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MULTICOMPONENT EFFECTS IN LIQUID-LIQUID

EXTRACTION

M. HAEBERL and E. BLASS*

Merck KGaA, T-Invest, Darmstadt, Germany*Lehrstuhl fur Fluidverfahrenstechnik, Technical University Munich, Munich, Germany

One of the reasons problems arise in the design of extraction equipment is an

unsatisfactory knowledge of the mechanisms responsible for the transport ofcomponents from the bulk of one phase across the interfacial area into the bulk of

the other contacting phase. An investigation was carried out on mechanisms relevant for masstransfer, the importance of multicomponent effects in liquid-liquid extraction and also which

models are suitable for describing mass transfer. For this, experiments were performed in acountercurrent spray column with the system ethylacetate-acetone-water. The saturation of the

feed phases, the extraction factor and the direction of mass transfer were varied. When phasesfed into the column are saturated, both phases change their concentration along the binodalline. When the phases are initially unsaturated, both extraction trajectories approach the

binodal line.Comparing the experimental concentration proles with simulation results, it is shown, that

in the area of undersaturation, extraction trajectories can be described only if the completematrix of multicomponent diffusion coefcients is known and the effects of diffusive couplingare taken into account. When mass transfer coefcients are calculated at bulk concentrations,the achieved results are closer to the measured extraction trajectories than in the case where

they are calculated depending on interfacial concentrations.

Keywords: liquid-liquid extraction; mass transfer; diffusion; extraction paths; saturation

INTRODUCTION

The calculation of mass transfer is one of the key problems

in the design of apparatuses for liquid-liquid extraction. Thenumber of publications on the subject is correspondinglylarge. Measurements with single droplets in stagnant

continuous phases as well as with swarms of droplets incountercurrent columns were performed in various systems.Sherwood et al.1 analysed previous work and gave their

own data for mass transfer in single droplets both inpacked columns and a spray column. Johnson and Bliss2

made multiple measurements in a spray column and gavesome empirical rules of design and operation of spraycolumns. Steiner3, Steiner et al.4 collected a large number ofexperimental mass transfer coefcients and compared the

results with calculated data.

Mass transfer in various countercurrent extractors wasinvestigated by Blass and co-workers at Munich TechnicalUniversity (Hirschmann5, Goldmann6, Otillinger7, Hufnagl8,Rauscher9, Zamponi10). Blass et al.11 recommend thedetermination of mass transfer coefcients in the dropletphase using the Handlos and Baron12 correlation and in thecontinuous phase with the help of the penetration theory.

Concentration Trajectories in Ternary Extraction

Only a few authors have investigated extraction paths in

ternary systems with partially miscible main components(Table 1). In a modied Lewis cell, Sethy and Cullinan

13

observed straight extraction paths in the n-heptane phase inthe system acetonitrile-benzene-n-heptane. The concentra-

tions follow the straight line connecting the initial compositionand the nal equilibrium composition, which means that nodiffusive coupling occurs between the component uxes.Krishna et al.

14show that the measured concentration

trajectories cannot be described even qualitatively by binarymass transfer calculations and it is absolutely necessary to take

into account the inuences of multicomponent effects.Schermuly

18, Schermuly and Blass

33used the system

glycerol-water-acetone in a countercurrent spray column forextraction experiments and determined the concentrationproles of both the phases. While the concentrationtrajectories measured in the stirred cell show some time-depending change of concentration, i.e. they are paths of

equilibration, the extraction paths determined by Schermuly

and Blass33 give local, but, as the column was run at steady-state, time-invariant concentration proles. Mass transfer ofwater was directed from the continuous acetone phase intothe dispersed glycerol phase in all the experiments. Whenphases are saturated, i.e. with binodal composition, the

extraction paths follow the binodal line all along the length.Schermuly and Blass

33successfully calculated mass transfer

in saturated phases, using a uctuation model, that presum esvanishing Fick

19diffusion (Hampe et al.

