Chemical Reaction EngineeringâBoston - American Chemical Society

31 Simultaneous Mass Transfer of Hydrogen Sulfide and Carbon Dioxide with Complex Chemical Reaction in an Aqueous Diisopropanolamine Solution Downloaded by PURDUE UNIV on June 27, 2016 | http://pubs.acs.org Publication Date: September 16, 1982 | doi: 10.1021/bk-1982-0196.ch031

P. M . M . B L A U W H O F F

1

and W. P. M . V A N SWAAIJ

Twente University of Technology, P.O. Box 217, 7500 A E Enschede, The Netherlands

The simultaneous absorption of H2S and CO2 into aqueous 2.0 M diisopropanolamine (DIPA) solutions is studied both experimentally and theoretically. The absorption phenomena observed, depend largely on the extent of depletion of the amine in the mass transfer zone and can be classified into three regimes: 1 negligible interaction, 2 medium interaction and 3 extreme interaction between H2S and CO2 absorption. In the latter regime, desorption of one of the gaseous components is observed a l though, based on its overall driving force, ab sorption would be expected. We studied these phenomena experimentally in a wetted wall column and two stirred cell reactors and evaluated the results with both a penetration and a film model description of simul taneous mass transfer accompanied by complex liquid-phase reactions [5,6]. The experimental results agree well with the calculations and the existence of the third regime with its desorption against overall driving force is demonstrated in practice (forced desorption or negative enhance ment factor). The removal o f the a c i d components H 2 S and CO2 from gases by means of alkanolamine s o l u t i o n s i s a w e l l - e s t a b l i s h e d process. The desc r i p t i o n o f the H 2 S and CO2 mass t r a n s f e r f l u x e s i n t h i s process, however, i s very complicated due to r e v e r s i b l e and, moreover, i n t e r a c t i v e l i q u i d - p h a s e r e a c t i o n s ; hence the r e l e v a n t p e n e t r a t i o n model based equations cannot be solved a n a l y t i c a l l y [63. Recently we, t h e r e f o r e , developed a numerical technique i n order t o c a l c u l a t e H S and CO2 mass t r a n s f e r rates from the model equations [ 6 ] . 2

1

Current address: Koninklijke/Shell Laboratorium Amsterdam, P.O. Box 3003, 1003 AA Amsterdam, The Netherlands. 0097-6156/82/0196-0377$06.00/0 © 1982 American Chemical Society Wei and Georgakis; Chemical Reaction Engineering—Boston ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

378

CHEMICAL REACTION ENGINEERING

In t h i s i n v e s t i g a t i o n we c a r r i e d out experiments with s i m u l taneous a b s o r p t i o n o f H 2 S and CO2 i n t o aqueous 2.0 M d i i s o p r o p a n o l amine (DIPA) s o l u t i o n s a t 25 °C. The r e s u l t s are evaluated by means o f our mathematical mass t r a n s f e r model both i n p e n e t r a t i o n and f i l m theory form. The l a t t e r v e r s i o n has been d e r i v e d from the p e n e t r a t i o n theory mass t r a n s f e r model [ 5 ] . The experiments may be d i v i d e d i n t o three regimes: 1st w i t h n e g l i g i b l e i n t e r a c t i o n between the H 2 S and CO2 mass t r a n s f e r r a t e s , r e a l i z e d a t r e l a t i v e l y low gas-phase c o n c e n t r a t i o n s , 2nd w i t h medium i n t e r a c t i o n and 3 * w i t h extreme i n t e r a c t i o n , r e s u l t i n g i n d e s o r p t i o n o f one o f the gaseous components a g a i n s t i t s o v e r a l l driving force. Under c o n d i t i o n s p r e v a i l i n g i n i n d u s t r i a l and l a b o r a t o r y absorbers o p e r a t i n g a t steady s t a t e , only the f i r s t two regimes can be a t t a i n e d . The t h i r d regime can probably be r e a l i z e d only under t r a n s i e n t operating c o n d i t i o n s .

