CENG 221
Lecture 4. Multi-component Distillation (4.5 h)
Learning Objectives:
(1) Multi-component flash distillation calculation
(2) Multi-component column distillation
Fenske Equation
Underwood Equation
Gilliland Correlation
(3) Column sizing
Column diameter
Column height
(4) Introduction to packed column
Learning Guides:
(1) Lecture handouts
(2) Chapters 3.3, 7.1, 9.1-9.3, 12.1, 12.3, 13.3 of Textbook:
Equilibrium-Staged Separations
Multi-component Column Distillation
QC
Total Condenser
D, xDi
R
Q=0
F, hf
zi
(n)
Partial
Reboiler
QR
B, xBi
A 2000 kmole/h feed containing benzene (0.2), toluene (0.3) and
xylene (0.5) are to be separated using the distillation column shown
above. 90 percent of the toluene is to be recovered at the distillate and
98 percent of xylenes is produced at the bottom.
(a) label the key and non-key components
(b) what is the value of D and B?
(b) what is the distillate and bottom composition?
Column Distillation
QC
Total Condenser
D, xDi
R
Q=0
F, hf
zi
(n)
Partial
Reboiler
QR
B, xBi
A 100 kmole/h feed containing methanol (0.3) and water (0.7) is to be
separated using the distillation column shown above. 90 percent of the
methanol is to be recovered at the distillate and 90 percent of water is
produced at the bottom.
(a) label the key and non-key components
(b) what is the value of D and B?
(c) what is the distillate and bottom composition?
Fenske Equation (Total Reflux)
Calculates for Nmin
Nmin = Ln [(xA/xB)d/(xA/xB)b]
Ln aAB
where xA is concentration of key component A (usually LKC)
xB is concentration of key component B (usually HKC
For binary components
Nmin = Ln [(xA/1-xA)d/(xA/1-xA)b]
Ln aAB
Underwood Equation (Minimum Reflux)
Calculates for Rmin
DVfeed = F(1-q) =
S
aiFzi
ai - f
S
aiDxi
ai - f
Calculates for Vmin
Vmin =
Column Distillation
QC
Total Condenser
D, xDi
R
Q=0
F, hf
zi
(n)
Partial
Reboiler
QR
B, xBi
Given that the amethanol/water = 3.5, determine the minimum number
of equilibrium stages (Nmin) needed for the separation.
- Use McCabe-Thiele method
- Use Fenske Equation
McCabe-Thiele Method
y (mole frac. methanol)
1
a =3.5
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
x (mole frac. methanol)
y (mole frac. methanol)
1
a =3.5
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
x (mole frac. methanol)
0.8
1
Column Distillation
QC
Total Condenser
D, xDi
R
Q=0
F, hf
zi
(n)
Partial
Reboiler
QR
B, xBi
Given that feed is saturated liquid, determine the minimum
reflux (Rmin)
- Use McCabe-Thiele method
- Use Underwood Equation
McCabe-Thiele Method
y (mole frac. methanol)
1
a =3.5
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
x (mole frac. methanol)
y (mole frac. methanol)
1
a =3.5
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
x (mole frac. methanol)
0.8
1
Column Distillation
QC
Total Condenser
D, xDi
R
Q=0
F, hf
zi
(n)
Partial
Reboiler
QR
B, xBi
Given that the reflux is 2 Rmin find the number of trays needed for
the separation (N)
- Use McCabe-Thiele method
- Use Gillaland Correlation
McCabe-Thiele Method
y (mole frac. methanol)
1
a =3.5
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
x (mole frac. methanol)
y (mole frac. methanol)
1
a =3.5
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
x (mole frac. methanol)
0.8
1
Example 25: The distillation column shown in the figure below was
used for the separation of 0.5 mole fraction methanol-water solution.
The desired distillate and bottom products are 0.20 and 0.9,
respectively. The feed enters the column as a subcooled liquid that
condenses 2 moles of vapor per mole of feed.
Condenser
QC
D, xD= 0.9, hD
Reflux ratio = L0/D
= 2 Rmin
Q=0 (a) What is q-value of the feed? Plot the
F, z, hf
10 Kmole/min,
0.5
Subcooled liquid
(n)
feed line.
(b) What is the number of equilibrium
stages?
(c) What is the actual number of stages if
the EMV = 0.5?
