23327726-DK1288-Ch08

8Principles of Industrial SolventExtraction

PHILIP J. D. LLOYD Energy Research Institute, University of CapeTown, Rondebosch, South Africa

8.1 INTRODUCTION

The theory of solvent extraction was considered in Chapter 1, and Chapter 7covered the application of liquid–liquid extraction in industry. The princi-ples underlying the design of industrial applications are addressed in thischapter.

At the very simplest level, an aqueous solution contains a valuablecomponent to be recovered, and a number of other components from whichthe desired component should be separated. It is assumed that, as a result oflaboratory studies such as those outlined in previous chapters:

1. A suitable extraction system has been identified that will extract thedesired component selectively from the less desired components.

2. Suitable physical and chemical conditions for carrying out the extrac-tion have been found.

3. The rates of extraction of the desired and possibly also some of theundesired components have been determined at least qualitatively.

To design a process to recover the valuable component, a number ofquestions which must be answered:

� What fraction of the desired component can be recovered?� How much of the extractant must be added to achieve the desired

recovery?� How much of the undesired components are extracted with the desired

component?

Copyright © 2004 by Taylor & Francis Group, LLC

� Can anything be done to reduce the concentration of undesired com-ponents in the extract phase?

� Having extracted the desired component, how can it be recovered fromthe extract in a useable form?

� How, physically, can the extraction be carried out, and what type andsize of apparatus is required?

� How much of the extract is lost to the raffinate, and can anything bedone to recover it?

This chapter therefore outlines the methods for answering these typesof questions, so that the solvent extraction process may be applied in practiceand desired components may be recovered in an energy-efficient, environ-mentally safe, and economical way.

The nomenclature used in solvent extraction has been defined inChapter 1 and is illustrated in Fig. 8.1. Not all of the steps shown in thisfigure will be found in every extraction process, but equally there may beoccasions where it is necessary to add additional steps; for example, torecover the extractant from the scrub raffinate. So while Fig. 8.1 is not acompletely general flow diagram it covers most of the processes likely to befound in practice. Variations of this flow sheet will become apparent duringthe remaining chapters.

Fig. 8.1 Basic processes in solvent extraction.


8.2 EXTRACTION

8.2.1 Single-Stage Extraction

As described in Chapter 4, if a solution containing a desired component X iscontacted with an immiscible solvent phase, then X distributes itself betweenthe feed solution and the solvent according to:

DX ¼ [Xe]=[Xa] (8.1)

where the subscript e represents the extract (solvent) phase and subscript athe aqueous phase.

If the phase volume ratio Y=Ve/Va, then the fraction extracted, EX,is given by:

EX ¼ Dx�=(Dx ��þ 1) (8.2)

that is, the fraction extracted in a single stage is a function of both the dis-tribution ratio and the phase ratio. This is an important finding. Much of thework in previous chapters has concentrated on the equilibrium distributionof species between the extract and raffinate phase. However, as soon as ananswer to the question ‘‘What fraction of the desired component can berecovered?’’ is sought, the volumetric ratio between the two phases becomesalmost as important as the equilibrium distribution. Consider now anothersimple case with a desired component A for which DA=10 and a con-taminant X for which DX=0.1. Table 8.1 shows the effect of varying thephase ratio on (1) the fractions of A and X which are extracted, and (2) theratio of the fractions extracted, which is a measure of the product purity.

This not only shows how the extent of extraction varies with phaseratio at a constant distribution ratio, but also how varying the phase ratioaffects the relative purity of the product. Increasing the phase ratio by afactor of 100 nearly doubles the recovery, but drops the relative purity by afactor of over 25. Note that, in a single stage, it is not possible to achieveboth high recovery and a high degree of separation simultaneously. Also,

Table 8.1 Effect of Phase Ratio in Single Stage Extraction

Phase ratioFraction extracted

Relative purity

Y EA EX EA/EX

0.1 0.500 0.010 50.50

1 0.909 0.091 10.00

10 0.990 0.500 1.98

Note: Assuming DA= 10, DX = 0.1.


although the distribution ratios of the two species differ by a factor of 100,the relative purity is always less than 100.

A second phenomenon of great industrial importance is the effect ofsaturation of the solvent on the product purity. Implicit in the derivation ofEq. (8.2) is the assumption that DX is constant. As discussed in Chapter 2,DX is only a constant under ideal and constant conditions (usually at traceconcentrations in both phases). It changes markedly as the concentrationsvary in the two phases.

At higher concentrations, so much of an extractable component maybe extracted that an appreciable fraction of the extractant is bonded to theextracted component, so that in turn the concentration of the free ligand inthe extract phase is significantly reduced.

Industrial practice naturally requires the maximum use of the rela-tively expensive extractant, so that saturation of the extractant phase withreduction of the free ligand concentration to a minimum is the general rule.A model is thus needed to quantify the effect of a reduction in DX as theconcentration of the extracted species in the organic phase increases.

In many extraction systems, DX is proportional to [L]n, where: [L] isthe free ligand concentration, and the exponent n is determined by thenumber of ligand molecules per molecule of extracted complex. In thesesystems, therefore, we may write:

DX=[Xe]=[Xa]=D0f[Le]tot �m � [Xe]gn (8.3)

in which:

D0 is the distribution ratio of species X at trace concentrations, readilydetermined in the laboratory.

[Le]tot is the total ligand concentration in the extract phase.m approximates the ratio of ligand molecules to extracted molecules close to

saturation.n approximates the ratio of ligand molecules to extracted molecules close to

infinite dilution.The term in curved brackets on the right-hand side of the equation is the free

ligand concentration.

It should be noted that m and n in Eq. (8.3) are sometimes equal, butoften differ in value, which underlines the fact that this equation has notheoretical basis. It is merely a convenient way of representing much ex-perimental data using three parameters that can readily be determinedexperimentally.

