1. DISTILLATION: McCABE THIELE METHOD 1.1 GENERAL INTRODUCTIONdempt.co.za/mso2015/handout4.pdf ·...

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1 1. DISTILLATION: McCABE THIELE METHOD 1.1 GENERAL INTRODUCTION At the end of this chapter you should be able to: Describe the distillation process Determine the vapour liquid equilibrium (VLE) data for a binary mixture Determine the number of stages required to achieve a specified separation using the McCabe and Thiele graphical method i.e The minimum and operating reflux ratio. The effect of feed conditions on the number of stages The minimum reflux ratio and the minimum number of stages The number of theoretical and actual plates. The vapour and liquid flow distribution in the column THE OBJECTIVES ARE: To introduce distillation. Define the necessary laws and concepts. Distillation is defined as: A process in which a liquid or vapour mixture of two or more substances is separated into its component fractions of desired purity, by the application and removal of heat. OR The separation of a liquid mixture of two or more substances of different boiling points by the processes of partial vapourisation and condensation Distillation is based on the fact that the vapour of a boiling mixture will be richer in the components that have lower boiling points. Therefore, when this vapour is cooled and condensed, the condensate will contain more volatile components. At the same time, the original mixture will contain more of the less volatile material. Distillation columns are designed to achieve this separation efficiently.

Transcript of 1. DISTILLATION: McCABE THIELE METHOD 1.1 GENERAL INTRODUCTIONdempt.co.za/mso2015/handout4.pdf ·...

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1. DISTILLATION: McCABE THIELE METHOD

1.1 GENERAL INTRODUCTION

At the end of this chapter you should be able to:

Describe the distillation process

Determine the vapour – liquid equilibrium (VLE) data for a binary mixture

Determine the number of stages required to achieve a specified separation using the McCabe

and Thiele graphical method i.e

The minimum and operating reflux ratio.

The effect of feed conditions on the number of stages

The minimum reflux ratio and the minimum number of stages

The number of theoretical and actual plates.

The vapour and liquid flow distribution in the column

THE OBJECTIVES ARE:

To introduce distillation.

Define the necessary laws and concepts.

Distillation is defined as:

A process in which a liquid or vapour mixture of two or more substances is separated

into its component fractions of desired purity, by the application and removal of heat. OR

The separation of a liquid mixture of two or more substances of different boiling points

by the processes of partial vapourisation and condensation

Distillation is based on the fact that the vapour of a boiling mixture will be richer in the

components that have lower boiling points. Therefore, when this vapour is cooled and

condensed, the condensate will contain more volatile components. At the same time, the original

mixture will contain more of the less volatile material. Distillation columns are designed to

achieve this separation efficiently.

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Although many people have a fair idea what “distillation” means, the important aspects that

seem to be missed from the manufacturing point of view are that:

• distillation is the most common separation technique

• it consumes enormous amounts of energy, both in terms of cooling and heating

requirements

• it can contribute to more than 50% of plant operating costs

The best way to reduce operating costs of existing units, is to improve their efficiency and

operation. To achieve this improvement, a thorough understanding of distillation principles and

how distillation systems are designed is essential.

The purpose of this chapter is to expose you to the terminology used in distillation practice and

to give a introduction to:

1. distillation principles

2. vapour liquid equilibria

3. basic distillation equipment and operation

4. distillation column design and

5. the factors that affect distillation column operation

Lets clarify some of the termonology that is used in distillation by considering a two component

mixture eg. a simple binary system of 50% water and 50% methanol.

Pure water has a boiling point of 100 0C and pure methanol has a boiling point of 65 0C.

But the 50-50 mixture of methanol and water has a boiling point of 84 0C.

At mixture boiling point of 84 0C pure methanol has a vapour pressure of 200 kPa and pure water

has a vapour pressure of 60kPa.

Based on the above physical properties, we say that methanol is the MORE VOLATILE

COMPONENT, because it has the lower boiling point OR because it has a higher vapour

pressure, and water is the LESS VOLATILE COMPONENT, because it has a higher boiling

point OR because it has a lower vapour pressure.

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NB. BOILING POINT of a liquid is the TEMPERATURE at which the VAPOUR

PRESSURE of the liquid is equal to the EXTERNAL PRESSURE, and VAPOUR

PRESSURE is the pressure that is exerted by the vapours of a liquid that is vapourizing

RELATIVE VOLATILTY

The ease or difficulty of separation of two components by distillation depends on the

relative volatility, α, of the two components.

Solving for y1,

The higher the average value of α, the easier it is to achieve desired separation.

2. VAPOUR LIQUID EQUILIBRIUM

OBJECTIVE: Discussion on VLE curves and methods to determine them.

Distillation columns are designed based on the boiling point properties of the components in the

mixtures being separated. Thus the sizes, particularly the height, of distillation columns are

determined by the vapour liquid equilibrium (VLE) data for the mixtures to be separated.

Constant pressure VLE data is obtained from boiling point diagrams. VLE data of binary

mixtures is often presented as a plot, as shown in the figure below. The curved line is called

the equilibrium line and describes the compositions of the liquid and vapour in equilibrium

at some fixed pressure. This particular VLE plot shows a binary mixture that has a uniform

vapour-liquid equilibrium that is relatively easy to separate. For distillation purposes it is

convenient to plot y against x at a constant pressure, since the majority of industrial

distillations take place at constant pressure.

