Chemical Engineering Science Volume 51 Issue 20 1996 [Doi 10.1016%2F0009-2509%2896%2900265-5] J.W.a. de Swart_ R.E. Van Vliet_ R. Krishna -- Size, Structure and Dynamics of “Large”

8/10/2019 Chemical Engineering Science Volume 51 Issue 20 1996 [Doi 10.1016%2F0009-2509%2896%2900265-5] J.W.a. de

1/11

Pergamon

Chemical En~lineerin Science,

Vol. 51, No. 20, pp. 4619 4629, 1996

Copyright :~ 1996 Elsevier Science Ltd

Printed in Great Britain. All rights reserved

P I t : S 0 0 0 9 - 2 5 0 9 ( 9 6 ) 0 0 2 6 5 - 5 ooo9 2509/96 15.00 + 0.00

S IZ E, S T R U C T U R E A N D D Y N A M I C S O F L A RG E B U B B L E S

I N A T W O - D I M E N S I O N A L S L U R R Y B U B B L E C O L U M N

J . W . A . D E S W A R T , R . E . V A N V L I E T a n d R . K R I S H N A *

Dep ar tme n t o f Chem ica l Eng ineer ing , Un ivers i ty o f Amste rdam, Nieuw e Ach te rg rach t 166 , 1018 WV

Amste rdam, The Ne ther lands

Firs t rece ived 16 N o v e m b e r 1995; rev ised m anuscr ip t rece ived a nd accepted 28 F e b r u a r y 1996)

bstract This paper repor ts p re l iminary resu l ts o f a study on the hy drodynam ics o f a two-d im ens iona l

slurry bubble column. Experiments have been carried out with air /paraffin oil s lurries with solids concen-

t ra t ions o f 0 , 28 .3 and 38 .6 vo l% of porous s i lica pa r t ic les (mean d iamete r o f 38 tam) . Bubb le s izes, bubb le

coa lescence and bubb le b reak-up ra tes were de te rmined by v ideo image ana lys is . Inc reas ing s lu r ry

conc entra tion increases the size and size distr ibu tion of the large bubbles, defined here as havin g

d iamete rs la rge r than 10 mm . Inc reas ing s lu r ry concen t ra t ion reduces the to ta l gas ho ldup to a s ign if ican t

ex ten t ; th is reduc t ion is to be la rge ly a tt r ibu ted to the des t ruc t ion o f the smal l bubb le popu la t ion , wh ich

have bubb le d iam ete rs smal le r than 10 mm . Video imag ing exper imen ts lead to new ins igh ts in to the mass

t rans fe r mechan ism s f rom la rge bubbles. These la rge bubb les a re con t inua l ly coa lesc ing and b reak ing

up . The coa lescence and b reaku p ra tes were de te rmined by a f rame-by- f rame ana lys is o f the v ideo

record ings and found to be a t leas t 4 s - t . A popu la t ion mode l fo r mass t rans fe r has been se t up and used to

es tab l ish tha t f requen t b ubb le -b ubb le in te rac t ions cou ld lead to an o rder o f magn i tude increase in the mass

transfer rates for the large bub ble class. Cop yrigh t :~ 1996 Elsevier Science Ltd

Ke y wor ds :

Bubble columns, large bubbles, small bubbles, bubble size distr ibution, gas holdup, bubble

coalescence, bubble breakup.

IN TR O D U C TIO N

T h e b u b b l e c o l u m n s l u r r y r e a c t o r i s a n a t t r a c t i v e

r e a c t o r t y p e f o r r e l a t i v e l y s l o w , e x o t h e r m i c l i q u i d

p h a s e c a t a l y t i c p r o c e s s e s . F o r e x a m p l e , f o r t h e i n d u s -

t r ia l l y i m p o r t a n t F i s c h e r T r o p s c h s y n t h es i s o f h y d r o -

c a r b o n s f r o m s y n t h e s i s , F o x ( 1 9 9 0 ) , J a g e r a n d

E s p i n o z a ( 1 9 9 5 ) a n d D e S w a r t

e t a l .

( 1 9 9 5 ) h a v e c o n -

c l u d e d t h a t t h e b u b b l e c o l u m n s l u r ry r e a c t o r , o p e r a t -

i n g in t h e c h u r n - t u r b u l e n t r e g i m e , i s t o b e p r e f e r r e d t o

t h e m u l t i - t u b u l a r t r i ck l e b e d t e c h n o l o g y o n b o t h t e c h -

n i c a l a n d e c o n o m i c g r o u n d s . I n t h e c h u r n - t u r b u l e n t

r e g i m e o f o p e r a t i o n o f a b u b b l e c o l u m n , l a r g e a n d

s m a l l b u b b l e s a r e k n o w n t o c o - e x is t ( E l l e n b e r g e r

a n d K r i s h n a , 1 9 9 4 ; K r i s h n a a n d E l l e n b e r g e r , 1 9 9 5 ) .

T h e l a r g e b u b b l e s , w h i c h h a v e ri s e v e l o c i t i e s t y p i -

c a l l y o f t h e o r d e r o f 1 .5 m s t , l a r g e l y d i c t a t e t h e g a s

p h a s e c o n v e r s i o n i n t h e c h u r n - t u r b u l e n t r e g i m e .

T h o u g h t h e h y d r o d y n a m i c s o f b u b b l e c o l u m n s s l u r ry

r e a c t o r s h a s b e e n s t u d i e d b y s e v e r a l w o r k e r s [ s e e e .g .

D e c k w e r e t a l . (1980 , 1992 , 1993) ; Kara e t a l . (1982);

K o i d e

e t a l .

( 1 9 8 4 ) ; K e l k a r

e t a l .

( 1 9 8 4 ) ; F u k u m a

e t a l .

( 1 9 8 7 ) ; S c h u m p e

e t a l .

( 1 9 8 7 ) ; O ' D o w d

e t a l .

(1987);

B u k u r

e t al .

(1987 , 1990) ; Saxena

e t a l .

(1992, 1993,

1 99 5) ; D e S w a r t a n d K r i s h n a ( 1 9 9 5) ] , th e r e i s n o s t u d y

i n w h i c h t h e c h a r a c t e r i s t i c s o f t h e s e l a r g e b u b b l e s

h a v e b e e n e l u c i d a t e d . T h e b r o a d o b j e c t i v e o f th e p r e s -

e n t s t u d y i s to p r d v i d e i n f o r m a t i o n o n t h e s iz e a n d

s t r u c t u r e o f t h e s e l a r g e b u b b l e s b y us e o f v i d e o

*Co rrespon ding author. E-m aih krishna@chemeng, chem.

uva.nl.

i m a g i n g t e c h n i q u e s i n a t w o - d i m e n s i o n a l c o l u m n .

A f r a m e - b y - f r a m e a n a l y si s o f t h e v i d e o i m a g e s a l s o

p r o v i d e d s o m e f r e s h i n s i g h t s i n t o t h e c o a l e s c e n c e -

b r e a k u p p h e n o m e n o n o f t h e l a r ge b u b b l e p o p u l a -

t i o n .

