Mass transfer and distillation column

Mass transfer
and distillation
column

Mass transfer and distillation column
1
Prepared by: F.R.ALI chemical engineer
Email: fetouhreda1000@gmail.com Mobile: +02 01069561172
1 Part (1): basics of mass transfer
1.1 Introduction
The term diffusion (mass transfer) is used to denote the transference of a
component in a mixture from a region where its concentration is high to a region
where the concentration is lower. Diffusion process can take place in a gas or
vapour or in a liquid, and it can result from the random velocities of the molecules
(molecular diffusion) or from the circulating or eddy currents present in a
turbulent fluid (eddy diffusion).
 Diffusion is the movement of an individual component
through a mixture. (the influence of a physical stimulus)
 Driving force is a concentration gradient of the diffusing
component.
 A concentration gradient tends to move the component in the
direction to equalize concentrations and destroy the gradient.
 Diffusion is the characteristic of many mass transfer
operations.
 Diffusion can be causes by an activity gradient such as by a
pressure gradient, by a temperature gradient, or by the
application of an external force field.
 Role of diffusion in mass transfer.
o Distillation
o Leaching
o Crystallization
o Humidification
o Membrane separation
Differences between heat transfer and mass transfer
Heat transfer is an energy transition but diffusion is the
physical flow of material.
Heat transfer in a given direction is based on one temperature
gradient and the average thermal conductivity.
Mass transfer, there are different concentration gradients for
each component and often different diffusivities.

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1.2 Theory of Diffusion
Assumption
Diffusion occurs in a direction perpendicular to the interface between the
phases and at a definite location.
Steady state. (The concentrations at any point do not change with time)
Binary mixtures.
Fick's Law of diffusion:
The rate of diffusion is governed by Fick's Law, first proposed by Fick in 1855
which expresses the mass transfer rate as a linear function of the molar
concentration gradient. In a mixture of two gases A and B, assumed ideal, Fick's
Law for steady state diffusion may be written as:
Where:
JA: is the molecular diffusion flux of A, (moles per unit area per unit time)
kmol/m2
.s.
CA: is the concentration of A (moles of A per unit volume) kmol/m3
.

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DAB: is known as the diffusivity or diffusion coefficient for A in B (unit area per
unit time) m2
s
Z: is distance in the direction of transfer (m).
Diffusion depends on:
1. Driving force (ΔC), moles per unit volume (kmol/m3
).
2. The distance in the direction of transfer (Δz), meter (m).
3. Diffusivity coefficient, unit area per unit time (m2
/s).
The Fick’s law is similar to Fourier’s law of heat conduction and Newton’s
equation for shear-stress-strain relationship.
1.3 Modes of diffusion

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Molar flow rate, velocity, and flux
The total molar flux (mole/time area)
N = ρMu0
Where ρM is the molar density of the mixture and u0is the volumetric average
velocity.
For component A and B, the molar fluxes are
NA= uACA
NB= uBCB
The molar flux of component A and B
JA= cAuA–cAu0 = cA(uA–u0)
JB= cBuB–cBu0 = cB(uB–u0)
The diffusion flux J is assumed to be proportional to the concentration gradient
and the diffusivity of component (D)
Diffusion with bulk of mass in motion:
The Fick's first law of diffusion describes the mass transfer from the random
movement of molecules of a stationary medium or a fluid in streamline flow. If
circulating currents or eddies are present, then the molecular mechanism will be
reinforced and the total mass transfer rate may be written as:
Total diffusion = Molecular diffusion + Convection term
Convection term = Eddy diffusion = Molar flux due to convection
Convection term = Concentration * mass transfer velocity = CA. V

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The total diffusion equation can be write in another forms:
Partial pressure for gases.
Mole fraction for gases and liquids.
a. Total diffusion equation in the partial pressure form:
If A and B are ideal gases in a mixture, the ideal gas law may be applied to each
gas separately and to the mixture:
Total diffusion equation in the form of partial pressure (normally used for gases)
b. Total diffusion equation in the mole fraction form:
Total diffusion equation in the form of mole fraction (used for gases and liquids)

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1. Stagnant diffusion (Mass transfer through a stationary second component):
In several important processes, one component in a gaseous mixture will be
transported relative to a fixed plane, such as a liquid interface, for example, and
the other will undergo no net movement. In gas absorption a soluble gas A is
transferred to the liquid surface where it dissolves, whereas the insoluble gas B
undergoes no net movement with respect to the interface. Similarly, in
evaporation from a free surface, the vapour moves away from the surface but the
air has no net movement. The mass transfer process therefore:
Since stagnant diffusion layer: NB = 0
2. Counter diffusion:
i. Equimolecular counter diffusion:
When the mass transfer rates of the two components are equal and opposite the
process is said to be one of equimolecular counter diffusion. Such a process
occurs in the case of the box with a movable partition. It occurs also in a
distillation column when the molar latent heats of the two components are the
same (λA = λB). At any point in the column a falling stream of liquid is brought
into contact with a rising stream of vapour with which it is not in equilibrium.
The less volatile component is transferred from the vapour to the liquid and the
more volatile component is transferred in the opposite direction. If the molar
latent heats of the components are equal, the condensation of a given amount of

