I n d . Eng. Chem. Res. 1989,28, 1405-1410 Morris, G. A.; Jackson, J. Absorption Towers; Butterworths Scientific Publication: Great Britain, 1953. Schiesser, W. E. DSSIP-Release 3. Internal Report, Lehigh University, Bethlehem, PA, 1977. Srivastava, R. K.; Joseph, B. Simulation of Packed-bed Separation Processes Using Orthogonal Collocation. Ind. Eng. Chem. 1984, 8(1),43-50.
Tan, K. S.; Spinner, I. H. Numerical Methods of Solution for Con-
1405
tinuous Countercurrent Processes in the Nonsteady State. AIChE
J. 1984, 30(5), 770-779.
Tommasi, G.; Rice, P. Dynamics of Packed Tower Distillation. Ind. Eng. Chem. Process. Des. Deu. 1970, 9, 234-243. Received for review November 12, 1987 Revised manuscript received May 1, 1989 Accepted May 16, 1989
Characteristics of a Cocurrent Multistage Bubble Column B. H. Chen and N. S. Yang* Chemical Engineering Department, Technical University of Nova Scotia, P.O. Box 1000, Halifax, Nova Scotia, Canada
Hydrodynamic and mass-transfer characteristics of a cocurrent multistage bubble column containing 37 plates have been determined as a function of column diameter, liquid viscosity, and flow rate of the two phases. The plates are of 6-mesh screen, having a fractional free area of 0.64. T h e use of screen plates has produced a homogeneous dispersion of nearly identical bubbles in the liquid in the column. It also has practically eliminated the diameter effect on the gas holdup, the bubble size, and the volumetric mass-transfer coefficient. In comparison with other gas-liquid contacting devices, the screen plate column has very small backmixing of the liquid phase, a large gas holdup, and a large mass-transfer coefficient. The coefficient is affected adversely by viscosity but positively by both gas and liquid flow rates. These favorable characteristics may manifest the high potential of the screen-plate column as an effective and economical gas-liquid contactor. The bubble column is generally an efficient and economical device for bringing about an intimate interfacial contact necessary for numerous gas-liquid or gas-liquidsolid operations in the chemical or biochemical industry. However, some of the hydrodynamic properties of the column, such as the bubble coalescence a t high gas flow rates and the severe backmixing of the liquid phase, may have limited its application at the present level. Detailed reviews of column characteristics were given recently by Shah et al. (1982) and Chen (1986). One method proposed to minimize these undesirable effects is to stage a bubble column. Voigt and Schugerl (1979) and Voigt et al. (1980) studied the absorption of oxygen in a countercurrent multistage bubble column containing perforated plates with downcomers and found a large increase in both a and kL over that reported for single-staged columns. The intensity of the longitudinal dispersion in the liquid was also lowered as a result of staging (Sekizawa and Kubota, 1974). Plates without downcomers but with up to 64% free area have also been tested, with similar findings (Yang et al., 1986a; Schugerl et al., 1977; Nishikawa et al., 1985). The level of accomplishment expected of a modified bubble column is obviously dependent on the nature of the internal solid. An ideal column plate must at least possess the following properties: (1) simple construction and operation, (2) a free area sufficient to produce a large gas holdup at low pressure drop, (3) uniform resistance to two-phase flow over the entire cross section, and (4) small volume relative to the column. It appears that plates made from wire-mesh screens could reasonably satisfy all of these criteria. This is well supported by the successful applications of wire screens in the aerodynamic industry (Schubauer et al., 1950; Laws and Livesey, 1978) and by their proven capability to improve the operation of many two-phase contacting devices (Chen, 1971). *Visiting Scholar from Dalian Institute of Technology, Dalian, People’s Republic of China.
Among the various types of screens that have been tested in previous studies (Chen and Vallabh, 1970; Voyer and Miller, 1968), the 6-mesh, 0.58-mm wire diameter woven screen has proven itself to be the most promising as a internal solid. This is mainly due to its particular geometry, which provides the least resistance to rising drops or bubbles while still being able to keep the bubble growth under control. The primary purpose of this study is to examine the operating characteristics of cocurrent multistage bubble columns fitted with screen plates and to compare the results with those previously published for other types of modified bubble columns. Some conclusions can then be drawn regarding its potential as a gas-liquid contacting device.
