Effects of Mass Transfer on the Steady State and Dynamic

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Ind. Eng. Chem. Res. 2009, 48, 3580–3588

Effects of Mass Transfer on the Steady State and Dynamic Performance of a Ku¨hni Column - Experimental Observations Luı´sa N. Gomes,† Margarida L. Guimara˜es,† Johann Stichlmair,‡ and Jose´ J. Cruz-Pinto*,§ Instituto Superior de Engenharia do Porto, Dep. Eng. Quı´mica, Rua Dr. Antońio Bernardino de Almeida 431, 4200-072 Porto, Portugal, Lehrstuhl fu¨r FluidVerfahrenstechnik Technical UniVersity of Munich, Boltzmannstr. 15, D-85748 Garching bei Mu¨nchen, Germany, and Dep. Quı´mica/CICECO, UniVersidade de AVeiro, Campus de Santiago, 3810-193 AVeiro, Portugal

Experimental data obtained in a pilot-scale Ku¨hni liquid-liquid extraction column were used to obtain local drop size distributions, dispersed-phase hold-up profiles, and solute concentrations. To obtain information about the dynamic behavior of the column, several experiments were planned and performed, under both steady and controlled transient conditions, with and without mass transfer. The analysis of the effects of the presence of a transferring solute (not of the mass transfer flux itself) on the dispersion’s steady state and dynamic behavior was the main objective. For this, we imposed forced step variations in the operating conditions - agitation intensity and continuous and dispersed-phase flowrates. Introduction Liquid-liquid extraction is a competitive separation technology in a number of important applications, like the treatment of effluent streams for the removal of toxic materials, petrochemical processes, pharmaceutical processes, food processing and fertilizer industries, and various inorganic processes. Typically, a liquid-liquid extraction column promotes the contact between a dispersed (drops) phase and a continuous phase, to maximize the interfacial area available to mass transfer. The interfacial area depends on the dispersion device at the feed entry and on the drop breakage and coalescence processes generated within the extractor. The separation efficiency depends on the solute distribution between the two phases, the mass transfer rate, and the contact time between phases. On the other hand, the column capacity depends on the feed flowrates. The compromise in the maximization of these two objectives leads to the common practice of running this operation at the maximum capacity, near the flooding point. The interplay between the breakage and coalescence processes, which depends on the contactor type, agitation intensity, and physical properties of the two liquids (especially the interfacial tension), determines the mean drop diameters and the drop size distribution, and the local dispersed-phase hold-ups. High agitation levels lead to strong drop breakage, consequently to very small drops and large interfacial areas, but too small drops lead to quick solute saturation, entrainment losses, excessive axial mixing, and higher local hold-ups, potentially also leading to the flooding of the column. Extraction does offer great flexibility in the choice of the operating conditions. The performance of counter-current liquid-liquid extraction columns depends on the physical properties of the liquid system, column type and dimensions, internals, and operating conditions.1 Successful design normally requires experimental work on a pilot plant scale, and few reliable experimental data exist for the Ku¨hni column extractor. * To whom correspondence should be addressed. Tel: 00-351-234370733/360. Fax: 00-351-234-3700084. E-mail: [email protected]. † Instituto Superior de Engenharia do Porto. ‡ Lehrstuhl fu¨r Fluidverfahrenstechnik Technical University of Munich, Boltzmannstr. § Universidade de Aveiro, Campus de Santiago.

