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TitlePerry Hambook
TagsMass Fraction (Chemistry) Concentration Solubility Phase (Matter)
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Total Pages109
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DOI: 10.1036/0071511385

Page 54

Equation (15-93) assumes that no solute enters the process with the
extraction solvent and that E i and E j are constant. An alternative
expression can be written in terms of transfer units; however, the cal-
culated results are essentially the same as a function of the number of
stages or the number of transfer units—because the models assume
that both solute i and solute j experience the same mass-transfer resis-
tance. Example results obtained by using Eq. (15-93) are shown in
Fig. 15-27. Note that performance is not uniquely determined by a
given value of αi,j = Ki�Kj = E i�E j, but depends upon the absolute value
of E i, as well. In principle, the purity of solute i in the extract will
approach a maximum value as the number of stages or transfer units

approaches infinity:

Maximum Pi,extract (%) = 100 ÷ �1 + � �
in limit as N → ∞ (15-94)

Of course, this theoretical maximum can never be attained in practice.
Equation (15-94) follows from Eq. (15-93), noting that θj�θi = 1�αij for
N → ∞ as discussed by Brian [Staged Cascades in Chemical Process-
ing (Prentice-Hall, 1972), p. 50]. As noted earlier, the ability to purify
a desired solute is greatly enhanced by using fractional extraction (see
“Fractional Extraction Calculations”).

X″j,feed

X″i,feed

1

αi, j

CALCULATION PROCEDURES 15-51

0

10
20

30
40

50

60
70

80

90
100

0 10 20 30 40 50 60

SEPARATION FACTOR �i,j

S
O

L
U

T
E

P
U

R
IT

Y
I
N

E
X

T
R

A
C

T
(

%
)

0

10

20
30

40

50

60

70

80
90

100

0 10 20 30 40 50 60

SEPARATION FACTOR �i,j

S
O

L
U

T
E

P
U

R
IT

Y
I
N

E
X

T
R

A
C

T
(

%
)

E i = 1.5, N = 5 (constant values)

E i = 5, N = 5 (constant values)

(X''j / X''i)feed = 3.0

(X''j / X''i)feed = 1.0

for (X''j / X''i)feed = 0.33

(X''j / X''i)feed = 3.0

(X''j / X''i)feed = 1.0

for (X''j / X''i)feed = 0.33

FIG. 15-27 Approximate purity of solute i in the extract (Pi,extract) versus separation factor
αi,j for standard extraction involving dilute feeds containing solutes i and j. Results obtained
by using Eq. (15-93). Concentrations are in mass fraction (X″).

CALCULATION PROCEDURES

SHORTCUT CALCULATIONS

Shortcut calculations can be quite useful to the process designer or
run-plant engineer; they may be used to outline process requirements
(stream and equipment sizes) early in a design project, to check the
output of a process simulation program for reasonableness, to help
analyze or troubleshoot a unit operating in the manufacturing plant or
pilot plant, or to help explain performance trends and relationships
between key process variables. In some applications involving dilute

or even moderately concentrated feeds, they also may be used to spec-
ify the final design of an extraction process. In carrying out such cal-
culations, Robbins [Sec. 1.9 in Handbook of Separation Techniques
for Chemical Engineers, Schweitzer, ed. (McGraw-Hill, 1997)] indi-
cates that most liquid-liquid extraction systems can be treated as hav-
ing immiscible solvents (case A), partially miscible solvents with a low
solute concentration in the extract (case B), or partially miscible sol-
vents with a high solute concentration in the extract (case C). These
cases are illustrated in Examples 1 through 3 below.

Page 55

Example 1: Shortcut Calculation, Case A Consider a 100-kg/h
feed stream containing 20 wt % acetic acid in water that is to be extracted with
200 kg/h of recycle MIBK that contains 0.1 wt % acetic acid and 0.01 wt %
water. The aqueous raffinate is to be extracted down to 1% acetic acid. How
many theoretical stages will be required and what will the extract composition
be? The equilibrium data for this system are listed in Table 15-8 (in units of
weight percent). The corresponding Hand plot is shown in Fig. 15-20. The
Hand correlation (in mass ratio units) can be expressed as Y′ = 0.930(X′)1.10, for
X′ between 0.03 and 0.25.

