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14 EXTRACTION

xtraction is a process whereby a mixture of several substances in the liquid phase is at least partially separated upon addition of a liquid solvent in which E the original substances have different solubilities.

When some of the original substances are solids, the process is called leaching. In a sense, the role of solvent in extraction is analogous to the role of enthalpy in distillation. The solvent-rich phase is called the extract, and the solvent-poor phase is called the raffinate. A high degree of separation may be achieved with several extraction stages in series, particularly in countercurrent flow.

crystallization, or adsorption sometimes are equally possible. Differences in solubility, and hence of separability by extraction, are associated with differences in chemical structure, whereas differences in vapor pressure are the basis of separation by distillation. Extraction often is effective at near-ambient temperatures, a valuable feature in the separation of thermally unstable natural mixtures or pharmaceutical substances such as penicillin.

The simplest separation by extraction involves two substances and a solvent. Equilibria in such cases are represented conveniently on triangular diagrams, either equilateral or right-angled, as for example on Figures 14.1 and 14.2. Equivalent representations on rectangular coordinates also are shown. Equilibria between any number of substances are representable in terms of activity coefficient correlations such as the UNlQUAC or NRTL. In theory, these correlations involve only parameters that are derivable from measurements on binary mixtures, but in practice the resulting accuracy may be poor and some multicomponent equilibrium measurements also should be used to find the parameters. Finding the parameters of these equations is a complex enough operation to require the use of a computer. An extensive compilation of equilibrium diagrams and UNlQUAC and NRTL parameters is that of Sorensen and Ark (1979- 1980). Extensive bibliographies have been compiled by Wisniak and Tamir (1 980- 198 1).

The highest degree of separation with a minimum of

Processes of separation by extraction, distillation,

AND LEACHING

14.1. EQUILIBRIUM RELATIONS

On a ternary equilibrium diagram like that of Figure 14.1, the limits of mutual solubilities are marked by the binodal curve and the compositions of phases in equilibrium by tielines. The region within the dome is two-phase and that outside is one-phase. The most common systems are those with one pair (Type I, Fig. 14.1) and two pairs (Type 11, Fig. 14.4) of partially miscible substances. For instance, of the approximately lo00 sets of data collected and analyzed by Sorensen and Arlt (1979), 75% are Type I and 20% are Type 11. The remaining small percentage of systems exhibit a considerable variety of behaviors, a few of which appear in Figure 14.4. As some of these examples show, the effect of temperature on phase behavior of liquids often is very pronounced.

Both equilateral and right triangular diagrams have the property that the compositions of mixtures of all proportions of two mixtures appear on the straight line connecting the original

solvent is attained with a series of countercurrent stages. Such an assembly of mixing and separating equipment is represented in Figure 14.3(a). and more schematically in Figure 14.3(b). In the laboratory, the performance of a continuous countercurrent extractor can be simulated with a series of batch operations in separatov funnels, as in Figure 14.3(c). As the number of operations increases horizontally, the terminal concentrations E, and R3 approach asymptotically those obtained in continuous equipment. Various kinds of more sophisticated continuous equipment also are widely used in laboratories; some are described by Lo et a/. (1983, pp, 497-506). Laboratory work is of particular importance for complex mixtures whose equilibrium relations are not known and for which stage requirements cannot be calculated.

In mixer-separators the contact times can be made long enough for any desired approach to equilibrium, but 80-90% efficiencies are economically justifiable. If five stages are required to duplicate the performance of four equilibrium stages, the stage efficiency is 80%. Since mixer-separator assemblies take much floor space, they usually are employed in batteries of at most four or five units. A large variety of more compact equipment is being used. The simplest in concept are various kinds of tower arrangements. The relations between their dimensions, the operating conditions, and the equivalent number of stages are the key information.

Calculations of the relations between the input and output amounts and compositions and the number of extraction stages are based on material balances and equilibrium relations. Knowledge of efficiencies and capacities of the equipment then is applied to find its actual size and configuration. Since extraction processes usually are performed under adiabatic and isothermal conditions, in this respect the design problem is simpler than for thermal separations where enthalpy balances also are involved. On the other hand, the design is complicated by the fact that extraction is feasible only of nonideal liquid mixtures. Consequently, the activity coefficient behaviors of two liquid phases must be taken into account or direct equilibrium data must be available.

mixtures. Moreover, the relative amounts of the original mixtures corresponding to an overall composition may be found from ratios of Line segments. Thus, on the figure of Example 14.2, the amounts of extract and raffinate corresponding to an overall composition M are in the ratio E , / R N = M R N / E , M .

Experimental data on only 26 quaternary systems were found by Sorensen and Arlt (1979), and none of more complex systems, although a few scattered measurements do appear in the literature. Graphical representation of quaternary systems is possible but awkward, so that their behavior usually is analyzed with equations. To a limited degree of accuracy, the phase behavior of complex mixtures can be predicted from measurements on binary mixtures, and considerably better when some ternary measurements also are available. The data are correlated as activity coefficients by means of the UNIQUAC or NRTL equations. The basic principle of application is that at equilibrium the activity of each component is the same in both phases. In terms of activity coefficients this

459

460 EXTRACTION AND LEACHING

Solute C A ‘ /

-k -P

G

s m

+ .

qpT\ locus

50 0 $ 40

r” 30 20

10

-

0 0 p, 0 20 40 60 80 100

A-rich

C I (A + C), A-rich phase

(C)

Figure 14.1. Equilibria in a ternary system, type 1, with one pair of partially miscible liquids; A = 1-hexene, B = tetramethylene sulfone, C = benzene, at 50°C (R.M. De Fre, thesis, Gent, 1976). (a) Equilateral triangular plot; point P is at 20% A, 10% B, and 70% C. (b) Right triangular plot with tielines and tieline locus, the amount of A can be read off along the perpendicular to the hypotenuse or by difference. (c) Rectangular coordinate plot with tieline correlation below, also called Janecke and solvent-free coordinates.

condition is for component i,

YJ, = y:x:, (14.1)

where * designates the second phase. This may be rearranged into a relation of distributions of compositions between the phases,

xt = ( Y , / Y : ) ~ , = K,x,, (14.2)

where K, is the distribution coefficient. The activity coefficients are functions of the composition of the mixture and the temperature. Applications to the calculation of stage requirements for extraction are described later.

