Interstage Backmixing for Single-Phase Systems in Compartmented

Experimental and correlational results are reported here for two interstage openings: (1) a center hole and (2) a centered draft tube. Two impellers w...
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Ind. Eng. Chem. Res. 2005, 44, 6103-6109

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Interstage Backmixing for Single-Phase Systems in Compartmented, Agitated Columns: Design Correlations Bang Cheng Xu† ConocoPhillips Service Inc., RW6664, 1000 South Pine, Ponca City, Oklahoma 74602

W. Roy Penney* Department of Chemical Engineering, University of Arkansas, Fayetteville, Arkansas 72701

Julian B. Fasano‡ Chemineer, Inc., 5870 Poe Avenue, P.O. Box 1123, Dayton, Ohio 45401-1123

Experimental investigations were conducted for single-phase liquids to determine interstage backmixing rates in an agitated, fully baffled, 24-cm-diameter, two-stage, compartmented column. The backmixing rate was indirectly determined by introducing a tracer into one stage and then measuring the tracer concentration with time in both compartments as the tracer migrated from the injected stage to the noninjected stage. A transient tracer mass balance on both compartments allowed the use of the transient experimental tracer concentration to determine the interstage backmixing rate. The effect of flow through the column on interstage backmixing was determined. Experimental and correlational results are reported here for two interstage openings: (1) a center hole and (2) a centered draft tube. Two impellers were tested: a sixbladed disk (6BD) impeller and a high-efficiency impeller (the Chemineer HE-3). The data were correlated in dimensionless form, and predictive methods are presented that allow the prediction of the interstage backmixing rate as a function of (a) the impeller type, (b) fluid properties, (c) the interstage opening geometry, and (d) the forward flow rate. The correlations for the effect of the forward flow rate on backmixing allow the design of a compartmented column, using a draft tube attached to a center hole opening, which has no backmixing. Thus, a compartmented column can be designed and operated as a series of continuous stirred reactors (or compartments) in series, without any interstage backmixing. 1. Introduction Many process operations, including liquid-liquid extraction, absorption and stripping, and chemical reaction, are effectively accomplished in staged systems. Vertical, agitated compartmented columns are often the best economic choice to achieve staging. The process performance of a compartmented column is affected by the interstage backmixing rates between adjacent compartments. For a better understanding of backmixing, let us say that it is the phenomenon that causes cold air to enter the passenger compartment of an automobile and hot air to leave the passenger compartment as a window is lowered on a cold winter day. The driving force for this backmixing is the turbulence generated by the moving automobile, and it is obvious, with a bit of thought, that the volumetric flow rate of cold air entering the passenger compartment, through the window, is exactly balanced by the volumetric flow of warm air leaving the passenger compartment. The same backmixing processes that make you cold when you open an automobile window on a cold day cause fluid to migrate both ways through openings in a stage divider * To whom correspondence should be addressed. Tel.: (479) 575-5681. Fax: (479) 575-7926. E-mail: rpenney@ engr.uark.edu. † Tel.: (580) 767-6837. Fax: (580) 767-2635. E-mail: [email protected]. ‡ Tel.: (937) 454-3263. Fax: (937) 454-3370. E-mail: j.fasano@ chemineer.com.

between two mechanically agitated stages. The backmixing through stage-divider openings in staged columns acts to smooth concentration profiles throughout the column, thereby normally harming the process performance. For the design and scale-up of staged columns, methods are needed to (1) predict interstage backmixing rates in compartmented columns and (2) predict when forward flow (forward flow is the terminology used here to categorize any stream of fluid that enters the column at top/bottom and exits at bottom/ top and flows through the stage-divider openings) will reduce interstage backmixing to zero. Even though many staged columns are used for multiphase (gas-liquid systems are not considered here, but they have been investigated and reported by Takriff and co-workers1-3) processing, a logical starting point for predictive methods is the prediction of the singlephase backmixing rates for the most commonly used stage-divider openings of (1) a centered hole and (2) a centered draft tube. The comprehensive investigation by Xu,4 from which this paper was abstracted, provides predictive methods for several other stage-divider openings, including (1) off-center holes, (2) wall ring openings (i.e., the stage divider/column wall gap), (3) the gap between a stagedivider hole and a rotating disk attached to the agitator shaft, and (4) an elbow attached to the interstage opening. To give the reader a better visual impression of the full extent of Xu’s4 investigation, Figure 1 presents schematics of all openings tested by Xu.4

10.1021/ie040238m CCC: $30.25 © 2005 American Chemical Society Published on Web 04/05/2005