20) and exclusively

uid-dynamically induced mass transfer. When feed-phasesare unsaturated, the extraction trajectory does not reach thebinodal line and can be described only by taking intoaccount diffusive coupling because of multicomponent

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02638762/99/$10.00+0.00

Institution of Chemical EngineersTrans IChemE, Vol 77 Part A, October 1999

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mass transfer. Hence, for calculation of mass transfer

coefcients a complete matrix of diffusion coefcients isnecessary.

Berger21

performed experiments in a countercurrentspray column, using the system water-succinic acid-n-butanol. Though he did not give extraction trajectories in his

work, they may be obtained easily, by plotting his data into

the equilibrium diagram by Mis)ek et al.22. Independent of

the direction of mass transfer, the water phase as well as then-butanol phase approaches the binodal line asymptotically

and reaches it after only a short distance.In this work the phenomena and mechanisms of multi-

component mass transfer are discussed. Using saturated andunsaturated feeds, the way multicomponent effects inu-ence the extraction trajectories were investigated, and fromthis the dominant mechanisms of mass transfer weredetermined. It will be shown, whether it is necessary todifferentiate between saturated and unsaturated phases forcalculation of mass transfer.

FUNDAMENTALS OF LIQUID EXTRACTION MASS

TRANSFER

The following factors must be taken into account forcalculation of mass transfer in liquid extraction:

The presence of two coexistent phases, which may varyconsiderably in their physical properties and their molecular

interactions.

There is an interfacial area in between these two phases,

which may inuence mass transfer, depending on its width,physical properties and molecular structure, e.g. Marangonieffects are originated in the area.

Fluid dynamics are extremely complex especially in two

phase dispersed systems and there is a strong interdepen-dency of uid dynamics and mass transfer. Thus, mass

transfer is inuenced by mixing inside the droplet and by theow of the continuous phase in the vicinity of the droplet, aswell as by breakage and coalescence of droplets.

The molar ux Ji between the two phases in contact isdescribed analogously to a diffusive ux as the product ofthe transport coefcient and driving force. The difference of

molar concentrations at the interface and in the bulk phase isused as a driving force. The mass transfer coefcients kijmust take into account molecular and uid-dynamicalinuences. Hence they mainly depend on the transportmechanisms. Molar uxes relative to the mean molar

velocity (Taylor and Krishna23

) are determined in a ternary

system by:

J1

J2( ) = 2ctk11 k12

k21 k22[ ]xI1 2x

B1

xI2 2xB2

( ) (1)with J1 + J2 + J3 = 0

The molar uxes Ni relative to a stationary co-ordinatereference frame are, however, of technical importance. Thetotal ux Nt, which is given by the sum of all componentuxes, is needed for calculation of these uxes.

Ni = Ji +xi.Nt (2)

In liquid-liquid extraction, the total ux Nt is generallynonzero as is shown in this work. This total ux is alsoresponsible for variation of mass ows of both phases inextraction columns and inuences the concentration prolebetween bulk and interface.

MECHANISMS AND MODELS FOR MASS

TRANSFER

Ignoring interfacial effects, there are only the diffusiveand convective mechanisms of mass transfer left underdiscussion. With increasing mobility of droplets, anincreased inuence of convection is usually assumed. The

various inuences of both the mechanisms is reected bythe dependency of the mass transfer coefcient on the

diffusion coefcient.

k~ Dn

(3)

with the exponent n varying from zero to one.The various models for calculating mass transfer between

droplets and a continuous phase were described in detail by

Slater24

, Temos25

, and Javed26

. To investigate the inuence

of diffusion and convection only the following basic typesof models are considered:

1. The two equations by Schermuly and Blass33

forsaturated, respectively unsaturated phases which are

applicable for both continuous and dispersed phases.2. The models of Kronig and Brink

27and of Handlos and

Baron12

for dispersed phases.3. The penetration model of Higbie

28 for continuous

phases.

A detailed description of the models is given inHaeberl

29.