Experimental Section Apparatus. Figure 1 shows schematically the experimental apparatus used. Each of the three columns employed was constructed from two sections of 1.2-m-long Plexiglas tubing, with diameters of 0.05, 0.075, and 0.15 m, respectively. All three columns have an overall height of about 3 m. Only the 0.075-m-diameter column was insulated for dispersion study. The circular plates installed in each column were made from 6-mesh stainless steel wire-screen sheets having a fractional free area of 0.64. Thirty-seven such plates were mounted 0.05 m apart, forming a stack on a central shaft of 5-mm diameter. The plates were about 1.5 mm smaller in diameter than the column diameter for easy removal or installation. Air, after passing through a filter, a pressure regulator, and a calibrated rotameter, was admitted to a 0.2-m-long humidifying section at the bottom of the column. A distributor consisting of four 1.5-mm nozzles for the two smaller columns and eight such nozzles for the 0.15-m column was used to disperse the air through another 0.15-m-long humidifying section before entering the test section. The air rose in the form of bubbles through the series of 37 screen plates and left the column freely at the
0888-5885/ 8912628-1405$01.5010 0 1989 American Chemical Society
1406 Ind. Eng. Chem. Res., Vol. 28, No. 9, 1989
continuous withdrawal of heat at the top of the column, the temperature of the two-phase mixture upstream of the cooler under cocurrent flow condition is given by d2T/dX2 + VL/(l - t G ) D L dT/dx = 0 (4)
Figure 1. Flow diagram: A, stage column; B, plates; D, drain; E, distributor; F, exhaust; G , air inlet; H, heater; K, cooler; M, manometer; 0, overflow; R, rotameters; TT, thermocouples; w, water inlet.
top. Tap water and 0.2% (carboxymethy1)cellulose (CMC) aqueous solution, both are Newtonians, were the liquids used. The liquid entered the column a t the bottom and flowed cocurrently upward with the gas phase. Its flow rate was measured with a calibrated rotameter. Liquid temperatures were not controlled but did remain fairly constant throughout an experimental run. Liquid viscosities were evaluated at the mean bulk temperature. Gas holdup measurements were made in each of the three columns for two liquid systems: air-water and air0.2% CMC solution. The gas holdup was calculated from the following equation: (1) 6G = (h! - Ho)/H
Determination of Bubble Size and Interfacial Area. The photographic technique was used to measure the bubble size distributions. A rectangular Plexiglas jacket was mounted around a 0.1-m-long column section 1.5 m from the base and was filled with water to minimize refractive distortion. Bubbles in this short section during the two-phase operation were photographed under diffuse side light using a Pentax K 1000 SE camera with a 50-mm lens at exposure of about 1/1000 s and f 5.6-8.0. Enlarged prints were made, from which both the maximum and the minimum dimensions of the bubbles were measured. About 100-200 bubbles were measured in each of the two pictures taken during a run. The bubbles were not spherical but could be approximately represented by an oblate spheroid. The Sauter mean bubble diameter, d32,was calculated from n
n
i=1
i-1
E di3/
di2
(2)
and the specific interfacial area from a = (66~/d32)(1- E G )
(3)
d32 =
Determination of the Axial Dispersion Coefficient, DL. Previous studies (Shah et al., 1982; Schugerl et al., 1977) have indicated that the axial dispersion of a liquid in various types of bubble columns can be described satisfactorily by the one-dimensional dispersion model. In this study, the same model was used to determine the axial dispersion coefficient using heat as a tracer. For the
This equation is based on the following assumptions: (1) uniform radial temperature, (2) negligible evaporation and heat loss through the wall, (3) small heat conduction compared to convection, and (4) constant physical properties of the system. In this work, measures were taken to ensure that these assumptions could be approximately met. These included insulating the 0.075-m column used for dispersion measurements and maintaining the operating temperature low at around 5 "C above the room temperature, ranging from 20 to 24 "C. These two conditions were designed to meet the requirements of assumptions 1,3, and 4. As described in the Experimental Section, the present experimental setup (Figure 1) allowed the air to be adequately humidified before it entered the test section, thereby minimizing the possible evaporation loss. The solution to eq 4, satisfying the boundary conditions of x = 0, T = To and x m, T = Ti, is In [(Ti- T)/(Ti - T o ) ]= -[(vLx)/(1- ~G)]DL(5)
-
The temperature profile obtained experimentally at a given set of gas and liquid flow rates is fitted to eq 5 to determine the axial dispersion coefficient, DL.A Cole-Parmer Model 8502 thermistor coupled with YSI Series 700 thermometer probes was used for the temperature measurements. Determination of Volumetric Mass-Transfer Coefficient, k L a . The desorption of oxygen from the liquid solution by pure nitrogen gas was used for this purpose. Two gas-liquid systems, N,-water and N2-0.2% aqueous CMC solution, were tested. For each pair of gas and liquid flow rates, liquid samples were taken a t the column inlet and exit and were analyzed for oxygen content with YSI Type 58 dissolved oxygen meter. This instrument has a sensitivity of h0.03 mg/L of dissolved oxygen, and the 90% response time is 10 s. The data were reproducible to within *lo%. The measured oxygen concentrations are used normally in conjunction with the data on axial mixing to compute the volumetric masstransfer coefficient, but in the present study, the use of eq 6 is adequate because of the small axial dispersion in multistage columns: kLa = VL/Z(l - t ~ In ) (C,* - C,)/(C,* - C,) (6) Equation 6 gives results generally about 7% higher than that estimated from the dispersion model (Danckwerts, 1953) within the range of the present study.