Assuming immiscible solvents, we have

F′ = 100(1 − 0.2) = 80 kg water�h

X′f = �
0
0
.
.
2
8
� = 0.25 kg acetic acid�kg water

X′r = �
0
0
.
.
0
9
1
9

� = 0.01 kg acetic acid�kg water

S′ = 200(1 − 0.001) = 199.8 kg MIBK�h

Y′s = �
1
0
9
.
9
2
.8

� = 0.001 kg acetic acid�kg MIBK

If we assume R′ = F′ and E′ = S′, we can calculate Y′e from Eq. (15-47):

Y′e = = 0.097

Calculate X′1 = (0.097�0.930)1�1.10 = 0.128. Then

m′ = �
d
d

X
Y′


� = (0.930)(1.10)(X′)0.1 for X′ between 0.03 and 0.25

m′1 = 0.833 at X′ = 0.128

m′r = �
d
d

X
Y′


� = K′ = 0.656 for X′ below 0.03

K′s = 0.656 at Y′s = 0.001

E = �m1′mr′� = = 1.85

And N is determined from Fig. 15-24 and Eq. (15-48).

N = = 4.3 theoretical stages

This result is very close to that obtained by using a McCabe-Thiele diagram (Fig.
15-23). From solubility data at Y′ = 0.1039 kg acetic acid/kg MIBK (given in
Table 15-8), the extract layer contains 5.4/85.7 = 0.0630 kg water/kg MIBK, and
Y″e = (0.097)�(1 + 0.097 + 0.063) = 0.084 mass fraction acetic acid in the extract.

For cases B and C, Robbins developed the concept of pseudosolute
concentrations for the feed and solvent streams entering the extractor
that will allow the KSB equations to be used. In case B the solvents are
partially miscible, and the miscibility is nearly constant through the
extractor. This frequently occurs when all solute concentrations are
relatively low. The feed stream is assumed to dissolve extraction sol-
vent only in the feed stage and to retain the same amount throughout
the extractor. Likewise, the extraction solvent is assumed to dissolve
feed solvent only in the raffinate stage. With these assumptions the
primary extraction solvent rate moving through the extractor is

ln ���00
.
.
2
0
5
1



0
0
.
.
0
0
0
0
1
1




0
0
.
.
6
6
5
5
6
6

� �1 − �1.
1
85
� + �1.

1
85
��

�����
ln 1.85

0.739(199.8)
��

80
S&

F&

kg acetic acid
��

kg MIBK
80(0.25) + 199.8(0.001) − 80(0.01)
����

199.8

assumed to be S&, and the primary feed solvent rate is assumed to be
F′. The extract rate E′ is less than S′, and the raffinate rate R′ is less
than F′ because of solvent mutual solubilities.

The slope of the operating line is F′�S′, just as in Eqs. (15-45) and
(15-46), but only stages 2 through r − 1 will fall directly on the operat-
ing line. And X′1 must be on the equilibrium line in equilibrium with
Y′e by definition. One can also calculate a pseudofeed concentration XfB
that will fall on the operating line at Y′n+1 = Y′e as follows:

XfB = X′f + Y′e (15-95)

Likewise, one knows that Y′r will be on the equilibrium line with X′r.
One can therefore calculate a pseudoconcentration of solute in the inlet
extraction solvent YsB that will fall on the operating line where X′n−1 = X′r,
as follows:

YsB = Y′s + X′r (15-96)

For case B, the pseudo inlet concentration XfB can be used in the KSB
equation with the actual value of X′r and E = m′S′�F′ to calculate
rapidly the number of theoretical stages required. The graphical step-
wise method illustrated in Fig. 15-23 also can be used. The operating
line will go through points (X′r, YsB) and (XfB, Y′e) with a slope of F′�S′.