The equation can be fitted to a wide range of isotherms with quitesmall residual errors over the entire range of concentrations of interest. It isa liquid–liquid analogue of the Langmuir adsorption isotherm applicable to


vapor–solid interactions, with the extractant concentration taking the placeof the free surface area of the solid.

Where more than one component is extracted, then the free ligandconcentration will be reduced by all components present in the organicphase. For example, consider the extraction of two components, A and B,that have similar chemistries of extraction. Assume for both componentsm= n=2, that they have D0 values of 10 and 1 respectively.

The equilibria for the distribution of A and B between the two phasesare described by

DA ¼ [Ae]=[Ae] ¼ 10 � (1� 2[Ae þ Be])2 (8.4a)

DB ¼ [Be]=[Ba] ¼ 1 � (1� 2[Ae þ Be])2 (8.4b)

while two mass balance equations

[AF ] ¼ [Aa]þ� � [Ae] (8.4c)

[BF ] ¼ [Ba]þ� � [Be] (8.4d)

where subscript F indicates the feed, provide sufficient equations to solvesimultaneously for the four unknowns [Aa], [Ae], [Ba], and [Be] in terms of[AF], [BF], and Y. Simple analytical solutions are available only for caseswhere n=1. In the general case, it is easier to solve these sets of equationsusing spreadsheets and tools such as Solver in M-S Excel.

The results of one such set of calculations are shown in Fig. 8.2. Themore extractable species A competes strongly for the ligand, so that theequilibrium curve of A in the presence of B is depressed only slightly belowthat for the extraction of A on its own. In contrast, the equilibrium curve forthe extraction of B in the presence of A is depressed markedly relative to theextraction of free B. The effect of this is to improve the product puritysignificantly over what would have been possible at low concentrations ofthe extracted species in the extract. Thus, at high concentrations, saturationeffects can improve product purity to a far greater extent than the equilib-rium isotherms of the individual species would indicate superficially.

This is a key finding in understanding why solvent extraction is widelyadopted in industrial practice. It is possible to achieve a higher purity ofproduct than would be indicated by the separation between species whenthey are extracted individually. Clean separations between species with verysimilar extractabilities such as rare earth ions have proved practical byrelying on saturation effects more than on the inherent separability of thespecies.

The two phenomena, namely the effect of phase ratio on the fractionalrecovery and purity and the effect of saturation on purity, have thus far been


illustrated using only single-stage batch extraction. In both cases, if betterseparation was sought, then the recovery of the desired species was reduced.This explains why single-stage extraction is rarely adopted commercially.Multistage operation, outlined in Chapter 1.4.3, offers significant advan-tages, and in particular permits both high recovery and high purity of theproduct.

8.2.2 Repeated Extraction or ‘‘Cross-Flow’’ Systems

Returning to the example shown in Table 8.1, it is intuitively obvious thatthe low degree of extraction achieved when using a phase ratio Y=0.1could be improved if the raffinate could be reextracted with fresh solvent,and that if this reextraction were to be carried out at the same phase ratio,the second extract would show a similar purity. The first and second extractscould then be combined to give overall a better recovery than could beachieved in a single stage.

For a single, highly extractable component this argument is entirelyvalid. A mass balance over any one stage gives:

Fig. 8.2 Isotherms for the extraction of two species at a phase ratio of 1 and equal

concentrations in the feed.


Va[AF ]=Ve � [AE ]þ Va � [AR] (8.5)

which on rearranging becomes:

([AF ]� [AR])=[AE ] ¼ � (8.6)

where

[AF] is the concentration of A in the feed to any one stage,[AR] is the concentration of A in the raffinate leaving any one stage, and[AE] is the concentration of A in the extract that is in equilibrium with [AR]

[AE] and [AR] are related via the isotherm, which is known, so the series ofEq. (8.6) governing each individual stage of extraction can be solved ana-lytically. The properties of the solution can be readily understood graphi-cally.

Figure 8.3 is a graphical construction that represents a series of equa-tions such as Eq. (8.6), for the caseY=1 and the isotherm of Eq. (8.4). From[AF]1, a line of slope �1/Y=�1 intercepts the equilibrium curve at [A]1.A perpendicular from this intercept cuts the x axis at [AR]1= [AF]2, fromwhich a further line of slope �1 is drawn. Of course, Y may be varied from

Fig. 8.3 Graphic construction for a four-stage cross-flow cascade.


stage to stage, but there is no particular advantage in doing so. Four stagesare shown with a feed at a relative concentration of 1.

Table 8.2 gives the stage-by-stage performance of the four stages ofrepeated extraction, the cumulative extraction, ETOT, and the average con-centration of AE, [AE]AVG, in the organic phases mixed together after eachrepeated extraction. In addition, Table 8.2 also shows the performance of asingle stage in which the volume of extractant is the same as the total used inthe four stages, i.e., a single extraction at a phase ratio of 4.

This illustrates that even with a moderate distribution ratio (10 inthis case), useful recoveries (>99% as shown by ETOT for Stage 4) can beachieved in comparatively few stages by repeated extraction. However, asthe number of stages increases, the concentration of the extracted species inthe combined extract, [AE]AVG, drops significantly.

A single-stage extraction using the same total volume of solventachieves only 92% extraction, and the extract concentration is only 0.23, vs.nearly 0.25 for the cross-flow extraction. The use of four cross-flow extrac-tion stages is clearly preferable to a single extraction. Equally, of course, theuse of more than four extraction stages, each with a proportionately smallervolume, would improve the performance. In the limit, one would seek adifferential contacting process similar to the Soxhlet extractor employed forextraction from solid phases, but such a contactor has not found use insolvent extraction.