Downloaded by PURDUE UNIV on June 27, 2016 | http://pubs.acs.org Publication Date: September 16, 1982 | doi: 10.1021/bk-1982-0196.ch031

r(

Theory The l i q u i d - p h a s e r e a c t i o n s . The r e a c t i o n between HoS and aqueous alkanolamines i s instantaneous and r e v e r s i b l e [ 7 J : R N H 2 + HS"

H S + R NH 2

(1)

2

2

CHS"] [R NH+] 2

\ S

(

" CH S] fR NH] 2

2

)

2

Everywhere i n the l i q u i d , e q u i l i b r i u m (1) i s e s t a b l i s h e d due t o i t s instantaneous nature. For CO2 we c o n s i d e r only the r e v e r s i b l e r e a c t i o n w i t h primary and secondary alkanolamines as shown i n the o v e r a l l r e a c t i o n equation [7]: C0

+ 2 R NH

2

R NC00~ + R NH

2

2

2

(3)

2

with [R NC00"] I^NH*] 2

K

co,

=

5

~

2

(

Γ"" -

CC0 ] [ R N H ] 2

4

)

2

2

Reaction

(3) proceeds a t a f i n i t e o v e r a l l r a t e , expressed by [ 8 ] : . [R-NCOO ] [R,NH*] k CC0 ] [R.NH] (5) 2 ^2 Κ " ΠΓΝΗΤ VAJ2 ^ In f a c t the r e a c t i o n scheme i s c o n s i d e r a b l y more complicated than suggested by equation (3) [ 9 ] and consequently more complicated r a t e equations are proposed i n l i t e r a t u r e [3,9]. F o r the purpose of t h i s work, however, equation (5) was found t o be s u f f i c i e n t l y a c c u r a t e . Other C O 2 c o n v e r t i n g r e a c t i o n s , as w e l l as the h y d r o l y s i s of the carbamate i o n , are slow compared t o r e a c t i o n (3) and hence are not i n c o r p o r a t e d i n the model. -

1

2

J

oJ

2

2

2

a a j

Wei and Georgakis; Chemical Reaction Engineering—Boston ACS Symposium Series; American Chemical Society: Washington, DC, 1982.


31.

BLAUWHOFF AND VAN SWAAU

HtS and CO

Mass Transfer

2

379

The mass t r a n s f e r model. In our previous work [6] the mass t r a n s f e r model equations and t h e i r mathematical treatment have been d e s c r i b e d e x t e n s i v e l y . The r e l e v a n t d i f f e r e n t i a l equations, d e s c r i b i n g the process of l i q u i d - p h a s e d i f f u s i o n and simultaneous r e a c t i o n s o f the species according to the p e n e t r a t i o n theory, are summarized i n t a b l e 1. Recently we d e r i v e d from t h i s p e n e t r a t i o n theory d e s c r i p t i o n a f i l m model v e r s i o n , which i s i n c o r p o r a t e d i n the e v a l u a t i o n o f the experimental r e s u l t s . D e t a i l s on the f i l m model v e r s i o n are given elsewhere [ 5 ] . The process o f mass t r a n s f e r and simultaneous r e a c t i o n s i s g r a p h i c a l l y represented i n f i g u r e 1· In an a b s o r p t i o n s i t u a t i o n H 2 S and CO2 d i f f u s e from the bulk o f the gas-phase t o the i n t e r f a c e and are i n dynamic e q u i l i b r i u m w i t h t h e i r r e s p e c t i v e l i q u i d - p h a s e concen t r a t i o n s . From the i n t e r f a c e , H 2 S and CO2 d i f f u s e towards the l i q u i d bulk and both r e a c t simultaneously w i t h the alkanolamine according t o o v e r a l l r e a c t i o n s ( 1 ) and ( 3 ) . The r a t i o s of the t r a n s p o r t r a t e s t o the net conversion r a t e s o f the species i n v o l v e d both i n r e a c t i o n ( 1 ) and ( 3 ) ( R 2 N H and R 2 N H 2 ) , determine the extent o f d e p l e t i o n o f R 2 N H and surplus o f R2^H5 hence d e t e r mine the i n t e r a c t i o n between the r e a c t i o n s ( 1 ) and ( 3 ) . The de p l e t i o n o f R 2 N H and the surplus o f R 2 N H 2 i n t e r f a c e can be estimated u s i n g an approach s i m i l a r t o e.g. Ramachandran and Sharma [ 1 0 ] . a n Q 4

