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Chem. Eng. Technol. 10 (1987) 291 -29 6 291

Calculation of Reactive Extraction in C ountercurrent ColumnsHans Jorg Bart, Andreas Bauer and Rolf M a n *The kinetics of extraction processes with chemical reaction was studied experimentally on thesystem copper/Acorga PT 5050 and quantified according to meaningful kinetic models. Thesewere coupled with other models describing the behaviour of dispersions in columns in order topermit a computer aided simulation of reactive extraction. Thus, a better prediction of columnperformance is achieved.

1 IntroductionReactive extraction is a unit operation which plays an increas-ingly important role in the recovery of metal salts from leachingsolutions and waste waters.The separation is effected by contacting an aqueous phase con-taining the material to be extracted with an organic phase. Theorganic phase consists of an extractant which promotes thetransfer of the solute from the aqueous to the organic phase, analiphatic or aromatic hydrocarbon as diluent and, in most cases,also a modifier which improves the solubility of the complexI l l .The extractant may act as a liquid ion exchanger or a chelatingagent, reacting with the substances to be extracted. The formedcomplex is transferred to the organic phase and may be reex-tracted. It is decomposed by a suitable stripping agent such asan acid. Fig. 1 shows the chemical structure of a complexformed from two extractant molecules chelating a copper ion.The extraction/reextraction process results in an enrichmentand/or selective recovery of the desired material.

i 9

Fig. 1. Chemical structureof copper- Acorga P 50complex.

Whereas conventional liquid-liquid extraction is a physicalmass transfer process, in reactive extraction, chemical reactionsalso occur which may be the rate determining step of the overallprocess. Reactive extraction is nowadays usually carried out inmixer-settlers on account of easy scale-up and good adaptabilityto varying process parameters. Calculations of reactive extrac-tion in mixer-settlers are published elsewhere [2]. Columns pro-vide the advantage of smaller space requirements but fluid dy-

* Dipl.-Ing. D r . H.J. Bart, Dipl.-Ing. A. Bauer, and Prof. Dr.-Ing. R .Marr, Abteilung Thermische Verfahrenstechnik, Technische Univer-sitat Graz, Inffeldgasse 25, A-8010 Graz.

namic properties restrict their use to the conditions for whichthey have been designed. Reaction kinetics complicates theprocess design. In many cases of reactive extraction, e.g. withcopper, the kinetics of the reaction is in fact the rate determiningstep with respect to mass transfer. If reaction kinetics is neglec-ted in mixer-settler design, a slow reaction can be accounted forby running the mixer at lower throughput rates and thus longerresidence times. In columns, a reduction of throughput of thedispersed phase results in decreased hold-up which causes adecline in interfacial area per unit volume and hence in masstransfer rate. The latter is valid since, in kinetically controlledsystems, mass transfer is directly proportional to interfacialarea. Therefore, column height must be increased which oftendoes cause problems.To overcome these disadvantages, it is desirable to consider notonly chemical kinetics but also other physical phenomena suchas axial mixing and drop size distribution in the calculation ofcolumns. This can be very helpful in the performance of pilotplant experiments.The simulation may be divided into three steps:- Quantification of phenomena occurring at or near the inter-

face, i.e. mass transfer and chemical reaction.- Quantification of hydrodynamic behaviour of the dispersion

inside the column, whose major aspect is axial mixing.- Combination of steps 1 and 2 in a computer simulation

programme.

2 Mass Transfer and Chemical ReactionSelection of a mass transfer model including chemical reactioninvolves a decision on the location of the chemical reaction, i.e .whether it occurs in the aqueous phase, the organic phase or atthe interface. Location at the interface is plausible since, as arule, components dissolved in the aqueous phase are practicallyinsoluble in the organic phase and vice versa. Therefore, masstransfer is assumed to proceed in the following steps:- Metal ion and extractant diffuse to the interface from aque-- Metal ion and extractant react according to Eq. (1 ) forming- The complex and released H + ions diffuse from the interface

ous and organic phases respectively.the complex.into organic and aqueous phases respectively'.