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less volatile component releases exactly the amount of latent heat required to
volatilize the same molar quantity of the more volatile component. Thus at the
interface, and consequently throughout the liquid and vapour phases,
equimolecular counter diffusion is taking place (NB = - NA).
Since equimolecular counter diffusion: NB = - NA
ii. Unequimolecular counter diffusion:
When the mass transfer rates of the two components are unequal and opposite,
the process is said to be the Unequimolecular diffusion, such a process occurs in
a chemical reaction.
Since Unequimolecular counter diffusion: NB = - n NA

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1.4 Diffusion through a varying cross-section area
The mole rate (NA, kmol/s) through a system of a varying cross section area is
constant, while the mole flux (NA, kmol/m2
.s) is variable. The mass transfer
through a cone and sphere can be consider as a mass transfer through a system of
varying cross section area. On the other hand, the transfer through a cylinder can
be consider as a mass transfer through a system of constant cross section area.
1.4.1 Diffusion through a spherical body
NA1 = NA2 = NA3 NA1 > NA2 > NA3
PA1 = PV

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But: The surface area of sphere=A=4π r2
Case (I): Diffusion through a stagnant layer (𝐍 𝐁=𝟎):
The most important things is to calculate the mass transfer rate for the sphere
surface where the surface area is constant (𝟒𝛑 𝐫𝟎𝟐):
Mole flux from the sphere surface

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When the mass transfer from surface to a large distance compare to the sphere
surface (𝐫𝟎):
𝐫𝟏→ ∞ and 𝐂𝐀𝟐=0
In partial pressure form:
Case (II): Equimolecular Counter Diffusion (𝐍 𝐁=−𝐍 𝐀):

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For the mass transfer from surface (A=4π ro2
):
In the case of r1 is very large 𝐫𝟏=0
In the form of partial pressure:
Case (III): Unequimolecular Counter Diffusion (𝐍 𝐁=−𝐧 𝐍 𝐀):
Molecular diffusion in solid
 Rate of diffusion in solids is generally slower than rates in liquids and
gases.
For example
 Leaching of food
 Drying of foods
 Diffusion and catalytic reaction in solid catalyst
We can classify transport in solids into two types of diffusion
 Diffusion in solids following Fick’s law.
 Diffusion in porous solids that depends on structure. Separation of
fluids by membrane
1. Diffusion in solids following Fick’s law
 This type of diffusion does not depend on the actual structure of solid.
 The diffusion occurs when the fluid or solute diffusing is actually
dissolve in the solid to form a more or less homogenous solution.

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Using the general equation for binary diffusion
The bulk flow term is usually small, so it is neglected.
Integration of equation for a solid slab at steady
state
For the case of diffusion radially through a cylinder wall inner radius r1 and
outer r2 and length L.
2. Diffusion in porous solid that depends on structure
The porous solid that have pores or interconnected voids in the solid would
affect the diffusion.
For the situation where the voids are filled with liquid or gas, the concentration
of solute at boundary is diffusing through the solvent in the void volume takes
a tortuous path which is greater than z2 –z1 by a factor, τ, called tortuous.
For a dilute solution:
Where
ε is the open void fraction
τ is the correction factor of the path longer than z.

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Combined into an effective diffusivity
For diffusion of gases in porous solids
1.5 Mass transfer theories
1.5.1 The Two-Film Theory
The two-film theory of Whitman (1923) was the first serious attempt to represent
conditions occurring when material is transferred in a steady state process from
one fluid stream to another. In this approach, it is assumed that a laminar layer
exists in each of the two fluids. Outside the laminar layer, turbulent eddies
supplement the action caused by the random movement of the molecules, and the
resistance to transfer becomes progressively smaller as shown in Figure below.
The thicknesses of the two films are z1 and z2. Equilibrium is assumed to exist
at the interface and therefore the relative positions of the points C and D are
determined by the equilibrium relation between the phases.

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The rate of mass transfer per unit area in terms of the two-film theory for
equimolecular counter diffusion is given for the first phase as:
In the form of partial pressure:
Where: Z = Zg + ZL
The rate of mass transfer per unit area from the gas film:
The rate of mass transfer per unit area from the liquid film:
The relation between the partial pressure (PA) and concentration (CA):
Henry's law:
𝐏𝐀=𝐇 𝐂𝐀
Where: H is the Henry's constant.
𝐲𝐀=𝐊 𝐗𝐀

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1.5.2 The Penetration Theory
The penetration theory was suggested in 1935 by Higbie who was investigating
whether or not a resistance to transfer existed at the interface when a pure gas was
absorbed in a liquid. In his experiments, a slug-like bubble of carbon dioxide was
allowed rise through a vertical column of water in a 3 mm diameter glass tube.
As the bubble rose, the displaced liquid ran back as a thin film between the bubble
and the tube, Higbie assumed that each element of surface in this liquid was
exposed to the gas for the time taken for the gas bubble to pass it; that is for the
time given by the quotient of the bubble length and its velocity. It was further
supposed that during this short period, which varied between 0.01 and 0.1 s in the
experiments, absorption took place as the result of unsteady state molecular
diffusion into the liquid, and, for the purposes of calculation, the liquid was
regarded as infinite in depth because the time of exposure was so short.
The way in which the concentration gradient builds up as a result of exposing a
liquid - initially pure - to the action of a soluble gas is shown in Figure 10.6. The
percentage saturation of the liquid is plotted against the distance from the surface
for a number of exposure times in arbitrary units. Initially only the surface layer
contains solute and the concentration changes abruptly from 100 percent to 0
percent at the surface. For progressively longer exposure times the concentration
profile develops as shown, until after an infinite time the whole of the liquid
becomes saturated. The shape of the profiles is such that at any time the effective
depth of liquid which contains an appreciable concentration of solute can be
specified. If this depth of penetration is less than the total depth of liquid, no
significant error is introduced by assuming that the total depth is infinite.

