9 divided by column 5.

W T

Specifically, it i s

It can be shown t h a t t h e dissolved gas con-

centration w i l l reach 63% of i t s steady-state concentration (Css)

at this

18 distance from t h e graphite.

The f i l m thickness f o r l4'Xe,

141Xe, and ' I K r

i s very t h i n and t h e salt velocities t h i s close t o t h e graphite a r e i n deed very low.

It may be recalled that t h e d i f f e r e n t i a l equatlon f o r d i f -

fusion i n a flowing stream i n t h e section "Diffusion i n Salt" reduced t o an equation f o r diffusion i n a solid, but since t h e salt f i l m thickness involved i s small, t h i s i s an adequate reduction.

4. I n t h e case of 89Kr, t h e f i l m thickness is substantial and it i s probably coincidental that t h e model f i t s t h i s decay chain as well as it does.

Krypton-89 is not a short-lived noble gas i n t h e sense of t h i s de-

As a m t t e r of f a c t , i t s h a l f - l i f e (3.2 min) i s equivalent t o almost eight c i r c u i t times of f u e l salt around t h e laop (25 s e c ) . The velopment.

89Kr concentration i n t h e external loop w i l l therefore become appreciable, and e f f e c t s of t h e xenon s t r i p p e r and circulating bubbles a s additional krypton sinks must be considered.

19 REFERENCES 1. Oak Ridge National Laboratory, MSRP Semiann. Progr. Rept. Aug. 31, 1965, USAM: Report QRNL-3872.

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

R. J. Kedl, Development of a Model f o r Computing t h e 135Xe Migration i n t h e MSRE, WAEC Report ORNL-4069, Oak Ridge National Laboratory ( t o be published).

G. M. Watson and R. B. Evans, Xenon Diffusion i n Graphite: Effects of Xenon Absorption i n Molten S a l t Reactors Containing Graphite, Oak Ridge National Laboratory, unpublished i n t e r n a l document, Feb. 15, 1961.

P. N. Haubenreich e t al., MSRE Design and Operations Report, P a r t 111. Nuclear Analysis, USAEC Report ORNL-TM-730, Oak Ridge National Laboratory, February 1964.

6. B. E. Prince, Oak Ridge National Laboratory, personal communication.

APPENDIX A Derivation of Equation Describing Diffusion i n S a l t Flowina Between P a r a l l e l Plates Consider two p a r a l l e l plates, as shown below, with flow i n t h e z

ai-

rection only. Flow

1 z

Let AzAr(1) be an element of volume one unit i n width. flow t o be viscous, that is, no turbulent mixing.

Consider t h e

Dissolved material may

enter and leave t h e volume element by diffusion i n both t h e z and r directions. It may enter and leave the volume element by convection only i n t h e z direction. Mass i s generated i n t h e volume element a t a constant

rate resulting from f i s s i o n , andimass i s deplCted from t h e volume as a 0

r e s u l t of decay. tration.

The noble-gas decay r a t e i s proportional t o i t s concen-

A material balance around t h e element of volume w i l l y i e l d t h e

following terms i n u n i t s of atom

mass i n by diffusion at r mass out by diffusion at r

+ Ar

inass i n by diffusion a t z

mass out by diffusion at z

U T

qr/r Az(l) %/r+Ar A z ( l )

qz/z

+ Az

mass i n by convection a t z mass out by convection a t z + Az

Qz/z+Az flsz Ad1)

%(z+bz)

b(1)

22 mass generation

Q ArAz(1)

mass decay

XC,,

ArAz(1)

where the terms are defined as follows: %/r = mass flux in the direction of r and at position r (atoms/hr*ft*) qrIr* = mass flux in the direction of r and at position r 3. ,4r ’ ‘1

(atoms/hr-ft*) z = axial dimension (ft) r = traverse dimension (ft) v = salt velocity (ft/hr) Cs = noble-gas concentration dissolved in salt (atoms per ft3 of salt) Q = noble-gas generation rate (atoms/hr per ft3 of salt) X = noble-gas decay constant (hr”) Ds = noble-gas diffusion coefficient in salt (ft2/hr) By equating the input and output terms and dividing byArAz(1) we obtain

If clr and Az are allowed to approach zero,

and, by definition,

qr =

Therefore

% - D, ar

and

qz = -D,

% . aZ

Substituting we get

and i n t h e case of fully developed laminar flow between p a r a l l e l plates v = -3v- k - % ) .

