Reactive Extraction of Zinc Sulfate with Bis(2-ethylhexyl)phosphoric

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Ind. Eng. Chem. Res. 2003, 42, 4068-4076

Reactive Extraction of Zinc Sulfate with Bis(2-ethylhexyl)phosphoric Acid in a Short Ku 1 hni Column Used in Batch Mode Marcelo B. Mansur,*,† Michael J. Slater,‡ and Evaristo C. Biscaia Junior§ Departamento de Engenharia Quı´mica, Universidade Federal de Minas Gerais, Rua Espı´rito Santo 35/617-4, 30160-030 Belo Horizonte, MG, Brazil, Department of Chemical Engineering, University of Bradford, Bradford BD7 1DP, U.K., and Programa de Engenharia Quı´mica, COPPE, Universidade Federal do Rio de Janeiro, Caixa Postal 68502, 21945-970 Rio de Janeiro, RJ, Brazil

The nonstationary behavior of a four-stage Ku¨hni column operated in batch mode to the point of chemical equilibrium was investigated with the objective of determining a method of generating reliable engineering design data in an easy and cheap way. Experiments were carried out under extraction and stripping conditions with the liquid-liquid reactive system adopted by the European Federation of Chemical Engineering, ZnSO4/bis(2-ethylhexyl)phosphoric acid/nheptane. The following variables were evaluated: rotor speed, organic-phase throughput, and extractant concentration for extraction studies and proton and extractant concentrations for stripping studies. The closed-circuit method gave estimates of heights of transfer units of adequate accuracy for design purposes. On the other hand, hydrodynamic and mass-transfer parameters estimated from concentration profiles using the backflow model were found correlated, thus indicating that information on drop size distributions is required for the evaluation of individual parameters over the whole agitation range. 1. Introduction Experimental studies on hydrodynamic and masstransfer characteristics of liquid-liquid extraction columns are conventionally carried out using columns operated in an open-circuit loop. According to this method, the dispersed phase is fed to the column at practical throughput values resulting in a population of dispersed drops as commonly found at normal operation. The method is realistic, but the high consumption of reagents and the large storage vessels required when using pilot- or industrial-scale plants have motivated the development of cheaper alternative techniques for generating reliable design data for extraction columns. In this context, the single-drop method1 consisting of the introduction of individual spaced drops has been proposed. The method is very cheap, but it gives data which do not take into account any drop interactions in the columns. The single-drop method has been extended to short sections of columns2 and allows comprehension of the extraction column performance at reduced cost and with increased validity. The technique is particularly valuable in determining the characteristic velocity of drops because the column operates at essentially zero holdup conditions. Cabassud et al.3 have shown that holdup simulation calculations for countercurrent columns are very sensitive to the value of the characteristic velocity which must be known with good accuracy. Single-drop experiments have been helpful in describing the random character of drop motion inside a Ku¨hni * To whom correspondence should be addressed. Tel.: (55) (31) 3238-1780. Fax: (55) (31) 3238-1789. E-mail: mansur@ deq.ufmg.br. † Universidade Federal de Minas Gerais. ‡ University of Bradford. § Universidade Federal do Rio de Janeiro.

column. Fang et al.4 have found that, for single drops in a Ku¨hni column in the region of transitional turbine Reynolds numbers, drops break predominantly at the perforated plates, not at the turbines. Only when agitation is intense do most drops break under the influence of the turbines. Information on drop breakage probabilities is required for the calculation of drop size distributions in countercurrent column operating conditions, but the observation of single drops becomes difficult at higher speeds, even using a video camera (rotor speeds of up to 300 min-1 are commonly used for a Ku¨hni column of 150 mm diameter). A drop size specific axial backmixing coefficient has been proposed by Seikova et al.5 based on single-drop studies in a Ku¨hni column. It has proved possible to measure singledrop mass-transfer coefficients in short sections of rotating disk, pulsed sieve plate- and packed liquidliquid extraction columns,2 but further effects of drop interaction remain unknown because the extrapolation of the information obtained from single drops in vertical motion to describe a population of drops inside an extraction column is not simple.6 Complex effects observed in a swarm of drops (whose interactions affect hydrodynamics and mass transfer by drops coalescing and breaking up) are not measured by single-drop experiments, so direct application of single-drop data is therefore of an uncertain value.7-10 In this context, an alternative experimental method is proposed in this paper to investigate liquid-liquid extraction columns with normal countercurrent flow patterns at low cost. The method is illustrated using the liquid-liquid reactive recommended system adopted by the European Federation of Chemical Engineering, ZnSO4/bis(2-ethylhexyl)phosphoric acid (D2EHPA)/nheptane. According to this method of operation, both streams leaving a short section of the column are reintroduced; thus, the unit operates in a closed-circuit