A f u r t h e r i s s u e w h i c h h a s b e e n a d d r e s s e d i n t h i s

p a p e r i s t h e m a s s t r a n s f e r f r o m l a r g e b u b b l e s . V e r -

m e e r a n d K r i s h n a ( 19 8 1) m e a s u r e d t h e v o l u m e t r i c

m a s s t r a n s f e r c o e f f i c i e n ts f r o m t h e l a r g e b u b b l e s i n t h e

s y s t em n i t r o g e n t u r p e n t i n e a n d f o u n d v a l u e s a b o u t

a n o r d e r o f m a g n i t u d e h i g h e r t h a n t h a t e x p e c t e d o n

t h e b a s i s o f t h e v i s u a l l y o b s e r v e d b u b b l e s i z es f o r

c h u r n - t u r b u l e n t o p e r a t i o n . T h e y a t t r ib u t e d t h e m e a s -

u r e d h i g h v a l u e s o f m a s s t r a n s f e r c o e f f i c i e n t s t o t h e

v i o l e n t l y t u r b u l e n t n a t u r e o f t h e l i q u i d p h a s e . I n th e

p r e s e n t p a p e r , w e e x a m i n e w h e t h e r b u b b l e - b u b b l e

i n t e r a c t i o n s a r e t h e l i k e l y c a u s e o f t h e p a r a d o x i c a l l y

h i g h m a s s t r a n s f e r c o e f f ic i e n t s; S i t a n d G r a c e ( 1 98 1 )

h a v e s h o w n t h a t b u b b l e - b u b b l e i n t e r a c t i o n s in

a g a s - s o l i d b u b b l i n g f l u i d b e d l e a d s t o a n i m p r o v e -

m e n t i n t h e i n t e r p h a se m a s s t r a n s fe r r a t e a n d o n e m a y

w o n d e r i f a n a n a l o g o u s p h e n o m e n o n e x i st s f o r

g a s l i q u i d (s l u r ry ) b u b b l e c o l u m n s .

EX PER IM EN TA L SET U P A N D SY STEMS STU D IED

A l l e x p e r i m e n t s w e r e c a r ri e d o u t i n a t w o - d i m e n -

s i o n a l c o l u m n c o n s i s t in g o f t w o p a r a l l e l 7 m m t h i c k

g l a s s p l a t e s o f 2. 5 m h e i g h t a n d 0 .3 m w i d t h , p l a c e d a t

a d i s t a n c e o f 0 .0 0 5 m . T h e g a s p h a s e w a s d i s t r i b u t e d

i n t o t h e c o l u m n b y a g l as s s i n t e r e d p l a t e w i t h a p o r e

d i a m e t e r o f 2 00 ~t m . T h e c o l u m n w a s e q u i p p e d w i t h

4619


2/11

4620

a q u ic k c lo s in g v a lv e p l a c e d n e a r th e g a s d i s t r ib u to r .

A p re s s u re t a p w a s in s t a l l e d a t 1 . 2 0 m h e ig h t . T h e

t o t a l g a s h o l d u p w a s d e t e r m i n e d f r o m m e a s u r e m e n t s

o f t h e s t a t i c p r e ss u r e d r o p u s i n g h i g h a c c u r a c y

V a l i d y n e D P 1 5 p r e s s u r e tr a n s d u c e r s. A P a n a s o n i c

D S P c o l o u r C C D c a m e r a w a s p l a c e d p e r p e n d i c u l a r

to th e c o lu m n a t a d i s t a n c e o f 1 .1 5 m f ro m th e f ro n t

fa ce . T h e c a m e ra e i th e r r e c o rd e d a t a h e ig h t o f 0. 65 o r

1 .1 5 m f ro m th e g a s d i s t r ib u t o r p l a t e . A s h u t t e r s p e e d

o f 1 / 20 0 0 w a s e m p l o y e d t o a v o i d b l u r r i n g o f th e v i d e o

i m a g e s d u e t o t h e m o t i o n o f t h e g a s b u b b l e s . T o

i m p r o v e t h e c o n t r a s t b e t w e e n t h e b u b b l e s a n d t h e

l iq u id p h a s e , t h e t e c h n iq u e o f d i ffu s e b a c k l ig h t in g w a s

u s e d (L u n d e a n d P e rk in s , 1 9 9 5 ) a n d p p m q u a n t i t i e s o f

d y e S u d a n g re e n 9 8 8 w e re a d d e d to th e l i q u id . T w o

1 25 0 W h a l o g e n l a m p s w e r e d i r e c t e d o n a w h i t e p a n e l

t o p r o v i d e a s m o o t h a n d e v e n b a c k g r o u n d . T h e v i d e o

s i g n a l p r o d u c e d b y t h e c a m e r a w a s d i g i t i z e d a t a r a t e

o f 2 5 f r a m e s p e r s e c o n d us i n g a M i r o V I D E O D C I

d i g i t i z e r b o a r d p l a c e d i n s id e a P C . T h e r e a l t i m e

s i g n a ls w e re d i r e c t e d t o a S o n y c o l o u r v i d e o m o n i t o r

f o r o n - l i n e c o n t r o l o f t h e c a m e r a o u t p u t . T h e c a p t u r e d

i m a g e s w e re t r a n s f e rr e d t o a P C a n d p r o c e s s e d u s i n g

t h e c o m m e r c i a l i m a g e p r o c e s s i n g s o f t w a r e S C I L - I m -

a g e TM S C I L - I m a g e

M

i s d e v e l o p e d b y t h e C o m p u t e r

S y s te m s G r o u p o f th e U n i v e rs i ty o f A m s t e r d a m a n d

T N O I n s t i t u t e o f A p p l i e d P h y s i c s in D e l f t, T h e N e t h -

e r l a n d s . F ig u re 1 s h o w s th e e x p e r im e n ta l s e tu p s c h e -

ma t i c a l ly .

P a r a f f in i c m i n e r a l o i l ( d e n si t y , P L 8 0 0 k g m 3;

viscos i t y , L = 0 .027 Pa s ; su rface tens ion , cr =

0 .0 2 8 N m- 1 ) w a s u s e d a s l i q u id p h a s e . A i r w a s u s e d

J W A D E S W A RT e t a l

a s th e g a s p h a s e in a l l e x p e r ime n t s a n d p o ro u s s i l i c a

p a r t i c l e s ( s k e l et o n d e n s i t y = 2 1 0 0 k g m - 3 ; p o r e v o l -

u m e = 1 . 0 5 m l g - ~ ; p a r t i c l e si z e d i s t r i b u t i o n : 1 0 % ,

< 2 7 m; 5 0 %, < 3 8 m; 9 0 % , < 4 7 l~m) fo rm e d th e

s u s p e n d e d s o l i d s. E x p e r i m e n t s w e r e c a r r i e d o u t w i t h

s o l id s c o n c e n t ra t io n o f 0 , 28 .3 , a n d 3 8 .6 v o l% s o l id s

(on a gas -free s lu rry bas is ) .

I M A G E A N A L Y S I S

A t a g iv e n s u p e r f i c i a l g a s v e lo c i ty U a n d h e ig h t

a b o v e t h e d i s t r i b u t o r h , o n e e x p e r i m e n t a l r u n f o r

i m a g e p r o c e s s i n g p u r p o s e s i s p e r f o r m e d . A n e x p e r i -

me n ta l ru n c o n s i s t s o f t h re e s a m p le s o f e ig h t s e c o n d s ,

r e s u l t in g in 6 0 0 ima g e s . T h e c a p tu re d im a g e s a re o f

t h e T a g g e d I n t e r c h a ng e F i l e F o r m a t ( T I F F ) w i t h 2 4

b i t c o l o r d e p t h a n d a n a s p e c t r a t i o o f 1 :1 . A f t e r

c a p t u r i n g , t h e i m a g e s a r e s e p a r a t e l y p r o c e s se d u s i n g

t h e S C I L - I m a g e TM s o f tw a re p a c k a g e . U s in g th i s s o f t -

w a r e p a c k a g e s e v e r a l i m a g e p r o c e s s i n g s t e p s c a n b e

a u t o m a t e d , w h i c h i s a n e c e s s it y w h en a n a l y z i n g l a rg e

a m o u n t s o f d a ta . T h e f i rs t st e p i n t h e i m a g e p r o c e s s i n g

i s t h e c o n v e r s io n o f t h e 2 4 b i t (t ru e c o lo r ) ima g e s in to

8 b i t (g ra y s ca l e ) ima g e s . E a c h p ix e l i n th e im a g e h a s

n o w a s o -c a l l e d g ra y v a lu e r a n g in g f ro m 0 to 2 5 5.