Extraction behavior of highly complex mixtures usually can be known only from experiment. The simplest equipment for that purpose is the separatory funnel, but complex operations can be simulated with proper procedures, for instance, as in Figure 14.3(c). Elaborate automatic laboratory equipment is in use. One of them employs a 10,000-25,000rpm mixer with a residence time of 0.3-5.0 sec, followed by a highly efficient centrifuge and two chromatographs for analysis of the two phases (Lo et al., 1983, pp. 507).

Compositions of petroleum mixtures sometimes are represented adequately in terms of some physical property. Three examples appear in Figure 14.5. Straight line combining of mixtures still is valid on such diagrams.

Basically, compositions of phases in equilibrium are indicated with tielines. For convenience of interpolation and to reduce the clutter, however, various kinds of tieline loci may be constructed, usually as loci of intersections of projections from the two ends of the tielines. In Figure 14.1 the projections are parallel to the base and to the hypotenuse, whereas in Figures 14.2 and 14.6 they are horizontal and vertical.

Several tieline correlations in equation form have been proposed, of which three may be presented. They are expressed in weight fractions identified with these subscripts:

CA solute C in diluent phase A CS solute C in solvent phase S SS solvent S in solvent phase S AA diluent A in diluent phase A AS diluent A in solvent phase S SA solvent S in diluent phase A.

Solute C

100 0 0 Mol '/o 0 100

Diluent A Solvent B

(a)

0 + 9 m .

20

Tieline \ locus

0 20 40 60 80 100

L -1

C I (A + C), A-rich phase

(C)

Figure 14.2. Equilibria in a ternary system, type 11, with two pairs of partially miscible liquids; A = hexane, B =aniline, C = methylcyclopentane, at 34.5"C [Darwent and Winkler, J . Phys. Chem. 47, 442 (194311. (a) Equilateral triangular plot. (b) Right triangular plot with tielines and tieline locus. (c) Rectangular coordinate plot with tieline correlation below, also called Janecke and solvent-free coordinates.

461

Stoge Stage Stoge 1 2 3

Fin ext

Final roffinote

t

extroctnf\ Settler m2. Settler fill Sett I e r

Final T. 4 roffinote - + I J.

Feed - Solvent

S * Fresh solvent Fa Feed 10 be exlrocfed

R = Raffinofe € 0 Exfrocl

(b ) (C)

Figure 14.3. Representation of countercurrent extraction batteries. (a) A battery of mixers and settlers (or separators). (b) Schematic of a three-stage countercurrent battery. (c) Simulation of the performance of a three-stage continuous countercurrent extraction battery with a series of batch extractions in separatory funnels which are designated by circles on the sketch. The numbers in the circles are those of the stages. Constant amounts of feed F and solvent S are mixed at the indicated points. As the number of operations is increased horizontally, the terminal compositions E, and R , approach asymptotically the values obtained in continuous countercurrent extraction (Treybal, 1963, p . 360).

(a) (b)

Figure 14.4. Less common examples of ternary equilibria and some temperature effects. (a) The system 2,2,4-trimethylpentane + nitroethane + perfluorobutylamine at 25°C; the Roman numerals designate the number of phases in that region [Vreeland and Dunlap, J. Phys. Chem. 61, 329 (1957)l. (b) Same as (a) but at 51.3"C. (c) Gly- col+dodecanol+nitroethane at 24°C; 12 different regions exist at 14°C [Francis, J. Phys. Chem. 60, 20 (1956)). (d) Docosane + furfural + diphenylhexane at several temperatures [Varreressian and Fenrke, Ind. Eng. Chem. 29, 270 (1937)l. (e) Formic acid + benzene + tribromomethane at 70°C; the pair formic acid/benzene is partially miscible with 15 and 90% of the former at equilibrium at 2YC, 43 and 80% at 7 0 T , but completely miscible at some higher temperature. (f) Methylcyclohexane + water + -picoline at 20"C, exhibiting positive and negative tieline slopes; the horizontal tieline is called solutropic (Landolt-Bornstein 1126).

462

a1

14.2. CALCULATION OF STAGE REQUIREMENTS 463

Diphenylhexane

, os

(e) Figure 14.4-(continued)

Ishida, Bull. Chern. SOC. Jpn. 33, 693 (1960): Figure 14.2 is the basis for a McCabe-Thiele construction for finding the number of extraction stages, as applied in Figure 14.7.

14.2. CALCULATION OF STAGE REQUIREMENTS

Although the most useful extraction process is with countercurrent flow in a multistage battery, other modes have some application. Calculations may be performed analytically or graphically. On flowsketches like those of Example 14.1 and elsewhere, a single box represents an extraction stage that may be made up of an individual mixer and separator. The performance of differential contactors such as packed or spray towers is commonly described as the height

xCSxSA/xCAxSS = K ( X A S X S A / X A A X S S ) n ' (14.3)

Othmer and Tobias, Ind. Eng. Chern. 34, 693 (1942):

(14.4) (1 - x S S ) / x S S = K[( l - xAA)/xAAln.

