Determination of Fluid Dynamic Parameters in Bubble Column Design

31 Determination of Fluid Dynamic Parameters in Bubble Column Design T H . P I L H O F E R , H . F . B A C H , and K. H. M A N G A R T Z

Downloaded by MONASH UNIV on February 25, 2016 | http://pubs.acs.org Publication Date: June 1, 1978 | doi: 10.1021/bk-1978-0065.ch031

Lehrstuhl A für Verfahrenstechnik, Technische Universität München, West Germany

Bubble columns are applied to many processes. They are employed in the same way for chemical synthesis (1) as also in waste water cleaning (2). Quite recently, their use for microbial processes has become increas ingly important (3). In spite of the variety of these applications and the number of known experimental studies, the design and scale-up of a bubble column is still a difficult task. In this paper, results of ex periments are presented, which are concerned with the determination of fluiddynamic parameters for column design. The description of a process, taking place in a bubble column, requires the selection of a suitable model. In most cases the application of the one-dimen sional dispersion model has proven satisfactory. When a differential mass balance is made around a differen tial segment of the column, disregarding radial depen dencies, the following equations result for the case of counter-current:

The l i n e a r velocities o f the c o n t i n o u s and d i s p e r s e phase, u and u , can be a d j u s t e d arbitrarily, whereas the mass t r a n s f e r coefficient k depends first o f all on the system's p h y s i c a l p r o p e r t i e s . On the o t h e r hand the f l u i d d y n a m i c parameters like interfacial a r e a a, gas holdup ε and the d i s p e r s i o n coefficients and are i n f l u e n c e d s t r o n g l y by the phases throughputs. I t is t h e r e f o r e n e c e s s a r y to p r e p a r e a p p r o p r i a t e correlC

D

L

©

0-8412-0401-2/78/47-065-372$05.00/0

In Chemical Reaction Engineering—Houston; Weekman, Vern W., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

31.

PILHOFER

Parameters in Bubble Column Design

ET AL.

373

ations f o r the c a l c u l a t i o n o f these parameters i n o r der to solve equation ( l ) a n d ( 2 ) . The f o l l o w i n g state ments a r e concerned w i t h t h i s problem. F i r s t of a l l , the l a y - o u t of the gas d i s t r i b u t o r l l be treated. I t s t a s k i s t o g e n e r a t e swarms o f bbles. I f a sieve t r a y i s used, one should be aware the fact, that a l l the holes must be i n o p e r a t i o n . h e r w i s e , u n d e s i r e d c i r c u l a t i o n s come i n t o existence. rthermore, weeping must be a v o i d e d when u s i n g large enings. This i s most i m p o r t a n t , i f the l i q u i d tends incrustate o r s o l i d i f y . These phenomena a r e caused b y t h e mechanism o f t h e p a r t i c l e formation on the sieve t r a y . The openings work i n the j e t t i n g r e g i o n and n o t i n the b u b b l i n g r e g i o n (k). Therefore, to o b t a i n a f u l l y working sieve tray, so much a g a s t h r o u g h p u t h a s t o b e p r e s e n t e d , that a l l openings work at least at the beginning o f the j e t t i n g region. The minimum gas l o a d r e l a t i v e tqjeach h o l e c a n be d e t e r m i n e d b y t h e f o l l o w i n g e q u a t i o n s (k): Small hole diameters:


w i bu of Ot Fu op to

We.

=

w

L

Large

hole

,

d

L ' P p

=

2

(3)

a

L

diameters:

Fr^

= _ ί ί _ . ( _ 2 _ ) d -g ΔΡ

(4)

=0,37

T

The v a l i d i t y o f f o l l o w i n g value

d These

Q

=

Li both equations i s separated o f the hole diameter:

2,32 · ( a / p -

equations

D

a r e v a l i d

5

g

)°' · ( ρ / Δ ρ )

5

by the

/

(5)

8

0

f o r g a s / l i q u i d

systems

w e l l

as

as f o r l i q u i d / l i q u i d systems (k)· The swarms o f b u b b l e s p r o d u c e d b y t h e d i s t r i b u t o r moves upward t h r o u g h t h e l i q u i d . Now, the nature o f the bubble motion i s most important f o r t h e develop ment o f t h e p r o c e s s i n the column. A t l o w gas v e l o c i t i e s the bubble h a r d l y hinder each other and the swarm r i s e s u p w a r d i n a r e g u l a t e d manner. This i s c a l l ed t h e "bubbly f l o w regime (5.). P r e s u m i n g a constant bubble s i z e , there i s a maximum v a l u e o f gas t h r o u g h put w i t h i n t h i s bubbly f l o w regime, that can be deter mined by f l o o d i n g p o i n t c a l c u l a t i o n s (6). I f the throughputs a r e increased beyond t h i s p o i n t , a f l o w a l t e r a t i o n takes place. I n order to reach higher buoy ancy forces f o r gas transport, bubble c l u s t e r s o r plugs a r e formed. This i s c a l l e d the "churn turbulent regime" ( 5 ) · 1 1



