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Wh

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6

Two important questions in separation processes

1. How much separating agent is required?

2. How fast can the separation be achieved?The keys to these questions are the mass balance

analysis.

Processing methods

1. Single-stage process (batchwise or continuously)2. Multiple-stage process (batchwise or continuously)

Equilibrium relations between phases1. Phase rule and equilibrium

2. Gas-liquid equilibrium

7/31/2019 221-02

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Ap

licati n of epar

7

tion roce ses

8

7/31/2019 221-02

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Dist

lled ater

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Typ

(1)

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(2)

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ater

7/31/2019 221-02

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Pha

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15

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Single

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7/31/2019 221-02

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Equ

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Multip

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17

eratio

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18

Different Representation of VLE Data

(1) Ideal solution & Raoult's Law:

Raoult's Law states that, for an ideal solution, the

equilibrium partial pressure of a component at a fixed

temperature T equals the product of its vapor pressure

(when it is pure) and its mole fraction in the liquid:

For component A,

PA = YAPT = PA*XAYA = (PA*/PT)XA

where

PA = equilibrium partial pressure of component-A

in the gas at temperature T

PA* = vapor pressure of pure liquid A at temperature T

XA

= liquid-phase mole fraction of component-A

at temperature TYA = gas-phase mole fraction of component-A

at temperature T

PT = system total pressure

Note: The vapor pressure is a constant at constant

temperature.

Hence, from the equation, we see that Raoult's Law

predicts a linear equilibrium relationship between P

and X.

7/31/2019 221-02

8/15

Vap

whe

The

solu

Com

Benz

Etha

n-he

Tolu

Wate

r pres

Antoi

e A, B

consta

ion is

ound

ene

ol

tane

ne

r

ures o

e Equ

ln P

and C

nt-te

hown

f pure

ation:

are co

perat

in the

A

13.85

16.67

13.85

14.00

16.2

19

liquid

nstant

re ph

igure

94 27

58 36

87 29

98 31

62 37

an be

/

.

se di

below.

B

73.78

74.49

91.32

03.01

99.89

estima

gram

C

220.07

226.45

216.64

219.79

226.35

ed usi

for an

g

deal

20

For a binary mixture of A and B;

PA = PA*XA ; PB = PB*XB = PB*(1 - XA)

The partial pressures PA and PB vary linearly with XA.

This is shown as PA vs. X and PB vs. X respectively in

the Figure.

For ideal gas mixture, the total pressure is the sum of

the partial pressures.

Total pressure PT = PA + PB

Replacing for the partial pressures and re-arrange, we

have:

PT = ( PA* - PB* ) XA + PB*

The total pressure varies linearly with XA . This is

shown as PT vs. X in the Figure.

In addition, PA = YA PT thus PA*XA = YA PT, and we

have:

Substitute into earlier equation to remove XA:

7/31/2019 221-02

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21

PT PA* = (PA* - PB* ) ( YA PT ) + PA* PB*

PT PA* - (PA* - PB* ) ( YA PT ) = PA* PB*

The total pressure varies nonlinearly with YA. This isshown as PT vs. Y in the Figure.

Also, since PA* XA = YA PT ; we have ,

All the above equations are useful in determining the

equilibrium variables X and Y.

Boiling Points of Mixture of Liquids

Even at constant pressure, depending on relative

concentrations of each component in the liquid, many

boiling point temperatures are possible for mixture of

liquids (solutions). For mixture, we use the term bubble

point when the liquid starts to boil, and dew point

when the vapor starts to condense. For liquid solution,bubble points need not be the same as dew points.

Indeed, boiling of a liquid mixture takes place over a

range of boiling points. Likewise, condensation of a

vapor mixture takes place over a range of condensation

points.

Pha

e Dia ram (pressur

22

is constant):

7/31/2019 221-02

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Idea

l Solut on: be zene

23

nd tol ene

24

Example 1: Determine the T-x-y relationship for

ethanol and water using Antoine Equation assuming

that ethanol-water form an ideal solution. Plot the

resulting data. Please use ambient pressure.

Solution: Ambient pressure = 101.3 kPa

Take an example of 82.63185oC: 16.6758 3674.49/(82.63185 + 226.45)=4.7874PE* = 119.9885

lnPW*=16.2620 3799.89/(82.63185 + 226.35)=PW* = 52.66227

101.3 52.66227

119.9885 52.66227 0.722419

119.9885101.3 0.722419 0.855695

XW = 1- XE = 1- 0.722419 = 0.277581

YW = 1- YE = 1- 0.855695 = 0.144305

Repeat this process for other temperatures, we have the

following table:

7/31/2019 221-02

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The T-X-Y plot i as bel

25

ow:

26

Example 2: For the system of ethanol-water mixture at

ambient pressure, determine

1) What is the boiling point of pure ethanol and water?

2) What is the bubble point temperature of a mixturecontaining 0.25 mole fraction of ethanol? What is its

dew point temperature?

3) What are the bubble and dew point temperatures of a

solution containing 30 wt.% water?