0 CH Verlagsgeaellschaft mbH. D-6940 Weinheim, 1987 0930-7516/87/0510-0291 $02.50/0

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Me2+ + 2 RH t) MeR, +2 H + (1) 3 Phase EquilibriaEq. (1) explains why the extraction Process is accompanied bya change in PH. Concentration profiles from interface to bulk,as shown in Fig. 2 may, according to the two-film theory ofWhitman [3], be assumed as linear. Mass transfer rates per unitarea are proportional to the concentration differences between

Equilibrium distribution of the extracted material between or-ganic and aqueous phase can be described by a simple equation.Setting the chemical reaction rate equal to zero, to fulfil the con-dition of equilibrium, Eq. (6) can be transformed into:

the bulk and the interface and to the partial mass transfer coeff-cients. These, in turn, are proportional to the diffusivities of the [MeR2I [Hf12[RHyex = [Me2+ (8 )species (according to the two-film theory). On the basis of

Aqueous Interface Organicphase phase

Fig. 2. Concentration profiles around the interface.Assuming continuity (no storage effects) the reaction rate mustbe equal to the transfer rates. Reaction rate is calculated accord-ing to Eq. (6) or (7). Eq. (6) represents a first order reaction,proposed by Nitsch 141 and Teramoto [5], including a term forthe reverse reaction. This equation should be valid for both ex-traction and reextraction since it accounts for the reverse reac-tion. Nonetheless, Albery [6] proposed a different rate equationfor the stripping process (7). Combination of Eqs (2)- 5) and(6) or (7) yields concentration versus time profiles. The diffu-sional resistance of H+ ions is neglected because their diffusivi-ty is much higher than that of the other species, i.e. the interfa-cial H+ concentration can be set equal to the bulk concentrationand Eq. (5) is no longer taken into account:

-~R [MeR,] [H+] . (7)Me2 +] RHI2i'lR =k R [H+I Kex1 ) List of symbols at the end of the paper.

+pH 2. 00. 1 . 2. 3. 4.Concentrat ion (aqueous phase1

Fig. 3. Equilibrium curves for copper/5 vol-% Acorga PT 5050.

This implies thatD is not constant but decreases with decreasingconcentration of the free extractant [RH] and with increasingH + concentration. K,, is the individual extraction constant ofthe system. Equilibrium distribution curves shown in Fig. 3 fallinto two regions. In the first, the distribution coefficient is prac-tically constant while, in the second one, the organic phase issaturated. The curve reaches a plateau corresponding to maxi-mum capacity of the organic phase which depends on pH.

4 Column HydrodynamicsHydrodynamic features of a column are e.g. convection and axi-al mixing. The latter implies that, with respect to mixing,column behaviour deviates from the ideal plug flow. Axial mix-ing reduces the concentration differences which are the drivingforce of mass transfer and, thus, determine performance. Axialmixing can be described by various models, such as the tankcascade, backflow and dispersion models. In the present work,the dispersion model was chosen which describes axial mixingby a single parameter D,,, used in analogy to the usual diffusioncoefficient and measured via residence time distribution of the

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Chem. Eng. Technol. 10 (1987) 291 -296 293

phases in the colum n. D,, is correlated w ith the Bodensteinnumber (Bo) via a characteristic length and the axial velocityof the liquid. The overall mass balance of each species aroundany column section yields the usual mass transfer equation forcontinuous operation:

for the organic phase and

for the aqueous phase.The first term accounts for axial mixing, the second for convec-tion and the third represents the overall mass transfer includingdiffusional transport to and from the interface as well as the rateof chemical reaction. Naturally, the p-values in columns a re notthe same as those measured in the stirring cell on account ofdifferent hydrodynamic conditions. These v alues must be calcu-lated by suitable equations such as that of Linton-Su therland [7 ]which employs diffusivities via the dimensionless numbers Reand Sc . Mass transfer rate n per unit area is calculated by simul-taneous solution of Eqs (2)-(4) and (6) or (7).Eq s (10) an d ( 1 1) are solved by numerical integration with thefollowing boundary conditions which are approximations sincethe dispersion m odel is valid only for an infinitely long column.At the bottom of the column:

= 0 andC,qdh

At the top of the column:~- - 0 andc01dh

5 Experimental5.I ChemicalsAqueous acidic copper sulphate solutions were contacted withthe organic phase both in the stirring cell and in the column. Inaddition, equilibrium data were ob tained in shaking funnel ex-periments. The copper-Acorga PT 5050 complex is brown incolour and, therefore, its concentration in the organic phasecould be continuously monitored by a spectrophotometer. Addi-

Table 1. Concentration and pH' Ranges of Stirring Cell Experiments.Aqueous phaseinitial copper conc.

