Introduction to multicomponent distillation

Introduction to multicomponent distillationIntroduction to multicomponent distillation
• Most of the distillation processes deal with multicomponent mixtures
• Multicomponent phase behaviour is much more complex than that
for the binary mixtures
• Rigorous design requires computers
• Short cut methods exist to outline the scope and limitations of a
particular process

Multicomponent distillation in tray towersMulticomponent distillation in tray towers
• Objective of any distillation process is
to recover pure products
• In case of multicomponent mixtures we
may be interested in one, two
or more components
• Unlike in binary distillation, fixing mole
fraction of one of the components in a
product does not fix the mole fraction of other
components
• On the other hand fixing compositions of all
the components in the distillate and the bottoms
product, makes almost impossible to meet
specifications exactly
D
B
y1,y2,y3,y4…

Key componentsKey components
• In practice we usually choose two components
separation of which serves as an good indication
that a desired degree of separation is achieved
These two components are called key components
- light key
- heavy key
• There are different strategies to select these key
components
• Choosing two components that are next to each other
on the relative volatility scale often leads to all the components
lighter then the light key components accumulating in the distillate
and all the components heavier then the heavy key component
accumulating in the bottoms product: sharp separation

Distributed and undistributed componentsDistributed and undistributed components
• Components that are present in both the distillate and
the bottoms product are called distributed components
- The key components are always distributed components
• Components with negligible concentration (<10-6
) in one
of the products are called undistributed
A B C D E G
key
components
heavy non-distributed components
(will end up in bottoms product)
light non-distributed components
(will end up in the overhead product)

Complete designComplete design
A mixture of 4% n-pentane, 40% n-hexane, 50% n-heptane and 6%
n-octane is distilled at 1 atm. The goal is to recover 98%of hexane and
1% of heptane in the distillate. The feed is boiling liquid.
a) Design a distillation process
F, zf
condenser
boiler
n-pentane: 0.04
n-hexane:0.40
n-heptane: 0.50
n-octane: 0.06
100kmol/h

F, zf
condenser
boiler
n-pentane: 0.04
n-hexane:0.40
n-heptane: 0.50
n-octane: 0.06
100kmol/h
What is design of
a column?
- P (pressure)
- N (stages)
- R (reflux)
- D (diameter)
- auxilary
equipment
(condenser, boiler)

Rigorous methods (Aspen)
Stage j
F
j
F
j
F
jjij TPhzF ,,,, , jQ
11
11,1
,
,,,
−−
−−−
jj
L
jjij
TP
hxL
11
11,1
,
,,,
++
+++
jj
V
jjij
TP
hyV
jj
L
jjij
TP
hxL
,
,,, ,
jj
V
jjij
TP
hyV
,
,,, ,
jU
jW
(See my notes on the web)
Short-cut methods:
Fenske-Underwood-Gilliland
(+Kirkbride)

Complete short cut designComplete short cut design
xF F xF Moles in D xD Moles in B xB Ki
Pentane 0.04 4 3.62
Hexane 0.4 40 1.39
Heptane 0.5 50 0.56
Octane 0.06 6 0.23
100
I. Material balance conisderations

Pentane 0.04 4 3.62
Hexane
LK
0.4 40 39.2 1.39
Heptane
HK
0.5 50 0.5 0.56
Octane 0.06 6 0.23
100
I. Material balance considerations

Pentane 0.04 4 4 3.62
Hexane
LK
0.4 40 39.2 1.39
Heptane
HK
0.5 50 0.5 0.56
Octane 0.06 6 0 0.23
100
- Sharp split: components lighter than the Light Key (LK) will end up completely
in the overheads

Pentane 0.04 4 4 0.092 3.62
Hexane
LK
0.4 40 39.2 0.897 1.39
Heptane
HK
0.5 50 0.5 0.011 0.56
Octane 0.06 6 0 0 0.23
100 D=43.7

Pentane 0.04 4 4 0.092 3.62
Hexane
LK
0.4 40 39.2 0.897 0.8 1.39
Heptane
HK
0.5 50 0.5 0.011 49.5 0.56
Octane 0.06 6 0 0 0.23
100 D=43.7
i
F
ii DyFxBx −=

Pentane 0.04 4 4 0.092 0 3.62
Hexane
LK
0.4 40 39.2 0.897 0.8 1.39
Heptane
HK
0.5 50 0.5 0.011 49.5 0.56
Octane 0.06 6 0 0 6 0.23
100 D=43.7 B=56.3
- Sharp split: components heavier than the Heavy Key (HK) will
end up completely in the overheads

Pentane 0.04 4 4 0.092 0 0 3.62
Hexane
LK
0.4 40 39.2 0.897 0.8 0.014 1.39
Heptane
HK
0.5 50 0.5 0.011 49.5 0.879 0.56
Octane 0.06 6 0 0 6 0.107 0.23
100 D=43.7 B=56.3
- Sharp split: components heavier than the Heavy Key (HK) will
end up completely in the overheads

