THERMODYNAMICS OF
SEPARATION OPERATIONS
 Aseotropes
The increased repulsion between molecules can result in the
formation of an azeotrope, which is a liquid mixture whose
equilibrium vapor has the same composition as the liquid ( i.e. xi =
yi for an azeotrope).
a)
Minimum-Boiling Homogeneous Azeotropes:
This type of azeotropes occurs due to repulsion between the
molecules
ChE 334: Separation Processes
Dr Saad Al-Shahrani
THERMODYNAMICS OF
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
Pxy diagram
(T constant)
> 1.0
(+) deviation
from ideality
Txy diagram
P constant
subcooled
vapor
ChE 334: Separation Processes
vapor
subcooled
Dr Saad Al-Shahrani
THERMODYNAMICS OF
SEPARATION OPERATIONS
xy diagram,
ether P or T= constant
X=y
ChE 334: Separation Processes
Dr Saad Al-Shahrani
THERMODYNAMICS OF
SEPARATION OPERATIONS
b) Maximum-Boiling azeotropes
This type of azeotropes occurs due to attraction between the molecules.
Txy diagram

<1
(-) deviation
from ideality
Pxy diagram
ChE 334: Separation Processes
Dr Saad Al-Shahrani
THERMODYNAMICS OF
SEPARATION OPERATIONS
xy diagram
x=y
ChE 334: Separation Processes
Dr Saad Al-Shahrani
THERMODYNAMICS OF
SEPARATION OPERATIONS
Example:
Ethanol and n-hexane from a minimum boiling point azeotrope at 3.2
mole% ethanol at 58.68 oC and 760 mmHg pressure. The vapor
pressure of ethanol and n-hexane are 6 psia and 12 psia
respectively, at 58.68 oC, determine iL for ethanol and n-hexane at
the azeotropic condition
solution
At azeotrope
x=y
For methanol
sat
PyEth  PEth
xEth EthL
ChE 334: Separation Processes
y Eth  xEth
Dr Saad Al-Shahrani
THERMODYNAMICS OF
SEPARATION OPERATIONS
 EthL 
P
14.7

 2.45
sat
6
PEth
For methanol
sat
PyHex  PHex
xHex HexL
 HexL
y Hex  xHex
P
14.7
 sat 
 1.23
PHex
12
Note: foe ethanol and n-hexane L> 1.0, indicating repulsion (positive
deviation from ideality
ChE 334: Separation Processes
Dr Saad Al-Shahrani
THERMODYNAMICS OF
SEPARATION OPERATIONS
DePriester Charts For Light Hydrocarbons

Figures (a,b) give K-value charts for some Iight hydrocarbons. These
arts do not assume ideal vapor-phase behavior. Some corrections for
pressure effects are included.

Figure (a) is used for low temperatures and Figure (b) high
temperatures.

To find the appropriate K-values, a straight line is drown on the
diagram connecting the temperature and pressure of the system.
intersection of this line with the K-value curve for each hydrocarbons
its K-value at this temperature and pressure.
ChE 334: Separation Processes
Dr Saad Al-Shahrani
THERMODYNAMICS OF
SEPARATION OPERATIONS
RELATIVE VOLATILITY

The relative volatility is the ratio of K-values

For two component j and k
 jk 

Kj
Kk
,
 jk 
yj / xj
y k / xk

Pjsat jL
Pksat kL
If the system is ideal (i,e. obeys Raoult’s law, i.e. no attraction or
repulsion between molecules or =1.0)
ChE 334: Separation Processes
Dr Saad Al-Shahrani
THERMODYNAMICS OF
SEPARATION OPERATIONS
For component j
Py j  Pjsat x j ,
 jL  1.0 ,
yj / xj 
Pjsat
P
For component k
Pyk  P x ,
sat
k
k
 jk
 kL  1.0 ,
Pksat
yk / xk 
P
Pjsat
P


 sat  sat
y k / xk
P Pk
Pk
yj / xj
ChE 334: Separation Processes
Pjsat
Dr Saad Al-Shahrani
THERMODYNAMICS OF
SEPARATION OPERATIONS
Relative volatility for binary system

