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Distillation V Multicomponent Distillation Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

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Page 1: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

Distillation VMulticomponent Distillation

Mass Transfer for 4th Year

Chemical Engineering Department

Faculty of Engineering

Cairo University

Page 2: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

Distillation operations

Single Stage

Simple Differential Distillation

Steam Distillation

Flash vaporization Distillation

Multistage

Binary system

Multicomponent systems

√ √ √ √

Page 3: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

Introduction

Multicomponent Distillation

Lewis-Matheson Method

Shortcut Methods

Hengstebeck’s method

Gilliland, Fenske , Underwood

Method

Constant relative volatility method

Page 4: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

KEY COMPONENTS

The solution in some methods is based on choice of two “key” components between which it’s desired to make the separation: “Light Key (LK)” and “Heavy Key (HK)”.• Light Key: is the component that is desired to be

kept out of the bottom product.• Heavy Key: is the component that is desired to be

kept out of the top product.Concentrations of the key components in the top and bottom products must be specified.All other components except light and heavy keys are called the non-keys components.

a

Page 5: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

Logically ...

C4

C5

C6

C7

C8

C9

C6

C7

C8

C9

C4

C5

C6

C7V L

V’ L’

In the case shown:Heavy Key (HK):C7

Light Key (LK):C6

The solution in some methods is based on the fact that if the light key is eliminated (nearly or completely) from bottom product then OF COURSE the heavier components will be also eliminated from bottom product.And the same for the heavy key.

Page 6: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

1- Lewis Matheson Method

• Similar to Lewis method we used in binary system.

• Tray to tray calculations are done with the assumption of constant molar flow rates of liquid and vapour in each section.

• First Calculate L, V, L’, V’ (How?)• Top section tray to tray calculations are

done till xi≤xFi

• Bottom section tray to tray calculations are done till y ≥xFi

L’x’1i

FxFi

Vy1

V’yri

WxWi

LXoi

DxDi

V L

V’ L’

Page 7: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

E-9

V1

y1

Lxo

DxDL

x1

Lx2

Vy2

Vy1

1- Lewis Matheson Method

For Top Section:If total condensery1i=xoi=xDi

Equilibrium relation:x1i=y1i/Ki

Operating line:V.y2i=L.x1i + D.xDi

Di1i2i xV

Dx

V

Ly

Page 8: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

L’X’1

V’yr

Wxw

V’y’1

V’y’2

L’x’2

L’x’1

1- Lewis Matheson Method

For Bottom Section:First: Reboiler (m=0):Equilibrium relation:yri=KixWi

Operating line:L’.x’1i=V’.y’ri +W.xWi

Wi1iri xV'

Wx'

V'

L'y'

Page 9: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

L’X’1

V’yr

Wxw

V’y’1

V’y’2

L’x’2

L’x’1

1- Lewis Matheson Method

For Bottom Section:For m=1:Equilibrium relation:y1i=Kix1i

Operating line:L’.x’2i=V’.y’1i +W.xWi

Wi2i1i xV'

Wx'

V'

L'y'

Page 10: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

1- Lewis Matheson Method

NOTE:To do these calculations we must know the value of “K”K=f(T,P)Operating pressure is knownBUT operating temperature varies from tray to another, so each tray calculation will be done by assuming T and checking it from Sx or Sy (as if it’s a normal flashing problem)

Page 11: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

1) A distillation column is designed for light gases fractionation operates at a reflux ratio of 2.5, if the condenser temperature is 60oC and it’s required to get a top product of the following specs:

The temperature of the first plate is 65oC and that of the second plate is 70oC, the data for K values for the components are as follows:

Estimate the composition of vapour and liquid leaving the second stage.

Component Distillate flow rate (mol/sec)

xD

C3 5 0.111i-C4 15 0.333n-C4 24 0.532i-C5 1 0.022n-C5 0.1 0.002

Component K at 65oC K @70oC C3 2.36 2.58

i-C4 1.19 1.37n-C4 0.86 0.9i-C5 0.42 0.51n-C5 0.32 0.4

Page 12: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

V=(R+1)D=3.5*45.1=157.85 mol/sec L=RD=2.5*45.1=112.75 mol/sec

Since x1 and y1 left the first stage and total condenser (y1i=xDi=xoi )