Results and Discussion Gas Holdup. Typical data on the average gas holdup for the two liquids are shown in Figure 2. The air-water data were determined in both 0.15-m and 0.075-m columns, while the data for air-CMC solution were obtained in a 0.051-m column. It is clear from Figure 2 that the column diameter has only a negligible effect on tGover the ranges of flow rates used. The lower than expected values that occur for the CMC solution at relatively high gas flow arc due more to the viscosity change than to the column diameter. This conclusion is consistent with our visual observation that, at high gas flow through the viscous solution, large gaseous bubbles frequently form and cross the plates without being broken up. In other words, the present results indicate that the 6-mesh screen may have become less effective to control the growth of the bubble in highly viscous solutions.
Ind. Eng. Chem. Res., Vol. 28, No. 9, 1989 1407
VG, mtr
Figure 2. Gas holdup in various bubble columns. Symbol, n, a,D, (m), system, author: A,37,0.64,0.075, ah-water, present; +, 37,0.64, 0.15, air-water present; 0 , 37, 0.64, 0.051, air-0.2% CMC, present; ---,0, 1.0, 0.14, air-water, Schugerl et al. (1977); --, 12, 0.28, 0.14, air-water, Schugerl et al. (1977).
2
0
4
The present data can be correlated uniquely with the slip velocity, V,, of the two-phase mixture in the following form:
a
b
d32,
MM
Figure 3. Bubble-size distributions. ( 0 ) VG = 0.07 m/s, present data; ( X ) V , = 0.03 m/s, present data; (-.-) VG= 0.027 m/s, Yang et al. (1986b).
where The fact that this type of correlation is possible can be taken as strong evidence of the existence of a homogeneous mixture within the screen-plate column (Freeman and Davidson, 1969). It may be noted that the decrease of V, with increasing t G or, equivalently, VG is unique in this type of column because of the unusually fast increase of gas holdup with increasing gas flow rate. Bubble Size and Interfacial Area. Bubble size distributions were measured for the air-water system in two columns, 0.15 m and 0.075 m in diameter. Typical results are shown in Figure 3 along with those for Karr plate columns (Yang et al., 198613). The considerably more pointed distribution is indicative of the effectiveness of the screen plates in curbing the growth of bubbles. Nishikawa et al. (1978) have suggested that a size distribution can be considered uniform if its dimensionless variance (on/d3.$ is less than 0.03. On this basis, the bubble population in the present column is then one of uniform size under all conditions studied. Figure 4 shows the computed Sauter mean diameters as a function of gas and liquid flow rates and column diameter. In contrast with those obtained in a Karr column (Yang et d.,1986b), the bubbles in the screen-stage column are generally smaller. No clear influence on bubble size due to either gas or liquid flow rate can be seen, although previous workers (Yang et d.,1986b) have reported a slight but consistent increase of bubble size with increasing gas flow in Karr columns. These differences may suggest that, within the ranges of variables studied, the uniform-resistance plate, such as the screen plate, has shown itself to be a more effective bubble-size controller than Karr plate. The latter is characterized by a few large openings about 12.6 mm in diameter. Also seen from Figure 4 is that the average bubble size is unaffected by the change of column diameter from 0.075
uz 2
c
I 0
I
I
I
I
I
1
2
3
4
5
I 6~10-~
VG, M I S
Figure 4. Sauter mean diameter as a function of flow rates. Symbol, column, D,(m), V , (mm/s): 0,A, X, +, 0 , screen plate, 0.075, 3-67; 0 , screen plate, 0.15, 5-25; 0,Karr plate, 0.052, 9-62.