10.1021/ie020883y CCC: $25.00 © 2003 American Chemical Society Published on Web 07/18/2003

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loop with total recirculation of phases (batch mode). The method is based on the measurement of the time dependence of solute concentrations at the ends of the column until equilibrium is reached. Hydrodynamic and mass-transfer rate parameters can be estimated by fitting appropriate dynamic models to these concentration profiles. Associated work concerns the modeling of the complex equilibrium and kinetics of the zinc/ D2EHPA system,11,12 development of dynamic models,13 and application to a short Ku¨hni column14 to estimate rate coefficients (area-free basis). The use of parameter estimation from measured solute concentrations in a countercurrent column has the advantage of being applicable to full-scale industrial installations without requiring any disruption of production or introduction of tracers. However, the reliability of the parameter estimates depends on the accuracy of the concentration measurements and the number and location of the sampling points.15 In the case of a closed-circuit system, the time taken to reach equilibrium and the time intervals between samples need to be investigated. The characteristic times for the rates of physical processes of drop formation at the inlet distributor, drop breakage, and coalescence relative to the characteristic times of the mass-transfer processes in each phase must be important and case-specific. The zinc/D2EHPA system has kinetics partly controlled by chemical reaction rates, which are much slower than diffusion-controlled rates. Experimental investigations with closed-circuit plants, commonly used in adsorption column studies,16 have rarely been used to investigate liquid-liquid extraction equipment. Wichterlova and Rod17 have proposed analytical expressions to determine mass-transfer and extraction efficiency of a mixer-settler extractor. The method is based on solute tracer injection into the mixer of a mixer-settler unit, operating with total recirculation of both phases, and on the measurement and evaluation of the concentration responses in the phase outlets from the settler. According to these authors’ model, the unit must operate in a steady hydrodynamic regime and the phases must be in equilibrium when the solute tracer is injected.

Figure 1. Experimental arrangement of the pilot unit. Table 1. Technical Description of the Ku 1 hni Column diameter (mm) no. of stages height of the stage (mm) height of the stage above the top plate (mm) height of the stage below the bottom plate (mm) diameter of the rotor (mm) height of the rotor (mm) fractional free cross-sectional area (%)

150 4 70 120 77 85 10 30

Table 2. Technical Description of the Pipes (See Location in Figure 1) pipe length (m) diameter (mm) volume (approximately) (mL)

AEC

ASC

OEC

OSC

2.80 15 494

1.45 5 28

3.80 15 671

1.20 15 212

2. Experimental Section The reactive liquid-liquid recommended system adopted by the European Federation of Chemical Engineering, ZnSO4/D2EHPA/n-heptane (for details see IChemE learning portal, 2002, www.icheme.org/learning) was used in a short Ku¨hni column. D2EHPA molecules exist predominantly as dimers in aliphatic diluents, and reaction with zinc occurs at the liquidliquid interface.11,12 The main difficulties to be recognized in a short column are the end effects and inlet drops being of uncharacteristic size for a given geometry and degree of agitation.1 No drop size or hold-up measurements have been performed in this study. 2.1. Pilot-Scale Unit. The experimental pilot-scale unit is shown in Figure 1. The Ku¨hni column built in a cylindrical glass section was equipped with turbine agitators with accurate speed control and internal parts constructed in stainless steel (details are given in Table 1). The dispersed phase was introduced into the column using a conical distributor located off-center in the base of the column (35 mm diameter, 30 holes of 2 mm diameter). All piping was constructed of either stainless steel, glass, or Viton to prevent any contamination of

