Intze Overhead Water Tank Design by Working Stress - IS Method.pdf
Multicomponent system
1. Made By:-
Jay patel (18BCH153)
Tanmay patel (18BCH154)
Garvit Agrawal (18BCH155)
2. Multi-component Distillation
Introduction:-
As we do with binary columns, we’ll work with ideal stages
which can be converted to real stages using an efficiency
factor.
The limiting cases of total and infinite reflux apply to multi-
component columns just as they do to binary systems.
The overall approach to solving multi-component problems is
the same as we use for all equilibrium stage system. Use the
equilibrium relationships and the operating relationships.
Review multi-component bubble point and dew point
calculations.
4. Key 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
1. light key
2. heavy key
5. Number of methods used for calculation
1. Lewis-Matheson Method (equimolar flow rates).
2. Constant relative volatility method.
3. Short-cut methods for stage and reflux requirement.
I.Pseudo-Binary system method = Hengstebeck’s method
II.Gilliland, Fenske , Underwood Method.
6. Lewis-Matheson Method (equimolar flow rates).
• The method proposed by Lewis Matheson is essentially the
• application of Lewis-Sorel method to the solution of multi
• component problems (general method).
In this method we must specify the following variables:-
1)Feed composition, flow rate, reflux ratio and condition (q ).
2)Distribution of key-components.
3)Products flow rates.
4)Column pressure.
5)Assumed values for the distribution of non-key components.
7. Lewis Matheson Method:-
1-Similar to Lewis method.
2-Tray to tray calculations are
done with the assumption of
constant molar flow rates of
liquid and vapour in each
section.
3-Top section tray to tray
calculations are done till xi ≤
xFi
4-Bottom section tray to tray
calculations are done till yi ≥
xFi
L’
x’1i
F
xFi
V
y1
V’
yri
W
xWi
L
Xoi
D
xDi
V L
V’ L’
8. Calculation steps
Top section:-
1- Assume total condenser
conditions
i.e y1i = x Di = x oi
2-Knowing key components
compositions assume xDi′ s
3-Calculate x1i ′s from y1i = K1i x1i
( assume T1 , calculate ki1 = P◦1i / PT then check T1
at
∑ x1i = 1 if not repeat )
9. 4- Substitute in the overall material balance equation of
the top section.
i i i
i
n+1 n D
2 i 1 i D i 2 i
3 i 2 i D 3 i
2 i
2 i
2 i
L D
y = x + x
V V
for n = 1 first stage or plate
L D
y = x + x cal. y 's
V V
for n = 2 second stage or plate
L D
y = x + x cal. y 's
V V
y
(knowing x = fr
k
n i F i
om the previous step )
Repeat your calculations till reaching x x
10. Bottom section:-
• First start with the reboiler(partial vaporizer is considered as one
theoretical stage).
i
i
m i m+1 w i
r i 1i w i 1i
r i r i w i
1i 2 i D
L' W
y = x - x
V' V'
for m = 0 Reboiler
L' W
y = x x cal. x 's
V' V'
( after calculating y = k x )
for n = 1 first stage or plate
L' W
y = x x
V' V'
2 i
1i 1i 1i
m i F i
cal. x 's
(knowing y = k x from the previous step )
Repeat your calculations till reaching y x
11. Constant relative volatility method
• By calculating the equilibrium composition of vapor
and liquid at a single plate, K-values must be known,
but these cannot be determined until the stage
temperature is determined which is a function of
composition.
• Trial and error procedure is required.
• Much of trial and error can be eliminated if the relative
volatility is used in place of K.
• The relative volatilities are referred to one key
components(heavy key) .