The mathematical treatment of a cross-flow cascade is straightfor-ward. The mass, WE, which is extracted in n stages is given by:

WE ¼X

VEn � [CE ]n (8.7)

The cumulative recovery is given by:

ETOT ¼WE=([CF ] � V) (8.8)

while the average concentration in the combined extracts is given by:

Table 8.2 Extraction of a Single Component in a Cross-Flow Cascade at Y= 1

Aqueous Extract

Stage no. Feed Raffinate [AE] EA ETOT [AE]AVG

1 1.000 0.623 0.377 37.7% 37.7% 0.377

2 0.623 0.292 0.331 53.2% 70.8% 0.354

3 0.292 0.071 0.221 75.7% 92.9% 0.310

4 0.071 0.008 0.063 88.5% 99.2% 0.248

Single 1.000 0.079 0.230 92.1% 92.1% 0.230


[CE ]AVG ¼WE=(n � VE) (8.9)

provided the phase ratio is kept the same in each repeated extraction; if not,n�VE in Eq. (8.9) must be replaced by

PVEn.

Now consider the effect of repeated extraction on the degree ofseparation that can be achieved from contaminants. Table 8.3 shows how theperformance of the extraction deteriorates when a second component ispresent. Comparison with Table 8.2 shows that the percentage extraction ofA in four stages drops to slightly over 95%, while the extraction of theimpurity B rises to 37%. The purity of A, calculated as the ratio of A in theextract to the sum ofA and B in the extract, becomes poorer as more stages ofcross-flow extraction are added. A single stage, using the same total volumeof extractant as used in the four stages of cross-flow extraction, performsnearly as well as the cross-flow cascade.

The reasons for this poor performance are clear. In stages 3 and 4 ofthe cascade, the desired component A is at low concentration in the extractphase, so there is a relatively high concentration of the free ligand availableand the undesired component B is relatively highly extracted. Indeed, in thefourth stage, the concentration of A in the extract is lower than that of Beven though A is 10 times more extractable than B.

Clearly, it would be preferable from the point of view of the purity ofthe product if there were high concentrations of A in both the extract andthe raffinate of a stage. This can be achieved in countercurrent extraction,which allows both high recovery and the achievement of high product puritywhen properly designed.

8.2.3 Countercurrent Extraction

Consider the extract from the fourth stage of the cascade given in Table 8.3.The concentration of the desired species is 0.11, so it is clearly not saturated.Thus in principle it could form the feed to the third stage where the aqueous

Table 8.3 Extraction of Two Components in a Cross-Flow Cascade with Y = 1

Stage [AR] [AE] EA.TOT(%) [BR] [BE] EB.TOT(%) Purity of A(%)

Feed 1.000 - - 1.000 - - -

1 0.662 0.338 33.8 0.951 0.049 4.9 87.4

2 0.371 0.291 62.9 0.882 0.069 11.8 84.2

3 0.158 0.212 84.2 0.778 0.104 22.2 79.1

4 0.047 0.111 95.3 0.630 0.147 37.0 72.0

Single 0.144 0.214 85.6 0.627 0.093 37.3 69.7


concentration is higher. Systems in which such a strategy is employed areknown as countercurrent extraction systems.

A typical flow arrangement is shown in Fig. 8.4, which clearly showshow the name arises. A mass balance over any one stage ‘i’ gives:

VE([AE ]i � [AE ]iþ1) ¼ VA([AR]i�1 � [AR]i (8.10)

which on rearrangement yields:

� ¼ VE

VA¼ ([AR]i�1 � [AR]i)

([AE ]i � [AE ]iþ1)(8.11)

If the cascade is calculated by the same techniques as used for the cross-flowcascade in the previous section, but with the layout shown in Fig. 8.5, theorganic concentration increasing from stage to stage and a phase ratioY=1, the performance is shown graphically in Fig. 8.5. In this case, thecalculation has been carried out from the organic feed end, rather than theaqueous feed end as in the case of Fig. 8.3, to allow for the increase inorganic-phase concentration. In every other respect the calculation is iden-tical to that which led to Fig. 8.3. From [AR]3 a vertical line is drawn tointersect the equilibrium curve, from which point a line of slope �1 is drawnto reach the point [AR]2 on the axis. A vertical line from this point reaches theequilibrium curve at point E, and again a line of slope �1 is drawn, but onthis occasion it is only carried to point G, because there is contact betweenaqueous phase of concentration [AR]1 and organic phase not of zero con-centration but of concentration [AE]3. The calculation then continues in thesame way for another stage, making three stages in all.

As the calculation continues, it is found impossible to proceed muchbeyond the point marked A on the diagram, at which point the aqueousconcentration is about 0.34. The reason for this is that at a phase ratioY=1 the cascade has too little organic phase for the duty it is being askedto perform. Consider the rectangles ABCD and CEFG in Fig. 8.5. Thediagonals BD and EG have the same slope. The diagonals AC and CF thushave the same slope, and AF is therefore a straight line. The point A has thecoordinates [AF]; [AE]1 and the point F the coordinates [AR]2; [AE]3. Thus theslope of the line

Fig. 8.4 Countercurrent extraction.


AF ¼ ([AE ]1 � [AE ]3)

([AF ]� [AR]2)¼ 1=� (8.12)

which is identical to Eq. (8.11) except it represents the mass balance overtwo stages.

Thus to achieve an extraction equivalent to that shown in Fig. 8.3requires an overall mass balance for which, at the first stage, [AE]1=0.377and [AF]=1.0; while at the last stage [AE]3=0 and [AR]3=0.008. Then byEq. (8.11) over the whole cascade:

� ¼ (1:00� 0:008)

(0:377� 0)¼ 2:63

or the slope of the mass balance line=1/2.63=0.38.Mass balance lines such as AF are important and are known as

operating lines in countercurrent cascades. Clearly, an operating line can-not cross an equilibrium line. Wherever an operating line approaches an

Fig. 8.5 Graphic construction for a countercurrent cascade.


equilibrium line, a pinch point is the result and the number of stages neededto achieve the desired degree of extraction approaches infinity.