the process streams (see Table 2 for more details). Glass aspirators were used as tanks. 2.2. Reagents. In extraction column runs, an acidic aqueous solution at pH 3.0 (H2SO4 from BDH Chemicals, 98% purity) with 10 mol/m3 ZnSO4 (BDH Analar, 99% purity) was contacted with an organic solution of D2EHPA (supplied by Alpha Aesar, 94.4% purity) dissolved in n-heptane (Sigma-Aldrich, 99% purity) at a specified concentration. Water and n-heptane were previously mutually saturated before the preparation of the solutions on the day before each experimental run. In stripping column runs, a previously zinc-loaded organic phase was contacted with an aqueous sulfuric acid solution at a specified hydrogen ion concentration. The loaded organic phase was prepared by contacting the solvent at known D2EHPA concentration with the same volume of a 1 kmol/m3 ZnSO4 aqueous solution, and this was repeated three times in a stirred tank for a period of at least 12 h. A solution of non-surface-active detergent Decon 90 was used to clean the equipment after each run as described below.

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Figure 2. Experimental zinc concentration profile in an aqueous stream leaving the column at various rotor speeds (Qd ) 1 L/min; C0BD ) 75 mol/m3).

2.3. Procedure. The column was slowly filled with the continuous aqueous phase until it reached a set level (about 70 mm above the upper stage), and then recirculation was started at a flow rate of 2 L/min (flow rates are relatively low because the kinetics are slow). After stabilization of the top level, the rotor motor was started and the dispersed organic phase was introduced from the bottom of the column at a specified throughput (0.52.0 L/min). Organic-phase recirculation started within about 30 s of the interface being formed, followed by overflow of the solvent. Samples were withdrawn at time intervals at both ends of the column, i.e., in the aqueous stream leaving the column (ASC) and in the organic stream entering (OEC) and leaving (OSC) the column (see Figure 1). The zinc content in the samples was analyzed by atomic absorption (Pye Unicam SP 190 series atomic absorption single-beam spectrophotometer, operated at a wavelength of 213.9 nm in an airacetylene flame). Solvent samples were first stripped with sulfuric acid. The interface height, the stream flow rates, and the liquid levels in the tanks were constantly monitored during experiments. In all runs, the total volumes of the aqueous and organic phases were unchanged (10 and 5 L, respectively). At the end of the run, the rotor was stopped, all inlet valves were closed, both phases were removed from the column, and the organic phase was recovered by treatment with zinc or acid solutions. The loaded organic phase can be reused in extraction runs by stripping the zinc with 2.5 kmol/m3 H2SO4 repeated twice and at least twice washing with water, with a phase ratio of 1.0, until neutrality is reached.18 To clean up the column, the unit was filled with a 2-3% (v/v) Decon 90 solution in water and left for a period of 3 h. The column was then emptied and rinsed three times with tap water and once with distilled water. All joints and pipes were washed to ensure thorough removal of the detergent. 3. Results and Discussion The continuous phase is the aqueous solution in all column runs carried out in this study so, in extraction

runs, the mass-transfer direction is c f d and the opposite direction is the case in stripping runs. Some observations can be made concerning the effect on mass transfer of the distributor and initial drop size, but nothing certain can be said about the coalescence at the interface. Drop formation times were very short, and drops coalesced in a short time relative to the residence time of a very few minutes spent in the column. 3.1. Extraction Runs. Extraction runs were carried out under various conditions to evaluate the effect of the following variables on the start-up behavior of the Ku¨hni column operated in batch mode: rotor speed (60, 120, 150, and 180 min-1), organic feed flow rate (0.5, 1.0, and 2.0 L/min), and initial dimer/D2EHPA concentration (7.5, 37.5, and 75.0 mol/m3). In all runs, the aqueous feed flow rate was kept constant at 2 L/min, so operational conditions were far from the flooding point known from other work to be several times these flow rates. The effect of the rotor speed on zinc concentration profiles in aqueous and organic streams leaving the column is shown in Figures 2 and 3, respectively. The maximum point observed in the zinc concentration profile curve in the organic phase is due to the organic feed zinc concentration remaining zero so that the driving force is at a maximum for the first minutes or so until the organic phase overflows and changes the feed concentration at the inlet. Increasing the rotor speed leads to smaller drops of dispersed phase and higher holdup, resulting in larger specific interfacial areas. Higher zinc extraction rates are obtained and equilibrium is reached faster in more highly agitated conditions. As expected, the same equilibrium condition has been reached in these runs. The response of the organic phase appears to be more sensitive to small perturbations than the aqueous phase, presumably because of the short residence time compared to that of the aqueous phase. It was seen that the liquid-liquid interface level was very sensitive to small variations in throughput. Nonhomogeneous distribution of drops was observed in stages 1 and 2 at low rotor speed (60 min-1). This

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Figure 3. Experimental zinc concentration profile in an organic stream leaving the column at various rotor speeds (Qd ) 1 L/min; C0BD ) 75 mol/m3).