12. 1i D i 0 i
Di
1i
Top Section:- (for any component (i)):
1-Assume total condenser conditions:-
y = x = x
Knowing key components compositions assume x '
2- For n = 1 (for first plate)
calculate x ' fro
s
s
i
1i
1i
r i i
1i r i r HK
1i r
r i
n+1 n i D i
m y '
y
α K
x = where α = ( K =K )
y K
α
3- Substitute in the top operating line equation :-
L D
y = x + x
V V
s
13. 2 1 i D i 2 1i
3 i 2 i D i
For n = 1
L D
y = x + x (calculate y ' after calculating x '
V V
from equilibrium relations)
4- For n = 2
L D
y = x + x
V V
i i s s
i
3 i 2 i
2 i
r i
2 i
2
r i
( calculate y ' after calculating x '
from equilibrium relations)
y
α
where x = (Repeat your calculations till reaching feed ent
y
α
s s
rance)
14. w i r i
r i
w i r i
m i m+1 i w i
r i 1 i w i
Bottom Section:-
1- Reboiler where ( m = 0)
x α
y =
x α
2- Substitute in the bottom operating line equation:-
L' W
y = x - x
V' V'
L' W
y = x - x ( calculate x
V' V'
1 i
1 i 2 i w i 2 i
1 i r i
1 i
1 i r i
' )
3- For m = 1 (first plate from the bottom)
L' W
y = x - x ( calculate x ' )
V' V'
x α
where y
x α
s
s
15. • Repeat your calculations till reaching feed entrancethen make
matching between top and bottom and feedstreams to check whether
the assumption of xDi’s is correct or not.
• If not repeat your assumption, but if it match calculate the number of
stages.
16. Short-cut methods for stage and reflux
requirement.
Most of the short-cut methods were developed
for the design of separation columns for hydrocarbon
Systems in the petroleum and petrochemical system
industries. They usually depend on the assumption for
severely non-ideal systems.
From these methods:-
1- Pseudo-Binary system method = Hengstebeck’s method
2-Gilliland, Fenske , Underwood Method.
17. 1-Pseudo-Binary system method =
Hengstebeck’s Method:-
Changes the multi-component system to binary
system.
Using Mc-cabe Thiele Equations:-
n+1 n
i i i
i i i
i i i
Upper Section:- V = L + D
V = L + D
For any component (i) v = l + d
For equilibrium relation y = k x
v / V = k l /
i i i
L
v = k l ( V/ L )
18. m+1 m
i i i
i i i
i i i
Bottom Section:-
L' = V' + W
L' = V' + W
For any component (i) l' = v' + w
For equilibrium relation y' = k' x'
v' / V' = k' l' / L'
i i iv' = k' l' ( V'/ L' )
To reduce the multicomponent system to an equivalent binary
system we must estimate the flow rates of the key components:-
Upper Section:-
Le i
e i
e e
L - l
V = V - v
where L &V are the flow rates of key components of upper section
19. i i
e i
e i
e e
l & v are the flow rates of components lighter
than key components in the upper section.
Bottom Section:-
L' L' - l'
V' = V' - v'
where L' &V' are the flow rates of key components
of upper sectio
i in l' & v' are the flow rates of
components heavier than key components
in the bottom section.
20. i
i i i i
i
e i e i
i i i
i i i
i
i i
i
LK
For Top Section:-
d
l = & v = d + l
α -1
L L - l & V = V - v
For Bottom Section:-
l' = v' + w
L'
( ) v' v' + w
V'K'
L'
( -1 ) v' w
V'K'
For light key:-
L'
( - 1
V'K'
i
LK
i
w L'
) = = zero & K' =
v' V'
21. LK
LK
LK
F
LK HK
LK
D
LK HK
LK
w
LK HK
Equilibrium Relations:-
α x
y =
(α - 1) x +1
Also a new compositions
f
x =
f + f
d
x =
d + d
w
x =
w + w
22. Gilliland Equation for calculation the number of stages
at operating reflux:-
A simple empirical method is used for preliminary
Estimates. The correlation requires knowledge only of
the minimum reflux ratio. This is shown in the following
figure, where the group :-
(N - N min)/(N + 1) is plotted against
( R – R min ) / ( R + 1 ) .
Gilliland, Fenske , Underwood Method:-
23. Where N = no. of plates. R = reflux ratio.
N min=minimum no. of plates. R min= minimum
reflux ratio.
