Liquid-Liquid Equilibrium

Ternary System

Most practical situations involving liquid-liquid equilibrium involve
three or more components.

Our attention is with three component systems. In this process, a
solute is removed from a feed stream by contacting it with a solvent.

The solute is quite soluble in the solvent, while the other component
in the feed is less soluble.
ChE 334: Separation Processes
Dr Saad Al-Shahrani
Liquid-Liquid Equilibrium

Terminology

Solute ≡ Component (1)

Original solvent ≡ Component (2)

Extractive solvent ≡ Component (3)

x1S, x2S and x3S are the composition of the three components in (solvent
rich phase) 1,2,3 respectively.

x1R, x2R and x3R are the composition of the Three components in the
(raffinate phase) 1,2,3 respectively.
Feed
(component +original solvent)
Raffinate-rich phase
(x1R1, x2R1 , x3R1)
solvent-rich phase
Extractive solvent
ChE 334: Separation Processes
(x1S1, x2S1 , x3S1)
Dr Saad Al-Shahrani
Liquid-Liquid Equilibrium

The solvent phase is rich in solvent and preferentially soaks up
component 1 (the solute), which we are trying to separate from the
other component in the feed (component 2, raffinate).

The raffinate phase is the liquid phase which is rich in the component
2 (raffinate) and from which the solute (component 1) is being
removed.

The original feed is usually a mixture of solute (component 1) and
raffinate (component 2).

The solvent-rich phase contains mostly solvent (component 3) and
solute (component 1) and only a small amount of raffinate (component
2)

The raffinate-rich phase contains mostly solute (component 1) and
raffinate (component 2), but also possibly some small amount of
solvent.
ChE 334: Separation Processes
Dr Saad Al-Shahrani
Liquid-Liquid Equilibrium
ChE 334: Separation Processes
Dr Saad Al-Shahrani
Liquid-Liquid Equilibrium

Triangular Diagrams

Ternary systems are represented on two types of triangular diagrams:
1. Equilateral triangles
ChE 334: Separation Processes
Dr Saad Al-Shahrani
Liquid-Liquid Equilibrium
2. Right Triangles
ChE 334: Separation Processes
Dr Saad Al-Shahrani
Liquid-Liquid Equilibrium
Mixture [50% Acetic + 20 H2O
+ 30%vinyl acetate
(Solute)
.
Original
solvent
ChE 334: Separation Processes
Extractive
solvent
Dr Saad Al-Shahrani
Liquid-Liquid Equilibrium
b) Liquid-liquid Equilibrium tie lines (LLE Tie lines)

Different chemical systems give different types of triangular diagrams.
ChE 334: Separation Processes
Dr Saad Al-Shahrani
Liquid-Liquid Equilibrium

The phase boundary, called the solubility line, is the solid line. Within
the two-phase region,

liquid-liquid equilibrium lines (the dashed lines) connect compositions
of the two phases that are in equilibrium with each other

The left side of the phase boundary gives the compositions of the
raffinate-rich liquid phase (xjR).

The right side of the phase boundary gives the compositions of the
solvent-rich liquid phase (xjS).

The LLE tie-lines and the equilibrium phase boundary are normally
found by laboratory experimentation.

A mixture that has an overall composition inside the two-phase region
will split into two liquid phases with compositions given at the two ends
of the LLE tie-line.
ChE 334: Separation Processes
Dr Saad Al-Shahrani
Liquid-Liquid Equilibrium

A conjugate line can be used to
locate the tie-lines.

From point A on-the left phase
boundary, the other end of the
tie-line is found by drawing a
horizontal line to the conjugate
line.

A vertical line is then drawn from
the point M intersection to the
right phase boundary. The point
of intersection of this line and
the right phase boundary (point
B in the figure) is the other end
of the tie-line.
ChE 334: Separation Processes
M
Dr Saad Al-Shahrani
Liquid-Liquid Equilibrium

As the system becomes richer in solute, the tie-lines get shorter and
ultimately become just a point at the plait point P. Outside the twophase region, a single, homogeneous liquid phase exists.

Effect of Temperature on solubility

Usually, the solubility increases as the
temperature increases, for this reason,
most liquid-liquid extraction systems
operate at low temperatures and some
times even require refrigeration.

Pressure, on the other hand, has little
effect on solubility.
ChE 334: Separation Processes
Dr Saad Al-Shahrani
Liquid-Liquid Equilibrium

if we specify only one concentration of one liquid phase, all the other
concentrations can be immediately determined from the phase diagram

For example, if we fix the concentration of component 1 in the
raffinate-rich phase (x1R), we can read from the diagram:
1. The concentration of component 3 in the raffinate-rich phase (x3R),
by using the left side of the solubility curve.
2. The concentrations of components 1 and 3 in the solvent-rich phase
that is in equilibrium with the raffinate-rich phase, by going to the other
end of the LLE tie-line. The concentrations x1S and x3S are read from
the right side of the solubility curve.
ChE 334: Separation Processes
Dr Saad Al-Shahrani
Liquid-Liquid Equilibrium
Example: Thirty thousand kg/hr
of a ternary mixture of 19
weight percent isopropyl
alcohol (IPA), 41 weight
percent toluene, and 40
weight percent water are
fed
into
a,
decanter
operating at 25°C. the figure
gives the LLE data for the
system.
Determine
the
compositions and flow rates
of the two liquid streams
leaving the decanter.
ChE 334: Separation Processes
Dr Saad Al-Shahrani
Liquid-Liquid Equilibrium

The overall compositions of the feed
(z1 = 19 percent and z2 = 40
percent)
are
located
on
the
diagram.

The compositions of the two liquid
phases are read off the diagram at
the two ends of the LLE tie-line.

The raffinate-rich phase is 14
percent IPA and 2 percent water
(the rest being toluene).