a

t

t

n

e

A s u b s t a n t i a l amine conversion by H 2 S and CO2» combined w i t h a r e l a t i v e l y high a b s o r p t i o n mole f l u x o f one o f the gaseous com ponents, e.g. H 2 S , gives r i s e to an i n t e r e s t i n g f e a t u r e induced by the i n t e r a c t i o n o f the l i q u i d - p h a s e r e a c t i o n s . Due t o the r e l a t i v e l y high amine conversion r a t e i n the p e n e t r a t i o n zone and the consequent d e p l e t i o n o f amine, the competitive C02~amine r e a c t i o n i s reversed and l o c a l l y produces amine and f r e e C O 2 . This l o c a l CO2 c o n c e n t r a t i o n can exceed i t s i n t e r f a c i a l c o n c e n t r a t i o n and leads t o d i f f u s i o n o f p a r t o f the CO2 towards the gas phase (see f i g u r e 2 ) . The n e t r e s u l t w i l l be d e s o r p t i o n o f C 0 2 , although based on i t s o v e r a l l d r i v i n g f o r c e , a b s o r p t i o n would have been expected. Consequently the enhancement f a c t o r of CO2 y i e l d s negative v a l u e s . P r e v i o u s l y we d e f i n e d t h i s phenomenon as f o r c e d d e s o r p t i o n o r negative enhancement f a c t o r [ 2 , 6 ] . No experimental evidence of t h i s phenomenon has been a v a i l a b l e u n t i l now. In general the r a t e of mass t r a n s f e r o f e.g. H 2 S may be expressed by: ο [H S] 2

CH S]? 2

-

g

Γ

~ 1

H S 2

k

= k,

1

SH S 2

m

H

S 2

'

k l H

o v

H S

»*«îl [H S] 2

g

2

s

2 '

f H

2

S


( ) 6


T a b l e 1. P e n e t r a t i o n t h e o r y e q u a t i o n s f o r t h e mass t r a n s f e r model (boundary c o n d i t i o n s as u s u a l i n p e n e t r a t i o n t h e o r y [6 ] ) . the c a r b o n d i o x i d e r e a c t i o n 2

3[C0 ]

3 [C0 ]

2

9

=


k

balance:

D C 0

2

"

k

2

C C 0

2

3 C R

2

N H : I

+

[R NC00"][R NH ]

2

2

2

+

2

[R^NH]

the t o t a l

carbon d i o x i d e b a l a n c e :

3[C0~] £-

2

3[R NC00~]

3 [CO-]

0

+

±

3t

s Π

3t

—

C0

2 χ

2

^

2

Ô [R NCOO"] 2

+

D

~2

R NCOO 2

t o t a l sulphur

balance: 2

3

C

H

2

S

]

3

, -9[HS~] _ _

at

=

at

H

D

S

2

C

H

3 χ

2

S

]

2

. _ +

2

3 [HS~]

H S "

D

3 χ

2

t o t a l amine b a l a n c e +

3[R NH]

3[R NH ]

2

2

+

3t

at

+

2

the a c i d

2

N H

2

=

3t

2

D R

3 [R NH]

2

3 [R NH +

2

3[R NCOO~]

2

+ 2

2

D

R NH

^2

2

2

]