Diffusion effects on mass transfer are taken into

648 HAEBERL and BLASS

Trans IChemE, Vol 77, Part A, October 1999

Table 1. Extraction paths during equilibration in a stirred cell.

Author System Experimental conditions Concentration trajectories

Sethy and Cullinan13

Acetonitrile / benzene /

n-heptaneHeavy (acetonitrile)

phase is recirculated

n-Heptane phase: all straight

Standart et al.15

Glycerol / acetone /

water

P ha se s a re n ot ci rc ul ate d B ot h ph as es : d is ti nc tly c ur vi lin ea r,

straight only in 9tie-line 9 experiments

Cullinan and Ram16

Glycerol / acetone /

water

Heavy (glycerol) phase is

recirculated

Acetone phase: distinctly curvilinear,

straight only in 9tie-line 9 experiments

Krishna et al.

14

Glycerol / acetone /water P ha se s a re not ci rc ul ate d T he s am e r es ults a s give n byStandart et al.15

Bulic3ka and Prochazka17

MIBK / acetic acid /

water

P hases are not circulated N o data published

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account most strongly using the models by Higbie28 and

Kronig and Brink27. The results calculated with the equationof Schermuly and Blass33 for unsaturated phases are very

similar, as the direct proportionality between mass transfercoefcient and diffusion coefcient is just replaced by a

square root proportionality.Based on his theory of transport mechanisms at phase

boundaries, Hampe30,31 concluded that in the vicinity of thephase boundary, molecular diffusion vanishes and is

replaced by another transport mechanism. Schermuly18

and Schermuly and Blass32,33 developed a model for anexclusively uid-dynamically determined transportmechanism on this basis. A mixing process betweencontinuous and dispersed phases takes place in a circulatingdroplet by the uctuation of uid elements around theirstream lines. It can be described by effective diffusivity asdened by Handlos and Baron12.

Some General Remarks on Fluid Dynamical Models forMass Transfer

Formally, a convective ux can be calculated in the sameway as a diffusive ux. The concentration differencebetween bulk and interface is the driving force for mass

transfer. If this becomes zero, there will be no mass transfer.The mass transfer coefcient however does not depend ondiffusion coefcients, but on the relative velocity between

sedimenting droplets and the continuous phase. Thus masstransfer affects all components according to their concen-

tration in the exchanged uid element. With purelyconvective mass transfer there can be no coupling effectsbetween the uxes of components, and the matrix of mass

transfer coefcients will always be diagonal.

STRUCTURE OF MATRIX [k] AND DIRECTION OFEXTRACTION TRAJECTORIES

Sethy and Cullinan34, as well as Schermuly and Blass33,

show that the extraction path is directed towards equili-brium, in the case where the matrix of mass transfer

coefcients [k] is diagonal, i.e. both the cross coefcientsk12 and k21 are zero. In all the other cases a curved extractionpath is obtained, the tangent of which does not coincide withconnecting straight lines between bulk concentration andinterface concentration, while the area of possible direc-tions, which the extraction path can take, is stretched

between both eigenvectors of the matrix of the mass transfer

coefcients (Gupta and Cooper)35.The matrix of mass transfer coefcients [k] is diagonal if:

The matrix of diffusion coefcients [D] is diagonal

or there is purely convective mass transfer.

Thus conclusions can be drawn about the relevant

transport mechanism from the course of the extractionpaths: if the extraction path is directed towards equilibrium,

nevertheless cross coefcients D12 and D21 are distinctlydifferent from zero, diffusion is not a dominant transportmechanism and uid dynamic effects prevail. If the matrixof diffusion coefcients is diagonal, differentiation of boththe mechanisms is certainly no longer possible. Then bothdiffusive and convective transport result in decoupled uxesand the extraction path is a straight line towards theequilibrium state.

