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US. ATOMIC ENERGY COMMISSION ORNL - TM- 2245 COPY NO. DATE

-

85

July 23, 1968

REMOVAL 0~ EON-135 FROMCIRCULATING FUELSALT BY MASSTRANSFER TO HELIUMBUBBLES F. N. Peebles

-., q$‘.fb& f

ABSTRACT Removal of dissolved Xenon-135 by mass transfer to helium bubbles offers an attractive means of controlling the Xenon-135 poison level in molten salt breeder reactors (MSBR'S). In order to provide necessary engineering information for evaluation of the proposed method, th,e, I existing data on rates of mass transfer to gas bubbles have been%. reviewed. Rather extensive literature for prediction of mass transfer stationary

liqui$s

under

the

two

references.point to reliable equations rates to single bubbles/lCrjsing in extreme

cases

of

a rigid'bubble

inter-.

face and of a perfectly mobile bubble interface. In general, experiNo reliable mental data are available which support these predictions. criterion for predicting the transition from one,type behavior to '. : another is available. An elementary analysis of the rates of mass transfer to bubbles carried along by turbulent liquid,in a pipe is presented. The results indicate that the bubble mass transfer coefficient for 0.02 in. diameter bubbles will be approximately 13 ft/hr for mobile-interface bubbles, and approximately 2 f%/hr for rigid-interface bubb1e.s.' An experiment is suggested to provide specific data on the mass transfer rates to bubbles carried,along by turbulent liquid ina pipe for hydrodynamic conditions which simulate.the MSBR,

NOTICElhis document contains information of o preliminary nature and was prepared primarily for internal use at thd Oak Ridge Notional Laboratory.It is subject to revision or correction and therefore does not represent a final report.


7

LEGAL

This

report

was prepared

OS an account

of Government

nor the Commission, nor any person acting A. Makes any warranty or representation, completeness, or usefulness any information, apparatus, 6.

privately Aswmes

owned rights; any liabilities

any information,

of the method,

NOTICE

-,

sponsored

work.

on behalf of the Commission: expressed or implied, with information or process

Neither

the

respect

United

to the

States,

accuracy,

contained disclosed

in this report, or that the use of in this report may not infringe

of,

d&ages

or

apparatus,

with

respect

method,

to the use or process

disclosed

or for

in this

resulting

from the use of

report.

As used in the above, “person acting on behalf of the Commission� includes mny employee ,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, 01 provides access to, any information pursuant to his employment or contract with the Commission, M his employment

with

such contractor.


CONTENTS Page 1

Abstract 1.0

Introduction

5

2.0

Mass Transfer Theory

5

2.1

.t

Mass Transfer Coefficients f o r Spherical Bubbles

9

Rigid I n t e r f a c e Case

13

Mobile I n t e r f a c e Case

i4

2.2

Experimental Data on Mass Transfer Coefficients t o Single Bubbles

17

2.3

Mass Transfer Coefficients f o r Bubbles Carried Along by Turbulent Liquid

20

3.0

Proposed Mass Transfer Experiment t o Simulate MSBR Contact Conditions

25

4.0

Conclusions

30-

References Cited

32

~

~

LEGAL N O T I C E

~

This report was prepared an m account of QoverIIIqent sponmred work. Neither the United states,. nor the Commission. nor m y wrmn acting on hehalf of the Commission: A. Makes m y w u r n t y or repreezelltaUon. expressed or Implled, wlth rsmpect to the ICCUrscy. completeness, or unehrlnesa of the informstion contained in thls report. or that the we of m y information. apparatus, method. or proceoo dinclooed in thln report may not iniringe privately owned rights; or B. Assumes MYUabillties wtth respect to the w of. or for damages nsulW from the use of any information, apparatus, method, or process disclosed Iri thls report. As used in the h v e . "person acting on hehalf of the Commiesion" includes m y employee or contractor of the Commlosion. or employee of such contractor. to the eMnt that such employee or contractor of the Commission, or employes of much contractor prepares. disseminates, or provides access to, MY Lnformatlw pursuant to hi8 employment or contract with the Commission, or h l w employment n t hsuch epntractor.


c

d


5

’b’

REMOVAL OF XENON-135 FROM CIRCULATING FUEL SALT OF THE MSBR BY MASS TRANSFER TO HELIUM BUBBLES 1.0

Introduction A proposed method”

of removing Xenon-135 from t h e fuel s a l t i n t h e

Molten S a l t Breeder Reactor (MSBR) involves circulation of helium bubbles with t h e l i q u i d fuel.

Bubbles a r e t o be injected i n t o t h e flowing stream

near t h e pump, and then dissolved Xenon-135 i s removed from t h e l i q u i d .

by mass t r a n s f e r (combined diffusion and convection) i n t o t h e bubbles. The circulating bubbles a r e then t o be removed f r o m t h e l i q u i d a t t h e o u t l e t of t h e heat exchanger by a centrifugal separator. Although t h e p o t e n t i a l f o r Xenon435 removal by mass t r a n s f e r t o helium bubbles i s high, t h e actual effectiveness of removal i s controlled by t h e surface area of t h e bubbles exposed t o t h e l i q u i d and t h e mass

c

t r a n s f e r coefficient between bubbles and l i q u i d flowing cocurrently i n a pipe. This report deals with t h e bubble mass t r a n s f e r r a t e expected under t h e MSBR operating conditions, based on t h e information available i n t h e l i t e r a t u r e , and a proposed experiment t o provide additional data. The experiment involves simulation of t h e reactor flow and mass t r a n s f e r conditions through use of a glycerine solution as t h e l i q u i d , oxygen as t h e solute gas, and helium as t h e stripping medium. 2.0

