I n d . Eng. Chem. Res. 1988, 27, 1910-1916
1910
Pentini, F. A.; Parisi, V.; Zirilli, F. “Global Optimization and Stochastic Differential Equations”. JOTA 1985, 47, 1-16. Powell, M. J. D. “A Fast Algorithm for Nonlinearly Constrained Optimization Problems”. In Lecture Notes in Mathematics; Watson, G. A,, Ed.; Springer-Verlag: Berlin, 1978. Prausnitz, J. M.; Anderson, T. F.; Grens, E. A.; Eckert, C. A.; Hsieh, R.; O’Connell, J. P. Computer Calculations for Multicomponent Vapor-Liquid and Liquid-Liquid Equilibria; Prentice-Hall: Englewood Cliffs, NJ, 1980. Prokopakis, G. J.; Seider, W. D. “Feasible Specification in Azeotropic Distillation”. AZChE J . 1983, 29, 49-60. Prokopakis, G. J.; Seider, W. D.; Ross, B. A. “Azeotropic Distillation Towers With Two Liquid Phases”. Foundations of Computer Aided Chemical Process Design Vol. II.; Mah, R. S. H., Seider, W. D., Eds.; AIChE: New York, 1981. Rose, A.; Sweeny, R. F.; Schrodt, V. N. “Continuous Distillation Calculations by Relaxation Method”. Ind. Eng. Chem. 1958,50, 737-740. Ross, B. A.; Seider, W. D. “Simulation of Three-phase Distillation Towers”. Comput. Chem. Eng. 1980,5, 7-20. Stadtherr, M. A.; Chen, H. S. “Strategies for Simultaneous Modular Flowsheeting and Optimization”. In Foundations of Computer
Aided Process Design; Westerberg, A. W., Chien, H. H., Eds.; CACHE: Ann Arbor, MI, 1984. Treccani, G.; Trabattoni, L.; Szego, G. P. “A Method for Isolation of Minima”. In Minimization Algorithms, Mathematical Theories and Computer Results; Szego, G. P., Ed.; Academic: London, 1972. Van Dongen, D. B.; Doherty, M. F. ’Calculation and Stability of Multiple Equilibrium Points for Nonideal Mixtures”. Fluid Phase Equilib. 1983, 14, 335-343. Venkataraman, S.; Lucia, A. “Exploiting The Gibbs-Duhem Equation in Separation Calculations”. AZChE J . 1986,32, 1057-1066. Venkataraman, S.; Lucia, A. “Solving Distillation Problems by Newton-like Methods”. Comput. Chem. Eng. 1988, 12, 55-69. Wilson, R. B. “A Simplified Algorithm for Concave Programming”. Ph.D. Dissertation, Harvard University, Cambridge, MA, 1963. Wolfe, P. “Methods in Nonlinear Programming”. In Nonlinear Programming; Abadie, J., Ed.; Wiley: New York, 1967. Received for review November 19, 1987 Revised manuscript received June 16, 1988 Accepted July 6, 1988
Studies on Gas Holdup in a Bubble Column Operated at Elevated Temperatures Zou Renjun*+ Hebei Academy of Sciences, Shijiazhuang, The People’s Republic of China
Jiang Xinzhen, Li Baozhang, Zu Yong, and Zhang Laiqi Chemical Engineering Department, Northwestern University, Xi”.,
The PeopleS Republic of China
Gas holdup was studied in a bubble column operated a t elevated temperatures for the systems air-water, air-alcohol, and air-5% NaCl solution. The influence of temperature on the gas holdup was studied focally nearing the boiling points. The bubble column is 100 mm in diameter and 1.05 in height, and the gas distributor has a single nozzle that is 10 mm in diameter. The gas and liquid flowed upward concurrently through the column. The gas and liquid superficial velocities were 1-16 and 0.7 cm-s-l, respectively. The temperature range was 25-96.56 “C. A gas holdup correlation implicating the effect of the operating temperature was developed with an average deviation of 3.1%. The result of this paper can be used for the scale-up and the design of bubble columns. Bubble columns are widely used in the fields of the chemical, biochemical, and food industries as well as environmental engineering as absorbers, desorbers, or reactors; see Schugerl et al. (1977), Jiang and Zhang (1981), Jiang (1983), Shah et al. (1982), and Zou (1985). Gas holdup is the basic parameter indicating the hydrodynamical characteristics of bubble columns. It affects directly the geometric sizes of bubble columns, and the gas-liquid interfacial areas thus affects the mass-transfer rates of bubble columns. So it is one of the necessary and important parameters for the design of bubble columns. Hence, many investigators used measuring methods to study the gas holdup in bubble columns to correlate the gas holdup, the physical properties of the system, and the sizes of the apparatus, as well as the operating conditions. On the basis of the experiments, many gas holdup correlations were suggested by different investigators. However, most of the previous correlations were developed based on the experimental data in bubble columns operated at ordinary temperatures, less than 40 “C, but the commercial bubble columns are commonly operated at elevated temperatures, often nearing the boiling points. It is wondered In accordance with the authors’ wishes, their family names are listed first. Zou Renjun is concurrently a t Hebei Institute of Technology and Northwestern University.