In Table 8.4, the calculations behind Fig. 8.5 are repeated for a valueof Y=2.63. Comparison with the results of Table 8.2 indicates clearly thatthe countercurrent cascade offers a similar overall extraction in the samenumber of stages, together with an extract of significantly higher con-centration.

The data of Table 8.4 are also shown in Fig. 8.6, which is shown as anequilibrium isotherm, an operating line, and a series of steps between theoperating line and the isotherm. These steps are entirely equivalent to thelines establishing the mass balances for each stage in Figs. 8.3 and 8.5.For instance, the horizontal line AB represents [AF]1�[AR]1, while the ver-tical line BC represents [AE]1�[AE]2.

The graphical construction of an extraction isotherm, an operatingline, and the stepwise evaluation of the number of stages in this manner isknown as a McCabe-Thiele diagram. Historically, it found great applicationin a variety of mass transfer operations, from gas adsorption through dis-tillation to solvent extraction. However, the advent of modern computa-tional techniques has made it largely redundant, as it is often easier andcertainly more accurate to calculate the cascade directly.

In part also this is because better equilibrium data are now availablethrough the use of equipment such as AKUFVE, which has brought therealization that it is not sufficient to view the isotherm as fixed. Quite smallchanges in aqueous composition or in phase ratio can change the isothermsand cause dramatic effects on the performance of a countercurrent cascade.Even relatively crude models for the isotherms, such as Eq. 8.3, can demon-strate these effects in cascades.

Consider now the extraction of two species simultaneously in a coun-tercurrent cascade. To obtain the equilibria requires solving two equationssimilar to Eq. (8.4) simultaneously. Determining the concentrations withinthe cascade means taking into account a mass balance such as Eq. (8.11) at

Table 8.4 Extraction of a Single Component in a Countercurrent Cascade at Y= 2.63

Aqueous Extract

Stage no. Feed Raffinate [AE] EA ETOT [AE]AVG

1 0.172 0.008 0.062 95.3% 99.2% 0.062

2 0.780 0.172 0.294 77.9% 83.8% 0.294

3 1.030 0.780 0.388 24.2% 26.7% 0.388

4 1.064 1.030 0.401 3.2% 3.2% 0.401


each stage. Table 8.5 presents such calculations for the same two equilibria asused before, with A having D=10 and B having D=1.0. It should be notedthat the calculation is not simple, and requires estimation of the equilibriumat each stage before the next stage is computed.

The behavior of the system is very counterintuitive. The more extract-able component is relatively well behaved and a recovery of 99.4% isachieved in four stages. In contrast, the less extractable component behavesunusually. Its concentration increases in the aqueous phase between the firstand the third stages. In the extract phase, it has a peak concentration in theextract from the fourth stage. Thus, the less extractable component circulatesbetween the first and last stages, being ‘‘squeezed out’’ of the organic phaseby the more extractable component, then being extracted back from theaqueous phase once the concentration of the more extractable component inthe aqueous phase has fallen.

This is caused by the coupling of the two equilibria. The presence ofhigh concentrations of the less extractable component so disturbs the equi-libria that the more extractable component has a distribution ratio of onlyabout 2.5 in the fourth stage of the cascade. If the less extractable component

Fig. 8.6 McCabe-Thiele graphic construction for a countercurrent cascade.


were not present, the distribution ratio would approach the infinite dilutionvalue of 10.

Because of the high concentrations of the less extractable componentwithin the cascade, the final separation between the two components is notparticularly good. The final extract is only 85% pure. This could be improvedby reducing the phase ratio, which would have the effect of loading the moreextractable component sooner in the cascade, and thus squeezing out theless extractable component better. In practice, however, one cannot reducethe phase ratio too far without running the risk of the cascade becomingunstable, or requiring, for instance, temperature control. It is preferable toscrub the extract, as described in the next section.

It should be noted that this was a fairly severe test. Having a feedcontaining equimolar quantities of components whose extractability differsby a factor of only 10 is rare. Usually the differences in extractability aregreater, or the less extractable component is present in low concentrationsrelative to the more extractable. In both these cases, good separations can beachieved in a countercurrent cascade.

The cascade can be drawn graphically in the McCabe-Thiele form, butthe equilibria are so distorted that the exercise is not very valuable. This is ageneral finding in industrial practice. Graphical methods are adequate togive an indication of the number of stages likely to be needed for a partic-ular duty. They fail when separations between similar species are sought.

Highly selective extractants are desirable, but often show poorer phys-ical or chemical properties than less selective extractants. As the exampleabove illustrates, a difference of a factor of only 10 in the distribution ratios

Table 8.5 Calculation of a Countercurrent Cascade with Two Components, Y= 3.0

Aqueous Extract

Stage no. Feed Raffinate Feed Extract

1. The more extractable component

1 1.00 0.686 0.227 0.332

2 0.686 0.265 0.086 0.227

3 0.265 0.058 0.017 0.086

4 0.058 0.006 0.0 0.017

2. The less extractable component

1 1.00 1.208 0.127 0.058

2 1.208 1.491 0.221 0.127

3 1.491 1.496 0.223 0.221

4 1.496 0.826 0.0 0.223


gave a reasonably purified product in four countercurrent extraction stages,even when the contaminant was present at relatively high concentrations.One can improve the performance of the cascade if the desired product ispresent at a higher concentration than other extractable species. This is thebasis for further purification by means of scrubbing of the final extract.

8.2.4 Extraction with Scrubbing

Where a high-purity product is sought, the same philosophy of saturating theaqueous phase with the unwanted component is used in scrubbing theextract. A recycle stream of the pure product is used to ‘‘scrub’’ the impureextract. In the process, the extract is saturated with the desired product, andthe impurities are removed. The final raffinate from scrubbing is then recy-cled to the aqueous feed so that the now-contaminated desired product canbe recovered. This is shown in Fig. 8.1.

