Chemical Reactors - American Chemical Society

---

12 A New Model for Heat Transfer Coefficients in Bubble Columns 1

YATISH T. SHAH, J. B. JOSHI , and M . M .

1

SHARMA

Downloaded by UNIV OF SYDNEY on February 1, 2014 | http://pubs.acs.org Publication Date: September 21, 1981 | doi: 10.1021/bk-1981-0168.ch012

Chemical and Petroleum Engineering Department, University of Pittsburgh, Pittsburgh, PA 15261

In many multiphase ( g a s - l i q u i d , g a s - s o l i d , liquid-liquid and g a s - l i q u i d - s o l i d ) c o n t a c t o r s , a l a r g e degree of c i r c u l a t i o n of both d i s c r e t e and c o n t i n u ous phases occurs. T h i s c i r c u l a t i o n causes a good degree of mixing and enhances heat and mass t r a n s f e r between fluid and w a l l s . The degree of circulation depends on a number of parameters such as the s i z e of equipment, the nature of the phases i n v o l v e d , v e l o c i t i e s of v a r i o u s phases, nature of the i n t e r n a l s w i t h i n the equipment and many o t h e r s . The importance of circulation in bubble columns, g a s - s o l i d fluidized beds and a g i t a t e d contactors has been e x t e n s i v e l y examined in the literature. In this paper we present a g e n e r a l i z e d procedure f o r the c a l c u l a t i o n of bed-wall heat t r a n s f e r coefficient in bubble columns on the b a s i s of t h e i r hydrodynamic behavior. I t has been shown that the high values of heat t r a n s f e r c o e f f i c i e n t obtained in bubble columns, as compared to the s i n g l e phase pipe flow, can be explained on the b a s i s of the enhanced l o c a l liquid v e l o c i t i e s in the presence of gas phase. A comparison between the p r e d i c t e d and experimental values of heat t r a n s f e r c o e f f i c i e n t is presented over a wide range of design and o p e r a t i n g v a r i a b l e s . There are s e v e r a l i n d u s t r i a l l y important multiphase r e a c t o r s in which the chemical r e a c t i o n is accompanied by l a r g e heat e f f e c t s (Table I ) . Heat is e i t h e r s u p p l i e d or removed depending upon whether the r e a c t i o n is endothermic or exothermic. F o r the heat to be t r a n s f e r r e d an area is provided in the form of e i t h e r c o i l s or v e r t i c a l or h o r i z o n t a l bundle of tubes or the column 1

Current address: Department of Chemical Technology, U n i v e r s i t y of Bombay, Bombay, I n d i a . 0097-6156/81/0168-0243$05.00/0 © 1981 American Chemical Society In Chemical Reactors; Fogler, H.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

244

CHEMICAL REACTORS

TABLE I THE REACTIONS OF INDUSTRIAL IMPORTANCE WHICH ARE CARRIED OUT IN BUBBLE COLUMNS AND SLURRY REACTORS AND ARE ACCOMPANIED BY LARGE HEAT EFFECTS (i)

(ii)

Downloaded by UNIV OF SYDNEY on February 1, 2014 | http://pubs.acs.org Publication Date: September 21, 1981 | doi: 10.1021/bk-1981-0168.ch012

(iii) (iv) (v) (vi)

O x i d a t i o n of organic compounds such as toluene, cumene, o-xylene, ethylene, acetaldehyde, butane, s e c - b u t y l benzene. C h l o r i n a t i o n of benzene, toluene, phenol, ethylene, ethanol, a c e t i c a c i d , and p a r a f f i n wax. Hydrogénation of benzene, nitrobenzene, acetone, a d i p o n i t r i l e , b u t y n e d i o l and "oxo" aldehydes, Hydration of o l e f i n s to a l c o h o l s . Fischer-Tropsch synthesis, Manufacture of organic chemicals by a l k y l a t i o n such as cumeme and s e c - b u t y l benzene.

