5304
Ind. Eng. Chem. Res. 2005, 44, 5304-5311
Liquid Backmixing and Phase Holdup in a Gas-Liquid Multistage Agitated Contactor Lifeng Zhang, Qinmin Pan, and Garry L. Rempel* Department of Chemical Engineering, University of Waterloo, Ontario, N2L 3G1, Canada
Axial backmixing of the liquid phase in a multistage agitated contactor (MAC) is investigated through residence time distribution (RTD) experiments over a large range of variables such as gas velocity, liquid velocity, stirring speed, and the number of stages using an air-water system. The experimental RTD curves are satisfactorily compared with the cascade of stirred tanks with backflow (CTB) model. The backflow ratio of the liquid phase is evaluated. The effects of the operating variables on the backflow ratio are examined. The phase holdup in a MAC is also investigated. Based on the data from the present study and the literature, a correlation is developed to predict the backflow ratio in a MAC for an air-water system operated in co-current manner. It is also observed that low backmixing is achieved in the MAC. 1. Introduction Multistage agitated contactors (MACs) have already been used for liquid, liquid-liquid, and gas-liquid processes. MACs, compared with normal stirred tank contactors, require thinner contactor walls for highpressure operations and have a more uniform shear rate inside the contactors and higher gas utilization, as well as narrower residence time distribution. A MAC was initially proposed for liquid-liquid extraction.1-3 Subsequently, it was also applied for single-phase applications.4,5 The application as a gas-liquid contactor was only investigated by a few researchers.6-9 In Table 1, a summary of axial dispersion studies in gas-liquid MACs reported in the literature is provided. The cascade of equal, ideally mixed tanks in series with a backflow model (the CTB model), which is shown in Figure 1, has been considered to be a suitable model to describe the axial liquid mixing in MACs.4,5,9-11 In the CTB model, the fluid within a compartment is assumed to be well-mixed and the backmixing is described by a backflow between two adjacent compartments. The backmixing between adjacent stages can significantly decrease the stage efficiency of a MAC. Minimizing backflow in MACs is critical for real applications. Considerable efforts have been made to develop relationships between axial backmixing and operating variables in MACs; however, limited studies that are available for gas-liquid systems are summarized in Table 2. In Table 2, all equations predict that DLax and fL increase linearly or almost linearly with the agitation speed. Equations BE5 and BE6 in Table 2 predict that DLax and fL decrease linearly as the dispersed phase holdup (d) increases. In contrast, equation BE7 predicts that the backflow rate will increase strongly as the gas holdup increases (fL is proportional to (1 - G)-1.86). This scenario is also observed by Meister et al.6 for an airwater system at relatively low stirring speed, whereas at higher stirring speed, the backflow decreases with G. Equation BE8 in Table 2 incorporates the effects of
fluid properties such as viscosity and surface tension on the backflow rates. However, equation BE8 was based on the experiments of nonflow operations and the effect of liquid velocity on axial liquid mixing was not included, which could be significant,as indicated in eqs BE2, BE3, and BE7. Both equations BE2 and BE7 show that increasing the liquid velocity increases backflow rates, whereas the opposite influence is observed in eq BE3. In eq BE4, the effect of liquid flow rate is also assumed to be zero and the correlation is based on nonflow experiments or the experiments in which the flow effects are small. Ingham3 investigated the entrainment effect of drops in a liquid-liquid extraction column. The larger drops have stronger capacity for entrainment. The entrainment could considerably affect the backmixing at a low stirring speed, whereas at high stirring speed, the eddy turbulence generated by agitation is predominant on backmixing. In co-current operation, the entrainment effect of drops is expected to reduce the backflow. For gas-liquid flow in MACs, the phase holdup is also an important parameter. Studies on gas holdup in MACs that have been reported in the literature are summarized in Table 3. Briefly, the backflow ratio is a function of phase holdup, stirring speed, liquid flow rate, and drop size, in addition to fluid properties and geometry of MACs. The study on the axial backmixing in MACs for gasliquid systems is scarce, and contradictive results have been reported in the literature. The objective of the present study is to investigate the influences of operating parameters, such as liquid flow rate, gas flow rate, stirring speed, and phase holdup on axial liquid mixing, to provide the fundamental data for the application of the MAC as a gas-liquid contactor operated in a cocurrent fashion. The backflow in the liquid phase is investigated based on the CTB model via residence time distribution (RTD) experiments over a wide range of operating conditions. The phase holdup is also measured experimentally. 2. Experimental Section
* To whom correspondence should be addressed. Tel: (519)888 4567, ext 2702. Fax: (519)746 4979. E-mail:
[email protected].