+

+

_

3 [R NCOO ] 2

D

r

2

N

C

0

°

3^

balance:

3[H S] at

+

3[C0 ]

2

at

+

2

3[R NH ]

2

2

at

+

3 [H S]

2

2

=

D

H S

2

2

3 [C0 ] °

C 0

2

+

3 CR NH ]

2

+

+

2

2

+

R

° 2

N H

2

2

+



'

H

C 0

m

2

m

2

'°°

2

H

. 2

2

S

+

+

penetration

"

2

CXU

2

H„S

zone

0

2

2

2

2

t

R„NH„+ 2""2

R NH =^ir R N H +

D

I R NH

2R NH = ^

Liquid

+

+

2

D R NH

R NC00 o

HS

t

2

9

^R NCOO

—~D.

2 +

'HS

Scheme of the absorption process with interaction by the common product R NH * and reactant R NH.

C0

H S

m

Figure 1.

2

S

*H S 2

Interface




382



31.

383

H S and CO* Mass Transfer t

where: CH S3Î 2

(7) [H S]^ 2

and: .

k

!

(8)

For CO2 an expression analoguous t o equation (6) can be d e r i v e d . The values o f the enhancement f a c t o r s i n (6) and i t s CO2 analogon, f f l g and fc(>2 P c t i v e l y , a r e obtained from our mass t r a n s f e r model and account f o r the i n t e r a c t i o n between H 2 S - and C02-amine reactions. I f the amine d e p l e t i o n i n the p e n e t r a t i o n zone i n a simultaneous a b s o r p t i o n s i t u a t i o n i s n e g l i g i b l e , the mass t r a n s f e r f l u x e s are independent o f each other and the r e s p e c t i v e enhancement f a c t o r s may be obtained e a s i l y from a n a l y t i c a l s o l u t i o n s o f s i n g l e gas mass t r a n s f e r models. r e s

e


2

Selectivity. I n many cases i t i s d e s i r e d t o remove H 2 S s e l e c t i v e l y from a gas stream, r e j e c t i n g CO2 t o the h i g h e s t p o s s i b l e extent. I t i s , t h e r e f o r e , u s e f u l t o introduce the s e l e c t i v i t y f a c t o r S, being a y a r d s t i c k f o r the process s e l e c t i v i t y independent o f mass t r a n s f e r d r i v i n g f o r c e s [ 8 ] : C C 0

J

C C 0

H S 9 2

[H S]?

'

2

3

2 1 2 g " ^SCÔT" — C0 2 ]

(9)

J

[H S]£ ° E which y i e l d s a f t e r s u b s t i t u t i o n o f equation (6) and i t s C 0 analogon: _ ! _ ι 0

2

J G

M

S

2

2

+

êC0 S . — p i k

_ 1 — K

m

9

SH S 2

C0

o

k

2

+

lC0

o

f

2

C0

K

3 :

H S lH S H S 2

2

=

ovH S 2_ K

* m

k o

2

ov

(

1

0

)

c o Z

2

and represents the r a t i o o f the o v e r a l l mass t r a n s f e r c o e f f i c i e n t s . Our a b s o r p t i o n experiments i n the regime w i t h n e g l i g i b l e i n t e r a c t i o n are e n t i r e l y gas-phase l i m i t e d with respect t o H 2 S , as was checked using the a n a l y t i c a l mass t r a n s f e r e x p r e s s i o n of Secor and B e u t l e r [ 1 1 ] . The CO2 a b s o r p t i o n i s i n the p s e u d o - f i r s t order regime and hence the s e l e c t i v i t y f a c t o r can be s i m p l i f i e d t o :


384


-V

s

,

k g C 0

S m

2

C0

2

8

^ 2 ^ ° \ θ

P l o t t i n g of S versus kgj^s slope l/mco

2

/k [R NH]°D 2

2

Experimental procedures


, s n o u

C 0 2

and

5

S ^

2

^

(11) 2

^

%

^

^ ^ y i e l d a l i n e a r dependency with

and y - a x i s i n t e r c e p t

1.

results.