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Fig 1.1: Typical equlibrium graph

NB. The mole fraction, xA, of a two component system A and B is the number of moles of

A in the liquid phase divided by the total number of moles present in the liquid phase.

xA = mole fraction of A in liquid phase = phase liquidin B of moles +A of moles

phase liquidin A of moles

similarly

yA = mole fraction of A in vapour phase = phasein vapour B of moles +A of moles

phasein vapour A of moles

The VLE data can be obtained via experimental methods or by computational methods. In this

section we derive the necessary equations that can be used to determine the VLE curve. In order

to determine the VLE data, we make use of some physical chemistry laws:

DALTON’S LAW

Dalton’s law state that:

P=Pi. i.e. the total pressure is equal to the summation of the partial pressures.

Where Pi is the partial pressure of component i

But in an ideal gas or vapour, the partial pressure exerted a component is proportional to the

mole fraction of the component, i.e.

xA

x=y

yA

0 1

1

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PyP ii .................................................................... 1

where: P = Total pressure, yi is the vapour mole fraction of component i, and

Pi = Partial pressure of component i.

RAOULT’S LAW:

Raoult’s law states that:

The partial pressure exerted by a component equals the product of the mole fraction of

that component in the liquid phase and its vapour pressure.

It can be written as:

P P xA A A 0......................................................................2

PA

0 is the vapour pressure of pure component A at the same temperature, and xA is the mole

fraction of component A in the liquid phase.

This relation is usually found to be true only for high values of xA , or corresponding low values

of xB. But mixtures of organic isomers and some hydrocarbons follow the law closely, so that

we can assume it to be valid.

PA can be related to xA by Henry’s law

PA = H xA

This law is reliable for low values of xA

Now lets see how the above laws are used to generate VLE data. Lets consider a binary mixture

containing components A and B

We know that for mixtures that follow Raoult’s law that:

P P xA A A 0 from Eq 2

and PA = yAP from Eq 1.

P x y PA A A

0

yA=

P x

P

A A

0

....................Eq 3

Also from Dalton’s law we have :

0000 1 BAAABBAABA PxPxPxPxPPP

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It can be seen from the above equations that if the vapour pressures ( 0

iP ) of the two

components at a specified temperature are known, then the complete set of VLE data can be

obtained.

The complete set of VLE data can then be calculated if PA

0 and P is given . The method is as

follows:

We assume different values for Ax ranging from 0.0 to 1.0, and determine the corresponding Ay

values using Eqn 3.

3. THE FRACTIONATING COLUMN

OBJECTIVE:

You must be able to describe and sketch the fractionating column.

3.1 Main Components of Distillation Columns

Distillation columns are made up of several components, each of which is used either to transfer

heat energy or enhance material transfer. A typical distillation contains several major

components:

a vertical shell where the separation of liquid components is carried out

column internals such as trays/plates and/or packings which are used to enhance component

separations

a reboiler to provide the necessary vaporisation for the distillation process

a condenser to cool and condense the vapour leaving the top of the column

a reflux drum to hold the condensed vapour from the top of the column so that liquid (reflux)

can be recycled back to the column

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The vertical shell houses the column internals and together with the condenser and reboiler,

constitute a distillation column. A schematic of a typical distillation unit with a single feed and

two product streams is shown below:

Fig 2.1. A Typical Distillation Colum

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3.2 Operation of a typical Distillation Column

The fractionating column is usually a cylindrical structure which is divided into sections by

trays. The trays are perforated (sieve trays) and the vapour rises from the bottom of the

column through each tray to the top. The liquid flows down from the top, across the trays,

guided by downcomers to the bottom. At each tray an equilibrium of mass transfer and heat

transfer is established.

The rising vapour come into contact with the down flowing liquid and mass- and heat

transfer occur.

The distillate is drawn off as a vapour at the top, and condensed, either fully or partially.

Depending on the reflux ratio, after the condenser, an amount of liquid is put back at the

top of the column to flow back down either by gravity or pumped from a holding drum to

the top of the column. This is done to ensure continuous vapour-liquid contact above the

feed tray. We will define reflux ratio in the next section.

At the bottom of the tower, part of the liquid is drawn off as bottoms product and the rest is

put back into the tower after the reboiler as vapour.

Thus a liquid molecule will come into contact with the vapour at each tray and is also

“recirculated” through the column to ensure the required composition of product.

The feed stream is introduced continuously to the column on some intermediate tray where

the liquid composition is approximately the same as the feed stream.

The part of the column above the feed tray is known as the rectifying or enrichment section

and the part of the column below the feed tray is known as the stripping section.

I just want to explain what the more volatile component mean, as this will be used later on. The

more volatile component is one component in the binary mixture, which have the lowest boiling

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point. As we will later on do a mass balance over the column, we would automatically only use

the more volatile component, and ignore the other component.

Thus, if we refer to xf, xd, and xw, we automatically mean the molfraction of the feed of the more

volatile component, the molfraction of the distallite of the more volatile component and the

molfraction of the bottoms of the more volatile component.

Thus: If we have two components A and B and the more volatile component is A, then if we

write:

xf, xd and xw we refer to component A. If we then want to refer to component B, we must write:

xfB, xdB, and xwB.

NUMBER OF PLATES REQUIRED IN A DISTILLATION COLUMN –

MCCABE AND THIELE METHOD

OBJECTIVE:

After this section you must be able to:

Write down the top operating line equation.

Write down the bottom operating line equation.

Derive the top operating line equation in terms of the reflux ratio R.

Define the reflux ratio.

Use the McCabe and Thiele method to determine the number of plates.

Determine the flow rates of the vapour and liquid.

As mentioned, distillation columns are designed using VLE data for the mixtures to be

separated. The vapour-liquid equilibrium characteristics (indicated by the shape of the

equilibrium curve) of the mixture will determine the number of stages, and hence the

number of trays, required for the separation. A method which is easy to use have been

developed by McCabe and Thiele and is known as the McCabe-Thiele graphical method.

The McCabe-Thiele approach is a graphical one, and uses the VLE plot to determine the

theoretical number of stages required to effect the separation of a binary mixture. It

assumes constant molar overflow and this implies that:

molal heats of vaporisation of the components are roughly the same

heat effects (heats of solution, heat losses to and from column, etc.) are negligible

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for every mole of vapour condensed, 1 mole of liquid is vaporised

The design procedure is simple. Given the VLE diagram of the binary mixture, operating

lines are drawn first. The operating lines define the mass balance relationships between the

liquid and vapour phases in the column.

There is one operating line for the bottom (stripping) section of the column, and on for the

top (rectification or enriching) section of the column. Use of the constant molar overflow

assumption also ensures the operating lines are straight lines.

We shall derive the equations that can be used to construct these operating lines. In general

we have a distillation column as shown in Figure 1.3:

Figure 3: Distillation Column

Where: D = Distillate

F = Feed

W = Bottom product

F

xf

Vn

Ln+1

Vt D

xd

n+1

n

W

xw

Vm

Lm+1 m+1

m

Loop I

Ln

Lm

Loop II

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V = Vapour

L = Liquid

Subscripts: n = plate n

m = plate m

n + 1 = plate n + 1

m + 1 = plate m + 1

If we take an overall material balance over the distillation column:

Then:

Thus F = D + W...............................................................Eq 9

F go in

D and W go out

with mole fractions of the more volatile component:

Fxf = Dxd + Wxw..............................................................Eq 10

A material balance above plate n indicated by a loop I in Figure 1.3 for the more volatile

component gives:

F

D

W

F

D

W

D

Vn Ln + 1

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Vn = D + Ln+1 ..........................Eq 11

Expressing this balance on the more volatile component:

yn Vn = Ln + 1 xn + 1 + Dxd

Thus : y

L

Vx

D

Vxdn

n

n

n

n

11

Since the mols of liquid overflow are constant, Ln may be replaced by Ln + 1 and;

yL

Vx

D

Vxdn

n

n

n

n

1 ................................................Eq 14

Similarly, taking a material balance for the total streams and for the more volatile component

from the bottom to above plate m (indicated by Loop II in Figure 1.3) and noting that

Lm = Lm + 1 :

L V Wm m ......................................................Eq 12

or

V L Wm m ......................................................Eq 13

Y V L x Wxm m m m w 1

YL

Vx

W

Vxm

m

m

m

m

w1 ......................................Eq 15

W

Vm Lm + 1

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Equation 15 is similar to Equation 14, and gives the corresponding relation between the

compositions of the vapour rising to a plate and the liquid on the plate, for the section below the

feed plate.

Equations 14 and 15 are the equations of the operating lines.

The top operating line is a straight line in the form:

yL

Vx

Dx

Vn

n

n

nd

n

1 ............................................Eq 14

where

L

V

n

n = gradient of the top operating line equation

and

Dx

V

d

n = cut off point of the top operating line equation on the y-axis.

Remember that the general equation for a straight line is:

y mx c

Where m = gradient and c = cut off point on y axis.

The bottom operating line equation is in the form:

yL

Vx

Wx

Vm

m

m

m

w

m

1 .......................................Eq 15

L

V

m

m = gradient and

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Wx

V

w

m = cut off point on the y-axis

But reflux ratio is defined as the ratio

L

D

n

or the liquid feedback rate divided by the top

product flow rate

RL

D

n..........................................................Eq 16

If the top operating line is given by Equation 14:

yL

Vx

Dx

Vn

n

n

n

d

n

1

and from Equation 11 we know that Vn = D + Ln

substitute 11 in Equation 14:

YL

L Dx

Dx

L Dn

n

n

nd

n

1 ..................................Eq 17

Now we do a bit of mathematical magic by dividing Equation 17 with D at the top and

bottom:

y

L

DL

D

D

D

X

D

Dx

L

D

D

D

n

n

n

n 1

d

n

And we know that R

L

D

n

the equation reduces to:

yR

Rx

x

Rn n

d

1 1

1 .......................................Eq 18

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where

R

R 1 = gradient of the top operating line equation in terms of the reflux ratio R

and x

R

d

1 = cut off point on the y axis in terms of the reflux ratio R.

Equation 18 relates the vapour mol fraction and the liquid mol fraction at the liquid and vapour

that is in equilibrium at every stage.

Another factor that will greatly affect the number of stages required in a distillation column is the

condition of the feed stream entering the column. Therefore a third operating line is introduced,

which takes into account the condition of the feed.

The Effect of Feed Conditions

The condition of the entering feed determines the relationships between:

the vapour flowrates in the stripping and enriching sections i.e. nV and mV , and

the liquid flowrate in the stripping and enriching sections i.e. nL and mL

The vapour and liquid flowrates in the enriching and stripping sections are related in the

following manner;

qFLL nm and FqVV nm 1

where q is used to represent the condition of the feed, and is defined as :

q = heat required to vaporize 1 mol of feed divided by the molar latent heat of feed,

OR

q = energy required to bring one mole of feed to a saturated vapour divided by the molar

latent heat of vaporization.

i.e.

Tmq

cpL .........................................19

q = (100 - % of feed which is vapour) / 100

and m is always 1 because we work with a unit mass (per definition) and = latent molar heat of

vaporization [kJ/kmol], and cp is the heat capacity.

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If cp is given in units of kJ/kmolK then use as is in the equation.