to 0.15 m. It should be noted that the large majority of the bubbles generated in the present column falls within the preferred size range between 4 and 5 mm for interfacial transfer processes (Calderbank and Moo-Young, 1961). The interfacial area, a, were estimated from eq 3 for various gas and liquid flow rates. The liquid flow rate was found to have only a minor effect on a, as indicated by the following empirical correlation of the present results: u = 1.43 X 104V~1~z5VL-O~1 (9) The average deviation is less than 8%. The negative effect of VL reflects the fact that most of the bubbles accumulated below each plate are being cleared and carried upward by the increased liquid flow. Equation 9 points out the excellent capability of a multiscreen plate column to produce a high interfacial area. In fact, the area produced may approach or exceed that obtainable in many other gas-liquid contacting devices such as reciprocating plate column or stirred vessel for which a large power consumption is always required. Axial Dispersion Coefficient, D,. Figure 5 presents typical temperature profiles for air-water flow through the 0.075-m column. The excellent linearity of the plots may justify the use of eq 5 for estimating DL. Values of DL thus estimated are shown in Figure 6. It is seen that, within the ranges of variables studied, DL is rather insensitive to the change in VL, in common with the
1408 Ind. Eng. Chem. Res., Vol. 28, No. 9, 1989
L 0
I
I
I
I
I
.10
.25
.4 0
-55
.70
I .85
x, m Figure 5. Typical temperature profiles in screen stage column. Symbol, VL (mm/s), Vc (mm/s), 104DL(m2/s): 0 , 3.23, 34, 16.4; X, 1.62, 8.6, 4.5; 0 , 3.23, 46, 20.7.
I 4-1 I
I
4
1 . 1
6
8
vG,
2-
l.XlO-’
I
I
I
2
4
6
1x1
MIS
Figure 7. Volumetric mass-transfer coefficients for various bubble columns. Curve, column type, D,(mm), V , (mm/s), reference: 0 , screen plate 75, 6.72, present; +, screen plate, 75, 3.2, present; X, screen plate, 75, 16.4, present; 0 , screen plate, 75, 32.8, present; 0, screen plate, 51, 23.4, present; B, screen plate, 150, 25, present; A, screen plate (air-0.2% aqueous CMC solution), 51, 21, present; 1, sieve plate, 140, 22, Schugerl et al. (1977); 2, Karr, unagitated, 51, 46, Yang et al. (1986a); 3, bubble, N/A, 5-16, Deckwer et al. (1974); 4, packed bubble, N/A, 28, Alexander and Shah, 1976.
P
-. * x
10-
i 8 -
a
6 4-
I
I
2
1
.2
I
I
I
1
I
I
I
1
.4
.6
.8
I.
2
4
6
8 IOX~O-~
vG,
M I S
where C = 0.64 for sufficiently high V G and n is the number of stage in series. Thus, the circulation velocity, V,, is related to VG by
Figure 6. Axial dispersion coefficient as a function of flow rates. (0, A, 0, 0 , X ) Present data, 1.5 mm/s < VL < 7.0 mm/s; (--) Karr column, V , < 12.4 mm/s.