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The work of Higbie laid the basis of the penetration theory in which it is assumed
that the eddies in the fluid bring an element of fluid to the interface where it is
exposed to the second phase for a definite interval of time, after which the surface
element is mixed with the bulk again. Thus, fluid whose initial composition
corresponds with that of the bulk fluid remote from the interface is suddenly
exposed to the second phase. It is assumed that equilibrium is immediately
attained by the surface layers, that a process of unsteady state molecular diffusion
then occurs and that the element is remixed after a fixed interval of time. In the
calculation, the depth of the liquid element is assumed to be infinite and this is
justifiable if the time of exposure is sufficiently short for penetration to be
confined to the surface layers. Throughout, the existence of velocity gradients
within the fluids is ignored and the fluid at all depths is assumed to be moving at
the same rate as the interface.
The diffusion of solute A away from the interface (y-direction) is thus given by:
The following boundary conditions apply for the penetration theory:
The mass transfer rate per unit area of surface is then given by:

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1.5.3 The Film - Penetration Theory
A theory which incorporates some of the principles of both the two-film theory
and the penetration theory has been proposed by Toor and Marchello (1958).
The whole of the resistance to transfer is regarded as lying within a laminar film
at the interface, as in the two-film theory, but the mass transfer is regarded as an
unsteady state process. It is assumed that fresh surface is formed at intervals from
fluid which is brought from the bulk of the fluid to the interface by the action of
the eddy currents mass transfer then takes place as in the penetration theory,
except that the resistance is confined to the finite film, and material which
traverses the film is immediately completely mixed with the bulk of the fluid. For
short times of exposure, when none of the diffusing material has reached the far
side of the layer, the process is identical to that postulated in the penetration
theory. For prolonged periods of exposure when a steady concentration gradient
has developed, condition are similar to those considered in the two-film theory.
The diffusion of solute A away from the interface (y-direction) is thus given by:
The following boundary conditions apply for the penetration theory:
𝐭=𝟎 → 𝐂𝐀=𝐂𝐀𝟎
𝐲=𝟎 → 𝐂𝐀=𝐂𝐀∗
𝐲=𝐋 → 𝐂𝐀=𝐂𝐀𝟎
The mass transfer rate across the interface per unit area is therefore given by:
The concentration profiles near an interface on the basis of:
(a) The film theory (steady-state)
(b) The penetration-theory (unsteady-state)
(c) The film-penetration theory (unsteady-state)

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1.6 Mass transfer coefficients
Consider the two-film theory as shown in Figure
The rate of mass transfer per unit area from the gas film:

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The rate of mass transfer per unit area from the liquid film:
Where:
(𝐃𝐀𝐁)𝐠= (𝐃𝐀𝐁)𝐋 𝐍𝐀𝐠=𝐍𝐀𝐋
Since the film thickness 𝐙𝐠 and 𝐙𝐋 are difficult to define or estimate, then we
rewrite the above equations as follow:
But: 𝐏𝐀𝐢 and 𝐂𝐀𝐢 are difficult to measure, therefore we define the overall mass
transfer coefficient:
Where:
𝐤𝐋 is the individual liquid film mass transfer coefficient.
𝐤𝐠 is the individual gas film mass transfer coefficient.
𝐊𝐎𝐋 is the overall mass transfer coefficient based on liquid phase.
𝐊𝐎𝐆 is the overall mass transfer coefficient based on gas phase.
𝐏𝐀𝐢 is the partial pressure of the gas (A) at the interface.
𝐂𝐀𝐢 is the concentration of the liquid (A) at the interface.
𝐏𝐀∗ is the partial pressure of the gas phase which is in equilibrium with the liquid
phase 𝐂𝐀.
𝐂𝐀∗ is the concentration of the liquid phase which is in equilibrium with the gas
phase 𝐏𝐀.

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The Relationships between the various mass transfer coefficients.

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2 Part (2): Distillation
2.1 Introduction
Distillation is a method used to separate the components of liquid solution,
which depends upon the distribution of these various components between
a vapor and a liquid phase.
The vapor phase is created from the liquid phase by vaporization at the
boiling point.
Distillation is concerned with solution where all components are
appreciably volatile such as in ammonia-water or ethanol-water solutions,
where both components will be in the vapor phase.
2.2 Vapor-Liquid Equilibrium Relations
Raoult’s Law
An ideal law, Rault’s law, can be defined for vapor-liquid phases in
equilibrium (only ideal solution e.g. benzene-toluene, hexane-heptane etc
A
A
A x
P
p 
Where
PA is the partial pressure of component A in the vapor in Pa (atm)
PA is the vapor pressure of pure A in Pa (atm)
XA is the mole fraction of A in the liquid.
Composition in liquid: B
A x
x 

1
Composition in vapor: B
A y
y 

1
Boiling-Point Diagrams and xy Plots
Boiling-point diagram for system benzene (A)-toluene (B) at a total pressure of
101.32 kPa.

