p   psiaPressPresspsiaPressure,   psiasure,   sure,

Lecture

Lecture 5. 5.

( ) ( ) Single Equilibrium Stages (1) Single Equilibrium Stages (1)

[Ch. 4]

[Ch. 4]

[Ch. 4]

[Ch. 4]

• Phase Separation

• Degree of Freedom Analysis

- Gibbs phase rule F  C  P  2

- 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 Phase Separation

• Simplest separation processes

- Two phases in contact  physical equilibrium  phase separation

If th ti f t i l

- If the separation factor is large, a single contact stage may be sufficient

- If the separation factor is not large, p g , ^V/L multiple stages are required

• Separation factor for vapor-liquid equilibrium

L

p p q q

,

( )

LK HK

HK

relative volatility K

  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

Gibbs Phase Rule Gibbs Phase Rule

• Variables

- Intensive variables : Do not depend on system size;

temperature, pressure, phase compositions

E t i i bl : D d t i ;

- Extensive variables : Depend on system size;

mass, moles, energy; mass or molar flow rates, energy transfer rates

f f d

• Degree of freedom, F

Number of independent variables (variance)

• Gibbs phase rule

Relation between the number of independent intensive variables at equilibrium

equilibrium

 2



 C P F

C : Number of components at equilibrium P : Number of phases at equilibrium

Degree of Freedom Analysis (1) Degree of Freedom Analysis (1)

• Gibbs phase rule : consider equilibrium intensive variables only

y_i

Variables

T, P : 2 variables

x_i, y_i, … : C×P variables

Equations

T, P

1 1

C C

i i

x  and y 

 

Equations

1 1

i i

or

L V i

i i i

f  f K  y

x_i ^{i i i}

i

f f

x

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) Degree of Freedom Analysis (2)

• General analysis: consider all intensive and extensive variables Variables

T, P : 2

+

V

y x_i, y_i ,… : C×P

Equations

+

[V, L,…] (C+6 for VLE) y_i

P + C(P-1) equations

q

F

z_i Q

T,P

+

L z_i

T_F P_F

Q

i i i

F V L

Fz Vy Lx

Fh Q Vh Lh

 

  

F = (2+CP) + (C+P+4) – [P+C(P-1)] - (C+1)

= C + 5

x_i

If we consider  F = C + 4

1

1

C i i

z



 

Binary Vapor

Binary Vapor- -Liquid Systems Liquid Systems

• Experimental vapor-liquid equilibrium data for binary Experimental vapor liquid equilibrium data for binary systems (A and B) are widely available

e.g. Perry’s handbook

• Types of equilibrium data - Isothermal : P-y-x

If P d T fi d  h i i l l

Isothermal : P y x - Isobaric : T-y-x

• If P and T are fixed  phase compositions are completely defined

⇒ separation factor (relative volatility for vapor liquid) is

( / ) ( / )

K

⇒ separation factor (relative volatility for vapor-liquid) is also fixed

,

( / ) ( / )

( / ) (1 ) /(1 )

A A A A A

A B

B B B A A

K y x y x

K y x y x

   

 

Examples of Binary System 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

Di till ti ti i i ti l b t 1 000 t i d

- Distillation separation is impractical : about 1,000 trays are required

⇒ Crystallization or adsorption is preferred

Equilibrium Data for Equilibrium Data for Methanol

Methanol- -Water System (1) Water System (1)

250 8

9

Methanol

Methanol Water System (1) Water System (1)

T = 50 ℃ T = 150 ℃

150 200

sure, psia

4 5 6 7 8

sure, psia

0 50 100

Press

0 1 2 3 4

Press

0 0.2 0.4 0.6 0.8 1

Composition

0 0.2 0.4 0.6 0.8 1

Composition

T = 250 ℃

1000 1200 1400

psia

T 250 ℃

• As T becomes higher, relative volatility becomes smaller

200 400 600 800

Pressure, p

y

 Separation becomes difficult

• At 250

C  no separation by

0 200

0 0.2 0.4 0.6 0.8 1

Composition

p y

distillation when x ≥ 0.772

Equilibrium Data for Equilibrium Data for Methanol

Methanol- -Water System (2) Water System (2) Methanol

Methanol Water System (2) Water System (2)

•  (relative volatility) = 1.0

 The separation by distillation is not possible

∵ Th iti f th

∵ The compositions of the

vapor and liquid are identical and two phases become one phase

y_A = x_A T_c (℃) P_c (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 P_c

Phase Equilibrium Diagram Phase Equilibrium Diagram

di t 1 t

Methanol-water system n hexane-n octane system y-x diagram at 1 atm

T-y-x diagram at 1 atm

Dew point

Tie line

P-x diagram at 150 ℃

Bubble point

q

q- -line line

H H H

Fz  Vy  Lx

n hexane-n octane system

 

H

y

F   V L

y-x phase diagram at 1 atm

( / ) 1 1

( / ) ( / )

H H H

y V F x z

V F V F

  

   

 

Feed mixture, F with overall composition z_H = 0.6

F 60 l% i ti

For 60 mol% vaporization, slope = (0.6-1)/0.6 = -2/3

⇒ Equilibrium composition q p from equilibrium curve

: y_H = 0.76 and x_H = 0.37 Slope=0, (V/F)=1 : vapor only Slope=∞, (V/F)=0 : liquid only

y

y- -x Phase Diagram for Constant x Phase Diagram for Constant Relative Volatility

Relative Volatility Relative Volatility Relative Volatility

• Relative volatility

,

/ /

/ (1 ) /(1 )

A A A A

A B

B B A A

y x y x

y x y x

  

 

If _A,B is assumed constant over the entire composition range, the

 x

y-x phase equilibrium curve can be determined using _A,B

) 1 (

1

,



 

B A A

A B A

A

x

y x





sat sat

For an ideal solution, _A,B can be approximated with Raoult’s law

sat B

sat A sat

B sat A B

A B

A

P

P P

P

P P

K

K  

 /

/



Azeotropic

Azeotropic systems (1) systems (1)

• Azeotropes : formed by liquid mixtures exhibiting minimum- or

i b ili i t

maximum-boiling points

- 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 

Azeotropic

Azeotropic systems (2) systems (2)

• Azeotropes limit the separation achievable by ordinary distillation

distillation

⇒ Changing pressure sufficiently : shift the equilibrium to break the azeotrope or move it

break the azeotrope or move it

• Azeotrope formation can be used to achieve difficult separations

separations

An entrainer (MSA) is added

 combining with one or more

 combining with one or more of the components in the feed

 forming a minimum-boiling azeotrope

azeotrope

 recover as the distillate

e g heterogeneous azeotropic e.g. heterogeneous azeotropic distillation: addition of benzene to an alcohol-water mixture