CuSO,, H,SO,0.05- 12.40 [ g / l ]initial pH 1. 0 -4.0

Organic phaseextractantactive extractant (P 50) conc.diluent Shellsol T

5 vol-% Acorga PT 50500.090 [mol/l]

tionally, the aqueous phase was analyzed by atom ic absorptionspectroscopy before and after the experiment. F urthermore, thepH was continuously recorded. Each experiment was termina-ted after 5- h on attaining 30- 0% of equilibrium. Table lshows the concentration and pH ranges of the experiments:

5 .2 Stirring CellThere a re two principal techniques for the measurement of in-terfacial mass transfer processes:- rising/falling drops and- stirring cell/constant interface cell.A stirring cell shown in Fig. 4 was chosen for mass transfer ex-periments aiming at the determination of kinetic parameters be-cause of known interfacial area and hydrodynamics. The cellcontains 0.5 1each of aqueous and organic phase. The relativelysmall interfacial area per unit volume of 3.7 m2/m3 s one ofthe drawbacks of the stirring cell because it restricts the meas-urements to the initial stage of the reaction and the proximityof equilibrium cannot be examined.

Fig. 4. Stirring cell. 1 stirrer, 2 PP flange, 3 glass tube, 4 steel draft tubewith baffles, 5 organic phase, 6 interface, 7 aqueous phase.

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294 Chem. Eng. Technol. I0 (1987) 291 -29 6

Each phase was stirred by a four-blade impeller, located withina draft tube in orde r to achieve a well-defined phase circulation.The aim of this arrangement is to obtain a smooth interface anda radial flow parallel to it [4].

5. 3 ColumnExperiments with a countercurrent extraction column (SHE 80mm in diameter and 2 m in active height [8]) were performedin order to verify the results of computer simulations. Aftereach column experiment, the loaded organic phase was strippedby 2 M sulphuric acid and re-used.

6 Results6.1 Stirring Cell ExperimentsThere are two methods of evaluating k,:- From the initial mass transfer rate or- by integration of the mass transfer and reaction rate equa-tions (Eqs (2) - (7) ) over the whole period of each ex-periment.As a rule, th e first method is employed since, at a considerabledistance from equilibrium, the concentration profiles a re almostlinear and the reverse reaction can be neglected. This is particu-larly true for rising/falling drop experiments where contacttimes are significantly shorter than those in the stirring cell. Inthis case, equilibrium had been achieved to the extent of 50%and, consequently, the reverse reaction must be taken intoaccount.Models, w hich do not consider the reverse reaction, are far lesscapable of fitting the experimental data, even at the start of theexperiment when the reverse reaction is least important.Therefore, k , and f l were determined by numerical integrationof Eqs (2)-(7 ) and fitting the resulting concentration versustime curves to the measured ones. Th e problem is to determinewhether diffusion or chemical reaction is rate controlling. T heobjective of the stirring cell experiments is to quantify chem icalkinetics and to eliminate diffusional resistances as far as possi-ble since diffusional parameters measured in the stirring cellwould not be valid in mixer-settlers or columns on account ofdifferent fluid dynamics. One method of separating diffusionand reaction influenc es is to vary the impeller speed . If the over-all mass transfer rate becomes independent of stirrer speed, itcan be assumed that diffusion effect had been eliminated. A var-iation of the overall mass transfer rate with pH implies thatchemical reaction is rate limiting because resistance caused byH + diffusion can almost certainly be neglected. k , is deter-mined in the kinetic regime, i.e. at low metal concentrations andlow pH , where the influence of transport phenomena is minimaland chemical reaction is assumed to be rate determining.Fig. 5 represents the stirring cell experiments. The initial masstransfer rates depend not only on the initial aqueous metal con-

1. 5 . I I I I I I I , I I , , , ,-

+v1VIE

X

c - 0m._+.-w

0 . 0 ' ' ' ' ' ' ' ' ' ~ ' 1 ~ '0. 5. 10. 15.In itia l copper conce ntration 1g/1]

Fig. 5 . Initial mass transfer rates as functions of initial pH and initial copperconcentration.

