et b

' iiifl -oafi -::-.i ‘l.

  

 

\.'.

Y

 

OAK RIDGE NATIONAI. LABORATORY
~ operated by

UNION CARBIDE CORPORATION
| NUCLEAR DIVISION - S
. for the

us. ATOMIC.ENERGY COMMISSION |
 ORNL-TM- 2245

 COPY NO.--.V 86

| -_DATE - July 23, 1968

 

F. N. Peebles -

' 'ABSTRACT :

Removal of dissolved Xenon-135 by mess transfer to helium bubbles

‘offers an attractive means of controlling the Xenon-135 poison level

in molten salt breeder reactors (MSBER's). In order to provide neces-

| sary engineering information for evaluetion of the proposed method, the:*

existing date on rates of mess transfer to ges bubbles ‘have been: -

'reviewed

. Rather extensive literature references point to reliable equations
for prediction of mass transfer rates to single bubblee,‘ising in '

 stationary liquids under the two extreme cases of a rigid bubble inter-
- face and of & perfectly mobile bubble interface. In general, experi-
" mentel deta ere availsble which support these predictions. No relisble
criterion for predicting the transition from one. type behavior to
-another is available. o s S :

- An_elementary analyais'of‘the'ratee_of mass tranefer'to'bubblesl
cerried along by turbulent liquid in & pipe is presented. The results
indicate that the bubble mass trensfer coefficlent for 0.02 in.

- diemeter bubbles will be epproximately 13 ft/hr for mobile-interface
'rbubbles, end approximately 2 ft/hr for rigid-interfece bubbles. An

 experiment is suggested to. provide specific data on the mass transfer
.retes to bubbles carried aslong by turbulent liquid 1n & pipe for hydro-
fdynamic conditions Wthh simulate the MSBR._-

ROTICE This document. contains information of ‘o preliminary nature .

and was prepared primorily for internal use at the Oak Ridge National
~ Laboratory. It is subject to revision or correcnon and therefore does .

not represent a final report. oo :

-

RO OF TS DOCUNM 1S UNURTER

 
 

 

 

 

 

 

LEGAL NOTICE -

This raporl was preparad as an occounf of Govarnmnf sponsorod work. Nmther tho Unn‘ed S!crres,

nor the Comn‘ussmn, nor any person acting on behalf of the Commission:

A, Mokes any warranty or represonfutlon, expressed or implied, ‘with respect to iho dcecuracy,

" completeness, or usefulness. of the information contained in this report, or that the use of -

any informatien, apparatus, methed, of process disclosed in this report may not infrings

privately owned rights; or

B. Assumes ony lichilities with- respect to the use of, or for dumages resulhng from the use of -

any information, apparatus, methed, or process dlsc!osod in this report.

~ As used in the above, “‘person acting.

on behalf of the Commlssmn" includes any employee ,of

‘eontractor of the Comrmsswn, of omp!oyee of such centractor, to the extent that such cmployoe

-or contractor of the Commission, or employee of such contractor prepares, dlssemmdies or

‘Vprowdos access to, any information pursucnf to !'us empioymenf or contract wnh the Commission, =

“of his omployment with such centracter,’

 

 

 

R T A e e

R T RAspaR RS AR et 4

)

-,
~

'fla.(""‘f

 
 

+

v CONTENTS
Page

Abstract 1

1.0 Introduction 5

2.0 Mass Transfer Theory ‘ 5

2.1 Mass Transfer Coefficients for Spherical Bubbles 9

Rigid Interface Case 13

Mobile Interface Case 14

2.2 Experimental Data on Mass Trangfer Coefficients 17

to Single Bubbles

2.3 Mess Trensfer Coefficients for Bubbles Carried 20
) Along by Turbulent Liquid
4 3.0 Proposed Mass Transfer Experiment to Simulate MSBR 25
) Contact Conditions
L.0 Conclusions 30
References Cited 32

 

LEGAL NOTICE

This report was prepared as an account of Government sponsored work. Neither the United

States, nor the Commission, nor any person acting on behalf of the Commission:
) A. Makes any warranty or representation, expreszed or implied, with respect to the accu-
- racy, completeness, or usefulness of the information contained in this report, or that the use
of any information, apparatus, method, or process discloged in this report may not infringe
privately ovned rights; or

B. Assumes any liabilitles with respect to the use of, or for damages resulting from the

- use of any Information, apparatus, method, or process disclosed in this report.

As used in the above, *‘person acting on behalf of the Commission® includes any em-
ployee or contractor of the Commission, or employee of such contractor, to the extent that
such employee or contractor of the Commission, or employee of such contractor prepares,

_ disseminates, or provides access to, any information pursuant to his employment or contract
" with the Commission, or his employment with such centractor. -

)

QISTREUTON OF THIS HOCUMENS @ ONL
 

»

L)

REMOVAL OF XENON-135 FROM CIRCULATING FUEL SALT OF THE-MSBR
BY MASS TRANSFER TO HELIUM BUBBLES

1.0 Introduction |

A pr0posed'method10 of removing XenonQiBS from the fuel salt in the
Molten Selt Breeder Reactor (MSBR) involves circuletion of helium bubbles
with the liquid fuel. Bubbles ere to be injected into the flowing stream

near the pump, and then dissolved Xenon—135‘is removed from the liquid.

" by mess transfer (combined diffusion and convection) into the bubbles.

The circulaeting bubbles are then to be removed from the liquid at the

outlet of the heat exchanger by a centrifugel separator.