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Boiling-point diagram for system benzene (A)-toluene (B) at a total pressure of
101.32 kPa.
The boiling point diagram can be calculated the pure vapor-pressure
Where
pA, pB are the partial pressure of component A and B in the vapor in Pa (atm)
PA , PB are the vapor pressure of pure A and pure B in Pa (atm)
P is total pressure in Pa (atm)
xA is the mole fraction of A in the liquid.
Example Use of Raoult’s Law for Boiling-Point Diagram
Calculate the vapor and liquid compositions in equilibrium at 95ºC (368.2K) for
benzene-toluene using the vapor pressure from the table 1 at 101.32 kPa.

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The boiling point diagram can be calculated from the pure vapor-pressure data
in the table below and the following equations:

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A common method of plotting the equilibrium data is shown in Fig where yA is
plotted versus xA for the benzene-toluene system. The 45º line is given to show
that yA is richer in component A than is xA.
Fig. Equilibrium diagram for system benzene (A) – toluene (B) at 101.32 kPa
(1atm).
An azeotrope is a mixture of two or more liquids in such a ratio that its
composition cannot be changed by simple distillation.
This occurs because, when an azeotrope is boiled, the resulting vapor has the
same ratio of constituents as the original mixture.

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2.3 Single-Stage Equilibrium Contact for Vapor-Liquid System
A single equilibrium stage is
The two different phases are brought into intimate contact with each other.
The mixing time is long enough and the components are essentially at
equilibrium in the two phases after separation.

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Example Equilibrium Contact of Vapor-Liquid Mixture
A vapor at the dew point and 101.32 kPa containing a mole fraction of 0.40
benzene (A) and 0.60 toluene (B) and 100 kg mol total is contacted with 110 kg
mol of a liquid at the boiling point containing a mole fraction of 0.30 benzene and
0.70 toluene. The two streams are contacted in a single stage, and the outlet
streams leave in equilibrium with each other. Assume constant Molal overflow.
Calculate the amounts and compositions of the exit streams.

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2.4 Relative Volatility of Vapor-Liquid Systems
Relative volatility )
( AB

It is a measure of the differences in volatility between 2 components, and hence
their boiling points. It indicates how easy or difficult a particular separation will
be.
2.5 Introduction to distillation methods
Distillation has two main methods in practice.

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1. Production of vapor by boiling the liquid mixture to be separated in a single
stage and recovering and condensing the vapors. No liquid is allowed to
return to the single-stage still to contact the rising vapors.
2. Returning of a portion of the condensate to the still. The vapors rise
through a series of stages or trays, and part of the condensate flows
downward through the series of stages or trays counter currently to the
vapors (“fractional distillation, distillation with reflux, or rectification”).
There are 3 important types of distillation that occur in a single stage or still:
Equilibrium or flash distillation, Simple batch or differential distillation and
simple steam distillation
2.5.1 Equilibrium or Flash Distillation
Flash distillation is a single stage separation technique.
1. A liquid mixture is pumped through a heater to raise the temperature and
enthalpy of the mixture.
2. It then flows through a valve and the pressure is reduced, causing the liquid to
partially vaporize.
3. Once the mixture enters a big enough volume (the “flash drum”), the liquid and
vapor separate.
4. Because the vapor and liquid are in such close contact up until the “flash”
occurs, the product liquid and vapor phases approach equilibrium.

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Example A mixture of 50% mole normal heptane and 50% normal octane at 30ºC
is continuously flash distilled at 1 standard atmosphere so that 60 mol% of the
feed is vaporized. What will be the composition of the vapor and liquid products?

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2.5.2 Simple Batch or Differential Distillation

32

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2.5.3 Simple Steam Distillation

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Note that by steam distillation, as long as water is present, the high-boiling
component B vaporizes at a temperature well below its normal boiling point
without using a vacuum. The A and B are usually condensed in condenser and
the resulting two immiscible liquid phases separated.
Disadvantage: large amounts of heat must be used to simultaneously evaporate
the water with high-boiling compound.

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2.6 Distillation with Reflux and McCabe-Thiele method (Introduction to
Distillation with Reflux)
Rectification (fractionation) or stage distillation with reflux is
A series of flash-vaporization stages are arranged in a series which the vapor and
liquid products from each stage flow counter currently to each other.
The liquid in a stage is conducted or flows to the stage below and the vapor from
a stage flow upward to the stage above.

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In a distillation column the stages (referred to as sieve plates or trays) in a
distillation tower are arranged vertically, as shown schematically in figure
below.
1) Feed enters the column somewhere in the middle of the column.
2) Feed is liquid, it flows down to a sieve tray or stage.
3) Vapor enters the tray and bubbles through the liquid on this tray as the
entering liquid flows across.
4) The vapor and liquid leaving the tray are essentially in equilibrium.
5) The vapor continues up to the next tray or stage, where it is again contacted
with a down flowing liquid.
6) The concentration of the more volatile component is being increased in the
vapor form each stage going upward and decreased in the liquid from each
stage going downwards.
7) The final vapor product coming overhead is condensed in a condenser and
a portion of the liquid product (distillate) is removed, which contains a high
concentration of A.
8) The remaining liquid from the condenser is returned (refluxed) as a liquid
to the top tray.
9) The liquid leaving the bottom tray enters a reboiler, where it partially
vaporized, and the remaining liquid, which is lean in A or rich in B, is
withdrawn as liquid product. The vapor from the reboiler is sent back to
the bottom stage or trays is much greater.