3.0

2.5

2.0\-c,z 1.5mL+cg 1 . 0U

c . ' I,P 1.\t -1

t0. 2. 4. 6.

Time [ h lFig. 6. Stirring cell experiment; initial pH 3.1.

3.0

2.5

c.o 1 . 5+m

0.5

L+cz 1.0U 1

. 20. 40. 60.rn Time \ h lFig. 7. Stirr ing cell experiment; initial pH 3.1 extrapolated to 50 h.

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Chem. Eng. Technol. I 0 (1987) 291 -296 295

centration but also on pH, which suggests a kinetic limitationthroughout the whole concentration range.Fig. 6 shows a plot of concentration versus time for an initialaqueous copper concentration of 0.02 mol/l and an initial pHof 3.1. The interfacial concentration of the complex is compara-tively high at the beginning of the experiment which indicatesthat the interface is saturated by complex molecules. This wouldconfirm the suggestion of very fast adsorption kinetics and asubsequent slow diffusion of the complex into the organic bulk.k , values were found to be scattered in the range of 0.0006 to0.002 cm/s which indicates that the model does not describe thechemical reaction correctly. Fitting of the reaction orders to ex-perimental values showed that the discrepancies are due to theincorrect order of reaction with respect to H + which is between-0.2 and -0.3, in contrast to - assumed in the model. Theorder of reaction with respect to the metal ion was determinedas 2, th e extractant but, in fact, it is with respectto the metal ion and 1 with respect to the extractant. Orders ofreaction, determined by Lorbach [9] for this system, are in goodagreement.

, s-51.O -

m._W0.s -

0.00.00 0.01 0.02

Concentration [rnol/l llclselFig. 8. Concentration profiles in the countercurrent column; comparison ofsimulation and experiment.Table 2. Results of Column Experiments, System CopperiAcorga PT 5050.

Fig. 7 shows the simulation of a stirring cell experiment, ex-trapolated to a period of 50 h. The interface concentrations ap-proach those in the bulk as equilibrium is attained and masstransfer comes to a standstill. This relatively long delay inreaching equilibrium is due to the small interfacial area per unitvolume of the stirring cell, compared to the conventional extrac-tion equipment.

6.2 Column ExperimentsEqs (10)and (1 1) are solved numerically by the method of finitedifferences, simultaneously solving Eqs (2)- 7) represented bythe third term in Eq. (10) or (11). Mass transfer coefficientswere calculated from Sh numbers. The drops were approxi-mately 1 mm in diameter which was determined from photo-graphs. With respect to this diameter, a constant Sh number of6.58, valid for rigid spheres, was assumed. The Sh number forthe aqueous phase was calculated according to the Linton-Sutherland equation [7], resulting in the following @values:

PMe= 0.012 (cm/s), /3MleR2 =0.00014 (cm/s),PRH = 0.00015 (ads).Computer simulation yields concentration profiles of all speciesin the bulk and in the interface (Fig. 8) . By using the equilibriumfunction (Eqs (8), (9)), it is possible to calculate the number ofideal transfer stages NSTachieved in the column. The respectiveHETS values which denote the column height corresponding toone theoretical stage, found in column experiments, are listedin Table 2. Copper/Acorga PT 5050, known to be a very slowreaction, gave N s , values mostly less than unity, depending onphase throughput. In solvent extraction, however, one theoreti-cal stage can achieve as much as 99% recovery. Earlier work[8 ] on the system copper/LIX 64 N also produced very lowHETS values.

[ M ~ '+ I , PH, ua q "or xd Recovery HETS[gill [ - I [l/hl Whl [ % I [ % I [ml1 o 1.00 10 10 23.1 81.4 1.621 .o 1.00 20 20 24.0 63.5 2.891 o 1.02 50 50 30.2 42.6 5.341.o 3.00 20 20 24.0 99.8 1.471 .o 3.00 50 50 30.2 93.8 3.20

.~ ~ ~

Axial mixing of aqueous phase was estimated from the initialconcentration step at the top of the column. Eqs (15) and (16)yield Eq. (17), where Bo is the Bodenstein number based on acharacteristic length of 1 m. The experiments showed a relative-ly high axial mixing depending on throughput (Boa, =2 for 10m3/m2hor Boa, =4 for 40 m3/m2h). The respective dispersioncoefficient D,, is 0.001 m2/s:

dcaqdh

' (161, (17)"a,Boa, = ~ , Boa, =Daxaq ',,in - % h = H k

Experimental concentration profiles could be simulated withina scatter range of f l o%, he errors resulting mainly from thekinetic model. The influence of axial mixing lies within the scat-ter range.