Although the potentisl for Xenon-135 removel by mass transfer to
helium bubbles is high, the actual effectiveness of removal is controlled
by the surface area of the bubbles exposed to the liquid and the mass
transfer coefficient between bubbles and liquid flowing cocurrently in.
e pipe. This report deals with the.bubblevnass‘transfer rete expected
under the MSBR operating conditions, based on the information available
in the literature, and & proposed experiment to provide additional detsa.
The experiment involves simulation of the reactor flow and mass transfer
conditions through use of a glycerine solution es the liquid, oxygen as
the solute gss, and helium as-the stripping medium,

2.0 Mass Trensfer Theory

 

The esgsential features of the mass transfer situation of interest
is shown in Figure 1. Liquid flowiné along & pipe at the rate QL enters
the system with -dissolved concentra.tion, I1° end the inlet stripping gas

-at a flow rate, QG, is 1nJected into ‘the liquid. As the liquid.end gas

streams move cocurrently slong the pipe the dissolved ges content of - the
liquid is reduced to the exit concentra.tion,‘cL2
For-e& steady gtate system, conservation of the. dissolved ges .requires

thet the concentration change in accord with

% (cLl L).: 8 %> (1)
’(/,-Pipeline Contactor, Length = L, Croés Section = A,

ORNL-Dvg 68-6780

 

U Oy

Liquid Flow

 

&
QQ‘

e QL, r.CL -

 

|

 

QG,'Gas Flow Rate

Fig. 1. Flow Diagram for Pipeliné Contactor..

G2

 
. [ ™

N

-)

- where C

7

G represents the local concentration of the solute geas in the
bulk bubble stream. Equation (1) is based on the case of negligible
solute gas in the inlet stripping ges.

At eny location aslong the contactor, the concentration of dissolved
gas in the vicinity of the-liquid;gas interface of a typical bubble is
depicted in Figure 2. The:solute gas concentration difference between
thet of the bulk liquid and the liquid et the interface provides the

driving force for mass transfer at the rate,

e

RTQL
-, dp =K e &, (s Ec;g‘" Fa L] (2)
where

KL = liquid phaese mass. transfer coefficient,

e = gas-liquid. interfecial area per unit volumn of contactor,
AC = contactor cross-section,

dL = differentiel length of contactor,

T = absolute temperature,

R = universal ges constant,

H = Henry's lew constent for solute ges.

Equation (2) results from the clessic assumption of negligible interfacial
resistance,z and the assumption of small ges-phese resistence to mass
transfer. The latter assumption is en approximation which is eppropriate
for the case of & gas having & low solubility in the liquid of interest.
When Equetion (2) is integrated-to give the change in solute gas concen-
tretion over the total length of the liquid-gas contactor, it is found thet

C - -8

L2 o+ e
e ot e (3)
CLl l+a

K, & AL (1 + a)

 

 

where o = =——— gand B = —_
o HQG | QL | |
e e R | - 1 - %o
If the effectiveness for solute gas removal 1s expressed as E = —c >
SRR e R e 11

then for & given mass transfer system theieffectiveneés_fpr golute removel

is given.by _
3 -

_l~e

E==57—> (L)
 

 

 

 

 

 

ORNL-Dvg 68-6761 "
btk Tiqut tiquid.ces
‘Bulk Liquid - Interface
"
C.
- Bulk Ges G
For Negligible Gas Phase Resistance,
a1 = G
. Fig. 2. Concentration Profiles Near Interface..-
 

 

 

fl(: s

»

9

The maximnm,ralue of E is for a liquid-gas contactor of infinite volume,
1
l+o0 °

 

or infinite msss transfer coefficient, and is EMax

Figure 3 shows a plot of the Xenon-135 removel effectiveness ags e
function of liquid phese mess transfer coefficient for the MSER operating
conditions and helium bubbles 0.02 in. dismeter. The plot illustrates

_that the effectiveness for Xenon-135 removel is sherply related to the

liquid: phase me.ss transfer coefficient in the renge of 1 < KL < 100 ft/hr.
Kedlll has shown that the Xenon-135 ‘poison fraction in the MSBR is
influenced in en importent way by the bubble stripplng effectiveness, and"
hence successful reactorfanalysis‘and design for the.MSBR depends on rether

accurate_knouledge'of.the bubble mass'transfer-coefficient.

2.1 Mass Transfer Coefficients for Spherical Bubbles

- Previous.studies on mess transfer to and from sPherical ges bubbles
have been extensive, including esnalyticel and experimental,investigations.
A brief summary'of'the‘important results is given in this section. First,
e description of the pertinent enelyticel model is presented and then a
summery of-the most recent experimental findings is given.

Figure L4 ghows the model situation of & spherical bubble of radius,

, imbedded in e stationery liguid. The bubble moves with a velocity

‘fi' relative to the 1iquid. For the case of an inert gas bubble removing

& solute ges-from a liquid, the approPriate diffu51on equation is:
2

ac 3c_ 3¢ | -
u S + v 3y D —x éya ’ (5)

velocity components in the x and y directions.

where;u,rv_
C
D

local conoentration of solute gas in the liquid,
mass diffusivity for the solute gas in the liquid.

| The velocity components u and v are generally available from a solution
~of -the momentum equations, and would satisfy the bulk liquid continuity

reletion for points in the immediate V1cinity of the bubble surface
_gfur !Vr ’ : (6)
x .

where r is the redial distance from a point on the bubble surface to the
exis of symmetry. Emphasis is placed on the immediate vicinity of the
L, )/CLI

Xenon-135 Removal Effecfi:l.ven'ess, E = ‘(CL e C
_ B 1

o
o
*—l

o
o
\h

 

10

4

ORNL-Dwg 68-6782

o
o
N

0.