II. Pressure consideration:
- what if you were not given P=1atm, how would you choose it?
- how do you validate that P=1atm is appropriate?
F, zf
condenser
boiler
- condenser uses cooling water
(20C). Let say the exit water
temperature is 30C.
- To maintain the temperature delta
at 10C, the dew point can not be
lower than 40C.
- Thus, the dew point of the distillate
has to be at least 40C.
- If not, will need higher pressure

III. Gilliland correlation: Number of idealIII. Gilliland correlation: Number of ideal
plates at the operating refluxplates at the operating reflux






+
−
=
+
−
11
min
D
DmD
R
RR
f
N
NN

III. Gilliland correlation: Number of idealIII. Gilliland correlation: Number of ideal
plates at the operating refluxplates at the operating reflux






+
−
=
+
−
11
min
D
DmD
R
RR
f
N
NN
Nmin
Rmin
R=1.5Rmin
Nmin

IV. Fenske equation for multicomponentIV. Fenske equation for multicomponent
distillationsdistillations
Assumption: relative volatilities of components remain constant
throughout the column
1
ln
ln
,
,
,
,
,
min −






=
HKLK
HKD
HKB
LKB
LKD
x
x
x
x
N
α
LK – light component
HK – heavy component
)(
)(
)(,
TK
TK
T
HK
LK
HKLK =α

V. Minimum reflux ratio analysisV. Minimum reflux ratio analysis
• At the minimum reflux ratio condition
there are invariant zones that occur
above and below the feed plate, where
the number of plates is infinite and the
liquid and vapour compositions do not
change from plate to plate
• Unlike in binary distillations, in
multicomponent mixtures these zones
are not necessarily adjacent to the feed
plate location
y
x
zf
zf
xB xD
y1
yB
xN

V. Minimum reflux ratio analysis:V. Minimum reflux ratio analysis:
Underwood equationsUnderwood equations
∑ −
=−
i HKi
iFHKi
A
x
q
,
,,
)1(
α
α
∑ −
==+
i HKi
iDHKi
m
A
x
D
V
R
,
,,
1
α
α
For a given q, and the feed composition
we are looking for A satisfies this equation
(usually A is between αLK and αHK)
Once A is found, we can calculate the
minimum reflux ratio

VI. Kirkbride equation: Feed stage locationVI. Kirkbride equation: Feed stage location
206.02
,
,
,
,
























=
D
B
x
x
x
x
N
N
HKD
LKB
LKF
HKF
S
R

Complete short cut design:Complete short cut design:
Fenske-Underwood-Gilliland methodFenske-Underwood-Gilliland method
Given a multicomponent distillation problem:Given a multicomponent distillation problem:
a) Identify light and heavy key components
b) Guess splits of the non-key components and compositions
of the distillate and bottoms products
c) Calculate
d) Use Fenske equation to find Nmin
e) Use Underwood method to find RDm
f) Use Gilliland correlation to find actual number of ideal stages
given operating reflux
g) Use Kirkbride equation to locate the feed stage
HKLK ,α

VII. Stage efficiency analysisVII. Stage efficiency analysis
In general the overall efficiency will depend:
1) Geometry and design of contact stages
2) Flow rates and patterns on the tray
3) Composition and properties of vapour and
liquid streams

Lin,xin
Lout,xout
Vout,yout
Vin,yin
Local efficiency
1
*
1
+
+
−
−′
=
nn
nn
mv
yy
yy
E
Actual separation
Separation that
would have been
achieved on an
ideal tray
What are the sources of inefficiencies?
For this we need to look at what actually happens
on the tray
Point efficiency

Depending on the location on the tray
the point efficiency will vary
high concentration
gradients
low concentration
gradients
stagnation points
The overall plate efficiency can
be characterized by the Murphree
plate efficiency:
1
*
1
+
+
−
−
=
nn
nn
mV
yy
yy
E
When both the vapour and liquid
phases are perfectly mixed the plate
efficiency is equal to the point
efficiency
mvmV EE =

In general a number of
empirical correlations exist
that relate point and plate
efficiencies
ce
L
Pe
tD
Z
N
2
=
Peclet number
length of liquid
flow path
eddy diffusivity residence time of liquid
on the tray

VII. Stage efficiency analysis: O’Connell (1946)VII. Stage efficiency analysis: O’Connell (1946)
(Sinnott)

VII. Stage efficiency analysis: Van Winkle (1972)VII. Stage efficiency analysis: Van Winkle (1972)
(Sinnott)

- AICHE method- AICHE method
- Fair-Chan- Fair-Chan
Chan, H., J.R. Fair,” Prediction of Point Efficiencies for Sieve Trays, 1. Binary Systems”,
Ind Eng. Chem. .Process Des. Dev., 23, 814-819 (1984)
Chan, H., J.R. Fair, ,” Prediction of Point Efficiencies for Sieve Trays, 1. Multi-component Systems”,
Ind Eng. Chem. .Process Des. Dev., 23, 820-827 (1984)
(Sinnott)

Finally the overall efficiency of the process defined as
actual
ltheoretica
O
N
N
E =
If no access to the data: E0=0.5 (i.e. double the number of plates)

VIII. Column diameter, etcVIII. Column diameter, etc
Sinnott,
Jim Douglas, Conceptual design of chemical process

Introduction to multicomponent distillation

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