V, = 1.04VG0,5 (13) Combining eq 10 and 13 and setting m = 0.12 yield
behavior of a simple bubble column. In addition, the values are extremely low in comparison with an unbaffled column for which DL varies between 0.01 and 0.03 mz/s under normal operating conditions. Therefore, a true cocurrent flow may be assumed with a negligible error for screen plate columns. Previous studies on bubble columns have reported a close correlation between the axial dispersion and the liquid circulation velocity. An examination of the two sets of data shown in Figure 6 reveals that such a characteristic also prevails in baffled columns. Joshi and Sharma (1979) have in fact correlated some available dispersion data in the following form:
DL = 9.4 x (14) m is taken to be 0.12 because the resulting curve best fits the experimental data. Equation 14 is compared with the experimental data in Figure 6 as the solid line. The good agreement may indicate there is no fundamental change in the dispersion process because of the presence of a large number of screen plates. Equation 14 is also compared with the results of Chen and McMillan (1982) for conventional bubble columns and that of Yang et al. (1986a) for gas-liquid Karr column. Clearly, the use of screens has resulted in a drastic reduction of the axial dispersion coefficient in bubble columns. Volumetric Mass-Transfer Coefficient, kLa Measurements of kLa were made for two systems and in columns of three sizes: 0.051,0.075, and 0.15 m in diameter. Typical kLa values calculated from eq 6 are shown in Figure 7. An examination of the figure shows at least three distinct characteristics of a screen plate column. With the screens in place, the mass-transfer coefficient, in addition to the gas holdup and bubble size, becomes rather insensitive to the change of the column diameter from 0.051 to 0.15 m. The problem of scale-up could therefore be considerably simplified. The result for the 0.2% CMC solution indicates the importance of the effect of viscosity on kLa. The gaseous bubbles in a highly viscous solution are able to grow in size with increasing gas flow rate despite the presence of screens, thereby lowering the gas holdup and hence kLa. Furthermore, the result shows that the rate of change of kLa with VG is lower for the thick solution than for water. This may be explained in terms of the change of flow pattern from turbulent to laminar flow when nitrogen-0.2% CMC solution is used in place of the nitrogenwater system. It may also be noted that the mass-transfer
DL/(D,VJ = m
(10)
where m = 0.31 for the air-water system. If one assumes that a multistage column is made up from a number of short bubble columns connected in series, eq 10 should be applicable to the present case with one exception: that the constant m is expected to be smaller to reflect the presence of screens. This is because screens are known to be capable of homogenizing the turbulence in a flow system. Chen et al. (1986) reported that the pressure drop for two-phase flow through a column of 37 screen plates was given by
ap, = 1.86 x
104vG
(11)
It was further reported (Chen and Wakao, 1988) that the pressure drop was also well represented when the liquid circulation velocity, V,, was used as the characteristic velocity; that is,
.
Ind. Eng. Chem. Res., Vol. 28, No. 9, 1989 1409 coefficient increases significantly not only with gas flow rate but also with liquid flow, in contrast with an unbaffled column for which the liquid flow rate is usually not a factor. The influence of these two flow rates may be seen quantitatively from the empirical correlation of the present data for the nitrogen-water system: kLa = 2.62v~0'85v~o'19
(15) Therefore, it is clear that the screen plate column is best suited for continuous operation. Comparison of Data. Also included in Figure 7 are four sets of mass-transfer data representative respectively of the conventional bubble column (Deckwer et al., 1974), the packed bubble column (Alexander and Shah, 1976), and the two-stage bubble columns, one having plates of Karr design with a = 0.54 (Yang et al., 1986a) and the other having sieve plates with a = 0.125 (Schugerl et al., 1977). This comparison demonstrates conclusively the superiority of screen plate for improving the bubble column performance. The data of Schugerl et al. (1977) obtained in a six-stage column with a = 0.125 show somewhat higher values of kLa, but the pressure drop across such a column is also higher. In fact, if the comparison were made on the basis of kLa/(AP/L), the superiority of the screen plate column would become much more evident. The individual mass-transfer coefficient, kL, is obtained by dividing eq 15 by eq 9: kL = 1.83 x 10-4vG-o'4vL0'29
(16)
The substantial, positive effect of the liquid velocity on the individual coefficient is normally expected of mass transfer in packed or staged bubble columns (Wang and Fan, 1978; Tojo et al., 1974; Yang et al., 1986a). However, the strong, negative effect of gas flow in this column is quite surprising. Although such observations have been reported in the literature (Tojo et al., 1974; Yang et al., 1986a), the reason is unclear. Since the slip velocity, V,, is dependent solely on the gas holdup and hence on the gas flow rate for a given gas-liquidsolid system, eq 16 can be rewritten in terms of V, in dimensionless form as eq 17.