Mass Transfer T h e o q

The e s s e n t i a l features of t h e mass t r a n s f e r s i t u a t i o n of i n t e r e s t i s shown in Figure 1. Liquid flowing along a pipe at t h e r a t e &L enters t h e system with dissolved concentratim, CL1,

and t h e i n l e t stripping gas at a flow rate, QG, i s injected i n t o t h e l i q u i d . As t h e l i q u i d and gas streams move cocurrently along t h e pipe t h e dissolved gas content of t h e

l i q u i d i s reduced t o t h e e x i t con For a steady s t a t e system, conservation of t h e dissolved gas requires t h a t t h e concentration change i n accord with

&r,

(CL1

- CL)

(1)


ORNLDwg 68-6780 /

Pipeline

Contactor,

Length = L, Cross Section = Ac

Liquid Flow I II

A Gas Flow Rate

Fig.

1.

Flow Diagram for Pipeline

Contactor.

. ’

* c-._ J

0

‘I


7

r'

where CG represents t h e l o c a l concentration of t h e solute gas i n t h e 8

bulk bubble stream.

Equation (1) i s based on t h e case of negligible

solute gas i n t h e inlet stripping gas. A t any location along the contactor, t h e concentration of dissolved gas i n t h e v i c i n i t y of t h e liquid-gas interface of a t y p i c a l bubble i s

depicted i n Figure 2.

The solute gas concentration difference between

t h a t of t h e bulk l i q u i d and t h e l i q u i d at t h e interface provides t h e driving force f o r mass t r a n s f e r a t t h e r a t e ,

where

5 = l i q u i d phase mass t r a n s f e r

coefficient,

a = gas-liquid i n t e r f a c i a l area per u n i t volumn of contactor,

AC = contactor cross-section, c

dL = d i f f e r e n t i a l length of contactor, T = absolute temperature, R = universal gas constant,

H = Henry's l a w constant f o r solute gas. Equation (2) results from t h e c l a s s i c assumption of negligible i n t e r f a c i a l resistance ,2 and t h e assumption of small gas-phase resistance t o mass transfer.

The l a t t e r assumption is an approximation which i s appropriate

f o r t h e case of a gas having a low s o l u b i l i t y i n t h e l i q u i d of i n t e r e s t . When Equation (2) i s integrated t o give t h e change i n solute gas concent r a t i o n over t h e t o t a l length of t h e liquid-gas contactor, it i s found that

-' =~ 2

+ e-* l + u

u

(3)

5 a AcL (1 + RTQL and B = . QL a)

where u =

"QG

If t h e effectiveness f o r solute gas removal i s expressed as E =

c,.L L

- c,,

LZ Y

cL1

then f o r a given mass t r a n s f e r system t h e effectiveness f o r solute removal is given by

1 - e -%

LJ r

8

E = l + u

(4)


8

*

ORNL-DWg 68-6781

LI c

Bulk Liquid

cLd Y

‘Gi

For Negligible Gas Phase Resistance, ‘Gi3

Fig, 2.

‘0

Concentration Profiles Near Interface.

.. t


9

r

u c

The meximum,value of E i s f o r a liquid-gas contactor of i n f i n i t e volume, 1

o r i n f i p i t e mass t r a n s f e r coefficient, and i s

EMax

=

l + u '

Figure 3 shows a p l o t of t h e Xenon-135 removal effectiveness as a function of l i q u i d phase mass t r a n s f e r coefficiept f o r t h e MSBR operating conditions and helium bubbles 0.02 i n , diameter.

The plot i l l u s t r a t e s

t h a t t h e effectiveness f o r Xenon-135 removal is sharply r e l a t e d t o t h e

l i q u i d phase mass t r a n s f e r coefficient i n the range of 1 <

5 < 100 f%/hr.

has shown that t h e Xenon-135 poison f r a c t i o n i n t h e MSBR i s

Kedl"

influenced i n an important way by t h e bubble stripping effectiveness, and hence successful reactor analysis and design f o r t h e MSBR depends on r a t h e r accurate knowledge of the bubble mass t r a n s f e r coefficient. 2.1

Mass Transfer Coefficients f o r Spherical Bubbles

Previous studies on mass t r a n s f e r t o and from spherical gas bubbles have been extensive, including; analytical and experimental investigations.

A brief summary of t h e important results i s given i n t h i s section.

First,

a description of the pertinent a n a l f i i c a l model i s presented and then a

summary o f - t h e most recent experimental findings i s given. Figure 4 shows t h e model s i t u a t i o n of a spherical bubble of radius, rb, imbedded i n a stationary liquid. The bubble moves with a velocity Ub relative t o t h e liquid. For t h e case of an i n e r t gas bubble removing a solute gas-from a l i q u i d , the appropriate diffusion equation is:

-

= velocity components i n t h e x and y directions. C = l o c a l concentration of solute gas i n the l i q u i d , D = mass d i f f u s i v i t y f o r the solute gas i n t h e liquid. The velocity components u and v are generally available from a solution of t h e momentum equations, and would s a t i s f y t h e bulk l i q u i d continuity r e l a t i o n f o r points i n t h e immediate v i c i n i t y of the bubble surface where

U, V

where r is t h e radial distance from a point on t h e bubble surface t o t h e

W

axis of symmetry,

Emphasis is placed on t h e immediate v i c i n i t y of t h e


10

J

ORNL-Dwg 68-6782

I

s

u

Y

I(

.

W

a a

u .

i

1

2

5 10 Mass Transfer Coefficient,

20

%

50

(ft/hr)

Fig. 3. Xenon-135 Removal Effectiveness â&#x20AC;&#x2DC;as a Function of Liquid Phase Mass Transfer Coefficient.