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2.7 McCabe-Thiele Method of Calculation for Number of Theoretical
Stages
A mathematical – graphical method for determining the number of theoretical
trays or stages needed for a given separation of a binary mixture of A and B has
been developed by McCabe and Thiele.
The method uses material balances around certain parts of the tower, which give
operating lines and the xy equilibrium curve for the system.
Main assumption
1) Equimolar overflow through the tower between the feed inlet and the top tray
and the feed inlet and bottom tray.
2) Liquid and vapor streams enter a tray, are equilibrated, and leave.
Equation for enriching section

38

39
Equation for stripping section

40
The theoretical stages for the stripping section are determined by starting at xw,
going up to yW, and then across to the operating line, etc

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Effect of feed conditions
The condition of feed stream is represented by the quantity q, which is the
mole fraction of liquid in feed.
Location of the feed tray in a tower and number of trays.
From eqn, the q-line equation and is the locus of the intersection of the two
operating lines. Setting y = x in eqn, the intersection of the q-line equation with
the 45º line is y=x=xF, where xF is the overall composition of the feed.

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In given below the figure, the q line is plotted for various feed conditions. The
slope of the q line is q/ (q-1).
Using Operating Lines and the Feed Line in McCabe-Thiele Design
q = 0 (saturated vapor)
q = 1 (saturated liquid)
q > 1(subcooled liquid)
q < 0 (superheated vapor)
0 < q < 1 (mix of liquid and
vapor)

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Example A continuous fractioning column is to be designed to separate 30,000
kg/h of a mixture of 40 percent benzene and 60 percent toluene into an overhead
product containing 97 percent benzene and a bottom product containing 98
percent toluene. These percentages are by weight. A reflux ratio of 3.5 mol to 1
mol of product is to be used. The molal latent heats of benzene and toluene are
7,360 and 7,960 cal/g mol, respectively. Benzene and toluene from a nearly ideal
system with a relative volatility of about 2.5. The feed has a boiling point of 95ºC
at a pressure of 1 atm.
a) Calculate the moles of overhead product and bottom product per hour.
b) Determine the number of ideal plates and the position of the feed plate
(i) If the feed is liquid and at its boiling point;
(ii) If the feed is liquid and at 20ºC (specific heat 0.44 cal/g. ºC);
(iii) If the feed is a mixture of two-thirds vapor and one-third liquid.
Solution (b) (i),
We determine the number of ideal plates and position of the feed plate.
1) Plot the equilibrium diagram, erect verticals at XD, xF, and xB.
2) Draw the feed line. Here q=1, and the feed line is vertical.

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3) Plot the operating lines. The intercept of the rectifying lie on the y axis is,
XD/(R+1) = 0.974/ (3.5+1) = 0.216. From the intersection of the rectifying
operating line and the feed line, the stripping line is drawn.
4) Draw the rectangular steps between the two operating lines and the
equilibrium curve. The stripping line is at the seventh step. By counting
steps it is found that, besides the reboiler, 11 ideal plates are needed and
feed should be introduced on the seventh plate from the top.

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Solution (b) (iii),
From the definition of q it follows that for this case q = 1/3 and the slope of the
feed line is -0.5. The solution is shown in Fig. below. It calls for a reboiler and
12 plates, with the feed entering on the seventh plate.

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Total and Minimum Reflux Ratio for McCabe-Thiele Method

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C) Operating and optimum reflux ratio
Total reflux = number of plates is a minimum, but the tower diameter is infinite.
This corresponds to an infinite cost of tower and steam and cooling water. This
is the limit in the tower operation.
Minimum reflux = number of trays is infinite, which again gives an infinite cost.
These are the two limits in operation of the tower.
Actual operating reflux ratio to use is in between these two limits. The
optimum reflux ratio to use for lowest total cost per year is between the
minimum Rm and total reflux (1.2Rm to 1.5Rm).
2.8 General Design Consideration
1. A tower design is normally divided into two main steps, a process design
followed by a mechanical design. The purpose of the process design is to
calculate the number of required theoretical stages, column diameter and
tower height. On the other hand, the mechanical design focuses on the
tower internals and heat exchanger arrangements.