If cp is given in units of kJ/kgK then multiply cp with the mean molar mass of the feed

kJ

kgK

kg

kmol

kJ

kmolK

T is defined as: (Tboiling point - Tof the feed)

For a superheated vapour, this equation can be used

TTmCpq Dv

The equation for the q-line (feed condition line) is:

yq

qx

x

qq q

f

1 1...................20

This is also a straight line of the form y = mx + c

where q

q 1 = gradient and

x

q

f

1 = cut off point on the y axis

For example, if feedstream to a distillation column is at boiling point,

then T= 0, and

q =

0 =

= 1

which means the gradient of q-line:

gradient =11

1

1

q

q = = infinity

Which means that the q line is vertical

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Therefore, depending on the state of the feed, the feed lines will have different slopes. For

example,

q = 0 (saturated vapour)

q = 1 (saturated liquid)

0 < q < 1 (mix of liquid and vapour)

q > 1 (subcooled liquid)

q < 0 (superheated vapour)

The resulting q-lines for the various feed conditions are shown in the diagram below.

Fig.1.4 Typical slopes of q lines

Therefore the construction lines required to determine the number of stages required to

separate a binary mixture are: the equilibrium line, only two other pairs of lines. These are:

feed-line and rectification section operating line, or

feed-line and stripping section operating line, or

stripping and rectification operating lines

Let us now explain the difference between a “partial” and “total condenser”.

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In a partial condenser you have:

Because you have two phases, they will automatically be in equilibrium and the condenser will

count as an equilibrium stage. Vapour and liquid in contact with each other and in equilibrium.

In a total condenser:

You only have a single product (liquid) as everything has been condensed (total). There is no

question about an equilibrium stage as there is nothing else than pure liquid present. The

condenser will not count as an equilibrium stage.

This means:

In the McCabe Thiele method, when you step off stages on the graph, the first stage will only be

a condenser if it is specified that the column is equipped with a partial condenser.

If a total condenser is used, the first stage on the McCabe Thiele graph will be the first stage and

not the condenser.

How do we know how to draw in the plates on the equilibrium graph?

You always start at the x = y line at the xd point.

F

Vapour

Liquid

F Liquid

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At that point you draw a horizontal line till it touches the equilibrium graph. Then a vertical line

straight down till it touches the top operating line.

Carry on like this till you pass the xf mark. Then you have to draw the line straight down till it

touches the bottom operating line.

You stop only after the vertical line passes the xw point and you count the plates from top to

bottom. This is the theoretical number of plates which include one as the condenser, if it is a

partial condenser.

TO DRAW IN THE GRADIENT OF THE Q-LINE:

Your starting point on the Equilibrium graph is where xf cross the x=y line on graph:

Now the gradient of 3,5 that you have calculated means the following:

3,5 positive units on the y axis and 1 positive unit on the x axis

OR

3,5 negative units on the y axis and 1 negative unit on the x axis (- - = + )

OR

1,4 positive units on the y axis and 0,4 positive unit on the x axis(1,4 0,4 = 3,5 ).

xcl xw xf

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If the scale on the y and x axis are the same on the Equilibrium graph then you can use 3,5

cm and 1 cm for example on your ruler BUT if the scale on the y and x axis are NOT the

same, then you HAVE TO MEASURE 3,5 UNITS on the y axis and 1 UNIT on the x axis.

Thus it follows very clearly that the slope of the q-line is determined by the nature of the

feed. When the feed is:

Cold-feed as liquor q 1 q line

Feed at boiling point q = 1 q line

Feed partly vapour 0 q 1 q line

Feed saturated vapour q = 0 q line

Feed superheated vapour q 0 q line

6. PLATE EFFICIENCY:

It could be given to you that the plate efficiency is 70% .Then if you calculate the

theoretical number of plates, the actual number of plates will be more Because:

Plate efficiency = (theoretical number of plates) / (actual number of plates) 100%.

7. MINIMUM REFLUX RATIO:

OBJECTIVES:

AT THE END OF THIS SECTION YOU MUST BE ABLE TO:

Define minimum reflux ratio.

Calculate minimum reflux ratio using two different methods.

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Discuss the importance of reflux ratio.

From Equation 18 we can see that a change in the reflux ratio will have an influence on the

top operating line.

yR

Rx

x

Rn n

d

1 1

1

At minimum reflux ratio the top operating line cross the Equilibrium data where the q-line

cross the Equilibrium data:

Figure:1.5

Before we draw in the top operating line:

Now draw in the top operating line so that point where the q-line and equilibrium line cross

Figure: 1.6

Thus, at minimum reflux ratio the number of stages become infinite.

xw xf xcl

q-line

q-line

xf xw xcl

top operating line

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7.1 TO CALCULATE THE MINIMUM REFLUX RATIO RM:

There is two methods of determining Rm -either by using the

1. cut off point on the y axis for the top operating line.

2. the gradient of the top operating line.

Let’s look at the cut off point first:

At minimum reflux you can read of the cut off point on the y axis of the top operating line:

Figure 1.7

Say it is 0,6. Then from our equation for the top operating line the cut off point on the y

axis is:

Cut off point on the y axis = 1R

xd

But R is now Rm

cut off point on the y axis = 1m

d

R

x

then the only unknown in this equation above is the Rm.