Experimental work in different agitated columns, using pilot plants equipped with sophisticated techniques and devices to measure drop diameters, solute concentrations, and hold-ups along the column height have along the years been successfully conducted by several researchers. Cruz-Pinto,2 Bonnet and Tavlarides,3 Schmidt et al.,4 Tsouris and Tavlarides,5 Weiss et al.,6 Zamponi,7 and Kentish8 are some of the researchers that worked successfully in this field. More recently, Oliveira9 carried out an experimental study of the hydrodynamic behavior in a section of a pilot-scale Ku¨hni column. Kolb and Bart10 also conducted experimental studies using a mini-plant (laboratoryscale continuous plant) extractor to acquire hydrodynamic data. As a result, the modeling of liquid-liquid extraction columns showed significant recent development due to the knowledge gained from the experiments with the equipment and the use of advanced models and computational procedures. However, in the studies of column hydrodynamics, the experiments were predominantly carried out in the absence of mass transfer, their main goal being the acquisition of experimental data to quantify the relevant hydrodynamic (including drop interaction) model parameters. As well known, however, the mere presence of a solute transferring between the two phases, even when Marangoni effects are deliberately excluded, significantly affects the interfacial tension and, consequently, modifies the drop diameters. Considering organic systems with high interfacial tension, when mass transfer is from the continuous to the dispersed phase (which is the current industrial practice), the interfacial tension generally decreases with solute concentration (as well documented11,12 for many liquid-liquid test systems), and smaller drops are produced. Tsouris and Tavlarides13 were one example of very few groups of authors who investigated experimentally the effect of solute mass transfer on the drop size distribution and hold-up profiles of the dispersed phase in a multistage extraction column. More work involving data acquisition when mass transfer occurs is therefore still needed, involving the determination of solute concentration profiles and of their effects on the dispersion’s interacting behavior and the ensuing local dispersedphase hold-ups and drop diameters. This is deemed essential to thoroughly identify the detailed phenomenologies that the newest models and algorithms14 must also directly address and successfully describe in the end. The collection and classification

10.1021/ie801034a CCC: $40.75  2009 American Chemical Society Published on Web 02/19/2009

Ind. Eng. Chem. Res., Vol. 48, No. 7, 2009 3581

Figure 2. Detailed scheme of the probe used in the mass transfer experiments.23

Figure 1. Scheme of the Ku¨hni column with its measurement equipment. Table 1. Physical Properties of Pure Toluene and Water at 20 °C density (kg · m-3) toluene Water

866.7 998.2

viscosity (Pa · s)

interfacial tension (N · m-1) -3

0.586 × 10 1.003 × 10-3

-3

33.4 × 10

Figure 3. Steady-state concentration profile in the raffinate vs column height under B12 standard operating conditions (QC ) 94 L · h-1, QD ) 120 L · h-1, 170 rpm), xC,0 ) 0.05 kg · kg-1 and xD,0 ) 0.0 kg · kg-1.

of this experimental information when mass transfer occurs was thus the main objective of this work. Other reports elaborate on the transient, purely hydrodynamic, behavior in the absence of mass transfer.15 Experimental Work The experimental work was carried out by Gomes16 in a Ku¨hni pilot plant column, schematically shown in Figure 1 (150 mm inside diameter, active height of 2520 mm, divided into 36 stirred compartments with 25% free area baffle plates), at the TUM - Technical University of Munich. The test system was the standard equilibrated high interfacial tension toluene (dispersed phase) - water (continuous phase) and acetone (transferring solute) system. The aqueous feed is introduced at the top of the column and flows downward to its bottom, and the dispersed-phase flows counter-currently. The toluene/acetone extract is post-processed by distillation. The physical properties of the fluids (at 20 °C) are reported in Table 1, and refs 11 and 12 quantitatively specify the effect of the acetone solute concentration on the system’s interfacial tension. Mass transfer was always from the continuous to the dispersed phase, which ensured that no Marangoni effects2,17,18 interfered with and enhanced interdrop coalescence and local interfacial mass transfer fluxes, given that the system’s interfacial tension decreases with solute concentration,11,12 and thus the drainage

Figure 4. Experimental dispersed-phase hold-up profiles before, during, and after a negative step variation in agitation rate (170 to 140 rpm), under B12 operating conditions (QC ) 94 L · h-1, QD ) 120 L · h-1), xC,0 ) 0.057 kg · kg-1 and xD,0 ) 0.0 kg · kg-1.

of the continuous-phase film separating any colliding drops was effectively depressed. Equipment and Procedures. The experimental plant used for the investigation of the transient behavior of liquid-liquid extraction processes is divided in two parts: • One stirred extraction column for the transfer of the solute component from the aqueous feed to the organic. • Two distillation columns: One for the recovery of the solvent, and another for the stripping of the raffinate. The required volume of the transfer component acetone is added to distilled water and pumped into the upper disengage-