 

1 2.5 .. - 1 - 2 - 5 . - 100
Mass Transfer Coefficiep;, K, (£t/hr)

Fig. 3. Xenon-135 Removal Effectiveness as a Function of L1qu1d

. Phase Mass Transfer Coefficient.

i’

 
 

»

)

11

ORNL-Dwg 68-6783

fib’ Bubble Velocity

 

      
 

 
 

Interface

‘Bulk Liquid
cggcentr%tion Concentration,

L oa—Ax1is of Symmetry
|

 

Fig. 4. Coordinates for Thin Region Near Spherical Bubble Surface.
 

12

bubble surface because the region of important concentreation variation is
expected to be thin, and even thinner then the region of significent velo-
city veriations. Thus for such & situstion it is reasonable to represent the
velocity in~the_immediate-viginity of -the bubble surface as

u_f:us_fu;y. - (Tl

The term u, is the velocity component in the x—direction at the surface
of the sphere, possibly non-zero since the sphere is fluid, end u s is the
derivetive of the x~component of the velocity with respect to the normal
coordinate, y, and evaluated at the bubble surface.

The tengential velocity component can'bé“determined'by integrating
the continuity equation after making use of Equation (T) Thus it is
found thet

v = -g— [rluy + u's'- ¥/2)1. - (8)

"'l|l—‘

| '
In this formuletion, it is recognized that U, end U | are functions of
the position elong the bubble surface in the x-direction.
Upon use of Equetions (7) and (8) in the diffusion equation, we find

that the solute ges concentration must satisfy the relation:

' 2
! oC 139 2 oCc ., 9C
u u ——— — o ——
(B + 0 y) = -2 = [r(uy + u e Y /2)]'ay. _D.aya. (9)

Rather then proceeding with & general discussion of this equation, we now
consider two limiting cases; namely; the situation of & rigid,inferface with
us equal to zero, and secondly the case of-zerb tengentisl stress &t the
interface. The letter case certainly is relevant for gas bubdbles in a -
liquid such thet the liquid viscosity is.many‘fimes thet of the ges vis-

cosity. Thet the rigid interface situation is elso relevant constitutes

somewhet of & paradox, but it is known thet smell ges bubbles do beheve

to some extent &s rigid spheres.

 

 
 

Ft

Ny

"with- C, =1leatt =0, C,

13

Rigid Interface Cease.
The eppropriate modification of Equation (9) expressed. in non~

dimensionel variables ie:
! 2 2

 

 

aC _
Wyt 1a Mata¥Ni, 2 Th (10)
8 - ’
1l Y1 axl rl‘axl 2 ayl NPe- ayl2
where
t
' u
w o X _ Y o 8
xl -— rfi s Yl = rb u. Sl - _fi_ /r ?
- b b
- r_ o - C-~-C P 2.rb Ufi
= > = ’
1 rb 1l % - C Pe D

CO'= solute gas concentration in bulk liquid,
C*¥ = solute gas concentration in interface liquid.
If we now define new position varisbles end restrict our attention to

the bubble interface region, Equation (10) reduces to

ac 3201‘ |
n =32 ° | (11)
! ' ' 99
_ 1/2
where n = (rl u l) Yla
l
dé =_————-———r————— d xl.
N u :
Pe- sl . .

Equation (11) can be expressed g5 an ordinary differential equation in.

terms of e, similarity varidble,lj -n/(9¢)l/3 thus

*',dc o8 |
az”

 

p = 1@ p=0sett =
 

 

 

 

 

14

The integration of Equation (12) can be cerried out in e straightforward
way end then the result used to obtain the mass transfer rate expressed

in terms of the Sherwood number, a'rb-KL :
| - D P
P L

Ny, = - 0.6 N1/3 of(uSl 1)1/2 roax | O 13)

es reported by Baird end Hemilec,  end Lochiel end Calderbenk.’>

It should be noted that the result given by Equation (13) is general.
The specific value of the mass transfer number depends on thevnature of
the relative motion between the bubble and the surrounding liquid. Table I

gives results for u at very low and large Reynolds number flow regimes

sl
- and-the final expressions for the Sherwood number for these regimes,

based on the use of Equation (13).

Mobile Interface Case

At least for bubbles heving diemeters greater than e&.few millimeters,
the surfece condition is.more,reasonably expressed a5 being one of ~
negligible tangential stress and.having‘a non-zero tengential velocity; a
mobile interface. Thus for this situation the appropriate diffusion
equation, as obtained from Equetion (9), |

2
aC . 9 C
1 1 oC 2 1
u R .= [u r.y 1 =_—-—? (lll-)
s1 9x; r, sl 71 l] 5;;- Nog ayi

where Uy is the non-dimensional tangential velocity at the bubble inter-
face‘(qsl‘= :;EL—Q. Agein, when new position variebles are. used and ve
restrict  Ub/Tb. attention to the immediete,vicinity of the bubble inter-
face, Equetion (1k) is reduced to & simpler expression:

aC) 9°C;
38 902 ° - - ' : *(lS)
where c = usl ry yl;
2(usl rl)
¥, u, S
Pe “sl

 
_;

- TABLE I

ANALYTICAL RESULTS POR MASS TRANSFER RATES TO SINGLE GAS BUBBLES

»i ( &

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Flow Regime _Interface Condition Sherwood Number References
Case I: Rigid Inteffacg
Creeping Flow u.=0-> . 1/3
L sl o gy, = 0.99 N;. 1,13
_ ’ ' . =3
Moo < 7 u'gy =5 8in 6
i‘Lam:l'har.'Boum.laty Layer u, =0
Npe »> 1 ‘u'sl (6a sin 8)/$ Ng, = 0.84 N - Np, 13 H
' § = boundary layer thickness
Case II: ‘Mobile Interface
Creeping Flow u ., _8in 6 '
' ?l 2 Bg, = 0.65 Npe 1/2 1,13
HP\e <1l u sl =0 :
Potential Flow ‘-‘,1 =3 sin 0 ' 1/2
‘ v o
Npo > 17 v 0