A g r a y v a l u e o f 0 c o r r e s p o n d s t o b l a c k a n d a g r a y

v a lu e o f 2 5 5 to w h i t e . A re g io n o f i n t e re s t i s t h e n

d e f in e d b y c ro p p in g th e im a g e to 2 6 0 2 7 6 p ix e l s ,

r e p re s e n t in g th e 0. 3 x 0 .3 m w in d o w o f o b s e rv a t io n in

t h e c o l u m n . O n e p i x e l l e n g t h i s t h e r e f o re a p p r o x i m -

a te ly e q u a l t o 1 mm d i s t a n c e . A ty p ic a l p i c tu re r e s u l t -

in g f ro m th e f i r s t ima g e p ro c e s s in g s t e p s i s s h o w n in

F ig . 2 (a ) fo r t h e a i r /p a ra f f in o i l s y s t e m.

im a g e c a p t u r i n g v i d e o

P C

m o n i t o r

image processing

P C

0 0 0 5 m

g r a d u a te d - - i

ru le r

2 D g l a s s

c o l u m n

c V I t

0 3 0 m

1 T h

g x , y) = i f f x , y ) < T h ' (1)

w h e r e g x , y ) i s t h e g re y l e v e l o f t h e c o r re s p o n d in g

p ic tu re in th e r e s u l t in g b in a ry im a g e .

A p p l i c a t io n o f t h i s t h re s h o ld in g to F ig . 2 (a ) r e s u l t s

i n t h e b i n a r y i m a g e s h o w n i n F i g . 2 (c ) . T h e e n t r o p y

m e t h o d f o r t h r e s h o l d i n g a n i m a g e i s p r e f e r a b l e w h e n

t h e t w o p e a k s i n t h e g r a y l e ve l d i s t r i b u t i o n a r e s e p a r -

a t e d b y a w id e a n d f l a t v a l l e y . A s th i s i s n o t t h e c a s e in

th e p re s e n t e x p e r im e n t , t h e th re s h o ld l e v e l i s c h o s e n

b y v i s u a l i n s p e c t io n a s in d ic a t e d in F ig . 2 (b ) ; d u e to

t h e s h a r p v a l l e y i n t h e h i s t o g r a m t h e r e i s n o a m b i -

g u i t y r e g a r d i n g t h e v al u e o f T h . N o t e t h a t n o i m a g e

e n h a n c e m e n t h a s b e e n a p p l i e d i n o r d e r t o p r e s e r v e a s

m u c h o f t h e r a w d a t a a s p o s s i bl e . T h e b i n a r y i m a g e

i s t h e n s u b d iv id e d ( l a b e l l e d ) i n to d i f f e re n t c o m p o -

n e n t s , b a s e d u p o n a c o n n e c t iv i ty a n a ly s i s . T h e l a s t

s t e p i n t h e a n a l y s i s o f t h e i m a g e s i s th e m e a s u r e m e n t

o f th e s h a p e o f e a c h o b je c t i n th e im a g e . O b je c t

p r o p e r t i e s s u c h a s a r e a , p e r i m e t e r , w i d t h a n d h e i g h t

c a n b e m e a s u re d . T h e p re s e n t s tu d y i s fo c u s e d o n th e

a re a o f t h e o b je c t s .

A f t e r c o m p l e t i o n o f t h e i m a g e a n a l y s i s t h e d a t a

h a v e to b e p ro c e s s e d . A s th e a s p e c t r a t io o f t h e im a g e s

i s 1 : 1 , t h e n u m b e r o f p ix e l s t h a t fo rm a n in d iv id u a l

b u b b l e a r e e a s i l y c o n v e r t e d t o t h e b u b b l e a r e a A b b y

m u l t ip ly in g w i th a l i n e a r s c a l e f a c to r . T h e e q u iv a le n t

b u b b l e d i a m e t e r c a n b e c a l c u l a t e d d i re c t l y f r o m t h e

b u b b l e a r e a :

d b = X / ~ A ~ .

(2)

T h e c a l c u l a t i o n o f th e g a s h o l d u p i n a n i m a g e f o l lo w s

f ro m :

2 Aobj

e , - , 3 )

Aim

w h e re A o b j i s t h e a re a o f o n e o b je c t i n p ix e l s a n d

A im re p re s e n t s t h e to t a l a re a o f t h e im a g e ( i . e .

2 6 0 x 27 6 = 7 1 , 7 6 0 p ix e ls ) . T h e s a m e e x p re s s io n c a n

a l s o b e u s e d to c a l c u la t e th e g a s h o ld u p o f a c e r t a in

bubble s ize c lass ; in th is

case ob j

r e p re s e n t s t h e a re a

o c c u p ie d b y o n e o b je c t i n th a t b u b b le c l a s s . T h e

p r o c e d u r e w a s f i r s t c a l i b r a t e d b y v i d e o i m a g i n g o b -

j e c t s ( c i rc l e s, s q u a re s ) o f k n o w n a re a s .

TOTAL GAS HO LDU P, BUBBLE SIZE AND BUBBLE SIZE

DISTRIBUTION

F ig u re 3 s h o w s th e to t a l g a s h o ld u p v s th e s u p e r f i -

c i a l g a s v e lo c i ty fo r a i r /p a ra f f in s lu r r i e s c o n ta in in g 0 ,

2 8 .3 a n d 3 8 .6 v o l% s i l i c a p a r t i c l e s . T h e to t a l g a s h o ld -

u p d e c re a s e s s ig n i f i c a n t ly w i th in c re a s in g s o l id s c o n -

c e n t r a t i o n . T h e s a m e t r e n d h a s b e e n f o u n d f o r c o l -

u m n s o f c i r c u l ar c r o s s se c t i o n b y K o i d e e t a l . (1984),

K a r a

e t a l .

(1982) , Ke lkar

et a l .

(1984) , De Swart and

K r i s h n a (1 9 9 5 ) a n d Y a s u n i s h i e t a l . (1986).

T h e e f fe c t o f t h e s u p e r f i c i a l g a s v e lo c i ty a n d th e

s o l i d s c o n c e n t r a t i o n o n t h e b u b b l e s i z e d i s t r i b u t i o n

w a s in v e s t ig a t e d u s in g im a g e a n a ly s i s . F o r e a c h e x -

p e r i m e n t a l r u n t h e b u b b l e s i z e d i s t r i b u t i o n w a s c a l -

c u la t e d u s in g 6 0 0 f r a m e s ( c o r re s p o n d in g to 2 4 s v id e o

r e c o rd i n g ) . T o s h o w t h e g a s h o l d u p s t r u c t u r e t h e

b u b b l e s i z e d i s t r i b u t i o n s a r e e x p r e s s e d i n i n d i v i d u a l

g a s f r a c t io n s in th e c o lu m n . F ig u re 4 s h o w s th e in f lu -

e n c e o f t h e s u p e r f i c i a l g a s v e lo c i ty o n th e b u b b le s i z e

d i s t r ib u t io n fo r p a ra f f in o i l . In c re a s in g th e s u p e r f i c i a l

g a s v e l o c it y l e a d s t o f o r m a t i o n o f l a r g e r b u b b l e s a n d

a l s o in c re a s e s th e b u b b le s i z e d i s t r ib u t io n . In F ig . 5

th e b u b b le s i z e d i s t r ib u t io n i s s h o w n fo r p a ra f f in o i l

s lu r r i e s o f 0 , 2 8 .3 a n d 3 8 .6 v o l% c o n c e n t ra t io n . F o r

th e s e th re e s e r i e s th e s u p e r f i c i a l g a s v e lo c i ty i s k e p t