Hand, J . Phys. Chern. 34, 1961 (1930):

(14,5)

These equations should plot linearly on log-log coordinates; they

x C S / x S S = K ( X C A / X A A ) n .

to a stage (HETS) in ft Or m.

are tested in Example 14.1. A system of plotting both binodal and tieline data in terms of 'INGLE STAGE

certain ratios of concentrations was devised by Janecke and is illustrated in Figure 14.1(c). It is analogous to the enthalpy- concentration or Merkel diagram that is useful in solving distillation problems. Straight line combining of mixture compositions is valid in this mode. Calculations for the transformation of data are made most conveniently from tabulated tieline data. Those for Figure 14.1 are made in Example 14.2. The x-y construction shown in

ne material balance is

feed + solvent = extract + raffinate, F + S = E + R. (14.6)

This nomenclature is shown with Example 14.3. On the triangular diagram, the proportions of feed and solvent locate the mix point


\

NITROBENZENE

(a)

PROPANE

0.90 1 .oo 1.10 OIL Specific gravi ty a t 70F ASPHALT

(cl

Figure 14.5. Representation of solvent extraction behavior in terms of certain properties rather than direct compositions [Dunstun et LIZ., Sci. Pet., 1825-1855 (1938)l. (a) Behavior of a naphthenic distillate of VGC = 0.874 with nitrobenzene at 10°C. The viscosity-gravity constant is low for paraffins and high for naphthenes. (b) Behavior of a kerosene with 95% ethanol at 17°C. The aniline point is low for aromatics and naphthenes and high for paraffins. (c) Behavior of a dewaxed crude oil with liquid propane at 70°F, with composition expressed in terms of specific gravity.

M. The extract E and raffinate R are located on opposite ends of the tieline that goes through M.

CROSSCURRENT EXTRACTION

IMMISCIBLE SOLVENTS

The distribution of a solute between two mutually immiscible solvents can be represented by the simple equation,

In this process the feed and subsequently the raffinate are treated in successive stages with fresh solvent. The sketch is with Example 14.3. With a fixed overall amount of solvent the most efficient where process is with equal solvent flow to each stage. The solution of Example 14.3 shows that crosscurrent two stage operation is superior to one stage with the same total amount of solvent.

Y = K'X,

X = mass of solute/mass of diluent, Y = mass of solute/mass of solvent.

(14.7)

14.2. CALCULATION OF STAGE REQUIREMENTS 465

i ne

Figure 14.6. Construction of points on the distribution and operating curves: Line ab is a tieline. The dashed line is the tieline locus. Point e is on the equilibrium distribution curve, obtained as the intersection of paths be and ade. Line Pfg is a random line from the difference point P and intersecting the binodal curve in f and g. Point j is on the operating curve, obtained as the intersection of paths gj and f i j .

When K' is not truly constant, some kind of mean value may be EY, + M k - , = E& + RX,. applicable, for instance, a geometric mean, or the performance of the extraction battery mai be calculated stage by stage with a different value of K' for each. The material balance around the first In terms of the extraction ratio,

stage where the raffinate leaves and the feed enters and an intermediate stage k (as in Fig. 14.8, for instance) is A = K ( E / R ) ,

(14.8)

(14.9)

EXAMPLE 14.1 The Equations for Tieline Data

The tieline data of the system of Example 14.1 are plotted according to the groups of variables in the equations of Ishida, Hand, and Othmer and Tobias with these results:

Ishida: y = ~ . O O X ~ . ~ ' [Eq. (14.3)], Hand: y = 0.07&r1." [Eq. (14.5)], Othmer and Tobias: y = 0 . 8 8 ~ ~ . ~ [Eq. (14.4)J.

The last correlation is inferior for this particular example as the plots show.

XAA

98.945 92.197 83.572 75.356 68.283 60.771 54.034 47.748 39.225

XCA

0.0 6.471

14.612 22.277 28.376 34.345 39.239 42.849 45.594

XSA

1.055 1.332 1.816 2.367 3.341 4.884 6.727 9.403

15.181

xAS

5.615 5.81 1 6.354 7.131 8.376 9.545

11.375 13.505 18.134

xcs

0.0 3.875 9.758

15.365 20.686 26.248 31.230 35.020 39.073

xss

94.385 90.313 83.889 77.504 70.939 64.207 57.394 51.475 42.793

6.34 9.30

16.46 28.90 58.22

119.47 339.77 516.67

1 640

0 0.0088 0.0129 0.021 1 0.0343 0.0581 0.0933 0.1493 0.3040

0.0107 0.0846 0.1966 0.3270 0.4645 0.6455 0.8507 1.0943 1 .5494

0.0595 0.1073 0.1928 0.2903 0.4097 0.5575 0.7423 0.9427 1.3368

0 0.070 0.178 0.296 0.416 0.565 0.726 0.897 1.162

0 0.043 0.116 0.198 0.292 0.409 0.544 0.680 0.913

LOG X . VARIOUS SCALES


EXAMPLE 14.2 Tabulated Tieliie and Distribution Data for the System A = 1-Hexene, B = Tetramethylene Sulfone, C = Benzene, Represented in Figure 14.1

Experimental tieline data in mol %:

Calculated ratios for the Janecke coordinate plot of Figure 14.1:

Left Phase Right Phase

__ B C B C A + C A+C A+C A+C 0.0108 0.0135 0.0185 0.0248 0.0346 0.0513 0.0721 0.1038 0.1790

0 0.0656 0.1488 0.2329 0.2936 0.3625 0.4207 0.4730 0.5375

16.809 9.932 5.190 3.445 2.441 1.794 1.347 1.061 0.748

0 0.4000 0.6041 0.6830 0.7118 0.7333 0.7330 0.7217 0.6830

Left Phase Right Phase

A C B A C B

98.945 92.197 83.572 75.356 68.283 60.771 54.034 47.748 39.225

0.0 6.471

14.612 22.277 28.376 34.345 39.239 42.849 45.594

1.055 1.332 1.816 2.367 3.341 4.884 6.727 9.403

15.181

5.61 5 5.81 1 6.354 7.131 8.376 9.545

11.375 13.505 18.134

0.0 3.875 9.758

15.365 20.686 26.248 31.230 35.020 39.073

94.385 90.313 83.888 77.504 70.938 64.207 57.394 51.475 42.793

The x-y plot like that of Figure 14.6 may be made with the tieline data of columns 5 and 2 expressed as fractions or by projection from the triangular diagram as shown.