In Table 8.6, the results of computations identical in principle to thosedescribed previously are given. The final extract from the countercurrentcascade described in Table 8.5 was contacted with a pure stream of the moreextractable component at a high phase ratio. The high phase ratio is chosento minimize the volume of aqueous phase that must be recycled to the feed.

The cascade is fed with an extract of the same composition as thatresulting from the extraction shown in Table 8.5, with EA=0.332 andEB=0.058. In four stages, using a concentrated solution of A at Y=10,EA=0.350 and EB=0.00014, the purity of the product is increased from85–99.96%. Note that the composition of the scrub solution is the same as

Table 8.6 Calculation of a Countercurrent Cascade in Scrubbing, Y = 10

Aqueous Extract



1 0.500 0.390 0.339 0.350

2 0.390 0.328 0.333 0.339

3 0.328 0.299 0.329 0.333

4 0.299 0.297 0.332 0.329


1 0.0002 0.0016 0.00014 0.00028

2 0.0016 0.0027 0.00028 0.00039

3 0.0027 0.0035 0.00039 0.00047

4 0.0035 0.0041 0.00047 0.0584


the composition of the final extract after scrubbing. In practice, additionalpurification can often take place during recovery of the components fromsolution after stripping, which allows the scrub solution to be even purer, andin turn allows the product purity to be higher than shown in this example.

Also of note in Table 8.6 is the composition of the final raffinate, withAA=0.297 and AB=0.004. This can clearly be recycled directly to the feedto the extraction cascade, where the fact that this stream is purer than thefeed stream will further aid the achievement of product purity.

Techniques for achieving high-purity products by countercurrentextraction and scrubbing of the extract have proved essential for the pro-duction of nuclear-grade uranium. They have also found application in theseparation of the rare earths and a number of other difficult separations. Afeature of the operation of these systems is the need for close control offlow rates and even temperature in order to achieve a consistent productquality. The product quality is a very nonlinear function of the operatingparameters. However, with modern control systems this disadvantage can beovercome.

8.2.5 Summary of Extraction

In this section, the first three questions posed in the introduction have beenanswered. It has been shown that:

� The fraction of the desired component that can be recovered is deter-mined not only by its inherent extractability but also by the phase ratioand the presence of competing extractable components.

� The volume of solvent needed for a particular duty depends on thesystem adopted for the extraction; in general, a single-stage extractionrequires more solvent phase than a cross-flow cascade, which in turnneeds more than a countercurrent cascade.

� The purity of the product is determined not only by the inherent selec-tivity of the solvent system for the component sought, but also on thephase ratio, the concentration of the contaminants, and the performanceof any scrubbing of the extract.

8.3 STRIPPING

The general principles established for extraction apply to stripping, althoughof course distribution ratios are sought that are significantly less than unity inorder to accomplish the strip as efficiently as possible.

Stripping can equally be done in single-stage, cross-flow, or counter-current systems. To illustrate how the overall concepts remain valid, the per-formance of a countercurrent cascade accepting as feed the scrubbed extract


of Table 8.6 is calculated assuming that the equilibria involved are describedby:

DA ¼ 0:1(1� 2[Ae þ Be]) (8.13a)

DB ¼ 0:01(1� 2[Ae þ Be]) (8.13b)

that is, as for Eq. (8.4) but with m not equal to n. Further, the cascade shouldstrip over 95% of the desired component and yield a strip raffinate which isas concentrated as possible (assuming a solubility of A in the strippingsolution of 2).

As before, the same mass balance limitations on phase ratio apply.Although this is a stripping cascade, it remains countercurrent in its struc-ture. For an organic feed concentration of 0.350 (that is, the extract afterscrubbing, as shown in Table 8.6), assuming >95% strip and a final aqueousof <2, the maximum phase ratio is Ymax=2/(0.95*0.350)=6.02. (Max-imum in this case because stripping is in the reverse direction to extraction.)Choosing a phase ratio of 5.0 gives the results shown in Table 8.7.

Four stages are needed. The strip raffinate has a concentration of 1.71,and the stripped organic contains only 2% (0.0073/0.35) of the component Ain the scrubbed extract, so the stripping efficiency is 98%. The less extrac-table (more readily stripped) component B was completely stripped in threestages.

Note that the stripped extract still contains traces of the desired com-ponent. This is a slight nuisance as the stripped extract will, in the normalcourse of events be recycled to the extraction stages where it will reduce the

Table 8.7 Calculation of a Countercurrent Cascade in Stripping, Y= 5.0

Aqueous Extract



1 0.000 0.074 0.022 0.0073

2 0.074 0.232 0.054 0.022

3 0.232 0.601 0.128 0.054

4 0.601 1.713 0.350 0.128


1 0.000 0.0000 0.000 0.000

2 0.0000 0.0000 0.0000 0.0000

3 0.0000 0.00003 0.00001 0.0000

4 0.00003 0.00070 0.00014 0.00001


extraction efficiency in the first stage. This practice is fairly common inindustrial practice, as it is more economic to lose a little of the desiredcomponent in the extraction stages than to have too dilute a strip raffinate byseeking a total strip.

The purpose of seeking a concentrated strip solution is to reduce theenergy required to recover the product from the strip solution. In the caseof metal salts, precipitation, electrolysis, direct reduction, and a host ofother techniques may be used to generate the final product. In the case ofthe extraction of organic compounds, distillation, crystallization, or similarseparation methods are used. In each case, the more concentrated the stripsolution, the less energy is required to recover the desired components.