3582 Ind. Eng. Chem. Res., Vol. 48, No. 7, 2009

Figure 5. Drop volume distributions under steady-state B12 operating conditions (QC ) 94 L · h-1, QD ) 120 L · h-1). a) without mass transfer, b) with mass transfer, xC,0 ) 0.05 kg · kg-1 and xD,0 ) 0.0 kg · kg-1 and two different agitation speeds (left side 140 rpm and right side 170 rpm).

Figure 6. Dispersed-phase hold-up profiles under steady-state B12 operating conditions (QC ) 94 L · h-1, QD ) 120 L · h-1): a) without mass transfer; b) with mass transfer, xC,0 ) 0.05 kg · kg-1 and xD,0 ) 0.0 kg · kg-1 and two different agitation speeds (left side 140 rpm and right side 170 rpm).

ment section of the extractor. It flows through the column and is withdrawn at the bottom to a storage tank; the dispersed phase (toluene) is fed into the lower disengagement section and rises

counter-currently to the continuous phase to the top of the extractor. In the upper disengagement section, the rising toluene drops coalesce and a boundary layer is formed between water and toluene. An overflow at the top of the column leads the extract into another tank. The volumetric flowrate of the incoming dispersed phase, which is measured by a rotameter, is set manually during the operation of the extraction column. The volumetric flowrate of the continuous phase is controlled by a computer system, whereby the aqueous-phase outflow is held constant at a specified value, whereas the inflow is regulated so that the boundary layer between the phases at the disengagement section is held at a constant height. Because of this boundary layer regulation, the flow velocities in the active part of the column are held constant and are not affected by the level control of


Figure 7. Drop volume distributions under steady-state B16 operating conditions (QC ) 125 L · h-1, QD ) 160 L · h-1): a) without mass transfer; b) with mass transfer xC,0 ) 0.044 kg · kg-1 and xD,0 ) 0.0 kg · kg-1 for two different agitation speeds: (left side 140 pm and right side 182 rpm).

Figure 8. Steady-state concentration profile in the raffinate vs column height under B16 standard operating conditions (QC ) 125 L · h-1, QD ) 160 L · h-1, 140 rpm), xC,0 ) 0.05 kg · kg-1, xD,0 ) 0.0 kg · kg-1.

the boundary layer. After the extraction process, the extract and the raffinate are post-processed for the next experiment.

Figure 9. Dispersed-phase hold-up profiles under B16 operating conditions (QC )125 L · h-1, 140 rpm) during a negative step variation in the dispersedphase flowrate from 208 L · h-1 to 112 L · h-1.

Extraction Column Measurement Systems. The extraction column was equipped with measurement devices that allowed the investigation of the hydrodynamic conditions along the


Figure 10. Transient acetone concentration profiles under B16 operating conditions (QC )125 L · h-1, 140 rpm), xC,0 ) 0.044 kg · kg-1 and xD,0 ) 0.0 kg · kg-1, during a step variation in the dispersed-phase flowrate from 208 L · h-1 to 112 L · h-1. [At about 5000 s, an anomalous sampling disturbance occurred.]