the material balance becomes solution for the number of stages is

(A /K)YF + X k - l = A X k + X,,. (14.10)

When these balances are made stage-by-stage and intermediate compositions are eliminated, assuming constant A throughout, the result relates the terminal compositions and the number of stages. The expression for the fraction extracted is

(14.12)

When A is the only unknown, it may be found by trial solution of these equations, or the Kremser-Brown stripping chart may be used. Example 14.4 applies these results.

(14.11) 14.3. COUNTERCURRENT OPERATION

In countercurrent operation of several stages in series, feed enters the first stage and final extract leaves it, and fresh solvent enters the last stage and final raffinate leaves it. Several representations of

This is of the same form as the Kremser-Brown equation for gas abso'rption and stripping and the Turner equation for leaching. The

C Line Equilibrium 4'

I xC

I lperat ibg / A / .ine I

X C R ~ xC F XCR, xc in raffinate

Figure 14.7. Locations of operating points P and Q for feasible, total, and minimum extract reflux on triangular diagrams, and stage requirements determined on rectangular distribution diagrams. (a) Stages required with feasible extract reflux. (b) Operation at total reflux and minimum number of stages. (c) Operation at minimum reflux and infinite stages.

14.3. COUNTERCURRENT OPERATION 467

Figure 14.7-(continued)

such processes are in Figure 14.3. A flowsketch of the process together with nomenclature is shown with Example 14.5. The overall material balance is

F + S = E , + R , = M (14.13)

or

F - E , = R , - S = P. (14.14)

The intersection of extended lines FE, and R,S locates the operating point P. The material balance from stage 1 through k is

F + Ek+l= E , + Rk (14.15)

or

F - E , = Rk - Ektl = P. (14.16)

Accordingly, the raffinate from a particular stage and the extract from a succeeding one are on a line through the operating point P . Raffinate Rk and extract E, streams from the same stage are located at opposite ends of the same tieline.

X ^ -

y i I Y Y I

I I I

J X C R ~ xC F xC R,

xc in raffinate

'C R N 'C F xC R, xc in raffinate

The operation of finding the number of stages consists of a number of steps:

1. Either the solvent feed ratio or the compositions E , and R ,

2. The operating point P is located as the intersection of lines FE,

3. When starting with E , , the raffinate R , is located at the other

4. The line PR, is drawn to intersect the binodal curve in E,.

serve to locate the mix point M.

and R,S.

end of the tieline.

The process is continued with the succeeding values R,, E,, R , , E,, . . . until the final raffinate composition is reached.

When number of stages and only one of the terminal compositions are fixed, the other terminal composition is selected by trial until the stepwise calculation finds the prescribed number of stages. Example 14.6 applies this kind of calculation to find the stage requirements for systems with Types I and I1 equilibria.

Evaluation of the numbers of stages also can be made on rectangular distribution diagrams, with a McCabe-Thiele kind of construction. Example 14.5 does this. The Janecke coordinate plots like those of Figures 14.1 and 14.2 also are convenient when many stages are needed, since then the triangular construction may


EXAMPLE 14.3 Single Stage and Cross Current Extraction of Acetic Acid from Methylisohutyl Ketone with Water

The original mixture contains 35% acetic acid and 65% MIBK. It is charged at 100 kg/hr and extracted with water.

a. In a single stage extractor water is mixed in at 100 kg/hr. On the triangular diagram, mix point M is midway between F and S. Extract and raffinaLe compositions are on the tieline through M. Results read off the diagram and calculated with material

0.5

0

.U F m .- 0 m C ._ c

e

5

c

1

0

u

u m

.- c

.- s c

e L

Acetic acid

-

0.5 1 .o Ketone Mass fraction water

(Acetic acid)

0'5 m Water

0 0.5 1:o

Ketone Mass fraction water Water

balance are

E R Acetic acid 0.185 0.16 MlBK 0.035 0.751

0.78 0.089 Water k d h r 120 80

b. The flowsketch of the crosscurrent process is shown. Feed to the first stage and water to both stages are at 100 kg/hr. The extract and raffinate compositions are on the tielines passing through mix points M I and M2. Point M is for one stage with the same total amount of solvent. Two stage results are:

4 R, 4 Acetic acid 0.185 0.160 0.077 0.058 MlBK 0.035 0.751 0.018 0.902 Water 0.780 0.089 0.905 0.040 k d h r 120 80 113.4 66.6

become crowded and difficult to execute accurately unless a very large scale is adopted. The Janecke method was developed by Maloney and Schubert [Trans. AZChE 36, 741 (1940)]. Several detailed examples of this kind of calculation are worked by Treybal (1963), Oliver (Diffusional Separation Processes, Wiley, New York, 1966), and Laddha and Degaleesan (1978).

MINIMUM SOLVENT/FEED RATIO

Both maximum and minimum limits exist of the solvent/feed ratio. The maximum is the value that locates the mix point M on the binodal curve near the solvent vertex, such as point M,, on Figure 14.7(b). When an operating line coincides with a tieline, the number of stages will be infinite and will correspond to the minimum solvent/feed ratio. The pinch point is determined by the intersection of some tieline with line R,S. Depending on whether the slopes of the tielines are negative or positive, the intersection that is closest or farthest from the solvent vertex locates the operating point for minimum solvent. Figure 14.9 shows the two

cases. Frequently, the tieline through the feed point determines the minimum solvent quantity, but not for the two cases shown.

