Topics
 Vapor-liquid equilibrium
 Types of Distillation
 Mass Balance in a Distillation Column
 Determination of Ideal Number of Plates –
McCabe –Thiele &
 Multicomponents Distillation
Introduction
What is Distillation
Distillation is a process wherein 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.
method of separating mixtures based on differences in their
volatilities in a boiling liquid mixture.
less volatile, "heavy" or "high boiling", components
concentrate in the liquid phase; the more volatile, "light",
components concentrate in the vapor.
used for many commercial processes, such as production of
gasoline, distilled water, alcohol, and many other liquids
2.1: Vapor-Liquid Equilibrium (VLE)
 Equilibrium in Chemical Engineering
 Chemical equilibrium
 rates of reaction in both directions are same.
 Phase equilibrium
 the rate of changing from one phase to another is same to
the rate of the reverse change.
 Vapor-liquid phase equilibrium: ??: ??
Vapor-Liquid Equilibrium (VLE)
 Condition or state where the rate of evaporation (liquid changing
to vapor) equals the rate of condensation (vapor changing to
liquid).
 VLE data can be determined experimentally using an equilibrium
still.
 or
 VLE data can be determined or approximated with the help of
certain theories such as Raoult's Law, Dalton's Law, and/or
Henry's Law.
Binary system-VLE Data
 There are several different types of plots for binary system:
Pxy diagram: x and y as functions of pressure at constant
temperature.
2. Txy diagram: x and y as functions of temperature at constant
pressure.
3. xy diagram: x versus y at constant pressure (temperature is a
parameter along the curve).
1.
 Since most applications require data at constant pressure,
Txy and xy diagrams are the most commonly used.
Txy Diagram (Phase Diagram)
Binary system-VLE Data
xy Diagrams

xy diagram for a binary system,
relates the compositions of the liquid
and vapor phases in equilibrium with
each other.

These diagrams be generated from
Constant pressure- boiling point
diagram
xy diagram for binary system
Binary system-VLE Data
 How to present
VLE data?
Temperature-composition diagram(Txy)
Binary system-VLE Data
VLE data is obtained from Boiling points diagram
Step 1
T
Tb(B)
V
T1
T2
T3
T4
Tb(A)
L
x1
x2
x3 y1
x4 y2
y3 y4
xA
Binary system-VLE Data
Step 2
Plots x-y diagram
yA
T4
T3
T2
T1
xA
VLE Relationship
If experimental data are not available, estimation of VLE can still be
done. HOW?
 simplest method assumes ideal vapor and ideal liquid phases.
Raoult’s Law
Pyi  Pi xi
sat
Where
p i  Pi o xi
pi= partial pressure of species i in the vapor
Pi o = the vapor pressure of pure species
xi=mole fraction of species i in the liquid
12
VLE at Low Pressures – Raoult’s Law
Calculations Using Raoult's Law
Bubble-point pressure problem -- T,x given -- P,y unknown.
The vapor pressures are found at the given temperature, which allows direct
calculation of the pressure and vapor mole fractions:

Pyi  P   Pi sat xi
Pi sat xi
yi 
P
Where
P
Pi sat
xi
= total pressure of component A in the vapor.
= vapor pressure of species i
=mole fraction of species i in the liquid
VLE at Low Pressures – Raoult’s Law
Calculations Using Raoult's Law
Dew-point pressure problem -- T,y given -- P,x unknown.
No trial and error is needed, as P can be directly calculated.
Pyi
xi  sat
Pi
P

x
1
yi / Pi sat
i

1
Example 1: (Use of Raoult’s Law for boiling point Diagram)
Use Raoult's Law and calculate the vapour and liquid compositions in
equilibrium at 95Co (368.2 K) (in mole fractions, y and x) for the benzenetoluene system using vapour pressure data measure at a pressure of 101.32
kPa as shown in Table 1 below :
Table 1:
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.
 AB 
y A / xA
y A / xA

y B / xB (1  y A )(1  x A )
Where αAB is the relative volatility of A with respect to B in the binary system.
Raoult’s law:
yA 
 AB
P xA
P
PB0 x B
yB 
P
PA0
 0
PB
yA 
16
0
A
 AB x A
1  ( AB  1) x A
when αAB is above 1.0, a separation is possible.
Example: Using data from table 1 calculate the relative volatility for
the benzene-toluene system at 85ºC (358.2K) and 105ºC (378.2K)
Solution: At 85ºC, substituting into equation below for a system following
Raoutl’s law,
 AB
PA0 116.9
 0 
 2.54
PB
46.0
Similarly at 105ºC,