column height, as well as the mass transfer taking place in the extractor, as shown in Figure 1. A photoelectric technique, initially developed by Pilhofer (cited in Genenger et al.19) was used to measure the axial drop size distribution profiles. The drop slug length in a calibrated capillary was determined with two pairs of photoelectric cells. This instrumentation was installed in five compartments (2nd, 5th, 11th, 21st, and 35th) of the column. Unfortunately, the experimental setup could not provide the direct acquisition of the feed drop size distribution nor even the drop size distribution at the first column stage. Local hold-ups were monitored at four compartments, namely, the 4th, 10th, 16th, and 22nd, using a noninvasive ultrasonic technique. The same ultrasonic technique has been employed earlier by Tsouris et al.20 to study the hydrodynamic behavior of a multistage liquid-liquid contactor. The basic components of the technique are a pulse generator, a pair of ultrasonic transducers per each measuring point, a preamplifier, and an oscilloscope. Sound transmittance time through either of the pure phases and through the dispersion enables the calculation of the volume fraction of each phase. The transmission of sound through liquid dispersions was studied by Yi and Tavlarides21 and Tsouris and Tavlarides.22 This information was used for the estimation of the interfacial area for mass transfer. The calibration of the ultrasonic technique was carried out by measuring the sound travel time in the pure phases before each set of experiments. Dispersion hold-ups were then calculated using an expression previously developed by the same authors. As a check, the overall column holdup was also determined by measuring the pressure difference between the top and bottom of the active part of the column. When mass transfer takes place, the solute concentration in both phases varies and, because the ultrasonic velocity is a function of solute concentration,13 the travel times through the phases have to be updated to take into account the concentration variations. For this purpose, the ultrasonic device was also calibrated under mass transfer conditions, using single-compartment similar equipment. The concentrations in both phases were measured in four compartments (8th, 14th, 23rd, and 32nd) axially positioned as shown in Figure 1. Special probes in PTFE - poly(tetrafluoroethylene) - shown in Figure 2 and described by Hufnagl,23 which promote the separation between the two phases, were used to withdraw both phases separately; samples of the inlet

and the outlet streams were also taken. The samples collected through capillary tubes (at about 1 mL/min of dispersion) fed density transducers, which continuously measured their densities, from which the phase concentrations were derived. As the density of a liquid is very sensitive to changes in temperature, the samples were kept at a constant temperature, thus eliminating measurement errors due to temperature variations. Before each measurement, the density transducers were calibrated. Spot checks were performed by comparing the measured concentrations with values obtained by the samples’ titration at the chemical laboratory. All of these measurements (hold-ups and concentration values) were carried out both at steady and unsteady states. Although uncontrolled environmental conditions could be expected to be an important source of variation on the dispersedphase drop size and hold-up measured data (in particular, ambient temperatures were not measured), no significant difference was observed between measurements in two experimental campaigns carried out at different seasons. Also, only periodical removal of impurities accumulated at the top and bottom interfaces was adopted, in line with the fact that it is also almost impossible and highly uneconomical to stop an industrial installation to perform fluid cleaning operations. So we performed repeat runs to study their reproducibility and the resulting measurement and sampling errors, and these were also used to realistically assess the quality of theoretical performance predictions, as previously discussed and presented elsewhere.24 For this study involving mass transfer, experiments at room temperature, under both steady state and dynamic conditions, were performed under normal and extreme agitation intensity and dispersed and continuous-phase flowrates, and a constant continuous-/dispersed-phase flow ratio (QC/QD ) 1.28) was used. The standard operating conditions were defined as those corresponding to 70% of the global dispersed-phase hold-up measured near the flood-point, for two different sets of fluid flow velocities23 labeled as follows: B12:QD ) 120 L·h-1;

QC ) 94 L·h-1;

B16:QD ) 160 L·h-1;

QC ) 125 L·h-1;

agitation rate ) 170 rpm

agitation rate ) 140 rpm Details of the data reported by Gomes16 may be obtained from the authors, and other similar data are available from Zamponi.7 The solute concentration in the continuous-phase feed stream, xC,0 used in all experiments was about 5 mass % and the solute concentration in the dispersed phase, xD,0, was 0%. Hence, the mass transfer direction was always from the continuous to the dispersed phase, to avoid the well documented Marangoni effects2,17,18 and the resulting increased coalescence. Effects of the Presence of Solute: Results and Discussion. Experiments with mass transfer are time-consuming and disturbances induced by variation of the operating conditions take a long time to die out before reaching a new steady state. Also, because of strict instrumentation probe space restrictions, the readings of the solute concentration in the raffinate could not be taken at stages coincident with those of the other measurements, which made their correlation difficult. The experimental results, which appear as files on the computer interfaced to the column, were copied into an Excel flow sheet and later checked against and corrected by the results of the titration analyses performed in the chemical laboratory. As already mentioned, the concentration measurements were performed either under transient or steady-state conditions. In