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Figure 1. Schematic drawing of the experimental apparatus used by Xu.4

Xu’s4 work clearly indicates that the gap between the stage divider and the column wall (i.e., the wall ring opening) must be eliminated in order to design and operate a multistage, compartmented column with zero or minimal backmixing. For small columns, less than about 1.5-m diameter, this is often accomplished by constructing the agitator, baffles, and stage dividers as a unit, which is inserted into the top head of the column. The stage divider/column wall gaps are sealed with elastometric donut rings attached to the tops of the cylindrical divider plates. For large columns, greater than 1.5-m diameter, the stage divider/column gaps are often sealed by attaching sealing devices to the divider plates after the agitator/baffle/divider mechanism is installed or built into the column.

Two mathematical flow models have been used to mathematically describe the effects of backmixing in staged columns: (1) the “eddy diffusion” model, which is explained by Miyauchi et al.5 and (2) the “ideal stages with backmixing” model (the ISB model). The ISB model is a one-parameter model, and that parameter is the volumetric backmixing rate (Fb). The ISB model is the preferred model for staged columns because the dimensionless interstage backmixing parameters can be directly determined from experimental data and the parameters are directly relatable to the independent dimensionless parameters of the system. Interstage backmixing through a stage-divider opening is influenced by fluid flow (the flow can be in either direction; here we identify any flow through the divider

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openings as “forward” flow) through the opening. Interstage backmixing is maximum at zero forward flow and is reduced as the forward flow increases, and it becomes zero at some finite value of forward flow. Other parameters that significantly affect interstage backmixing are (1) the gap between the stage divider and the column wall, (2) the geometry of the divider plate opening, (3) draft tubes, (4) the stage geometry [including the stage height/column diameter (Z/DT)], (5) baffling, (6) the impeller type, and (7) fluid properties. 2. Literature Review Gutoff6 studied six-bladed disk (6BD) impellers in a six-stage, 10.2-cm column. He found that backmixing increased directly with the impeller speed (N) at a given forward flow rate (Ff), above a minimum impeller speed. Reducing the area of the stage-divider opening was found to reduce the backmixing in direct proportion to the flow area, which indicates that, for a given impeller operating at a particular speed, the backmixing velocity through the stage-divider opening is constant and, over the range of Gutoff’s6 investigation, independent of the opening size. For a center hole stage opening, doubling the forward flow rate reduced the interstage backmixing rate by about 50%. Adding a double thickness of an 8-mesh screen decreased the backmixing by about 40%; a 16-mesh double screen reduced backmixing by about 75%. Miyauchi et al.5 did research on backmixing in a continuous-flow, 15-stage column and a zero-forwardflow, 2-stage column. Their interstage backmixing correlation for the zero-forward-flow condition is

( )

vb0 DT ) 0.017Np1/3 NDi Z

1/2

(1)

The power number was included to bring data together for 6BD and rotating-disk impellers. They did not correlate the effect of forward flow on the interstage backmixing rate; however, their plotted data indicate that forward flow decreased interstage backmixing. Experiments were conducted by Haug8 in 15-, 120-, and 240-cm-diameter, six-stage Oldshue-Rushton columns. A generalized correlation was recommended:

[

( )(

)]

Np NDi Di2Ao vb ) 0.0098 vf (Np)6BD vT DTZAT

1/2 1.24

(2)

This correlation fails as vf w 0 and as Ao w 0 because it predicts vb ∝ vf-0.24 and vb ∝ Ao0.62, and it is well established that vb remains finite as vf w 0 and as Ao w 0. Although the correlation is not generally applicable, it does predict other reasonable dependencies: vb ∝ (NDi)1.24, vb ∝ (Di/DT)1.24, and vb ∝ (DT/Z)0.62. Ingham9 conducted tests in a 15.24-cm, 12-stage Oldshue-Rushton column. He found that backmixing was reduced considerably by forward flow and by using a draft tube as the stage-divider opening. As the impeller speed (N) increased, vb increased, and vb decreased as vf increased. As the draft tube length increased, backmixing was eventually reduced to zero for a given N and Ff. Lelli et al.10,11 investigated backmixing in OldshueRushton columns. Lelli et al.10 tested 8.15-, 13.2-, and 23-cm-diameter, six-stage Oldshue-Rushton columns with 4BD turbines, using water glycerol solutions. The