Figure 4. Experimental zinc concentration profile in an aqueous stream leaving the column at various organic feed flow rates (NR ) 120 min-1; C0BD ) 75 mol/m3).

behavior was seen only in stage 1 when the column operated at 75-85 min-1, and a fully dispersed phase was observed at rotor speeds higher than 100 min-1. This observation corroborates Fang et al.,4 who stated that drops break at the plates, not at the turbines, when agitation is low. Only those results for high speeds can therefore be expected to give valid data for the design of a column; only for this condition are drops likely to be of a size unaffected by the size produced at the distributor. Further experiments ideally need to be carried out using different hole sizes in the distributor to demonstrate the hole size for which a condition of independence is reached. There is too much uncertainty involved in using empirical equations to predict drop sizes produced by a distributor to match drop sizes expected in the column. The effect of the organic feed flow rate (or the A/O feed ratio with the aqueous feed flow rate kept constant

at 2 L/min) on the zinc concentration in the aqueous stream that leaves the column is shown in Figure 4. Equilibrium is reached faster with a higher organicphase feed rate to the column because the amount of extractant present to extract zinc ions by chemical reaction is higher and holdup is higher. Different equilibrium conditions are reached when organic phases with different concentrations of D2EHPA are contacted with the same aqueous liquor at constant throughput. The degree of extraction of zinc is reduced at lower D2EHPA concentrations and, as shown in Figure 5, lower peaks of loaded organic concentration are obtained in the organic stream that leaves the column during the initial few minutes of extraction. The initial disturbance is less because less extractant passes through before recirculation starts. A 22 factorial design has been performed to qualitatively analyze the combined effect of variables rotor

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Figure 5. Experimental zinc concentration profiles in an organic stream leaving the column at various initial dimer/D2EHPA concentrations (NR ) 120 min-1; Qd ) 1 L/min).

Figure 6. Influence of the rotor speed and the organic feed flow rate on the experimental zinc concentration profile in an aqueous stream leaving the column (C0BD ) 75 mol/m3).

speed (120 and 180 min-1) and organic feed flow rate (0.5 and 1 L/min). Bonnet19 has found these variables to be most significant in affecting hydrodynamics and mass-transfer characteristics in a five-stage Scheibel column. Figure 6 shows zinc concentration profiles in the aqueous stream leaving the column with time. According to the experimental results, rotor speed has a main effect; organic feed flow rate is significant only at lower agitation conditions. 3.2. Stripping Runs. Stripping runs have been carried out to qualitatively evaluate the combined effect of the following variables using a 22 factorial design of experiments: total dimer/D2EHPA concentration (15 and 150 mol/m3) and initial hydrogen ion concentration (100 and 1000 mol/m3). The experiments were carried out at constant aqueous flow rate (2 L/min), feed flow ratio (A/O ) 2), and rotor speed (120 min-1). Total dimer/D2EHPA concentration and initial hydrogen ion

concentration showed a significant effect. Stripping rates of zinc are notably enhanced when more highly acidic aqueous phases are used, thus reversing the direction of the interfacial reaction of zinc with D2EHPA. Experimental results for the zinc concentration in aqueous and organic streams leaving the column are shown in Figures 7 and 8, respectively. 4. Column Modeling and Parameter Estimation A transient backflow model20 has been used to describe the nonstationary behavior of the column. The present objective is to obtain a reliable mathematical formulation able to generate design data from short columns operated in batch mode. Data from zinc extraction with D2EHPA in a short Ku¨hni column have been used to evaluate this method. The backflow model assumptions include the following:

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Figure 7. Influence of dimer/D2EHPA and hydrogen ion concentrations on the experimental zinc concentration profile in an aqueous stream leaving the column.

Figure 8. Influence of dimer/D2EHPA and hydrogen ion concentrations on the experimental zinc concentration profile in an organic stream leaving the column.