N e g l i g i b l e and medium i n t e r a c t i o n regimes. Experiments were c a r r i e d out with an aqueous 2.0 M DIPA s o l u t i o n at 25 °C i n a s t i r r e d - c e l l r e a c t o r (see réf. [1]) and a 0.010 m diameter wetted w a l l column (used only i n n e g l i g i b l e i n t e r a c t i o n regime, see r e f . [ 4 , 5 ] ) . Gas and l i q u i d were continuously fed to the r e a c t o r s ; mass t r a n s f e r r a t e s were obtained from gas-phase analyses except f o r C 0 i n the wetted w a l l column where due to low C 0 gas-phase conversion, a l i q u i d - p h a s e a n a l y s i s had to be used [ 5 ] . In the n e g l i g i b l e i n t e r a c t i o n regime some 27 experiments were c a r r i e d out i n both r e a c t o r s . The s e l e c t i v i t y f a c t o r s were c a l c u l a t e d from the measured H S and C0 mole f l u x e s and are p l o t t e d versus kgjj^s 2

2

2

2

i n f i g u r e 3. The dependency i s l i n e a r , as p r e d i c t e d by equation (11). The p s e u d o - f i r s t order C0 -DIPA r e a c t i o n r a t e constant c a l c u l a t e d from the slope i s : k D I P A 1200 s ~ l , which i s s l i g h t l y higher than found i n our separate k i n e t i c s study [3,5] (800 s " ) . Two s e r i e s of experiments were c a r r i e d out i n the medium i n t e r a c t i o n regime at a constant entrance gas flow r a t e , c o n t a i n i n g 50% of H S or C 0 and v a r y i n g concentrations of the other component (0, 20, 30, 40 and 50%). Measured and c a l c u l a t e d ( p e n e t r a t i o n and f i l m theory) mole f l u x e s are shown i n f i g u r e 4 a,b as a f u n c t i o n of the v a r i e d c o n c e n t r a t i o n s . The D I P A f l u x i s obtained from a f l u x balance equation (JoiPA JH S 2 Jc0 )· f i g u r e 4a i t obvious that J D I P A remains constant w i t h i n c r e a s i n g C 0 concen t r a t i o n , implying that the maximum enhancement given by complete DIPA d i f f u s i o n l i m i t a t i o n i s r e a l i z e d . The measured H S molef l u x e s f a l l between f i l m and p e n e t r a t i o n theory c a l c u l a t i o n s while C 0 agrees more with the f i l m theory. For each experimental r u n , measured and c a l c u l a t e d s e l e c t i v i t y f a c t o r s are shown i n f i g u r e 5 a,b. The values measured are r a t h e r s c a t t e r e d due to experimental i n a c c u r a c i e s but the f i l m theory c a l c u l a t i o n seems to y i e l d the minimum values of the s e l e c t i v i t y f a c t o r s and hence should be p r e f e r r e d f o r ( c o n s e r v a t i v e ) absorber design. 2

β

2

1

2

2

β

+

F

2

r

o

m

2

2

2

2

Extreme i n t e r a c t i o n regime. The experimental set-up i s given i n f i g u r e 6. The s t i r r e d - c e l l r e a c t o r was operated batchwise with respect to the l i q u i d and semi-batchwise w i t h r e s p e c t to the gas-phase which was a l s o c i r c u l a t e d by means of a p e r i s t a l t i c pump over an i n f r a r e d spectrophotometer f o r C 0 d e t e c t i o n . The experiments s t a r t e d w i t h e q u i l i b r a t i o n of ~ 720 ml 0.35 mole 2


HtS

and

COt

Mass Transfer

385



Figure 5. Selectivity factor S as a function of kg a In the negligible interaction regime. Key: O, stirred cell reactor; +, wetted wall column, cocurrent; and X, wetted wall column (countercurrent). Ht


386


Ο JH2S •


—

JDIPA

calculated JH£JDIf^penetration th.) calculated JH2S,JDIFA(film th.)

