McCabe & Thiele - TM -1- Jan 2012

8/17/2019 McCabe & Thiele - TM -1- Jan 2012

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McCabe-Thiele Method


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The objective is:

To understand the distillation process

To make material balance for a distillation system

To understand the concept of equilibrium staes and their

estimation


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Total condenser

Feed

Overhead vapor

Boilup

N

2

1

Distillation

f

Reflux drum

Rectifying section stages

Stripping section stages

Feed Stage

Bottoms

Partial reboiler

Reflux Distillate


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Total condenser

Feed (L/V)

Overhead vapor

Boilup

N

2

1

Distillation

f

Reflux drum

Rectifying section stages

Stripping section stages

Feed Stage

Bottoms

Partial reboiler

Reflux Distillate

LK mole fraction zF

LK mole fraction xD

LK mole fraction xB


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The general countercurrent-flow, multistage, binary distillation

column shown below consists of:

• A column of N theoretical stages.

• A total condenser to produce a reflux liquid to act as an

absorbent and a liquid distillate.

• A partial reboiler to produce boilup vapor to act as a stripping

agent and a bottoms product.

• An intermediate feed stage.

This configuration allows one to achieve a sharp separation,

except in cases where an azeotrope exists where one of the

products will approach the azeotropic concentration.


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05/02/16 Dr.T.M 6

McCabe-Thiele Method:Equilibrium Curve

relative volatility can be defined in terms of the mole

fractions of the lighter compound in a binary mixture as

follows:

α 1,2 = K 1 / K 2 = y

1

/ x1

y2 / x2 = y

1

/ x1

1− y1( ) / 1− x1( ) = y1

1− x1( ) x1 1− y1( )

α will be nearly constant in the column.

Solving for the mole fraction of the Lighter compound

in the vapor gives:

y1 =α 1,2 x1

1+ x1 α 1,2 −1( )


7/3805/02/16 Dr.T.M #

For components which do not have close boiling points α will

vary depending on composition. The equilibrium curve willappear similar to that of fixed α, but won’t fit the equation

above for constant α.

y1

x1

Equilibrium

curve

45° line

y1

x1

45° line

Increasing

relative

volatility


8/3805/02/16 Dr.T.M $

Feed (L/V)

Boilup

N

2

1

f

Bottoms

Reflux

F,xF

D, xD

B, xB

Distillate

A total mass balance around the

column gives:F = D+ B

A mass balance in the Lighter

component

B D F Bx Dx Fx

+=

−−

= B D

B F

x x

x x

F

D

−−

= B D

F D

x x

x x

F

B

Overall mass Balance


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Rectifying Section

n

1 Reflux

L0 , x

D= x

0

Distillate

xD

L

xn

V

yn+1

The rectifying section extends from stage 1

to the stage just above the feed stage. If we

perform a material balance in the lighter

compound around the n stages of therectifying section including the condenser:

V n+1 yn+1 = Ln xn + Dx DOn rearranging

yn+1 = Ln

V n+1 xn +

D

V n+1 x D

If L and V are constant in the column from stage to stage, then

this is a straight line.


10/3805/02/16 Dr.T.M 10

Constant Molar Overfow

Feed ( L / V )

BoilupN

n

1

f

Bottoms

Reflux

Z F

L, x D= x0

x B

Distillate

x D

yn+1 = Ln

V n+1 xn +

D

V n+1 x D

For this condition the amount of

vapor transferred to the liquid

stream in each stage is equal to

the amount of liquid transferred tothe vapor stream. Thus the liquid

and vapor stream flow rates are

constant in the entire section.


11/3805/02/16 Dr.T.M 11

Feed (L/V)

BoilupN

n

1

f

Bottoms

Reflux

F,

X F

B,xB

Distillate

D, x

D

& ' (/DL

)peratin line for rectification section

D

n

n

n

nn x

D L

D x

D L

L y

++

+=+1

*+ 1 D Lv nn +=+

Di,ide by -D

D

n

n

n

nn x

D D L D D x

D D L D L y

/*+/*+

/*+/*+

1 ++

+=+

111

+

+

+

=+ R

x x

R

R y Dnn


12/3805/02/16 Dr.T.M 12

x

Equilibrium

curve

45° line

x0= xD x1

y

y1

y2

y =1

R+1 x D

Rectifying Section

Operating line

Slope= L / V = R /( R+1)


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05/02/16 Dr.T.M 1!