Example 2: Shortcut Calculation, Case B Let us solve the prob-
lem in Example 1 by assuming case B. The solute (acetic acid) concentration is
low enough in the extract that we may assume that the mutual solubilities of the
solvents remain nearly constant. The material balance can be calculated by an
iterative method.

From equilibrium data (Table 15-8) the extraction solvent (MIBK) loss in the
raffinate will be about 0.016/0.984 = 0.0163 kg MIBK/kg water, and the feed sol-
vent (water) loss in the extract will be about 5.4/85.7 = 0.0630 kg water/kg MIBK.

First iteration: Assume R′ = F′ = 80 kg water�h. Then extraction solvent in
raffinate = (0.0163)(80) = 1.30 kg MIBK/h. Estimate E′ = 199.8 − 1.3 = 198.5
kg MIBK�h. Then feed solvent in extract = (0.063)(198.5) = 12.5 kg water/h.

Second iteration: Calculate R′ = 80 − (0.063)(198.7) = 67.5 kg water�h. And
E′ = 199.8 − (0.0163)(67.5) = 198.7 kg MIBK�h.

Third iteration: Converge R′ = 80 − (0.063)(198.7) = 67.5 kg water�h. And Y′e
is calculated from the overall extractor material balance [(Eq. (15-47)]:

Y′e = = 0.0983

Ye = = 0.0846 mass fraction acetic acid in extract

From the Hand correlation of equilibrium data,

Y′e = 0.930(X′)1.10 for X′ between 0.03 and 0.25
The raffinate composition leaving the feed (first stage) is

X′1 = �
1�1.10

= 0.130

m′1 = �
d
d

X
Y
� = (0.930)(1.10)(X′)0.1

0.0983


0.930

0.0983
���
1 + 0.0983 + 0.0630

kg acetic acid
��

kg MIBK

(80)(0.25) + (199.8)(0.001) − (67.5)(0.01)
�����

198.7

F′ − R′


S′

S′ − E′


F′

15-52 LIQUID-LIQUID EXTRACTION AND OTHER LIQUID-LIQUID OPERATIONS AND EQUIPMENT

TABLE 15-8 Water + Acetic Acid + Methyl Isobutyl Ketone Equilibrium Data at 25�C

Weight percent in raffinate X′ Weight percent in extract Y′

Water Acetic acid MIBK Acetic acid Water Acetic acid MIBK Acetic acid

98.45 0 1.55 0 2.12 0 97.88 0
95.46 2.85 1.7 0.0299 2.80 1.87 95.33 0.0196
85.8 11.7 2.5 0.1364 5.4 8.9 85.7 0.1039
75.7 20.5 3.8 0.2708 9.2 17.3 73.5 0.2354
67.8 26.2 6.0 0.3864 14.5 24.6 60.9 0.4039
55.0 32.8 12.2 0.5964 22.0 30.8 47.2 0.6525
42.9 34.6 22.5 0.8065 31.0 33.6 35.4 0.9492

SOURCE: Sherwood, Evans, and Longcor, Ind. Eng. Chem., 31(9), pp. 1144–1150 (1939).

Page 108

on the shape, size, and motion of the dispersed drops. The potential
advantages of this technology include more precise control of drop size
and motion for improved control of mass transfer and phase separation
within an extractor. Potential disadvantages include the requirement for
more complex equipment, difficulties in scaling up the technology to han-
dle large production rates, and safety hazards involved in processing flam-
mable liquids in high-voltage equipment.