100


11

ORNL-Dwg 68-6783

-%,

Bubble Velocity

Concentration

-Axis

Bulk Liquid Concentration,

of m e t r y

I

Fig. 4 .

Coordinates f o r Thin Region Near Spherical Bubble Surface.


12 bubble surface because the region of important concentration variation i s expected t o be t h i n , and even thinner than t h e region of significant veloc i t y variations.

Thus f o r such a s i t u a t i o n it is reasonable t o represent t h e

velocity i n t h e immediate.vicinity o f . t h e bubble surface as u = u

I

S

+ u S. y ,

The term us is t h e velocity component i n t h e x-direction at the surface I is the of t h e sphere, possibly non-zero since the sphere i s f l u i d , and U derivative of t h e x-component of t h e velocity w i t h respect t o t h e normal coordinate, y, and evaluated at the bubble surface, The tangential velocity component can be determined by integrating the continuity equation afier making use of Gguation (7). Thus it i s found t h a t v =

--r aax

I

EdUSY

+u

8

y2/2)].

I n t h i s formulation, it is recognized that Us and U ' s we functions of t h e position along t h e bubble surface i n t h e x-direction. Upon use of Equations (7) and (8) i n t h e diffusion equation, we f i n d t h a t t h e solute gas concentration must satisfy t h e r e l a t i o n : (us + u

1

SY

)

- -ax r ax

A

'

2

(9)

Rather than proceeding with a general discussion of t h i s equation, we now consider two limiting cases; namely, the s i t u a t i o n of a r i g i d interface w i t h u

S

equal t o zero, and secondly t h e case of zero tangential stress at t h e

interface.

The l a t t e r case c e r t a i n l y i s relevant f o r gas bubbles i n a

l i q u i d such that t h e l i q u i d viscosity i s many times t h a t of t h e gas viscosity.

That t h e r i g i d interface s i t u a t i o n i s a l s o relevant constitutes

somewhat of a paradox, but it i s known t h a t s m a l l gas bubbles do behave t o some extent as r i g i d spheres.


13 Rigid Interface Case

The appropriate modification of Equation (9) expressed i n nondimensional variables is:

where 1

Co = solute gas concentration i n bulk l i q u i d , C* = solute gas concentration i n interface l i q u i d .

If we now define new position variables and r e s t r i c t our attention t o the bubble interface region, Equation (10) reduces t o

NPe

sl

Equation (11) can be expressed as an ordinary d i f f e r e n t i a l equection i n

terms of a , s i m i l a x i t y variable, 6 =n/[94)1â&#x20AC;&#x2122;3; n

with

V E

C1 = 1 at C = 0, C1

= 0 at 6 =

QJ.

thus


14 The- integration of Equation (12) can be carried out i n a straightforward way and then t h e r e s u l t used t o obtain the mass trans'fer r a t e expressed b ' : i n terms of t h e Sherwod number,

D

5

as reported by Baird and Hemilec,l and Lochiel and Calderbank. 13

It should be noted t h a t t h e result given by Equation (13) is general.

The specific value of t h e mass t r a n s f e r number depends on t h e nature of t h e r e l a t i v e motion between t h e bubble and t h e surrounding l i q u i d . Table I t gives r e s u l t s f o r u a t very low and large Reynolds number flow regimes sl and t h e f i n a l expressions f o r t h e Sherwood number f o r these regimes, based on t h e use of Equation (13). Mobile Interface Case A t least f o r bubbles having diameters greater than a few millimeters,

t h e surface condition i s more reasonably expressed as being one of negligible tangential s t r e s s and having a non-zero tangential velocity; a mobile interface.

Thus f o r t h i s s i t u a t i o n t h e appropriate diffusion

equation, as obtained from Equation (9) is:

where u

sl i s t h e non-dimensional tangential velocity at t h e bubble i n t e r face (usl = %). Again, when new position variables a r e used and w e r e s t r i c t %'b' attention t o the immediate v i c i n i t y of t h e bubble i n t e r face, Equation (14) i s reduced t o a simpler expression:


*"

C'

TAELE I ANALYTICAL RESULTS FOR WASS TRANSFER RATES TO SI1oGLB GAS EUEELES

Flaw Reaime

Interface Condition

I

Shenaod Number

References

Case I: Rigid Interface

Creeping Flaw

u

Sl

ut

'Re

>> 1

81

%h

-3sine

-

0.99 Npe 1/3

1a13

2

-

Laminar Boundary Layer 'Re

D O >

O

u ' ~ ~(6a - s i n 0)/6 6 boundary layer thickness

N~~

-

0.84

N~~1/6

13

1/3

NPe

Case 11: Mobile Interface Creeping Plow

u sin 0 61- 2 ut

91

-

0

%h

0.65 Npe

1/?

I 1,13

Potential Plow

3 a13 NW >> 1


16 Equation (15) has a s i m i l a r i t y solution i n terms of t h e variable

E = a/2B1/* which satisfies t h e ordinary d i f f e r e n t i a l equation

w i t h C1 = 1 at 6 = 0 and C1 = 0 a t 5 =

00.

Lochiel and Calderbank13

give t h e solution f o r the concentration flrnction as:

The concentration gradient at t h e bubble interface can be obtained from Equation (17) and t h e average mass t r a n s f e r r a t e t o t h e bubble can be evaluated.