S h = 1.13 X 10-4Re,1.75S~0.5ReLo.285 (17) The effect of wire diameter was not studied; its use is therefore arbitrary. As shown in Figure 8, this conventional form of correlation is the basis for a comparison of the present data with those of other investigators (Higbie, 1935; Schugerl et al., 1977; Reuss, 1970) obtained in unbaffled bubble columns. When these earlier correlations are considered, the exponent r in the ordinate is zero, indicative of the absence of liquid flow effect on kL This comparison is significant in three aspects. (1)The use of slip velocity has resulted in a satisfactory correlation for both baffled and unbaffled bubble columns, and this confirms the earlier suggestion that the negative effect of VG on kL is due to the lowering of V,. (2) The use of screen baffles has enhanced the importance of slip velocity since the exponent on Re, has increased from 0.85 for conventional bubble columns to 1.75 for the present column. (3) It should be pointed that there is good agreement between the results of Reuss (1970), Schugerl et al. (1977), and the present work over the ranges of variables studied. Therefore, the large value of kLa as found in the screen plate column is mainly a result from the increased interfacial area or gas holdup.
Summary and Conclusions Hydrodynamic and mass-transfer characteristics of multistage bubble columns have been determined over the ranges 0.26 X low2m/s IVG 8 X m/s, 0 IVL 3.3
2
4
8 1 0
6
20x10
Re,
Figure 8. Comparison of kL for stage and conventional bubble columns. Curve, authors; 0, A, 0 , 0,A, present data, r = 0.283; 1, Higbie (1935),r = 0; 2, Schugerl et al. (1977); r = 0; 3, Reuss (1970), r = 0. X m/s, 0.001 kg/(m.s) IpL I0.038 kg/(ms), and 0.051 m I D,I 0.15 m. In comparison with the other types of gas-liquid contactors, the screen plate column shows the following advantages: (1) The bubble size varies only slightly and a nearly uniform dispersion can be obtained. (2) The axial mixing is very small; a true cocurrent flow may be assumed with negligible errors. (3) The column has high kLa despite the adverse effect of V G on kL. (4) The diameter effect is minimal, thereby simplifying the scale-up process. ( 5 ) It is well suited for continuous gas-liquid contacting operations.
Acknowledgment This study was financially supported by the Natural Sciences and Engineering Research Council of Canada.
Nomenclature A = interfacial area, m2/m3of column a = interfacial area, m2/m3of liquid C = loss coefficient, dimensionless C* = concentration at the interface, mol/L C, = exit concentration, mol/L C, = reference concentration, mol/L d32 = Sauter mean diameter, m d , = wire diameter, m D = molecular diffusivity, mz/s DL = axial dispersion coefficient, m2/s D, = column diameter, m H = column height with aeration, m H,,= column height without aeration, m k L = liquid-side mass-transfer coefficient, m/s kLa = volumetric mass-transfer coefficient, s-l n = number of plates, dimensionless r = constant, dimensionless AP, = pressure drop due to liquid circulation, N/m2 ReL = liquid Reynolds number, d,VLpL/gL,dimensionless Re, = Reynolds number, d32VspL/pL,dimensionless Sh = Sherwood number, kLd32/D,dimensionless Sc = Schmidt number, pL/pLD, dimensionless T = temperature, "C
1410 Ind. Eng. Chem. Res., Vol. 28, No. 9, 1989
V = superficial velocity, m / s V , = liquid circulation velocity, m / s V , = slip velocity, m / s x = axial distance, m 2 = column height, m Subscripts G = gas L = liquid Greek Letters a = fractional free area t G = gas holdup p = density, kg/m3 y = viscosity, kg/(m.s) a, = standard deviation
Literature Cited Alexander, B. F.; Shah, Y. T. Gas-Liquid Mass Transfer Coefficients for Co-current Upflow in Packed Beds - Effect on Packing Shape at Low Flow Rates. Can. J. Chem. Eng. 1976,54, 556-559. Calderbank, P. H.; Moo-Young, M. B. The Continuous Phase Heat and Mass Transfer Properties of Dispersion. Chem. Eng. Sci. 1961, 16, 39-45. Chen, B. H. Cylindrical Screen Packings. Br. Chem. Eng. 1971, 16, 197-199. Chen, B. H. Handbook of Heat and Mass Transfer; Gulf Publishing Company: Houston, 1986; Chapter 23. Chen, B. H.; McMillan, A. F. Heat Transfer and Axial Dispersion in Batch Bubble Columns. Can. J. Chem. Eng. 1982,60, 436-439. Chen, B. H.; Vallabh, R. Holdup and Mass Transfer in Bubble Columns Containing Screen Cylinders. Ind. Eng. Chem. Process Des. Deu. 1970, 9, 121-126. Chen, B. H.; Wakao, N. Frictional Loss in Multiplate bubble Columns. Can. J. Chem. Eng. 1988,66, 145-149. Chen, B. H.; Yang, N. S.; McMillan, A. F. Hold up and Pressure Drop for Air-Water Flow through Plate Bubble Columns. Can. J . Chem. Eng. 1986, 64, 387-392. Danckwerts, P. V. Continuous Flow Systems. Chem. Eng. Sci. 1953, 2, 1-16. Deckwer, W. D.; Burckhart, R.; Zoll, G. Mixing and Mass Transfer in Tall Bubble Columns. Chem. Eng. Sci. 1974,29, 2177-2188. Freeman, W.; Davidson, J. F. Holdup and Liquid Circulation in Bubble Columns. Trans. Inst. Chem. Eng. 1969,47, T251-262.