EXPERIMENTAL RESULTSThe system ethylacetate-acetone-water has one misci-

bility gap: both ethylacetate and water are completelymiscible with acetone and partially miscible with eachother. The experimental values of density, viscosity,

interfacial tension, and equilibrium concentrations canbe found in Haeberl29. While density and viscosity arelinearly dependent on acetone concentration in the

ethylacetate phase, there is a distinct maximum ofviscosity at about 10 mole % of acetone in the aqueous

phase. The interfacial tension between saturated ethylace-tate and aqueous phases at 20C, was measured as 6.20 mN/m, which decreases with increasing concentrations of

acetone.

Ternary Diffusion Coefcients

The ternary diffusion coefcients were measured in thesystem ethylacetate-acetone-water with holographic inter-

ferometry by Pertler36. He determined the matrices ofdiffusion coefcients in the aqueous phase at 10 mass % of

acetone at ve different concentrations of ethylacetate andin the ethylacetate phase at 20 mass % of acetone at veconcentrations of water at 20C.

The diffusion coefcients were approximated for calcula-tion of mass transfer by polynomial equations. It wasassumed that the changes in the structure of the matrix do

649MULTICOMPONENT EFFECTS IN LIQUID-LIQUID EXTRACTION


Table 2. Investigated models for diffusive and convective mass transfer.

Continuous phase

Diffusive Convective

Higbie28

Schermuly and Blass33

(Unsaturated phases)


(Saturated phases /

Fluctuation model)

D is pe rse d pha se D if fus ive K ronig a nd B rink 27

Diffusive/

diffusive


(Unsaturated phases)

Diffusive/diffusive

C on ve ctiv e H and lo s a nd B ar on12

Diffusive/convective


(Saturated phases /

Fluctuation model)

Convective/

convective

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not depend qualitatively on acetone concentrations, but thebinodal composition is decisive. The binary diffusioncoefcients were assumed to be constant within the rangeof concentrations under discussion.

Pertler36

found the following characteristic behaviour ofdiffusion coefcients in both phases:

The cross-coefcient D21 strongly depends on concentra-tion with a distinct minimum. At medium concentrations its

absolute value is much higher than both the main

coefcients.

The cross-coefcient D12 approaches zero at the binaryline.

Both cross coefcients simultaneously approach zero andthe main coefcients have identical values at the binodal

line:

D12 = D21 = 0 and D11 = D22 0

The m atrix of the diffusion coefcients is diagonal. H ence

the diffusive uxes are not coupled there. However, thisdoes not mean that there is no diffusive transport.

Extraction Column

The counter-current spray column described by Scher-muly and Blass

33was used for the extraction experiments.

The column has an active height of 4.3 m, an inner diameterof 25 mm, and is thermostated by a water-lled double

jacket. The heavier aqueous phase is fed at the top of thecolumn through a 1.0 mm PTFE nozzle, the lighter

ethylacetate phase enters the column at the bottom end.To prevent droplets of aqueous phase from wetting the glass

wall, the column was silanized.Five sampling points for continuous and dispersed

phases, where probes can be positioned in the centre ofthe column, were built in along the column. Droplets of the

dispersed phase are collected in a small cup where they

coalesce, while a sample of the continuous phase iswithdrawn through a coaxial outer tube. The uppermostprobe is positioned in a distance of 170 mm from the nozzle,where droplet formation is nished. Along with samplingfrom the feed and drain pipes, concentrations can bedetermined at seven positions in each phase.

Droplets can be photographed through at windows builtin at the sampling points. The photos of droplets were read

through a CCD camera (having processing facilitiesallowing the contrast to be raised between droplet and

background) into a PC system and interpreted using thepicture analysing software Optimas. The droplets appearedas spheres and rotation ellipsoids and length of radius and of

both the main axes respectively, was determined auto-matically. The system was calibrated by a picture of one ofthe probes. The reliability of the method was proved by

comparing with the results of manual measuring.

EXPERIMENTAL PROGRAM

The experiments accomplished can be divided into 4groups. Despite the fact that because of wide range ofsolubility all the three components take part in masstransfer, the direction of mass transfer is described here in aclassical style by the direction of transfer of acetone.