The variation in α is about 7%.
17
204.2
 2.38
86.0
Answer
The types of distillation
There are 3 types in which the distillation may be carried out;

Differential or batch distillation

Flash Distillation or equilibrium distillation

Continuous Distillation with reflux – Binary systems
Differential or Batch distillation
 Batch distillation without reflux




is often called differential
distillation.
Because there is no reflux, the
vapor product is in equilibrium
with the liquid residue in the
tank at any given time.
Feed to the column is
introduced batch-wise.
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.
Flash Distillation
 Flash distillation is used most for separating components that boil at
widely different temperatures. Example: separation of crude oil.
 The process involves heating a feed stream and then allowing it to
expand into a vessel maintained at low pressure.
 Partial vaporization then occurs, and a phase equilibrium is (ideally)
reached.

May be represented in equilibrium curve, in terms of;
 x (concentration of liquid),
 y (concentration of vapor) and
 f ( molal fraction of feed that is vaporized and withdrawn
continuously as vapor)
xf
1 f
y
xf 
f
f
Flash Distillation
More volatile component will be
concentrated in the vapor stream – the
less volatile in the liquid stream
Feed is preheated before
entering the separator
It is “flashed” by throttling
the feed stream through a
nozzle or valve into the
chamber – the pressure
drops through the valve.
A feed stream is
“flashed” into flash drum
and the liquid and vapor
are allowed to separate
under equilibrium.
Continuous Distillation with Reflux
 It effective separating components of comparable volatility.



This requires the column to be constantly fed with new raw
material and the reboiler drained of the bottoms product
Feed – somewhere near the middle of column;
 Top of the feed – enriching/rectification
 Bottom of the feed – stripping
Concentration of the more volatile component is being increased
in the vapor from each stage going upward and decreased in the
liquid from each stage going downward
To cool and condense the vapor leaving
the top of the column
Trays/plates
and/or
packings which
are used to
enhance
component
separations
Bottoms B richer in the
less volatile
component,
where the mole
fraction of the
more volatile
component is,
xB
To hold the condensed
vapor so that liquid
(reflux) can be recycled
back to the column
Distillate D
which is
richer in the
more
volatile
component
of mole
fraction,
xD.
provide the necessary vaporization for
the distillation process
Distillation with reflux and McCABE-THIELE
method
 Rectification
(fractionation )or
stage distillation with reflux ;
can be considered to be a process in
which a series of flash-vaporization
stages are arranged in a series in such
a manner that the vapor and liquid
products from each stage flow
counter current to each other
Hence in each stage , a vapor V and
a liquid stream L enter, are contact
and mixed and equilibrated , and a
vapor and a liquid stream leave in
equilibrium
Lin,xin
Vout,yout
Lout,xout
Vin,yin
At each stage of the column
two phases come in contact
with each other, mix, approach
thermal and composition
equilibrium to the extent which
depends on the efficiency of
the contact stage
Streams leaving the stage are in thermodynamic
equilibrium with each other
Streams coming to the stage are not in equilibrium
McCabe-Thiele method of calculation for Number of
theoretical Stages
 It is 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.
 The main assumption in this method is that There must be an
equi-molar flow through the tower between the feed inlet and the top
tray and the feed inlet and the bottom tray
Action on an Ideal Plate