whether the previous correlations can be used for the scale-up of the commercial bubble columns. Although Quick and Deckwer (1981) measured the gas holdup in a bubble column operated at the temperature range 60-170 “ C for some liquid hydrocarbons, they didn’t developed a new correlation to correlate quantitatively their data. Jiang (1983) has suggested a gas holdup correlation. In the present paper, a complementary gas holdup correlation implicating the effect of the temperature in a bubble column operated at elevated temperatures is developed. Experimental Section The flow diagram of the bubble column is shown in Figure 1. The bubble column is made of stainless steel. It is 100 mm in inside diameter and 1.05m in height. Four pressure taps were drilled in the wall at 250-mm intervals, the lowest, tap 1, being 150 mm above the bottom plate of the column. The gas and liquid spargers are of single nozzle type, and the nozzle’s inside diameter is 10 mm. The gas and liquid nozzles are located 50 mm and 25 mm above the bottom plate of the column, respectively. Taps 1 and 3 are also used as the insertion points of the thermocouples. The column was operated continuously, and the gas and liquid flowed upward concurrently. The feed superficial velocities were 1-16 cms-’ with respect to the gas flow and
088~-58S5/S8/2627-1910$01.50/0 0 1988 American Chemical Society
Ind. Eng. Chem. Res., Vol. 27, No. 10, 1988 1911 Table I. Physical Properties for the Experimental Systems system temp, OC 103po, g . ~ m - ~ 1 O 2 r ~CP , air-water 25 1.185 1.833 96.5 0.955 2.161 air-alcohol 40 1.128 1.904 75 1.015 2.067 air-5% NaCl 40 1.128 1.904 95 0.959 2.1545
rll
P
Figure 1. Flow diagram of the bubble column: A, bubble column; B, gas-liquid separator; C, air heater; D, liquid heater; E, air bumper; tank 1; G2, tank 2; P, pressure gauge; R, rotameter; T, F, pump; GI, thermocouples; W, condenser.
0.7 cms-’ with respect to the liquid flow. The air was used as the gas phase and was not presaturated. The liquids used as the liquid phase are given in Table I, together with their physical properties. The water was deionized and was used to prepare the aqueous solution of NaC1. After separately measuring the flow rate with rotameters and heating to the given temperature through the heater, the air and liquid were separately fed from the nozzle to the bottom of the column. The gas was dispersed in liquid in the bubble form in the column. The gas-liquid mixture leaving the column was separated through the separator above the top of the column. The liquid flowed to tank 1through the overflow tube, and the gas-entraining liquid spray left the separator for the condensor, where the liquid spray entrained by gas was condensed and then the gas was vented to the sky. In order to keep the column temperature uniform, the column was enveloped in a film wrapper. The inside temperature of the column was measured by two thermocouples a t tap 1 and tap 3 and recorded by a autorecorder. The heating medium was water stream. The reverse U-tube was used to measure the gas holdup in the column. The dispersion height, HGL,was kept at 1.05 m. In the case where the reverse U-tube was used, the gas holdup, t G , was calculated by CG = A h / L (1) where Ah is the difference in the liquid level of the reverse U-tube. In order to reduce the fluctuation of the liquid level of the tube, a damper between the taps and the tube was adopted.