EXTRACT REFLUX

Normally, the concentration of solute in the final extract is limited to the value in equilibrium with the feed, but a countercurrent stream that is richer than the feed is available for enrichment of the extract. This is essentially solvent-free extract as reflux. A flowsketch and nomenclature of such a process are given with Example 14.7. Now there are two operating points, one for above the feed and one for below. These points are located by the following procedure:

1. The mix point is located by establishing the solvent/feed ratio. 2. Point Q is at the intersection of lines R,M and E,S,, where S,

refers to the solvent that is removed from the final extract, and may or may not be of the same composition as the fresh solvent S. Depending on the shape of the curve, point Q may be inside

14.3. COUNTERCURRENT OPERATION 469

EXTRACT the binodal curve as in Example 14.7, or outside as in Figure

'N- 1' ' i .

FN' 'iN

14.7. 3. Point P is at the intersection of lines R,M and E,S,, where S,

refers to the solvent removed from the extract and may or may not be the same composition as the fresh solvent S.

Determination of the stages uses Q as the operating point until the raffinate composition R, falls below line FQ. Then the operation is continued with operating point P until R, is reached.

MINIMUM REFLUX

For a given extract composition E,, a pinch point develops when an operating line through either P or Q coincides with a tieline. Frequently, the tieline that passes through the feed point F determines the reflux ratio, but not on Figure 14.7(c). The tieline that intersects line FS, nearest point S, locates the operating point Q, for minimum reflux. In Figure 14.7(c), intersection with tieline Fcde is further away from point S, than that with tieline ubQ,, which is the one that locates the operating point for minimum reflux in this case.

RAFFINATE

Figure 14.8. Model for liquid-liquid extraction. Subscript i refers to a component: i = 1,2, . . . , c. In the commonest case, F, is the only feed stream and FN is the solvent, or F, may be a reflux stream. Withdrawal streams U, can be provided at any stage; they are not incorporated in the material balances written here.

MINIMUM STAGES

As the solvent/feed ratio is increased, the mix point M approaches the solvent point S, and poles P and Q likewise do so. At total reflux all of the points P, Q, S, S,, and M coincide; this is shown in Figure 14.7(b).

Examples of triangular and McCabe-Thiele constructions for feasible, total, and minimum reflux are shown in Figure 14.7.

EXAMPLE 14.4 Extraction with an Immiscible Solvent

A feed containing 30wt % of propionic acid and 70wt % trichlorethylene is to be extracted with water. Equilibrium distribution of the acid between water (Y) and TCE ( X ) is represented by Y = K'X, with K' = 0.38. Section 14.3 is used.

a. The ratio EIR of water to TCE needed to recover 95% of the acid in four countercurrent stages will be found:

X , = 30/70, X,, = 1.5170, Ys = 0, @ = (30 - 1.5)/(30 - 0) = 0.95 = (A5 - A / ( A 5 - 1).

By trial,

A = 1.734, EIR =A/K' = 1.73410.38 = 4.563.

b. The number of stages needed to recover 95% of the acid with EIR = 3.5 is found with Eq. 14.12.

A = K'EIR = 0.38(3.5) = 1.330,

n = - l +

@ = 0.95, ln[(A - @M1 - $11 = -1

In A + ln[(1.330 - 0.95)/(1 - 0.95)]/1n(1.330) = 6.11


EXAMPLE 14.5 Countercurrent Extraction Represented on Triangular and Rectangular Distribution Diagrams

The specified feed F and the desired extract E , and raffinate R , compositions are shown. The solvent/feed ratio is in the ratio of the line segments MSIMF, where the location of point M is shown as the intersection of lines E,RN and FS.

Phase equilibrium is represented by the tieline locus. The equilibrium distribution curve is constructed as the locus of intersections of horizontal lines drawn from the right-hand end of a

Rk-1

C

tieline with horizontals from the left-hand end of the tielines and reflected from the 45” line.

The operating curve is drawn similarly with horizontal projections from pairs of random points of intersection of the binodal curve by lines drawn through the difference point P. Construction of these curves also is explained with Figure 14.6.

The rectangular construction shows that slightly less than eight stages are needed and the triangular that slightly more than eight are needed. A larger scale and greater care in construction could bring these results closer together.

F - X Q)

c .- E

Naturally, the latter constructions are analogous to those for distillation since their forms of equilibrium and material balances are the same. References to the literature where similar calculations are performed with Janecke coordinates were given earlier in this section.

Use of reflux is most effective with Type I1 systems since then essentially pure products on a solvent-free basis can be made. In contrast to distillation, however, extraction with reflux rarely is beneficial, and few if any practical examples are known. A related kind of process employs a second solvent to wash the extract countercurrently. The requirements for this solvent are that it be only slighly soluble in the extract and easily removable from the extract and raffinate. The sulfolane process is of this type; it is described, for example, by Treybal (1980) and in more detail by Lo et al. (1983, pp. 541-545).

14.4. LEACHING OF SOLIDS

Leaching is the removal of solutes from admixture with a solid by contracting it with a solvent. The solution phase sometimes is called the overflow, but here it will be called extract. The term underflow or raffinate is applied to the solid phase plus its entrained or occluded solution.