374

CHEMICAL

REACTION

ENGINEERING—HOUSTON

F o r t h e s e two f l o w r e g i m e s f i g u r e 1 shows s c h e m a t i c a l l y t y p i c a l c u r v e s f o r the dependency o f the gas h o l d u p on t h e gas v e l o c i t y . D u r i n g b u b b l y f l o w t h e gas h o l d u p i n c r e a s e s s u p e r p r o p o r t i o n a l l y w i t h t h e gas throughput. With the b e g i n n i n g f o r m a t i o n of bubble c l u s t e r s , these curves are s h i f t e d to the r i g h t because of the c o n t i n u o u s l y i n c r e a s i n g bubble s i z e . This r e s u l t s i n a s u b p r o p o r t i o n a l r i s e o f t h e gas h o l d u p w i t h gas t h r o u g h p u t . I t i s t h e r e f o r e n e c e s s a r y t o d i s t i n g u i s h b e t w e e n t h e s e two f l o w r e g i o n s . A t t h e moment i t i s n o t p o s s i b l e t o s p e c i f y t h e l i m i t s of both regimes. For a rough approximation the f o l l o w i n g c a l c u l a t i o n may be c a r r i e d o u t : W a l l i s recommends t h e f o l l o w i n g e q u a t i o n f o r t h e m o t i o n o f a swarm o f b u b b l e s i n t h e b u b b l y f l o w r e g i m e : (6 )

= ( ι - ε ) Using a batch-type l i q u i d , f o r the r e l a t i v e the f o l l o w i n g h o l d s : w = u / R

The

flooding

D

velocity

ε

(7)

condition i s : du

D

/ άε

=

0

F r o m e q u a t i o n (6) a n d (7) we g e t a t t h e f l o o d i n g a g a s h o l d u p o f 0,5 and the r e l a t i o n s h i p : u

D

=

0,25-Woo

(8) point (9)

F o r a u s u a l r i s e v e l o c i t y o f a s i n g l e b u b b l e o f 23 cm/s, f r o m e q u a t i o n (9) a maximum l i n e a r g a s v e l o c i t y o f 5i7 cm/s a r i s e s . A t h i g h e r g a s v e l o c i t i e s o n l y t h e c h u r n t u r b u l e n t r e g i m e e x i s t s . Y e t , e x p e r i m e n t s show, t h a t f l o w a l t e r a t i o n may a l r e a d y o c c u r a t l o w e r g a s t h r o u g h p u t s. A t hi^te moment e q u a t i o n (6) may be r e c o m m e n d e d f o r t h e c a l c u l a t i o n o f t h e gas h o l d u p i n t h e b u b b l y f l o w r e g i m e . A b e t t e r c o r r e l a t i o n can be o b t a i n e d , i f equations f o r the motion of s o l i d s are m o d i f i e d i n a c o n v e n i e n t way. T h i s h a s a l r e a d y b e e n a c h i e v e d f o r t h e m o t i o n o f d r o p l e t swarms ( 7 ) · T h o u g h 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 h e more s i g n i f i c a n t r e g i o n , t h e r e a r e no e q u a t i o n s g e n e r a l l y a p p l i c a b l e t o d e t e r m i n e the gas h o l d u p . Beyond t h i s , most e x p e r i m e n t s have been c a r r i e d out w i t h a i r / w a t e r s y s t e m s . I n o u r e x p e r i m e n t s p r e f e r e n c e was t h e r e f o r e given to the v a r i a t i o n of the system's p h y s i c a l pro p e r t i e s . F o u r l i q u i d s w e r e u s e d u n d e r d i f f e r e n t tem p e r a t u r e s ; experiments under pressure are s t i l l going on b u t n o t y e t e v a l u a t e d . F o r e x a m p l e , i n f i g u r e 2 measurements o f t h e gas h o l d u p a t d i f f e r e n t l i n e a r gas


PILHOFER


ET AL.


bubbly

flow

Figure 1. Dependency of the gas holdup on the linear gas velocity for different flow regions

0.3-

C O O C ο ο c

»