Correlation In Figure 2, the present data for the air-water system at ordinary temperature was compared with the previous data obtained by using the single-nozzle or multinozzle gas sparger. It is seen from Figure 2 that the present data are near the values of Akita and Yoshida (1973) and Yoshida
p ~ g, - ~ m - ~
0.99708 0.96086 0.7879 0.7483 1.0268 0.9958
rL,CP 0.8937 0.2946 0.814 0.509 0.7277 0.33
u, dyn-cm-’
P,,mmHg
71.97 60.46 22.19 18.77 70.9 61.1
23.756 669.75 134.21 700 54 622.5
Table 11. variance origin regression residue total
Variance Analysis for the Air-Water System variance freedom mean F R, sum degree variance sum u = 1.3645 3 0.4583 1261.7 0.9840
Table 111. variance origin regression residue total
Variance Analysis for the Air-Alcohol System variance freedom mean sum degree variance sum F R, 3 0.4599 694.8 0.9786 u = 1.3798 Q = 0.0609 92 6.6196 X lo4 Q, = 1.4407 95
Q = 0.0447 Q, = 1.4092
124 127
3.6048
X
lo4
Table IV. Correction Factor for the Air-5% NaCl System t , “C 85 90 95 40 60 70 80 1.210 1.2468 1.1804 1.1607 1.1215 1.1505 1.2634
and Akita (1965) at the lower gas velocities, and the present data agree well with the data of Hikita et al. (1980) at higher gas velocities. Many factors affect the gas holdup in bubble columns. The effects of the nozzle diameter, do, the column diameter, D, and the clear liquid height, HL,on the gas holdup can be neglected (Hikita et al., 1980). The effect of the superficial liquid velocity can neglected when uL < 4.4 cms-’ (Akita and Yoshida, 1973). Thus, the factors concievably affecting eG are considered to be the superficial gas velocity, uG, the liquid density, pL, the liquid viscosity, pL, the surface tension of the liquid, u, the gravitational constant, g, and the liquid vapor pressure, Pa. Thus, the relationship is
= f ( u G , PL, PL, u, pa, g) (2) When the dimensional analysis was applied, the following correlation was derived from eq 2: €G
In light of the least-squares method to the experimental data, we obtained the following correlation of the gas holdup for the air-water and air-alcohol systems: eG = 0.17283( -0.1544 p + pa 16105
5)(7(y ) )
(4)
The variance analyses are shown in Tables I1 and I11 for the air-water and air-alcohol systems. It is seen that the correlation agrees well with the data from the tables. For the air-5% NaCl solution, the following correction factor was defined:
f = CG/CGo (5) where cG0 is the calculated values from eq 4 for the electrolyte solutions. It was found from the experiment that depends on the operating temperature. Table IV gives the
1912 Ind. Eng. Chem. Res., Vol. 27, No. 10, 1988 I/ h
I1
I
I
1
I
4
Hills
I)
M i y i u c h i CI S I 19iu H i k i r i CI 1 1 19xii P l C l 111 u orli
tl
1
in
i
*&
d ( m
I976
h
h
1
liill
5
Figure 2. Comparison of the present data with previous data of the gas holdup for the air-water system.
-
e,
I.
i
Figure 4. zG versus t plot for the air-alcohol system.
0 - u ~=i 31 OU,
0
n
,
=3
' j
,
,
2n
RO t
Figure 3.
Q
.
,
, 40
,
,
sn
.
,
loo
i
versus t plot for the air-water system.
L
correction factor for the air+% NaCl solution system at different temperatures.