A number of different equipment configurations and operating con-
cepts have been proposed. Yamaguchi [Chap. 16 in Liquid-Liquid
Extraction Equipment, Godfrey and Slater, eds. (Wiley, 1994)] classifies
the proposed equipment into three general types: perforated-plate and
spray columns, mixed contactors, and liquid-film contactors. For exam-
ple, Yamaguchi and Kanno [AIChE J., 42(9), pp. 2683–2686 (1996)]
describe an apparatus in which a dc voltage is applied between two elec-
trodes in the presence of a nitrogen gas interface. Aqueous drops form
in the presence of the electric field, and they are first attracted to the
gas-liquid interface. Once the drops contact the interface, the charge on
the drops is reversed, and the drops fall back to coalesce at the bottom
of the vessel. Bailes and Stitt [U.S. Patent 4,747,921 (1988)] describe a
rotating-impeller extraction column containing alternating zones of
high voltage (to promote dispersed drop coalescence) and high-inten-
sity mixing (to promote redispersion of drops). In this design, the elec-
tric field serves to promote drop coalescence so that dispersed drops
experience alternating drop breakup and growth as they move through
the agitated column. Scott and Wham [Ind. Eng. Chem. Res., 28(1), pp.
94–97 (1989)] and Scott, DePaoli, and Sisson [Ind. Eng. Chem. Res.,
33(5), pp. 1237–1244 (1994)] describe a nonagitated apparatus called
an emulsion-phase contactor. This device employs an electric field to
induce formation of a stable emulsion or dispersion band, with clear
organic and aqueous layers above and below. The aqueous phase is fed
to the middle or top of the dispersion band; it flows down through the
band and is removed from a clarified aqueous zone maintained at the
bottom. The lighter organic phase is fed to the bottom; it moves up
through the dispersion band and is removed from the top. The net
result is countercurrent contacting with very high interfacial area and
significantly improved mass transfer in terms of the number of transfer
units achieved for a given contactor height.

Another approach involves electrostatically spraying aqueous solu-
tions into a continuous organic phase to create dispersed drops within a
spray column contactor [Weatherley et al., J. Chem. Technol. Biotech-
nol., 48(4), pp. 427–438 (1990)]. A high voltage is applied between elec-
trodes, one connected to a nozzle where dispersed drops are formed
and the other placed within the continuous organic phase. Petera et al.
[Chem. Eng. Sci., 60, pp. 135–149 (2005)] discuss the modeling of drop
size and motion within such a device. For additional discussion, see
Tsouris et al. [Ind. Eng. Chem. Res., 34(4), pp. 1394–1403 (1995)],
Tsouris et al. [AIChE J., 40(11), pp. 1920–1923 (1994)], Gneist and Bart
[Chem. Eng. Technol., 25(2), pp. 129–133 (2002)], Gneist and Bart
[Chem. Eng. Technol., 25(9), pp. 899–904 (2002)], and Elperin and
Fominykh [Chem. Eng. Technol., 29(4), pp. 507–511 (2006)].

PHASE TRANSITION EXTRACTION
AND TUNABLE SOLVENTS

Phase transition extraction (PTE) involves transitioning between sin-
gle-liquid-phase and two-liquid-phase states to facilitate a desired
separation. Ullmann, Ludmer, and Shinnar [AIChE J., 41(3), pp.
488–500 (1995)] showed that extraction of an antibiotic from fermen-
tation broth into an organic solvent could be improved by transition-
ing across a UCST phase boundary using heating and cooling. The
results showed much higher stage efficiency compared to a standard
extraction technique without phase transition and much faster phase
separation. The phase transition may be induced by a change in tem-
perature or a change in composition through addition and/or removal
of organic solvents or antisolvents [Gupta, Mauri, and Shinnar, Ind.
Eng. Chem. Res., 35(7), pp. 2360–2368 (1996)]. Alizadeh and Ashtari
describe a temperature-induced phase transition process for extracting
silver(I) from aqueous solution using dinitrile solvents [Sep. Purification

Technol., 44, pp. 79–84 (2005)]. Another process that exploits a phase
transition to facilitate separation and recycle of solvent after extraction
utilizes ethylene oxide–propylene oxide copolymers in aqueous two-
phase extraction of proteins [Persson et al., J. Chem. Technol. Biotech-
nol., 74, pp. 238–243 (1999)]. After extraction, the polymer-rich
extract phase is heated above its LCST to form two layers: an aqueous
layer containing the majority of protein and a polymer-rich layer that
can be decanted and recycled to the extraction.