The r e s u l t i n terms of t h e Sherwood mass t r a n s f e r number,

Table I a l s o includes r e s u l t s f r o m t h e . l i t e r a t u r e which deal with t h e mobile interface situation. It is important t o note that t h e mobile interface r e s u l t s show t h a t t h e mass t r a n s f e r c o e f f i c i e n t , expressed a s t h e non-dimensional Sherwood number (%%/D)

, varies

w i t h t h e Peclet

number (t$,Cb/D) raised t o t h e one-half power. I n t h e case of t h e r i g i d interface bubble t h e Sherwood number varies w i t h t h e Peclet number r a i s e d t o the one-third power,

The higher power on t h e Peclet number gives r i s e

t o s i g n i f i c a n t l y higher mass t r a n s f e r coefficients f o r t h e xenon-135 , f u e l salt system i f the mobile interface bubble case i s applicable. The a n a l y t i c a l r e s u l t s given i n Table I agree i n general w i t h those

obtained by other investigators.

I n 1935 Higbie7 made an important

contribution t o t h e mass t r a n s f e r l i t e r a t u r e i n h i s analysis of t h e r a t e of gas absorption 'from bubbles r i s i n g i n l i q u i d s . The analysis was, based on a mobile interface model and the assumption that t h e l i q u i d surrounding a bubble i s continuously replenished with f r e s h l i q u i d as it rises

throwgh a l i q u i d pool.

A solution of t h e time dependent diffusion equation


17 was obtained which can be expressed as,:

where te i s t h e exposure time of t h e bubble t o a given l i q u i d envelope. Then on t h e assumption t h a t t h e l i q u i d exposed t o t h e l i q u i s i s renewed each time t h a t , t h e bubble moves through a height equal t o t h e bubble diameter, equation (19) i s equivalent t o : NSh = 1.13 Npe 1 / 2

(20)

Thus Higbie's r e s u l t i s identical t o t h e mobile-interface equation of Boussinesq. 3 Ruckenstein16 has a l s o considered mass t r a n s f e r between spherical bubbles and l i q u i d s by solving the mass convection equations f o r various hydrodynamic situations. In essence h i s development follows that presented here and t h e results f o r t h e extreme cases of t h e r i g i d interface and t h e mobile interface agree rather well w i t h t h e equations given i n Table I.

I n particular Ruckenstein found NSh

= 1.04 NPe "3,

r i g i d interface, N~~ c 1,

and ' 2 , Ngh = 1.10 NPe 1

mobile interface, N

Re

< 1.

The constant i n Equation (22) f o r t h e mobile-interface bubble a t low Reynolds numbers differs significantly from t h e corresponding equation of Lochiel and Calderbank. 13 2.2

Experimental Data on Mass .Transfer Coefficients t o Single Bubbles Rather comprehensive surveys of t h e experimental data on mass. trans-

fer coefficients f o r gas bubbles have.been reported i n t h e liter&ture4 y5s13'14. No attempt w i l l 6e made t o give detailed results, however, data from these reference.s indicate tha$ gas bubbles of diameter l e s s than

W c

2 millimeters behave as r i g i d interface p a r t i c l e s , and t h a t gas bubbles

of diameter greater than 2 t o 3 millimeters seem t o behave as mobile-


interface p a r t i c l e s , as shown by t h e i r f l u i d drag and mass t r a n s f e r characteristics. Scott and Hayduk" carried out pipeline contactor experiments w i t h various l i q u i d s using carbon dioxide and helium as solute gases. The experimental variables covered in t h e mass t r a n s f e r t e s t s were: Liquid s u p e r f i c i a l velooity Liquid phase d i f f u s i v i t y Gas-liquid i n t e r f a c i Liquid viscosity Tube diameter

0.5 t o 3.6 f t / s e c 0.14 x 10-5 t o 4.8 x 10-5 cm2/sec 23.4 t o 73.5 dynes/cm 0.6 t o 26.5 centipoise 1.23 t o 2.50 cm

An empirical correlation equation which described t h e i r r e s u l t s i s :

where

2 s a = mass t r a n s f e r coefficient ( f t / s e c ) ft bubble surface

-Vg = l i q u i d velocity

f t 3 -contactor colume

i n pipeline contactor, f%/sec.

u = l i q u i d surface tension, dynes/cm, 1.1 = l i q u i d viscosity, centipoise, D = l i q u i d phase d i f f u s i v i t y , cfn2/sec x 1 05 , d

= pipe diameter, cm,

+

= volume f r a c t i o n of gas bubbles i n contactor. Use of t h e MSBR heat exchanger flow data and physical properties of t h e MSBR , f u e l .salt i n Equation (23) gives & a = 2'17 hr-l. If one assumes a bubble surface area of 3000 f t 2 (0.02 i n diameter bubbles) dispersed over t h e 83 ft3 of fuel system, t h i s result i s equivalent t o a mass t r a n s f e r coefficient of 7.7 f t / h r . Lamont and Scottlg a l s o reported experimental studies on t h e pipeline contacting of carbon dioxide bubbles and water under cocurrent flow conditions.

Experimental variables covered i n t h e mass t r a n s f e r tests.were:

- 22,400

Liquid Reynolds numbers Bubble diameter

1800 0.22

Tube diameter

0.793 cm.

- 0.55

cm


19

'rd

An empirical correlation equation which f i t s t h e i r data i s :

1

5 = 0.030

NRe 0*49 (+18%),

where

% = mass

t r a n s f e r coefficient (cm/min)

NRe = l i q u i d phase Reynolds number, dVp/M If one assumes a reasonable non-dimensional form consistent w i t h

Equation (24) and makes use of t h e physical properties of t h e carbon dioxide-water system, t h e reported correlation equation may more properly be written as :

5d= 1.02 SJRe0.49 0.5 NSc ' D where NSc

= Schmidt number, (p/plD)

5 - =Jd D

Pipeline Sherwc?od number.