effect of forward flow on interstage backmixing was determined. Their data were plotted as Fb/NDi3 vs NRe with NRef as a parameter. Unbaffled columns gave higher backmixing than baffled columns. Their results showed that Fb/NDi (∝vb/NDi) was unaffected by the Reynolds number for NRe > 6000. Thus, the “fully turbulent” regime is NRe > 6000. Their data show that forward flow decreased the backmixing rate. Magelli et al.12 tested a four-stage, 13-cm column with six sizes of stator openings (Do/Di ) 1.01, 1.27, 1.5, 1.75, and 2.53) and a six-stage, 23-cm column with Do/Di ) 1. 4BD turbines were used. The nonflow data for the small column were correlated in a fundamentally sound manner as FbF/µDi vs NRe with Do/Di as a parameter. FbF/µDi increased gradually as Do/Di increased. Magelli et al.13 determined interstage backmixing through perforated-plate stage dividers in a four-stage, 13-cm column and in four-stage, 0.375- and 3-mdiameter columns. The data were correlated as (Fb/ NDi3)/(DT/Z)1/2(Do/Di)2 vs NRe. Magelli et al.14 tested non-Newtonian fluids in a fourstage, 13-cm column and a six-stage, 23-cm column with Do/DT ) 1. 6BD turbines were used. All of the data were correlated as FbF/µDi vs NRe with NRef as a parameter. This dimensionless backmixing parameter (i.e., FbF/µDi) decreased as the forward flow Reynolds number (NRef) increased. The data for Newtonian fluids correlated the same as the data of Lelli et al.10 Fb was lower for the non-Newtonian fluids than for the Newtonian fluids. In fact, a fluid with a power law exponent of 0.67 gave a 10-fold lowering of interstage mixing for 3000 < NRe < 10 000. Vidaurri et al.15 tested a 5-stage, 15.2-cm column and also a 20.3-cm 10-stage column having small annular openings. All experiments used draft tubes as a center hole opening. Backmixing increased with the agitator speed and decreased with an increase in the draft tube length. At high forward flow, the backmixing was reduced to zero, and it was reduced to zero also by an increase in the fluid viscosity. They found the backmixing rate was dependent on µ-1/2. 3. Experimental Equipment The flow schematic of the experimental unit is presented in Figure 1. The unit consisted of two fully baffled agitated compartments in series. The shell was a 24.27-cm-inside-diameter by 48.26-cm-tall Plexiglas cylinder. The partition between compartments had various openings, which are shown schematically in Figure 1. Only the results for a center hole and a center hole with a draft tube are presented here. Refer to Xu’s4 thesis for the results for all stage-divider openings. One injection/sample port was installed at the midplane of each compartment. Impellers were placed at the midplane of each compartment. Two types of impellers were used in this study: (a) a 6BD with Li/Di ) 0.20 and Wb/ Dib ) 0.25 and (b) a three-bladed high-efficiency impeller (Chemineer HE-3). For both impellers, two diameters were used: 8.89 and 12.7 cm. Water and an aqueous carboxymethylcellulose (CMC) solution were used as test fluids. KCl and food coloring were used as tracers. A conductivity meter was used to measure the electrical resistance of the aqueous KCl samples, and a spectrophotometer was used to measure the transmittance of the colored CMC solution samples.

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4. Experimental Procedures For high Reynolds number experiments, tap water was used as a test fluid and KCl was used as a tracer. The following procedure was used to determine the rate of interstage backmixing: 1. An aqueous KCl solution was injected into the upper stage. 2. Twelve samples were taken with time from each compartment. 3. The electrical conductivity of each sample was measured with a conductivity meter. 4. The electrical conductivity measurements were used to calculate the KCl concentration from previously determined calibration curves. 5. The ISB model was fitted to the experimental data of tracer concentration vs time (since tracer injection) to obtain the interstage mixing rate that best-fitted the experimental data. For the lowest NRe experiments, Newtonian CMCwater solutions were used. Food coloring was used as the tracer. The same procedure as that above was used except that color measurements by a spetrophotometer were used to determine the tracer concentration.