L

xm

V

ym+1

Boilup

N

Bottoms

B, xB

m+1

L, xN

V, yB

Stripping Section

B

m

m

m

mm x

B L

B x

B L

L y

−

−

−

=+1

*+ 1 B Lv mm −=+

B

m

m

m

mm x

V

B x

V

L y

11

1

+++ −=


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x

Equilibrium

curve

45° line

xNx

B

y

yB

yN

xm

Ym+1


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Feed Stage Conditions

1. If the feed is subcooled Liquid

F

L V < V

V L > F + L

q - moles of liquid flow in the striping section whichresults from the introduction of one mole of feed

L - Flow of liquid in the stripping section

Flow of vapor in the stripping section

V

q > 1 q > 1

λ

*+1

F bp pL T T C q

−

+=


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F

L

V

V = V

L = F + L

2. The feed is at its Bubble Point (Liquid)

q = 1


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F

L

V

V = V F +V

L = L + L F

3. If the feed is Partially Vaporized

! q ! 1


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F

L

V

V = F +V

L = L

4. If the fees is at its Dew Point ( Vapor)

q =


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F

L

V

V > F +V

L


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"n general we have two operating lines

yV = Lx + Dx D yV = Lx − Bx B

The q-line

#ubtracting the equations

y V − V ( )= L − L( ) x + Dx D + Bx B*+ F B D Fx Bx Dx =+( ) ( ) F Fx x L LV V y +−=−

qF L L += qF L L =− i.e.

F qV V *1+ −+= i.e. F qV V *1+ −=−

#ubstituting the values

−

−

−

=11 q

x x

q

q y F


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q=1 q>1

0


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Equilibrium

curve

45° line

xFxB

y

yB

yN

Stripping Section:

Operating line

Slope=

xD

q-line

y = L

V x +

D

V x D

y = L

V

x − B

V

x B

y = q

q −1

x −

zF

q −1

Rectifying Section:Operating line

Slope= L / V = R /( R+1)


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Equilibrium

curve

xF x B

y

y B

y N

x D

1

2

3

4


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x=xF x B

y

y B

y N

x D x=xF x B

y

y B

y N

x D

1

2

3

4

1

2

3

4

5

Feed stage located one tray too low. Feed stage located one tray too high.

Feed Stage Location singMcCabe-Thiele Method

Equilibrium

curve

Equilibrium

curve


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Equilibrium

curve

xFxB

y

yB

yN

xD

Equilibrium

curve

xFxB

y

yB

yN

xD

1

2

3

4

1

2

3

4

5

Feed stage located one tray too low. Feed stage located one tray too high.

6


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Equilibriumcurve

xFxB

y

yB

yN

xD

1

2

3

4

Optimum feed stage location.

inary Distillation 26


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05/02/16 Dr.T.M 2#

Minimum Reux for

McCabe-ThieleEquilibrium

curve

xFxB

y

yB

yN

xD


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Construction !or the McCabe-Thiele

MethodStep 1: Plot equilibrium curve and 45 degree line.

Step 2: Plot given compositions (XF, X

B,X

D)

Step 3: Draw q-line

45° line

xFxB

y

xD

equilibrium

curve

x

45° line

y

equilibrium

curve

1. 2.

xFxB xD

y

equilibrium

curve

3.


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Step 4: Determine Rmin from intersection of the rectifying section OL and the

equilibrium curve.

Step 5: Determine R from R/Rmin

Step 6: Draw OL for Rectifying section

Step 7: Draw OL for Stripping section

x=zFxB xD

y

equilibrium

curve

R/(R+1)

x=zFxB xD

y

equilibrium

curve

x=zFxB xD

y

equilibrium

curve

Rmin /(Rmin+1)

4. 5. and 6.7.