(i) Spherical drops are uniformly dispersed into the N column stages, each of which is assumed perfectly mixed. (ii) The column is short enough to assume an instantaneous steady hydrodynamic regime. (iii) No volumetric variation is considered in the model. Physical properties of the liquids (density, viscosity, and interfacial tension) are constant with time and column height. (iv) Null chemical reaction and mass-transfer rates occur at end zones of organic-phase introduction (bottom of the column) and coalescence (top of the column). (v) A first-order delay is proposed to describe the dynamic response in the tanks. The inclusion of a dead time in the recirculation streams to take into account the fluid flow through pipes is proposed if very long pipes are used to recirculate the streams. (vi) Equilibrium and kinetics of zinc with D2EHPA are described by Mansur et al.11,12 According to these models, zinc is extracted by heterogeneous reaction with

dimer/D2EHPA, producing a ZnR2RH complex. Part of this zinc complex is consumed as loading of the organic phase increases, resulting in another zinc complex ZnR2 with regeneration of dimer/D2EHPA to react again at the liquid-liquid interface. The boundary conditions used to solve the model are determined by the start-up strategy adopted to initialize the nonstationary operation of the column. Different start-up strategies have been previously discussed.13 In the present work, the column is assumed to recirculate both streams at t ) 0-, but chemical reaction and masstransfer rates start only at t ) 0+. The numerical solution is easier to obtain with this approach because no regularization function is required, but it would not be appropriate to simulate longer columns or stripping operations. The transient backflow model is a differentialalgebraic system solved numerically by the DASSL code.21 Hydrodynamic (R, β, φ, and d32) and masstransfer (kA and kCD) parameters, assumed constant

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Table 3. Parameter Estimation for Extraction Runs (r Calculated from Breysse et al.28 and β ) 0) NR (min-1)

Qd (L/min)

C0BD (mol/m3)

φ (%)

d32 (mm)

kA (µm/s)

kCD (µm/s)

R

120 180 120 180 60 150 120 120

1 1 0.5 0.5 1 1 2 1

75 75 75 75 75 75 75 37.5

8 ( 16 9.2 ( 0.3 10 ( 4 10.5 ( 0.1 9 ( 10 10.1 ( 0.3 10 ( 9 9 ( 17

0.3 ( 0.5 0.06 ( 0.3 1(3 0.22 ( 0.003 0.6 ( 3 0.16 ( 0.003 0.14 ( 0.03 1(2

8 ( 13 ∞ 12 ( 49 ∞ 4 ( 24 4(2 2(2 52 ( 495

0.07 ( 0.003 0.02 ( 0.1 0.2 ( 0.8 0.05 ( 0.0006 2 ( 81 0.08 ( 0.07 ∞ 2 ( 10

0.76 1.30 0.73 1.28 0.19 1.01 0.73 0.75

with time and column height, have been estimated by data fitting using the direct search method of Hooke and Jeaves.22 The method consists of solving the model at given initial values for the parameters and exploring the surroundings at specified increments in order to find the direction of search that reduces the deviation between calculated and experimental responses. The objective function adopted in this work is the total squared deviation between estimated and experimental concentrations of zinc in the ASC, OEC, and OSC streams. Preliminary estimates indicated that the backmixing coefficient of the dispersed phase was negligible (β f 0), while that of the continuous phase (R) was appreciable. The former effect corroborates experimental runs; thus, no backflow of drops from upper to lower stages was observed visually inside the column. Similar results have been obtained elsewhere.23,24 Real backmixing does not exist within the elements of the dispersed phase because of its discontinuity.25 However, the opposite is the case for the continuous phase; i.e., the movement of elements of the continuous phase can be so high that the concentration change of species in the aqueous phase is much reduced along the column. The dispersed-phase behavior was then simulated assuming β ) 0, but apparent high backmixing values for the continuous phase (R > 103) were still obtained. The steady-state concentration profiles for countercurrent flow are not sensitive enough to backmixing to allow reliable estimation of backmixing coefficients by data fitting; backmixing coefficients determined from the concentration profiles are very sensitive to small errors in the experimental measurements, particularly in the end sections.26,27 In other words, very similar concentration profiles are predicted by the backflow model using considerably different values of R. Column scale-up procedures are strongly dependent on the axial mixing of both phases, so they cannot be ignored. Further fitting was, therefore, carried out using well-validated (for single-phase conditions) empirical correlations to quantify R. The hydrodynamic and mass-transfer parameters shown in Table 3 have been estimated with β ) 0 and R calculated using the correlation given by Breysse et al.28 Mass-transfer coefficients denoted by ∞ in Table 3 are insignificant in the zinc extraction process. In this fitting attempt, higher values of the objective function have been found but similar theoretical concentration curves were predicted by the model, so a statistical analysis of the estimated parameters has been performed to evaluate the backflow model in describing short-column operations. According to the statistical analysis, a total of 16 pairs of parameters have been found strongly correlated (bold values in Table 3), predominantly between drop size and mass-transfer coefficients. The poor confidence levels found for correlated parameters indicate that most values shown in