Another approach utilizes pressurized CO2 to control phase splitting
and tune partition ratios in organic-water mixtures. Addition of pres-
surized CO2 yields an organic phase rich in CO2 (the gas-expanded
phase) and an aqueous phase containing little CO2. Adrian, Freitag,
and Maurer [Chem. Eng. Technol., 23(10), pp. 857–860 (2000)] report
data demonstrating the ability to induce phase splitting in the com-
pletely miscible 1-propanol + water system by pressurization with CO2
at near-critical pressures above 74 bar (about 1100 psia). The authors
also show that the partition ratio for transfer of methyl anthranilate
from the aqueous phase to the organic phase can be varied between 1
and about 13 by adjusting pressure and temperature. Jie Lu et al. [Ind.
Eng. Chem. Res., 43(7), pp. 1586–1590 (2004)] demonstrate a reduc-
tion in the lower critical solution temperature for the partially miscible
THF + water system by addition of CO2 at more moderate pressures
(on the order of 10 bar, or about 145 psia). The authors show that the
partition ratio for transfer of a water-soluble dye from the organic
phase to the aqueous phase can be increased dramatically by increas-
ing CO2 pressure. For more detailed discussion of gas-expanded-liquid
techniques used to facilitate various reaction and extraction processes,
see Eckert et al., J. Phys. Chem. B, 108(47), pp. 18108–18118 (2004).

IONIC LIQUIDS

The potential use of ionic liquids for liquid-liquid extraction is gaining
considerable attention [Parkinson, Chem. Eng. Prog, 100(9), pp. 7–9
(2004)]. Ionic liquids are low-melting organic salts that form highly
polar liquids at or near ambient temperature [Rogers and Seddon, Sci-
ence, 302, p. 792 (2003)]. The potential use of ionic liquids to extract
metal ions from aqueous solution is discussed by Visser et al. [Sep. Sci.
Technol., 36(5–6), pp. 785–804 (2001)] and by Nakashima et al. [Ind.
Eng. Chem. Res., 44(12), pp. 4368–4372 (2005)]. In another example,
phenolic impurities are extracted from an organic reaction mixture
using an acidic ionic liquid such as methylimidazolium chloride [BASF
promotional literature (2005)]. After extraction, the extract phase is
separated by evaporation of the phenolic content, and the raffinate
containing the desired product is washed with water to remove small
amounts of ionic liquid that saturate that phase. Other potential appli-
cations are described in Ionic Liquids IIIB: Fundamentals, Challenges,
and Opportunities, Rogers and Seddon, eds. (Oxford, 2005). The pos-
sibility of switching a solvent system from ionic to nonionic states also
is being investigated [Jessop et al., Nature, 436, p. 1102 (2005)]. The
authors report that a 50/50 blend of 1-hexanol and 1,8-diazabicyclo-
[5.4.0]-undec-7-ene (DBU) becomes ionic when CO2 is bubbled
through the solution. The CO2 reacts to form a mixture of 1-hexylcar-
bonate anion and DBUH+ cation, a viscous ionic liquid. The reaction
can be reversed by using N2 to strip the weakly bound CO2 from solu-
tion. This returns the solution to its less viscous, nonionic state and pro-
vides a basis for a switchable solvent system.

The challenges involved in using ionic liquids for extraction appear
similar to those encountered using nonvolatile extractants dissolved in
a diluent, including difficulty dealing with buildup of heavy impurities
in the solvent phase over time. Additionally, solvent stability and
recovery need to be very high for the process to be economical due to
the high cost of makeup solvent. Potential advantages include the pos-
sibility of obtaining higher K values, allowing use of lower solvent-to-
feed ratios, and simplification of extract and raffinate separation
requirements. For example, volatile components may easily be
removed from the ionic liquid by using evaporation under vacuum
instead of multistage distillation; and, in certain cases, the solubility of
ionic liquid in the raffinate may be very low.

EMERGING DEVELOPMENTS 15-105

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