A schematic diagram of the experimental setup of the multistage agitated contactor (MAC) used in the present
10.1021/ie0491701 CCC: $30.25 © 2005 American Chemical Society Published on Web 02/09/2005
Ind. Eng. Chem. Res., Vol. 44, No. 14, 2005 5305 Table 1. Review of Data for Axial Dispersion Studied in a Gas-Liquid Multistage Agitated Contactor (MAC) Value parameter
al.6
Meister et
Sullivan and Treybal7
dvb (m) dhb (m) δhb (m) D (m) H (m) dI (m) NI NC
Geometry and Configuration 0.015 (4 baffles) 0.065 unknown 0.15 0.2 0.06 (6 bladed) 2 (at HI ) 0.2H and HI ) 0.67H) or 1 (at HI ) 0.2H) 9
gas(es) present liquid(s) present manner of operation pressure, P (bar) temperature, T (K) N range (rev-1) uG (m/s) uL (m/s)
air water co-current 1.0123 293 7-18 0.005-0.03 0.004-0.012
Breman et al.9
0.013 (4 baffles) 0.082 0.003/0.013 0.152 0.083 0.051 (6 bladed) 1 (at HI ) 0.5H) 12
0.009 (4 baffles) 0.04 0.005 0.09 0.09 0.03 (12 bladed) 1 (at HI ) 0.5H) 9
air water counter-current 1.0123 278-3-3 3.3-33.3 0.007-0.123 0.0018-0.0266
air, helium, CFK12 water, octane, MEG single-phase flow 1.0123 293 10-36.7 0.01-0.1 0
Operating Conditions
Table 2. Literature Equations for Liquid Backmixing in MACs equation number
relation
( )] ( )] [ [ ( )( ) ]
[
Re2 0.038µLdI Re1 1 + 19.5 2FL Re1
BE1
fL )
BE2
DLax ) 0.449 + 0.0118
BE3
fL ) 0.0098 ξ
BE4
fL ) 0.027NdI
BE5
DLax ) 0.375(1 - d)NdI
BE6a
fL ) fLG)0(1 - G)
BE7b
DLax ) 0.239 + 0.014
(Hd)
(for Re1 > 5000)
dIN uL H uL
NdI dI2Ahb uL HDA
[
0.5 1.24
( ) µdI2 FL
Haug11
uL A
Miyauchi et al.10
[
( )
dhb H D
( )]
Ingham3 Nocentini et al.12
dIN uLH (for G ) 0) uL
]
FLN(1 - G)2 µ
Sullivan and Treybal7
-0.928
fL ) fLentr + (1 - G)3fLma fLma ) 0.07
Lelli et al.4 Bibaud et al.2
0.5
DLax ) 227.6NdIH BE8b
reference -1
(for G * 0) Breman et al.9
0.75
N0.28
fLentr ) (3.14 × 104)µ1.2σ3.4N-1.4uG0.61 a
Without interstage baffle. b Gas-liquid system.
Figure 1. Cascade of N mixed vessels with backmixing.
investigation is shown in Figure 2. The MAC consists of six stages (H/D ) 1 (where H is height of the vessel and D is the diameter of the vessel), D ) 0.15 m) separated by horizontal baffles with a central circular opening of 0.02 m inner diameter (I.D.) and a thickness of 2 mm. Each compartment is equipped with a standard Rushton Turbine agitator. Four vertical baffles with a width of 1/10D are equally spaced. A conductivity cell is installed at the outlet of the column. In a typical residence time distribution (RTD) experiment, a known liquid flow rate was allowed into the
column co-current to a designated gas flow rate. After the flow was steady, a pulse input of a tracer (3 mL of NaCl solution) was applied to the inlet of the liquid flow by means of a syringe. The tracer concentration at the outlet was recorded by a data acquisition system. The experimental procedure was repeated for various gas and liquid flow rates, stirring speeds, and numbers of stages. Two different impellers, with dI/D ) 1/3 and dI/D ) 1/2 (where dI is the diameter of the impeller), were investigated. The liquid superficial velocity was varied from 0.00094 m/s to 0.006 m/s, and the gas superficial
5306
Ind. Eng. Chem. Res., Vol. 44, No. 14, 2005
Figure 3. Effect of liquid velocity (uL) on residence time distribution (RTD).