Figure 9. Influence of the rotor speed on the estimated drop size (Qd ) 1 L/min; C0BD ) 75 mol/m3).

Table 3 are very uncertain. The existence of a strong correlation between pairs of parameters (so that neither can be confidently predicted) seems to be associated with axial mixing and drop size effects not adequately described by the backflow model. These fitting investigations have shown that once the axial mixing effect is determined, the drop size distribution seems to be the next most important prevailing effect to be considered because the drop size parameter is present in all correlated pairs when R f ∞ is assumed. It was found that the drop size effect is significant mainly at low rotor speed (NR e 120 min-1) and high organic flow rates (Qd g 2 L/min). Figure 9 shows the influence of rotor speed on the estimated drop size including 95% confidence levels, so smaller drops are obtained at higher rotor speeds; however, the drop size estimated at 180 rpm seems to be highly improbable. Regarding mass-transfer diffusive effects, it has been found that mass-transfer rate coefficients in the dispersed phase are significant mainly when drops are small, i.e., at high rotor speeds. On the other hand, mass-transfer rate coefficients in the continuous phase are significant at lower agitation conditions. No diffusive effect was identified in the transitional agitation region when R f ∞ is considered. To bypass the problem of parameter correlation, the average drop size and holdup were lumped as the specific interfacial area a ) 6φ/d32 and the kinetic coefficients were lumped as Koc. As shown in Figures 10 and 11, the backflow model was suitable for simulating extraction data in terms of the overall volume coefficient Koca with acceptable accuracy. Typical concentration/time responses are shown in Figure 12. Points are experimental data, while the full line is the model response with estimated parameter values. In these calculations, the holdup was determined according to the slip velocity (Vslip) concept with the characteristic velocity (Vk) given by Fang et al.4 According to Pratt,29 the variation in Koca values is due almost entirely to changes in the interfacial area, which is determined by the holdup and drop size of the dispersed phase,

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Figure 10. Estimated overall volume coefficient versus rotor speed for extraction runs (R calculated from Breysse et al.28 and β ) 0).

Figure 11. Estimated overall volume coefficient versus organic feed flow rate for extraction runs (R calculated from Breysse et al.28 and β ) 0).

recommended by the European Federation of Chemical Engineering, ZnSO4/D2EHPA/n-heptane. The following conclusions can be drawn: (i) The concentration/time responses were easily followed and varied significantly as the operating conditions were changed. Modeling of such data is, therefore, not obviously subject to serious problems as a result of lack of sensitivity. (ii) The concern about the performance of the batch system being dependent on inlet drop sizes can be minimized in agitated columns by operating at higher rotor speeds when drops are well-mixed in a compartment and, in the case of the Ku¨hni column, being broken by the rotors and not just the plates. (iii) The time scale for sampling and column operation was satisfactory, although it may not be in other cases if kinetics are controlled by fast diffusion rather than partly or wholly by chemical kinetics. (iv) Extraction runs have shown that small perturbations suffered by the system are rapidly observed in the organic phase but not in the aqueous phase. (v) Individual hydrodynamic and mass-transfer parameters appeared statistically correlated using the backflow model and so cannot be individually estimated with acceptable accuracy, except when agitation is high. From data fitting, it appears that axial mixing effects are more important than drop size effects, which in turn are more important than mass-transfer effects. (vi) Because mass-transfer rates are directly affected by drop size distributions, more accurate and detailed descriptions of behavior should incorporate drop size distributions in order to avoid or eliminate the existence of correlation between estimated hydrodynamic and mass-transfer parameters. The closed-circuit method is, therefore, able to provide engineering design data under conditions close to those expected in a countercurrent column with much reduced reagents consumption and lower capital costs compared to operation of a continuous pilot plant. Unexpected operating problems not revealed by single- drop experiments will be shown in a short column with both an inlet distributor and a coalescence interface. It deserves more study. Acknowledgment