If xd = 0,9 for example and the cut off point on the y axis is 0,6 then:

xf xw xcl

q-line top operating line

cut

off

point

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5,0

6,0

6,09,0

9,06,06,0

9,016,0

1

9,06,0

m

m

m

m

R

R

R

R

Rm can also be calculated by using the slope of the top operating line:

Usually when we calculate the slope of any straight line you must use 2 points on the line:

Thus choose 2 points: say points A and B:

Figure: 1.8

Then slope = y/x

= y2-y1/x2-x1

= 0,9 - 0,6 / 0,9 - 0

= 0,333

xf xw

xc

q-line top operating line

A B y2

y1

x1 x2

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But slope = 0,333 = 1m

m

R

R

Rm (0,333) + 0,333 = Rm

0,333 = Rm - 0,333 Rm

0,333 = 0,666 Rm

Rm = 0,333/0,666

= 0,5

7.2 THE IMPORTANCE OF REFLUX RATIO AND TOTAL REFLUX:

If D = 0 (Distallate rate is 0) then the column is said to operate under total reflux. In other

words if no product is withdrawn from the column then the top operating line coincides

with the line x = y.

And then at total reflux the number of stages required will be a minimum:

Figure: 1.9

The cost of a distillation unit is made up by capital costs and running costs. Capital cost is

determined by the number and diameter of plates and the running costs by the heating and

cooling medium requirements.

The reduction in the required number of plates as R is increased beyond Rm will tend to

reduce the cost of the column. Thus, an increase in R, at values near Rm, gives a marked

1

2

3

xw xf xd

y

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reduction in the number of plates, but at higher values of R, further increases have little

effect on the number. Increasing the reflux ratio from Rm therefore affects the capital and

running cost of a column in the following ways:

The operating cost rise and are approximately proportional to (R+1)

The capital cost initially falls since the number of plates fall off rapidly at this stage.

The capital cost rises at high values of R, since there is then only a very small reduction in

the number of plates, but the diameter, and hence the area, continually increases because

the vapour load becomes greater. The associated condenser and reboiler will also be larger

and more expensive.

MULTIPLE FEEDSTREAMS AND SIDESTREAMS

OBJECTIVES:

At the end of this section you should be able to:

Apply the McCabe and Thiele graphical method with a side stream.

Write down the equation for the side stream.

MULTIPLE FEEDS

Occasionally we have more than one mixture of the same components, but of different

compositions that we wish to separate. We could mix the solutions and introduce them as one

feed. That would make the design of the fractionator easier, but it would waste energy. After all,

separating a mixture takes energy, and if we mix two solutions of different compositions. we

waste a partial separation that has already taken place.

It would be better to feed the two solutions to different stages in the fractionator (the optimum

stage, in each case). The design problem is now more complicated because the addition of each

additional feed results in one additional material-balance or operating line.

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Consider the case of two feeds. The composition, rate, and condition of both feeds must be

known.

The diagram below shows the case with two feeds. The upper operating line, above where F1

enters is not affected; the middle line has larger slope than the upper line, because of the liquid

added from F1; and the line for the lowest section, where the amount of liquid is greatest, has the

largest slope.

xw xF1 xF2 xd

Figure 2.1

SIDESTREAMS

A sidestream is a stream withdrawn from a fractionator at a stage intermediate to the top and

bottom, we may need products of two different compositions over- head or below. Rather than

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waste separation energy, by taking a product at a higher than needed purity, we draw off the

product at the intermediate stage. Sidestreams are almost always liquid.

Sidestreams are exactly analogous to multiple feeds in basic construction. However,

sidestreams remove material and therefore the intermediate operating line has a slope less

than that in the zone immediately above.

In principle the sidestream should have the same composition as the liquid on the stage from

which it is withdrawn. However. the equilibrium stage composition and the real fractionator

composition will differ, in general. We may specify, the sidestream composition, then. The

sidestream rate is also specified.

A side stream is defined as any product stream other than the overhead product (or

Distallate, D) and residue (or Bottoms product, W).

Figure: 2.2

S1

S2

S3

W

D

F2

S1, S2 and S3

are 3 different

side streams.

F1

F1and F2 are different

feed streams

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You will normally associate side streams with multi-component systems, but it can be used

with binary systems as well.

Let’s have a look at a binary system with one side stream:

Figure 2.2

Assuming a constant molar overflow, then for the part of the column above the sidestream

the top operating line is given by:

yL

Vx

Dx

Vn

n

n

n

d

n

1

which is the normal top operating line equation.

But: Balances for that part of the column between the feed plate and the side stream:

Vs = Ls + S + D

Lm

Vm

D

S

F

Vn

Ln+1

m+1

m

m-1

n+1

n

Ls

Ln Vs

S

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Vsyn = Lsxn+1 + S xs + D xd

yn = Ls/Vs xn+1 + (Sxs + Dxd)/Vs........................A

Since the side stream is normally removed as a liquid Ls = Ln - S and Vs = Vn

The effect of any additional side stream or feed stream is to introduce an additional

operating line for each side streamer or extra feedstream as shown in fig 2.3. In all other

respects the method of calculation is identical with that for the straight separation of a

binary mixture outlined earlier in chapter 1.

We are looking for a point on the x = y line that satisfy the equation A:

If y = x then:

y = Ls/Vs y + (Sxs + Dxd)/Vs

multiply with Vs

y Vs = Ls y + S xs + D xd

y( Vs - Ls ) = S xs + D xd

y =( S xs + D xd )/ Vs - Ls

But Vs = Ls + S + D

Vs - Ls = S + D

y =

DS

DxSx ds

DS

DxSxxy ds

NN

We note that in order to calculate the slopes of the various operating lines, we need to know the

vapour and liquid flowrates in the various sections.

The slope of the operating line in any section is the ratio of the liquid flowrate in that section to

the vapour flowrate in that section

It can be seen that the sidestream increase the number of plates required, owing to the

decrease in liquid rate below the side stream.

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The steps that need to be followed by using the graphical method of McCabe-Thiele to

construct operating including a side stream are as follows:

First you mark of xd, xf and xw.

Then draw in the q-line

Mark off xN on the x = y line.

