Lecture 5.
Single Equilibrium Stages (1)
( )
[Ch. 4]
• Phase Separation
• Degree of Freedom Analysis
F C P2
- Gibbs phase rule
- General analysis
• Binary Vapor-Liquid Systems
-
Examples of binary system
Phase equilibrium diagram
q-line
Phase diagram for constant relative volatility
• Azeotropic Systems
Phase Separation
V
• Simplest separation processes
- Two phases in contact  physical
equilibrium  phase separation
- If th
the separation
ti ffactor
t iis llarge, a
single contact stage may be sufficient
- If the separation
p
factor is not large,
g ,
multiple stages are required
V/L
• Separation
factor for vapor-liquid
equilibrium
p
p
q
q
K LK
 LK , HK (relative volatility ) 
K HK
 = 10,000 : almost perfect separation in a single stage
 = 1.10 : almost perfect separation requires hundreds of stages
• Calculation for separation operations : material balances, phase
equilibrium relations, and energy balance
L
Gibbs Phase Rule
• Variables
- Intensive variables : Do not depend on system size;
temperature, pressure, phase compositions
-E
Extensive
t
i variables
i bl : Depend
D
d on system
t
size;
i ;
mass, moles, energy; mass or molar flow rates, energy transfer rates
• Degree off freedom,
f d
F
Number of independent variables (variance)
• Gibbs phase rule
Relation between the number of independent intensive variables at
equilibrium
F C P2
C : Number of components at equilibrium
P : Number of phases at equilibrium
Degree of Freedom Analysis (1)
• Gibbs phase rule : consider equilibrium intensive variables only
Variables
yi
T, P : 2 variables
xi, yi, … : C×P variables
Equations
T, P
C
x
i 1
 1 and
fi  fi
L
xi
i
C
y
i 1
V
i
yi
or K i 
xi
1
P equations
C  (P
1) equations
(P-1)
F = ((2 + CP)) – P – C(P
( - 1)) = C – P + 2
For a binary VLE system (F=2) : given T, P  determine x and y
Degree of Freedom Analysis (2)
• General analysis: consider all intensive and extensive variables
V
yi
Variables
T, P : 2
xi, yi ,… : C×P
+
zi, TF, PF,
F Q,
F,
Q
[V, L,…]
C+P+4 in general
(C+6 for VLE)
q
Equations
F
zi
TF
PF
T,P
P + C(P-1) equations
+
Fzi  Vyi  Lxi
Q
L
xi
C+1 equations
FhF  Q  VhV  LhL
F = (2+CP) + (C+P+4) – [P+C(P-1)] - (C+1)
=C+5
C
If we consider
z
i 1
i
1  F = C + 4
Binary VaporVapor-Liquid Systems
• Experimental vapor-liquid
vapor liquid equilibrium data for binary
systems (A and B) are widely available
e.g. Perry’s handbook
• Types of equilibrium data
P y x
- Isothermal : P-y-x
- Isobaric : T-y-x
• If P and
d T are fixed
fi d  phase
h
compositions
ii
are completely
l l
defined
⇒ separation factor (relative volatility for vapor
vapor-liquid)
liquid) is
also fixed
 A, B
K A ( y A / xA )
( y A / xA )



K B ( yB / xB ) (1  y A ) /(1  x A )
A is the more-volatile
component (yA > xA)
Examples of Binary System
• Water + Glycerol
- Normal boiling point difference : 190 ℃
- Relative volatility : very high
⇒ Good separation in a single equilibrium stage
• Methanol + Water
- Normal boiling point difference : 35.5 ℃
- Relative volatility : intermediate
⇒ About 30 trays are required for an acceptable separation
• p-xylene + m-xylene
- Normal boiling point difference : 0.8 ℃
- Relative volatility : close to 1.0
- Distillation
Di till ti separation
ti iis iimpractical
ti l : about
b t1
1,000
000 ttrays are required
i d
⇒ Crystallization or adsorption is preferred
T = 50 ℃
9
8
7
6
5
4
3
2
1
0
200
150
100
50
0
0
0.2
0.4
0.6
0.8
1
Composition
0
0.2
0.4
0.6
0.8
1
Composition
T = 250 ℃
1400
• As T becomes higher, relative
volatilityy becomes smaller
 Separation becomes difficult
1200
Pressure, p
psia
T = 150 ℃
250
Presssure, psia
Presssure, psia
Equilibrium Data for
MethanolMethanol
-Water System (1)
1000
800
600
400
p
by
y
• At 250 oC  no separation
distillation when x ≥ 0.772
200
0
0
0.2
0.4
0.6
Composition
0.8
1
Equilibrium Data for
MethanolMethanol
-Water System (2)
•  (relative volatility) = 1.0
 The separation by distillation
is not possible
∵ Th
The compositions
iti
off th
the
vapor and liquid are identical
and two phases become one
phase
yA = xA
Tc (℃)
Pc (psia)
0.000
374.1
3,208
0.772
250
1,219
1.000
240
1,154
In industry, distillation
columns operate at pressures
below Pc
Phase Equilibrium Diagram
Methanol-water system
y-x diagram
di
att 1 atm
t
n hexane-n octane system
T-y-x diagram at 1 atm
Dew
point
Tie line
P-x diagram at 150 ℃
Bubble
point
q-line
n hexane-n octane system
y-x phase diagram at 1 atm
Fz H  VyyH  LxH
F V  L
 (V / F )  1 
1
yH  
xH 
zH

(V / F )
 (V / F ) 
Feed mixture, F with overall
composition zH = 0.6
For 60 mol%
F
l% vaporization,
i ti
slope = (0.6-1)/0.6 = -2/3
⇒ Equilibrium
q
composition
p
from equilibrium curve
: yH = 0.76 and xH = 0.37
Slope=0, (V/F)=1 : vapor only
Slope=∞, (V/F)=0 : liquid only
y-x Phase Diagram for Constant
Relative Volatility
• Relative volatility
 A, B
y A / xA
y A / xA


yB / xB (1  y A ) /(1  x A )
If A,B is assumed constant over
the entire composition range, the
y-x phase equilibrium curve can
be determined using A,B
 A, B x A
yA 
1  x A ( A, B  1)
For an ideal solution, A,B can be
approximated with Raoult’s law
 A, B
K A PAsat / P PAsat

 sat
 sat
K B PB / P PB
Azeotropic systems (1)
• Azeotropes : formed by liquid mixtures exhibiting minimum- or
maximum-boiling
i
b ili points
i t
- Homogeneous or heterogeneous azeotropes
Isopropyl ether-isopropyl alcohol
at 101 kPa
Acetone-chloroform at 101 kPa
• Identical vapor and liquid compositions at the azeotropic composition
 all K-values are 1  no separation by ordinary distillation
Azeotropic systems (2)
• Azeotropes limit the separation achievable by ordinary
distillation
⇒ Changing pressure sufficiently : shift the equilibrium to
break the azeotrope or move it
• Azeotrope formation can be used to achieve difficult
separations
An entrainer (MSA) is added
 combining with one or more
of the components in the feed
 forming a minimum-boiling
azeotrope
 recover as the distillate
e.g.
e
g heterogeneous azeotropic
distillation: addition of benzene
to an alcohol-water mixture