 

 

 

 

 

 
 

16

Equation (15) has a similerity solution in terms of the variable L.j
E = 0/281/2 which satisfies the ordinary differentiel equation
dacl acy - 3
—5 t 2 dg = 0 o (16)
da E \ :
with.Cl_# lat E=0 and-Cl = 0 at £ = », Lochiel and'Calderbank13
give the solution for the concentration function as: ‘
_ c H
c, = P dE. ' (17)
- | o

The concentretion gradient at the bubfile interface cen be obtained from
Equation,(17)-and the average mess transfer rate to the bubble can be

evaluated. The result in terms of the Sherwood mass trensfer number ,

=:2rbKL/D.is:

T - qi/2 o "
2 2, e
NSh - S ‘g uSl .rl dxl NPe . - (18) -
o

Table I elso includes results from the literature which deal with
the mobile interface situetion. It is important to,note;that—thé mbbile
interface results show thet the mass transfer coefficient, expréSSed as
the non—dimensional Sherwood number- (KLdb/D)’ varies with the Peclet
number (dbU /D) raised to the one-half power. In the case of the rigid
interface. bubble the Sherwood number varies with the Peclet number raised
to the one-third power. The higher power. on the,Peclet‘number giyes rise
to significantly higher mess transfer coefficients for the xenon-135,
fuel salt.systgm if the mobile interface bubble case;ié applicabie, _

The anelyticel results given in,Table I egree in general with those
obtained by other investigators. In 1935 Higbie'

contribfition to the mess trensfer literature in his,analysié of;the rete

made an importent

of ges ebsorption from bubbles rising in liquids. The enelysis was, based
on & mobile interface model and the assumption‘that the liquid surround—

ing e bubble is continuously replenished with fresh liquid as ifi rises
throfigh & liquid pool. A golution of .the time dependeht difffision equeation

L;;

 

 

 
 

17
wes .obtained which can be expressed &s:
5 1/2
‘ o 2
! Nn =17z 5o | (19)

 

wvhere te is the exposure time of the bubble to a given liquid envelope.
Then on the assumption that the liquid exposed to the liquis is renewed .
each.time.thatwthe bubble moves through a héight:equgl to the bubble
diemeter, equation (19) is equivelent to:

a2

Nen (20)

Thus Higbie's'result is identical to the mobile-interface equétion of
.Boussinesq.3 '

Ruckénstein;é'has elso considered mass transfer between spherical
bubbles end liquids_by solving the mess convéction equations for various
hydrodynamic situatiqns.,-In essence his development follows that pre-
sented here and the results for the extreme cases of the rigid interface
end the mobile interface agree rather well with the equations given in
Teble I. In particular Ruckenstein found

1/3

= l.Qh Npe ' ~» rigid interface, Np <1, (21)

Noy Re

and

l/?, mobile interface, N, < 1. (22)

"N, = 1.10 N Re

‘Sh - Pe
The constent in'EQnationi(22) for the mobile—interfaée bubble at low
»Reynolds numbers differs significantly frqm the corresponding equation of .
Lochiel and Calderbank.13

2s2"Egperimental'Data7on,Mass.Transfer\Coefficiénts;tc‘Single;Bubbles
Rather comprehensive surveys of the experimental dsta on mess trans—

fer coefficients for gas bubbles have been reported -in’ the litere-

tup h 5 13,1k

date from these reférenCQS‘indicate thaet gas bubbles of diemeter less than

2 millimeters behave &s rigid interface particles, and that gas bubbles

of diemeter greater than 2 to 3 millimeters seem to behave as mobile-

No attempt will ‘be made to give detailed results, however,
 

18 . | :

interface perticles, es shown by their fluid drag and mess transfer | kbj
characteristics. o .

- Scott and Haydule carried out pipeline contactor experiments with
verious ‘liquids using carbon dioxide end helium as solute gases. The
experimental variebles covered in the mass trensfer tests were:

Liquid superficial velocity - ~~ 0.5 to 3.6 ft/sec

Liquid phase diffusivity @ 0.1h x 10-5 to 4.8 x 10-5 cm2/sec
Gas-liquid interfacial tension 23.4 to 73.5 dynes/cm

Liquid viscosity - ‘" 0.6 to 26.5 centipoise

Tube diemeter .23 to 2.50 cm

An empirical correlation equation which described their results is:
0.0068 ¥, ¢o.7hh oo.sli'no.088D0.390'
= 4+ _
e = — - 1.88. #15%, . (23)

 

 

- mase transfer coefficient (ft/sec) £t bubble surface | |
' -t~ -contactor colume - A

t{f

<
I

‘liquid velocity in pipeline contactor, ft/sec.

liquid surface tension, dynes/cn,

liquid viscosity, centipoise,
liquid phese diffusivity, em2/sec x 107,

pipe diemeter, cm,

I

e o O r QqQ
"

volume fraction of gas bubbles in contector.