Figure 12. Typical concentration profiles at ends of the column (NR ) 180 min-1; Qd ) 0.5 L/min; C0BD ) 75 mol/m3).

whereas the mass-transfer coefficients are relatively constant for a given system. The continuous-phase superficial velocity is Vc ) 1.89 mm/s, and the overall continuous-phase transfer unit height Hoc is Vc/Koca. The values of Hoc on the order of 3 m indicate the effect of slow chemical reaction because simple physical extraction systems have values on the order of 0.5 m in a Ku¨hni column. 5. Conclusions The nonstationary behavior of a four-stage Ku¨hni column (150 mm diameter) has been investigated experimentally using the liquid-liquid reactive system

This work has been carried out with financial support for Dr. Marcelo Borges Mansur from CAPES (Brazilian Government Agency, PICDT/UFMG, and PDEE Doctorate Grant 0299/99-5) in the Department of Chemical Engineering, University of Bradford (U.K.), and in the Programa de Engenharia Quı´mica (COPPE), Universidade Federal do Rio de Janeiro (Brazil). The authors thank Ing. Daniele Antonelli (Universita´ de L’Aquila, Italy) for his assistance with the column experiments. Nomenclature a ) specific interfacial area ()6φ/d32), m2/m3 A/O ) aqueous/organic phase ratio ASC ) aqueous stream leaving the column Ci ) concentration of species i, mol/m3 d32 ) drop size, m Hoc ) overall continuous-phase transfer unit height, m ki ) mass-transfer coefficient of species i, m/s Koc ) overall rate coefficient based on the continuous phase, m/s N ) number of stages

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NR ) rotor speed, min-1 OEC ) organic stream entering the column OSC ) organic stream leaving the column Q ) volumetric flow rate, m3/s t ) time, s Greek Letters R ) backmixing coefficient of the continuous phase β ) backmixing coefficient of the dispersed phase φ ) holdup of the dispersed phase Subscripts A ) zinc ion BD ) dimer/D2EHPA c ) continuous phase CD ) dimer/D2EHPA complex d ) dispersed phase H ) hydrogen ion Superscript 0 ) at the initial value

Literature Cited (1) Fan, Z.; Oloidi, J. O.; Slater, M. J. Liquid-liquid extraction column design data acquisition from short columns. Chem. Eng. Res. Des. 1987, 65, 243. (2) Bahmanyar, H.; Chang-Kakoti, D. K.; Garro, L.; Liang, T.B.; Slater, M. J. Mass transfer from single drops in rotating disc, pulsed sieve plate and packed liquid-liquid extraction columns. Chem. Eng. Res. Des. 1990, 68, 74. (3) Cabassud, M.; Gourdon, C.; Casamatta, G. Single drop break-up in a Ku¨hni column. Chem. Eng. J. 1990, 44, 27. (4) Fang, J.; Godfrey, J. C.; Mao, Z.-Q.; Slater, M. J.; Gourdon, C. Single liquid drop breakage probabilities and characteristic velocities in Ku¨hni columns. Chem. Eng. Technol. 1995, 18, 41. (5) Seikova, I.; Gourdon, C.; Casamatta, G. Single-drop transport in a Ku¨hni extraction column. Chem. Eng. Sci. 1992, 47 (1516), 4141. (6) Modes, G.; Bart, H.-J.; Rodriguez-Perancho, D.; Bro¨der, D. Simulation of the fluid dynamics of solvent extraction columns from single droplet parameters. Chem. Eng. Technol. 1999, 22 (3), 231. (7) Slater, M. J. Rate coefficients in liquid-liquid extraction systems. In Liquid-Liquid Extraction Equipment; Godfrey, J. C., Slater, M. J., Eds.; John Wiley & Sons: London, U.K., 1994. (8) Kentish, S. E. Forward mixing in a countercurrent solvent extraction contactor. Ph.D. Thesis, University of Melbourne, Melbourne, Australia, 1996. (9) Brodkorb, M. J.; Slater, M. J. Multicomponent and contamination effects on mass transfer in a liquid-liquid extraction rotating disc contactor. Chem. Eng. Res. Des. 2001, 79, 335. (10) Barnard, P.; Slater, M. J.; Wu, X.-P. A case study of an industrial packed column design using single drop mass transfer data. Proceedings of ISEC2002, Cape Town, South Africa, Mar 2002; p 1316. (11) Mansur, M. B.; Slater, M. J.; Biscaia Junior, E. C. Equilibrium analysis of the reactive liquid-liquid test system ZnSO4/D2EHPA/n-heptane. Hydrometallurgy 2002, 63 (2), 117.