Mark off the cut off point on the y-axis for the top operating line.

Draw in the top operating line from xd to cut off point on the y-axis.

Draw in side stream line from point xN to xs on the top operating line xs = 0,6.

Draw in the bottom operating line from xw on the x = y line to the point where the side

stream line cross the q-line.

This is your recipe to draw in the sidestream line!!

USE OF MURPHREE EFFICIENCY

The McCabe-Thiele method assumes that the two phases leaving each stage are thermodynamic

equilibrium. In industrial, countercurrent, multistage equipment, it is not always the practical to

provide the combination of residence time and intimacy of contact required to approach

equilibrium closely. Hence the concentration of changes for a given stage are usually less than

predicted by equilibrium.

Referring to the diagram below, the Murphree efficiency is given by the ratio of ab/ac

To apply a known Murphree efficiency to an entire column, it is necessary only to replace the

true equilibrium curve ye versus xe by an effective equilibrium curve y’e versus xe whose

ordinates are calculated from the equation

𝑦𝑒′ = 𝑦 + 𝜂𝑀(𝑦𝑒 − 𝑦)

Once the effective equilibrium curve has been plotted, the usual step-by-step construction is

made and the number of actual plates determined.

The reboiler is not subject to a discount for plate efficiency, and the true equilibrium curve is

used for the last step in the stripping section.

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CONDENSER AND REBOILER DUTIES

An energy balance around an entire column gives

FhF + QR = DhD + BhB + QC + Qloss

Qloss can be considered negligible in most cases

For a total condenser,

QC = D(R+1) ∆Hvap

∆Hvap = average molar heat of vapourization of the two components being separated

For a partial condenser

QC = DR ∆Hvap

For a partial reboiler,

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QR = BVB∆Hvap

VB is the vapour boil-up ratio.

Note that when the feed is at the bubble point and a total condenser is used, QC = QR

If the feed is partially vapourised and a total condenser is used, the heat required by the reboiler

is less than the condenser duty and is given by

𝑄𝑅 = 𝑄𝐶 [1 −𝑉𝐹

𝐷(𝑅 + 1)]

If saturated steam is the heating medium for the reboiler, the steam rate required is given by

energy balance:

𝑚𝑠 =𝑀𝑠𝑄𝑅

∆𝐻𝑠𝑣𝑎𝑝

Where

ms = mass flow rate of steam

QR = reboiler duty (rate of heat transfer)

Ms = molecular weight of steam

∆Hsvap = molar enthalpy of vapourisation of steam

The cooling water flowrate for the condenser is

𝑚𝑐𝑤 =𝑄𝐶

𝐶𝑝𝑐𝑤(𝑇𝑜𝑢𝑡 − 𝑇𝑖𝑛)

Where

mcw = mass flow rate of cooling water

QC = condenser duty (rate of heat transfer)

Cpcw = specific heat of water

Tout, Tin = temperature of cooling water out of and into the condenser, respectively.

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Operational Aspects of Distillation

4.1. FACTORS AFFECTING DISTILLATION COLUMN OPERATION

The performance of a distillation is determined by many factors, for example:

1. feed conditions

2. state of feed

3. composition of feed

4. trace elements that can severely affect the VLE of liquid mixtures

5. internal liquid and fluid flow conditions

6. state of trays (packings)

7. weather conditions

Some of these will be discussed below to give an idea of the complexity of the distillation

process.

4.1.1. Feed Conditions

The state of the feed mixture and feed composition affects the operating lines and hence

the number of stages required for separation. It also affects the location of feed tray.

During operation, if the deviations from design specifications are excessive, then the

column may no longer be able handle the separation task. To overcome the problems

associated with the feed, some columns are designed to have multiple feed points when

the feed is expected to containing varying amounts of components.

4.1.2. Reflux Conditions

As the reflux ratio is increased, the gradient of operating line for the rectification section

moves towards a maximum value of 1. Physically, what this means is that more and more

liquid that is rich in the more volatile components is being recycled back into the column.

Separation then becomes better and thus less trays are needed to achieve the same degree

of separation. Minimum trays are required under total reflux conditions, i.e. there is no

withdrawal of distillate.

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On the other hand, as reflux is decreased, the operating line for the rectification section

moves towards the equilibrium line. The ‘pinch’ between operating and equilibrium lines

becomes more pronounced and more and more trays are required This is easy to verify

using the McCabe-Thiele method.

The limiting condition occurs at minimum reflux ratio, when an infinite number of trays

will be required to effect separation. Most columns are designed to operate between 1.2

to 1.5 times the minimum reflux ratio because this is approximately the region of

minimum operating costs (more reflux means higher reboiler duty).

4.1.3. Vapour Flow Conditions

Adverse vapour flow conditions can cause

foaming

entrainment

weeping/dumping

flooding

4.1.3.1.Foaming

Foaming refers to the expansion of liquid due to passage of vapour or gas. Although it

provides high interfacial liquid-vapour contact, excessive foaming often leads to liquid

buildup on trays. In some cases, foaming may be so bad that the foam mixes with liquid

on the tray above. Whether foaming will occur depends primarily on physical

properties of the liquid mixtures, but is sometimes due to tray designs and condition.

Whatever the cause, separation efficiency is always reduced.

4.1.3.2. Entrainment

Entrainment refers to the liquid carried by vapour up to the tray above and is again

caused by high vapour flow rates. It is deterimental because tray efficiency is reduced:

lower volatile material is carried to a plate holding liquid of higher volatility. It could

also contaminate high purity distillate. Excessive entrainment can lead to flooding.

