Dr Saad Al-ShahraniChE 334: Separation Processes Aseotropes The increased repulsion between...

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


Txy diagramP constant

subcooled

vaporsubcooled

vapor

Pxy diagram(T constant)

> 1.0

(+) deviation

from ideality



xy diagram,ether P or T= constant

X=y

45 o lin

e



b) Maximum-Boiling azeotropes

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

< 1

(-) deviation

from ideality Pxy diagram

Txy diagram



xy diagram

x=y



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

EthLEthsatEthEth xPPy

EthEth xy



23.112

7.14

satHex

HexL P

P

For methanol

HexLHexsatHexHex xPPy

HexHex xy

45.26

7.14

satEth

EthL P

P

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



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.



RELATIVE VOLATILITY

The relative volatility is the ratio of K-values

For two component j and k

kLsatk

jLsatj

kk

jj

k

jjk P

P

xy

xy

K

K

/

/ , jk

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

repulsion between molecules or =1.0)



For component j

P

PxyxPPy

satj

jjjsatjj / , 0.1 , jL

P

PxyxPPy

satk

kkksatkk / , 0.1 , kL

For component k

satk

satj

satk

satj

kk

jjjk P

P

P

P

P

P

xy

xy

/

/



Relative volatility for binary system

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

)1/()1(

/

/

/

jj

jj

kk

jjjk xy

xy

xy

xy

jjk

jjkj x

xy

)1(1

Solve for yj

This equation is very important in distillation operation



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).



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



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

xy

K

K

/

/1

(1) )(111H

HH x

yxy




By the same manner

HHHH xy

xy

K

K

/

/ 2222

(2) )(222H

HH x

yxy

HHHH xy

xy

K

K

/

/ 3333

(3) )(333H

HH x

yxy

.

.

.

.

.

.

.

.



HH

jj

H

jjH xy

xy

K

K

/

/

(4) )(H

HjjHj x

yxy

(5) 1)(1

H

HjjH

n

jj x

yxy

(6) 1

/

1

n

jjjH

HH

xxy



Substitute (6) in (4)

1

n

jjjH

jjHj

x

xy



Example:

A multi-component liquid mixture has the compositions and relative

volatilities given in the table below. Calculate the composition of the

vapor phase.



The lever ruleVap.

yi

V, mol/h

Liq.

xi

L, mol/h

F = L + V

zi F = xi L + yi V

liq.phase

vap.phase

yz

zx

L

V

ii

ii

F

zi



0 1.0

y

Temperature

zi

x

T

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

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