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.
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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: