SEPARATION PROCESSES
Lecture 2
VAPOR-LIQUID
EQUILIBRIUM
Dr. Ibrahim Suleiman
VAPOR-LIQUID EQUILIBRIUM
The aims of this chapter are:
1. Discuss the nature of equilibrium
2. Discuss the rules that give the number of
independent variables required to determine
equilibrium state
3. Discuss V-L phase behavior
4. Discuss V-L equilibrium calculations
THE NATURE OF EQUILIBRIUM
Macroscopic regime
a. Static conditions in which no changes occur in the
macroscopic properties of the system with time
b. Balance of all potential that may cause change
T, p, and are fixed
THE NATURE OF EQUILIBRIUM
Microscopic regime
Dynamic as the molecules in phase at are not
the same in the same phase at
MEASURE OF COMPOSITION
The mole fra ction 𝑥
𝑛 𝑛̇
𝑥 = =
𝑛 𝑛̇
Where
𝑛 : nu mber of moles of species 𝑖
𝑛 tota l number of moles
𝑛̇ molar flow rate of species 𝑖
𝑛̇ tota l m ola r flow rate
The ma ss fraction 𝑤
𝑚 𝑚̇
𝑤 = =
𝑚 𝑚̇
Where
𝑚 : ma ss of species 𝑖
𝑚 tota l mass
𝑚̇ ma ss flow rate of species 𝑖
𝑚̇ tota l mass flow rate
MEASURE OF COMPOSITION
Molar concentration
Where V is the molar volume
Where q is the volumetric flow rate
The molar mass of the mixture M is given by
Where
is the molar mass of species
THE PHASE RULE
DUHEM’S THEOREM
The degree of freedom, F, for non-reactive systems is
given by the equation
Where
N is the number of species
is the number of phases
F is the number of variables which must be arbitrary
specified in order to fix the intensive state of the
system at equilibrium
RAOULT’S LAW
Consider liquid and vapor phases of N species at
equilibrium at temperature T and pressure p, two
major assumptions are required to reduce VLE
calculations to Raoult’s law:
1. The vapor phase is an ideal gas
This can be applied for low to moderate pressure
systems.
2. The liquid phase is an ideal solution
This can be applied for solutions with chemically
similar species
RAOULT’S LAW
Raoult’s law is given by
(1)
: vapor phase mole fraction of component
: liquid phase mole fraction of component
p: total pressure
: vapor pressure of species
CALCULATIONS OF
The Antoine’s equation can be used to estimate the vapor
pressure of species
(2)
Where
T is the temperature and it can be in or K
are coef ficients available in the literature.
Equation (2) is known as three parameter equation
A two parameter equation is given by
Two points can be used to estimate the parameters such
as critical and boiling points.
PHASE DIAGRAM EQUILIBRIUM
Temperature composition phase diagram
PHASE DIAGRAM EQUILIBRIUM
T-COMPOSITION PHASE DIAGRAM
Som e rem arks:
Line 1 is ca lled dew point cur ve
Line 2 is ca lled bu bble point cu r ve
Consider a bina ry mixture of components 1 & 2, where component 1 is
more volatile tha n component 2.
1. The points on the diagram:
For vaporization at constant p, point “a ” represents a subcooled liquid
mixture
Point “b” represents satura ted liquid mixture
Point “b’” represents satura ted vapor mixture in equilibrium with
sa tu rated liquid mixture at bubble point “b”
Point “c” represents satura ted va por m ixture
Point “c’ ” represents saturated liquid mixture in equilibrium with
sa tu rated vapor mixture at dew point “c”
Point “d” represents superheated va por mixture
2. Point “b” shows bubble point a nd point “c” shows dew point
PHASE DIAGRAM EQUILIBRIUM
T-COMPOSITION PHASE DIAGRAM
3. Upon heating a mixture at point “a” it passes through
points “b, m, c, and d”
4. Any mixture “m” in the two phase region can be
subscribed into a vapor phase of composition
and a liquid phase of composition which are at
equilibrium. The horizontal line that connects with
is called the tie line.
5. The end points represent saturated temperatures of
pure species.
@
@
6. Two phase equilibrium lies between bubble point
and dew point
PHASE DIAGRAM EQUILIBRIUM
P-COMPOSITION PHASE DIAGRAM
Pressure composition phase diagram
PHASE DIAGRAM EQUILIBRIUM
P-COMPOSITION PHASE DIAGRAM
Line 1 is bubble point
Line 2 is dew point
The ef fect of pressure is the opposite to that of
temperature vaporization curves at constant T, when the
pressure is reduced.
For a binary mixture of composition 1 & 2 where
composition 1 is more volatile
1. Points “a, b, b’, c, c’, m, and d” have the same
significance as for temperature composition diagram
2. As pressure is reduced, the mixture moves for
subcooled liquid @ “a” to superheated vapor @ point “d”
in the same way as for temperature effect.
PHASE DIAGRAM EQUILIBRIUM
P-COMPOSITION PHASE DIAGRAM
3. The end points represent saturated pressure of
pure species at the given temperature
@
@
4. Two phase equilibrium lies between bubble
point and dew point
EXAMPLE
BENZENE-TOLUENE PHASE DIAGRAM
X-Y PHASE DIAGRAM
K-VALUE RELATIVE VOLATILIT Y
The K-value reflects the tendency of component to
vaporize. It is a function of temperature, pressure
and composition. It is given by the equation
Also
If the K-vale is high, the component tends to
concentrate in the vapor, if low it tends to concentrate
in the liquid. If K-value is unity, then the component
will split equally between the vapor and the liquid.
K-VALUE RELATIVE VOLATILIT Y
The relative volatility of components is defined as
If the relative volatility is high, the mixture will be easy
to separate
As the relative volatility goes to unity, then the mixture
becomes more difficult to separate
If relative volatility is unity, each component is as
volatile as the other, and they cannot be separated by
distillation
K-VALUE RELATIVE VOLATILIT Y
For a binary mixture
HOW?
Then
This equation expresses the more volatile component
(MVC) mole fraction in the vapor phase as a function of the
MVC in the liquid phase and relative volatility.
K-VALUE RELATIVE VOLATILIT Y
For a binary mixture
HOW?
Then
This equation expresses the more volatile component
(MVC) mole fraction in the vapor phase as a function of the
MVC in the liquid phase and relative volatility.
K-VALUE RELATIVE VOLATILIT Y
EXAMPLE
The following vapor pressure were obtained for
phenol (A) and orthocresol (B). Assume Raoult’s and
Dalton’s laws are applicable. For pressure of 10
kPa, Find:
1. Temperature-composition diagram
2. X-Y diagram T(K) 𝒔𝒂𝒕 𝒔𝒂𝒕
𝑨 𝑩
-X diagram 387 10.00 7.70
388.7 10.80 8.21
390.3 11.60 8.75
391.9 12.40 9.40
393.3 13.30 10.00
SOLUTION
From Raoult’s Law T(K) 𝑨𝑩
387 1 1 1.33
388.7 0.691 0.746 1.315
390.3 0.437 0.506 1.325
Then
391.9 0.200 0.248 1.329
393.3 0 0 1.33
K-VALUE RELATIVE VOLATILIT Y
THE END
Q&A