Figure 2. Schematic description of the continuous setup.
velocity was varied from 0.01 m/s to 0.1 m/s. The stirrer speed was varied from 10 rps to 30 rps for dI/D ) 1/3 and from 5 rps to 15 rps for dI/D ) 1/2. Air was chosen as the gas phase, and distilled water was used as the continuous liquid phase. 3. Experimental Results and Discussions 3.1. Experimental Results of RTD. The variables investigated to characterize liquid-phase mixing are liquid velocity, stirring speed, superficial gas velocity, and the number of stages. 3.1.1. Effect of Liquid Velocity on RTD. The effect of liquid flow rate on RTD is shown in Figure 3. It indicates that backmixing decreases with increasing liquid velocity, which is reflected in the spread of RTD. It can be interpreted that the interstage backflow is suppressed by the bulk flow. This is consistent with the studies reported by Meister et al.6 and Sullivan and Treybal.7 3.1.2. Effect of Stirring Speed on RTD. The effect of stirring speed on RTD is shown in Figure 4. Generally, it can be interpreted that the increase in stirring speed increases the spread of RTD, because of the turbulence generated by mechanical agitation. The average residence time decreases slightly with increasing stirring speed. This occurs because a higher stirring
Figure 4. Effect of stirring speed on RTD (dI/D ) 1/3).
speed can decrease the average bubble size in the column so that the residence time of bubbles in the column increases and then the liquid holdup decreases, which results in a lower mean liquid residence time. 3.1.3. Effect of Gas Flow Rates on RTD. Figure 5 shows the effect of gas velocity on backmixing. It can be seen that, generally, the mixing decreases as the gas velocity increases, which is reflected in the spread of RTD. The increase in superficial gas velocity results in an increase in the gas holdup, which favors the hindrance of liquid backmixing. 3.1.4. Effect of Number of Stages on RTD. To achieve the same residence time for a different number of stages, the liquid flow rate was varied. Figure 6 shows that the spread of RTD becomes narrower when a larger number of stages is used, which is consistent with common knowledge of chemical reaction engineering. 3.2. Modelling and Simulation for Backflow Rates. The backflow rate can be evaluated by the CTB model. For a single tracer component, the mass conser-
Table 3. Correlation for Phase Holdup in a MAC reference al.6
Meister et for one impeller per stage for two impellers per stage Sullivan and Treybal7 for N ) 0-8.33 r/s for N ) 8.33-33.3 r/s Breman et al.8
correlation G ) (1.21 × 10-2)N0.54uG0.35 G ) (3.16 × 10-3)N0.63uG0.56 G ) (8.876 × 10-4)N + 1.874uG + 2.31uL + 0.052 G ) (2.315 × 10-2)N + 0.691uG + 0.137uL + 0.052 0.67 uG dI2 N0 ) 0.15g0.5D1.5dI-2, G ) 0.16 + 0.32 (N - N0) (gσ/FL)0.25 D(gD)0.5
{ [
]
[
]
} ( ) ( ) ×
gµL4 F L σ3
-0.042
FG Fair
0.12
Ind. Eng. Chem. Res., Vol. 44, No. 14, 2005 5307
Figure 5. Effect of superficial gas velocity (uG) on RTD (dI/D ) 1/ ). 3
Figure 6. Dimensionless RTD curves for different numbers of stages (dI/D ) 1/3).