4/11

4622

J . W . A . D E S W A R T

e t a l

c o n s t a n t a t a v a l u e o f a r o u n d 0 .1 0 m s - 1 . I t c a n b e

s e e n

t h a t a s t h e s o l i d s c o n c e n t r a t i o n i s i n c r e a s e d th e

s m a l l b u b b le s , s m a l l e r t h a n s a y 1 0 m m in s iz e , d i s -

a p p e a r , t h e i r c o n t r i b u t i o n t o t h e g a s h o l d u p d e c r e a s e s

s i g n if i c a nt l y . F u r t h e r m o r e , t h e b u b b l e s iz e d i s t r i b u -

t i o n b r o a d e n s a n d t h e a v e r a g e b u b b l e s i z e b e c o m e s

l a r g e r . F i g u r e 6 s h o w s t h r e e g r a b b e d , a n d r e t r a c e d ,

v id e o im a g e s a s v i s u a l s u p p o r t fo r t h i s c o n c lu s io n ;

f ro m th e s e p i c tu re s i t c a n c l e a r ly b e s e e n th a t t h e

s m a l l b u b b l e s d i s a p p e a r a n d t h e l a r g e b u b b l e s

b e c o m e l a r g e r a s t h e s o l i d s c o n c e n t r a t i o n i s i n c r e a se d .

F r a m e - b y - f r a m e v i s u a l e x a m i n a t i o n o f th e v i d e o

i m a g e s a l s o r ev e a l e d th a t b u b b l e s s m a l l e r t h a n 1 0 m m

h a v e t h e b a c k m i x i n g c h a r a c t e r i s t i c s o f t h e l i q u i d

p h a s e . B u b b l es l a r g e r t h a n 1 0 m m , o n t h e o t h e r h a n d ,

0.5

t r a v e r s e d u p t h e c o l u m n v i r t u a l l y i n p l u g f l ow . T h e

l a r g e b u b b l e p o p u l a t i o n c a n t h e r ef o r e b e d e f in e d a s

h a v i n g b u b b l e s iz e s la r g e r t h e n 1 0 m m . U s i n g t h e

S C I L - I m a g e s o f t w a r e a l l o b j e c t s s m a l l e r t h a n

1 0 r a m c a n b e a u t o m a t i c a l l y r e m o v e d i n o r d e r t o

fo c u s o n th e l a rg e b u b b le p o p u la t io n ; s ee F ig s 7 (a )

a n d (b ) . F o r th e 2 8 .3 a n d 3 8 .6 v o l% s lu r ry c o n c e n t ra -

t i o ns , th e b u b b l e p o p u l a t i o n s m a l l e r t h a n 1 0 m m i s

v i r t u a l l y d e s t r o y e d c f F ig . 6 ) a n d th e w h o le b u b b le

p o p u l a t i o n c a n b e c o n s i d e r e d t o b e l a r g e .

T h e a v e ra g e l a rg e b u b b le s i z e in c re a s e s w i th in -

c re a s in g s u p e r f i c i a l g a s v e lo c i ty a n d s lu r ry c o n c e n t ra -

t io n ; s e e F ig . 8 . F o r th e 2 8 . 3 v o l% s lu r ry c o n c e n t ra -

t io n s , t h e a v e ra g e b u b b le s i z e h a s b e e n m e a s u re d a t

h e ig h t s H = 0 .6 5 a n d 1 . 1 5 m a b o v e th e d i s t r ib u to r .

T h e r e s u l t s s h o w a s l ig h t i n c re a s e in th e a v e ra g e

b u b b l e d i a m e t e r w i t h i n c r e a s i n g H , p o i n t i n g t o i n -

c r e a s i n g c oa l e s c e n c e a s o n e p r o c e e d s u p t h e c o l u m n .

[ 1

[ ]

[ ] c = o

c = 0 . 2 8 3

v c . = 0 . 3 8 6

0 I I

U l [ m l s ] 0 . 4

Fig. 3. Influence of increased solids concen tratio n on th e

total gas holdup with air/paraffin slurries.

B U B B L E B U B B L E I N T E R A C T IO N S

I n o r d e r t o g a i n f u r t h e r i n s i g h ts i n t o t h e m e c h a n i s m

o f m a s s t r a n s f e r f r o m t h e l a r g e b u b b l e p o p u l a t i o n w e

r e s o r t e d t o a c a r e f u l f r a m e - b y - f r a m e a n a l y s i s o f th e

v id e o r e c o rd in g s . F ig u re 9 s h o w s e ig h t s e q u e n t i a l p i c -

t u r e s ( f r a m e s ) t a k e n f r o m a n e x p e r i m e n t a l r u n w i t h

th e 2 8 . 3 v o l% p a ra f f in o i l s lu r ry a t a s u p e r f i c i a l g a s

v e lo c i ty o f 0 .0 9 m s - 1. T h e t im e in t e rv a l b e tw e e n th e

i n d i v i d u a l f r a m e s i s 4 0 m s a n d t h e s m a l l b u b b l e s ,

s m a l l e r t h a n l 0 m m , h a v e b e e n f i l te r e d o u t . T w o b u b -

b le s A a n d B a re fo l lo w e d a s th e y r i s e th ro u g h th e

c o lu m n . I t c a n b e s e e n f ro m f ra m e s 1 to 4 th a t b u b b le

B r i s e s f a s t e r t h a n b u b b le A . In f r a m e 5 b u b b le

0 0 1 8

E

[ ]

. . . . . . .

. . - - '

. . . . . . '

i i

i /

. .. .. . o . 2 o m s

. . , ~ U - -

. . . -

a b [ m ]

. -

0 1 5

Fig. 4. Influence of the superficial gas velocity on the gas hol dup structure for the system: air/paraffin oil.

Measurements made at a height H = 0.65 m a bove the dis tributor.


5/11

Large b u b b l e s i n a t w o - d i m e n s i o n a l s l u rr y b u b b le c o l u m n 4623

0 0 1 8

. . . . . . . . . . , . , .

. . - , ' ~ " ~ . . . . . . . .

. , . . . . . . . .

. . " ' " i " ~ " " " " " " - . . .

. . . . .- " " . - " " ' ~ . . . . .. . . . .. . . . .. - . . ~ : . . . . . ~ . . . . . .

" " " " " " " "

I

. . . - . :

E

[ ]

/ co =o 386

/ U = 0 0 9 m / s

. . "

~=0

U = 0 t 1 m / s

0 2 0

F i g . 5 . I n f l u en ce o f in crea s ed s o l i d s co n ce n tra t i o n o n th e g a s h o l d u p s t ru c tu re fo r th e s y s t em a i r / p a ra f f i n o i l

s l urr ie s . M ea s u r em en ts m a d e a t a h e i g h t H = 0 . 6 5 m a b o v e th e d i s t r ib u to r .

3 0 c m

c = o

U = 0 1 1 m / s

C s = 0 2 8 3

U = 0 0 9 m / s

C s = 0 3 8 6 /

U = 0 0 9 m / s

F i g . 6 . I n f l u en ce o f in crea s ed p a r t i c l e co n cen tra t i o n : i mp r es s i o n o f th ree re tra ced v i d eo i m a g es o b ta i n ed a t

0 . 6 5 m a b o v e th e d i s t r ib u to r .