Use of the MSER heat exchanger flow dets and physical properties
of the MSER fuel selt in Equation (23) gives = 2(7 hr=1, If one
assumes & bubble surface area of 3000 £t2 (0.02 in diemeter bubbles) dis-
persed over the 83 £t3 of fuel. gystem, this result is equivalent to 8 mess
transfer coefficient of 7.7 ft/hr.

| Lamont'and Scott12 also reported experimental studies on the pipeline
contacting of .carbon dioxide bubbles end weter under cocurrent flow con-

ditions. . Experimental variables covered in the mess transfer tests were:

Liquid Reynolds numbers L 1800 - 22 hOO |
Bubble diemeter | _ , ,‘0.227f.0.55lcm
Tube diemeter - - .0.793 cm,

C
9 . M

 

 
 

 

19
An empiricel correlation equation which fits their data is:
K, = 0.030 80:"7 (228%), , (24)

where
KL = mass transfer coefficient (em/min),

NRe 1iquid phase Reynolds number, dVp/u

If one assumes & reesonable non-dimensional form consistent with
Equetion (2k4) and mekes use of the physicel properties of the carbon
dioxide-weter system, the reported correletion equation mey more properly

be written es:

d
—-K" = 1.02 Np: 49 N2, (25)
c-
vhere _
TN, = Sclrmidt number , (u/p4D)
a |
—5—-— Pipeline Sherwood number.

It is then found thet for the MSER fuel salt Equation (25) gives &

mess transfer coefficient Ei 6.1 ft/hr.
Various authors 9 20 have cited the influence of surfactants, which

sccumulate in the ges bubble interfece, on the motion of ges bubbles.
In perticuler, it is found that such interface contamination brings about .
"solidificetion" or "rigidity" of the gas-liquid interface. Under the con-
ditions of & rigid interfece due to presence of surfactants in the inter-
face bubbles, follow the welleknown"Stqkes dreg reletion

at low Reynolds numbers, vhile under conditions of & .clean interface the

bubbles show & drag behavior represented by

16
‘D LNRe

et low Reynolds numbers.
 

 

20
As pointed out earlier in this paper the "solidificetion" of the

gas bubble interface would bring about a reduction in the rate of mass.
transfer to & ges bubble interface.- Griffith 19 hes shown specific ev1—
dence of this- effect in citing the results on the reduction in solution_
rates of oxygen bubbles as surface active matter is adsorbed at the bubble -
interface. . |

5iHaberman\and,Morton?; elso. found that surface contamination of gas
bubbles can influence the motion of gas bubbles &t larger Reynolds numbers,
-i,e.,NRefif'lOO to 500. Their observed.increase in gas bubble drag
coefficient under conditions of interfece "solidification,” considering
the theoretical mass transfer results presented previously, suggests that
low mess transfer retes to bubble interfaces should prevail under these
conditions. | |

4

2.3 Mess Transfer Coefficients for Bubbles Carried Along by Turbulent quuid

The previous discussion of the mess transfer theory for ges bubbles
moving in a stationary liquid dealt with steady flows, and the results aere.
most epproprietely applied to the. cases of freely rising bubbles or uniform.
flow;of-liquid-past‘a bubble. In the MSBR injected helium bubbles would be
cerried along by fuel salt flowing. in e state ‘of turbulent motion. - The
Reynolds number besed on the heat exchanger tube -diameter end bulk velocity
is expected to be about-BOOO;.'The'following*discussion‘of the mess trans-
fer for bubbles carried elong by & turbulent 1iquid indicetes the. approxl-
mate magnitudes of mess trensfer coefficients for this situation.

Hinze8 hes ‘treated the case of relative motion between & small ges -
bubble and a turbulent liquid, and for the limiting case of large inertis
forces in comparison to viscous . forces he found that the bubble velocity

fluctuateS-with & lerger amplitude than the surrounding turbulent liquid;

nemely
NE - W (26)

"2’ T : : '
where Vb - an g ere r.m.s. values of the instanteneous bubble and

liquid velocities, respectively, for the turbulent motion. Equation (26)
in essence results from integration of the equation for the fluctuating
motion of the geas. bubble |

 

 
 

21

! '

dv dvz
(pb + k pg) dt TT Py (l + k) T (27)
vhere V; = bubble volume
Pps Py = bubble density, liquid density
k = added mess coefficient for accelerating spherical
bubble
t = time.

15 the bubble accelera-

Thus, it is noted that since p << Py end k is 1/2,
tion is about three times the liquid ecceleration. Upon use of Equation (26),
it is found that the velocity of the gas bubble relative to the turbulent
liquid motion on the average is:
V. =2 /%
relative 2 (28)
For pipe flows_f%??’varies across the radius and en approximate value

repregsentive of the pi%e cross section is:

o~
) 'vfz v, /2 , (29)
where Vk = average liquid velocity,
f = pipe flow friction factor.

Thus combination of Equations (28) and (29) indicates that an estimate of
the time average velocity of gas bubbles relative to liquid moving under
turbulent conditions is

v m2 ¥, VIT2 . o 30)

‘?brelative AR

Since £ = 0,046 N '";/5, as obtained from experimental measurements a

| mpre useful form. of the result is:

__ 'ir' e 008 N_1/10 (31)

brel_e.tiv'e - 2 “Re

where N = dvg/v, pipe Reynolds number.
 

22

It seems reasoneble to use the result given by Equation (31) in the
mess trensfer equations for sphericel particles to obtain the desired
relation for the mass transfer coefficient. The results obtained are given
for the two cases: (&) mobile gas-liquid interfece =nd (b) rigid gas-
liquid interface.

Mobile Interfeace:

The mobile-interface ‘theory for mess transfer to & single bubble
yields an explicit formula for the mass transfer coefflcient eppliceble
to turbulent conditions; namely -

=13 0%, el . G
relative
where KL“é liquid phaSé-msss transfer coeffiqiefit,
D = liquid phase.diffusivity,

bubble diemeter.