Q ο

α

α · ο

ο·

δ

ο

t%

*

• Ί ° * *

°· „

·

ο ° . \ ο

°. ν

η α

• 0 ι °· ο

»*

•

8

ο

3

liquid

ndo

butane diol

29.5 6,8

ethylene glycol octanol

11.7

•

3.2

tetrabromo eth 0

5

10

1.7

15 cm/s

gas phase linear velocity u

20

0

Figure 2. Measured gas holdup values for four different liquids as a function of gas linear velocity


376

CHEMICAL

REACTION

ENGINEERING—HOUSTON

v e l o c i t i e s w i t h d i f f e r e n t l i q u i d s are p l o t t e d . E v a l u a t i n g o u r own m e a s u r e m e n t s a n d c o n s i d e r i n g t h e r e s u l t s o f K u s t e r s (£0 a n d Hammer/Rahse (9.) , u s i n g c o l u m n s w i t h t h e same d i m e n s i o n s , t h e f o l l o w i n g e q u a t i o n f o r the dependency o f the gas h o l d u p f r o m the l i n e a r gas v e l o c i t y and t h e p h y s i c a l p r o p e r t i e s h o l d s :


——

= 0,115

( u

3

/

( v . g - A p /p c

))

c

0 , 2 3

do)

E q u a t i o n (10) i s v a l i d f o r a c o l u m n w i t h a n i n n e r d i a m e t e r o f 100 mm a n d a c l e a r l i q u i d h e i g h t g r e a t e r t h a n 1200 mm. I n a f u r t h e r s t e p we t h e r e f o r e e x a m i n e d , wèther g a s h o l d u p i s i n f l u e n c e d b y t h e c o l u m n d i m e n sions. In f i g u r e 3 S holdup measurements are p l o t t e d v e r s u s g a s l i n e a r v e l o c i t y . The e x p e r i m e n t s w e r e c a r r i ed o u t i n c o l u m n s w i t h i n n e r d i m e n s i o n s l a r g e r t h a n 150 mm a n d c l e a r l i q u i d h e i g h t s h i g h e r t h a n 1000 mm. F u r t h e r m o r e , t h e e m p l o y e d gas d i s t r i b u t o r s c a u s e d a c h u r n t u r b u l e n t f l o w a l r e a d y a t l o w gas throughputs. I t c a n be s e e n , t h a t a l l t h e v a l u e s a r e d e s c r i b e d b y one r e g r e s s i o n l i n e j w i t h s a t i s f a c t o r y a c c u r a c y . C o n s e q u e n t l y , t h e r e i s no d e p e n d e n c y o f g a s h o l d u p f r o m column d i m e n s i o n s . Because of the agreement of the e x p o n e n t o f t h e gas l i n e a r v e l o c i t y i n e q u a t i o n (10) w i t h t h e r e s u l t s o f f i g u r e 3, e q u a t i o n (10) c a n be r e commended f o r g a s h o l d u p c a l c u l a t i o n s . I t i s p o s s i b l e , t h a t t h e c o n s t a n t v a l u e o f 0,115 m u s t be c o r r e c t e d i n s i g n i f i c a n t l y , a s e q u a t i o n (10) has been d e r i v e d f o r a column o f 100 mm i n n e r d i a m e t e r w h e r e a s f i g u r e 3 f e r s to columns w i t h a d i a m e t e r equal or g r e a t e r than 150 mm. The m e n t i o n e d d e p e n d e n c i e s c o m p l y w e l l w i t h t h e r e s u l t s o f R i q u a r t s ' s c o n s i d e r a t i o n s ( 10 ) f o r . f l u i d i z e d beds. An a d d i t i o n a l f l u i d d y n a m i c p a r a m e t e r t o be d e t e r m i n e d i s t h e i n t e r f a c i a l a r e a a: a s

r e

a

=

6·ε

/ d

3 2

(11)

I n e q u a t i o n (11) t h e g a s h o l d u p c a n be d e t e r m i n e d by e q u a t i o n (10) o r r e s p . (6). Further informations are n e e d e d w i t h r e g a r d t o t h e medium b u b b l e s i z e d . U n f o r t u n a t e l y t h e r e i s n o t much e x p e r i m e n t a l data on b u b b l e s i z e s r e s p . b u b b l e s i z e d i s t r i b u t i o n s due t o the c o m p l i c a t e d m e a s u r i n g methods. For our measurements a new e l e c t r i c m e a s u r i n g d e v i c e (11 ) ,(12 ) was u s e d . A p a r t i a l stream of the d i s p e r s e f l u i d two-phase system i s s u c k e d o f f by a v e r t i c a l f u n n e l c o n n e c t e d w i t h a g l a s s c a p i l l a r y . The c a p i l l a r y d i a m e t e r i s c h o s e n s o , t h a t most o f t h e b u b b l e s a r e d e f o r m e d t o p l u g s . These a r e d e t e c t e d t w i c e b y a s u i t a b l e l i g h t s e n s i n g means t h a t i n f o r m s on t h e l e n g t h o f t h e p l u g s . I f t h e p l u g



31.