vation in the ith stage is expressed as follows:
dci Vi ) (FL + fL)ci-1 - (FL + 2fL)ci + fci+1 dt
(1)
The variance of RTD for n stages can be calculated using the relation13
2x (1 - xn) n n(1 - x)2
1 - x2 2
σθ )
(2)
where x is the modified backflow ratio, which is given by
fL x) fL + FL
(3)
The backflow ratio is defined as
R)
fL FL
reported in this study are then estimated by solving eq 2. 3.2.1. Effect of Liquid Velocity on the Backflow Ratio. Figure 8 shows that the backflow ratio decreases considerably with an increase in liquid velocity. This was also observed by Haug,11 Ingham,3 and Meister et al.6 for single-phase and two-phase systems. Backflow can be considerably suppressed by the liquid bulk flow. In a single-phase system, the backflow ratio is inversely proportional to the liquid velocity (R ∝ uL-1.24), according to Haug’s correlation.11 It is also demonstrated that the majority of the backflow ratios are lower than that obtained in a single-phase system, because the existence of the gas phase hinders backmixing. With an increase in gas flow, a decrease in backmixing is observed, because of the increase in gas holdup, which results in an increase in the liquid flow rates. 3.2.2. Effect of Stirring Speed on Backmixing. Figure 9 indicates that the backflow ratio increases as the stirring speed increases, which is to be expected, because the increase in stirring speed intensifies the eddy turbulence in the system. Figure 9 also shows that increasing the gas superficial velocity decreases the backmixing, which is due to the increase in gas holdup, which favors the hindrance of backmixing of the continuous phase, as mentioned previously. A similar phenomenon was observed by Ingham3 in a multi-mixer liquid-liquid extraction. Figure 9 also shows that the effect of stirring speed on backflow ratio at high superficial gas velocity is not as significant as that at low gas velocity. 3.2.3. Effect of Stage Number on the Backflow Ratio. Figure 10 indicates that the backflow ratios are almost the same when the number of stages was increased from 3 to 6. This implies that the flow pattern in the MAC investigated has reached a steady state in the first stage and is also consistent with the theoretical perspective of using the CTB model to evaluate the backflow ratio. 3.2.4. Phase Holdup in an Air-Water System. Figures 11 and 12 show that gas holdup increases as the stirring speed and superficial gas velocity each increase, which is consistent with the results shown in Table 3. To facilitate the analysis of the effect of gas holdup on backflow in the next section, the following correlation is used to predict gas holdup:
G ) p1Np2ugp3
where p1, p2, and p3 are coefficients in the equation. The accuracy of the relation between the correlation and experimental data is expressed in terms of a MARR function (average relative residual deviation):
(4)
MATLAB can be used to solve eq 2 to obtain x and the backflow ratio, R Figure 7a and b show a typical comparison of the experimental RTD data with the CTB model. These figures show that the model can satisfactorily predict the experimental data. All backflow ratios
(5)
MARR )
1 Nd
∑|1 -
Gcal Gexp
| × 100%
(6)
where Nd is the number of experimental data points used. The parameters in eq 5 are optimized by minimizing the MARR function. Two correlations with MARR of 6%
5308
Ind. Eng. Chem. Res., Vol. 44, No. 14, 2005
Figure 7. Comparison of experimental RTD data and the prediction of the cascade of stirred tanks with backflow (CTB) model (dI/D ) 1/ ). 3
Figure 8. Effect of liquid velocity uL on backflow ratio (R) at various gas velocities (dI/D ) 1/3).
Figure 10. Effect of the number of stages on the backflow ratio R (dI/D ) 1/3).
Figure 9. Effect of stirring speed on backflow ratio R at various superficial gas velocities (dI/D ) 1/3).
Figure 11. Effect of stirring speed on phase holdup under various uG values (dI/D ) 1/3).
(eq 7) and 7% (eq 8) are achieved for two different impellers, respectively.
because of their smaller volume for each compartment (D ) 0.15 m and H ) 0.083 m). A comparison is also performed for the values of a single agitated tank theoretically predicted by Garcia-Ochoa and Gomez.14 A mean deviation of 8% is observed, which implies the coalescence/re-dispersion of the bubbles has reached equilibrium in the first stage in the investigated MAC. 3.2.5. Empirical Correlation for Backflow Ratio. An attempt is made to correlate backflow ratio with the backmixing parameter B, and the following relation is achieved for a single liquid-phase flow with a MARR of 13%:
G ) 17.2N0.7ug0.52
(for dI/D ) 1/3)
(7)
G ) 29.4N0.7ug0.52
(for dI/D ) 1/2)
(8)
The relations are shown in Figure 13. The phase holdup predicted by the proposed correlations and literature correlations are shown in Figure 14. Meister et al.6 has the largest MARR value (33%), according to our experimental data, because of its lower impeller position (HI ) 0.2H). The correlation proposed by Breman et al.8 can predict the present data quite well (the mean deviation is 6%). The correlation proposed by Sullivan and Treybal7 has a mean deviation of 19%,
RL ) 0.0006
[ ( )] NdI dI2Ahb uL HDA
0.5 1.38
(9)
Ind. Eng. Chem. Res., Vol. 44, No. 14, 2005 5309
Figure 12. Effect of superficial gas velocities under various stirring speed (dI/D ) 1/2).
Figure 15. Backmixing in a single phase (B ) (NdI/uL)(dI2Ahb/ HDA)0.5).