Figure 11. Volume drop size distributions under steady-state B16 operating conditions (QC )125 L · h-1, 140 rpm): a) without mass transfer, b) with mass transfer, xC,0 ) 0.044 kg · kg-1 and xD,0 ) 0.0 kg · kg-1 (left side QD ) 112 L · h-1, right side, QD ) 208 L · h-1).

the former case, we obtained curves of acetone concentrations versus experimental time. Then concentration readings allowed us to follow every step of each run from the beginning, where the continuous phase starts being fed into the column, until the steady state is reached. Figure 3 shows the steady-state acetone concentration profile in the raffinate versus column height under low flowrate conditions B12 (standard operating conditions). Variation of the Agitation Intensity. Figure 4 shows the experimental dispersed-phase hold-up profiles before, during, and after a negative step variation in agitation rate (170 to 140 rpm) for QC ) 94 L · h-1 and QD ) 120 L · h-1, with mass transfer. It is noticeable that, after such negative disturbance in agitation, the drop volume fraction of the larger drops, as shown in Figure 5, increases mainly at the upper stages, where a drop population of smaller sized droplets is predominant. This fact may be interpreted by a greater increase of the coalescence to breakage frequency ratio where local holdups are higher.

Comparing now the drop volume distributions with and without mass transfer, in the 170 rpm experiments, the presence of solute originates an increase in smaller drops, but mainly at the upper stages, that is after a sufficiently long residence time of the drops within the agitated flow field; on the contrary, for the 140 rpm experiments, the solute’s presence originates an increase in larger drops, which we may possibly interpret as a result of relatively higher coalescence frequencies, for the corresponding lower interfacial tension values, due to a greater deformability of the colliding drops. Figure 6 shows local dispersed-phase hold-up profiles for experiments with and without mass transfer. For the same operating conditions (QC ) 94 L · h-1, QD ) 120 L · h-1 and 170 rpm), as may be seen, an increase of the agitation rate causes an expected increase of the holdup values. The same and an even stronger effect is produced by the presence of the solute, which is the result of the decreased interfacial tension. Also, at lower agitation levels, the larger drops thus formed rise swiftly


Figure 12. Volume drop size distributions under steady-state B16 operating conditions (QD ) 160 L · h-1, 140 rpm): a) without mass transfer, b) with mass transfer, xC,0 ) 0.043 kg · kg-1 and xD,0 ) 0.0 kg · kg-1 (left Qc ) 87.5 L · h-1, right, Qc ) 162.5 L · h-1).

through the column and do not suffer as significant breakage, being responsible for the decrease in hold-up at the upper stages. Figure 7 shows the volume drop size distributions for the B16 operating conditions (QC ) 125 L · h-1, QD ) 160 L · h-1 under two different agitation intensities - 140 and 182 rpm). Once again, it may be noticed that an increase in agitation intensity causes an increase in the smaller drop fraction along the column height, thus increasing the interfacial area and reducing the final acetone concentration at the raffinate (cf. Figure 8 vs Figure 3). Again, the presence of solute seemed to be responsible for an increase/decrease in the smaller drop fraction at the higher/lower agitation rate, possibly as the result of higher/lower breakage to coalescence ratios. Variation of the Dispersed-Phase Flowrate. Figure 9 presents the time-dependent dispersed-phase hold-up profiles for two different dispersed-phase flowrates. It should be noticed that a decrease in the dispersed-phase flowrate implies a decrease in the dispersed-phase hold-up, due to the presence of a lower