wall. In the l a s t two decades, s e v e r a l i n v e s t i g a t o r s have r e ported the experimental values of heat t r a n s f e r c o e f f i c i e n t s in the multiphase o r bubble columns and proposed c o r r e l a t i o n s to exp l a i n t h e i r data. Table I I gives a summary of the heat t r a n s f e r s t u d i e s made in bubble columns. The experimental observations may be summarized as f o l l o w s : (i) The heat t r a n s f e r c o e f f i c i e n t a t the w a l l ( h ) is independent of the column diameter. (ii) The values of h are 20 to 100 times l a r g e r than the s i n g l e phase pipe flow and are comparable to those obtained from mechanically a g i t a t e d c o n t a c t o r s . (iii) The values of h are p r a c t i c a l l y independent of the sparger design. (iv) The heat t r a n s f e r c o e f f i c i e n t does not i n c r e a s e i n d e f i n i t e l y with the s u p e r f i c i a l gas v e l o c i t y (VQ). The value of h l e v e l s o f f at some value of VQ depending upon the column diameter and the other p h y s i c a l p r o p e r t i e s of the g a s - l i q u i d system. In the past, there have been two major approaches to analyze the problem of heat and mass t r a n s f e r across the liquid-solid i n t e r f a c e . The f i r s t approach can be b r o a d l y c l a s s i f i e d as "Analogies. This method e s s e n t i a l l y c o n s i s t s of (von Karman (1) and Wasan and Wilke ( 2 ) ) : ( i ) development of v e l o c i t y p r o f i l e near the i n t e r f a c e , ( i i ) s u i t a b l e assumption f o r the v a r i a t i o n of eddy d i f f u s i v i t y with respect t o the d i s t a n c e from the i n t e r f a c e , and ( i i i ) s o l u t i o n of the Reynolds m o d i f i c a t i o n of the Navier-Stokes equation f o r the t u r b u l e n t flow. For the case of s i n g l e phase pipe flow, von Karman (1) s e l e c t e d the u n i v e r s a l v e l o c i t y p r o f i l e . The value of eddy v i s c o s i t y was obtained from the slope of the v e l o c i t y p r o f i l e . F u r t h e r , it was assumed that the numerical values of eddy v i s c o s i t y and the eddy d i f f u s i v i t y are the same. The f o l l o w i n g equation was obtained: w

w

w

w

11

In Chemical Reactors; Fogler, H.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

12.

SHAH

ET AL.

245

Heat Transfer Coefficients

TABLE I I EXPERIMENTAL DETAILS OF HEAT TRANSFER STUDIES IN BUBBLE COLUMNS Symbols in F i g u r e s 1 and 4

Tank D i a . T, m

1 J

Investigator

System

O.46

Ο

1.06

Φ

Δ Downloaded by UNIV OF SYDNEY on February 1, 2014 | http://pubs.acs.org Publication Date: September 21, 1981 | doi: 10.1021/bk-1981-0168.ch012

k

V

7.6

O.099

3.0

O.099

36.5

•

-do-

\ )

Permer (12)

air-water

8.0 O.19

Hart (11)

air-ethylene glycol

6.0

θ -ο

F a i r et a l . (10)

axr-water

air-ethylene -alcohol

6.0

air-water

Burke1

(13)

6.0

air-water

Muller

(14)

Louisi

(15)

O.09*1 O.19 O.29

+ Θ

X

Τ J

O.1

4.0

air-xylene

O.1

6.1

air-kogasene

O.1

10.2

1 St

A +

1.

f

f

air-decalin „

f (Pr)

(1)

where f is the fanning f r a c t i o n f a c t o r and i t s v a l u e is obtained from a s u i t a b l e c o r r e l a t i o n . There are s e v e r a l other analogies a v a i l a b l e in the published l i t e r a t u r e . The equations widely used f o r the c a l c u l a t i o n of heat t r a n s f e r c o e f f i c i e n t are the dimens i o n l e s s c o r r e l a t i o n s which f i n d t h e i r b a s i s in a n a l o g i e s . For i n s t a n c e , Sieder and Tate (3) have proposed the f o l l o w i n g cor­ relations: h Τ w -f- = k

m T 7

O.8

TV, p O.027

{—M y

„

1/3

O.14

c

^ (-2-) ^ k Vw )