B r e a c h e s th e w a k e o f b u b b le A a n d c o a l e s c e n c e

f o l l o w s ; in f r a m e 6 , A a n d B a r e c o a l e s c e d a n d b u b b l e

A B i s f o r m e d . B u b b l e s D a n d E i n f l a m e 7 c o a l e s c e t o

f o r m D E i n f r a m e 8 . L e t u s n o w t r a c k t h e h i s t o r y o f

b u b b l e C i n f r a m e s 1 , 2 , 3 a n d 4 . I n f l a m e 4 b u b b l e

C b r e a k s u p i n t o b u b b l e s C 1 a n d C 2 .

T o o b t a i n q u a n t i t a t i v e d a t a o n t h e b u b b l e b r e a k - u p

a n d c o a l e s c e n c e r a t e s f o r t h e 28 . 3 v o l s l u r r y a t


6/11

4624 J .W .A . DE SWART

t a l

Fig. 7. Im age processing: f i ll ing of gaps in the bina ry image (b) remov al of objects sma ller than 10 mm

from the image.

0 . 0 7 C , = 0 . 3 8 6, H = 0 .6 5 m / . 1 ~ s ~ . ~ - ~ - - - ~ '

o .o 6 ~ < ~ v j

0.0 5 C, = 0.283,H = 1.15 m

d b , ~ . ~ 0 , 0 4

[, n ] 0 .0 3 ~ - ~

= 0 . 65 m ~ 3

0 , 0 2 [ , C~ = 0 , H = 0 . 65 m

0 . 0 1

0 0 0 , 0 5 0 1 0 . 1 5 0 2 0 , 2 5

u4m/s]

Fig. 8. Influe nce of superficial gas veloci ty and slurry con-

cen t ra t ion on the mean d iamete r o f the l a rge bubb le popu-

la t ion . Measurements a t H = 0 .65 m above the d i s t r ibu to r

for air /paraff in oi l s lurries for 0, 28.3 and 38.6 vol% slurr ies

and at H = 1.15 m for the 28.3 vol% slurry.

a s u p e r f i c i a l g a s v e l o c i t y o f 0 .0 9 m s - 1 , a d e t a i l e d

f r a m e - b y - f r a m e a n a l y s i s o f t h e 8 - s r e c o r d i n g , e q u i v a -

l e n t to 2 0 0 f r a m e s , w a s c a r r i e d o u t . F i r s t l y , t h e l a r g e

b u b b l e p o p u l a t i o n , d e f in e d a s i n d i c a te d a b o v e b y u s -

i n g a c u t - o f f b u b b l e s i ze o f 1 0 m m , w a s s p l i t u p i n

6 d i f f e r e n t b u b b l e s i z e c l a s s e s ( 0 .0 1 - 0 .0 2 , 0 . 0 2 - 0 .0 4 ,

0 .0 4 - 0 .0 6 , 0 . 0 6 - 0 .0 8 , 0 . 0 8 - 0 .1 a n d > 0 .1 m ) . F o r e a c h

o f t h e s e b u b b l e c l a s s e s , i n d i v i d u a l b u b b l e s w e r e v i s -

u a l l y tr a c k e d t o d e t e r m i n e t h e d e a t h r a te s , d e f in e d a s

t h e f r a c t i o n o f t h e g a s h o l d u p i n t h e b u b b l e c l as s

u n d e r c o n s i d e r a t i o n w h i c h d i s a p p e a r s b y e i th e r c o -

a l e s c e n c e o r b r e a k - u p t o o t h e r b u b b l e s i z e c l a s s e s .

A p a r a l l e l a n a l y s i s w a s c a r r i ed o u t t o d e t e r m i n e t h e

b i r t h r a t e o f a c e r t a i n b u b b l e c la s s, r e p r e s e n t i n g t h e

c r e a t i o n o f t h e g a s f ra c t i o n p e r s e c o n d b y a p r o c e s s o f

c o a l e s c e n c e o r b r e a k u p o f o t h e r b u b b l e s i z e cl a ss e s.

B y a c l a s s -b y - c l a s s a n a l y s i s o f 2 0 0 c o n s e c u t i v e f r a m e s ,

t h e b i r t h a n d d e a t h r a t e s w e r e c a lc u l a t e d ; t h e s e a r e

s h o w n i n F i g . 1 0. I t is to b e n o t e d t h a t f o r e a c h b u b b l e

c l a ss t h e b i r t h a n d d e a t h r a t e s a r e c l o s e t o e a c h o t h e r ,

a s w o u l d b e e x p e c te d f o r a s y s t e m a t d y n a m i c e q u i l i b -

r i u m i n w h i c h t h e b u b b l e s i ze d i s t r i b u t i o n i s p r e s e r-

v e d . L e t u s d e n o t e s Ri a s t h e r e f r e s h m e n t r a t e , b i r t h o r

d e a t h r a t e , o f t h e b u b b l e c l a s s i, w i th t h e u n i t s s - 1. W e

n o t e t h a t t h a t s B i i n c r e a s e s a s t h e s i z e o f t h e b u b b l e

c l a ss i n c re a s e s . P u t a n o t h e r w a y , l a rg e r s i z ed b u b b l e s

a r e r e f r e s h e d m o r e o f t e n , d u e t o c o a l e s c e n c e a n d

b r e a k - u p t h a n s m a l l e r s iz e d b u b b l e s ; th i s i s i n c o n -

f o r m i t y w i t h o u r i n t u i t i o n . T h e r e f r e s h m e n t f r e q u e n c y

f o r t h e s m a l l e s t s i z e c l a s s 1 ( w i t h a n a v e r a g e d i a m e t e r

o f 0 . 0 15 m ) i s a b o u t 4 s - x. T h e r e f r e s h m e n t f r e q u e n c y

i n c r e a s e s to a b o u t 1 5 s - 1 f o r l a rg e s t b u b b l e s i ze c la s s

6 ( d ia m e t e r s l a r g e r t h a n 0 .1 m ). L a r g e r s i z ed b u b b l e

c l a ss e s t h e r e f o r e s u f fe r m o r e fr e q u e n t i n t e r c h a n g e

w i t h o t h e r b u b b l e c l as s es .

F u r t h e r , s o m e i d e a o f i n t e r c h a n g e b e t w e e n b u b b l e

c la s se s w a s o b t a i n e d b y t r a c k i n g t h e n u m b e r o f b u b -

b l e s i n c la s s i w h i c h b r e a k - u p o r c o a l e sc e i n t o c l a ss j .

T h e b u b b l e e x c h a n g e m a t r i x f o r t h e 2 8 .3 v o l % s l u r ry

i s s h o w n i n T a b l e 1. T h i s s h o w s t h a t t h e n u m b e r o f

b u b b l e s i n v o l v e d i n t h e b u b b l e c la s s i n t e r c h a n g e p r o -

c e s s d e c r e a s e s w i t h i n c r e a s i n g b u b b l e s i z e c l a ss . I f

a s u f f i c ie n t ly la r g e n u m b e r o f f r a m e s i s a n a l y z e d , t h e

b u b b l e e x c h a n g e m a t r i x m i g h t b e ex p e c t e d t o b e s y m -

m e t r i c ; o u r r e s u l ts i n T a b l e 1 s h o w t h i s m a t r i x t o b e

n e a r l y s y m m e t r i c .

S u m m a r i z i n g i n w o r d s t h e f i n d i n g s o f F i g . 1 0 a n d

T a b l e 1 , w e c a n s a y t h a t l a r g e r b u b b l e s i z e cl a ss e s a r e

r e f re s h e d m o r e f r e q u e n t l y b u t a s m a l l e r n u m b e r o f t h e s e

a r e i n v o l v e d i n a n i n t e r c h a n g e p r oc e ss . T h e b u b b l e -

b u b b l e e x c h a n g e r a t e b e t w e e n a n y t w o c l as s e s c a n b e

e x p e c t e d t o b e d i c t a t e d b y t h e r e f r e s h m e n t r a t e o f t h e

s m a l l e r b u b b l e c l a ss s B i . F o r e x a m p l e , i n t e r c h a n g e

b e t w e e n c la s s es 1 a n d 2 c a n b e e x p e c t e d t o b e a t

a f requency o f , say , 4 s - 1 .