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2. Many factors have to be considered in designing a distillation column such
as the safety and environmental requirements, column performance,
economics of the design and other parameters, which may constrain the
work.
The first step in distillation column design is to determine the separation
sequences, which depends on the relative volatility and concentration of each
component in the feed. King has outlined a few design rules as follows:
1) Direct sequences that remove the components one by one in the distillate are
generally favored.
2) Sequences that result in a more equal-molar division of the feed between
distillate and bottoms products should be favored.
3) Separations where the relative volatility of two adjacent components is close
to unity should be performed in the absence of other components; i.e., reserve
such a separation until the last column in the sequence.
4) Separations involving high-specified recovery fractions should be reserved
until last in the sequence.
Once the separation sequence is decided, engineering calculations follow to
determine the number of theoretical stages, operating parameters and tower
dimensions. In general, the steps included in distillation calculations are
summarized into the following:
1) Performing a material balance for the column
2) Determining the tower operating pressure (and/or temperature)
3) Calculating the minimum number of theoretical stages using the Fenske
equation
4) Calculating the minimum reflux rate using the Underwood equations
5) Determining the operating reflux rate and number of theoretical stages
6) Selection of column internals (tray or packings)
7) Calculating the tower diameter and height
Some general design rules that should be considered are as follows:
1) Distillation is usually the most economical method of separating liquids.
2) For Ideal mixtures (low pressure, medium temperature, and non-polar), relative
volatility is the ratio of vapor pressures i.e. α = P2/P1
3) Tower operating pressure is determined most often by the temperature of
the available cooling medium in the condenser or by the maximum allowable
reboiler temperature.
4) Tower Sequencing:
A. Easiest separation first – least trays and reflux

49
B. When neither relative volatility nor feed concentrations vary widely,
remove components one by one as overhead products.
C. When the adjacent ordered components in the feed vary widely in relative
volatility, sequence the splits in order of decreasing volatility.
D. When the concentration in the feed varies widely but the relative
volatilities do not, remove the components in the order of decreasing
concentration in the feed.
5) Economically optimum reflux ratio is about 120% to 150% of the minimum
reflux ratio.
6) The economically optimum number of stages is about 200% of the minimum
value.
7) A safety factor of at least 10% above the number of stages by the best
method is advisable.
8) A safety factor of at least 25% about the reflux should be utilized for the
reflux pumps.
9) Reflux drums are almost always horizontally mounted and designed for
a 5 min holdup at half of the drum's capacity.
10) For towers that are at least 3 ft (0.9 m) in diameter, 4 ft (1.2 m) should be
added to the top for vapor release and 6 ft (1.8 m) should be added to the bottom
to account for the liquid level and reboiler return.
11) Limit tower heights to 175 ft (53 m) due to wind load and foundation
Considerations.
12) The Length/Diameter ratio of a tower should be no more than 30 and
preferably below 20.
13) A rough estimate of reboiler duty as a function of tower diameter is
given by:
Q = 0.5 D2 for pressure distillation
Q = 0.3 D2 for atmospheric distillation
Q = 0.15 D2 for vacuum distillation
Where,
Q: Energy in Million Btu/hr
D: Tower diameter in feet.
2.9 The Selection of Column Internals
The selection of column internals has a big impact on the column performance
and the maintenance cost of a distillation tower.
There are several choices of column internals and the two major categories are
trays and packing. The choice of which to utilize depends on the
1) Pressure,

50
2) Fouling potential,
3) Liquid to vapor density ratio,
4) Liquid loading, and
5) Most importantly the life cycle cost.
Trays can be divided into many categories, such as baffle trays, dual flow trays,
conventional trays, high capacity trays, multiple down comer trays and system
limit trays. According to some rules of thumb, trays should be selected if:
1) The compounds contain solids or foulants
2) There are many internal transitions
3) Liquid loads are high
4) There is a lack of experience in the service
5) Vessel wall needs periodic inspection
6) There are multiple liquid phases
On the other hand, packing divisions include grid packing, random packing,
conventional structured packing, and high capacity structured packing. The rules
of thumb for selecting packing are:
1) The compounds are temperature sensitive
2) Pressure drop is important (vacuum service)
3) Liquid loads are low
4) Towers are small in diameter
5) Highly corrosive service (use plastic or carbon)
6) The system is foaming
7) The ratio of tower diameter to random packing is greater than 10
Some design guidelines should be considered when designing a tray tower, such
as follows:
1) Tray spacing should be from 18 to 24 inches, with accessibility in mind
(Generally, for a tower diameter of 4 feet and above, the most common tray
spacing is 24 inches to allow easy access for maintenance. However, for a
tower diameter below 4 feet, a tray spacing of 18 inches is adequate as the
column wall can be reached from the man way.)
2) Peak tray efficiencies usually occur at linear vapor velocities of 2 ft/s (0.6 m/s)
at moderate pressures, or 6 ft/s (1.8 m/s) under vacuum conditions.
3) A typical pressure drop per tray is 0.1 psi (0.007 bar)
4) Tray efficiencies for aqueous solutions are usually in the range of 60-90%
while gas absorption and stripping typically have efficiencies closer to 10-
20%
5) Sieve tray holes are 0.25 to 0.50 in. diameter with the total whole area being
about 10% of the total active tray area. Maximum efficiency is 0.5 in and 8%.