(2)

K

A t h e o r e t i c a l approach t o analyze the problem of heat trans­ f e r is t o develop some form of surface renewal model. The r a t e of surface renewal is found from the knowledge of energy input per u n i t mass. Recently Deckwer (4) has analyzed the problem of heat t r a n s f e r in bubble columns on the b a s i s of surface renewal model. The present study uses the e a r l i e r approach.

In Chemical Reactors; Fogler, H.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

246

CHEMICAL

Mathematical

REACTORS

Model

Downloaded by UNIV OF SYDNEY on February 1, 2014 | http://pubs.acs.org Publication Date: September 21, 1981 | doi: 10.1021/bk-1981-0168.ch012

The enhancement in the bed-wall heat t r a n s f e r c o e f f i c i e n t s in bubble columns as w e l l as the two- and three-phase contactors as compared to the s i n g l e phase pipe flow is l i k e l y because of the strong c i r c u l a t i o n flow p a t t e r n in the continuous phase. J o s h i (5) has shown that the average continuous phase c i r c u l a t i o n v e l o c i t i e s in multiphase contactors are 1 to 2 orders of magnitude l a r g e r than the net s u p e r f i c i a l continuous v e l o c i t i e s . J o s h i (5) has proposed the f o l l o w i n g equations : The average liquid c i r c u l a t i o n v e l o c i t y is given by the f o l lowing equation. V

c

= 1.31'feT ( V - e V G

b o o

)}

1 / 3

(3)

The average a x i a l and radial components of the c i t y are given by the f o l l o w i n g equations:

liquid

velo-

V

= 1.18' {gT ( V - e V J }

1 / 3

a

(4)

V

= O.42' {gT ( V - e V

1 / 3

r

(5)

G

b

G

b o o

)}

The values of V p r e d i c t e d by Equation (4) as w e l l as the p r e d i c t e d v e l o c i t y p r o f i l e agree with the experimental values reported by s e v e r a l i n v e s t i g a t o r s w i t h i n 15 percent. Since the v e l o c i t y p r o f i l e in bubble columns is known, the procedure f o r the c a l c u l a t i o n of heat t r a n s f e r c o e f f i c i e n t can be developed on a more r a t i o n a l b a s i s . S u b s t i t u t i o n of Equation (4) in (1) g i v e s : a

-S--

O.031'{

5_J^

1

}

(_£_)

() 6

From Equation (6) it can be seen that h is p r a c t i c a l l y independent of the column diameter (T * ) which agrees with the experimental o b s e r v a t i o n . However, the values of h calculated from Equation (6) are about 25 to 35 percent of the experimental v a l u e s . This may be because of the presence of radial component of the liquid v e l o c i t y in bubble columns as against i t s absence in the pipe flow. In the case of h e l i c a l c o i l s it is known that the enhancement in h occurs because of the presence of radial flow. The enhancement f a c t o r is given by the f o l l o w i n g equation (Perry and Chilton (6)): w

w

w

In Chemical Reactors; Fogler, H.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

12.

SHAH ET AL.

247

Heat Transfer Coefficients

Ε

= 1 + 3.5 d/D η

(7)

u

c

where, d/D„ = Re /De H c

(8)

dV p =— — c u

(9)

Re

Downloaded by UNIV OF SYDNEY on February 1, 2014 | http://pubs.acs.org Publication Date: September 21, 1981 | doi: 10.1021/bk-1981-0168.ch012

dV p De = — —

(10)

and 2

, v d H

D

= =

(11)

r V a

2

The above a n a l y s i s can be a p p l i e d f o r the case of bubble columns. From F i g u r e I it can be seen that, near the w a l l the a x i a l component of the liquid v e l o c i t y is downwards, whereas the radial component of the liquid v e l o c i t y is towards the w a l l in the top h a l f o f the c i r c u l a t i o n c e l l and away from the w a l l in the lower h a l f o f the c i r c u l a t i o n c e l l . As a r e s u l t , f o r one c i r c u l a t i o n c e l l the enhancement f a c t o r is given by the f o l l o w i n g equation: 2