%

- Use of Equetion (31) in Equation (32) fives the result:

DV 172

g, =062 () Ry

-1/20

d g V2 |
K 0.5 0.5

-5 = 0.62 Noo Nsc (db) (33)
The parameter (KLd.b/D) is the Sherwood number and NS = v/D is the ratio

of the liquid kinemeatic viscosity to the 1iquid phese diffuslvlty, or
gchmidt number. o -
- Rigid Interfeace: _
The equetion of Griffith
eguatiops}for rigid, sphe:ical particles;

5

isvfeprsSentative of the mass trensfer

K"db =2+ 0.57 (4.7, )° 2 gc35. C(3h)
relative;

 

 

 

 
 

 

 

23

Combinetion of Equetions (31) and (3k4) yields:

1/2
4y v 03w 0P, 03 (& (35)
q, o g,
_Figure 5 shows a plot of values of KL predicted by Equations (33)
end (35), elong with other values from the literature, for the MSBR heat
exchanger.flow conditions. Shown elso are calCulations by Kedlll based

&d(

on the mobile interface equations for "free-rise" velocity conditions.

The enelysis presented-must be regerded as an approximation. Random
migration of bubbles in.a turbulent liquid is certainly affected by viscous.
drag. This effect was not considered. Other important'assumptions implicit
in the analysisrare'that‘the bubble is small compered to the scale of
turbulent motion and that the bubble moves in the same liquid envelope
during the course of each turbulent "event." These effects which cause
departure of the actual turbulent bubble motion from the assumed model
probably- give rise to some attenuation of the bubble’s fluctuation-
velocity emplitude, and, hence, the results given by Equetions. (33) end
(35) are likely optimistic. That is, the bubble's turbulent fluctuation
velocity may'be'less than three times that of the liquid's fluctuation
velocity; In spite of the speculative nature of the assumptions made in
the analysis, the final equations give results which egree reasonably
well with the aveileble experimental data.

A rather'importent point Of'the preceding analysislis that the rela-
tive motion between bubbles and turbulent liquid gives rise to mass trans-

fer coefficients which are . appreciably greater than the mass . trensfer

'coefficients for "free rise" (or "free fall") flow conditions., This indi-

cation is supported by the experimental results of Harriott6 for mass .

transfer coefficients between small rigid particles carried elong by tur-
bulent liquid in & pipe. The experimental ness transfer results, ex-
pressed as the- pipeline Sherwood number (KLd/D), were correlated with

‘Reynolds number and Schmidt number by the equation g

0 913 0.346

SB( pipe)
 

24

' ORNL-Dwg 68-6784 O/
30

20

10

5.0

K;, Liquid Phase Mass Transfer Coefficient, (ft/hr)

- 2.0

 

1.0 1L
0.01 0.02 0.05 0.10

. Bubble Diameter

Fig. 5. Liquid Phase Mass Transfer Coefficient Versus Bubble Diame- (;;
ter Liquid: MSBR Fuel Salt, NRe'= 7200, NSc = 2880, 4 = 0.305 in. )

 

 
 

25

4 2

If one uses appropriate MSBR dats (NRe = 10", No = 2880, D = 5 x 10
ftzlhr, d = 0,305 in.), Equetion (36) gives K =1.3 ft/hr. Now if one

uses the rigid-interface mass transfer relation for a bubble with diameter
equal to 0,02 in. end rising in MSBR fuel salt, it is found that the mass
transfer coefficiént for these conditions is 0.38 ft/hr.- Thus, the pipeline
mass transfer coefficient may be 3 to 4 times the value predicted for the
"free-rise" condition. Further, if an 0.02 in. diemeter bubble behaves

es & mobile~interface particle; it is noted that the pipeline mass trans-
fer coefficient as predicted by Equation (33) is again about 3.6 times the

"free-rige" bubble mass transfer coefficient.

3.0  Proposed Mess Transfer Experiment to Simulste MSBR Contact Conditions
The literature informetion on mass trensfer to gas bubbles discussed
in the previous section does not yield e firm estimate of the liquid phase
mass transfer coefficient expected for the MSBR flow conditions, Two
points need:further clerificetion; namely identification of the precise
criteria for rigid-interface and mobile-interface bubble behavior, and
determinetion of the mess transfer coefficients for bubbles carried by
turbulent liquid at the hydrodynamic conditions expected to prevail in the
MSBR. It seems that this information should be obtained by experimental
megsurements, in contrast to depending on further analytical investigation.
An experimental study of mass transfer rates in the detail to furnish
values of the liquid phase mass transfer coefficients carried out using
MSBR fuel salt would be & formideble end expensive underteking. In con-.
sidering these factors a more attractive alternative:is to attempt
determinetion of -the needed data using e suiteble fluid which simulates
the MSER situation and,fihich would'nct require tests et eleveted tempera-
tures. Fo;iowing is & brief aescfiption of\a.prOPOSed experiment involving
the use of 46% gljcerol, oxygen &s the solute gas, and helium as the
strippingAmEdium in!oraer to éimnlaté'the'MSBR_hydrodynamic conditions,
‘The choice of the glycerol solution fétommendgd for the mass trens-
fer tests is bfised on the requiremehts for:dynmmic similitude in the test
end MSBR situstions. TableIIigives_the importgnt'factors that should be
maintained’dyfiamifially-similar in-thé_mpdél and profbtype systems. Con-
sideration of these factors leads.to'the conclusion that the model experi-

ment should be carried out et the same Reynolds number (dV&/v), bubble
TABLE II

' IMPORTANT VARIABLES FOR DYNAMIC SIMILITUDE

 

