Unit3 Binary Rectification 1

7/31/2019 Unit3 Binary Rectification 1

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The McCabe-Thiele

Graphical MethodEpisode 1

Application toBinary Rectification

Whats Showing?

Rewind of the McCabe Thiele Method Special Clip on Binary Rectification Rectification and Stripping in Plates Drama of the Rectifying and Stripping Sections

Intrigues of the Feed Plate Putting our Act Together to Determine the

Number of Ideal Plates

It is a graphical method for solvingmultistage applications.

It assumes constant molal overflow fromeach stage.

Like the Kremser Equation, the M-T

Method assumes that some constantrates exist in the flow.

However, the equilibrium relation for thesystem is not linear.

The McCabe-Thiele MethodA Rewind This is a distillation application to a

binary system where a fractionatingcolumn is used.

A Reflux Rate from a Condenser and aBoil-up Rate from a Reboiler generatethe liquid and vapor flows throughseveral contact plates.

The Feed is introduced in a properplate; the section above the feed iscalled the Rectifying Section; below it isthe Stripping Section.

Binary Rectification


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A Simple FractionatingColumn

Distillate

Feed

Bottoms

Reflux

TC

PR

Total Condenser

Partial Reboiler

F

D

B

x

x

xF

D

B

LV

V L

RectifyingSection

StrippingSection

Boil-up

Visualization of the Column

Plates are numbered serially fromtop to bottom.

The McCabe-Thiele Methodassumes that the liquid and vaporflows from each plate are constant

in each section.For Rectifying Section: L & VFor Stripping Section: L & V

Plate Analysis Plate Analysis

n

n - 1

n + 1


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As contact between liquid and vaporoccurs in each plate, the vaporbecomes richer in MVC; while MVC isremoved from the liquid.

Rectification - enrichment of the vaporwith MVCStripping- removal of MVC from theliquid

Plate Analysis

This means that the MVC fraction inthe vapor (y) increases from bottomto top and the MVC fraction in the

liquid (x) decreases from top tobottom.

The plate temperature (T) increasesfrom top to bottom.

Plate Analysis

Plate Analysis

n

n - 1

n + 1 T

T

T

n + 1

n

n - 1

xn

xn-1yn

yn+1

Equilibrium Data

Binary Equilibrium Data Sources Handbook Distillation Section Ideal System

A plot of y versus x equilibrium data isneeded.

A diagonal (x = y) plot is also drawn for

use in the McCabe-Thiele Method.


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Methanol -Water Equilibrium Data

y

x0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

11

0

10

DistillateReflux

TC Total Condenser

D xD

n

LV

n + 1y x

n

L

VAnalysis of the Rectifying Section

Material Balances:Stream Balance:

V = L + D

MVC Balance: V y = L x + D xn + 1 n D

n + 1y x

nxD

L D

V V= +

Rectifying LineEquation

n + 1y x

nxD

D

V

L

V= +

Rectifying LineEquation

Analysis of the Rectifying Section

But: V = L + D Let: RD

L

D= Reflux Ratio

The RLE is a straight line with slope:L

V

L

V

RD

RD 1+

=

n + 1y

RD

RD

1+

xn

xD

RD

1++=

1

D

V

=

RD +

1

Another Form ofthe RLE

Analysis of the Rectifying Sectionn + 1

y

RD

RD

1+

xn

xD

RD

1++=

Slope =

RD

RD

1+

Y-Intercept =

xD

RD

1+

Diagonal (x=y) Analysis:

If x = y , then x = xD

This means that the RL willintersect the diagonal when

Dx x=


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Analysis of the Rectifying SectionProcedure To Plot the Rectifying Line:

1. Given the Reflux Ratio and Distil late Composition,calculate the y-intercept of the RL.

2. Plot xD in the diagonal.3. Connect xD in the diagonal with the y-intercept.

Example:

Given a Distillate with 90 mole% Methanol, 10 mole% Waterand a Reflux Ratio of 0.8.

xD =0.9

RD

= 0.8xD

RD

1+= 0.5

xD

Y-int

RL

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

11

0

yi

di

10 xi

Analysis of the Stripping Section

BottomsPR

Partial Reboiler B xB

xm - 1m

y

V L

Material Balances:Stream Balance:

BL V= +

V L B= -

MVC Balance: L xm - 1

Vm

y B xB

= +

L

V

B

Vm

y xm - 1

xB=

Stripping LineEquation

m

V

L

Analysis of the Stripping SectionL

V

B

Vm

y xm - 1

xB=

The SLE is a straight line with slope:L

V

Note that the Y-intercept of the SLE is negative.


This means that the SL will

intersect the diagonal when

x =

If x = y , then x = xB

xB

To plot easier the SL, another straight line equation may bederived by combining the RLE and SLE. This is the FeedLine Equation (FLE).