By definition, a vapour and liquid leaving a plate are brought into
equilibrium.
Assume that the plates are numbered serially from top down and
that the plate under consideration is the nth plate from the top.
Then the immediately above plate n is plate n-1, and the
immediately below is n+1.
Vn-1
Ln-2
Xn-2
yn-1
Plate n-1
Ln-1
Vn
Xn-1
yn
Plate n
Ln,
Vn+1
xn
yn+1
Plate n+1
Material –balance diagram for plate n
Ln+1
Vn+2,
Xn+1
yn+2
3.0 Material balances for two components systems
1. Total material balance on the entire column
F=D+B
2. Component material balance on component A
F xF= D xD+ BxB
W=B
Fig 1.10: Material balance for
continuous fractionating column
. Material Balances (top section)
3
Material Balances (top section)
 Material balance around condenser:
V  LD
 Overall material balance over the Fig 1.11:
Vn1  Ln  D
 Components material balance over the Fig 1.11:
Vn 1 y n 1  L n x n  D x D
L
D
yn 1  n xn 
xD
Vn 1
Vn 1
 R 
 1 
y
 x
 xD
R

1
R

1




where
30
R
Ln

D
Reflux ratio = constant
July 2012
Material Balances (top section)
Ln
 slope
D
Ln
R
R

Vn 1 R  1
R
31
July 2012
Operating Line: Rectifying
y
yn 1
R
1

xn 
xD
R 1
R 1
slope=R/(R+1)
1
xD
R 1
xD
32
x
4. Material Balances (bottom section- Stripping)
Vm 1  Lm  W
Vm 1 y m 1  Lm x m  WxW
y m 1
Lm
Wx w

xm 
Vm 1
Vm 1
liquid flow to plate m+1 = Vapour flow from plate m+1 + Bottom product withdrawn
Overall components material balance over plate m+1:
Rearranging the equation :
Since equi-molar flow is assumed ,the
slop is
Lm
Vm 1
Feed Line (q-line)
 The conditions of the vapour rate or the liquid rate may change
depending of the thermal condition of the feed.
 It is related to the heat to vaporise one mole of feed divided by molar


latent heat (q)
It is the locus of the intersection of the two operating lines
Its intersection with the 450 line is y=x=xf where xf is the overall
composition of the feed.
Feed Line Equation
 If xq = xF, and yq =xF then;
 The point of intersection of the two operating lines lies on the
straight line of slope (q/q -1) and intercept (xF, yF)
yq
q
q
xF

xq 
q 1
q 1
the heat needed to vaporize 1 mole of feed entering conditions
molar latent heat of vaporization of feed
Feed line behavior (q-line)
Feed at saturated liquid
q=1
y
Feed partial vapor
Feed at saturated vapour
Feed superheated
Cold feed
q>1
0<q<1
x=xf
q=0
q<0
yq
q
xF

xq 
q 1
q 1
x
37
THEORETICAL STAGES
 Starting at xD and stepping of the
plate xW
 Since reboiler is considered a
theoretical step, the no of theoretical
trays in a tower is equal to the
number of the theoretical step,
minus 1.
 No of trays = No of steps– 1(reboiler)
4 stages + reboiler
Construction for the McCabe-Thiele Method
1.
2.
equilibrium
curve
equilibrium
curve
45° line
Step 1: Plot equilibrium curve and 45 degree line.
Step 2: Plot given compositions (xF, xB, and xD)
Step 3: Draw q-line from xF and yF
Step 4: Determine Rmin from intersection of the
rectifying section OL and the equilibrium curve.
Step 5: Determine R from R/Rmin
Step 6: Draw OL for Rectifying section
Step 7: Draw OL for Stripping section
y
y
45° line
xB
x
x=zF
xD
y
y
xB
x=zF
xD
equilibrium
curve
equilibrium
curve
equilibrium
curve
equilibrium
curve
7.
5. and 6.
4.
3.
y
y
xB
x=zF
Rmin/(Rmin+1)
xD
xB
x=zF
R/(R+1)
xD
xB
x=zF
xD
Complete picture McCabe Thiele
yn 1 
R
1
xn 
xD
R 1
R 1
y
y1
xF
q
y
x
q 1
1 q
y m 1
Lm
Wx w