7/11

3

c m

L a r g e b u b b l e s i n a t w o - d i m e n s io n a l s l u r ry b u b b l e c o l u m n

1

4625

4 m s 4 m s 4 m s

Fig . 9 . E ight c o nse c ut ive f r a m e s of the a i r /28 .3 vol% oi l s lur ry : c oa le sc e nc e of the l a rge bub ble s . Re c orde d

at a h e igh t of 0.65 m an d a su perf ic ia l gas ve loci ty of 0.09 m s 1.

B~

[ s q

2

death birth i Cs= 0.283

rate ~ ~ r a t e [I h=O.65mU=O'O9m/s

? u b ? i y c l a ~ y l

1 2 3 4 5 6

Bubble Class

Fig . 10 . B i r th a nd de a th r a te s for d i f f e re nt bubble c la s se s ,

e xpre s se d a s the f r a c t ion of the ga s holdup of a bubble c la s s

whic h i s los t (de a th) or ga ine d (b i r th) due , r e spe c t ive ly to

bre a k up or c oa le sce nc e . Sys te m : a ir /28 .3 vol% oi l s lur ry ,

r e c orde d a t a he igh t of 0 .65 m a nd a supe r f i c ia l ga s ve loc ity

of 0.09 m s- i .

A P O P U L A T I O NB A L A N C EM O D E L F O R M A S ST R A N S F E R

F R O M L A R G E B U B B L E S

F o r t h e l a r g e b u b b l e p o p u l a t i o n c o n t a i n i n g

n b u b b l e s i z e c l a s s e s , w e e n v i s a g e a m a s s t r a n s f e r

m e c h a n i s m a s p i c t u r e d i n F i g . 1 1 . E a c h b u b b l e c l a s s

e x c h a n g e s m a s s w i t h t h e l i q u i d ( o r s l u r ry ) p h a s e w i t h

a t r a n s f e r c o e f f i c i e n t

kL ~ai .

F u r t h e r , t o a c c o u n t f o r t h e

b u b b l e - b u b b l e i n t er a c t io n s w e a ss u m e t h a t e a c h

b u b b l e c l as s e x ch a n g e s m a s s w i t h e v e ry o t h e r b u b b l e

c l as s , e i t h e r b y a p r o c e s s o f c o a le s c e n c e o r b r e a k - u p ,

T a b l e 1 . B u b b l e e x c h a n g e m a t r i x

Fro m / t o C la s s 1 C la s s 2 C la s s 3 C la s s 4 C la s s 5 C la s s 6

Class 1 31 16 5 9 4

Class 2 43 x 30 10 8 10

Class 3 12 22 l0 4 8

Class 4 5 9 14 x 2 4

Class 5 6 7 5 5 x 3

Class 6 3 7 1 0 0

N o te :

T h e n u m b e r s r e p r e s e n t t h e n u m b e r o f b u b b l e s i n

a c e r ta in s i ze c la s s whic h unde rg o e xc h a nge w i th a d i f f e re nt

s iz e c la s s . The num be rs we re m e a sure d f r a m e -by- f r a m e for

a n e ight s e c ond pe r iod ove r 200 f r a m e s of ope ra t ion a t

supe r f ic ia l ga s ve loc i ty of 0 .09 m s - 1 a nd s lur ry c o nc e nt ra -

t ion o f 28 .3 vol%.

w i t h a n e x c h a n g e c o e f f i c i e n t Ei ~, e x p r e s s e d i n t h e

u n i t s s - 1

F o r e a c h b u b b l e c l a s s , w e d e f i n e t h e n u m b e r o f

m a s s t r a n s f e r u n i t s f o r t r a n s f e r t o t h e l i q u i d p h a s e

k L ia l H

N T U i - U L a r g e ~ (4)

w h e r e U L a,g o.i i s t h e s u p e r f i c i a l g a s v e l o c i t y t h r o u g h

t h e l a rg e b u b b l e p o p u l a t i o n i. T h e n u m b e r o f e x -

c h a n g e t r a n s f e r u n i t s f o r d ir e c t e x c h a n g e o f m a s s

b e t w e e n c l a s s e s i a n d j

E i j e i H

N E x T U q U L a r g e , ' ( 5 )

w h e r e E i j i s t h e e x c h a n g e c o e f f i c i e n t b e t w e e n t h e

b u b b l e c l a ss e s i a n d j . E x c h a n g e o f g a s b e t w e e n t h e

b u b b l e c l a s s e s d o e s n o t a l t e r t h e i r g a s h o l d u p s ; t h i s


8/11

4626 J.W .A. DE SWART t al .

Fig. 11. Mass transfer model for transfer from large bubbles involving bubble bubble interchange

coefficients Eli and transfer coefficients o the liquid phase

kLia~.

implies that we have the relation

E l i 8 i : E j i .

The bubble refreshment rate sni of class i is then:

S B i ~ ~ E i j

j = l , j= ~ 1

d C g )

- [ A ] C q ) + B ) C L , 8 )

d e

6)

where is the dime nsional distance along the reactor

~ = h / H ) . C g ) is the n-d imension al colum n matrix of

gas phase concentrations in the individual bubble

(7) classes, Cgi. The n x n dim ensiona l transfer coefficient

matrix [A] has the elements

[A] =

NTU1 ~ NExTU u

m j=l

j l

NExTU21

N E x T U 1 2

NTU2 ~ NExTU2j

m /=1

j 2

NExTU.1 NExTU.2

.- NExTU1,

NExTU2.

NTU.

m

NExTU,j

j = 1

i n

, 9 )

The experimental results on the refreshment rates

s B i c f Fig. 10) can th en be used i n conj uncti on with

eqs (6) and (7) to estimate the values of the exchange

coefficients Eij.

Assuming plug flow of all the bubble classes, the

differential equations for mass transfer to a com-

pletely mixed liquid phase, of uniform concentr ation

CL can be expressed in n-dimens ionalmatrix notation

a s

where m is the dis trib ution coefficient between gas and

liquid phases.

The n-dimensionalcolumn matrix (B) has the elements

B ) =

NTU1

NTU2

NTUn

(10)


9/11

Large bubb les in a two-d im ens iona l s lu r ry bubb le co lumn

T o d e m o n s t r a t e t h e i n f lu e n c e o f t h e e x c h a n g e o f g a s

b e t w e e n t h e c l a s s e s o n t h e o v e r a l l m a s s t r a n s f e r r a t e

t h e m o d e l o f n l a r g e b u b b l e c l a s s es i s n o w w o r k e d o u t

i n d e t a i l f o r t h r e e c l a s s es : c l a ss 1 w i t h a b u b b l e

d i a m e t e r d b, ~ o f 0 .0 1 m , c l a s s 2 w i t h a b u b b l e

d i a m e t e r

d b . 2

o f 0 .0 4 m a n d c l a s s 3 w i t h a b u b b l e

d i a m e t e r db , 3 o f 0 .1 m . T h e r i s e v e l o c i t y o f t h e 0 .1 m

b u b b l e s i s e s t i m a t e d f r o m o u r e x p e r i m e n t s a n d e q u a l s

0 . 95 m s - 1. T h e b u b b l e r i s e v e l o c i t y i s a s s u m e d t o b e

p r o p o r t i o n a l t o d b a n d s o t h e r i s e v e l o c i t y o f t h e

0 .0 1 m a n d 0 . 0 4 m d i a m e t e r b u b b l e s c a n n o w b e c a l-

c u l a t e d t o b e 0 . 3 m s - 1 a n d 0 .6 m s - i , r e s p e c t i v e l y .