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Analysis of the Feed Plate

FeedF

L

LV

V

Let q = mole of liquid contributed by 1 moleof feed to the Stripping Section1 - q = mole of vapor contributed by 1 moleof feed to the Rectifying Section

Analysis of the Feed Plate

FeedF

L

LV

V

Therefore: L L

(1 - q)

q

+=

F= +

V V F

Derivation of the Feed Line Equation From the RLE: V y = L x + D xDFrom the SLE: V y = L x - B xB

Subtracting: (V - V) y = (L - L) x + D xD + B xB

Also the Over-all MVC Balance is: F xF = D xD + B xB

From the Analysis of the Feed Plate:

Eqn A

(V - V) = (1 - q) F and (L - L) = -q F

Eqn A therefore becomes: (1 - q) F y = -q F x + F xF

(1- q)y x=

-q

(1- q)+

xF

(1- q)y x= +

xFq

(q - 1)Feed LineEquation

Derivation of the Feed Line Equation(1- q)

y x= +xFq

(q - 1)

The FLE is also a straight line with slope:q

(q - 1)


If x = y , then x =This means that the FL willintersect the diagonal when

x =

xF

xF

Since the FLE is derived from the RLE and SLE, this meansthat the three lines intersect. Thus the SL should pass theintersection of the RL and FL.

NOTE: THE VALUE OF q DEPENDS ON THE TYPE OF FEED.


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Types of Feed

Saturated Liquid

FeedF

L

LV

V

q = 1

V V= LL = F+

Slope of the Feed Line is Infinity.

Types of Feed

Saturated Vapor

FeedF

q = 0

V V= LL =F+

Slope of the Feed Line is Zero.

L

LV

V

Types of Feed

Wet Mixture

FeedF

0 < q < 1

V V= LL =+ (1 - q) F + q F

Slope of the Feed Line is Negative.

L

LV

V

Types of Feed

Subcooled Liquid

FeedF

q > 1

V V


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Types of Feed

Superheated Vapor

FeedF

q < 0

V V= LL


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xF

Feed Line forWet Mixture

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

11

0

yi

di

10 xi

xF

Feed Line forSaturated Vapor

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

11

0

yi

di

10 xi

xF

Feed Line forSuperheated Vapor

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

11

0

yi

di

10 xi

Plotting of the Stripping Line

1. Plot the Rectifying Line.2. Plot the Feed Line.3. Plot xB in the Diagonal.4. From xB in the Diagonal, draw a straight

line passing through the intersection ofthe Rectifying and Feed Lines.


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xDxFxB0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

11

0

yi

di

10 xi

Determination of the Number of Ideal Stages

Example: A saturated liquid mixture of 50%methanol, 50% water by mole will be distilled in acolumn using a total condenser and partial reboiler.The distillate is to contain 90 mole% methanol whilethe bottoms shall have 5 mole% methanol. RefluxRatio is 0.8. Using a Feed Rate of 100 Moles/hr and

the McCabe-Thiele Method, determine:

a) Molal Rates of Liquid and Vapor in RS and SSb) Number of Ideal Plates Neededc) Mole % Methanol in L & V from each plated) Location of the Feed Plate


Given: F = 100 moles/hr xF = 0.5 q = 1xD = 0.9 xB = 0.05 Rd = 0.8

Required: a) L, V in RS & SSb) No. of ideal platesc) y and x from each plate

Solution:

V = L + D Rd = L/D = 0.8V = (Rd + 1)D F = D + B = 100F xF = D xD + B xB D = 52.9412L = 42.3529 V = 95.2941 = VL = L + F = 142.3529


Procedure to Get No. of Ideal Stages:1. Plot the RL, FL, and SL.2. From xD in the diagonal, draw triangular

steps using the EL and RL alternately.3. Shift to the SL once the intersection of

the RL and FL is reached or passed by.4. Continue drawing the triangular steps

until xB is reached or passed by.5. Number of Ideal Stages = No. of Steps

Number of Ideal Plates = No. of Steps - 1since the Partial Reboiler is an Ideal Stage


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xDxFxB0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

11

0

yi

di

10 xi


Reflux

TC Total Condenser

D xD1 L xo

V y1

x1y2

Analysis of the First Plate

y1 = xo = xD

(X1, y1) - equilibrium composition

Drawing the First Plate

xDxFxB

y1

x1

y2

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

11

0

yi

di

10 xi

Locating the Feed Plate

xDxFxB0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

11

0

yi

di

10 xi


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Shifting to the Stripping Section

xDxFxB0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

11

0

yi

di

10 xi

Completing All the Ideal Stages

xDxFxB0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

11

0

yi

di

10 xi

Determination of Plate Compositionsand Feed Plate Location

To Get the Liquid and Vapor Compositionsfrom Each Plate:

Using the EL, read the x and y valuesfor each step corresponding to a plate.

To Locate the Feed Plate:Locate the step that crosses over the

intersection of the RL and FL. Thiscorresponds to the feed plate.

xDxFxB

1

23

4

5

PR

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

11

0

yi

di

10 xi

Unit3 Binary Rectification 1

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