Ίξ

ΐξ -

β [C02l (moles/ft ) 3

g

2u"

Ο Jc02'2x) • —

JDIPA calculated JQ)2 » -OlPA (penetration th.) calculated JC02. DIPA (Mm th.) J

ι 5

»

1 1

I 0

1

lH2S]g (moles/m ) 3

5

1

1 20

·»

Figure 4. Measured and calculated molefluxesas a function of gas-phase concen tration in the medium interaction regime in a stirred cell reactor at 40 rpm.



H*S and

CO*

Mass Transfer


31.

Figure 5. Measured and calculated selectivity factors as a function of gas-phase concentration in a stirred cell reactor at 40 rpm. Key: O, measurements; , penetration theory; and ,filmtheory.




388

Figure 7. A typical example of measured concentration curves during extreme interaction experiments. Key: · , [H S] ; and O, [CO ] . t

g

g

g


31.


H S and CO* Mass Transfer t

389

CC>2/mole DIPA c o n t a i n i n g 2.0 M s o l u t i o n a t 25 °C. E q u i l i b r a t i o n was checked by the IR-spectrophotometer and a f t e r t h i s , H 2 S was introduced i n t o the system a t a constant flow r a t e . The H 2 S gasphase c o n c e n t r a t i o n was obtained from the combination o f the pressure readings ( H 2 S + C O 2 ) and the I R - e x t i n c t i o n ( C O 2 ) . D i r e c t l y on admittance o f H S, CO2 desorbed from the s o l u t i o n i n t o the gas-phase and thus immediately r e s u l t e d i n a p o s i t i v e o v e r a l l (absorption) d r i v i n g f o r c e , but d e s o r p t i o n continued. A f t e r some 20-30 minutes the H 2 S flow was stopped to enable r e - e q u i l i b r a t i o n . I t was observed that CO2 was again absorbed i n t o the s o l u t i o n to almost the i n i t i a l e q u i l i b r i u m (see f i g u r e 7 f o r a t y p i c a l example). T h i s unambiguously proves t h a t the recorded c o n c e n t r a t i o n curves i n the gas-phase a r e due t o r e a c t i o n processes i n the p e n e t r a t i o n zone and have nothing to do w i t h bulk e q u i l i b r i u m which would not have lead t o r e - a b s o r p t i o n o f C O 2 . The t o t a l amount o f absorbed H2S was n e g l i g i b l e (0.02 mole/mole DIPA) and d i d not a f f e c t the bulk e q u i l i b r i u m .