PILHOFER

ET AL.


377

c r o s s - s e c t i o n i s determined by a d d i t i o n a l c a l i b r a t i o n p r o c e d u r e s , the volume o f each p a r t i c l e c a n be c a l c u l a t e d ^ i t i s a n advatage o f t h i s m e a s u r i n g method t o enable high measuring f r e q u e n c i e s . I n f i g u r e 4 m e a s u r e d mean b u b b l e s i z e s a r e shown f o r the a e r a t i o n o f x y l e n e and propanol by n i t r o g e n . The m e a s u r e m e n t s t o o k p l a c e i n a c o l u m n o f 225 mm d i a m e t e r . The m e a s u r i n g h e i g h t w a s 850 mm a b o v e t h e g a s d i s t r i b u t o r , w h i c h was f o r m e d a s a s i e v e t r a y w i t h d i f f e r e n t h o l e d i a m e t e r s . I t can be seen, t h a t t h e s a u t e r mean d i a m e t e r d i s almost independent o f t h e g a s t h r o u g h p u t . K u s t e r s (8^) g o t s i m i l a r r e s u l t s . More d e t a i l e d i n f o r m a t i o n r e s u l t s f r o m a n a n a l y s i s o f b u b b l e s i z e d i s t r i b u t i o n s . These have been a p p r o x i mated b y a l o g a r i t h m i c normal d i s t r i b u t i o n so t h a t t h e v a l u e o f t h e s a u t e r mean d i a m e t e r r e m a i n e d t h e same a s b e f o r e . The c e n t r a l v a l u e s d and the standard d e v i a t i o n s 0£, c a l c u l a t e d i n t h e way m e n t i o n e d b e f o r e , a r e p l o t t e d i n f i g u r e 5- The d e p e n d e n c y o f t h e c e n t r a l v a l u e s o f t h e g a s t h r o u g h p u t i s b a s i c a l l y t h e same a s on s i n g l e h o l e s . A f t e r t h e t r a n s i t i o n o f a l l h o l e s i n t h e j e t t i n g r e g i o n ( u » l cm/s ) a s t r o n g d e c r e a s e o f d_ appears, which f l a t t e n s w i t h higher gas through p u t s . Y e t , i t must be c o n s i d e r e d , t h a t t h e s t a n d a r d d e v i a t i o n s a t f i r s t i n c r e a s e stroPgly w i t h gas holdup, before reaching a constant value. With respect t o t h e p a r a l l e l s t o s i n g l e o r i f i c e s , a f u r t h e r a s p e c t must be n o t e d : t h e b u b b l e s , e m e r g i n g f r o m t h e s i e v e p l a t e , s h o u l d b e n o t l a r g e r t h a n a c e r t a i n maximum v a l u e ; o t h e r w i s e t h e y a r e no l o n g e r s t a b l e a n d d e v i d e i n t o s m a l l e r p a r t i c l e s . A c c o r d i n g t o M e r s m a n n (13)> t h e maximum s t a b l e p a r t i c l e d i a m e t e r r e s u l t s f r o m t h e r e lation : n

Q

d

(12)

P · g

max Taking a l l experiments i n t o account, i f p a r t i c l e s c o l l a p s e , a churn t u r b u l e n t f l o w r e g i o n a l r e a d y appears at lower gas throughputs. I n sieve p l a t e design, t h i s a s p e c t h a s t o be checked a d d i t i o n a l l y . F o r the d e t e r m i n a t i o n o f t h e s i z e o f t h eemerging bubbles, w e l l - known methods l i k e t h a t o f R u f f ( l4) c a n be u s e d . I n d e t e r m i n i n g mean b u b b l e s i z e s i n c o l u m n s , t h e r e i s s t i l l a l a c k o f s u i t a b l e c o r r e l a t i o n s . Even o u r r e s u l t s do n o t e n a b l e m o r e p r e c i s e s t a t e m e n t s . T h e r e f o r e we r e c o m m e n d t o d e t e r m i n e mean b u b b l e s i z e s f r o m e q u a t i o n (12). A c c o r d i n g t o o u r c a l c u l a t i o n s t h e r e i s a n a c c u r a c y o f +_ JO % w i t h r e s p e c t t o m e a s u r e d v a l u e s , i f t h e l i q u i d v i s c o s i t y i s l o w e r t h a n 10 c P . F i n a l l y , the d e t e r m i n a t i o n o f the d i s p e r s i o n c o e f f i c i e n t s i n b o t h p h a s e s i s t o b e t r e a t e d . The