For two components system under equilibrium conditions (j,k):
 jk 
yj / xj
y k / xk

yj / xj
(1  y j ) /(1  x j )
Solve for yj
 jk x j
yj 
1  ( jk  1) x j

This equation is very important in distillation operation
ChE 334: Separation Processes
Dr Saad Al-Shahrani
THERMODYNAMICS OF
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
Relative volatilities (are essentially constant. In general, they are
functions of temperature and composition.
jk= f ( T and composition)

In most systems, () decreases as temperature increases, which
means that separation of components becomes more difficult.

Therefore, It is often desirable to keep temperatures as low as possible
(use low pressure) to reduce energy consumption.

The following figure shows some VLE curves on an xy diagram for
various values of .

The bigger the relative volatility, the fatter the VLE curve and the easier
the separation (low number of stages required).
ChE 334: Separation Processes
Dr Saad Al-Shahrani
THERMODYNAMICS OF
SEPARATION OPERATIONS

As  → 1.0, the VLE curve approaches the 45o line x = y.

It is impossible to separate components by distillation if the value of 
is too close to unity. Distillation is seldom used if  < 1.0 5.
X
ChE 334: Separation Processes
Dr Saad Al-Shahrani
THERMODYNAMICS OF
SEPARATION OPERATIONS
Relative volatility For a multicomponents system.

For a multi-component system, the relative volatilities are defined with
respect to some component, typically the heaviest one.

If we have multi-components system containing components (1,2,3,
H), H is the heaviest one and (1) is the lightest one.
 jH
yj / xj
K1


KH
yH / xH
yH
y1  1H x1 ( )
xH
ChE 334: Separation Processes
(1)
Dr Saad Al-Shahrani
THERMODYNAMICS OF
SEPARATION OPERATIONS
By the same manner
 2H
K2
y2 / x2


K H y H / xH
yH
y 2   2 H x2 ( )
xH
 3H
K3
y3 / x3


K H y H / xH
yH
y3   3 H x3 ( )
xH
.
.
.
.
ChE 334: Separation Processes
(2)
(3)
.
.
.
.
Dr Saad Al-Shahrani
THERMODYNAMICS OF
SEPARATION OPERATIONS
 jH 
Kj
KH
yj / xj

y H / xH
yH
y j   jH x j ( )
xH
n
 y j   ( jH x j )
j 1
yH / xH 
1

jH
(5)
(6)
n
j 1
ChE 334: Separation Processes
yH
1
xH
(4)
xj
Dr Saad Al-Shahrani
THERMODYNAMICS OF
SEPARATION OPERATIONS
Substitute (6) in (4)
yj 
 jH x j
n

j 1
ChE 334: Separation Processes
jH
xj
Dr Saad Al-Shahrani
THERMODYNAMICS OF
SEPARATION OPERATIONS
Example:
A multi-component liquid mixture has the compositions and relative
volatilities given in the table below. Calculate the composition of the
vapor phase.
ChE 334: Separation Processes
Dr Saad Al-Shahrani
THERMODYNAMICS OF
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Vap.
yi
V, mol/h
The lever rule
F=L+V
F
zi
zi F = x i L + yi V
Liq.
xi
L, mol/h
V x i  z i vap.phase


L zi  yi
liq.phase
ChE 334: Separation Processes
Dr Saad Al-Shahrani
THERMODYNAMICS OF
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The ratio of the product flows
(L,V) is the inverse of the ratio of
T2sat
y
the
lengths
of
the
lines
connecting the feed mole fraction
Temperature
x
T
T1sat
of each of the products. This is
known as ”Lever Rule”
0
xi
zi
yi
Note: the two phases must be under equilibrium conditions
ChE 334: Separation Processes
Dr Saad Al-Shahrani
1.0