2

Two experimental runs were performed. The H 2 S - and CO2 mole f l u x e s were obtained from the measured c o n c e n t r a t i o n curves by numerical d i f f e r e n t i a t i o n and are p l o t t e d i n f i g u r e 8a,b together with p e n e t r a t i o n and f i l m model c a l c u l a t i o n s . I t i s evident that f o r c e d d e s o r p t i o n can be r e a l i z e d under p r a c t i c a l c o n d i t i o n s and can be p r e d i c t e d by the model. In g e n e r a l , measured H 2 S mole f l u x e s are between the v a l u e s p r e d i c t e d by the models, whereas the CO2 f o r c e d d e s o r p t i o n f l u x i s l a r g e r than c a l c u l a t e d by the models. The CO2 a b s o r p t i o n f l u x , on the other hand, can c o r r e c t l y be c a l c u l a t e d by the models. T h i s probably i m p l i e s that the r a t e o f the r e v e r s e r e a c t i o n , i n c o r p o r a t e d i n equation ( 5 ) , i s underestimated. Moreover, i t should be kept i n mind that e s p e c i a l l y the r e s u l t s o f the c a l c u l a t i o n s i n the f o r c e d d e s o r p t i o n range are very s e n s i t i v e to i n d i r e c t l y obtained parameters ( d i f f u s i o n , e q u i l i b r i u m constants and mass t r a n s f e r c o e f f i c i e n t s ) and the numerical d i f f e r e n t i a t i o n technique a p p l i e d . Conclusions The phenomena d u r i n g simultaneous a b s o r p t i o n o f H 2 S and CO2 a r e c l a s s i f i e d i n t o three-regimes w i t h d i f f e r e n t extents o f i n t e r a c t i o n . I n the f i r s t regime ( n e g l i g i b l e i n t e r a c t i o n ) , the mole f l u x e s may be d e s c r i b e d by simple s i n g l e gas a n a l y t i c a l mass t r a n s f e r expressions and an e x p r e s s i o n f o r the s e l e c t i v i t y f a c t o r at complete H 2 S gas-phase l i m i t a t i o n i s d e r i v e d . I n the medium i n t e r a c t i o n regime, the mole f l u x e s measured f a l l between penet r a t i o n and f i l m theory c a l c u l a t i o n s . I n the extreme i n t e r a c t i o n regime, f o r c e d d e s o r p t i o n i s obtained both e x p e r i m e n t a l l y and t h e o r e t i c a l l y . The measured mole f l u x e s agree f a i r l y w e l l w i t h the c a l c u l a t i o n s , however with the e x c e p t i o n o f the CO2 d e s o r p t i o n f l u x which i s l a r g e r than c a l c u l a t e d . T h i s l a t t e r o b s e r v a t i o n may be a t t r i b u t e d to an incomplete d e s c r i p t i o n o f the r e v e r s e r e a c t i o n rate.



Figure 8a. Measured and calculated mole fluxes during extreme interaction experiments. Key: · , J ; O, J ; , penetration theory; and ,filmtheory. Ht8

COft



Figure 8b. Measured and calculated mole fluxes during extreme interaction experiments. Key is the same as in Figure 8a.



392 Legend o f Symbols f k kl,kg r 2

Ζ

enhancement f a c t o r r e a c t i o n r a t e constant (eqn.(5)) liquid/gas-phase mass t r a n s f e r c o e f f i c i e n t reaction rate dimensionless p e n e t r a t i o n depth a t t T , e

defined by : Ζ = x/J ο


1/8

mVmole s m/s mole/m^ s

vDco

π

τ

2

bulk liquid/gas

Literature Cited 1. Beenackers, A . A . C . M . , van Swaaij, W.P.M., Chem. Eng. J. 1978, 15, 25. 2. Blauwhoff, P.M.M., Assink, G . J . B . , van Swaaij, W.P.M., Proceedings NATO ASI, Turkey, August 1981. 3. Blauwhoff, P.M.M., Versteeg, G . F . , van Swaaij, W.P.M., to be published. 4. Blauwhoff, P.M.M., Van Swaaij, W.P.M., to be published. 5. Blauwhoff, P.M.M., Ph.D. Thesis, Twente University of Technology, the Netherlands, 1982. 6. Cornelisse, R . , Beenackers, A . A . C . M . , van Beckum, F . P . H . , Van Swaaij, W.P.M., Chem. Eng. Sci., 1980, 35, 1245. 7. Danckwerts, P . V . , Sharma, M.M., Chem. Eng. 1966, 10, CE 244. 8. Danckwerts, P . V . , "Gas-Liquid Reactions", McGraw-Hill, New York, 1970. 9. Danckwerts, P . V . , Chem. Eng. S c i . 1979, 34, 443. 10. Ramachandran, P . Α . , Sharma, M.M., Chem. Eng. S c i . 1971, 26, 349. 11. Secor, R . M . , Beutler, J.A., AIChE J. 1967, 13, 365. Received April 27, 1982.


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