25 ORNL- TM-1810 I n t e r n a l Distribution

1. G. M. 2. R. G. 3. L. G. 4. C. F.

5. 6. 7. 8. 9. 10. 11. 12. 13.

14 15. 16 s 17. 18. 19. 20. 21 22. 23.

24. 25. 26-27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41.

42. 43.

44. 45. 46. 47.

Adamson Affel Alexander

Baes

S. J. B a l l W. P. Barthold

H. F. Bauman S. E. Beall M. Bender E. S. B e t t i s R. E. Blanco F. F. Blankenship J, 0. Blomeke E. G. Bohlmann C. J. Borkowski M. A. Bredig R. B. Briggs J. R. Bronstein G. D. Brunton S. Cantor W. L. Carter G. I. Cathers J. M. Chandler E. L. Compere W. H. Cook D. F. Cope W. B. C o t t r e l l J. L. Crowley F. L. Culler S. J. D i t t o J. R. Engel E. P. Epler R. B. Wans D. E. Ferguson L. M. F e r r i s A. P. Fraas H. A. Friedman J. H. Frye, Jr. H. E. Goeller W. R. Grimes R. H. G w o n P. H. Harley D. G. Harmon C. S. Harrill P. N. Haubenreich F. A. Heddleson

48. 49. 50. 51. 52. 5357. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73.

74. 75. 76. 77. 78. 79.

J. R. Hightower Hoffman Horton Jordan Kasten J. Ked1 J. Kelley T. Kelley W. Kerlin T. Kerr S. K i r s l i s J. Knowles J. A. Lane R. B. Lindauer A. P. Litman M. I. Lundin R. N. Lyon â&#x201A;ŹI G.. MacPherson R. E. MacPherson C. L. Matthews Re W e MCClung H. C. McCurdy H. F. McDuffie C. J. McHargue L. E. McNeese A. J. Miller R. L. Moore J. P. Nichols H. R. W. P. R. M. M. T. H. S. D.

W. W. H. R.

80.

E. L. Nicholson

81. 82. 83. 84.

L. C. Oakes

P. P a t r i a r c a A. M. Perry H. B. Piper 85. B. E. Prince 86. R. C. Robertson 87. M. W. Rosenthal 88. H. C. Savage 89. A. W. Savolainen 90. C. E. S c h i l l i n g 91+4. Dunlap Scott 95. H. E. Seagren 96. W. F. Schaffer 97. 3. H. Shaffer 98. M. J. Skinner 99. G. M. Slaughter 100. A. N. Smith

101. F. 102. 0. 103. P. 104. W. 105* I. 106. H. 107. J. 108. R. 109.. D. 110. J. 111. S.

J. Smith L. Smith G. Smith F. Spencer Spiewak H. Stone R. Tallackson E. Thoma B. Trauger S. Watson S. Watson

112 .

C. F. Weaver

u3. A. M. Weinberg 114. J. R. Weir 115 K. W. West 116 M. E. Whatley 117. G. D. Whitman 118 H. C. Young 119-120 121-122. 123125 126. 0

Central Research Library Document Reference Section Laboratory Records Department Laboratory Records, RC

External Distribution 127. 128. 129. 130. 131-132. 133.

134-148.

A. Giambusso, AEC, Washington T. W. McIntosh, AEC, Washington H. M. Roth, A E , OR0 W. L. Smalley, AEC, OR0 Reactor Division, AEC, OR0 Research and Development Division, AEC, OR0 ' Division of Technical Information Extension (DTIE)

f L