Dr Saad Al-ShahraniChE 334: Separation Processes

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

THERMODYNAMICS OF SEPARATION OPERATIONS

Dr Saad Al-ShahraniChE 334: Separation Processes

Txy diagramP constant

subcooled

vaporsubcooled

vapor

Pxy diagram(T constant)

> 1.0(+) deviationfrom ideality

THERMODYNAMICS OF SEPARATION OPERATIONS

Dr Saad Al-ShahraniChE 334: Separation Processes

xy diagram,ether P or T= constant

X=y

45 o lin

e

THERMODYNAMICS OF SEPARATION OPERATIONS

Dr Saad Al-ShahraniChE 334: Separation Processes

b) Maximum-Boiling azeotropes

This type of azeotropes occurs due to attraction between the molecules.

< 1(-) deviationfrom ideality Pxy diagram

Txy diagram

THERMODYNAMICS OF SEPARATION OPERATIONS

Dr Saad Al-ShahraniChE 334: Separation Processes

xy diagram

x=y

THERMODYNAMICS OF SEPARATION OPERATIONS

Dr Saad Al-ShahraniChE 334: Separation Processes

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 conditionsolution

At azeotrope x=y

For methanol

EthLEthsatEthEth xPPy EthEth xy

THERMODYNAMICS OF SEPARATION OPERATIONS

Dr Saad Al-ShahraniChE 334: Separation Processes

23.112

7.14 sat

HexHexL P

P

For methanol

HexLHexsatHexHex xPPy

HexHex xy

45.26

7.14 sat

EthEthL P

P

Note: foe ethanol and n-hexane L> 1.0, indicating repulsion (positive deviation from ideality

THERMODYNAMICS OF SEPARATION OPERATIONS

Dr Saad Al-ShahraniChE 334: Separation Processes

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.

THERMODYNAMICS OF SEPARATION OPERATIONS

Dr Saad Al-ShahraniChE 334: Separation Processes

RELATIVE VOLATILITY

The relative volatility is the ratio of K-values

For two component j and k

kLsatk

jLsatj

kk

jj

k

jjk P

Pxyxy

KK

//

, jk

If the system is ideal (i,e. obeys Raoult’s law, i.e. no attraction or

repulsion between molecules or =1.0)

THERMODYNAMICS OF SEPARATION OPERATIONS

Dr Saad Al-ShahraniChE 334: Separation Processes

For component j

PP

xyxPPysatj

jjjsatjj / , 0.1 , jL

PPxyxPPysatk

kkksatkk / , 0.1 , kL

For component k

satk

satj

satk

satj

kk

jjjk P

PPP

PP

xyxy

//

THERMODYNAMICS OF SEPARATION OPERATIONS

Dr Saad Al-ShahraniChE 334: Separation Processes

Relative volatility for binary system

For two components system under equilibrium conditions (j,k):

)1/()1(/

//

jj

jj

kk

jjjk xy

xyxyxy

jjk

jjkj x

xy

)1(1

Solve for yj

This equation is very important in distillation operation

THERMODYNAMICS OF SEPARATION OPERATIONS

Dr Saad Al-ShahraniChE 334: Separation Processes

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).

THERMODYNAMICS OF SEPARATION OPERATIONS

Dr Saad Al-ShahraniChE 334: Separation Processes

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

THERMODYNAMICS OF SEPARATION OPERATIONS

Dr Saad Al-ShahraniChE 334: Separation Processes

For a multi-component system, the relative volatilities are defined with respect to some component, typically the heaviest one.

Relative volatility For a multicomponents system.

If we have multi-components system containing components (1,2,3, H), H is the heaviest one and (1) is the lightest one.

HH

jj

HjH xy

xyKK

//

1

(1) )(111H

HH x

yxy

THERMODYNAMICS OF SEPARATION OPERATIONS

Dr Saad Al-ShahraniChE 334: Separation Processes

THERMODYNAMICS OF SEPARATION OPERATIONS

By the same manner

HHHH xy

xyKK

// 222

2

(2) )(222H

HH x

yxy

HHHH xy

xyKK

// 333

3

(3) )(333H

HH x

yxy ....

.

.

.

.

Dr Saad Al-ShahraniChE 334: Separation Processes

THERMODYNAMICS OF SEPARATION OPERATIONS

HH

jj

H

jjH xy

xyKK

//

(4) )(H

HjjHj xyxy

(5) 1)(1

H

HjjH

n

jj x

yxy

(6) 1/

1

n

jjjH

HH

xxy

Dr Saad Al-ShahraniChE 334: Separation Processes

THERMODYNAMICS OF SEPARATION OPERATIONS

Substitute (6) in (4)

1

n

jjjH

jjHj

x

xy

Dr Saad Al-ShahraniChE 334: Separation Processes

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.

Dr Saad Al-ShahraniChE 334: Separation Processes

THERMODYNAMICS OF SEPARATION OPERATIONS

The lever ruleVap.

yi

V, mol/h

Liq.xi

L, mol/h

F = L + V

zi F = xi L + yi V

liq.phasevap.phase

yzzx

LV

ii

ii

F

zi

Dr Saad Al-ShahraniChE 334: Separation Processes

THERMODYNAMICS OF SEPARATION OPERATIONS

0 1.0

y

Temperature

zi

xT

T1sat

T2sat

The ratio of the product flows

(L,V) is the inverse of the ratio of

the lengths of the lines

connecting the feed mole fraction

of each of the products. This is

known as ”Lever Rule”

Note: the two phases must be under equilibrium conditions

yixi