The initial concentration of the extracted phase, i.e.ethylacetate phase in Group I and II and aqueous phase in

Group III and IV, as well as the e xtraction factor E, varied in

every of the four experiment groups.

E=xac,EA

xac,W

MEA

MW(4)

The extracting phase was fed into the column virtually

free of acetone in all the experiments. The variation of theextraction factor was achieved by changing of the ow rate

of the continuous phase. The ow rate of the aqueous phasewas kept constant to avoid the inuence of changing dropletsize distribution on mass transfer. Next to no interdropletcoalescence occurs during the experiments with masstransfer from the continuous to the dispersed phases(Groups I and II). The Sauter mean droplet diameter was

about 2 mm in all the experiments, with a maximum in thedrop size distribution between 1.5 mm and 2.0 mm.Interdroplet coalescence, however, was very intensive

with mass transfer from the dispersed water phase to thecontinuous ethylacetate phase (Gr. III and IV). This effectcan be explained by enrichment of the transferredcomponent in the drainage lm between two colliding

droplets, which results in a local decrease of interfacialtension. The experiments of Saboni et al.

37conrm this

mechanism. To exclude the inuence of coalescence onmass transfer, experiments with this direction of mass

transfer were done at a lower volumetric ow rate. Thus,hold-up of the dispersed phase in the column is so low thatinterdroplet coalescence occurs only at a very low scale and

the droplet size distribution is analogous to the one inexperiments with groups I and II. Performance of thesesingle droplet experiments was, of course, rather proble-matic because of the extremely long time of up to 19 hours

before a steady state was achieved, and in any case,sampling of the dispersed phase is very difcult.

EXTRACTION TRAJECTORIES

Mass Transfer from Ethylacetate Phase to AqueousPhase

Examples of extraction paths for experiments with

saturated and unsaturated feed phases are given in

Figure 1. The ratio of volumetric ow rate betweendispersed and continuous phases was 0.3, the extractionfactor had the value E= 3.8 during both the experiments.The ethylacetate phase was introduced into the column in



Table 3. Program of extraction experiments.

Group of experiments Direction of mass transfer Saturation state of feed phases

I ethylacetate (c)NacetoneNwater (d) Both unsaturated

II ethylacetate (c)NacetoneNwater (d) At least one unsaturated

III water (d)NacetoneNethylacetate (c) Both unsaturated

IV water (d)NacetoneNethylacetate (c) Both saturated

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the experiment in Figure 1 (top) in a saturated state with 30mass % of acetone. Its composition changed along the

binodal line and it left the column with 20 mass % ofacetone. As a consequence of the position of the binodalcurve, water concentration along with acetone concentrationmust also decrease in the ethylacetate phase . The aqueousphase entered the column in a nearly sa turated state and witha content of acetone of 1 mass %. In the beginning, itsextraction path seems to go parallel to the binodal line, butreaches it at the third measuring point and follows it up tothe exit with 21 mass % acetone. As well as in the

ethylacetate phase, changes of c oncentrations in the aqueousphase are determined mainly by the binodal line, hence

ethylacetate concentration must also increase from 7 mass% to 12 mass % while accepting acetone.

The experiment plotted in Figure 1 (bottom) differs fromthe above described only because both of the phases were

introduced into the column in a strongly unsaturated state.The ethylacetate trajectory immediately strives for the

binodal line with hardly any decrease of acetone concentra-tion. It is saturated and already follows the binodal line atthe lowest sampling point in the column. Thus it is alsoforced, together with a cetone, to deliver the w ater it initiallyaccepted. The water trajectory is nearly a straight line untilit reaches the binodal line.

Comparing the extraction trajectories in Figure 1, it is

obvious that the nal concentrations are almost identical.

They are determined by the equilibrium in the water phase,and by the mass balance in the ethylacetate phase. Toinvestigate the inuence of the increased, due to under-saturation of the feeds, mass transfer of water andethylacetate, the concentrations versus the column lengthwere plotted (Figure 2). The heavier aqueous phase enters

the column at the top at HK = 0. It is obvious that in theupper part of the column the unsaturated phase accepts

considerably more acetone and delivers more water than thesaturated one. The high negative ux of water may cause anincreased transfer of acetone due to diffusive coupling.