E

c

2V = 1+ (^) a

(12)

S u b s t i t u t i o n of Equations (4) and (5) in (12) g i v e s : Ε

c

= 2.8

(13)

Equation (12), t h e r e f o r e , takes the f o l l o w i n g form: T

1.33 1/3

- £ - = O.087' { κ

l/3 S_GJ£ μ

p

O.8 1/3

O.14

}

(

κ.

μ

1

4

)

ν

From F i g u r e I I it can be seen that the p r e d i c t e d and experimental values are w i t h i n 30 percent.

American Chemical Society Library 1155 16th St. N. W. In Chemical Reactors; Fogler, H.; Washington, O. C. 20036 ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

CHEMICAL

REACTORS

Downloaded by UNIV OF SYDNEY on February 1, 2014 | http://pubs.acs.org Publication Date: September 21, 1981 | doi: 10.1021/bk-1981-0168.ch012

248

Figure 2. Comparison between experimental and predicted (Equation 24) heat transfer coefficients: bubble column (analogy with pipe flow); for symbol key, see Table II

In Chemical Reactors; Fogler, H.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

12.

SHAH ET AL.

249

Heat Transfer Coefficients

Comparison with Mechanically A g i t a t e d Contactors. The heat t r a n s f e r c o e f f i c i e n t a t the w a l l of mechanically a g i t a t e d contac­ t o r s is given by the f o l l o w i n g equation (Perry and C h i l t o n ( 6 ) ) :

2

h Τ

2

/

3

c υ

1

/

3

° ·

1

4

W

for

40

2

3

/

1

c y

(

/

3

„ ° ·

1

4

( 2 3 )

^

Equation (23) w i l l be a p p l i c a b l e f o r bubble columns i f an appro­ p r i a t e value of V is i n c o r p o r a t e d . S u b s t i t u t i o n of Equation (3) in (23) g i v e s : c

hi I - ϊ - - O . 4 8 ' { κ

L

3

3

0 g

'

3

3

1

( V , V j

-

/

3

p

y

6

c /

/

3

} K

y

„ ° * fJL.)

1

4

(24)

y_ w T

F i g u r e IV shows a comparison between the experimental (Table II) values of and those p r e d i c t e d by Equation (24). I t can be seen that the agreement is w i t h i n 15 percent. F u r t h e r , from Equation (24) it can be seen that h v a r i e s as χ · . Because of low power on T, the v a l u e of are found to be p r a c t i c a l l y in­ dependent of Τ (the v a r i a t i o n of column diameter from 1 m to O.1 m gives only 22 percent r e d u c t i o n ) . Some more d e t a i l s on this com­ p a r i s o n and the a p p l i c a t i o n of the present model to other m u l t i ­ phase contactors are r e c e n t l y o u t l i n e d by J o s h i e t a l . ( 9 ) . - 0

1 1

w

Nomenclature Cp D De

s p e c i f i c heat of the liquid, i m p e l l e r diameter, m Dean's number, dV p/y

kcal/kg°C

r

In Chemical Reactors; Fogler, H.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