x1i=y1i/Ki

xC3)1=0.111/2.36=0.047

xi-C4)1=0.333/1.19=0.279

xn-C4)1=0.532/0.86=0.619

xi-C5)1=0.022/0.42=0.053

xn-C5)1=0.002/0.32=0.007

D xD

C3 5 0.111i-C4 15 0.333n-C4 24 0.532i-C5 1 0.022n-C5 0.1 0.002

E-9

V1

y1

Lxo

DxDL

x1

Lx2

Vy2

Vy1

K at 65oC K @70oC C3 2.36 2.58

i-C4 1.19 1.37n-C4 0.86 0.9i-C5 0.42 0.51n-C5 0.32 0.4

Page 13: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

Do material balance for the loop:VyC3)2=LxC3)1+DxC3)D

Vyi-C4)2=Lxi-C4)1+Dxi-C4)D

Vyn-C4)2=Lxn-C4)1+Dxn-C4)D

Vyi-C5)2=Lxi-C5)1+Dxi-C5)D

Vyn-C5)2=Lxn-C5)1+Dxn-C5)D

Substitue:157.85*yC3)2=112.75*0.047+5

157.85*yi-C4)2=112.75*0.279+15

157.85*yn-C4)2=112.75*0.619+24

157.85*yi-C5)2=112.75*0.053+1

157.85*yn-C5)2=112.75*0.007+0.1

yC3)2=0.0652 yi-C4)2=0.2943

yn-C4)2=0.5942 yi-C5)2=0.0442

yn-C5)2=0.0056

E-9

V1

y1

Lxo

DxDL

x1

Lx2

Vy2

Vy1

D xD

C3 5 0.111i-C4 15 0.333n-C4 24 0.532i-C5 1 0.022n-C5 0.1 0.002

K at 65oC K @70oC C3 2.36 2.58

i-C4 1.19 1.37n-C4 0.86 0.9i-C5 0.42 0.51n-C5 0.32 0.4

Page 14: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

Since x2and y1left the second stage

x2i=y2i/Ki

xC3)2=0.0652/2.58=0.0253

xi-C4)2=0.2943/1.37=0.2148

xn-C4)2=0.5942/0.9=0.6602

xi-C5)2=0.0442/0.51=0.0867

xn-C5)2=0.0056/0.4=0.0140

D xD

C3 5 0.111i-C4 15 0.333n-C4 24 0.532i-C5 1 0.022n-C5 0.1 0.002

K at 65oC K @70oC C3 2.36 2.58

i-C4 1.19 1.37n-C4 0.86 0.9i-C5 0.42 0.51n-C5 0.32 0.4

E-9

V1

y1

Lxo

DxDL

x1

Lx2

Vy2

Vy1

Page 15: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

2- Constant Relative Volatility Method

• Before in Lewis, during calculations you need to apply equilibrium relation but to do so you need temperature of that plate which is dependent on composition so trial and error needed.

• In this method to get red of this difficulty will use relative volatility instead of k-values in relating the vapor and liquid composition (which are in eqm).

• So, no more trial and error will be done on T.

How?

Page 16: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

2- Constant Relative Volatility Method

• What happens here is that for each component get average relative volatility (constant) and work with it a long the tower. So, Temperature will not be included in calculations.

• Finally, this method will be like Lewis-Matheson in steps but without trials on T only the difference that equilibrium relation will be.

Where is constant for each component along the tower.

Page 17: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

3- Shortcut Methods:a) Hengstebeck’s

• It’s also called Pseudo binary system method.

• System is reduced to an equivalent binary system and

is then solved by McCabe-Thiele method graphically.

• The only method that solves the multi-component

systems graphically (in our course of course).

• Used as for preliminary design work.

Page 18: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

Logically ...

• Using the concept of light and heavy key components• So, we can consider the system as a binary system

where it’s desired to separate the light key from the heavy key.

According to that the molar flow rate of the non-key components can be considered constant. ****Also the total flow rates of vapour and liquid are considered constant. The method used for these calculations was developed by R.J.Hengstebeck, that’s why it’s called Hengstebeck’s method.

Page 19: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

Hengstebeck’s Method

Let’s say that:V=total molar vapour flow rate in the top sectionL=total molar liquidflow rate in the top sectionV’=total molar vapour flow rate in the bottom sectionL’=total molar liquidflow rate in the bottom sectionyni=mole fraction of component “i” in vapour phase on tray “n”

xni=mole fraction of component “i” in liquid phase on tray “n”

uni=molar vapour flow rate of component “i” from stage “n”

lni=molar liquid flow rate of component “i” from stage “n”

di=molar liquid flow rate of component “i” in top product

wi=molar liquid flow rate of component “i” in bottom product a

Page 20: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

Hengstebeck’s Method

This means that:uni=yni*V

u'ni=y’ni*V’

lni=xni*L

l’ni=x’ni*L’

di=xDi*D

wi=xWi*W

yni=uni/V

y'ni=u'ni/V’

xni=lni/L

x’ni=l’ni/L’

a

Page 21: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

Hengstebeck’s Method

To reduce the system to an equivalent binary system we have to calculate the flow rates of the key components through the column (operating line slope is always L/V)The total flow rates (L and V) are constant, and the molar flow rates of non key components are constant, then we can calculate the molar flow rates of key components in terms of them.