It becomes clear from Figure 3, that the extractiontrajectories strongly depend on the extraction factor. Thefeeds were unsaturated in both the experiments withextraction factors of E= 3.8, E= 0.9, respectively. If at aconstant ow of dispersed phase the ow rate of thecontinuous phase is reduced, its extraction trajectory

becomes longer, linked to the mass balance. The aqueousphase is enriched in Figure 3 (top) up to the maximum

concentration of acetone, i.e. equilibrium concentration tothe feed of the ethylacetate phase. Thus there is a very lowdriving force for extraction of acetone from the ethylacetatephase. This explains why the ethylacetate phase rst gets

saturated with water and only then delivers acetone. For theentering water phase there is a high driving force for

acceptance of acetone. Thus its extraction trajectory isnearly a straight line.

In Figure 3 (bottom) none of the phases reachesequilibrium. Compared to the previous example, the drivingforce for the transfer of acetone is higher for the ethylacetatephase and lower for the aqueous phase, and the watertrajectory is now asymptotically curved towards the binodal

line.

It becomes clear from the examples shown in Figures 1and 3 that extraction trajectories are inuenced by localdriving forces in the column as well as by the matrix of

diffusion coefcients.

Mass Transfer from Aqueous Phase into EthylacetatePhase

The results of an experiment with unsaturated feed phasesare shown in Figure 4. As was discovered in the previous

experiments, with opposite direction of mass transfer,extraction trajectories approach the binodal line asympto-

tically and both the phases are already saturated after a short



Figure 1. Extraction trajectories in ethylacetate-acet one-water system.

Extraction factor E= 3.8; top: feeds nearly saturated; bottom: feedsunsaturated.

Figure 2. Concentration proles in the aqueous phase for the experimentsshown in Figure 1.

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time. The entering aqueous phase has a remarkably strong

tendency to become saturated with ethylacetate, thoughthere is a high driving force for extraction of acetone. It is

also obvious that the aqueous phase becomes very quicklyand completely depleted of acetone with this direction ofmass transfer. Thus the entering ethylacetate phase cannotbe enriched with acetone in the lower part of the extraction

column.

Column Model

The cell circulation model of Wasowski and Blass38

wasused for calculation of extraction paths in the c ountercurrentspray column. The wake ow, which contains some amountof the continuous phase carried behind droplets, was takeninto account in this model as well as ow rates of the

dispersed and continuous phases.The wake going from the top towards the bottom through

the column in an exactly opposite direction to the ow of the

continuous phase, is separated from the droplets at thebottom by coalescence of droplets, mixes with continuousphase there and raises with the ow in the direction of the

head of the column. The composition of the wake owcorresponds at every level of the column to the concentra-

tion of the outgoing continuous phase. As sedimentingdroplets cause the back mixing in the continuous phase, thewake ow is calculated depending on the ow rate of thedispersed phase, using the equations given by Letan andKehat

39for wake volume in liquid-liquid spray columns.

The wake ow rates must be taken into account in the massbalances of top and bottom stages as outow and inowrespectively.

Equations for Droplet Sedimentation Rate

Both circulating and oscillating droplets were observedduring the extraction experiments. The equations of Klee

and Treybal40

and of Kumar et al.41

were applied forcalculation of sedimentation velocities, both of the equations

were obtained by adopting to measured data of circulatingand oscillating droplets, and are applicable for a system withinterfacial tension between 0 .33 1023 N m21# s# 42.431023 N m21. The equations developed for spray columns byKumar et al.

41and by Harmathy

42were applied for

calculation of the relative droplet velocities in the column.

