Mc-Cabe Thiele Method

7/27/2019 Mc-Cabe Thiele Method

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Chapter 7: Distillation of Binary Mixtures 1

Chapter 7

Distillation of Binary Mixtures


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Graphical Methods for Analyzing Binary Distillation

In Chapter 5:

We described a graphical method for analyzing multistage separation systems which involved

drawing operating lines and equilibrium curves and stepping off stages. This approach is equivalent tothe algebraic method and group methods. This approach was demonstrated using absorption and

stripping.

Todays lecture will focus on:

Extending these types of analysis to multisection cascades.

We begin by describing a typical binary distillation column.

We then describe the process generally and make important definitions.

We perform mass balances to get operating lines.

We plot equilibrium data to get an equilibrium curve.

We step of stages noting the cross-over between sections.


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McCabe-Thiele Method for Trayed Towers

Absorption and stripping cascades are common methods for separating vapor and liquid mixtures. A morecomplete separation can be achieved by combining these processes into a binary distillation column.

Total condenser

Feed

Overhead vapor

BoilupN

2

1

Distillation

f

Reflux drum

Rectifying section stages

Stripping section stages

Feed Stage

Bottoms

Partial reboiler

RefluxDistillate

L0 (absorbent)

VN+1 (vapor to be

separated)

V1

LN

1

2

N1

N

Absorption

LN+1 (liquid to be separated)

V0(stripper)

VN

L1

12

N1

N

Stripping


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Distillation Column

Feed

Rectifying section s tages


Total condenser

Reflux drum

Reflux Distillate

Boilup

Feed Stage

Bottoms

Partial reboiler


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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.

The goal of distillation

is to achieve a distillate

rich in the light key anda bottoms rich in the

heavy key.

Total condenser

Feed

Overhead vapor

BoilupN

2

1

Distillation

f

Reflux drum



Feed Stage

Bottoms

Partial reboiler

Reflux Distillate


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The feed contains a more volatile component (the light key, LK) and a less volatile component (the heavy key, HK).

At the feed temperature and pressure it may consist of a liquid, vapor or mixture of vapor and liquid. The feed

composition is given by the light key mole fraction ZF. The bottoms composition is given by the LK mole fraction

XB, whereas the distillate composition is given by the LK mole fraction XD.

Total condenser

Feed (L/V)

Overhead vapor

BoilupN

2

1

Distillation

f

Reflux drum



Feed Stage

Bottoms

Partial reboiler

RefluxDistillate

LK mole fraction zF

LK mole fraction xD

LK mole fraction xB

The difficulty in achieving

the separation is determined

by the relative volatility, between the LK=1, and

the HK=2.

1,2 = K1/K2

If the two components form an

ideal solution then Raoults

Law applies and:

Ki = Pis

/P

The relative volatility is then

just the ratio of the vapor

pressures:

1,2= P

1

s/P2

sOnly a function of T

As T increases (pressure incresaes), decreasesuntil at some point it becomes equal to one and no

separation is possible.


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McCabe-Thiele Method: Equilibrium Curve

We can rewrite the relative volatility in terms of the mole fractions of the light key in a binary mixtureas follows:

1,2 = K1/K2 =y1/x1

y2/x2=

y1/x11 y1( )/ 1 x1( )

=y1 1 x1( )

x1 1 y1( )

For close boiling point components the temperature, and thus will be nearly constant in the column.Solving for the mole fraction of the LK in the vapor gives:

For components which do not have close boiling points will vary depending on composition. Theequilibrium curve will appear similar to that of fixed , but wont fit the equation above for constant .

y1 =1,2x1

1+ x1 1,2 1( )

y1

x1

Equilibrium

curve

45 line

y1

x1

45 line

Increasing relative

volatility


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Thermodynamic Considerations and Phase Equilibria: Binary Fluids

Lets consider a binary mixture AB, where

B is a heavy component (high boiling point)

and

A is a light component (low boiling point).

A T-x phase diagram of AB mixture, where

x is a mole fraction of component a might

look like this at some constant pressure P.