Figure 16. Comparison of experimental R data and model prediction. Figure 13. Correlations for two different impellers ((0) dI/D ) 1/ and (]) d /D ) 1/ ). 2 I 3
For the backflow ratio in the gas-liquid flow system, the following correlation equation is obtained:
aGL ) 0.34(1 - G)1.5aLdb-0.2
(10)
where the average bubble size db is predicted by the following correlation proposed by Bhavaraju et al.:15
()
µL σ0.6 db ) 0.7 (P/V)0.4FL0.2 µG
0.1
(11)
Power consumption under aeration is evaluated by the relation proposed by Michel and Miller:16
PG ) 0.95 Figure 14. Comparison of experimental G data with the literature data.
( ) P0NdI3 QG0.56
0.43
(12)
where P0 is the power input in unaerated systems: which is illustrated in Figure 15. The prediction of Haug’s correlation11 is also shown in this figure and is generally 3-5 times higher than that obtained from the present work. This disparity is possibly due to different impeller positions and the impeller correction factor (ξ) used in Haug’s correlation.11 The impeller position applied in the present study is 1/3 of the height of each compartment, and the height in Haug’s work was 1/2 of the height of the compartment. The backflow is attributed to the overall effect of fluctuation velocities over the opening. The short distance from the impeller might show a more profound relation with the agitation.
P0 ) NPN3dI5
(13)
where Np is the power number of the impeller and Np ) 5 is applied for a standard Rushton turbine. Figure 16 shows the agreement between the experimental data and eq 10. Currently, there are no other correlations available for predicting the backflow ratios in gas-liquid systems. Therefore, no comparison is given here, regarding the prediction capacity of eq 10 over others. However, the data reported by Sullivan and Treybal7 and Meister et al.6 are also shown in Figure 16, using the following
5310
Ind. Eng. Chem. Res., Vol. 44, No. 14, 2005
equation10 to convert their axial dispersion coefficients to backflow ratios:
(
)
NC DLax R) A uLH 2Nc - 1
(15)
Sullivan and Treybal’s systems7 were operated in a counter-current manner and Meister et al.’s system6 was equipped with impellers at a significantly lower position (HI ) 0.2H). Equation 10 has a mean deviation of 20% when it is applied to the data obtained by Sullivan and Treybal7 and has a fairly high mean deviation of 64% when it is applied to the data from Meister et al.6 Because of the difference of their systems, it is not expected that eq 10 would predict their results very well. However, eq 10 can provide an approximate estimation for those systems before more-suitable relationships are established for those systems. 4. Conclusions The backflow of the liquid phase and the gas holdup in an multistage agitated contactor (MAC) are studied. The experimental residence time distribution (RTD) data are satisfactorily fitted by the cascade of stirred tanks with backflow (CTB) model. The backflow ratios obtained in the present study are lower in the present column, compared to previous reports, which means a higher stage efficiency. The phase holdup achieved in the present study is comparable to previous literature data. Correlation equations are proposed to predict the gas holdup and the backflow ratios for the liquid phase in a MAC. Acknowledgment Support from the Natural Sciences and Engineering Research Council of Canada(NSERC) and Bayer, Inc., is gratefully acknowledged.