Simulation Program

The goal of the simulation was to prove how theapplication of various transport m echanisms affects theconformity between experimental and calculated data. Todemonstrate this inuence as clearly as possible, no tted

parameters were used. The calculation takes into accountthe following effects:

Back mixing in the continuous phase is caused by wakeeffects. The wake ow rate is calculated depending on the

ow rate of the dispersed phase.

The physical properties depend on the concentration ofthe phases. Viscosity and density are determined from 3

dimensional surface ts, interfacial tension and ternarydiffusion coefcientsfrom polynomial ts.

Mass transfer cannot be assumed to be equimolar. Thus

mass transfer coefcients depend on the total ux and mustbe calculated in an iterative procedure.

As mass transfer is not equimolar, the ow rates of both

the phases change along the column.

Because of multicomponent effects, the component uxesare not independent. They are calculated using thelinearized theory of Toor 43 . The ternary mass transfer

coefcients are calculated by decoupling the transportequations and subsequent inverse transformation.

The driving force for mass transfer, i.e. the difference of



Figure 3. Inuence of the extraction factor on the extraction trajectories.

Top: E= 3.80; bottom: E= 0.90.

Figure 4. Extraction trajectory w ith mass transfer from aqueous phase into

ethylacetate phase; ow of dispersed phase Vd = 0.08 l h21 , E= 1.8.

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concentration between bulk and interface, is determined ateach stage by solving the polynomial equation for thebinodal line.

As the drop size distribution at the upper and lower end of

the column differ only slightly, break-up and coalescenceof droplets were not taken into account, nor were the change

of droplet sizes by mass transfer. Convergence was very fastin most cases and constant values for mass transfer

coefcients were achieved already after the 3rd to 7th

iteration. There were problems with convergence only withthe Kronig and Brink model27.

Several routines from the NAG-FORTRAN library,

version mark 15, together with several algorithms ofNumerical Recipes (Press et al.)44 were used for the

calculation. It was helpful for programming to follow theIK-Cape

45guideline.

INTERPRETATION OF RESULTS

Figure 5 (top) shows the results of an experiment withsaturated feed phases and with extraction paths calculated

according to the mass transfer models by Higbie28

for

continuous phases, as well as by Handlos and Baron12

fordispersed phases. The path goes all its length by the binodalline and thus is constrained as to its direction. In addition, allthe equilibrium states lie on the binodal line and the pathmust always go towards equilibrium. A diagonal matrix of

mass transfer coefcients satises in this case to describethe mass transfer. As the model of Handlos and Baron12

presumes purely convective mass transfer, it will, in anycase, give a diagonal matrix. However, a transport matrixcalculated with diffusive models such as the penetrationtheory by Higbie

28, will certainly also be diagonal along the

binodal lines, since cross coefcients in the matrix ofternary diffusion coefcients will approach zero. That is

why it is no longer surprising that in this case all the modelscome to rather similar results, except for the equation byKronig and Brink27 which gives too small mass transfer

coefcients for long contact times.If feed is introduced into the column unsaturated, all the

directions in the concentration diagram are in general openfor the extraction path. T he experiment has nevertheless

shown that the paths of both the phases in the systemethylacetate-acetone-water strive for the binodal line and

only stay in the undersaturation area for a short segment. AsFigure 5 (bottom) for the experiment with unsaturated feedphases and extraction factor ofE= 1.8 shows, the course ofthe extraction path in this case c an also be described with the

help of the model by Higbie28

and Handlos and Baron12

recommended by Blass et al.11 with quite satisfactory

precision.As regards to the dominating transport mechanisms, it is

interesting to examine extraction paths in the undersaturatedarea more precisely. An experimental extraction path of theaqueous phase together with concentration curves, calcu-lated according to the equations by Higbie28 and Handlosand Baron

12, and to both the models by Schermuly

18,


, are plotted in Figure 6. Starting withpure water the experiment al trajectory is curved towards the

binodal line. It is best described with the mass transfermodel for unsaturated phases and diffusive transport bySchermuly and Blass33. While applying the model forcontinuous phases by Higbie

28and for dispersed phases by

Handlos and Baron12

, the calculated path is curved towardsthe binodal line obviously more strongly than the curve of

the measured data. If the calculation is based on theuctuation model by Schermuly and Blass

33, which assumes

purely uid-dynamical transport, the calculated trajectory isdirected straight towards the binodal line and the differencebetween experimental and calculated data becomes dis-tinctly bigger. Plotting the concentration prole versus theheight of the column conrms these conclusions (Figure 7).