Figure 2. Backmixing correlation for a center hole opening with zero forward flow.

geometry and was applied to all of the forward flow data of this investigation. 6. Summary of the Correlational Technique Application to Equipment Design For given geometries, experimental data are used to determine correlations of

5. Correlation Development 5.1. Zero Forward Flow. A correlating method was developed using the following postulates:

vb0 vs(DT/Z)1/2

) f (impeller type,NRe)

(3)

in which

vs ∝ vt (Di /DT)n ∝ NDi (Di /DT)n

(4)

Substituting eq 5 into eq 4, we obtain

vb0 NDi (Di /DT)n(DT /Z)1/2

) f (impeller type,NRe) (5)

Consequently, all data have been correlated here using the following dimensionless backmixing parameter:

Nb0,n )

vb0 (NDi)(Di /DT)n(DT /Z)1/2

(6)

This correlational form for the backmixing parameter is similer to that used by Miyauchi et al.5 except that the term (Di/DT)n is included. The value of n that best-fitted most of the data of the current investigation is 1.0. However, as will be explained later, for some geometries, n * 1 best-correlated the data. 5.2. Correlational Technique for the Effect of vf on vb. The effect of forward flow on interstage backmixing was correlated by plotting the ratio of the backmixing velocity (vb) to the backmixing velocity at zero forward flow (vb0) [i.e., vb/vb0] vs the ratio of forward flow velocity (vf) to vb0 [i.e., vf/vb0]. This method of correlating the effect of forward flow on the backmixing rate [i.e., vb/vb0 ) ×c4(vf/vb0)] is well suited for a given

Nb0 ) f (NRe)

(7)

vb /vb0 ) f (vf /vb0)

(8)

and

With these correlations in hand, vb and Fb are determined by the following procedure. (1) Calculate NRe. (2) Determine Nb0 from the appropriate graph of Nb0 vs NRe. (3) Calculate vb0 ) Nb0(NDi)(Di/DT)n(DT/Z)1/2. (4) Calculate vf ) Ff/Ao. (5) Calculate vf/vb0. (4) Go the appropriate graph of vb/vb0 vs vf/vb0 and determine vb/vb0. (5) Calculate vb ) (vb/vb0)vb0. (6) Calculate the volumetric backmixing rate, Fb ) vbAo. The volumetric backmixing rate (Fb) is the parameter needed to predict the effect of interstage backmixing on the process performance using the ISB model (Lelli and co-workers10,11 present an excellent description of the ISB model) for a compartmented, mechanically agitated column. 7. Results and Discussion 7.1. Backmixing for Zero Forward Flow: Center Hole Openings. The data were correlated as Nb0,1 vs NRe for all of the zero-forward-flow runs. Figure 2 is the result for the center hole opening with 6BD and HE-3 impellers. All data for 6BD for NRe < 6000 and for HE-3 for NRe < 20 000 were taken using the CMC solution. It was determined by visual experiments using dye injection that backmixing was zero for NRe < 339 for the 6BD impellers and NRe < 520 for the HE-3 impellers. 7.2. Backmixing for Zero Forward Flow: Centered Draft Tubes. The results for centered draft tubes with 6BD and HE-3 impellers are presented in Figures 3 and 4. Figure 3, with n ) 2, presents the best correlation for the 6BD impeller with draft tubes. Figure 4, with n

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Figure 3. Backmixing correlation for centered draft tubes with 6BD impellers with n ) 2.

Figure 6. Effect of the length to hydraulic diameter ratio (L/Dh) on the backmixing through a centered draft tube with HE-3 impellers.

Figure 4. Backmixing correlation for centered draft tubes with HE-3 impellers with n ) 1. Figure 7. Correlation for the effect of forward flow on backmixing for a center hole opening.

Figure 5. Effect of the length to hydraulic diameter ratio (L/Dh) on the backmixing through a centered draft tube with 6BD impellers.

) 1, presents the best correlation for the HE-3 impeller with draft tubes. 7.3. Backmixing for Zero Forward Flow: Effect of the Relative Draft Tube Length (L/Dh) on Nb0. Figure 5 correlates the effect of L/Dh on Nb0,2 for 6BD impellers, and Figure 6 correlates the effect of L/Dh on Nb0,1 for HE-3 impellers. Nb0 is reduced greatly with an increase of the draft tube length. The effect of L/Dh is much greater for the HE-3 impeller than for the 6BD impeller. 7.4. Effect of Forward Flow on the Intersage Backmixing Rate: Experimental Determination of the Zero Backmixing Condition for a Given Forward Flow Rate. The zero backmixing condition (i.e., vb/vb0 ) 0) at a particular vf/vb0 was measured by

Figure 8. Correlation for the fffect of forward flow on backmixing for a centered draft tube.

observing visually the condition at which food dye first migrated between stages as N was increased, for a particular vf, for a particular geometry. 7.5. Effect of Forward Flow on the Intersage Backmixing Rate: Correlation of Data for Center Hole Stage-Divider Openings. The correlated results for 6BD and HE-3 impellers with a center hole opening, without draft tubes, are presented in Figure 7. There is considerable scatter of the data at low vb’s and high vf’s because the backmixing rate is so low that it is difficult to accurately measure. Figure 8 presents the correlation of the effect of forward flow for 6BD and HE-3 impellers with draft tubes present.