(12) Mansur, M. B.; Slater, M. J.; Biscaia Junior, E. C. Kinetic analysis of the reactive liquid-liquid test system ZnSO4/D2EHPA/ n-heptane. Hydrometallurgy 2002, 63 (2), 107. (13) Mansur, M. B.; Slater, M. J.; Biscaia Junior, E. C. Startup behaviour of reactive systems in counter-current extraction columns. Lat. Am. Appl. Res. 2001, 31 (5), 447. (14) Antonelli, D.; Veglio`, F.; Mansur, M. B.; Biscaia Junior, E. C.; Slater, M. J. Experiments with a short Ku¨hni column used in batch mode. Proceedings of ISEC2002, Cape Town, South Africa, Mar 2002; p 1339. (15) Rod, V.; Wei-Yang, F.; Hanson, C. Evaluation of mass transfer and backmixing parameters in extraction columns from measured solute concentrations. Chem. Eng. Res. Des. 1983, 61, 290. (16) Lai, C. H.; Lo, S. L.; Lin, C. F. Evaluating an iron-coated sand for removing copper from water. Water Sci. Technol. 1994, 30 (9), 175. (17) Wichterlova, J.; Rod, V. Determination of mixer-settler efficiency by a response method. Chem. Eng. Res. Des. 1991, 69, 282. (18) Bart, H.-J.; Rousselle, H.-P. Microkinetics and reaction equilibria in the system ZnSO4/D2EHPA/isododecane. Hydrometallurgy 1999, 51 (3), 285. (19) Bonnet, J. C. Hydrodynamics and mass transfer in a Scheibel extractor. M.Sc. Thesis, Aston University, Birmingham, U.K., 1982. (20) Miyauchi, T.; Vermeulen, T. Diffusion and back-flow models for two-phase axial dispersion. Ind. Eng. Chem. Fundam. 1963, 2, 304. (21) Petzold, S. DASSL code; Computing and Mathematics Research Division, Lawrence Livermore National Laboratory: Livermore, CA, 1989. (22) Himmelblau, D. M. Applied Nonlinear Programming; McGraw-Hill: New York, 1972. (23) Chartres, R. H.; Korchinsky, W. J. Modelling of liquidliquid extraction columns: predicting the influence of drop size distributions. Trans. Inst. Chem. Eng. 1975, 53, 247. (24) Dongaonkar, K.; Pratt, H. R. C.; Stevens, G. Mass transfer and axial dispersion in a Ku¨hni extraction column. AIChE J. 1991, 37 (5), 694. (25) Misek, T. General hydrodynamic design basis for column. In Liquid-Liquid Extraction Equipment; Godfrey, J. C., Slater, M. J., Eds.; John Wiley & Sons: London, U.K., 1994. (26) Spencer, J.; Steiner, L.; Hartland, S. Model-based analysis of data from countercurrent liquid-liquid extraction processes. AIChE J. 1981, 27 (6), 1008. (27) Kumar, A.; Hartland, S. Mass transfer in a Ku¨hni extraction column. Ind. Eng. Chem. Res. 1988, 27, 1198. (28) Breysse, J.; Buhlmann, V.; Godfrey, J. C. Axial mixing characteristics of industrial and pilot scale Ku¨hni columns. AIChE Symp. Ser. 1984, 238 (80), 94. (29) Pratt, H. R. C. Interphase mass transfer. In Handbook of Solvent Extraction; Lo, T. C., Baird, M. H. I., Hanson, C., Eds.; John Wiley & Sons: New York, 1983.

Received for review November 7, 2002 Revised manuscript received May 22, 2003 Accepted June 12, 2003 IE020883Y