amount of dispersed-phase, which is responsible for the increase in the solute present in the raffinate (less extraction), as confirmed in Figure 10; the final aqueous phase concentration (at the bottom) rises from 0.0075 to 0.026, approximately. Figure 11 shows the drop volume distributions for the same two different dispersed-phase flowrates under B16 operating conditions. For the lower value of the dispersed-phase flowrate, a clear displacement of the distributions toward the smaller drop sizes under mass transfer may be noticed, as the result of decreased coalescence and increased agitation energy input (for drop breakage) per unit dispersed-phase volume. A comparison between a) and b) in Figure 11 also shows that, for both dispersed-phase flowrates, the size shift of one distribution relative to the other again supports the tendency toward slightly stronger breakage when the transferring solute is present. Variation of the Continuous-Phase Flowrate. Considering the volume drop size distributions represented in Figure 12, for the lower continuous-phase flowrate, the volume drop size


alternative to assess the suitability of the currently used drop interaction models to account for such interfacial tension effects. Acknowledgment This work was carried out under the gratefully acknowledged cooperation of Professor J. Stichlmair and his staff of Lehrstuhl fu¨r Fluidverfahrenstechnik at the Technical University of Munich. Literature Cited

Figure 13. Acetone concentration profile under B16 operating conditions (QD ) 160 L · h-1, 140 rpm), xC,0 ) 0.043 kg · kg-1 and xD,0 ) 0.0 kg · kg-1, during a step variation in the continuous-phase flowrate from 162.5 L · h-1 to 87.5 L · h-1.

distributions are displaced toward the smaller sizes, which may be attributed to a higher breakage rate in the upper column stages, in the presence of the transferring solute. For the higher continuous-phase flow, the effect is smaller (likely due to a compensating positive effect on drop coalescence at the corresponding higher holdup ratios) but is nevertheless still present. Figure 13 illustrates the evolution of the raffinate’s solute concentration profile before and after the negative step variation in the continuous-phase flowrate. Solute concentration expectedly decreases in time due to increased extraction by the dispersed phase. Conclusions 1. The combination of Pilhofer’s drop size distribution measurement technique (cited in Genenger et al.19) with the ultrasound Bonnet and Tavalarides3 for the dispersed-phase hold-ups and Hufnagl23 for the continuous measurement of the transferring solute concentrations provide satisfactorily fast, precise, reproducible, and almost noninvasive ways (due to sampling flows of only 2 to 3 × 10-4 of the main-phase flows) of quantitatively investigating and characterizing the dynamic behavior of liquid-liquid dispersions in extraction columns. 2. The comparison of the experimental local drop size distributions and dispersed-phase hold-ups in both steady and unsteady state column runs shows that the decreased values of the interfacial tension in the presence of solute significantly influence the hydrodynamics of the column, leading to smaller drops with longer residence times and to increased dispersedphase hold-ups. 3. The results of these measurements clearly point to the need to explicitly include these effects in future calculations of the drop-phase population dynamics inside contactors, through the adequate coupling of local solute concentrations and interfacial tensions. This may be achieved by recalculating local, interfacial tension-dependent, drop breakage, and coalescence frequencies along the column height, either (1) most simply, from the measured solute concentration and ensuing interfacial tension profiles, or (2) most completely, by using the same full trivariate (drop size, age, and concentration) description that we successfully implemented in earlier hydrodynamic and mass transfer simulation studies on ideally mixed liquid-liquid stirred tank contactors.25 The first approach will of course be much less predictive but may nevertheless still prove a useful initial