M a s s t r a n s f e r c o e f f i c ie n t s f o r e a c h o f t h e b u b b l e

a r e e s t i m a t e d f r o m t h e s u r f a c e r e n e w a l

l a s s e s

t h e o r y :

;

L i : ( l l )

7 ~ t c , i

w h e r e D i s t h e d i f f u s i v i t y a n d t c i s t h e c o n t a c t t i m e

b e t w e e n g a s a n d l i q u id . T h e c o n t a c t t i m e i s e s t i m a t e d

f r o m t c . i = d b . i / V b , i f o r e a c h b u b b l e c l a s s . T h e g a s

h o l d u p s o f th e t h r e e c l a s se s a r e e s t i m a t e d f r o m t h e

m e a s u r e d g a s h o l d u p s t r u c t u r e s ( e l = 0 . 05 , e 2 = 0 . 0 6 ,

e 3 = 0 .0 3 ). T h e i n t e r r a c i a l a r e a s a r e c a l c u l a t e d f r o m

a = 6 e / d b ;

t h i s y i e l d s a l = 3 0 , a 2 = 9 a n d a 3 =

1 .8 m 2 m - 3 . T h e s u p e r fi c i al g a s v e l o c i ti e s t h r o u g h

e a c h b u b b l e c l a s s i s

V b e ;

th is y ie ld s ULarge , 1 = 0 .015 ,

ULa ,gc ,2 = 0 .036 an d ULarge ,3 = 0 .028 m S- 1 .

S i m u l a t i o n s a r e n o w c a r r i e d o u t f o r c o n d i t i o n s r e l-

e v a n t fo r th e F i s c h e r - T r o p s c h s y n th e s is . H y d r o g e n

a b s o r p t i o n f r o m s y n t h e s i s g a s i n t o p a r a f f i n o i l a t

a p r e s s u r e o f 4 0 b a r a n d a t e m p e r a t u r e o f 5 13 K i s

c o n s i d e r e d . H y d r o g e n a n d c a r b o n m o n o x i d e a r e p r e s -

e n t i n t h e s y n g a s f e e d a t a r a t i o o f 2. T h e s u p e r f i c i a l

g a s v e l o c it y th r o u g h t h e t o t a l l a r g e b u b b l e p o p u l a -

t i o n , U L a rg c = 0 . 0 7 9 m S - 1 , i s a s s u m e d t o b e c o n s t a n t

o v e r t h e r e a c t o r h e i g h t H = 30 m . T h e d i f f u s iv i t y

D a n d d i s t r i b u t i o n c o e f f i c ie n t m o f h y d r o g e n a r e e q u a l

t o 5 .5 1 0 - 8 m z s - 1 a n d 5 , re s p e c t i v e l y . T h e c o n c e n -

t r a t i o n o f h y d r o g e n i n t h e l i q u i d p h a s e i s s e t a t

C L = 4 0 m o l m - 3 a n d i s a s s u m e d t o b e c o n s t a n t

a l o n g t h e h e i g h t o f t h e r e a c t o r. F r o m t h e d a t a g i v e n i n

F i g . 1 0 a n d T a b l e 1 , a n d k e e p i n g i n m i n d t h e c o n -

s t r a i n t s g i v e n b y e q s ( 6 ) a n d ( 7 ) , w e h a v e m a d e r o u g h

e s t i m a t e s o f t h e v a l u e s o f t h e e x c h a n g e c o e f f i c i e n t s

E u f o r t h e t h r e e - b u b b l e c l a s s e s : E 1 2 = 3 , E 1 3 = 1 ,

E 2 x = 2 .5 , E 2 3 = 3 , E a t = 1 .7 a n d E 3 2 = 6 s - 1 . T h e

r e f r e s h m e n t r a t e s c a l c u l a t e d u s i n g e q . (7 ) f o r t h e t h r e e

b u b b l e c l a s s e s a r e : s na = 4 , s n2 = 6 . 5 a n d

SB2

= 7 .7 S - 1, w h i c h a g r e e s w i t h t h e t r e n d p o r t r a y e d

i n F i g . 10 . T h e v a l u e s o f t h e n u m b e r s o f m a s s t r a n s f e r

u n i t s a r e c a l c u l a t e d f r o m e q s ( 4 ) a n d ( 1 1 ) t o b e

N T U ~ = 8 3 , N T U 2 = 7 .3 a n d N T U 3 = 1 .4 7. T h e c o -

e f f i c ie n t m a t r i x I -A ] c a n n o w b e c a l c u l a t e d f r o m e q . (9 )

a n d t h e s e t o f o r d i n a r y l i n e a r d i f f e r e n t i a l e q u a t i o n s ( 8)

c a n b e s o l v e d t o y i e l d t h e c o m p o s i t i o n p r o f i l e s f o r

h y d r o g e n i n t he g a s p h a s e a l o n g t h e h e i g h t o f t h e

r e a c t o r. F i g u r e 1 2 s h o w s t h e d i m e n s i o n l e s s h y d r o g e n

c o n c e n t r a t i o n

C o

H2/Co0 H 2 p r o f il e a l o n g t h e c o l u m n

h e i g h t. T h e t h r e e p r o f il e s c o i n c i d e w i t h o n e a n o t h e r

4627

C g H 2

C g o ~

1

0 8

0 6

0 . 4

0 . 2

0 01.2

0

X 0 .01 m bubb le c lass 1

0 0 . 0 4 n bubble class2

[ ] 0.10m bubble class 3

I

1 0 1 . 4 0 1 . 6 1 0 1 8 1 1

Fig . 12. Re la t ive hydrogen conce n t ra t ion as a fun c t ion o f

ax ia l pos i tion in a F ischer T ropsch s lu r ry reac to r opera t ing

at a superficial gas velo city of 0 .079 m s- L M odel c alcu-

lations based on a three bubble class and interaction coeffi-

c ien ts a s shown in the f igu re . The con t inuous l ine co r res -

ponds to the ensemble average concen t ra t ion ca lcu la ted

from eq. (12).

a n d t h e c o n v e r s i o n a t t h e r e a c t o r o u t l e t i s 6 8 % . T h e

c o n v e r s i o n b e h a v i o u r o f t h e t h r e e b u b b l e c l as s s y s te m ,

w i t h 0 . 01 , 0 . 0 4 a n d 0 .1 m d i a m e t e r b u b b l e s i s f o u n d t o

b e e q u i v a l e n t t o t h a t o f a s i n g le b u b b l e c l a s s s y s t e m o f

d i a m e t e r 0 .0 2 1 m m o v i n g t h r o u g h t h e r e a ct o r a t

a s u p e r f i c i a l g a s v e l o c i t y U

=

ULarg,1

~-

ULarge.2 4-

U L a r g e , 3

= 0 .0 7 9 m s 1 . P u t a n o t h e r w a y , d u e t o f r e -

q u e n t b u b b l e - b u b b l e i n t e r c h a n g e , t h e e ff e c ti v e b u b b l e

d i a m e t e r s f o r t h e 0 . 0 4 a n d 0 . 1 m d i a m e t e r c l a s s e s a r e

r e d u c e d t o a b o u t 0 .0 2 . T h i s i m p l i e s a n e n h a n c e m e n t

f o r t h e 0 .1 m b u b b l e c l a s s o f fi v e .