It sometimes happens that an undesired component is not stripped. Itthen builds up in the organic phase until it interferes seriously with theextraction. In this case, the solvent is given a more vigorous strip to regen-erate its performance by removing the contaminant. A small sidestream maybe bled continuously from the recycled organic phase and regenerated, orthe contaminant may be allowed to build up in the extract for some timebefore the solvent is regenerated on a batch basis. Because of its vigorousnature, regeneration of the organic phase can be expensive, but sometimesthe contaminant is very valuable-platinum, gold, and cobalt complexeshave acted as contaminants on occasions, and their recovery has paid for theregeneration!

8.4 EQUIPMENT FOR CONTINUOUS CONTACT

8.4.1 Stagewise Extraction

Thus far in the discussion of industrial practice, we have referred to ‘‘stages’’of extraction without defining a stage. Clearly these stages could be scaled-upversions of separatory funnels, but this is inefficient, because it implies batchrather than continuous operation. Industry prefers continuous operationbecause it is generally simpler to control automatically, and because it makesbetter use of labor.

The typical stage might be a mixer-settler. As its name suggests, thiscomprises some means for mixing the two phases and an adjoining means forseparating them. Mixers can be stirred tanks, of a sufficient size to retain themixed phases long enough to effect transfer of the desired species from onephase to the other. The mixer usually consists of some form of impeller orpropeller in a tank that usually contains some means to prevent the mixedliquids from swirling and thus reducing the efficiency of mixing. In circularcross-section mixers, this usually takes the form of vertical baffles mountedon the wall of the mixer.


Figure 8.7 illustrates two stages of a mixer-settler cascade. The aqueousfeed enters the first stage, where it is mixed with partially loaded extract fromthe second stage. The mixed phases pass to the settler, where they areseparated under gravity. The fully loaded extract overflows an upper weirand passes to scrubbing and/or stripping. The first-stage raffinate overflows alower weir and is pumped to the second stage, where it is mixed with thesolvent feed. After settling again, the final raffinate passes to treatmentbefore discharge as waste.

There are many variants on this simple theme. For instance, manyother methods for mixing have found use. In a design offered by Lurgi, thephases are mixed in what is essentially an axial flow pump, and then passdown a relatively long pipe where the turbulence of flow keeps the phasesmixed while the extraction takes place. In another design, the individualphases are pumped and then join and pass through a static mixer. There areno particular physicochemical reasons for preferring one type of mixer to

Fig. 8.7 Layout of two stages of a mixer-settler cascade.


another. As long as they provide adequate interfacial area for the extrac-tion to take place, without creating such small droplets that they will notsettle efficiently, and provided there is sufficient residence time for the desireddegree of extraction to take place, then one mixer will work as well asanother.

There is, however, one physicochemical criterion that is important inindustrial mixing, and that is ensuring that the correct phase is dispersed inthe other. There are several reasons for this:

� It is sometimes found that mass transfer is more rapid if one phase is thedispersed phase rather than the other.

� Alternatively, the dispersed phase is chosen because, by definition, it willnot contain droplets of the continuous phase. In this way the dispersedphase, after settling, will not entrain the continuous phase and entrain-ment losses from the settler will be reduced.

Whatever the reason for choosing the dispersed phase, it is important toensure that the mixer will keep that phase dispersed during operation, aschanges in the dispersed phase, i.e., phase inversion, can cause considerableoperating problems.

Usually the continuous phase is the phase present in greater volume. Itis possible to run for long periods with the greater volume phase dispersed,but phase inversion is always a risk in such circumstances. To overcome thisrisk, where it is desired that the lesser volume phase is continuous, then aportion of that phase may be recycled from the settler back to the samemixer to ensure that within each stage it is the greater volume, even if it isthe lesser volume phase overall.

In large-scale operation, the volumetric flow of the phase to be dis-persed is so large that it becomes necessary to disperse that phase into themixed phases. Otherwise ‘‘blobs’’ of the dispersed phase will act locally asthe continuous phase, and the intended continuous phase will be dispersedin the blobs before the shear forces in the mixer break them up. This canlead to excessive entrainment losses.

In some mixer-settler designs, the impeller is arranged both to mix thetwo phases and to provide the necessary energy to transfer the phases fromone stage to the next, in which case it is known as a pump-mix mixer. Thehead required to move a phase from one stage to the next is small, so theimpeller need not be efficient as a pump. Nevertheless, the design of impellersfor the dual purpose of both mixing and pumping is more of an art than ascience. Moreover, in full-scale operation it has been found difficult to startup cascades of pump-mix mixers and achieve equilibrium rapidly. Accord-ingly, this design has primarily found use in small-scale applications in thenuclear and pharmaceutical industries.


Settlers tend to be less varied in their design. They typically comprisea relatively large, shallow tank, rectangular in shape, with an inlet for themixed phases at one end and two outlets for the separated phases atthe other. Various devices are used to introduce the mixed phases gently intothe settler, and to control the flow of the mixed phases while they separate,but these do not change the basic principle of separation under gravity.

The level of the heavy phase outlet within the settler controls the levelof the interface (Fig. 8.8). At the interface, the static pressure due to lightphase above the interface is determined by the density of the light phase, ro,and the depth of the light phase, H. Similarly, the static pressure above theinterface in the overflow leg is determined by the density of the heavy phase,r, and the height h of the weir above the interface. The pressure must be thesame at the same elevation, so h�r=H�ro, or

H ¼ h � ð�=�oÞ (8.14)

Because the difference between the densities of the two phases is oftensmall, and may vary from one stage to the next, H can vary strongly with h.Thus it is often necessary to make the height of the weir adjustable. Similarly,if there are significant differences in flow rate, then the depth of the liquidoverflowing the weir has an effect on h and thus on the height of the interface.

The importance of these considerations is that the shallower the settler,the more difficult the interface control. Shallow settlers are desired becausethey reduce the inventory of the solvent. However, it is possible to make thesettler so shallow that interface control can be lost. In one case, large, shallowsettlers suffered from the effects of wind pressure, that caused such massive

Fig. 8.8 The control of the level of the interface in a settler.


oscillations in the level of the interface that light phase often passed over theheavy phase weir.