(1) Liquid-Liquid Extraction Equipment; Godfrey, J. C.; Slater, M. J., Eds.; John Wiley & Sons: Chichester, 1994. (2) Cruz-Pinto, J. J. C. Experimental and Theoretical Modelling Studies of the Hydrodynamic and Mass Transfer Processes in Countercurrent-Flow Liquid-Liquid Extraction Columns. Ph.D. Dissertation, The Victoria University of Manchester, U.K., 1979. (3) Bonnet, J. C.; Tavlarides, L. L. Ultrasonic Technique for DispersedPhase Holdup Measurements. Ind. Eng. Chem. Res. 1987, 26, 811–815. (4) Schmidt, H.; Tsouris, C.; Eggert, E.; Tavlarides, L. L. Laser Photometric Probe for Concentration Measurements in Liquid Dispersions. AIChE J. 1989, 35 (3), 507–510. (5) Tsouris, C.; Tavlarides, L. L. Control of Dispersed-Phase Volume Fraction in Multistage Extraction Columns. Chem. Eng. Sci. 1991, 46 (11), 2857–2685. (6) Weiss, J.; Steiner, L.; Hartland, S. Determination of Actual Drop Velocities in Agitated Extraction Columns. Chem. Eng. Sci. 1995, 50 (2), 255–261. (7) Zamponi, G. Das Dynamische Verhalten Einer Geru¨hrten Solventeextraktionskollonne. Ph.D. Dissertation, Technische Universita¨t Mu¨nchen: Germany, 1996. (8) Kentish S. Forward Mixing in a Countercurrent Solvent Extraction Contactor. Ph.D. Dissertation, University of Melbourne: Australia, 1996. (9) Oliveira N. S. Estudo da Hidrodinaˆmica de uma Coluna de Extracçaõ Ku¨hni. MSc Dissertation, Universidade Federal de Minas Gerais: Brasil, 2005. (10) Kolb P.; Bart H. Liquid-Liquid Miniplant Extractor-A NoVel Tool for Process Design, Proceedings of ISEC 2002, South African Institute of Mining and Metallurgy, 2002. (11) Recommended Systems for Liquid-Liquid Extraction Studies, European Federation of Chemical Engineering, Working Party on Distillation, Absorption and Extraction; Misek T., Ed.; The Institution of Chemical Engineers: Rugby, 1978. (12) Standard Test Systems for Liquid-Liquid Extraction, European Federation of Chemical Engineering, Working Party on Distillation, Absorption and Extraction, Misek T. et al., Eds.; The Institution of Chemical Engineers: Rugby, 1985. (13) Tsouris, C.; Tavlarides, L. L. Mass Transfer Effects on Droplet Phenomena and Extraction Column Hydrodynamics Revisited. Chem. Eng. Sci. 1993, 48 (8), 1503–1515. (14) Gomes, L. N.; Guimara˜es, M. M. L.; Regueiras, P. F. R.; Stichlmair, J.; Cruz-Pinto, J. J. C. Simulated and Experimental Dispersed-Phase Breakage and Coalescence Behavior in a Ku¨hni Liquid-Liquid Extraction Column-Steady State. Ind. Eng. Chem. Res. 2006, 45, 3955–3968. (15) Gomes, L. N.; Guimara˜es, M. M. L.; Stichlmair, J.; Cruz-Pinto, J. J. C. Study of Dynamic Simulation and Its Influence on the Control of an Agitated Liquid-Liquid Ku¨hni Extraction Column, International Solvent Extraction Conference 2005, Beijing, China, 2005. (16) Gomes, M. L. A. C. N. Comportamento Hidrodinaˆmico de Colunas Agitadas de Extracçaõ Lı´quido-Lı´quido. Ph.D. Dissertation, Universidade do Minho: Portugal, 1999. (17) Sawistowski, H. Interfacial Phenomena. Recent AdVances in Liquid-Liquid Extraction; Hanson, C., Ed.; Pergamon: New York, 1975; pp 293-366. (18) Jeffreys G. V.; Davies G. A. Coalescence of Liquid Droplets and Liquid Dispersion. Recent AdVances in Liquid-Liquid Extraction; Hanson, C., Ed.; Pergamon: New York, 1975; pp 495-584. (19) Genenger, B.; Lohrengel, B.; Lorenz, M.; Vogelpohl, A. HydromessMeβsystem zur Bestimmung der Blasen - und Tropfengro¨βe in Mehrphasenstro¨mungen; Institut fu¨r Thermische Verfahrenstechnik der TU Clausthal: Germany, 1991. (20) Tsouris, C.; Ferreira, R.; Tavlarides, L. L. Characterization of Hydrodynamic Parameters in a Multi-Stage Column Contactor. Can. J. Chem. Eng. 1990, 68, 913–923.

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ReceiVed for reView July 3, 2008 ReVised manuscript receiVed November 16, 2008 Accepted January 19, 2009 IE801034A

Effects of Mass Transfer on the Steady State and Dynamic

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