Equilibrium relations in leaching usually are simpler than in liquid-liquid equilibria, or perhaps only appear so because few measurements have been published. The solution phase normally contains no entrained solids so its composition appears on the hypotenuse of a triangular diagram like that of Example 14.8. Data for the raffinate phase may be measured as the holdup of solution by the solid, K Ib solution/lb dry (oil-free) solid, as a function of the concentration of the solution, y Ib oil/lb solution. The correspond-

14.4. LEACHING OF SOLIDS 471

EXAMPLE 14.6 Stage Requirements for the Separation of a Type I and a Type I1 System

a. The system with A = heptane, B = tetramethylene sulfone, and C = toluene at 50°C [Triparthi, Ram, and Bhimeshwara, J . Chem. Eng. Data 20,261 (1975)l: The feed contains 40% C, the extract 70% C on a TMS-free basis or 60% overall, and raffinate 5% C. The construction shows that slightly more than two equilibrium stages are needed for this separation. The compositions of the streams are read off the diagram:

Feed Extract Raffinate

Heptane 60 27 2 TMS 0 13 93 Toluene 40 60 5

20 40 60 80 180 7 -

0 A Mol % B B

The material balance on heptane is

40 = 0.6E + 0.05(100 - E),

whence E = 63.6 lb/100 lb feed, and the TMS/feed ratio is

0.13(63.6) + 0.93(36.4) = 42 lb/100 Ib feed.

b. The type I1 system with A=octane, B =nitroethane, and C = 2,2,4-trimethylpentane at 25°C [Hwa, Techo, and Ziegler, J . Chem. Eng. Datu 8, 409 (1963)l: The feed contains 40% TMP, the extract 60% TMP, and the raffinate 5% TMP. Again, slightly more than two stages are adequate.

C E.

Mol % B A

ing weight fraction of oil in the raffinate or underflow is

x = K y / ( K + 1). (14.17)

Since the raffinate is a mixture of the solution and dry solid, the equilibrium value in the raffinate is on the line connecting the origin

C

B

with the corresponding solution composition y, at the value of x given by Eq. (14.17). Such a raffinate line is constructed in Example 14.8.

Material balance in countercurrent leaching still is represented by Eqs. (14.14) and (14.16). Compositions R, and E k f l are on a line through the operating point P, which is at the intersection of

L

A

Figure 14.9. Minimum solvent amount and maximum extract concentration. Determined by location of the intersection of extended tielines with extended line R,S. (a) When the tielines slope down to the left, the furthest intersection is the correct one. (b) When the tielines slope down to the right, the nearest intersection is the correct one. At maximum solvent amount, the mix point M,,, is on the binodal curve.


EXAMPLE 14.7 Countercurrent Extraction Employing Extract Reflux

The feed F, extract E , , and raffinate R N are located on the triangular diagram. The ratio of solvent/feed is specified by the location of the point M on line SF.

Other nomenclature is identified on the flowsketch. The solvent-free reflux point R , is located on the extension of line S E I . Operating point Q is located at the intersection of lines SR, and RNM. Lines through Q intersect the binodal curve in compositions of raffinate and reflux related by material balance: for instance, R, and E,+, . When the line Q F is crossed, further constructions are

L

made with operating point P, which is the intersection of lines FQ and SRN.

In this example, only one stage is needed above the feed F and five to six stages below the feed. The ratio of solvent to feed is

S / F = FM/MS = 0.196,

and the external reflux ratio is

r = E,, /E, , = (R,S/R,E,)(QE,/SQ) = 1.32.

Solvent Removal

I Solvent

Reflux

'Pgdduct

RN-F R, S Solvent

Flowsketch and triangular diagram construction with extract reflux.

EXAMPLE 14.8 Leaching of an Oil-Bearing Solid in a Countercurrent Battery

Oil is to be leached from granulated halibut livers with pure ether as solvent. Content of oil in the feed is 0.32Ib/Ib dry (oil-free) solids and 95% is to be recovered. The economic upper limit to extract concentration is 70% oil. Ravenscroft [Znd. Eng. Chem. 28, 851 (1934)l measured the relation between the concentration of oil in the solution, y , and the entrainment or occlusion of solution by the solid phase, K Ib solution/lb dry solid, which is represented by the equation

K = 0.19 + 0.126~ + 0.810y2.

The oil content in the entrained solution then is given by

x = K / ( K + l)y, wt fraction,

and some calculated values are

y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 x 0 0.0174 0.0397 0.0694 0.1080 0.1565 0.2147 0.2821 0.3578

Points on the raffinate line of the triangular diagram are located on lines connecting values of y on the hypotenuse (solids-free) with the origin, at the values of x and corresponding y from the preceding tabulation.

Feed composition is xF = 0.3211.32 = 0.2424. Oil content of extract is y, = 0.7. Oil content of solvent is y , = 0. Amount of oil in the raffinate is 0.32(0.05) = 0.016 Ib/lb dry, and the corresponding entrainment ratio is

KN = 0.016/yN = 0.19 + 0 . 1 2 6 ~ ~ + 0.81~5.

14.5. NUMERICAL CALCULATION OF MULTICOMPONENT EXTRACTION 473

EXAMPLE 14.&(continued)

Solving by trial,

yN = 0.0781, KN = 0.2049, xN = 0.0133 (final raffinate composition).

The operating point P is at the intersection of lines FE, and SR,. The triangular diagram construction shows that six stages are needed.

The equilibrium line of the rectangular diagram is constructed with the preceding tabulation. Points on the material balance line

are located as intersections of random lines through P with these results:

Y O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 x 0.013 0.043 0.079 0.120 0.171 0.229 0.295 0.368

The McCabe-Thiele construction also shows that six stages are needed.

Point P is at the intersection of lines E,F and SR,. Equilibrium compositions are related on lines through the origin, point A. Material balance compositions are related on lines through the operating point P.

S

lines FE, and SR,. Similarly, equilibrium compositions R, and E, are on a line through the origin. Example 14.8 evaluates stage requirements with both triangular diagram and McCabe-Thiele constructions. The mode of construction of the McCabe-Thiele diagram is described there.