Discussion The relationship between the gas holdup and the operating temperature is shown in Figures 3-5. It can be seen that the operating temperature influences remarkably the gas holdup in the bubble column. The effect of temperature on the gas holdup can be divided two stages. For the air-water system, t G is increased slowly with an increase of temperature a t t < 75 "C, and CG is increased remarkably with an increase of temperature at t > 75 "C. The air-alcohol and air+% NaCl systems like this, but the demarcation temperature points are 65 and 80 "C, respectively. The reason is mainly that the sizes of the bubbles in the liquid are smaller at elevated temperature. This phenomenon is relevant for the change of the physical properties of the system with temperature. The relationship between the gas holdup and the temperature is basically similar to the change tendency of the vapor pressure of liquid with temperature. Therefore, the vapor pressure of the liquid phase can be used to indicate the effect of temperature on the gas holdup. The t~ versus uGplots are shown in Figures 6-8. It can be seen that the gas holdup is increased with an increase of the superficial gas velocity. In addition, eG(ail-alcohol) > eG(air-5% NaCl) > cG(air-water) under the same operating conditions. This is because alcohol volatilizes easier
0
20
1.
Figure 5.
CG versus
60
40
80
100
c
t plot for the air-5% NaCl system
than water and 5% NaCl solution, the presence of the electrolyte in the water changes of the electric potential properties of the liquid surface, and the small steady bubbles form easily and coalesce difficulty. Hence, the values of the gas holdup for the air-electrolyte solution system are larger than for the air-water system. Up to now, more than 20 gas holdup correlations were presented in the literature, but only about 10 correlations are commonly used. They were suggested by the different investigators based on the experimental data at ordinary temperature. The deviation is great when these correlations are used to calculate gas holdup in the practical bubble columns operated at elevated temperatures. The present data are compared with the calculated values of these correlations as shown in Figures 9-27. It can be seen that the calculated values of the previous correlation agreed with the present experimental data at ordinary temperature, except for the correlations of Oels et al. (1976) and Hughmark (1967). But at elevated temperatures, the previous correlations give great deviations, except the present correlation agreed with the experimental data well. Hence, the correlations presented in the
Ind. Eng. Chem. Res., Vol. 27, No. 10, 1988 1913 E; 1
e G .
0.X
a-96
0.SZ. 0.48.
3.44.
j
C
Q - S ~ L
0-
90 C 081 L 0-75 C
0 -80
0-60 C 0- 3 L A- 40 L
0 48-
J
0.40.
0.36.
, /*
0e --9&0 C c
0 . 5 62 -
C
@-iOC
0.14-
0 .do0 .%-
0 .32, 0 .32.
0.25. 0.280 24' 0 24. 0.20.
.o 2 0 , 0.16' 0 16. 0.12. 0.12-
0.08. 0 .08-
0.w. I
0
2
3
6
8
U,, Figure 6.
€0versus U G
10
12
14
16
0.04t l
o
C m SI
plot for the air-water system.
'e
B
6
3
U,,cm
Figure 8.
€0versus U G
0
IO
12
11
tfi
s-1
plot for the air-5% NaCl system.
0.1
02
E,
03
0.4
0.5
(ap.1
Figure 9. Present experimental data compared with correlation of Han et al. (1983)for the air-water system. EG
lcal
'.
0.5-
0 A-
0-40
L
0 -40 L
A -70
c
A -7.i
C
0.3 -
0 04.
BG (UP.) Figure 10. Present experimental data compared with correlation of Han et al. (1983) for the air-alcohol system.
Conclusions The operating temperature influences remarkably gas holdup in bubble columns. In the present work, a gas holdup correlation implicating the effect of the tempera-
1914 Ind.
Eng.Chem. Res., Vol. 27, No. 10,1988 kG
cal '
L
C
0-2.i
0.5-
.
0 - ill 'f
0.4-
o{/ 0.
AAA
i/.
0
I
,
'
,
0.2
0.1,
1
0.4
0.3
0.5
CGrCxP,
Figure 11. Present experimental data compared with correlation of Hikita et al. (1980) for the air-water system.
11
01
0.3
0.2
EG
0.4
'w
E ; exp Figure 15. Present experimental data compared with correlation of Gestrich and Riihse (1975) for the air-water system.