(d) Solve the problem using Fenske,
Gilliland and Underwood methods.
Reboiler
QR
B, xB= 0.2, hB
Boilup ratio = Vn+1/B
Multi-component Column Distillation
Example 26. A mixture containing 0.2 mole frac. Benzene (aBT =
2.25), 0.3 toluene (aTT = 1.0), 0.1 xylene (aXT = 0.33) and 0.4 cumene
(aCT = 0.21) is to be separated by a distillation column equipped with
partial reboiler and total condenser. The 2-phase feed contains 30 %
vapor. 99.8 % of the cumene is to be recovered at the bottom and
99.5% of the toluene is to be recovered at the distillate. If the reflux
ratio is fixed at 3Rmin determine the number of stages needed for the
separation.
QC
Total Condenser
D, xDi
R
Q=0
F, hf
zi
(n)
Partial
Reboiler
QR
B, xBi
Sizing of Distillation Column
Number of separation trays (N)
Height of column (hC = N*tray spacing)
Column diameter (dc)
QC
Total Condenser
D, xDi
R
Q=0
F, hf
zi
(n)
Partial
Reboiler
QR
B, xBi
Sizing of Distillation Column Diameter
(1) decide on the tray spacing
values using increases by increment of 6 inches from 6”-36”
(2) use the graphical correlation that relates the constant Csb for
different tray spacing to Flv
Flv = WL/Wv [rL/rV]0.5
note: W is mass flow rates
(3) calculate the flooding velocity. This is the maximum flowrates
allowable that will prevent excessive entrainment of liquid.
uflood = K [(rL - rV)/rV]0.5
ft/s
(4) actual operation velocity is usually lower than flooding velocity
where 0.65 < (fraction) < 0.9
uop = (fraction) uflood
ft/s
(5) finally, uop is related to the column diameter by:
uop = V(MWav)/3600rVAnet
ft/s
Sizing of Distillation Column
Example 27a. Ethanol-water solution was to be separated using a
tray distillation column equipped with a total condenser and a partial
reboiler. 50 Kmole/h of saturated liquid feed (0.4 mole frac. ethanol)
was to be separated to obtain a distillate containing 0.6 mole frac.
Ethanol and a bottom of 0.1 mole frac. The reflux ratio is 1.8 Rmin.
The distillation company suggested a tray spacing of 24” for
optimum operation. Please calculate the diameter and height of the
distillation column if sieve trays were used as separation stage.
QC
Total Condenser
D, xDi
R
Q=0
F, hf
zi
(n)
Partial
Reboiler
QR
B, xBi
VLE Data
1
Y (ethanol)
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
0.8
1
X (ethanol)
1
Y (ethanol)
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
X (ethanol)
Multi-component Flash Distillation
Vapor product
V, yi, Hv
TF, PF, hF
Feed
F, zi,
T1, P1
Ta
~
Tb
<
Tc 
Td
heater
Pa
>
Pb
>
Pc >> Pd
Q
throttle
valve
pump
Tdrum
Pdrum
Liquid product
L, xi, hL
Rachford-Rice Equation
c
f(V/F) =
(Ki-1)zi
Si=1 1 + (K -1)(V/F) = 0
i
Solution Methods for Rachford-Rice Equation
c
f(V/F) =
(Ki-1)zi
Si=1 1 + (K -1)(V/F) = 0
i
(1) Secant method
(a) choose (V/F)1 such that f(V/F)1 < 0
(V/F)2 such that f(V/F)2 > 0
(b) use linear interpolation to determine V/F at f(V/F) = 0
(c) repeat (a) using new V/F value from (b) until f(V/F) =0
(2) Newtonian convergence
read page 55 of Textbook for details
Multi-component Flash Distillation
Example 26: Determine the amount and composition of the products
leaving the flash distillation shown below.
V, yi
T = 50°C
P = 200 kPa
F = 1000 kmole/h
zc3 = 0.3
znC4 = 0.1
znc5 = 0.15
znc6 = 0.45
L, xi
VLE Data
Multi-component Flash Distillation
Example 27: Determine the operating temperature for the flash drum
if the composition of propane in the vapor is 0.7.
V, yc3 = 0.7
T=?
P = 200 kPa
F = 1000 kmole/h
zc3 = 0.25
znC4 = 0.15
znc5 = 0.15
znc6 = 0.45
L, xi
VLE Data