These calculations are of equilibrium stages. The assumption is made that the oil retained by the solids appears only as entrained solution of the same composition as the bulk of the liquid phase. In some cases the solute may be adsorbed or retained within the interstices of the solid as solution of different concentrations. Such deviations from the kind of equilibrium assumed will result in stage efficiencies less than 100% and must be found experimentally.

14.5. NUMERICAL CALCULATION OF MULTICOMPONENT EXTRACTION

Extraction calculations involving more than three components cannot be done graphically but must be done by numerical solution of equations representing the phase equilibria and material balances over all the stages. Since extraction processes usually are adiabatic and nearly isothermal, enthalpy balances need not be made. The solution of the resulting set of equations and of the prior determination of the parameters of activity coefficient correlations requires computer implementation. Once such programs have been developed, they also may be advantageous for ternary extractions,


particularly when the number of stages is large or several cases must be worked out. Ternary graphical calculations also could be done on a computer screen with a little effort and some available software.

The notation to be used in making material balances is shown on Figure 14.8. For generality, a feed stream Fk is shown at every stage, and a withdrawal stream u k also could be shown but is not incorporated in the balances written here. The first of the double subscripts identifies the component i and the second the stage number k ; a single subscript refers to a stage.

For each component, the condition of equilibrium is that its activity is the same in every phase in contact. In terms of activity coefficients and concentrations, this condition on stage k is written:

Y%ik = y$zk (14.18)

(14.19)

where

Kik = %/r,“, (14.20)

is the distribution ratio. The activity coefficients are functions of the temperature and the composition of their respective phases:

(14.21) (14.22)

The most useful relations of this type are the NRTL and UNIQUAC which are shown in Table 14.1.

Around the kth stage, the material balance is

When combined with Eq. (14.19), the material balance becomes

R k - l X i , k - l - (Rk + EkKik)xik + E k + l K i , k + l X i , k + l = -Fkzik.

(14.24)

In the top stage, k = 1 and R, = 0 so that

- ( R l + VIK,&il + E , K i g i 2 = - F I z i l . (14.25)

In the bottom stage, k = N and E N + ] = 0 so that

RN-lxz ,N-I - (RN + ENKL”XtN = -FNz,N.

The overall balance from stage 1 through stage k is

(14.26)

which is used to find raffinate flows when values of the extract flows have been estimated.

For all stages for a component i, Eqs. (14.24)-(14.26) constitute a tridiagonal matrix which is written

Bl Cl l2 2 BN-l C, cN-I ][: xrN-l ] = [ DN-l ] (14.28)

AN BN xzN D N

When all of the coefficients are known, this can be solved for the concentrations of component i in every stage. A straightforward method for solving a tridiagonal matrix is known as the Thomas algorithm to which references are made in Sec. 13.10, “Basis for Computer Evaluation of Multicomponent Separations: Specifi- cations. ”

INITIAL ESTIMATES

Solution of the equations is a process in which the coefficients of Eq. (14.28) are iteratively improved. To start, estimates must be made of the flow rates of all components in every stage. One procedure is to assume complete removal of a ‘‘light’’ key into the extract and of the “heavy” key into the raffinate, and to keep the solvent in the extract phase throughout the system. The distribution of the keys in the intermediate stages is assumed to vary linearly, and they must be made consistent with the overall balance, Eq. (14.27), for each component. With these estimated flowrates, the values of xik and yik are evaluated and may be used to find the activity coefficients and distribution ratios, K i k . This procedure is used in Example 14.9.

PROCEDURE

The iterative calculation procedure is outlined in Figure 14.10. The method is an adaptation to extraction by Tsuboka and Katayama (1976) of the distillation calculation procedure of Wang and Henke [Hydrocurb. Proc. 45(8), 155-163 (1967)]. It is also presented by Henley and Seader (1981, pp. 586-594).

1.

2.

3.

4.

5.

6.

-

The initial values of the flowrates and compositions xik and yik are estimated as explained earlier. The values of activity coefficients and distribution ratios are evaluated. The coefficients in the tridiagonal matrix are evaluated from Eqs. (14.24)-(14.26). The matrix is solved once for each component. The computed values of iteration ( r + 1) are compared with those of the preceding iteration as

C N z1 E -x i : ) [ 5 = 0.01NC. (14.29)

i=l k = l

The magnitude, O.OlNC, of the convergence criterion is arbitrary. For succeeding evaluations of activity coefficients, the values of the mol fractions are normalized as

(14.30)

When the values of xik have converged, a new set of yik is calculated with

y rk = K . G . I rk‘ (14.19)

.I. A new set of extract flow rates is calculated from

C

E t + ’ ) = E f ) 2 yikt i=1

where s is the outer loop index number.

(14.31)

14.5. NUMERICAL CALCULATION OF MULTICOMPONENT EXTRACTION 475

TABLE 14.1. NRTL and UNIQUAC Correlations for Activity Coefficients of Three- Component Mixturesa

1 X1512G12 + x3s32G32

xlG12 + x2 X3G32 5 i 2 -

X2Gi2 -I

Gl2xl -k x2 + G32X3

r . . = 0

G;;= 1

UNIQUAC

6; ei @i

xi 9; xi In yi = In- + 5qi In- + 1; - - (x1Il + x212 + x313) + qi[ 1 - ln(Olrli + 02r2 + 83qi)]

'NRTL equation: There is a pair of parameters gik and gkj for each pair of substances in the mixture; for three substances, there are three pairs. The other terms of the equations are related to the basic ones by

Tjk = gjk/RT, G. I* = exp(-aikrik).

For liquid-liquid systems usually, a;., 3 0.4.

the mixture: UNIQUAC equation: There is a pair of parameters uik and uki for each pair of substances in

tik = exp(-uik/RT).