NOTE: The total flow rate is constant and the molar flow rates of non key components are constant, this does not mean that the molar flow rates of key components are constant as the mass transfer is equimolar.

a

Page 22: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

Hengstebeck’s Method

If Le and Ve are the estimated flow rates of the combined keys.

And li and ui are flow rates of the non-key components lighter than the keys in the top section.And l’i and u’i are flow rates of the non-key components heavier than the keys in the bottom section.Then slope of top section operating line will be Le/Ve

And slope of bottom section operating line will be L’e/V’e

SO:Le=L-Sli Ve=V-Sui

L’e=L’-Sl’i V’e=V’-S’ui

a

Page 23: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

Hengstebeck’s Method

The final shape of the x-y diagram will be as shown

Le/Ve

L’e/V’e FF

FF HKLK

LKx

DD

DD HKLK

LKx

WW

WW HKLK

LKx

We need to calculate:Le (or li’s)

Ve (or ui’s)

L’e

V’e

Page 24: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

Hengstebeck’s Method

To calculate them we will need to calculate “a” where “a” is the relative volatility WITH RESPECT TO THE HEAVY KEY FOR ALL COMPONENTS.So for components heavier than the heavy key a<1And for components lighter than the heavy key a>1

HK

i

T

oHK

T

oi

oHK

oi

i K

K

PP

PP

P

HK

LK

T

oHK

T

oLK

oHK

oLK

LK K

K

PP

PP

P

Page 25: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

Hengstebeck’s Method

For TOP SECTIONEquilibrium Relation:yi=Ki.xi

For heavy key:

Material balance:ui=li+di

L

lK

Vi

ii

iii lK

L

V

iiii dllKL

V

iiiHK dllKL

V

i

iHK l

d1K

L

V And di/li=0

V

LKHK

Page 26: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

Hengstebeck’s Method

For TOP SECTIONEquilibrium Relation:yi=Ki.xi

For any light non-key component:

Material balance:ui=li+di

L

lK

Vi

ii

iii lK

L

V

iiii dllKL

V

iiii dllKL

V

iiiiHK

dllKK

1 1-α

dl

i

ii

iii ld

Page 27: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

Hengstebeck’s Method

For BOTTOM SECTIONEquilibrium Relation:yi=Ki.xi

For Light key:

Material balance:l’i=u’i+wi

L

lK

Vi

ii

i

ii 'KV'

L' liii

i

w''K'V'

L'

And V'

L'KLK

iiiLK

w''K'V'

L'

iiLK

w'1K'V'

L'

Page 28: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

Hengstebeck’s Method

For BOTTOM SECTIONEquilibrium Relation:yi=Ki.xi

For any heavy non-key component:

Material balance:l’i=u’i+wi

L

lK

Vi

ii

i

ii υ'

'KV'

L'l' iii

i

w''K'V'

L'

iiii

LK w''K

K

iLK

iii α-α

wα'

iii wυ'l' iii

iLK w''

iiii

w''K'V'

L'

Page 29: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

2) Estimate the number of ideal stages needed in the butane-pentane splitter defined by the compositions given in the table below. The column will operate at a pressure of 8.3 bar, with a reflux ratio of 2.5. The feed is at its boiling point.Compositions of feed, top and bottom products are shown in table below:

Equilibrium constants were calculated and found to be:

Feed (F) Tops (d) Bottoms (w)Propane, C4 5 5 0

i-Butane, i-C4 15 I5 0n- Butane, n-C4 25 24 1i-Pentane, i-C5 20 1 19

n-Pentane, n-C5 35 0 35Total, kmol 100 45 55

Component Average value of KC3 5.0iC4 2.6nC4 2.0iC5 1.0nC5 0.85

Page 30: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

Light key will be:n-C4

Heavy key will be:i-C5

SOaC3=5/1=5

aiC4=2.6/1=2.6

anC4=2/1=2

aiC5=1/1=1

anC5=0.85/1=0.85

F d wPropane, C4 5 5 0

i-Butane, i-C4 15 I5 0n- Butane, n-C4 25 24 1i-Pentane, i-C5 20 1 19

n-Pentane, n-C5 35 0 35Total, kmol 100 45 55

Component Average value of KC3 5.0iC4 2.6nC4 2.0iC5 1.0nC5 0.85

96.0124

24

54

4

iCnC

nCD dd

dx

0.05191

1

ww

wx

iC5nC4

nC4w

0.560225

25

ff

fx

iC5nC4

nC4F

Page 31: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

For Top section:Le=L-SliL=R*D=2.5*45=112.5 Kmoles

Le=112.5-10.625=101.875 KmolesAndVe=V-SuiV=(R+1)*D=3.5*45=157.5 Kmoles

Ve=157.5-30.625=126.875

SO Le/Ve=0.8

F d wC3 5 5 0

i-C4 15 I5 0n-C4 25 24 1i-C5 20 1 19n-C5 35 0 35Total 100 45 55

Page 32: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

For Bottom section:L’=L+F (feed is at its boiling point)L’=112.5+100=212.5 KmolesV’=V=157.5 KmolesV’e=V-Su’i

Ve=157.5-25.87=131.63 Kmoles

AndL’e=L’-Sl’I

L’e=212.5-60.87=151.63 Kmoles

So L’e/V’e=1.15

F d wC4 5 5 0

i-C4 15 I5 0n-C4 25 24 1i-C5 20 1 19n-C5 35 0 35Total 100 45 55

Page 33: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

Equilibrium curve:

NTS in top section6NTS in bottom sectionReboiler+5.5

x

x

x

xy

LK

LK

1

2

11

x 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

y 0 0.18 0.33 0.46 0.57 0.66 0.75 0.82 0.88 0.94 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Page 34: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

• It is an empirical method for calculating number of stages in Multi-component distillation.

• I t is composed of 3 equations to work with.

1- Gilliland equation (Has graph.): Used to calculate N stages

(In this equation min. reflux ratio and min. number of stages is need)

2- Fenske equation: Used to calculate (N stages )min

3- Underwood equation: Used to calculate minimum reflux ratio

3- Shortcut Methods:b) Gilliland, Fenske , Underwood Method

Page 35: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

1- Gilliland equation:

2- Fenske equation:

3- Underwood equation: q: (Hv-hf)/ (Hv-hL)

Where θ : is a relative volatility lies between the relative volatility of light and heavy components.

3- Shortcut Methods:b) Gilliland, Fenske , Underwood Method

Page 36: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

3- Shortcut Methods:b) Gilliland, Fenske , Underwood Method

(Gilliland Chart to use instead of equation)

Page 37: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

component

Feed Distillate Residue Relative Volatility

F (kmole)

xf D (kmole)

xD W (kmole)

xW

Hexane 40 0.4 40 0.534 0 0 2.7Heptane 35 0.35 34 0.453 1 0.04 2.22Octane 25 0.25 1 0.013 24 0.96 1

3) A mixture of Hexane, Heptane, and Octane is to be

separated to give the following products. Use the shortcut

method to:

a) Calculate the approximate minimum number of stages

b) Calculate the approximate minimum reflux ratio

c) Show how to get the approximate number of stages

Note: The feed is liquid at its bubble point.

Page 38: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

- Calculate from Underwood Equation as follows:

Feed is saturated liquid so, (q=1)

The above is one equation in one unknown; however, it will be solved using trial and error

Note: the value of will lie between the relative volatilities of the light and heavy keys (Heptane and octane respectively)

Get = 1.1725

2 .7∗0 .42 .7−𝜃

+2 .22∗0 .35

2 .22−𝜃+

1∗0 .251−𝜃

=1−1

1−𝑞=∑ 𝛼 𝑖𝑥 𝑓𝑖

𝛼𝑖−𝜃

Page 39: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

- Calculate Rmin from Underwood Equation as follows:

Rmin = 0.8287- Calculate Nmin from Fenske Equation:

Nmin = 14.13- Finally to get approximate number of stage

1-ass. R=1.5Rmin=1.243 2-Get (R-R min)/(R+1)=0.185 3- Go to Gilliland chart and get the ratio (N-Nmin)/(N+1)=0.462 4- Knowing Nmin you can get N=27.13

2 .7∗0 .5342 .7−1.1725

+2 .22∗0 .4532.22−1 .1725

+1∗0 .013

1−1 .1725=𝑅𝑚𝑖𝑛+1

Page 40: Mass Transfer for 4 th Year Chemical Engineering Department Faculty of Engineering Cairo University

KOL SANA W ENTO TAYEBEN