Higbie, R. The Rate of Absorption of a Pure Gas into a Still Liquid during Short Periods of Exposure. Trans. AIChE 1935, 31, 365-388. Joshi, J. B.; Sharma, M. M. A Circulation Model for Bubble Columns. Trans. Inst. Chem. Eng. 1979,57, 244-251. Laws, E. M.; Livesey, J. L. Flow through Screens. Ann. Rev. Fluid Mech. 1978,10, 247-266. Nishikawa, M.; Yonezawa, Y.; Toyada, H.; Nagata, S.Studies of Bubble Size Distribution in Gas-Liquid Spouted Vessels. J. Chem. Eng. Jpn. 1978,11, 73-75. Nishikawa, M.; Shiino, K.; Kayama, T.; Nishioka, S.; Hashimoto, K. Gas Absorption in a Multistage Gas-Liquid Spouted Vessel. J. Chem. Eng. Jpn. 1985,18, 496-501. Reuss, M. Doctoral thesis, TU, Berlin, 1970. Schubauer, G. B.; Spangenberg, W. G.; Klebanoff, P. S.Aerodynamic Characteristics of Damping Screens. NACA Report 2001, 1950. Schugerl, K.; Lucke, J.; Oels, U. Bubble Column Bioreactors. Adu. Biochem. Eng. 1977, 7, 1-84. Sekizawa, T.; Kubota, H. Liquid Mixing in Multistage Bubble Columns. J. Chem. Eng. Jpn. 1974, 7,441-446. Shah, Y. T.; Kelkar, B. G.; Goodbole, S. P.; Deckwar, W. D. Design Parameters Estimations for Bubble Column Reactors. AIChE J . 1982, 28, 353-378. Tojo, K.; Miyanami, K.; Yano, T. Mass Transfer in a Multistage Vibrating Disk Column with Cocurrent Gas-Liquid Flow. J. Chem. Eng. Jpn. 1974, 7, 126-130. Voigt, J.; Schugerl, K. Absorption of Oxygen in Countercurrent Multistage Bubble Columns - I. Chem. Eng. Sci. 1979, 34, 1221-1229. Voigt, J.; Hecht, V.; Schugerl, K. Absorption of Oxygen in Countercurrent Multistage Bubble Columns - 11. Chem. Eng. Sci. 1980, 35, 1317-1323. Voyer, R. D.; Miller, A. I. Improved Gas-Liquid Contacting in Cocurrent Flow. Can. J. Chem. Eng. 1968,46, 335-341. Wang, K. B.; Fan, L. T. Mass Transfer in Bubble Columns Packed with Motionless Mixers. Chem. Eng. Sci. 1978, 33, 945-952. Yang, N. S.;Chen, B. H.; McMillan, A. F. Axial Mixing and Mass Transfer in Gas-Liquid Karr Column. Ind. Eng. Chem. Process Des. Dev. 1986a, 25, 776-780. Yang, N. S.; Shen, Z. Q.;Chen, B. H.; McMillan, A. F. Pressure Drop, Gas Hold up and Interfacial Area for Gas-Liquid Contact in Karr Columns. Ind. Eng. Chem. Process Des. Deu. 1986b, 25,660-664. Received for review July 27, 1987 Revised manuscript received February 2, 1988 Accepted May 11, 1989