The terms with single subscripts are properties of the pure materials which are usually known or can be estimated.

The equations are extended readily to more components. (See, for example, Walas, Phase Equilibria in Chemical Engineering, Butterworths, 1985).

8. The criterion for convergence is 9. I f convergence has not been attained, new values of Rk are

10. Distribution ratios K,, are based on normalized values o f xik

The magnitude, 0.01N, of the convergence criterion i s 11. The iteration process continues through the inner and outer

N calculated from Eq. (14.27). Tz = (1 - ~ j s ) / ~ j s + l ) ) ~ 5 E* = 0 . 0 1 ~ . (14.32)

k = l and y,,.

arbitrary. loops.


EXAMPLE 14.9 Trial Estimates and Converged Flow Rates and Compositions in All Stages of an Extraction Battery for a Four-Component Mixture

Benzene is to be recovered from a mixture with hexane using aqueous dimethylformamide as solvent in a five-stage extraction battery. Trial estimates of flow rates for starting a numerical solution are made by first assuming that all of the benzene and all of the solvent ultimately appear in the extract and all of the hexane appears in the raffinate. Then flow rates throughout the battery are assumed to vary linearly with stage number. Table 1 shows these estimated flowrates and Table 2 shows the corresponding mol fractions. Tables 3 and 4 shows the converged solution made by Henley and Seader (1981, p. 592); they do not give any details of the solution but the algorithm of Figure 14.10 was followed.

TABLE 1. Estimated mol/hr

Extract Raffhate

Stage Total H 6 D W Total H 6 D W

0 - 1 1100 0 100 750 250 400 300 100 0 0 2 1080 0 80 750 250 380 300 80 0 0 3 1060 0 60 750 250 360 300 60 0 0 4 1040 0 40 750 250 340 300 40 0 0 5 1020 0 20 750 250 320 300 20 0 0

N + 1 1000 0 0 750 250 300 300 0 0 0

TABLE 2. Estimated Mol Fractions

1 0.0 0.0909 0.6818 0.2273 0.7895 0.2105 0.0 0.0 2 0.0 0.0741 0.6944 0.2315 0.8333 0.1667 0.0 0.0 3 0.0 0.0566 0.7076 0.2359 0.8824 0.1176 0.0 0.0 4 0.0 0.0385 0.7211 0.2404 0.9375 0.0625 0.0 0.0 5 0.0 0.0196 0.7353 0.2451 1.0000 0.0 0.0 0.0

TABLE 3. Converged Mol Fractions

h 51 Stage j H B D W H B D W

1 0.0263 0.0866 0.6626 0.2245 0.7586 0.1628 0.0777 0.0009 2 0.0238 0.0545 0.6952 0.2265 0.8326 0.1035 0.0633 0.0006 3 0.0213 0.0309 0.7131 0.2347 0.8858 0.0606 0.0532 0.0004 4 0.0198 0.0157 0.7246 0.2399 0.9211 0.0315 0.0471 0.0003 5 0.0190 0.0062 0.7316 0.2432 0.9438 0.0125 0.0434 0.0003

TABLE 4. Converged mol/hr

Extract Raffinate

Hexane 29.3 270.7 Benzene 96.4 3.6 DMF 737.5 12.5 Water 249.0 0.1

Total 1113.1 286.9 - -

Solutions of four cases of three- and four-component systems are presented by Tsuboka and Katayama (1976); the number of outer loop iterations ranged from 7 to 41. The four component case worked out by Henley and Seader (1981) is summarized in Example 14.9; they solved two cases with different water contents of the solvent, dimethylformamide.

14.6. EQUIPMENT FOR EXTRACTION

Equipment for extraction and leaching must be capable of providing intimate contact between two phases so as to effect transfer of solute between them and also of ultimately effecting a complete separation of the phases. For so general an operation, naturally a substantial variety of equipment has been devised. A very general classification of equipment, their main characteristics and industrial applications is in Table 14.2. A detailed table of comparisons and ratings of 20 kinds of equipment on 14 characteristics has been prepared by Pratt and Hanson (in Lo et al., 1983, p. 476). Some comparisons of required sues and costs are in Table 14.3.

Selected examples of the main categories of extractors are represented in Figures 14.11-14.15. Their capacities and performance will be described in general terms insofar as possible, but sizing of liquid-liquid extraction equipment always requires some pilot plant data or acquaintance with analogous cases. Little detailed information about such analogous situations appears in the open literature. Engineers familiar with particular kinds of equipment, such as their manufacturers, usually can predict performance with a minimum amount of pilot plant data.

Literature data is almost entirely for small equipment whose capacity and efficiency cannot be scaled up to commercial sizes, although it is of qualitative value. Extraction processes are sensitive because they operate with small density differences that are sensitive to temperature and the amount of solute transfer. They also are affected by interfacial tensions, the large changes in phase flow rates that commonly occur, and even by the direction of mass transfer. For comparison, none of these factors is of major significance in vapor-liquid contacting.

CHOICE OF DISPERSE PHASE

Customarily the phase with the highest volumetric rate is dispersed since a larger interfacial area results in this way with a given droplet sue. In equipment that is subject to backmixing, such as spray and packed towers but not sieve tray towers, the disperse phase is made the one with the smaller volumetric rate. When a substantial difference in resistances of extract and raffinate films to mass transfer exists, the high phase resistance should be compensated for with increased surface by dispersion. From this point of view, Laddha and Degaleesan (1978, pp. 194) point out that water should be the dispersed phase in the system water + diethylamine + toluene. The dispersed phase should be the one that wets the material of construction less well. Since the holdup of continuous phase usually is greater, the phase that is less hazardous or less expensive should be continuous. It is best usually to disperse a highly viscous phase.

extraction and leaching e separated upon addition … and leaching... · 14 extraction xtraction is...

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