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Figure 9. Comparison of a center hole with 6BD results of this investigation with those of 4BD. Results of Magelli et al.12 Legend: upper curve, this investigation; middle curve, Magelli et al.,12 Di/DT ) 0.84; lower curve, Magelli et al.,12 Di/DT ) 0.33.

Figure 10. Relative effect of the ratio of the orifice size to the tank diameter (Do/DT) on backmixing through a center opening, from Magelli et al.12

8. Comparison of This Investigation with Literature Results The literature data were recalculated and recorrelated using the methods of this investigation; all of this work is documented by Xu.4 Ingham’s4 experimental data are about 10-fold lower than the results of this investigation. There is no apparent reason for this discrepancy. Gutoff’s1 backmixing velocity (vb) for a center hole opening is close to the results of this investigation. Lelli et al.’s10 correlated backmixing rate is about 65% of the rate determined by the current investigation. Some of this discrepancy results from different impellers: they used 4BD impellers, whereas 6BD impellers were used for this investigation. If Lelli et al.’s10 data are corrected upward by Np1/3, as suggested by Miyauchi et al.5 (Np ) 5.5 for 6BD and Np ) 4.2 for 4BD), then their corrected backmixing rate is about 70% of the current values. Considering the inherent difficulties of using transient residence time distribution data, as Lelli et al. did,10 fitted to a mathematical model to determine the experimental backmixing rate, this is good agreement. Magelli et al.’s12 correlated results for center holes, with varying Do/DT for zero forward flow, are compared with the correlated results for the center hole results of this investigation on a plot of Nb0,1 vs NRe in Figure 9. Their backmixing values for 4BD impellers for Do/DT < 0.837 are about 50-80% of the values determined by the current investigation for 6BD impellers. If their data are corrected by Np1/3 to a 6BD basis, then their data are about 55-88% of the current results. This is reasonable agreement between their investigation and the current investigation. Magelli et al.’s12 results indicated an effect of Do/DT on Nb0,1. Nb0,1 is about 1.4 times higher for Do/DT ) 0.837 than for Do/DT ) 0.334. Figure 10 is a plot of Nb0,1/ (Nb0,1)Aof0 vs Do/DT from Magelli et al.12 Lelli et al.’s10 correlated results with a forward flow condition are compared with the experimental results of this investigation on a plot of vb/vb0 vs vf/vb0 in Figure 11. Their backmixing rates are about 50-100% of the current results. The largest discrepancy occurs at the highest forward flow rate; this is expected because the relative accuracy of experimental backmixing rate data becomes greater as forward flow increases and the absolute magnitude of the backmixing rate decreases. Lelli et al.10 also used 4BD impellers for their investiga-

Figure 11. Comparison of the center hole with forward flow results of this investigation with the results of Lelli et al.10 Legend: upper curve, this investigation; lower curve, Lelli et al.10

tion. If their results are corrected to a 6BD basis, then the discrepancy between their results and the model prediction is decreased. Considering the difficulty of obtaining accurate backmixing data, especially from residence time distribution data, the agreement between Lelli et al.’s investigation10 and this investigation is reasonable. 9. Summary and Conclusions 1. The interstage backmixing rate (Fb) is proportional to the stage-divider opening area [i.e., the backmixing velocity (vb) is constant] for Do/DT < 0.4. 2. Forward flow (Ff) decreases backmixing flow (Fb) and eventually decreases Fb to zero at a finite value of Ff. 3. Attaching a draft tube to the center opening significantly decreases the backmixing rate. For example, for 6BD with L/Dh ) 7, Fb decreases by a factor of 5 compared to that of a center hole without a draft tube. For an HE-3 impeller with L/Dh ) 7, Fb is decreased by the draft tube addition by a factor of 100. 4. Nb0 [)vb0/(NDi)(Di/DT)n(DT/Z)1/2)] was used to correlate the effect of the agitator tip speed, Di/DT, and DT/Z on the backmixing velocity at zero forward flow (vb0). Nb0 is constant for NRe > 6000 but starts decreasing below NRe < 6000 and Nb0 ) 0 for NRe < 340 for 6BD and NRe < 520 for HE-3. 5. vb/vb0 vs vf/vb0 correlates well the forward flow effect on backmixing for a given geometry of the impeller and stage-divider opening.