I n o r d e r t o f u r t h e r d e m o n s t r a t e t h e s i g ni f i ca n c e o f

t h e b u b b l e - b u b b l e i n t e r c h a n g e , w e a l so c a r r ie d o u r

s i m u l a t i o n s t a k i n g a l l t h e e x c h a n g e c o e f f i c i e n t s E u t o

b e z e ro . T h e g a s p h a s e c o n c e n t r a t i o n p r o f il e s f or t h e

t h r e e b u b b l e c l a s s e s i n t h i s c a s e a r e s h o w n i n F i g . 1 3 .

T h e 0 . 0 1 m b u b b l e c l a s s e q u i l i b r a t e s w i t h t h e l i q u i d

p h a s e v e r y q u i c k l y w h e r e a s w e s e e t h a t t h e c o n v e r s i o n

o b t a i n e d f r o m t h e 0.1 m b u b b l e c l a s s i s e x t r e m e l y

l i m i t e d . A l s o s h o w n i n F i g . 13 is t h e w e i g h t e d a v e r a g e

c o n c e n t r a t i o n p r o f il e o f t h e b u b b l e e n s e m b l e c a l -

c u l a t e d f r o m :

ULarge i C

d C g _ ~ U g , i. ( 12 )

- ~ i = 1

T h e o v e r a l l c o n v e r s i o n a c h i e v e d b y t h e e n s e m b l e i s

o n l y 4 3 e /o , s i g n i f i c a n t l y l o w e r t h a n t h a t o b t a i n e d t a k -

i n g i n t e r a c ti o n s i n t o a c c o u n t .

A f u r t h e r p o i n t t o n o t e i s t h a t t h e r e f r e s h m e n t

f r e q u e n c i es d u e t o c o a l e s c e n c e o r b r e a k - u p a r e o f th e

s a m e o r d e r o f m a g n i t u d e a s t h e D a n c k w e r t s s u r fa c e

r e n e w a l f r e q u e n c i e s fo r m a s s t r a n s f e r. F o r a b u b b l e o f

0 .1 m d i a m e t e r t h e D a n c k w e r t s s u r f a c e r e n e w a l f r e-

q u e n c y i s c a l c u l a t e d t o b e o f t h e o r d e r o f 3 s - 1 w h i l e

w e s e e f r o m F i g . 1 0 t h a t t h i s b u b b l e c l a s s i s r e fr e s h e d

a t t h e r a t e o f 1 5 s - 1 . T h i s i m p l i e s t h a t d u r i n g t h e t i m e

s p a n o f u n s t e a d y - s t a t e t r a n s f e r t o t h e l i q u i d p h a s e ,

a b u b b l e w o u l d l o s e i t s i d e n t i t y , r e s u l t i n g i n a f u r t h e r


10/11

4628 J.W.A. DE

~ : ~ .IC C L F | T Q I J s ] Z ] q Z L F n

. ,.~ , ~ . ~ , ~ 4 _ t z ~ ~ . , ~ F

~'~ ......

2

c o . ~ 0 . 6 ~ ~ ? ~ + ~ ; L ' ; ~ ; . . . . . " - - - ? . .. .

C o ,.2 f

. :~ 'XXX,~,

X 0 . 0 1 m b u b b l e

cl ~

1

0 . 2 0 0 . 0 4 m b u b b le c l a8 8 2

[ ] 0 . 1 0 i l l b u b b l e c l a s s 3

0 I I . I I , I , I

0 0 2 0 4 0 6 0 18 1

Fig. 13. Relative hydrogen concentration as a function of

axial position in a Fischer Tropsch slurry reactor for the

three bubble class without bubble bubble interchange. Also

shown in dashed lines are calculations of the ensemble aver-

aged concentrations along the reactor height following

eq. (12).

S W AR T et al

cates coalescence-breakup rates of the order of

10-30 s- ~, providing some confirmat ion of our two-

dimensi onal results.

Another aspect which deserves further study is the

influence of the particle size and shape on the bu bble

hydrodynamics; in a recent study by Tsuchiya and

Fur umo to (1995) the influence of particle shape has

been emphasised.

A

Ab

A i m

Aobj

B

Cg

eo

enhancement of the mass transfer coefficient

kL

esti-

L

mated to be of the order of a factor 2. A detailed mass Cs

transfer model needs to be set up to take this also into

db

account. A combination of bu bble- bubble inter-

change and enhanced kL due to accelerated surface db Large

renewal leads to an order of magnit ude increase in the D

mass transfer coefficient above that estimated from Eu

conventional treatments ignoring bubble bubble

interactions, h

Vermeer and Kr ishna (1981) in a study of mass H

transfer from large bubbles with the system air/tur- kL

pentine had attributed the measured (paradoxically) m

high values of mass transfer coefficients to the violent- NT U

ly turbul ent nature of the liquid phase. We can now NEx TU

establish, albeit qualitatively, that frequent SB

bub ble -bu bbl e exchanges are the most likely cause of tc

high mass transfe r rates. Th

U

ULarge i

C O N C L U S I O N S

We have gained some insight into the hyd rodyna m-

Uay

ics of slurry bubble columns. Increasing slurry con-

centrat ion reduces the total gas holdup; this reduction

Vb

is to be largely attributed to the destruction of the

small bubbl e populati on, which have bubble dia-

meters smaller than l0 mm. Incre asing slurry concen-

tratio n increases the size and size distrib ution of the

large bubbles. A frame-by-frame analysis of the

video images shows that there is frequent bubble

coalescence and breakup. With the aid of a popula-

tion model for mass transfer we have established that

this could lead to an order of magnitude increase in

the mass transfer for the larger bubble sizes.

In view of the demonstrated significance of

bubbl e-bubb leinte racti ons n a two-dimensional col- #

umn, we consider it vital to confirm this phen omen on H2

in a three-dimensional colum n with the aid of say i

tomograph ic techniques or fibre optic probes. A re- L

cent study, using video imaging techniques, by Large

Stewart (1995) of bubb le inte racti ons in a three-di- 0

mension al colum n of 0.2 x 0.2 m cross section indi- 1,2,3

N O T A T I O N

interfacial area per unit volume of disper-

sion, m 2 m 3

transfer coefficient matrix defined by eq. (7)

bubble area, m z

total area of the image, pixels

area of one object in an image, pixels

column matrix defined by eq. (8)

gas phase concentration, mol m-3

gas phase concentration at inlet to reactor,

mol m- 3

liquid phase concentrat ion, mol m 3

solids volume fraction in gas free slurry

bubble diameter of the large bub ble popula-

tion, m

mean bubble diameter of dilute phase, m

liquid phase diffusivity, m e s- t

exchange coefficient of bubb le class i with

bubble class j, s 1

height above the gas distributor, m

height of expanded bed, m

liquid phase mass transfer coefficient, s-

dis tribut ion coefficient

number of transfer units

number of exchange transfer units

refreshment rate (birth or death rate), s-t

contact time, s

threshold grayscale value

superficial gas velocity, m s-

superficial velocity of gas through the large

bubble population i, m s-

superficial velocity of gas through the small

bubbles, m s

rise velocity of the large bubble po pulatio n,

m s 1

Greek letters

e gas voidage

~lL liquid viscosity, Pa s

,DE liqu id dens ity, kg m- 3

a surface tens ion of liquid phase, N m 1

axial coordinate,

h / H

Subscripts

referring to gas phase

hydrogen

ith bub ble class

referring to liquid phase

referring to the large bubble population

referring to ent rance to reactor

referring to bubble classes


11/11

L a r g e b u b b l e s i n a t w o - d i m e n s io n a l s l u r ry b u b b l e c o l u m n

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Chemical Engineering Science Volume 51 Issue 20 1996 [Doi 10.1016%2F0009-2509%2896%2900265-5] J.W.a. de Swart_ R.E. Van Vliet_ R. Krishna -- Size, Structure and Dynamics of “Large”

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