0.5
Figure 12. Present experimental data compared with correlation of Hikita et al. (1980) for the air-alcohol system.
M*
OA
A
&G
eKP
Figure 16. Present experimental data compared with correlation of Gestrich and Riihse (1975) for the air-alcohol system.
Oi/
E G *
O
CPI
O /
0 4
0 -2.j
'C
O-.io
C
A-7i
i
A -90
i
0.31
01
0
02
0 1
Ec
03 'CXP
'
04
05
Figure 13. Present experimental data compared with correlation of Hills (1976) for the air-water system.
/
;,
:,$
Figure 17. Present experimental data compared with correlation of Mashelkar (1970) for the air-water system. E G
'
Cal.'.
0.5-
o . 2 y A ,
0.4-
0 1
0.3 -
A
O A
A + A
0
0 1
0.2
0.3
0.1
o
5
$G'exp'
Figure 14. Present experimental data compared with correlation of Hills (1976) for the air-alcohol system.
ture was developed (eq 4),with an average deviation of 3.1%. It can be used for the scale-up and design of bubble columns.
Figure 18. Present experimental data compared with correlation of Mashelkar (1970) for the air-alcohol system.
Ind. Eng. Chem. Res., Vol. 27, No. 10, 1988 1915
0.T
0.3 0.2-
0.1-
0
0.1
0.2 e,G
0.1
0
0.3 0.4 0.5 (q.)'
0.3
0.2
E,(
Figure 19. Present experimental data compared with correlation of Kumar et al. (1976)for the air-water system.
0.4
0.5
=P'
Figure 23. Present experimental data compared with correlation of Kelkar et al. (1983)for the air-alcohol system. EG
/
0.51
'al..
0.50.4-
0 .4
0 - E i 0-i0
C C
A-75
C
A-90
-c
0.30
-40°C
0 -6OC
0
0
0.1
02EGpi~p,,o.4
01
Figure 20. Present experimental data compared with correlation of Kumar et al. (1976)for the air-alcohol system.
03
0.2
0.5
E G
0 4
0 5
(ev
Figure 24. Present experimental data compared with correlation of Hughmark (1967)for the air-water system.
E G
(tal,).
0.50.4 -
- 2.5
C
0-50
C
A-75
C
A - 90 C
0.3 -
A AAdA
02t
L
0
0.1
0.2
0.3 0.4 EG'exp)
0.5
0.5
Figure 21. Present experimental data compared with correlation of Oels et al. (1976)for the air-water system.
Figure 25. Present experimental data compared with correlation of Hughmark (1967)for the air-alcohol system. &G cal
E;
ical
0.50.4
-
03
-
Ohhi
0 5-
0-
25°C
0-
50'C
A-
75°C
0'1
0'2
0.2-
Figure 22. Present experimental data compared with correlation of Oels et al. (1976)for the air-alcohol system.
It was found that the deviation between the experimental data and the calculated values is large if the correlations Dresented in the literature are used to calculate the gas hbldup in bubble columns at elevated tempera-
0'3 €G
0'4
0'5
oh
exp
Figure 26. Present experimental data compared with the present correlation for the air-water system.
tures, because these correlations characterized the effect of the temDerature through such varameters as density, - . I
1916 Ind. Eng. Chem. Res., Vol. 27, No. 10, 1988
R , = adjusted multiple correlation coefficient t = operating temperature, O C UG =
superficial gas velocity, c m d
uL = superficial liquid velocity, cmss-l Greek Letters CG = gas holdup lL = viscosity of liquid, CP pL = density of liquid, g . ~ m - ~ 0 = surface tension of liquid, dyn-cm-’
Literature Cited
&G
exp
Figure 27. Present experimental data compared with the present correlation for the air-alcohol system.
