1. 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, , 12.1, 12.3, 13.3 of Textbook:
Equilibrium-Staged Separations

2. Multi-component Column DistillationQC QR
F, hf
D, xDi
B, xBi
Q = 0
(n)
Partial Reboiler
Total Condenser zi R
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?

3. Column Distillation QC D, xDi R Q = 0 F, hf zi QR B, xBi
Partial Reboiler
Total Condenser zi R
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?

4. 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

5. S S Underwood Equation (Minimum Reflux) aiFzi ai - f aiDxi ai - f
Calculates for Rmin
DVfeed = F(1-q) = S
aiFzi
ai - f
Calculates for Vmin
Vmin = S
aiDxi
ai - f

6. Column Distillation QC D, xDi R Q = 0 F, hf zi QR B, xBi
Partial Reboiler
Total Condenser zi R
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

7. McCabe-Thiele Method
a =3.5
a =3.5

8. Column Distillation QC D, xDi R Q = 0 F, hf zi QR B, xBi
Partial Reboiler
Total Condenser zi R
Given that feed is saturated liquid, determine the minimum
reflux (Rmin)
- Use McCabe-Thiele method
- Use Underwood Equation

9. McCabe-Thiele Method
a =3.5
a =3.5

10. Column Distillation QC D, xDi R Q = 0 F, hf zi QR B, xBi
Partial Reboiler
Total Condenser zi R
Given that the reflux is 2 Rmin find the number of trays needed for
the separation (N)
- Use McCabe-Thiele method
- Use Gillaland Correlation

11. McCabe-Thiele Method
a =3.5
a =3.5

12. Condenser QC D, xD= 0.9, hD Q=0 F, z, hf Reboiler QR B, xB= 0.2, hB
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. QC QR
F, z, hf
D, xD= 0.9, hD
B, xB= 0.2, hB
Q=0
Reflux ratio = L0/D
Boilup ratio = Vn+1/B
(n)
Reboiler
Condenser
10 Kmole/min,
0.5
Subcooled liquid
= 2 Rmin
(a) What is q-value of the feed? Plot the 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.

13. 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 % 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 QR
F, hf
D, xDi
B, xBi
Q = 0
(n)
Partial Reboiler
Total Condenser zi R

14. Sizing of Distillation Column
Number of separation trays (N)
Height of column (hC = N*tray spacing)
Column diameter (dc) QC QR
F, hf
D, xDi
B, xBi
Q = 0
(n)
Partial Reboiler
Total Condenser zi R

15. 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

16. 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 QR
F, hf
D, xDi
B, xBi
Q = 0
(n)
Partial Reboiler
Total Condenser zi R

17. VLE Data

18. S (Ki-1)zi f(V/F) = = 0 1 + (Ki-1)(V/F)
Multi-component Flash Distillation
Vapor product
V, yi, Hv
TF, PF, hF Tb Tc Td Ta  ~
<
Feed
F, zi,
T1, P1
heater
Tdrum
Pdrum Pb Pc Pd Pa
>>
>
pump
throttle
valve Q
Liquid product
L, xi, hL
Rachford-Rice Equation
f(V/F) =
(Ki-1)zi
1 + (Ki-1)(V/F) S
i=1 c
= 0

19. S (Ki-1)zi f(V/F) = = 0 1 + (Ki-1)(V/F)
Solution Methods for Rachford-Rice Equation
f(V/F) =
(Ki-1)zi
1 + (Ki-1)(V/F) S
i=1 c
= 0
(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

20. Multi-component Flash Distillation
Example 26: Determine the amount and composition of the products
leaving the flash distillation shown below.
F = 1000 kmole/h
zc3 = 0.3
znC4 = 0.1
znc5 = 0.15
znc6 = 0.45
V, yi
L, xi
T = 50°C
P = 200 kPa

21. VLE Data

22. 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.
F = 1000 kmole/h
zc3 = 0.25
znC4 = 0.15
znc5 = 0.15
znc6 = 0.45
V, yc3 = 0.7
L, xi
T = ?
P = 200 kPa

23. VLE Data