The introduction of the mixed phases into the settler has been found tobe important if clean separation is to be ensured. ‘‘Picket fences,’’ verticalplates set at an angle to the flow from the mixer into the settler, have beenused to calm the flow and ensure the spreading of the mixed stream across thewidth of the settler. Various packings have been employed to aid settling, butunder industrial conditions they are liable to clog with adventitious materialor ‘‘third phases.’’

Baffles placed across the settler, of progressively lower height fromentrance to overflow, have been employed to hold back the mixed phases topermit them to separate. The mixed phases will spread rapidly right across asettler unless there is a baffle to hold them back. There have been manyreports of ‘‘wedges’’ of mixed phase in small-scale settlers. These are neverseen in industrial practice because considerations of pressure at a given point,as were used above to determine the height of the interface, show that awedge is inherently unstable.

In one mixer-settler design, the mixed phases flow down a shallowtrough placed over the settler, which gives them an opportunity to coalesceand separate before entering the settler. In this way, the capacity of the settleris markedly increased, with a concomitant reduction in the inventory ofsolvent required for a given duty.

The manner in which individual mixer-settler stages can be linkedtogether to form countercurrent cascades is illustrated in Fig. 8.7. If eachstage is on the same level, then some form of pump must be provided tomove each phase from one stage to the next. As indicated earlier, it issometimes convenient to use the mixer for this duty. Another arrange-ment has the individual stages set at different elevations, so that one phase(usually the phase with the greatest flow rate) can gravitate from one stage tothe next.

8.4.2 Differential Extraction

Thus far we have been concerned with stagewise operations, doing just whatis done in the laboratory when a solvent is mixed with an aqueous phase in aseparatory funnel and allowed to settle before being separated.

While countercurrent cascades can be operated in stages, there is noneed do so. Consider, for instance, pumping the dense phase to the top of atower and letting it flow down against drops of the light phase rising upward.Assuming transfer from the dense to the light phase if the tower were highenough, at the top there would be saturated light phase and at the bottom,depleted heavy phase.


Clearly the concept of a stage has no meaning in such a tower. Instead,we deal with differential transfer units, which are a measure of the change inconcentration per unit of difference in concentration (recall that the rate ofextraction is determined largely by the difference between the actual and theequilibrium concentration of a solute, or ‘‘driving force’’).

At each point in the tower, a component A has an actual concentration[A] and an equivalent equilibrium concentration [A]e. Then the number oftransfer units (NTU) required for the extraction is given a first approx-imation by:

NTU ¼Z½A�f½A�r

d[A]=([A]� [A]e) (8.15)

where [A]f and [A]r are the feed and raffinate concentrations of A respec-tively. This is illustrated in Fig. 8.9. The driving force is [A]� [A]e and theinverse of the driving force is to be integrated between the feed and theraffinate concentrations (not shown in Fig. 8.9).

This integral clearly depends on the slope of the operating line and, asin the case of stagewise operations, if the operating line approaches theequilibrium curve too closely, then the driving force approaches zero andthe inverse becomes very large. That is, when the operating line is close to

Fig. 8.9 Illustration of the determination of the driving force from equilibrium and

operating lines.


the equilibrium curve and there is a pinch point, the number of transfer unitsbecomes large.

Equation 8.15 refers to a single phase, and [A]e is related to [A] at eachpoint via the phase ratio (or operating line, which is the same thing). TheNTU could be calculated for the extract phase instead of the aqueous phase,that is, either from the difference between [AR] and [AR]e or from thatbetween [AE]e and [AE].

Where there is an analytical expression for the equilibrium such asEq. (8.3), then Eq. (8.15) may be integrated directly. Otherwise it is neces-sary to perform the integration numerically or graphically.

Once the number of transfer units has been found, the height of thetower is determined from the product of the number and the height of eachtransfer unit (HTU). The HTU is determined by physical parameters such asthe droplet size, the flow patterns in the tower, and the effect of any packing.These all affect the rate of mass transfer, which is addressed in Chapter 9.Very often the rate of mass transfer cannot be estimated from first princi-ples, and it is necessary to estimate the height by determining the number oftransfer units achieved and then dividing the actual height of the columnemployed by the number of transfer units, i.e.:

HTU ¼ H=NTU (8.16)

where H is the height of the column employed.HTU is subjected to the effects of both radial and axial mixing,

and these are not readily quantified, so scale-up of columns of this kind isoften not based on fundamentals, but rather on correlations determinedfrom detailed studies of several systems in the particular design of columnchosen.

Physically, towers designed for countercurrent contact can be open,but more usually contain some form of packing or plates. The material ofthe packing is chosen so that one phase wets it preferentially, thus increas-ing the surface area for mass transfer. Similarly, the plates are designed tobreakup droplets and increase the surface area. In addition, the contents ofthe tower may be agitated either by an internal agitator or by pulsing thefluids. The energy imparted by agitation or pulsation breaks up the dropletsof the dispersed phase. Again, further details are given in Chapter 9.

When the equilibrium curve is relatively linear, the driving force doesnot vary greatly down the length of the column, and the number of transferunits approaches the number of McCabe-Thiele theoretical stages. In thiscase, it is reasonable to speak of the number of stages in the column, and tocalculate a height equivalent to a theoretical stage (HETS). However, if theequilibrium curve and the operating line are far from parallel, the number of


theoretical stages becomes a poor measure of the column’s performance,and the number of transfer units should be used.

8.5 EXTRACTION EFFICIENCY

Solvent extraction is a kinetic process. The key variables in determining therate of extraction are (1) the displacement of the system from equilibrium,also referred to as the driving force; (2) the area through which mass can betransferred, or the interfacial area; and (3) specific resistances in the inter-facial region, particularly any slow interfacial reactions.