PHENOMENON

IMPORTANT VARTABLES

NON-DIMENSIONAL PARAMETERS

 

Cchvective diffusion

© Bulk stream turbulence

 Bubble migration relative
"~ to turbulent liquid

d'b, p’ fib

d, st H

’ pL, €, L:

Eb’ N’ pL’ _d-b:' d, ’V §
) L

nRe’ NSc (°r‘NPe)
Np.» €/d, L/d

_NRe’ Npps dblé

e BRe’ db/d

 

 

Bubble stab*lity (coalescence or. V., p-, db g, d -
£ "L

rupture) , ° A ,

. . o _ o , ' 0 2
Bubble interface mobility Ub’ Prs T U db’ d o : -Ldb €

| S : | o= g g
‘scuUb e

N =‘d? /v (oz; U./v), N, = v/D N U./D, N, = / N ?'-.\_1-2 p /g o

Re 2" v'db-b * "Se db Fr 2_gdb, He j Eéb'L e

 

92

 
 

27

ratio (db/d) Froude number (V /dbg) Schmidt number (v/D), Weber Number
(Véfibp/g o), plpe roughness ratio (e/d), and pipe length-to-diameter ratio
(L/d) as those.values for the MSBR. It one decides to use the same bubble
diemeter in'the model and prototype situations, the similtude reguirements
ere satisfied if the model experiment has the same pipe roughness, pipe
length, pipe diameter,‘kinemetic viscosity, Schmidt number, and kinematic
surfaece tension asrthe MSBR. The physicel'prOPerty reqnirements,of equal
kinemetic viscosity and Schmidt number cen be met approximately by using
L6% by_weight_glycerol. Figure 6 shows & plot’ofrthese physical properties
es & function of glycerolconcentration. It should be noted that this test
1iquid will not meet thewkinemetic surface tensionsrequirement. In fact the.
MSBR Weber number will be about 1.8 times thet for the 46% glycerol.

Oxygen seems to be an appropriate solute-gas to be used in the pro-
posed mass trensfer tests. The concentration of oxygen in glycerol can be
determined using the Winkler18 method and assay accnracies_of +]1 per cent
are'expected,'based on the research of JOrdeng et al.

Other physicel pr0perties needed in the evaluation of mess transfer
coefficients from the experimental data are aveilable.9 These include
the solubillty deta, oxygen diffu51v1ty in glycerol solutlons, glycerol
viscosity end density data.

Helium is recommended es & satisfactory stripping medium because of
its low solubillty in glycerol and chemical 1nertness.

The mess transfer experiment proposed 1nvolves setting up the experi-
mental system diagrammed in Figure T. Tests would be carrled out by
establishing the MSBR liquid flow rate in the test section. Helium bubbles
- would be inJected at a flow rete corresponding to that of the MSBR. Oxy-
gen concentrations in the inlet and effluent liqnids would be determined
by chemical enalysis of liquid samples.

In order to evaluate the mass transfer coefficients, it would be
necessary tondetermine the bubble diameters produced in the experimental
bubble generetor. This probably can be done by photographlc methods

The experlmental dete on liquid oxygen concentretions at the inlet
and outlet points, gas and liquid flow rates, bubble diameter, test
section length, test temperature, and Henry's lew coefficient would be

used with Equation (3) to determine the liquid phase mass transfer
‘Schmidt Number (v/D x 10-3)

 

ORNL-Dwg 68-6785
' ' ). 20

.15

Kinematic Viscosity (f£t2/hr)

0.05

10 20 30 40 50 60
| Wt % Glycerol S -

Fig. 6. Schmidt Number and Kinematic Viscosity of Glycerol Solutions.

 

8¢

 
 

| ‘,p—-Oxygenated Glycerol Supply Tank,
Gravity Feed, Constant Head

 

 

Liquid Flow

Rate, QL

Helium

 

1

 

|

Ly

C

(Measured 02 Concentration)

 

_",—-Pipeline Contactor, L = 100 ft, 4 = 0 305 in.

 

 

 

 

 

it ( ?

ORNL-Dwg 68-6786

 

 

 

 

3

[y L

 

fij‘l~; \\s
y _ Helium Introduced Through Bubble N Window for

Generator (Capable of Producing , Bubble

Uniform Bubbles &, = 0.0l to 0.25 in. ) Photography

 

Helium Flow Rate, Q;

Fig. 7. Flow Diagram for Mass Transfer Test System.

—

: \
C, (Measured 0,

L,

Concentration)

To Glycerol
Receiver

62

 
 

30

coefficient. Figure 8 shows celculeted date on the oxygen concentration
rgtio as & function of the mess transfer coefficient for L = 100 ft,
db = 0.02 in. end 0.10 in.

4.0 Conclusions.

The study of existihg litérature on mess transfer between bubbles
and'liQuids and - the analysis presented in the previous sections permits the
following conclusions:

1. The effectiveness for Xenon-135 removal from the circulating
fuel salt in the MSER may rafige from about 3 to 33 per cent depending on.
the velue of liquid phase mass trensfer coefficient. The estimated
Xenon-135 removal éffectiveness;is based on the range of mass transfer
coefficients, 1 to 13.5”ft/hr;, dbtained from eveilable literature informa-
tion. - -

2. Availeble litersture ihformation provides & good basis for
estimeting mass transfer coefficients for bubbles moving at & steady.

‘velocity relative to liquid under conditions of a rigid interface and

& completely mobile interface. ‘

3. There does not exist a relisble criterion for spedifying the
type of bubble interface condition expected for a given condition.

4. The available 1iter§ture does not provide & good basis of
estimating the mass transfer coefficient for bubbles carried along by
turbulent liquid. Anelysis of this situation in approximate terms pro-
vided new reiationships-which are.in epproximate agreementVWith the date
that are available.