This phase diagram can be also transformed

in y-x diagram where composition of vapour

phase in terms of mole fraction of

component A is plotted as function of the

liquid phase composition.

x1 y1x2 y2x3 y3x4 y4

T

Tb(B)

Tb(A)

V

L

T1

T2

T3

T4

xA

xA

yA

T1

T2

T3

T4y4

y3

y1


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Specifications

F Total Feed Rate

zF Mole fraction composition of the feed

P Column operating pressure (assume uniform in column)

Phase condition of the feed @P

Vapor-liquid equilibrium curve for the binary @P

Type of overhead condenser (total or partial)

xD Mole fraction composition of the distillate

xB Mole fraction composition of the bottoms

R/Rmin Ratio of reflux to minimum reflux

Results

D Distillate flow rate

B Bottoms flow rate

Nmin Minimum number of equilibrium stages

Rmin Minimum reflux ratio, Lmin/D

R Reflux ratio, L/D

VB Boilup ratio, V/B

N Number of equilibrium stages

Optimal feed- stage location

Stage vapor and liquid compositions

Specifications for the McCabe-Thiele Method


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McCabe-Thiele Method: Column Mass Balance

FzF = xDD + xBB

Feed (L/V)

BoilupN

2

1

f

Bottoms

Reflux

F, zF

D, xD

B, xB

Distillate

A mass balance in the LK component around the column gives:

A total mass balance around the column gives:

F= D + B

So we know that the mole fraction of the light key of the

feed is between that of the distillate and bottoms:

D = FzF xB

xD xB

If D, F, are zF, specified, then either xD or xB can be specified.


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McCabe-Thiele Method: Rectifying Section

Vn+1yn+1 = Lnxn + DxD

Which we can rearrange to find:

The rectifying section extends from stage 1 to the stage just above the feed stage.

yn+1 =Ln

Vn+1xn +

D

Vn+1xD

Feed (L/V)

BoilupN

n

1

f

Bottoms

Reflux

ZF

L, xD= x

0

xB

Distillate

xD

n

1Reflux

L0, x

D= x

0

Distillate

xD

Lxn

Vyn+1

If L and V are constant in the column from

stage to stage, then this is a straight line.

If we perform a material balance in the light key

around the n stages of the rectifying section

including the condenser:


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McCabe-Thiele Method: Constant Molar Overflow

If L and V are constant, then this is a straight line.

This requires that:

9 The two components have equal and constant

enthalpies of vaporization

9 The heat capacity changes are negligible compared

to the heat of vaporization

9 The column is well insulated so heat loss is

negligible

9 The pressure in the column is uniform

These conditions lead to the condition ofconstant molar

overflow.

For this condition the amount of vaportransferred to the liquid stream in each stage is

equal to the amount of liquid transferred to the

vapor stream. Thus the liquid and vapor stream

flow rates are constant in the entire section.

Feed (L/V)

Boilup

N

n

1

f

Bottoms

Reflux

ZF

L, xD= x

0

xB

Distillate

xD

yn+1 =Ln

Vn+1xn +

D

Vn+1xD


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McCabe-Thiele Method: Rectifying Section Operating Line

y =L

Vx+

D

VxD

The liquid entering stage one is the reflux L and its ratio to the distillate L/D

is the reflux ratio R. If we have constant molar overflow, then R is a constant and

L

V=

L

L + D=

L/D

L/D + D/D=

R

R +1

D

V=

D

L + D=

1

R +1

and

We define this equation as the

operating line of the rectifying

section.

Feed (L/V)

BoilupN

n

1

f

Bottoms

Reflux

ZF

L, xD= x

0

xB

Distillate

xD

In the case of constant molar overflow

we can then drop the stage subscripts:

yn+1 =Ln

Vn+1xn +

D

Vn+1xD


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McCabe-Thiele Method: Operating Line

x

Equilibrium

curve

45 line

n

1

f

Reflux

xD= x0

Distillate

xD

L, xn V, yn+1

y = LV

x+ DV

xDWe can then rewrite:

asy =

R

R +1x+

1

R +1xD

x0=xDx1

y

y1

y2

y = 1R +1

xD

Rectifying Section Operating line

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


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McCabe-Thiele Method: Stripping Section

Lxm = Vym+1 + BxB

Which we can rearrange and use the constant molar overflow assumption to find:

The stripping section extends from the stage just below the feed stage to the bottom stage N.If we perform a material balance in the light key around the bottom stages of the rectifying section

including the condenser we have:

y = LV

x BV

xB

Feed (L/V)

BoilupN

n

1

f

Bottoms

Reflux

zF

L, xD= x0

xB

Distillate

xD

y =VB +1

VBx

1

VBxBand

L

xm

V

ym+1

Boilup

NBottoms

B, xB

m+1

L, xN

V, yB

Since:

L

V=

V+ BV

=VB +1

VB

L = V+ B

ThenVB is called the boilup ratio.