surface tension, md viscosity, but these parameters cannot indicate the rapid change of the gas holdup with an increase of the temperature. However, the change tendency of the gas holdup with temperature is basically similar to the relationship between the vapor pressure of the liquid and the temperature, the vapor pressure can be used to characterize the effects of the temperature on the gas holdup in bubble columns. The presence of electrolytes in the system affects notably the values of the gas holdup in bubble columns. Although previous investigators employed the correction factor to show the effect of the electrolytes on the gas holdup, they didn’t consider the effect of temperature on the correction factor. It was found that the correction factor is a function of temperature. Acknowledgment We thank the Fund Board of Chinese Academy of Sciences for financial support to aid this research. We also thank Fan Hengxin for his help in processing the experimental data. Nomenclature D = diameter of olumn, mm do = diameter of 3s sparger nozzle, mm f = correction fac.or g = gravitational constant, cm+? H = height of column, m HGL= dispersion height, m HL = clear liquid height, m Ah = difference of liquid level of U-tube, mm L = distance of two taps, mm P = total pressure of system, mmHg P, = vapor pressure of liquid phase, mmHg
Akita, K.; Yoshida, F. “Gas Holdup and Volumetric Mass Transfer Coefficient in Bubble Columns”. Ind. Eng. Chem. Process Des. Deu. 1973, 12, 76-80. Gestrich, W.; Rahse, W. “Der Relative Gasgehalt von Blasen-Schicten.” Chem.-Ing.-Tech. 1975, 47, 8-13. Han Wei; Feng Pusun; Shen Ziqiu “Gas Holdup in Bubble Columns”. Dalian Gongxueyuan Xuebao 1983,22(2), 45-51. Hikita, H.; Asai, S.; Tanigawa, K.; Segawa, K.; Kitao, M. “Gas Holdup in Bubble Column”. Chem. Eng. J. 1980, 20, 59-67. Hills, J. H. “The Operation of a Bubble Column at High Throughputs I. Gas Holdup Measurements.” Chem. Eng. J. 1976, 12, 89-99. Hughmark, G. A. “Holdup and Mass Transfer in Bubble Columns”. Ind. Eng. Chem. Process Des. Dev. 1967,6, 218-220. Jiang Xinzhen “Bubble Columns”. Bull. Achievement Sci. Res. 1983, 10, 33. Jiang Xinzhen; Zhang Qinling “Discussion on the Scaleup of Bubble Column Reactors”. Huagong Jixie 1981, 3, 21-36. Kelkar, B. G.; Godbole, S. P.; Honath, M. F.; Shah, Y. T.; Carr, N. L.; Deckwer, W. D. “Effect of Addition of Alcohols on Gas Holdup and Backmixing in Bubble Columns”. AIChE J . 1983, 29(3), 361-369. Kumar, A.; Dagaleesan, T. T.; Laddha, G. S.; Hoelscher, H. E. “Bubble Swarm Characteristics in Bubble Columns”. Can. J. Chem. Eng. 1976,54,503-508. Mashelkar, R. A. ”Bubble Columns”. Br. Chem. Eng. 1970,15(10), 1297-1304. Oels, U.; Schugerl, K.; Todt, J. “Gasanteil, Stofftransportgeschwindigkeits Koeffizient und Spezifische Phasengrenzflache in Gleichstrom-Blasensaulen”. Chem.-Ing.Tech. 1976, 48(1), 73-74. Quick, G.; Deckwer, W. D. “Gasgehalt und Phasengrenzflache in Begasten Kohlenwasserstoffen”. Chem.-Ing.-Tech. 1981, 53, 474-475. Shah, Y. T.; Kelkar, B. G.; Godbole, S. P.; Deckwer, W. D. “Design Parameters Estimations for Bubble Column Reactors”. AIChE J. 1982, 28(3), 353-379. Schugerl, K.; Liicke, J.; Oels, U. “Bubble Column Bioreactors”. Adu. Biochem. Eng. 1977, 7, 1-84. Yoshida, F.; Akita, K. “Performance of Gas Bubble Columns: Volumetric Liquid-phase Mass Transfer Coefficient and Gas Holdup”. AIChE J. 1965, 11,9-13. Zou Renjun, “Chemical Reaction Engineering in Basic Organic Chemical Industry; Chemical Industry Press: Beijing, 1985.
Received for review October 2, 1987 Revised manuscript received April 5, 1988 Accepted June 7, 1988