PG ) power consumption under aerated conditions (W/m3) QG ) gas flow rate (m3/s) Re1 ) Reynolds number based on impeller; Re1 ) FNdI2/µ Re2 ) Reynolds number based on the liquid flow; Re2 ) FuLD/µ t ) time (s) uG ) superficial gas velocity (m/s) uL ) liquid velocity (m/s) vb ) bubble rise velocity (m/s) Vi ) volume of each stage i (m3) Greek Symbols R ) backflow ratio aL ) backflow ratio for a liquid phase aGL ) backflow ratio in a gas-liquid system G ) gas phase holdup µ ) viscosity (Pa s) θ ) dimensionless time FL ) liquid density (kg/m3) FG ) density of gas (kg/m3) Fair ) density of air (kg/m3) σ ) surface tension (N/m) σ2 ) variance of residence time distribution σ2(θ) ) normalized variance of residence time distribution ζ ) impeller correction factor Subscripts 0 ) denotes value at time t ) 0 b ) bubble G ) gas GL ) gas-liquid L ) liquid i ) ith stage Superscripts ax ) axial dispersion cal ) calculation exp ) experimental entr ) entrainment ma ) mechanical agitation
Literature Cited Nomenclature A ) cross sectional area of column (m2) Ahd ) horizontal opening area (m2) ci ) species concentration in the ith stage (mol/m3) db ) bubble size (m) dhb ) diameter of opening area between stages (m) dI ) diameter of impeller (m) D ) diameter of the vessel (m) DLax ) axial dispersion coefficient (m2/s) E(t) ) residence time distribution (1/s) E(θ) ) normalized residence time distribution fL ) backflow rate (m3/s) fLentr ) backflow rate caused by entrainment (m3/s) fLma ) backflow rate caused by mechanical agitation (m3/ s) fLG)0 ) backflow rate for no gas presence (m3/s) fL ) liquid flow rate (m3/s) g ) gravitational constant (m/s2) H ) height of one compartment (m) n ) number of stages N ) stirring speed (rps) N0 ) critical stirring speed (rps) Nc ) stage number Nd ) the number of experimental points Np ) power number of applied impeller p1, p2, p3 ) coefficients P0 ) power consumption per unit volume (W/m3)
(1) Oldshue, J. Y.; Rushton, J. H. Continuous Extraction in a Multistage Mixer Column. Chem. Eng. Progress 1952, 48, 297306. (2) Bibaud, R. E.; Treybal, R. E. Axial Mixing and Extraction in a Mechanically Agitated Liquid Extraction Tower. AIChE J. 1966, 12 (3), 472-477. (3) Ingham, J. Backmixing in a Multi-mixer Liquid-liquid Extraction Column. Trans. Inst. Chem. Eng. 1972, 50, 372-384. (4) Lelli, U.; Magelli, F.; Sama, C. Backmixing in a Multistage Mixer Column. Chem. Eng. Sci. 1972, 27, 1109-1117. (5) Lelli, U.; Magelli, F.; Pasquali, G. Multistage Mixer ColumnssA Contribution to Fluid-Dynamic Studies. Chem. Eng. Sci. 1976, 31, 253-256. (6) Meister, D.; Post, T.; Dunn, I. J.; Bourne, J. R. Design and Characterization of a Multistage Mechanically Stirred Column Absorber. Chem. Eng. Sci. 1979, 34, 1367-1374. (7) Sullivan, G. A.; Treybal, R. E. Axial Mixing and Gas Adsorption in a Mechanically Agitated Absorption Tower. Chem. Eng. J. 1970, 1, 302-309. (8) Breman, B. B.; Beenackers, A. A. C. M.; Bouma, M. J. Flow Regimes, Gas Hold-up and Axial Gas Mixing in the Gas-Liquid Multistage Agitated Contactor. Chem. Eng. Sci. 1995, 50, 29632982. (9) Breman, B. B.; Beenackers, A. A. C. M.; Bouma, M. J.; Van Der Werf, M. H. Axial Liquid Mixing in a Gas-Liquid Multistage Agitated Contactor. Chem. Eng. Res. Des. 1996, 74 (A6), 669678. (10) Miyauchi, T.; Mitsutake, H.; Harase, I. Longitudinal Dispersion in a Rotating Impeller Types of Contactor. AIChE J. 1966, 12, 508-513.
Ind. Eng. Chem. Res., Vol. 44, No. 14, 2005 5311 (11) Haug, H. F. Backmixing in Multistage Agitated Contactors A Correlation. AIChE J. 1971, 17, 585-589. (12) Nocentini, M.; Magelli, F.; Pasquali, G.; Fajnet, D. A FluidDynamics Study of a Gas Liquid, Nonstandard Vessel Stirred by Multiple Impellers. Chem. Eng. J. 1988, 37, 53-59. (13) Vidaurri, F. C.; Sherk, F. T. Low Backmixing in Multistage Agitated Contactor Used as Reactor. AIChE J. 1985, 31, 705710. (14) Garcia-Ochoa, F.; Gomez, E. Theoretical Prediction of GasLiquid Mass Transfer Coefficient, Specific Area and Hold-up in Sparged Stirred Tanks. Chem. Eng. Sci. 2004, 59, 2489-2501.
(15) Bhavaraju, S. M.; Russell, T. W. F.; Blanch, H. W. The Design of Gas Sparged Devices for Viscous Liquid Systems. AIChE J. 1978, 24, 454-466. (16) Michel, B. J.; Miller, S. A. Power Requirement of Gas Liquid Agitated Systems. AIChE J. 1962, 20, 445-448.
Received for review September 1, 2004 Revised manuscript received December 3, 2004 Accepted December 7, 2004 IE0491701