Solution: Ambient pressure = 101.3 kPa1)

For pure ethanol, 101.3 4.618= 16.6758 3674.49/(T + 226.45)

The normal boiling point of ethanol is T = 78.3 oC

For pure water,

101.3 4.618

= 16.2620 3799.89/(T + 226.35)The normal boiling point of water is T = 100 oC

2)

Bubble point at XE = 0.25: from the Figure, TB = 92oC,

the equilibrium YE = 0.46

Dew point at YE = 0.25: from the Figure, TD = 96o

C,

7/31/2019 221-02

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3) 3

30w

Tot

Bub

equi

De

% w/

xW = 0

% wat

l mole

X

X

le poi

libriu

point

wate

.3, con

r =30/

= 1.= 3.1

= 1.6

= 1 -

t at X

YE =

at YE

= 30

vert to

18 mol

7 mol

7/3.19

W =

E = 0.4

0.68

0.476

27

wate

moles

es wat

s wat

= 0.52

.4765

765: T

5: TD

+ 70

er + 70

r + 1.

35

B = 87.

91.8

ethan

/46 m

2 mol

5 oC, t

C

ol:

les eth

s etha

e

anol

ol

28

(2) Tabulated data:

The experimental VLE data are usually obtained using

special stills where the temperature, pressure and

concentrations of the components in liquid and vapor

phases could be accurately determined.

X, Y (mole fraction) x, y (mass fraction)

for binary mixture (2-components):

x = X*MWA/(X *MWA + (1-X) *MWB)

** derive the equations for n-component and for x X

X ( e t h a n o l ) X ( w a t e r ) Y ( e t h a n o l ) Y ( w a t e r ) T ( C )

0 1 0 1 1 0 0

0 . 0 1 9 0 . 9 8 1 0 . 1 7 0 . 8 3 9 5 . 5

0 . 0 7 2 1 0 . 9 2 7 9 0 . 3 8 9 1 0 . 6 1 0 9 8 9

0 . 0 9 6 6 0 . 9 0 3 4 0 . 4 3 7 5 0 . 5 6 2 5 8 6 . 7

0 . 1 2 3 8 0 . 8 7 6 2 0 . 4 7 0 4 0 . 5 2 9 6 8 5 . 3

0 . 1 6 6 1 0 . 8 3 3 9 0 . 5 0 8 9 0 . 4 9 1 1 8 4 . 1

0 . 2 3 7 7 0 . 7 6 2 3 0 . 5 4 4 5 0 . 4 5 5 5 8 2 . 7

0 . 2 6 0 8 0 . 7 3 9 2 0 . 5 5 8 0 . 4 4 2 8 2 . 3

0 . 3 2 7 3 0 . 6 7 2 7 0 . 5 8 2 6 0 . 4 1 7 4 8 1 . 5

0 . 3 9 6 5 0 . 6 0 3 5 0 . 6 1 2 2 0 . 3 8 7 8 8 0 . 7

0 . 5 0 7 9 0 . 4 9 2 1 0 . 6 5 6 4 0 . 3 4 3 6 7 9 . 80 . 5 1 9 8 0 . 4 8 0 2 0 . 6 5 9 9 0 . 3 4 0 1 7 9 . 7

0 . 5 7 3 2 0 . 4 2 6 8 0 . 6 8 4 1 0 . 3 1 5 9 7 9 . 3

0 . 6 7 6 3 0 . 3 2 3 7 0 . 7 3 8 5 0 . 2 6 1 5 7 8 . 7 4

0 . 7 4 7 2 0 . 2 5 2 8 0 . 7 8 1 5 0 . 2 1 8 5 7 8 . 4 1

0 . 8 9 4 3 0 . 1 0 5 7 0 . 8 9 4 3 0 . 1 0 5 7 7 8 . 1 5

1 0 1 0 7 8 . 3

7/31/2019 221-02

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(3) raphi

T-x-y

al repr

iagra

esenta

29

ion: Exa

solu

Wh

equiWh

alco

Solu

At TWh

Wh

ple

ion if

t sho

libriut is th

ol?

tion:

B = 92.n xA =

n xA =

: Dete

its b

ld be

with tbubbl

5 oC:0.78 :

0.95 :

mine

bble

the et

his sole point

A = 0.TB = 7

TB = 7

30

he co

oint t

anol

tion?temp

4, yA8.3

oC

8.3oC

centra

emper

conten

rature

0.28

tion o

ture i

of t

of 78

an al

s 92.5

e vap

nd 95

oholoC?

r at

wt%

7/31/2019 221-02

14/15

(3)

Det

with

raphi

X-Y o

rmine

an 30,

al repr

McC

the co

60, 80

esenta

be-Th

positi

and 9

31

ion:

ele di

on of t

mol.

gram

e vap

etha

r at e

ol sol

uilibri

tion.

m

32

7/31/2019 221-02

15/15

33

(4) Relative Volatility (AB)

AB = (YA XB)/(YB XA)

YA = AB XA/(1 + (AB -1)XA)

T(C) Kic4 KC6 alpha

10 1.1 0.06 18.33333

20 1.5 0.095 15.7894730 2 0.15 13.33333

40 2.5 0.2 12.5

50 3 0.3 10

60 3.8 0.4 9.5

70 4.6 0.54 8.518519

80 5.5 0.7 7.857143

90 6.5 0.9 7.222222

Exa

mixt

X i c

ple 4

ure if t

4

: Plot

he rela

0

0 . 1

0 . 2

0 . 3

0 . 40 . 5

0 . 6

0 . 7

0 . 8

0 . 9

1

-Y di

tive vo

i c 4

0 . 1 5

0 . 2 9

0 . 4 2

0 . 50 . 6

0 . 7

0 . 7 9

0 . 8 7

0 . 9

34

gram

latility

0

8 8 7 9

8 2 4 6

1 4 8 8

3 1 2 52 9 6 3

1 8 3 1

8 6 5 8

1 7 9 5

3 8 6 5

1

for iso

is kno

utane

wn to

isopen

e 1.7

tane