xm 
Vm 1
Vm 1
zf
yB
1
xD
R 1
xB xN
zf
xD
x
Complete picture McCabe Thiele
Step 1: Plot equilibrium curve(VLE) data.
Step 2: Plot 45 degree line(diagonal line. y=x)
Step 3: Plot given compositions (xF, xB, and
xD)
Step 4: Draw q-line from xF and yF
Step 5: Draw OL for Rectifying section
Step 6 : Draw OL for Stripping section
Step 7: Start stepping off from the distillate
end until
the intersection of the two operating
lines is passed.
Step 8: Continue stepping but use the
stripping operating line.
Step 9: Count the number of stages.
Step 10: Subtract one for the reboiler to give
the number of theoretical trays
y
y1
zf
yB
xB xN
zf
xD
x
Reflux Ratio
 The analysis of fractionating columns is facilitated by the
use of a quantity called reflux ratio.
 Two ratios are used, one is the ratio of the reflux to the
overhead product and the other is the ratio of the reflux to
the vapour.
 Both ratios refer to quantities in the rectifying section.
The equations for those ratios are
L V D
RD  
D
D
and
L
L
RV  
V LD
Minimum Reflux Ratio Rm
• Reflux ratio, R that will require an infinite number of plate for the
given desired separation of xd and xb
• at any reflux less than total, the number of plates needed is larger
than at total reflux and increases continuously as the reflux ratio
decreased.
• This corresponds to the minimum amount of liquid return in the
tower, and hence the minimum reboiler duty and condenser cooling
capacity
If R is decreased, the slope of the (ROL) operating line R/(R + 1) is
decreased, and the intersection of this line and the stripping line with the
q line moves farther from the 450 line and closer to the equilibrium line.
To achieve separation, the number of steps required to give a fixed xD
and xW increases.
Separation more difficult when driving
force of mass transfer is zero
(operation at equilibrium point)
Minimum Reflux
Min Reflux happens when the two operating lines intersect
on equilibrium curve
1.0
0.9
0.8
0.7
Ya
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0
0.1
XB
0.2
0.3
0.4
0.5
Xa
0.6
0.7
0.8
0.9
XD
1.0
Minimum Reflux
Don’t forget the q line. Min reflux occurs at intersection with
equilibrium curve because all three lines should intersect
1.0
0.9
0.8
0.7
Ya
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0
0.1
XB
0.2
0.3
0.4
0.5
Xa
0.6
0.7
0.8
0.9
XD
1.0
Calculation of Minimum Reflux Ratio Rm
 Based on the previous figure, the slope of the line is
given by
yn 1 
R
1
xn 
xD
R 1
R 1
At this point: xn=x* and yn+1=y*
Rmin
1
y* 
x*
xD
Rmin  1
Rmin  1
Rmin
xD  y *

y * x *
Minimum Reflux Ratio Rm
y
Rmin
1
y* 
x*
xD
Rmin  1
Rmin  1
Rmin
xD  y *

y * x *
slope=R/(R+1)
y*
1
xD
R 1
xF
xB
x*
xD
x
Feed –liquid at bubble point
(saturated liquid feed) q=1
Feed –cold liquid (q>1)
Feed –partially vapour( 0<q<1)
Feed –saturated vapor (q=0)
Minimum num of plates or Total Reflux
 If no product is withdrawn from the still (D=0), the column is
said to operate under conditions of total reflux and, as seen from
equation , the top operating line has its maximum slope of unity,
and coincides with the line x=y.
Total reflux
yn 1 
R
1
xn 
xD
R 1
R 1
F=0
If R=L/D= ∞ then R/(R+1)=1; also L=V
yn 1  xn
D=0
R=L/D=∞
L/V=1
Ln  D  Vn1
Ln  Vn1
B=0
Total Reflux
 All vapour is condensed and returned as liquid
 Minimum number of theoretical steps
 Can use Fenske equation to calculate Nmin
N min
 xD