VB =V

B

We define this equation as the operating line

of the stripping section.

This is also the operating line of

the stripping section .


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McCabe-Thiele Method: Stripping Section

x

Equilibrium

curve

45 line

xNxB

y

yB

yN

Stripping Section Operating Line

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

If VB and XB are specified then we can graph this as the line shown in the

following plot.

y =VB +1

VBx

1

VBxB

L

xm

V

ym+1

Boilup

NBottoms

B, xB

m+1

L, xN

V, yB

xm

Ym+1

y =VB +1

VBx

1

VBxB


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Feed Stage Considerations

In determining the operating lines for the rectifying and stripping sections we needed the bottoms and

distillate compositions and reflux and reboil ratios. The compositions can be independently specified, but

R and VB are related to the vapor to liquid ratio in the feed.

FF

FFF

L

L

L

L

L

V

V< V

V

VV

V

V= VV= VF + V

V= F+ VV> F+ V

L > F+ L L = F+ L L = L + LF

L = L L < L

Subcooled Liquid Bubble Point Liquid Partially Vaporized

Dew Point Vapor Superheated Vapor


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Feed Conditions

So except in the cases where the feed is a supercooled liquid or superheated

vapor the boilup is related to the reflux by the material balance:

V= L + D VF

VB V

B=

L + D VFB

Distillation operations can be specified by the reflux ratio or boilup ratio

although the reflux ratio (or R/Rmin) is most often specified.

Dividing by B gives the boilup ratio:

L = B + V

V= D + L

VF

+ LF

= D + B

V= V+ VF

L = L + LFVF + L L = D + B

VF

+ L L = D + L V

V= L + D VF

Consider the cases where the feed is not a supercooled liquid or a superheated vapor:

Mass balance around the reboiler:

Mass balance around the condenser:

Mass balance around the column:

Vapor entering the rectifying section:

Liquid entering the stripping section:

Substitute this into the column balance:

Substitute in the reboiler balance:

In other words, the vapor

entering the rectifying section

is the vapor entering the condenserminus the feed vapor flow rate.


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The q-line

First, we define the parameter q by: q = L LF

yV= Lx BxByV= Lx+ DxD

Subtracting the two operating lines:

Gives: y V V( )= L L( )x+ DxD + BxBUsing a material balance in the LK: DxD + BxB = FzF

Using a material balance around the feed stage to elminate vapor flow rates:

F+V+ L = V+ L

Simplifying and using the definition of q results in the q-line:

y =q

q 1

x

zF

q 1

x= zF y = zF

minus

y V V( )= L L( )x+ FzF

V V= F+ L Ly F+ L L( )= L L( )x+ Fz

F

The q-line has slope q/(q-1)

and intercepts the 45 degree

line at y=zF


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Construction Lines for McCabe-Thiele Method

Equilibrium

curve

45 line

x=zFxB

y

yB

yN

Stripping Section:Operating line

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

xD

Rectifying Section:Operating line

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


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Feed Stage Location Using McCabe-Thiele

Equilibrium

curve

x=zFxB

y

yB

yN

xD

Equilibrium

curve

x=zFxB

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.


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Construction Lines for McCabe-Thiele Method

Equilibriumcurve

x=zFxB

y

yB

yN

xD

1

2

3

4


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Summary

This lecture:

We extended the analysis used for absorption and stripping to binary distillation.

We described a typical binary distillation configuration.

We made definitions such as reflux ratio, constant molar overflow, etc.

We described operating lines. We plotted the equilibrium curve.

We stepped through stages to show the change in composition as you go through

the column.

Next lecture well continue our discussion of binary distillation and the

McCabe Thiele method.

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Mc-Cabe Thiele Method