To a lesser extent, the rate is also affected by diffusion through thebulk liquids, but in general industrial practice there is sufficient turbulenceto ensure that the bulk phases are well mixed. There is some control overinterfacial area, though not too much flexibility is available because a verylarge interfacial area is associated with very fine droplets or very thin films.This may result in excessive loss of solvent by entrainment. These aspects areextensively discussed in Chapters 7 and 9.

There is little to be done about the displacement of the system fromequilibrium (although it may be noted that the average displacement ismaximal in a countercurrent cascade). As shown in section 8.4.2, the drivingforce can be increased by reducing the slope of the operating line, i.e., in-creasing the phase ratio y, but this is generally not economical. Very littlecan be done about interfacial resistances once the extraction system has beenchosen, although renewal of the surface during bubble coalescence anddispersion assists in overcoming some forms of this kind of resistance. Thusindustry either has to make the time of contact long enough to ensure thatequilibrium is essentially attained, or it has to accept the inherent ineffi-ciency of a single stage, and employ more stages than would otherwise beneeded. In practice, it employs the latter strategy.

8.5.1 The Efficiency of a Single Stage

Figure 8.5 gives a graphic construction for a series of equations of the typegiven in Eq. (8.11), for a single stage at equilibrium. The same basic equa-tion governs a nonequilibrium stage, that is:

([AR]f � [AR]e)=([AE ]e � [AE ]f ) ¼ � (8.17)

except that the product streams [AR]e and [AE]e are no longer at equilibrium,but are reduced by the inefficiency to [AR]i and [AE]i. This is illustrated inFig. 8.10.


8.5.2 The Efficiency of a Cascade

The concepts of section 8.5.1 are readily extended to determine the efficiencyof a cascade. To illustrate this, the results of calculations identical to those ofTables 8.2 and 8.4, but with an 80% stage efficiency, are given in Table 8.8.The resultant McCabe-Thiele diagram is given in Fig. 8.11.

Comparison with the earlier data for equilibrium conditions shows thatan extra stage is needed. In spite of this, the final raffinate is significantlyhigher than was achieved at 100% extraction efficiency. The influence of theinefficiency is clearly greater the more dilute the solutions.

Figure 8.11 shows how the equilibrium curve ‘‘shrinks’’ in the presenceof inefficiencies. In multicomponent systems where there is mutual inter-ference in extraction by several components, the efficency shrinkage comeson top of the other reductions in the equilibrium curve, and for this reasonthere is stress in such systems on achieving high efficiency.

8.6 SOLVENT LOSSES

Throughout, we have made the tacit assumption that the two phases, whichfor convenience, we have called the aqueous and the organic phases, aretotally immiscible. For many systems this is a reasonable approximation, but

Fig. 8.10 Illustration of the effect of reduced efficiency of extraction.


for some systems mutual miscibility must be taken into account, particularlywhen the primary solute is organic.

The methods for doing so are described in Chapter 9. The basic prin-ciples remain unchanged-the primary difference is the choice of a consistentbasis for calculation, such as a solvent-free basis. Graphic techniques basedon triangular coordinates provide approximate answers, but modern com-putational techniques are to be preferred.

Some consideration should be given at this point to the need to pre-vent loss of the organic phase in the aqueous raffinate. This loss can arise byeither solubility in the aqueous phase or by entrainment of droplets not fullysettled. The solvent lost in this way can offer a finite environmental hazardand be an economic cost on the process.

Clearly the primary duty is good engineering practice, which is coveredespecially in Chapter 9. Often, however, additional security is provided inthe following form:

� Additional settler capacity for final raffinate� Extraction of residual organic phase using a third diluent, from which it

is later separated, typically by distillation� Coalescence on a solid wetted preferentially by the organic phase� Flotation with air in the presence of surfactants

8.7 SUMMARY

In this chapter, we have seen the way in which laboratory studies of solventextraction are adapted to industrial use. Starting from a batch extraction, itwas shown how both recovery and product purity could be markedly influ-enced by the volumetric phase ratio, and how it was impossible to achieveboth high recovery and high purity in a single stage. Cross-flow or repeatedextraction was then evaluated, and it was shown how this could improve

Table 8.8 Extraction at 80% Efficiency, Phase Ratio 2.63

Aqueous Extract

Stage no. Feed Equilibrium Inefficient extract Extract Feed

1 0.105 0.004 0.024 0.037 0.006

2 0.402 0.031 0.105 0.150 0.037

3 0.875 0.284 0.402 0.330 0.150

4 1.038 0.834 0.875 0.392 0.330

5 1.064 1.031 1.038 0.402 0.392


both recovery and purity, yet often resulted in mixed extract solutions thatwere too dilute to be processed without further upgrading.

The concept of countercurrent extraction was then introduced, and itwas shown how the minimum phase ratio for a given degree of extractionwas determined. Countercurrent extraction could yield both high recoveriesand concentrated extracts, but studies on two-component extractions soonshowed that product purity suffered.

This led to the discussion of scrubbing as an essential adjunct tocountercurrent extraction where purity was important, and it was shown thatwashing the extract with a small amount of aqueous phase could improvepurity markedly. Stripping was shown to follow the same underlying prin-ciples as extraction for achieving efficient removal of extracted species, andthe need to choose phase ratios carefully to maximize the concentration ofthe desired species in the strip solution was stressed.

There followed a brief discussion of equipment for carrying out sol-vent extraction in industrial practice, both by stagewise and differentialcontact. Some of the first principles for the design of differential contactorswere outlined and the part played by the efficiency of extraction in con-tinuous equipment was discussed. Finally there was an outline of methodsfor the control of solvent loss which forms probably the most importantenvironmental aspect of the application of solvent extraction.

Fig. 8.11 McCabe-Thiele diagram showing the effect of reduced efficiency of extrac-

tion.


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