2. New mass transfer meesurements are proposed to_prdvidé additional
date needed in overcoming thé 11mi£ati°ns for mass transfer predictions
cited in Conclusions 3 end 4. Glycerol (L46% by weight) is recommended as
the test fluid in order to_simuiate.the MSER hydrodynemic conditions and .

 meet most of the requirements for dynemic similitude in the model end -

prototype situetions.

 
 

31

ORNL-Dwg 68-6787

1.0

0.9

~
o U,
5 0.8
O
S~
N
=
(&)
L e
o
5
a
S 0.7
o
O
o
2
«
3N
+
8
Q
& 0.6
O
O

0.5

 

0 _ T | I
K, Liquid Phase Mass Transfer Coefficient (ft/br).

Fig. 8. Oxygen Concentration Ratio as a Function of the Mass Trans-
fer Coefficient. e
 

References Cited

1.

2.

L~ W

O & =1 O W

10.

11.

12.

13.
L.

15.

16.

17.
18.

19..

20.

2l.

?aigd) M.H.I. end A. E. Hamilec, Canaed. Journ. Chem. Engr., 40, 119
1962 ' '

Bird, ‘R. B., W. E. Steward and E. N. Lightfoot "Transport Phenomena,

P. 522 John Wiley, New York 1960._

Boussinesq, J., Journ. Math., 6 285 (1905)

:Calderbank P, H.,_Trans._Inst Chem. Engr., 31, 173 (1959)
. zGriffith R. M., Chem. Engr. Science, 12, 198 (1960)
Harriott P. and R. M. Hamilton Chem. Engr. Science, 20 1073-(1965) .

iHigbie, R., Trens. Am. Inst. Chem. Engrs , 31, 365 (1935)

Hinze J. 0., "Turbulence, p.‘360 McGraweHill New York 1960. e

. 'Jordan J., E. Ackermen and R. L. Berger Journ Am. Chen. Soc., TB
2979 (1956) | o

iKasten P. R., et al., "Design Studies of 1000 MWe Molten Salt Breeder

Reactors," ORNL-3996, August 1966

-Kedl, R. J.,. “Xenon-135 Poisoning in the MSBR," MSR-ST-hS, Oak Ridge

National Laboratory (internal distribution only), June 28 1967

.Iemont J. C. and D. S Scott, Canad Journ. Chem Engr s hh 201 (1966)

Lochiel, A. C. end P H. Calderbank Chem Engr. Science 19, 411 (1964).
Redfield, J. A. and G. Houghton, Chem Engr. Science, 20 131 (1965).

Roberteon, J. M., "Hydrodynamics in Theory end Application, p. 20k,
Prentice~Hall, 1965

Ruckenstein, E., Chem Engr. Science, _2, 131 (196h)

' Beott, D. s. end W. Hayduk Cenad. Journ Them Engr. . hh 130 (1966).

Americen Public Heaith Asgocietion, et al., "StandarduMethods for the
Exeminetion of‘Water—and-Sewerage,"-9th Ed., p. 135, New York, 194T.

Griffith, R, M Chem. Engr. Science, 17, 1057 (1962)
Davis, R. E. and A. Acivos, Chem. Engr. Science, 21, 681 (1966)

Hebermsn, W. L. and Morton, R. K., David Teylor, Model Basin Report

No. 802, NS T15-102 (1953).
 

12.
13.
14.
15.
16.
17.
18,
19.
20.
21.
.22,
23.
24-31.
32,
33.
34,
35.
36.
37.

- 78,
79.
80.

81-82.
83.
84.
85.

86-100.

z:g:&i?*£:¢4?=t1;:yxmiElt:nflc:c:pab;
g

t

G. Alexander
. E., Beall
Bender
. S. Bettis
. G. Bohlmann
J. Borkowski
. E. Boyd
Briggs
. F. Cope, AEC
. B. Cottrell
. Culler
J. Ditto
Eatherly
Ferguson
P. Freaas
H. PFrye
R. Grimes
G. Grindell
. N. Haubenreich
W
H
R

o

=

=

£

=

. Hoffman

. Jordan

. Kasten

R. J. Kedl

M. T. Kelley

J. J. Keyes

T. S. Kress

M. I. Lundin

R. N. Lyon

H. G. MacPherson

33

ORNL-TM-2245

Internal Distribution

.38,
-39,
40.
41.
42.
43.
44,
45,
46-48,
49.
50-51.
52.
53-57.

58..

59.
60.
6l.
62.
63.
64 .
65.
66.
67.
68.
69.
70-71.
72-73.
74-76.
77.

Bz C e E e

MacPherson
McDuffie

McCoy

McCurdy

Miller

Moore

Nicholson

Oakes

Peebles

Perry

Rosenthal
Savolainen

unlap Scott

J. Skinner

N. Smith

Spiewak

A, Sundberg

E. Thoms

B. Trauger

M. Weinberg

R. Weir

E. Whatley

C. White

. D. Whitman

G. Young

Central Research Library
Document Reference Section
Laboratory Records Department

EEEEorruoEEnE

- o

QHEUPORTHE R

Laboratory Records, RC

‘External Distribution

 

C. B. Deering, AEC, ORO |
‘A, Giambusso, AEC, Washington, D.C.
W. J. Larkin, AEC, ORO
T. W. McIntosh, AEC Washlngton, D.C.
H. M. Roth, AEC, ORO

M. Shaw, AEC, Washington, D.C.
. W. L. Sma,lley, AEC, ORO

Divigion of Technical Informatlon Exten31on