It is then found t h a t f o r t h e MSBR f u e l salt Equation (25) gives a 6.1 fk/hr. mass t r a n s f e r coefficient I&= Various authors19s20 have c i t e d the influence of surfactants, which accumulate i n the gas bubble interface, on t h e motion of gas bubbles. In p a r t i c u l a r , it .is found t h a t such interface contamination brings about "solidification" o r "rigidity" of t h e gas-liquid interface. Under t h e cond i t i o n s of a r i g i d interface due t o presence of surfactants i n t h e i n t e r face bubbles, follow t h e well-known Stokes drag r e l a t i o n CD

NRe

= 24

at low Reynolds numbers, while under conditions of a ,clean interface the bubbles show a drag behavior represented by

16 D '

at low Reynolds numbers. r


20

gas

As pointed out e a r l i e r i n t h i s paper t h e "solidification" of t h e bubble interface.would bring about a reduction i n t h e r a t e of mass

t r a n s f e r t o a gas bubble interface.

Griffith"

has shown specific evi-

dence of t h i s e f f e c t i n c i t i n g the r e s u l t s on t h e reduction i n solution r a t e s of oxygen bubbles as surface a c t i v e matter i s adsorbed a t t h e bubble interface. Haberman. and Morton21 also found ,that surface contamination of gas bubbles can influence t h e motion of gas bubbles at l a r g e r Reynolds numbers, i.e., NReH. 100 t o 500.

Their observed increase i n gas bubble drag

coefficient under conditions of interface "solidification," considering t h e t h e o r e t i c a l mass t r a n s f e r r e s u l t s presented previously, suggests t h a t low mass t r a n s f e r r a t e s t o bubble interfaces should prevail under these conditions. \

2.3

Mass Transfer Coefficients f o r Bubbles Carried Along by Turbulent Liquid The previous discussion of the mass t r a n s f e r theory f o r gas bubbles

moving i n a stationary l i q u i d dealt w i t h steady flows, and t h e results are most,appropriately applied t o t h e cases of f r e e l y rising bubbles o r uniform flow of l i q u i d past a bubble. In t h e MSBR injected helium bubbles would be carried along by f u e l salt flowing i n a state of turbulent motion.

The

Reynolds number based on the heat exchanger tube diameter and bulk velocity

i s expected t o be about 8000. The following discussion of t h e mass transfer f o r bubbles carried along by a turbulent l i q u i d indicates t h e approximate magnitudes of .mass t r a n s f e r coefficients f o r t h i s s i t u a t i o n . 8 Hinze has t r e a t e d t h e case of r e l a t i v e motion between a small gas bubble and a turbulent l i q u i d , and f o r t h e limiting case of large i n e r t i a forces i n comparison t o viscous forces he found t h a t t h e bubble velocity fluctuates with a l a r g e r amplitude than t h e surrounding turbulent l i q u i d ; namely (26) wbererF-an$Fare I

I

r.m.8.

values of t h e instantaneous bubble and

l i q u i d v e l o c i t i e s , respectively, f o r the turbulent motion.

Equation (26)

I

i n essence r e s u l t s from integration of t h e equation f a r t h e fluctuating motion of the gas bubble:


21

U 1

where

bubble volume bubble density, l i q u i d density added mass coefficient f o r accelerating spherical bubble

time

.

Thus, it i s noted that since p

1c

<c

p a and k i s 1/2,L'

t h e bubble accelera-

t i o n is about t h r e e times t h e l i q u i d acceleration.

Upon use of Equation (26), it i s found that t h e velocity of t h e gas bubble r e l a t i v e t o t h e turbulent

l i q u i d motion on t h e average is:

b ' relative

-2m

R'

*

(28)

For pipe flows J's v m i e s across t h e radius and an approximate value ' representive of t h e Rpipe cross section i s :

-

where VR = average l i q u i d velocity, f = pipe flow f r i c t i o n factor.

Thus combination of Eqwtions (28) and ( 2 9 ) indicates t h a t an estbmte of the time average ve

i t y of gas bubbles r e l a t i v e t o l i q u i d moving under turbulent conditions i s

b '

Since f = 0.046 NRe -1/5

S2vQ

relative

,

m.

(30)

d from experimental measurements, a

more useful form of t h e r e s u l t is: c

b'

W

= 0.303 relative

where NRe = dTR/v, pipe Reynolds number.

v2 NRe-1/10 ,

(31)


22 ,

It seems reasonable t o use t h e r e s u l t given by Equation (31) i n t h e

mass t r a n s f e r equations f o r s p h e r i c d p a r t i c l e s t o obtain the desired

The r e s u l t s obtained a r e given

r e l a t i o n f o r t h e mass t r a n s f e r coEfficient. f o r t h e two cases:

(a) mobile gas-liquid i n t e r f a c e and (b) r i g i d gas-

l i q u i d interface. Mobile Interface : The mobile-interface theory f o r mass t r a n s f e r t o a single bubble yields an e x p l i c i t formula f o r t h e mass t r a n s f e r coefficient applicable t o turbulent conditions; namely

5 = 1.13 where

% = liquid

1/2

[Db /%I relative

(32)

9

phase mass t r a n s f e r coefficient,

D = l i q u i d phase d i f f u s i v i t y ,

\

= bubble diameter.