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05/02/16 Dr.T.M !0

Minimum Number of Stages for

McCabe-ThieleEquilibriumcurve

xFxB

y

yB

yN

xD

1

2

3

4

By returning all the exiting vapor

as reflux and all the exiting liquid

as boilup the operating lines have

slope of one.

Although this is the minimum

number of stages, no product is

produced (note the feed must then

go to zero).


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0

.1

.2

.3

.4

.5

.6

.7

.8

.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

y

x


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$ continous fractionating column is used to separate % &g moles 'min of a

binar( mi)ture containing * mole + of ben,ene and the rest toluene The top

product must contain ./ mol + of ben,ene and the bottom product contains ./

mole + of toluene $ reflu) ratio of 0% moles to 1 mole of product is to be used

The feed enters the column at its boiling point

alculate the moles of overhead product and bottom product

alculate the minimum reflu) ratio

alculate the number of ideal stages

$ssume the relative volatilit( is 00%

2roblem - 1


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feed of 50 mol3 he4ane and 50mol3 octane is fed into a pipe still throuh a

pressure reducin ,al,e and then into a flash disenain chamber. The ,apor

and liquid lea,in the chamber are assumed to be in equilibrium. f the fraction

of the feed con,erted to the ,apor is 0.5 find the compositions of the top and

bottoms products. Table 1 belo shos equilibrium data for this system.

2roblem -

Table 1: Liquid and vapor mole fractions of he)ane

Liquid mole fraction of

hexane, x

1.00 0.69 0.40 0.19 0.05 0.00

Vapor mole fraction ofhexane, y

1.00 0.93 0.78 0.54 0.18 0.00


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1 moles of ben,ene$8 and toluene68 mi)ture containing

% mol+ of ben,ene is subjected to a differential distillation

at atm pressure till the composition of the ben,ene in the

residue is mol + alculate the total moles of the mi)ture

distilled $ssume a relative volatilit( of 0%


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feed to a distillation unit is 10000 k moles /h of a solution of

alcohol and ater containin "5 mol3 of alcohol is to be

separated to i,e an o,erhead product of %5mol3 alcohol and

the bottom product containin 5 mol3 of alcohol. The feed is

at its boilin point and a total condenser is used. The

equilibrium relation is i,en belo.

7 0.01# 0.1! 0.25$ 0."11 0.5$1 0.#$

8 0.0!% 0.261 0."$6 0.6!2 0.### 0.%

1. calculate the amount of the alcohol produced per hour.

2. 9stimate the total number of theoretical staes required

under total reflu4 conditions.

!. 9stimate the minimum reflu4 ratio.

". f 2 times of the minimum reflu4 is used estimate the

number of theoretical staes required for the desired

separation.


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05/02/16 Dr.T.M !#

2roblem :* $ feed to a pac&ed distillation tower has an overall

composition of *0 mol+ heptane and the rest as eth(l ben,ene is to be

distilled at atmospheric pressure to produce a distillate containing .5 mol

+ of heptane and the bottoms containing 11 mol+ of heptane $ partiall(

vapori,ed feed containing * mol+ of liquid is fed into the tower at a rate

of 00% mol'h The equilibrium data are given in T$6L; ?

alculate the following: i 7oles per hour of distillate and bottoms

ii 7inimum reflu) ratio

iii 9umber of theoretical stages3 if the tower is operated under

total reflu) conditions

iv 9umber of theoretical stages3 if the tower is operated at a reflu)ratio of 0% : 1

v Location of feed tra( from the top of the tower


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T$6L; ?: 9quilibirum data for heptane and ethylben:ene system

ole fraction of

heptane in the liquid

pha!e, x

ole fraction of

heptane in the "a!

pha!e, y

0.000 0.000

0.080 0.#3

0.#50 0.5140.485 0.730

0.790 0.904

1.000 1.000

McCabe & Thiele - TM -1- Jan 2012

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Transcript of McCabe & Thiele - TM -1- Jan 2012