51
6) Valve trays typically have 1.5 in. diameter holes each with a lifting cap. 12-14
caps/square foot of tray is a good benchmark.
7) the most common weir heights are 2 and 3 in and the weir length is typically
75% of the tray diameter.
The packed tower design concepts are listed below:
1) Packed towers almost always have lower pressure drop compared to tray
towers.
2) Packing is often retrofitted into existing tray towers to increase capacity or
separation.
3) For gas flow rates of 500 ft3/min (14.2 m3/min), use 1 in (2.5 cm) packing,
for gas flows of 2000 ft3/min (56.6 m3/min) or more, use 2 in (5 cm) packing.
4) Ratio of tower diameter to packing diameter should usually be at least 15
5) Due to the possibility of deformation, plastic packing should be limited to an
unsupported depth of 10-15 ft (3-4 m) while metal packing can withstand 20-25
ft (6-7.6 m).
6) Liquid distributor should be placed every 5-10 tower diameters (along the
length) for pall rings and every 20 ft (6.5 m) for other types of random
packing.
7) For redistribution, there should be 8-12 streams per sq. foot of tower area for
towers larger than three feet in diameter. They should be even more numerous
in smaller towers.
8) Packed columns should operate near 70% flooding.
9) Height Equivalent to Theoretical Stage (HETS) for vapor-liquid contacting is
1.3- 1.8 ft (0.4-0.56 m) for 1 in pall rings and 2.5-3.0 ft (0.76-0.90 m) for 2 in
pall rings.
10) Design pressure drops should be as follows:

52

53
3 Part (3): Distillation column
Distillation Definition
3.1 Definition:
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.
3.2 Distillation Process Types
 Batch
 Continuous
Batch Process
In batch operation, the feed to the column is introduced batch-wise. That is,
the column is charged with a 'batch' and then the distillation process is carried
out. When the desired task is achieved, a next batch of feed is introduced.
Continuous Columns
In contrast, continuous columns process a continuous feed stream. No
interruptions occur unless there is a problem with the column or surrounding
process units. They are capable of handling high throughputs and are the more
common of the two types. We shall concentrate only on this class of columns.
3.3 Distillation Types
Continuous columns can be further classified according to:
 The nature of the feed that they are processing,
 Binary column -feed contains only two components
 multi-component column -feed contains more than two components
 The number of product streams they have
 multi-product column -column has more than two product streams
 Where the extra feed exits when it is used to help with the separation,
 extractive distillation -where the extra feed appears in the bottom
product stream

54
 azeotropic distillation -where the extra feed appears at the top product
stream
 The type of column internals
 Tray column -where trays of various designs are used to hold up the
liquid to provide better contact between vapor and liquid, hence better
separation
 packed column -where instead of trays, 'packings' are used to enhance
contact between vapor and liquid .
3.4 Distillation Equipment
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 Sep.
 a reboiler to provide the necessary vaporization 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

55
3.5 Process Description
 The liquid mixture that is to be processed is known as the feed and this is
introduced usually somewhere near the middle of the column to a tray
known as the feed tray. The feed tray divides the column into a top
(enriching or rectification) section and a bottom (stripping) section. The
feed flows down the column where it is collected at the bottom in the
reboiler.
 Heat is supplied to the reboiler to generate vapor. The source of heat input
can be any suitable fluid, although in most chemical plants this is normally
steam. In refineries, the heating source may be the output streams of other
columns. The vapor raised in the reboiler is re-introduced into the unit at
the bottom of the column. The liquid removed from the reboiler is known
as the bottoms product or simply, bottoms
 The vapour moves up the column, and as it exits the top of the unit, it is
cooled by a condenser. The condensed liquid is stored in a holding vessel
known as the reflux drum. Some of this liquid is recycled back to the top
of the column and this is called the reflux. The condensed liquid that is
removed from the system is known as the distillate or top product.

56
3.6 Column Internals
Trays: stage wise process (used to hold up the liquid to give better separation)
 Sieve
 Valve
 Bubble cap
Packings: continuous process (packed columns are used to enhance contact
between vapour & liquid)
 Random packings
 Structured packings
3.7 Distillation Trays
 Sieve tray:
Metal, diameter & number of holes are design
considerations (cheap and simple)
 Bubble Cap tray:
Has raised chimneys fitted over each
holed, a cap covers the riser. There is
a space between riser and cap to allow the
passage of vapour. The vapour rises
through the chimney directed downwards
by the cap on discharging through slots in
the cap bubbling through the liquid on the
tray.
 Valve Tray:
Perforations are covered by lift able
caps, self-creating a flow area for
passage of vapour through the liquid.
The lifting caps direct the vapour to
flow horizontally into the liquid (better
mixing)
3.8 Packed Columns
Packing characteristics in operation:
 Large surface area for maximum vapour/ liquid contact
 High degree of turbulence to promote rapid, efficient mass transfer
between phases

57
 Open structure for low resistance to vapour flow, hence low pressure
drops
 Promote uniform liquid distribution on surface
 Promote uniform gas flow across column cross-section
3.8.1 Packing Types
 Shaped packing/ random packing
 Structured packing
Various random shaped packing including:
 Rasching Rings: simple hollow ring, oldest, cheapest, most widely used,
less effective, not necessarily most economic. Can be made in various
material and ceramic and carbon.
 Lessing Rings: Rasching Rings with partitions across its Centre, increased
surface area and strength. Ceramic and metals
 Pall Rings: superior performance, highly effective give better wetting and
distillation. Liquid smaller pressure drop than Rasching under same
conditions, available in metals, ceramics and plastics.
 Berl saddles: less free gas space better aerodynamic shape, ceramic or
plastic