Use of Equation (31) i n Equation (32) f i v e s t h e result:

-

5 = 0.62 -%d = D

The parameter (%4,/D)

(3

1/2

pNe

0 45 0.5 0.62 NRd NSc

-1/20 Âś

or

(-1d4,1/2

i s t h e Sherwood number and Elsc

(33)

= v/D i s the r a t i o

of t h e l i q u i d kinematic viscosity t o the l i q u i d phase d i f f u s i v i t y , o r

Schmidt number. Rigid Interface:

The equation of G r i f f i t h5 i s representative of t h e mass t r a n s f e r equations f o r r i g i d , spherical p a r t i c l e s ; L

-54, - 2 + 0.57 D

/ v ) o * 5 0.35 NSc ' brelat ive

(4,F

(34)


23 Combination of Equations (31) and (34) yields:

Figure 5 shows a plot of values of

5 predicted

by Equations (33)

and (35), along with other values from t h e l i t e r a t u r e , f o r t h e a B R heat exchanger flow conditions. Shown also are calculations by Kedl'l based on t h e mobile interface equations f o r "free-rise" velocity conditions. The analysis presented must be regarded as an approximation. Random migration of bubbles i n a turbulent l i q u i d i s certainly affected by viscous This effect was not considered. Other important assumptions implicit i n t h e analysis a r e t h a t t h e bubble is small compared t o t h e scale of

drag.

turbulent motion and t h a t t h e bubble moves i n t h e same l i q u i d envelope during t h e course of each turbulent "event." These e f f e c t s which cause departure of t h e actus turbulent bubble motion from t h e assumed model probably give rise t o some attenuation of t h e bubble's fluctuationi

velocity aslplitude, and, hence, t h e results given by Equations (33) and (35) are l i k e l y optimistic.

That i s , t h e bubble's turbulent fluctuation

velocity may be less than three times that of t h e l i q u i d ' s fluctuation velocity.

I n s p i t e of t h e speculative nature of t h e assumptions made i n t h e analysis, t h e f i n a l equations give r e s u l t s which agree reasonably well with t h e available experimental data.

A r a t h e r important point of t h e preceding analysis i s t h a t t h e relat i v e motion between bubbles and turbulent l i q u i d gives rise t o mass t r a n s -

fer coefficients which a r e appreciably greater than t h e mass t r a n s f e r coefficients for "free-rise" (or "free-fall") flow conditions. This indication i s supported by t h e experimental results of Harriott 6 f o r mass t r a n s f e r coefficients between small r i g i d p a r t i c l e s carried along by t u r bulent l i q u i d i n a pipe, The experimental mass t r a n s f e r r e s u l t s , expressed as t h e pipeline Sherwood number (%d/D), were correlated w i t h Reynolds number and Schmidt number by t h e equation

NSh(pipe)

= 0.0096 NRe 0.913 NSc0.346

.

(36)


24

ORNL-DWg 68-6784 30

20

10

5.i

2.(

1.( 0.01

0.02 ,

0.05

0.10

Bubble Diameter

Fig. 5. Liquid Phase Mass Transfer Coefficient Versus Bubble Diamet e r Liquid: MSBR Fuel S a l t , N R e â&#x20AC;&#x2122; = 7200, NSc = 2880, d = 0.305 in.

G .


25

hj f

If one uses appropriate MSBR data (NRe

4

= 10

ft2/hr, d = 0.305 i n . ) , Equation (36) gives

, NSc

= 2880, D =

5 = 1.3 f t / h r .

-5 5 x 10

Now i f one

uses t h e rigid-interface mass t r a n s f e r r e l a t i o n f o r a bubble w i t h diameter

equal t o 0.02 i n . and r i s i n g i n MSBR f u e l s a l t , it i s found t h a t t h e mass t r a n s f e r coefficient f o r these conditions i s 0.38 f t / h r . Thus, t h e pipeline mass t r a n s f e r coefficient may be 3 t o 4 times t h e value predicted f o r t h e

"free-rise" condition. Further, i f an 0.02 i n . diameter bubble behaves as a mobile-interface p a r t i c l e , it i s noted t h a t t h e pipeline mass transf e r coefficient a s predicted by Equation (33) i s again about 3.6 times t h e "free-rise" bubble mass t r a n s f e r coefficient. 3.0

Proposed Mass Transfer Experiment t o Simulate MSBR Contact Conditions The l i t e r a t u r e information on mass t r a n s f e r t o gas bubbles discussed

i n t h e previous section does not yield a firm estimate of t h e l i q u i d phase mass t r a n s f e r coefficient expected f o r t h e MSBR flow conditions,

Two

points need f u r t h e r c l a r i f i c a t i o n ; namely i d e n t i f i c a t i o n of t h e precise c r i t e r i a f o r rigid-interface and mobile-interface bubble behavior, and determination of t h e mass t r a n s f e r coefficients f o r bubbles carried by turbulent l i q u i d a t t h e hydrodynamic conditions expected t o prevail i n t h e

MSBR. It seems t h a t t h i s information should be obtained by experimental measurements, i n contrast t o depending on further a n a l y t i c a l investigation. An experimental study of mass t r a n s f e r rates i n t h e d e t a i l t o furnish values of t h e l i q u i d phase mass t r a n s f e r coefficients carried out using MSBR f u e l salt would be a formidable and expensive undertaking. I n considering these f a c t o r s a more a t t r a c t i v e a l t e r n a t i v e is t o attempt determination of t h e needed data using a s u i t a b l e f l u i d which simulates t h e MSBR s i t u a t i o n and which would not require t e s t s at elevated temperatures. Following i s a brief description of a proposed experiment involving t h e use of 46% glycerol, oxygen as t h e solute gas, and helium as t h e stripping medium i n order t o simulate t h e MSBR hydrodynamic conditions, The choice of t h e glycerol solution recommended f o r t h e mass transf e r tests i s based on t h e requirements f o r dynamic similitude i n t h e test and MSBR situations. Table I1 gives t h e important f a c t o r s t h a t should be maintained dynamically similar i n t h e model and prototype systems. Con-