The concentrations of all the three components are best



Figure 5. Extraction trajectories calculated by Higbie and Handlos andBaron. Top: saturated feed phases, E= 3.8; bottom: unsaturated feedphases, E= 1.8.

Figure 6. Experimental trajectory of aqueous phase with unsaturated feed,compared to the results of different mass transfer models.

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described by Schermuly9s model for multicomponent

diffusion, especially near the entrance point of the dispersedphase.

Inuence of Diffusion

In general, diffusion coefcients can be calculated eitherat the bulk or at interfacial concentration. Cullinan andRa m

10concluded from the experiments in a stirred cell, that

mass transfer is controlled by the situation at the interfaceand that diffusion coefcients should be determined for thisconcentration.

Calculating ternary mass transfer coefcients in theaqueous phase at a position of H= 2180 mm in the columnfor the experiment shown in Figure 5 (bottom) with the helpof the diffusive model of Schermuly and Blass

33, produced

the following results:

At bulk phase concentration:

k= 1.533

1024

8.903

1027

27.723 1025 1.733 1024( )

ms

At interfacial concentration:

k=1.463 1024

0

0

1.463 1024( ) msAs the matrix of the Fick

19diffusion coefcients becom es

diagonal at the binodal line, the matrix of mass transfer

coefcients must be diagonal there as well. Extractiontrajectories calculated with the diffusive model of Scher-muly and Blass

33using different sets of mass transfer

coefcients are shown in Figure 8. It becomes obvious that

in the case where mass transfer coefcients are calculated atbulk concentrations, the experimental results can be

described better. As the matrix of mass transfer coefcients[k] is diagonal at interfacial concentrations, diffusivecoupling is not taken into account and the calculated

trajectory is curved more strongly towards the binodal line,than the experimental one.

CONCLUSIONS

As shown by Pertler36

, Fick19

diffusion does not vanish atthe binodal line, but the matrix of ternary diffusioncoefcients becomes diagonal. Thus the matrix of masstransfer coefcients is a diagonal matrix in saturated phases,independent of whether it is c alculated with a purely uid-

dynamical model or with a diffusive model. It is thusimpossible to distinguish from the extraction trajectory,

running along the binodal line, between the diffusive andconvective mechanisms of mass transfer.

The results show that using the diffusive model for thecalculation of mass transfer, the extraction trajectories canbe well described in the area of miscibility and along thebinodal line. From our results it does not become clearwhether molecular clusters a re formed in saturated phases.

However, following Ficks19

phenomenological denitionof diffusion, mass transfer can surely be named diffusive in

extraction with saturated phases.The presence of diffusion, and resulting from it the

inuence of diffusive coupling on multicomponent masstransfer, does not mean that a complete matrix of diffusion

coefcients is always necessary for design of liquid-liquidextraction columns. As these results for the system

ethylacetate-acetone-water show, extraction trajectoriesusually reach the binodal line shortly after the feed pointand then follow the binodal line. If, for an extractionprocess, the part of the trajectory in the area of miscibility isnot important or both main components are nearlyimmiscible, sufcient results can be obtained even withpurely uid-dynamical models. However, if, for the process

or apparatus design, it is necessary to calculate extractiontrajectories for unsaturated phases, it is denitely necessary

to take into account all the set of multicomponent effects inmass transfer.

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ADDRESSCorrespondence concerning this paper should be addressed to Dr Ing. M.

Haeberl, Frankfurter Strasse 19A, D-64807 Dieburg, Germany.

The manuscript was received 3 March 1999 and accepted for publicationafter revision 1 June 1999.


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