The
solvent-rich
phase
is
23
percent IPA and 74 percent water.
ChE 334: Separation Processes
Dr Saad Al-Shahrani
Liquid-Liquid Equilibrium
Total mass: 30000 = S + R
Water = (30000)(0.4) = S(0.74) + R(0.02)
Solving the last two equations simultaneously gives
S = 15833 kg/h
R = 14176 kg/h
IPA in = (30000)(0.19) = 5700 kg/h
IPA out = S(0.23) + R(0.14)
= (15833)(0.23) + (14176)(0.14) = 5625 kg/h
The difference is due to the accuracy of reading composition from the diagram
ChE 334: Separation Processes
Dr Saad Al-Shahrani
Liquid-Liquid Extraction

In liquid-liquid extraction, a liquid of two or more components to be
separated is contacted with a second liquid phase, called the solvent,
which is immiscible or partially miscible with one or more components
of the liquid feed.

The simplest liquid-liquid extraction involves only a ternary system. The
feed consists of two miscible components, the carrier (C) and the
solute (A). Solvent (S) is a pure component. Components (C,S) are at
most only partially soluble in each other. Solute (A) is soluble in (C)
and completely or partially soluble in S.

During the extraction process, mass transfer of (A) from the feed to the
solvent occurs, with less transfer of (C) to the solvent, or (S) to the
feed.
ChE 334: Separation Processes
Dr Saad Al-Shahrani
Liquid-Liquid Extraction

Liquid-liquid extraction is used to separate components in situations where:
1. Relative volatilities are quite close to unity ( < 1.1), making distillation
very costly. (Distillation requires tall towers due to the existence of
many trays, and high energy consumption because of high reflux
ratios.)
e.g. A mixture of benzene and cyclohexane. The normal boiling points of these organics
are 80.1°C and 80.7°C, respectively, making their separation by distillation impractical
2. Thermally sensitive components will not permit high enough
temperatures to produce a vapor-liquid system at reasonable pressures
(pressures greater than 10-50 mm Hg).
ChE 334: Separation Processes
Dr Saad Al-Shahrani
Liquid-Liquid Extraction

EQUIPMENT

Different mechanical devices are used in liquid-liquid extraction such as:
1. The simplest is a mixer/settler, or decanter, in which the two liquid
phases are separated.
2. Plate towers, packed towers, and mechanically agitated mixers
(rotating disk contactors)

the number of stages tends to be much smaller than in distillation
columns. This is due to the larger settling times required for liquid-liquid
separation because of the small density differences between the liquid
phases.

Liquid-liquid extraction columns are sometimes operated in a pulsed
mode.
ChE 334: Separation Processes
Dr Saad Al-Shahrani
Liquid-Liquid Extraction
Extractor/stripper process.
ChE 334: Separation Processes
Dr Saad Al-Shahrani
Liquid-Liquid Extraction
1. Mixer/ Settler
Mixing vessel with variable-speed
turbine agitator
ChE 334: Separation Processes
Horizontal gravity-settling vessel.
Dr Saad Al-Shahrani
Liquid-Liquid Extraction
2. Spray column
ChE 334: Separation Processes
Dr Saad Al-Shahrani
Liquid-Liquid Extraction
3. Packed column
Extract
Single-section
cascade
ChE 334: Separation Processes
Two-section
cascade
Dual solvent with
two-section cascade
Dr Saad Al-Shahrani
Liquid-Liquid Extraction
ChE 334: Separation Processes
Dr Saad Al-Shahrani
Liquid-Liquid Extraction
ChE 334: Separation Processes
Dr Saad Al-Shahrani
Liquid-Liquid Extraction

GRAPHICAL MIXING RULES
If we have two streams that contain three components and mix them together.
Let one of these streams be stream A with flow rate FA (kg/h) and composition
x1A, x2A and x3A (weight fractions of components 1,2, and 3), and let the other be
stream FB with corresponding composition x1B, x2B and x3B . The mixed stream
leaving the mixer will have a flow rate FM and composition x1M, x2M and x3M . A
flow diagram is as follows:
FA
x1A, x2A , x3A
FM
x1M, x2M , x3M
FB
x1B, x2B , x3B
ChE 334: Separation Processes
Dr Saad Al-Shahrani
Liquid-Liquid Extraction

To determine the location of the mixture composition on a graph, since there are
three components, only two coordinates are needed to completely specify the
composition of any stream. We can use either right or equilateral triangular plots.

If we use right-triangular plot. locate point A with coordinates (x1A, x2A ) and point
B with coordinates (x1B, x2B). The point M with coordinates (x1M, x2M ) representing
the mixture will lie some place on the graph.
ChE 334: Separation Processes
Dr Saad Al-Shahrani
Liquid-Liquid Extraction

After mixing point M is supposed to lie on a straight line joining the A
and B points. If we can show that the angles  and  in the figure are
equal, then M must lie on a straight line between A and B.

The total mass balance for the system is
(1)

Component balances for components 1 and 2 are
(2)
and
ChE 334: Separation Processes
(3)
Dr Saad Al-Shahrani
Liquid-Liquid Extraction

Rearranging these two equations, we obtain:

Solving for the ratio FAIFB, we have:
or
ChE 334: Separation Processes
Dr Saad Al-Shahrani
Liquid-Liquid Extraction

These two ratios are the tangents of the angles  and , hence, tan 
= tan . Therefore,  = , and we have proven that the line AMB is a
straight line.

The coordinates of the point M can be solved for analytically by using
equations (1), (2), and (3). Alternatively, M can be located graphically
where the distance from the point A to the point M divided by the
distance from the point M to the point B is equal to the ratio FB/FA.
ChE 334: Separation Processes
Dr Saad Al-Shahrani