W

sideration of these f a c t o r s leads t o t h e conclusion t h a t t h e model experiment should be carried out at the sane Reynolds number (dTk/v), bubble


TABU I1

IMPORTANT VARIABLES FOR DYNAMIC SIMILITUDE PHENOMENON

IMPORTANT VARIABLES

NON-DIMENSIONAL PARAMcreRS

Convective d i f f i s i o n Bulk stream turbulence Bubble migration relative t o turbulent l i q u i d Bubble s t a b i l i t y (coalescence o r rupture )

4

m c

-‘b’ -VQ,

c1 9

pL,

PL’

5

$9

d,

N

cn

a, d

NWe’ %e’

I

u

%Id


27

b

r a t i o (%/d), Froude number (vg/$g),

Schmidt number ( v / D ) , Weber Number

(Tg%p/gco), pipe roughness r a t i o (€/a), and pipe length-to-diameter r a t i o (L/d) as those values f o r t h e MSBR. It one decides t o use the same bubble diameter i n t h e model and prototype s i t u a t i o n s , the similtude requirements

a r e s a t i s f i e d i f t h e model experiment has t h e same pipe roughness, pipe length, pipe diameter, kinematic viscosity, Schmidt number, and kinematic surface tension a s t h e MSBR.

The physical property requirements of equal

kinematic viscosity and Schmidt number can be met approximately by using

46% by weight glycerol.

Figure

6

shows a plot of these physical properties

as a function of glycerol concentration.

It should be noted t h a t t h i s t e s t

l i q u i d w i l l not meet t h e kinematic surface tension requirement.

In f a c t t h e

MBR Weber number w i l l be about 1.8 times t h a t f o r t h e 46% glycerol.

Oxygen seems t o be an appropriate solute gas t o be used i n t h e proposed mass t r a n s f e r t e s t s . The concentration of oxygen i n glycerol can be determined using t h e Winkler” method and assay accuracies of +1per cent a r e expected, based on t h e research of Jordan’ et a l . Other physical properties needed i n t h e evaluation of mass t r a n s f e r coefficients from t h e experimental data a r e ,available .9 These include t h e s o l u b i l i t y data, oxygen d i f f u s i v i t y i n glycerol solutions, glycerol viscosity and density data.

H e l i u m i s recommended as a s a t i s f a c t o r y stripping medium because of i t s low s o l u b i l i t y i n glycerol and chemical inertness. The mass t r a n s f e r experiment proposed involves s e t t i n g up t h e experimental system diagrammed i n Figure 7. Tests would be carried out by establishing the MSBR l i q u i d flow r a t e i n t h e t e s t section. H e l i u m bubbles would be injected a t a flow rate corresponding t o t h a t of t h e MSBR. Oxygen concentrations i n t h e i n l e t and effluent l i q u i d s would be determined by chemical analysis Qf l i q u i d samples. I n order t o evaluate t h e mass t r a n s f e r coefficients, it would be necessmy t o determine t h e bubble diameters produced i n t h e experimental bubble generator. This probably can be done by photographic methods. The experimental data on l i q u i d oxygen concentrations a t t h e i n l e t and o u t l e t points, gas and l i q u i d flow rates, bubble diameter, t e s t section length, t e s t temperature, and Henry’s law coefficient would be used with Equation ( 3 ) t o determine t h e l i q u i d phase mass t r a n s f e r


I

4

t

A

0

0 0

Y

Kinematic Viscosity (ft2jhr)

P

0

0

P

P

0

Schmidt Number (V/D x

0

ru

0

;"


m,

Âś

ORNL-DWg 68-6786

f l o x y g e n a t e d Glycerol Supply Tank, Gravity Feed, Constant Head

Rate,

%

O2 Concentration) /Pipeline

Contactor, L = 100 f t , d = 0.305 i n .

I

I

Helium

H e l i u m Introduced Through Bubble Generator (Capable of Producing Uniform Bubbles = 0.01 t o 0.25 i n . )

't"-

H e l i u m Flow Rate,

Fig. 7.

Concentration ) Bubble Photography

&G

Flow Diagram f o r Mass Transfer Test System.

I

To Glycerol Receiver


50 coefficient.

Figure 8 shows calculated data on t h e oxygen concentration

r a t i o as a function of t h e mass t r a n s f e r coefficient f o r L = 100 f t ,

4, =

0.02 in. and 0.10 in.

4. O Conclusions The study of' existing l i t e r a t u r e on mass t r a n s f e r between bubbles and liquids and t h e analysis presented i n t h e previous sections permits t h e following conclusions: 1. The effectiveness f o r Xenon435 removal from t h e circulating

f u e l salt i n t h e MSBR may range from about 3 t o 33 per cent depending on t h e value of l i q u i d phase mass t r a n s f e r coefficient. The estimated Xenon-135 removal effectiveness i s based on t h e range of mass t r a n s f e r coefficients, 1t o 13.5 f t / h r . , obtained from available literature information. 2. Available literature information provides a good basis f o r estimating mass t r a n s f e r coefficients f o r bubbles moving at a steady velocity r e l a t i v e t o l i q u i d under conditions of a r i g i d interface and a completely mobile interface. 3. There does not e x i s t a r e l i a b l e c r i t e r i o n for specifying t h e type of bubble interface condition expected f o r a given condition.

4. The available l i t e r a t u r e does not provide a good basis of estimating the mass t r a n s f e r coefficient f o r bubbles carried along by turbulent liquid.

Analysis of t h i s s i t u a t i o n i n approximate terms pro-

vided new relationships which a r e . i n approximate agreement w i t h t h e data that a r e available.