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6. The correlations presented here can be reliably used to determine the interstage backmixing rates for compartmented columns using 6BD or HE-3 impellers with center hole openings and center hole openings with draft tubes attached. Nomenclature Ao ) area of the stage-divider opening, m2 Dh ) hydraulic equivalent diameter of the stage-divider opening, 4 × flow area/wetted perimeter, m Di ) impeller diameter, m Do ) stage-divider opening diameter, m DT ) column diameter, m Fb ) volumetric rate of interstage backmixing through the stage-divider opening, m3/s Ff ) volumetric forward flow rate, m3/s L ) draft tube height, m Li ) height of the impeller blades, m n ) exponent of Di/DT in eq 7 N ) impeller rotational speed, rpm Nb0,n ) dimensionless backmixing parameter at zero forward flow, eq 7, where n is the exponent of Di/DT Np ) P/FN3D5, impeller power number NRe ) NDi2F/µ, impeller Reynolds number NRef ) FfF/µDi, forward flow Reynolds number vb ) backmixing velocity through the stage-divider opening, m/s vb0 ) backmixing velocity through the stage-divider opening at zero forward flow, m/s vf ) forward flow velocity through the stage-divider opening, m/s vt ) impeller tip speed, m/s vT ) superficial velocity based on a column cross section, m/s Wb ) width of the baffle, m Wib ) radial width of the impeller blades on a disk impeller, m Z ) height of the compartment, m

Literature Cited (1) Takriff, M. S. Column Flooding, Gas Holdup and Interstage Backmixing of an Aerated Multistage, Mechanically-Agitated, Compartmented Column. Ph.D. Dissertation, University of Arkansas, Fayetteville, AR, 1996.

(2) Takriff, S. B.; Penney, W. R.; Fasano, J. B. Interstage Backmixing of an Aerated Multistage, Mechanically-Agitated, Compartmented Column. Can. J. Chem. Eng. 1998, 76, 365369. (3) Takriff, S. B.; Penney, W. R.; Fasano, J. B. Effect of Design and Operating Parameters on the Flooding of a Gas-liquid Mechanically-Agitated, Compartmented Column. Jurnal KejuruTeraan, Universiti Kebangsaan Malaysia 2000, No. 12, 99104. (4) Xu, B. C. Interstage Backmixing in Compartmented, Agitated Columns: Experimental Determination and Correlation of Results. Ph.D. Dissertation, University of Arkansas, Fayetteville, AR, 1994. (5) Miyauchi, T.; Mitsutake, H.; Harase, I. Longitudinal Dispersion in Rotating Impeller Type Contactors. AIChE J. 1966, 12, 508-513. (6) Gutoff, E. B. Interstage Mixing in an Oldshue-Rushton Liquid-Liquid Extraction Column. AIChE J. 1965, 11, 712715. (7) Haug, H. F. Backmixing in a Multistage Agitated Contactorssa Correlation. AIChE J. 1971, 17, 585-589. (8) Ingham, J. Backmixing in a Multistage Liquid-Liquid Extraction Column. Trans. Inst. Chem. Eng. 1972, 50, 372385. (9) Lelli, U.; Magelli, F.; Sama, C. Backmixing in Multistage Mixer Columns. Chem. Eng. Sci. 1972, 27, 1109-1116. (10) Lelli, U.; Magelli, F.; Pasquali, G. Multistage Mixer Columnssa Contribution to Fluid-dynamic studies. Chem. Eng. Sci. 1976, 31, 253-256. (11) Magelli, F.; Pasquali, G.; Lelli, U. Backmixing in Multistage Mixer ColumnssII. Chem. Eng. Sci. 1982, 37, 141-145. (12) Magelli, F.; Pasquali, G.; Machon, V.; Kudrna, V.; Hasal, P. Scale-up of Backmixing Phenomena in Multistage, Mechanically Agitated Stirred Columns with Perforated Plates. Ing. Chim. Ital. 1983, 19, 91-94. (13) Magelli, F.; Fajner, D.; Pasquali, G. Backmixing in Multistage Mixer ColumnsIII, Slightly Viscoelastic Liquids. Chem. Eng. Sci. 1986, 41, 2431-2433. (14) Vidaurri, F. C.; Sherk, F. T. Low Backmixing in Multistage Agitated Contactors used as Reactors. AIChE J. 1985, 31, 705710.

Received for review September 1, 2004 Revised manuscript received January 10, 2005 Accepted January 11, 2005 IE040238M