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4.1.3.3. Weeping/Dumping

This phenonmenon is caused by low vapour flow. The pressure exerted by the vapour is

insufficient to hold up the liquid on the tray. Therefore, liquid starts to leak through

perforations. Excessive weeping will lead to dumping. That is the liquid on all trays

will crash (dump) through to the base of the column (via a domino effect) and the

column will have to be re-started. Weeping is indicated by a sharp pressure drop in the

column and reduced separation efficiency.

4.1.3.4. Flooding

Flooding is brought about by excessive vapour flow, causing liquid to be entrained in

the vapour up the column. The increased pressure from excessive vapour also backs up

the liquid in the downcomer, causing an increase in liquid holdup on the plate above.

Depending on the degree of flooding, the maximum capacity of the column may be

severely reduced. Flooding is detected by sharp increases in column differential

pressure and significant decrease in separation efficiency.

4.1.2. Column Diameter

Most of the above factors that affect column operation is due to vapour flow conditions:

either excessive or too low. Vapour flow velocity is dependent on column diameter.

Weeping determines the minimum vapour flow required while flooding determines the

maximum vapour flow allowed, hence column capacity. Thus, if the column diameter is

not sized properly, the column will not perform well. Not only will operational

problems occur, the desired separation duties may not be achieved.

4.1.3. State of Trays and Packings

Remember that the actual number of trays required for a particular separation duty is

determined by the efficiency of the plate, and the packings if packings are used. Thus,

any factors that cause a decrease in tray efficiency will also change the performance of

the column. Tray efficiencies are affected by fouling, wear and tear and corrosion, and

the rates at which these occur depends on the properties of the liquids being processed.

Thus appropriate materials should be specified for tray construction.

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4.1.4. Weather Conditions

Most distillation columns are open to the atmosphere. Although many of the columns are

insulated, changing weather conditions can still affect column operation. Thus the

reboiler must be appropriately sized to ensure that enough vapour can be generated

during cold and windy spells and that it can be turned down sufficiently during hot

seasons. The same applies to condensors.

These are some of the more important factors that can cause poor distillation column

performance. Other factors include changing operating conditions and throughputs,

brought about by changes in upstream conditions and changes in the demand for the

products. All these factors, including the associated control system, should be considered

at the design stages because once a column is built and installed, nothing much can be

done to rectify the situation without incurring significant costs. The control of distillation

columns is a field in its own right, but that's another story.

4.2. Operating Conditions

The two most important factors that affect the operating conditions of a distillation tower are

temperature and pressure. Both temperature and pressure must be controlled in order for the

distillation process to result in good separation and pure products. Although they are discussed

separately, it is important to remember that temperature and pressure work together, and that

changes in one affect the other.

4.2.1. Temperature

Temperature control is crucial to the distillation Process, because correct temperatures are

necessary to maintain the proper boiling range for each desired product. Correct temperatures are

important at several places in a distillation tower, these places include the feed point, the top of

the tower, the bottom of the tower, and the reboiler. If these temperatures are either too high or

too low, the desired products will not be produced.

The temperature at the feed point of a distillation tower should normally be the boiling point

of the mixture introduced into the tower. If the temperature of methanol and water mixture at

the feed point is higher than its boiling point, an excess amount of the heavier product, which

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is the water, will vaporize and move up the tower instead of condensing and moving down. If

the feed point temperature is lower than its boiling point, not enough methanol will vaporize.

The temperature at the top of the tower should be the boiling point of the desired overhead

product at whatever pressure the tower is operating under. For the methanol/water example,

the temperature at the top of the tower should be the boiling point of methanol. If the

temperature at the top of the tower is higher than the methanol boiling point, part of the water

will vaporize and become part of the overhead product, instead of flowing down as a liquid.

If the tower top temperature is lower than the methanol boiling point, not enough of the

methanol will vaporize. Some of the methanol will remain as a liquid and flow down the

tower.

The temperature in the reboiler should be the boiling point of the bottoms product, because

the purpose of the reboiler is to supply heat to the tower and to vaporize any lighter products

that may have become part of the bottoms product. In the methanol/water example, the

reboiler temperature should be the boiling point of water. If the reboiler temperature is

incorrect, i.e. If the bottom temperature is lower than the water boiling point, some of the

methanol entrained at the bottom will not be boiled off and sent up; it will remain part of the

bottoms product.

Where more than two products are separated from a liquid mixture, as in a side-draw tower, the

temperatures at each draw-off tray are also important. The temperature at each draw-off tray

must correspond with the boiling range of the desired product to be drawn off from that

particular tray.

4.2.1.1. Temperature Gradient

While specific temperatures at various places in a distillation system are important, the

relationships between the temperatures in the system are also important. Starting from the bottom

of the tower and moving up, the temperature in each successive tray is lower. Because lighter

materials boil at lower temperatures, the lighter product tends to move up, while the heavier

product flows down. The gradual decrease in temperature from the reboiler to the reflux

condenser is called the temperature gradient.

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The temperature gradient is measured in terms of the difference between the specified tower

bottom temperature and the specified tower top temperature. For the mixture of methanol and

water, the temperature gradient is the difference between 65oC and 100oC. To achieve the highest

purity and best separation, the temperature gradient should be at a maximum consistent with

proper operation. The temperature gradient is increased by applying heat at the bottom of the

tower with the reboiler and by cooling the top of the tower with reflux. Heating the bottom of

the tower will cause more of the lighter product to vaporize. Cooling the top of the tower by

pumping in more reflux will prevent any heavier product from vaporizing and becoming part of

the overhead product.