New mass t r a n s f e r measurements are proposed t o provide additional data needed i n overcoming the limitations f o r mass t r a n s f e r predictions

5.

c i t e d i n Conclusions 3 and 4. Glycerol (46% by weight) i s recommended a s the t e s t f l u i d i n order t o simulate the MSBR hydrodynamic conditions and meet most of the requirements f o r dynamic similitude i n t h e model and prototype situations.

f

Li


31

ORNL-DWg 68-6787 1.0

0.9

s 0.8

n

u

1

u3

W

0

74 +,

d

0.7

c

0

74 +, (d

k

+,

c al

: 0.6

0 u

0.5 I

0 0

2.5

%,

5.0

7.5 10.0 Liquid Phas &ss Transfer Coefficient (ft/hr)

12.5

Fig. 8. Oxygen Concentration Ratio as a Function of the Mass Transfer Coefficient.


I

Li

References Cited 1. Baird, M.H.I.

and A. E. Hamilec, Canad. Journ. Chem. Engr.

, 40,

119

(1962) 2

Bird, R. B. , W. E. Steward and E. N. Lightfoot "Transport Phenomena," p. '522, John Wiley, New York, 1960.

3.

Boussinesq, J , , Journ. Math.

4.

Calderbank, P. H., Trans. I n s t . Chem. Engr.,

5.

G r i f f i t h , R. M.,

, 6, 285

(1905)

. 37, 173

Chem. Engr. Science, l2, 198 (1960).

6. H a r r i o t t , P. and R.

(1959). ,

M. Hamilton, Chem. Engr. Science, 20, 1073 (1965).

7. Higbie, R., Trans. Am. I n s t . Chem. Ewrs., 3 l , 365 (1935). 8. Hinze , J. 0. , "Turbulence ,"p. 360, McGraw-Hill, New York, 1960. 9. 10.

Jordan, J., E. Ackerman and R. L. Berger, Journ. Am. Chem. SOC., 78, 2979 (1956). W e Molten S a l t Breeder Kasten, P. R. , et al. , "Design Studies of 1000 M Reactors ,11 0 ~ ~ ~ ~,3August 9 9 6 1966.

11. K e d l , R. J. , "Xenon-135 Poisoning i n t h e MSBR," MSR-67-45 , oak Ridge National Laboratory ( i n t e r n a l d i s t r i b u t i o n only) , June 28 , 1967.

f x c

i, I

/ ! I

I

12.

Lamont, J. C. and D. S. Scott, Canad. Journ. Chem. Engr., 44, 201 (1966).

13.

Lochiel, A. 6 , and P. H. Calderbank, Chem. Ewr. Science,

471 (1964).

14.

Redfield, J. A. and G. Houghton, Chem. Engr. Science, 20, 131

(1965).

15. Robertson, J. M., "Hydrodynamics i n Theory and Application," p. 204, Prentice-Hall , 1965.

16. Ruckenstein, E., Chem. Engr. Science,

re, 131 (1964).

17. Scott, D. S. and W. Hayduk, Canad. Journ. Them. Engr., 44, 130 (1966). 18. American Public Health Association, e t a l . , "Standard Methods f o r t h e Examination of Water and Sewerage," 9th Ed., p. 135, New York, 1947. 19. G r i f f i t h , R. M., Chem. Engr. Science, JJ,

1057 (1962).

21, 681

20.

Davis, R. E. and A. Acivos, Chem. Ewr. Science,

(1966)

21.

Haberman, W. L. and Morton, R. K., David Taylor, Model Basin Report No.' 802, NS 715-102 (1953).

,


33

ORNL-TM-2245 Internal Distribution 1. L. G. Alexander 2. S. E. Beall 3. M. Bender 4. E. S. B e t t i s 5. E. G. Bohlmann 6. C J. Borkowski 7. G. E. Boyd 8. R. B. Briggs 9-10, D. F. Cope, AEC 11. W. B. C o t t r e l l 12. F. L. Culler 13. S. J. Ditto 14. W. P. Eatherly 15. D. E. Ferguson 16. A. P. Fraas 17. J. H. Frye 18. W. R. Grimes 19. A. G. Grindell 20. P. N. Haubenreich 21. H. W. Hoffman 22. W. H. Jordan 23. P. R . Kasten 24-31. R. J. Ked1 32. M. T. Kelley 33. J. J. Keyes 34. T. S. Kress 35. M. I. Lundin 36. R. N. Lyon 37 H. G. MacPherson

.

138

E. MacPherson F. McDuffie E. McCoy C. McCurdy J. Miller L. Moore L. Nicholson C. Oakes F. N. Peebles A. M. Perry M. W. Rosenthal A. W. Savolainen Dunlap Scott M. J. Skinner A . N. Smith I. Spiewak D. A. Sundberg R. E. Thoma D. B. Trauger A . M. Weinberg J. R. Weir M. E. Whatley J. C . White G. D. Whitman G. Young Central Research Library Document Reference Section Laboratory Records Department 77. Laboratory Records, RC

39. 40. 41. 42. 43. 44. 45. 46-48 49. 50- 51. 52. 53-57. 58. 59. 60. 61 62. 63. 64. 65. 66. 67 68. 69. 70-71. 72-73. 74-76

R. H. H. H. A. R. E. L.

External Distribution

78. C. B. Deering, AEC, OR0 A. Giambusso, AEC, Washington, D.C. W. J. Larkin, AEC, OR0 T. W. McIntosh, AEC, Washington, D.C. 83. H. M. Roth, AEC, OR0 84. M. Shaw, AEC, Washington, D.C. 85;. W. L. Smalley, AEC, OR0 86-100. Division of Technical Information Extension 79. 80. 81-82.

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