Π0 3

°- 3

atr/water nitrogen /n-proponol atr/glycol 30

40

50

60

relative velocity wR

70 cm/s

Figure 7. Gas phase dispersion coefficient as a function of the relative velocity be tween gas and liquid


CHEMICAL

382 N o m e n c l a2 t u r3e : a m /m c kmol/kmol c* / m d_p m dg m d Q m Fr g-" D m /g g m/s HQ m m/s t s u m/s w m/s We χ m ε m /m η |g/ms V m / s ρ kg/m^ Δρ »/" Cf N/m 11

lf


1

subscripts : C D F G L co

REACTION ENGINEERING—HOUSTON

i n t e r f a c i a l area concentration equilibrium concentration hole diameter s a u t e r mean d i a m e t e r column diameter central value d i m e n s i o n l e s s mod, F r o u d e - n u m b e r dispersion coefficient gravitational acceleration clear l i q u i d height mass t r a n s f e r c o e f f i c i e n t time linear velocity velocity d i m e n s i o n l e s s Weber-number length gas holdup dynamic v i s c o s i t y kinematic v i s c o s i t y density density difference surface tension standard d e v i a t i o n

continuous phase d i s p e r s e phase liquid gas hole referring to single

bubbles

Literature cited: (1) Mashelkar R.A., Brit. Chem. Eng, (1970),15,1297 (2) Ploos v. Amstel J.J.Α., Rietema Κ . , Chem.Ing. Techn.,(1970),42,981 (3) Todt J., Lücke J., Schügerl Κ., Renken A., Chem. Engng.Sci.,(1977),32,369 (4)RuffΚ., Pilhofer T h . , Mersmann Α., Chem.Ing. Techn.,(1976),48,759 (5) Wallis G . B . , ASME Int.Dev.Heat Trans.,(1962),319 (6) Lapidus L., Elgin J.C., AIChE J.,(1957),3,63 (7) Pilhofer T h . , Chem.Ing.Techn.,(1976),48,273 (8) K ü s t e r s W., Ph.D.Diss. TH Aachen Germany 1976 (9) Hammer H., Rähse W.,Chem.Ing.Techn.,(1973),45,968 (10) Riquarts H . P . , Verfahrenstechnik,(1977),11,164 (11) Pilhofer T h . , Jekat Η . , Miller H . D . , M ü l l e r J.H., Chem.Ing.Techn.,(1974),46,913


31. piLHOFER ET AL. (12) (13) (14) (15) (16) (17) (18)


(19) (20) (21) (22) (23) (24) (25) (26)


US Pat. 3.818.200 Mersmann Α . , Verfahrenstechnik,(1976),10,641 Ruff Κ . , Chem.Ing.Techn.,(1972),44,1360 Ohki Υ . , Inoue Η . , Chem.Engng,Sci.,(1970),25,1 Badura R . , Deckwer W.D., Warnecke H.J., Lange mann Η . , Chem.Ing.Techn.,(1974),46,399 Hikita Η . , Kikukawa Η., Chem.Eng.J.,(1974),8,191 Towell G.D., Ackermann G.H., 2.Int.Symp.Chem. React.Eng., Amsterdam 1972, Preprints B3 Kastanek F., Nyvlt V., Rylek Μ., Coll.Czech.Chem. Comm.,(1974),39,528 Deckwer W.D., Burckhart R . , Zoll G., Chem.Engng. Sci.,(1974),29,2177 Freedman W., Davidson J.F., Trans.Instn.Chem. Engrs.,(1969),47,251 Akita Κ . , Yoshida F., Ind.Eng.Chem.Proc.Des.Dev. (1973),12,76 Reith T., Chem.Engng.Sci.,(1968),23,619 Towell G.D., Strand C.P., Ackermann G.H., AIChE - I.Chem.E.Symp.Ser.,(1965),10,97 F a i r J.R., Ind.Eng.Chem.Proc.Des.Dev.,(1962),1,33 Jekat Η . , Ph.D.Diss. TU München Germany 1976


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Determination of Fluid Dynamic Parameters in Bubble Column Design

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