1  xB  

log
.
1  xD  xB 


ln  av
 (Ref.Transport Process and Separation Process Principles, Geankoplis 4th
ed. Page:716)
 Sometimes a column is operated in total reflux at startup
MULTI COMPONENT SYSTEM
 Separation of more than two components.
 Base on the relative volatility i value of each components,
(light or heavy components)
A
A, B
Key component:
-light key
A,
B,C
1
-Heavy key
2
C
B
MULTICOMPONENT SYSTEM
 For non ideal solution (hydrocarbons), the equilibrium data
can be described by K factors (distribution coefficient)
yi  K i x i
yi
Ki 
xi
 “K”= ratio of mole fraction in vapor and liquid phases at
equilibrium
 The value of K are available from Depriester Chart.
 Raoult’s law (ideal
system)
 K (for non ideal
system-dependant on T
and P)
y A  K A xA
MULTICOMPONENT SYSTEM
Phase equilibrium in multicomponent
 For ideal solutions, the equilibrium data can be calculated from
the Raoult’s and Dalton’s Law
pi
yi 
P
pi  x P
o
i i
(Raoult’s Law)
(Dalton’s Law)
x i Pio Pio
Ki 

Px i
P
p A PAo x A
yA 

 K A xA
P
P
MULTICOMPONENT SYSTEM
Phase equilibrium in multicomponent
 Relative volatility (αi) for each component in a multicomponent
can be defined similar with binary mixture.
 If component C in a mixture of A, B, C and D is selected as the
base component,
Ki
i 
KC
Pio
 ij  o
Pj
MULTICOMPONENT SYSTEM
Phase equilibrium in multicomponent
 K factor strongly temperature dependent because of the change in
vapor pressure.
 The ratio of K factor is the same as the relative volatility of
components:
o
yi / xi
K i Pi
 ij 

 o
y j / x j K j Pj
MULTICOMPONENT SYSTEM
Bubble Point
 ….initial boiling point of a liquid mixture.
 Must satisfy the relation yi=1.0
 y  K x
i
i
i
 1.0
 The temperature is assumed and values of Ki are obtained
from vapor pressure data and the known total pressure.
MULTICOMPONENT SYSTEM
Bubble Point
 If the summation Kixi
> 1.0, a lower temperature is chosen
and repeat the calculation until the equation is satisfied.
 If the summation Kixi = 1.0, the composition of the vapor in
equilibrium with liquid
MULTICOMPONENT SYSTEM
Bubble Point
For a mixture of A, B, C and D with C as the base component:

Assume the temperature.

Calculate the value of αi from the value of Ki at this
temperature.
K C  1.0

Calculate the value of KC from
  i xi

Compare the temperature corresponding to the calculated
value of KC to the assumed temperature.
MULTICOMPONENT SYSTEM
Bubble Point


If the values differ, the calculated temperature is used for the
next iteration.
After the final temperature is known, the vapor composition is
calculated from
i x i
yi 
  i x i 
Example 1
A liquid feed to a distillation tower at 405.3 kPa abs is fed
to a distillation tower. The composition in mole fractions is
as follows: n-butane (xA=0.40), n-pentane (xB=0.25), n
hexane (xC=0.20), n-heptane (xD=0.15). Calculate the
boiling point and the vapor in equilibrium with the liquid.
Let n-hexane will be the base component.
Solution: Assume a temperature and find the K values for
all component.
MULTICOMPONENT SYSTEM
Dew Point
 ...initial condensation temperature
 Must satisfy the relation xi=1.0
 yi 
 xi   
  1.0
 Ki 
 Also trial and error calculation
 After final T is known, liquid composition calculated
from
yi  i
xi 
  yi  i 
EXAMPLE:
BOILING POINT,DEW POINT, AND FLASH
VAPORIZATION OF MULTICOMPONENT FEED
 A liquid feed to a distillation tower at 405.3 Kpa abs is fed to a
distillation tower. The composition in mole fractions is as
follows:
 N-butane (xA=0.40)
 N-pentane (xB=0.25)
 N-hexane (xC=0.20)----------base component
 N-heptane (xD=0.15)
a) Calculate the boiling point of feed and composition of vapor in
equilibrium.
b) Calculate the dew point of feed and composition of liquid in
equilibrium.