252

CHEMICAL

REACTORS

DH d dg Efc

h e l i x diameter o f a c o i l , m tube diameter, m average bubble diameter, m enhancement f a c t o r f o r heat t r a n s f e r c o e f f i c i e n t due to the presence of radial component of the liquid v e l o c i t y : bubble column E enhancement f a c t o r f o r heat t r a n s f e r c o e f f i c i e n t due t o the presence of radial component of the liquid v e l o c i t y : helical coil Fr Froude number, VQ^/gdg f fanning f r i c t i o n f a c t o r g a c c e l e r a t i o n due to g r a v i t y , m/s H liquid height in mechanically a g i t a t e d contactors h heat t r a n s f e r c o e f f i c i e n t , k c a l / h r m °C \j bed-wall heat t r a n s f e r coe f f i c i e n t , k c a l / h r m °C k thermal c o n d u c t i v i t y of the continuous phase, k c a l / h r m °C ki,k2 constants in Equations (30) and (32), r e s p e c t i v e l y L length of the path in a c i r c u l a t i o n c e l l , m Ν i m p e l l e r speed, r e v o l u t i o n s / s Pr P r a n d t l number, c p / k Re Reynold's number f o r bubble (Equation (3)) Re Reynold's number f o r c o i l (Equation (15)) St Stanton number, h /pCpV Τ column diameter or v e s s e l diameter, m V average a x i a l component of the continuous phase v e l o c i t y , m/s V^oo t e r m i n a l r i s e v e l o c i t y of bubbles, m/s V average continuous phase c i r c u l a t i o n v e l o c i t y , m/s VQ s u p e r f i c i a l gas v e l o c i t y , m/s mf minimum v e l o c i t y f o r f l u i d i c a t i o n , m/s VQ average r i s e v e l o c i t y of bubbles, m/s V radial component of the continuous phase v e l o c i t y t c i r c u l a t i o n time, s p d e n s i t y o f the liquid, g/cc ε f r a c t i o n a l gas holdup, dimensionless μ v i s c o s i t y of the continuous phase, cp ^mix mixing time, s c

2

Downloaded by UNIV OF SYDNEY on February 1, 2014 | http://pubs.acs.org Publication Date: September 21, 1981 | doi: 10.1021/bk-1981-0168.ch012

2

2

p

c

w

a

a

c

v

r

c

Literature Cited 1. 2. 3. 4. 5. 6. 7.

von Karman, Th. Trans. ASME 1939, 61, 705. Wasan, D. T.; Wilke, C. R. Int. J. Heat and Mass Transfer 1964, 7, 87. Sieder, Ε. N.; Tate, G. E. Ind. Eng. Chem. 1936, 28, 1429 Deckwer, W. D. Chem. Eng. Sci. 1980, 35, 1341. Joshi, J. B. Trans. Instn. Chem. Engr. 1980, 58, 155. Perry, R. H.; Chilton, C. H. "Chemical Engineers Handbook," 5th ed.; McGraw-Hill: New York, NY, 1973. Holmes, D. B.; Voncken, R. M.; Dekker, J. A. Chem. Eng. Sci 1964, 19, 201.

In Chemical Reactors; Fogler, H.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

12.

8. 9. 10.

Downloaded by UNIV OF SYDNEY on February 1, 2014 | http://pubs.acs.org Publication Date: September 21, 1981 | doi: 10.1021/bk-1981-0168.ch012

11. 12. 13. 14. 15.

SHAH

ET

AL.

Heat Transfer Coefficients

253

Norwood, K. W.; Metzner, Α. Β. AIChE J. 1960, 6, 432. Joshi, J. Β.; Sharma, M. M.; Shah, Y. T.; Singh, C. P. P.; Ally, M.; Klinzing, G. E. "Heat Transfer in Multiphase Con­ tactors," Chem. Eng. Communication 1981 (in press). Fair, J. R.; Lambright, A. J.; Anderson, J. M. I&EC Proc. Des. and Develop. 1962, 1, 33. Hart, W. F. I&EC Proc. Des. and Develop. 1976, 15, 109. Permer, D. Dipl. Arbeit, TU Berlin, 1960. Burkel, W. Dr. Ing. Thesis, TU Munchen, 1974. Muller, D. Dr. Ing. Thesis, TU Berlin, 1962. Louisi, Y. Dr. Ing. Thesis, TU Berlin, 1979.

RECEIVED

June 16, 1981.

In Chemical Reactors; Fogler, H.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.