Typical Temperature Profile for Methanol/water Systems

0

10

20

65 100TEMPERATURE (oC)

Water

Feedmethanol &water

Methanol

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4.2.1.2. Temperature Control

Temperatures in a distillation system are typically controlled in three ways:

by controlling the temperature of the feed mixture,

by controlling the reflux rate; and

by controlling the boil-up rate.

1. The temperature of the feed mixture can be controlled by using a preheater. Using a preheater

to raise the temperature of the feed mixture regulates the temperature at the midsection of the

tower.

2. The reflux rate is the amount of liquid pumped back into the tower.Pumping in more reflux

decreases the temperature at the top of the tower. This reflux comes from the condenser

where top vapor was cooled to change it back into a liquid. This cooled reflux will therefore

lower the temperature at the top of the tower.

3. The boil-up rate is the amount of vapors reintroduced into the tower from the reboiler.

Reintroducing more hot vapors increases the temperature at the bottom of the tower.

However, if the boil-up and reflux rates are too high, the rising vapors will block the

descending reflux, and the reflux will block the vapors. This condition is known as flooding.

Flooding can also be caused by other factors, such as a loss of heat through leaks in the

system or bad insulation. These factors can vary tower temperatures, which, in turn, will

affect the amount of vapors produced.

To run a distillation tower properly, the temperature gradient should be increased as much as

possible, but not so much that the tower is flooded. Temperature adjustments can be made as

necessary by increasing or decreasing the reflux rate and/or the boil-up rate

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4.2.2. PRESSURE

Pressure in a distillation system is especially important in two places. One place in the feed

tank. Most mixtures are kept at atmospheric pressure and room temperature. However,

some mixtures can vaporize at atmospheric pressure, so they must be kept under pressure to

maintain them in a liquid form. The pressure in the feed tank containing such a mixture must

be controlled to keep the mixture from vaporizing prematurely, before it is introduced into

the tower.

A second place where pressure is important is in the distillation tower. The proper pressure in

a tower is whatever pressure corresponds with the boiling range of the overhead product. This

pressure is controlled at the top of the tower. Proper pressures must be maintained in a

distillation system to ensure that reasonably pure products are produced. If pressures are not

maintained at steady values, the tower's vapor rate, that is, the amount of vapors flowing up

the tower, will not be constant, and product

purity will decrease.

Normal Operation Flooding

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One result of changes in tower pressure is puking, which is the eruption of vapors and liquid

out of the top of a tower. Puking is actually the third stage of a sequential event. The first

stage is overloading, which is a condition brought about when the rate of liquid flow down a

tower and the rate of vapor flow up the tower are sufficiently high to cause flooding.

Flooding is the second stage. As the flow rates of liquid and vapor increase, the pressure drop

across each tray increases, which causes the liquid level in the downcomer to rise. When the

liquid level reaches the top of the downcomer, the tray will begin to flood.

Liquid builds up above the bubble caps on the flooding tray and enters the risers on the tray

above. As the liquid builds up above the bubble caps, the pressure drop through the tray

increases and, consequently, the backpressure on the downcomer increases. This causes

further liquid buildup on the tray above, and a greater pressure drop occurs. This further

worsens the condition- all the trays above the flooding tray will progressively flood and,

eventually, liquid will be carried overhead in "slugs," as "puking."

What basically happens in the puking cycle is that the pressure of the flooded trays is

eventually overcome by the vapor pressure pushing upward, but only momentarily, and in a

repeated cycle. The vapor pressure continues to build up until it overcomes the downward

pressure of the flooded trays. When this happens, the tower "pukes," and the pressure

becomes equalized again. As the cycle continues, the upward pressure builds up again, and

the tower pukes again.

Puking causes the liquid in a tower to surge up and down. If this condition is not corrected, it

can eventually tear the tower apart.

Generally, a decrease in pressure at the top of a distillation tower increases the vapor rate.

One mechanical cause of this type of pressure decrease could be a riser corroding and failing

off, allowing liquid to escape. Conversely, an increase in pressure at the top of the tower

decreases the vapor rate. A mechanical cause of this problem might be plugged holes in

bubble caps or clogged downcomers.

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The pressures at the top and bottom of a distillation tower are related. Both pressures must be

correct if the tower is to work property. Changes in these pressures may indicate that a

problem exists.

For example, a decrease in the pressure at the top of a tower and an increase in the pressure at

the bottom of the tower may be an indication that the feed rate is too high. When too much

feed mixture enters the tower, too much liquid moves down. The excess liquid blocks the

vapors moving up, and causes the tower to flood. To avoid flooding, the feed rate should be

decreased.

If the pressure at the bottom of the tower and the pressure at the top of the tower both

increase, either of two problems may exist- (1) the tower may be overworked, or (2) the

condenser may have failed. The term overworked means that the boil-up rate is too high,

that is, the reboiler is reintroducing too much vapor into the tower. This problem is solved by

reducing the boil-up rate. Condenser failure means that the condenser may not be condensing

all of the vapors coming off the top of the tower. A condenser might fail if it is fouled with

debris, or if not enough cooling water is circulating through it. The condenser should be

inspected to find the exact cause of the failure, and then corrective action should be taken.

Note: The problems discussed here are fairly common. causes in addition to those mentioned.

They may be others.

Temperature, Pressure, and Product Purity

Although the effects of temperature and pressure on distillation can be examined separately,

it is important to remember that temperature and pressure work together. Both must be

correct for the distillation process to work properly.

The key to whether a distillation system is working properly is product purity. Tower

products are checked often for purity. Generally, samples are taken from the top, from the

bottom, or from draw-off trays, if a multi-component mixture is being distilled. If product

purity is unacceptable, it may be necessary to adjust the feed rate, the boil-up rate, or the

reflux rate. Tower pressures may also be adjusted.