CLB 20804 MASS TRANSFER 1

CHAPTER 2 DISTILLATION

MULTI COMPONENT SYSTEM

Separation of more than two components.Base on the relative volatility i value of

each components, (light or heavy components)

A

A, B,C

A, B

C B

1 2

Key component:-light key-Heavy key

MULTICOMPONENT SYSTEMFor non ideal solution (hydrocarbons), the

equilibrium data can be described by K factors (distribution coefficient)

“K”= ratio of mole fraction in vapor and liquid phases at equilibrium

The value of K are available from Depriester Chart.

iii xKy

i

ii xyK

Raoult’s law (ideal system)

K (for non ideal system-dependant on T and P)

A A Ay K x

MULTICOMPONENT SYSTEMPhase equilibrium in multicomponentFor ideal solutions, the equilibrium data can be

calculated from the Raoult’s and Dalton’s Law

oiii Pxp P

py ii

PP

PxPxK

oi

i

oii

i

(Raoult’s Law) (Dalton’s Law)finallyfinally

AAAAA

A xKPxP

Pp

y

MULTICOMPONENT SYSTEM

Phase equilibrium in multicomponentRelative volatility (αi) for each component in a

multicomponent can be defined similar with binary mixture.

If component C in a mixture of A, B, C and D is selected as the base component,

C

ii K

K o

j

oi

ij PP

MULTICOMPONENT SYSTEM

Phase equilibrium in multicomponentK factor strongly temperature dependent

because of the change in vapor pressure.

The ratio of K factor is the same as the relative volatility of components:

oj

oi

j

i

jj

iiij P

PKK

xyxy

//

MULTICOMPONENT SYSTEMBubble Point….initial boiling point of a liquid mixture.Must satisfy the relation yi=1.0

The temperature is assumed and values of Ki are obtained from vapor pressure data and the known total pressure.

0.1iii xKy

MULTICOMPONENT SYSTEMBubble PointIf the summation Kixi > 1.0, a lower

temperature is chosen and repeat the calculation until the equation is satisfied.

If the summation Kixi = 1.0, the composition of the vapor in equilibrium with liquid

MULTICOMPONENT SYSTEMBubble PointFor a mixture of A, B, C and D with C as the base

component: Assume the temperature. Calculate the value of αi from the value of Ki at

this temperature. Calculate the value of KC from

Compare the temperature corresponding to the calculated value of KC to the assumed temperature.

ii

C xK 0.1

MULTICOMPONENT SYSTEMBubble Point If the values differ, the calculated

temperature is used for the next iteration. After the final temperature is known, the

vapor composition is calculated from

ii

iii x

xy

Example 1A liquid feed to a distillation tower at 405.3 kPa abs is

fedto a distillation tower. The composition in mole fractions

isas follows: n-butane (xA=0.40), n-pentane (xB=0.25), nhexane (xC=0.20), n-heptane (xD=0.15). Calculate theboiling point and the vapor in equilibrium with the liquid.

Solution: Assume a temperature and find the K values for

all component.

Depriester Chart

T = 65oC

Cont’Assuming T = 65oC

1/ 1/ 3.643 0.2745C i iK x Referring to figure 11.7-2, at 0.2745, the T is 69oC.

j

iij K

K

Get the K value from from Depriester Chart.

For the second trial, use 69oC and follow the same procedure.

MULTICOMPONENT SYSTEMDew Point...initial condensation temperatureMust satisfy the relation xi=1.0

Also trial and error calculationAfter final T is known, liquid composition

calculated from

ii

iii y

yx

01.

Kyxi

ii

MULTICOMPONENT SYSTEM

Flash Distillation, f = V/FFrom equation

Since the distillate and bottom streams are in equilibrium,

iFi

i xff

fxy

1

11 f

xx

fK

xy

i

Fii

i

i

MULTICOMPONENT SYSTEM

Flash DistillationAfter rearrange the equation before

cc N

i i

FiN

ii Kf

xx11 1)1(

1

MULTICOMPONENT SYSTEMNumber of Plates RequiredIf the composition of the liquid on any plate

is known, then the composition of the vapor in equilibrium is calculated from a knowledge of the vapor pressure or relative volatilities of individual component.

A mixture of components A, B, C & D, etc have mol fractions xA, xB, xC, xD etc. in the liquid and yA, yB, yC, yD etc. in the vapor;

1.... DCBA yyyy

MULTICOMPONENT SYSTEMNumber of Plates RequiredIf B is the base component;

BB

DDB

B

CCB

B

BBB

B

AAB

BB

D

B

C

B

B

B

A

yxx

xx

xx

xx

yyy

yy

yy

yy

1.....

1......

AAB

BB

B

AAAB

xxy

yxx

AAB

DBDD

AAB

CBCC

AAB

ABAA

xxy

xxy

xxy

Number of Plates Required

MULTICOMPONENT SYSTEM

EXAMPLE: EXAMPLE: BOILING POINT,DEW POINT, AND BOILING POINT,DEW POINT, AND

FLASH VAPORIZATION OF FLASH VAPORIZATION OF MULTICOMPONENT FEEDMULTICOMPONENT FEED

• A liquid feed to a distillation tower at 405.3 Kpa abs is fed to a distillation tower. The composition in mole fractions is as follows:

• N-butane (xA=0.40)• N-pentane (xB=0.25)• N-hexane (xC=0.20)----------base component• N-heptane (xD=0.15)a)Calculate the boiling point of feed and

composition of vapor in equilibrium.b)Calculate the dew point of feed and composition

of liquid in equilibrium.

SOLUTIONSOLUTION• a) Calculate the boiling point and composition of

vapor in equilibrium

• 1) Assume 1st temperature = 650C• 2) Obtain value of K from Depriester Chart• 3) Construct temperature trial table• 4) Stop the iteration when the assumed

temperature gives same values with the exact temperature. (means it is the bubble point)

• Trial 1 (Temperature = 650C)

* Since the final temperature is not same with the assume temperature, do next trial using last temperature.

• Trial 2 (Temperature = 690C)

* Since the final temperature is not same with the assume temperature, do next trial using last temperature.

• Trial 3 (Temperature = 700C)

* Since the final temperature is same with the assume temperature, stop the iteration.* The last value of temperature is called bubble point.

SOLUTIONSOLUTION• b) Calculate the dew point and composition of

liquid in equilibrium

• 1) Assume 1st temperature = 1060C• 2) Obtain value of K from Depriester Chart• 3) Construct temperature trial table• 4) Stop the iteration when the assumed

temperature gives same values with the exact temperature. (means it is the dew point)

• Trial 1 (Temperature = 1060C)

* Since the final temperature is not same with the assume temperature, do next trial using last temperature.

• Trial 2 (Temperature = 1070C)

* Since the final temperature is almost the same with the assume temperature, stop the iteration.