7 ConclusionsParameters of a model for interface mass transfer and chemicalreaction in reactive extraction were determined by measuringconcentration-time profiles in a stirring cell. These parameterswere used in a column simulation programme together withhydrodynamic parameters. The resulting concentration profilesalong the column permitted the evaluation of column perfor-

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mance. Measured and calculated concentration profiles show asatisfactory agreement. It was found necessary to account forthe reverse reaction and the influence of pH. Although axialmixing was comparatively high in the employed column, the in-fluence of chemical kinetics proved to be much stronger thanthat of axial mixing.Th e high HETS values indicate that a mixer-settler is m ore suit-able for the investigated process, on account of lower capitalcosts. W ith kinetically controlled systems, long residence timesare required and the main advantage of columns, namely main-tenance of high concentration gradients, is less important.

AcknowledgementThis investigation was supported by the Oesterreichische Na-tionalbank, Project 2467.

Received: November 7, 1986 [CET 181

Symbols usedinterfacial area per unit volumeBodenstein number (based on 1 m)partial mass transfer coefficient (metal ion)partial mass transfer coefficient (complex)partial m ass transfer coefficient (extractant)partial mass transfer coefficient (proton)concentrationequilibrium distribution coefficientaxial dispersion coefficientcolumn height coordinatehydrogen ion concentration (aq. phase)height of a theoretical stageactive column heightreaction rate constantequilibrium constantmetal ion concentration (aq. phase)complex concentration (org. phase)mass transfer rate, reaction ratenumber of ideal transfer stagesextractant concentration (org. phase)

v [m/sl effective convection velocityv [l/hl phase throughput'd 1 -1 hold-up

Subscripts0aqaxbulkexFHinintMeMeR,orRRH

initialaqueous phaseaxialbulkextractionforwardprotoninflowinterfacemetal ionmetal complexorganic phasereverseextractant

References[I] Marr, R., Bart, H.J., Chem.-Ing.-Tech. 54 (1982) No . 2, pp.[2] Bauer, A , , Bar t, H.J . , M a r , R ., Chem.-Ing.-Tech. 58 (1986) No . 2,[3] Whitman, W.G., Chem. Metal. Eng 29 (1923) p. 147.[4] Nitsch, W. , Ber. Bunsenges. Phys. Chem. 83 (1979) pp. 1171- 1177.[5] Teramoto, M., et al., Extraction of Copper with SME 529 J. Chem.Eng Jpn 16 (1983) No . 3, p. 203.[6] Alhery, J.W., Fisk, P.R., The Kinetics of Extraction of Copper withAcorga P 50 studied by a diffusion cell. Proceedings of Hydrometal-lurgical Symposium, Manchester 1981.171 Linton, M., Sutherla nd, K. L. , Chem. Eng Sci. 12 (1960) pp.(81 Gauhinger , W., M ax , R., alculation of Counter-Current ExtractionColumns Using Mass Transfer Propenies of Single Drops and the

Hydrodynamic Behaviour of the Dispersion, AIChE Summ er meeting1984, 19.122. 8. 1984, Philadelphia, Pa. Paper 47a.[9] Lorbach, D. , Bart, H.J., Marr, R., Ger. Chem. Eng 9 (1986) No. 5,

[lo] Bauer, A,, Bart, H.J . , M arr , R., Numerical Calculation of Extractionwith Chemical Reaction 5th Italian-Yugoslavian-Austrian CEC,16 .- 8. 9. 1986, Portoroz (YU).[ ll] Miiller , H., Diplomarbeit, TU Graz 1985.[I21 Martinak, A ,, Diplomarbeit, TU Graz 1986.

119- 129.pp. 154- 155.

2 14- 29 .

pp. 321-327.