58
Common tower packings:
(a) Raschig rings; (b) metal Pall ring; (c) plastic Pall ring; (cl) Bed saddle;
(e) ceramic Intalox saddle; (f) plastic Super Intalox saddle; (g) metal
Intalox saddle.
3.9 Column Components
3.9.1 Column Reboiler
There are a number of designs of re‐boilers, they can be regarded as heat
exchangers that are required to transfer enough energy to bring the liquid at the
bottom of the column to boiling point.
Kettle Type Reboiler:
In this reboiler, the bottom product from the tower flows to the bottom of the
reboiler and comes in contact with the hot coils which are heated by steam or
another heating medium. Part of the liquid is vaporized and returns back to the
tower. It is this hot vapor that passes up through the trays to fractionate the
product on each tray. Stated another way, the heat drives the tower. The liquid
that is not vaporized passes over the weir plate behind the tube bundle and is level
controlled out of the reboiler.

59
The thermal syphon Reboiler:
The thermal syphon reboiler uses convection alone to produce circulation. The
bottom product flows to the bottom of the reboiler by gravity. The addition of
heat causes some of the liquid in the reboiler to vaporize and the remaining heated
liquid expands. The mixture of vapor and hot liquid in the reboiler has a much
lower relative density than the bottom liquid and a thermal syphon flow is
produced.
Fired Heater Reboiler:
The flow through the fired heater type reboiler must be positive to prevent
overheating of the tubes in the heater. The fractionator bottom pump circulates
allor nearly all, of the bottom product through the reboiler. A positive flow
through all passes of the reboiler is very critical and the controls must be
interlocked so flow failure will shut down the burners to the heater. In some
operations the fired heater will supply heat to more than one fractionator.
Other Types:
 Internal Reboiler and Jacketed Kettle Reboiler

60
3.10 Column Condenser
Liquid-vapor contact in the top of the tower is required to purify the overhead
product and to condense any bottom product that is being driven overhead. The
condensing of some or all, of the overhead product is accomplished by cooling
the overhead product in a heat exchanger.
 The overhead condenser may use any of the following for a cooling
medium:
1. "Fin Fan Cooler", which is a heat exchanger containing finned tubes to
increase the heating surface. Air is forced across the tubes by fans, “Fin
Fan".
2. "Water Cooled Condensers", in which the overhead product temperature
may be controlled by regulating the flow of cooling water through the
condenser. This method may be employed to condense all or part of the
overhead product.
3.10.1Condensers Types
Partial Condensers:
 The partial condenser is best used when there is a large difference in the
overhead vapor compositions. For example when there is a small amount
of methane and hydrogen mixed in a propylene stream, like in the
propylene towers. The partial condenser condenses the propylene and
leaves the methane and hydrogen as a vapor to be vented from the
overhead receiver.
Total Condensers:
 Total condensers are used to condense all the vapor product coming from
the top of the fractionator. The reflux and the condensed product are
essentially of the same composition and control is maintained by
regulating the amount of cooling medium passing through the condenser.
Total condensers are commonly used in condensing LPG and heavier
products.
3.11 Column Reflux
The word reflux is defined as "flowing back". Applying it to distillation tower,
reflux is the liquid flowing back down the tower from each successive stage.

61
Kinds of Reflux
A. Cold Reflux
Cold reflux is defined as reflux that is supplied at temperature a little below that
at the top of the tower. Each pound of this reflux removes a quantity of heat equal
to the sum of its latent and sensible heat required to raise its temperature from
reflux drum temperature to the temperature at the top of the tower.
B. Hot Reflux
It is the reflux that is admitted to the tower at the same temperature as that
maintained at the top of the tower. It is capable of removing the latent heat
because no difference in temperature is involved.
C. Internal Reflux
It is the reflux or the overflow from one plate to another in the tower, and may be
called hot reflux because it is always substantially at its boiling point. It is also
capable of removing the latent heat only because no difference in temperature is
involved.
D. Circulating Reflux
It is also able to remove only the sensible heat which is represented by its change
in temperature as it circulates. The reflux is withdrawn and is returned to the
tower after having been cooled.
E. Side Reflux
This type of reflux (circulating reflux) may conveniently be used to remove heat
at points below the top of the tower. If used in this manner, it tends to decrease
the volume of vapor the tower handles.
F. Total Reflux
Total reflux is the conclusion when all the condensate is returned to the tower as
reflux, no product is taken off and there is no feed.
3.12 Column Problems
Foaming
 Refers to the expansion of liquid due to passage of vapor or gas, caused by
high vapor flow rates.
 Although it provides high interfacial liquid-vapor 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.

62
 Whatever the cause, separation efficiency is always reduced.
Entrainment
 Caused by excessively high vapor flow rates.
 Entrainment refers to the liquid carried by vapor to the tray above.
 It is detrimental because tray efficiency is reduced: lower volatile material
is carried to a plate holding liquid of higher volatility.
 Excessive entrainment can lead to flooding.
Flooding
 Is brought about by excessive vapor flow, causing liquid to be entrained in
the vapor up the column.
 The increased pressure from excessive vapor also backs up the liquid in the
down comer, 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
Weeping and Dumping
 Caused by excessively low vapor flow.
 The pressure exerted by the vapor is insufficient to hold up the liquid
on the tray. Therefore, liquid starts to leak through perforations.
 Excessive weeping will lead to dumping - 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.

63

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