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CENG 221
Lecture 4. Multi-component Distillation (4.5 h)
Learning Objectives:
(1) Multi-component flash distillation calculation
(2) Multi-component column distillationFenske EquationUnderwood EquationGilliland Correlation
(3) Column sizingColumn diameterColumn 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
CENG 221
Lecture 4. Multi-component Distillation (4.5 h)
Learning Objectives:
(1) Multi-component flash distillation calculation
(2) Multi-component column distillationFenske EquationUnderwood EquationGilliland Correlation
(3) Column sizingColumn diameterColumn 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
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?
Column Distillation
QC
QR
F, hf
D, xDi
B, xBi
Q = 0
(n)
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?
Fenske Equation (Total Reflux)
Calculates for Nmin
Nmin = Ln [(xA/xB)d/(xA/xB)b]
Ln AB
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 AB
Underwood Equation (Minimum Reflux)
Calculates for Rmin
Vfeed = F(1-q) =i -
iFzi
Calculates for Vmin
Vmin =i -
iDxi
Column Distillation
QC
QR
F, hf
D, xDi
B, xBi
Q = 0
(n)
Partial Reboiler
Total Condenser
zi
R
Given that the methanol/water = 3.5, determine the minimum number of equilibrium stages (Nmin) needed for the separation.
- Use McCabe-Thiele method- Use Fenske Equation
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
x (mole frac. methanol)
y (m
ole
fra
c. m
eth
ano
l)
McCabe-Thiele Method
=3.5
=3.5
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
x (mole frac. methanol)
y (m
ole
fra
c. m
eth
ano
l)
Column Distillation
QC
QR
F, hf
D, xDi
B, xBi
Q = 0
(n)
Partial Reboiler
Total Condenser
zi
R
Given that feed is saturated liquid, determine the minimum reflux (Rmin) - Use McCabe-Thiele method
- Use Underwood Equation
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
x (mole frac. methanol)
y (m
ole
fra
c. m
eth
ano
l)
McCabe-Thiele Method
=3.5
=3.5
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
x (mole frac. methanol)
y (m
ole
fra
c. m
eth
ano
l)
Column Distillation
QC
QR
F, hf
D, xDi
B, xBi
Q = 0
(n)
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
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
x (mole frac. methanol)
y (m
ole
fra
c. m
eth
ano
l)
McCabe-Thiele Method
=3.5
=3.5
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
x (mole frac. methanol)
y (m
ole
fra
c. m
eth
ano
l)
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,0.5Subcooled 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.
Multi-component Column Distillation
QC
QR
F, hf
D, xDi
B, xBi
Q = 0
(n)
Partial Reboiler
Total Condenser
zi
R
Example 26. A mixture containing 0.2 mole frac. Benzene (BT = 2.25), 0.3 toluene (TT = 1.0), 0.1 xylene (XT = 0.33) and 0.4 cumene (CT = 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.
Sizing of Distillation Column
QC
QR
F, hf
D, xDi
B, xBi
Q = 0
(n)
Partial Reboiler
Total Condenser
zi
R
Number of separation trays (N)Height of column (hC = N*tray spacing)Column diameter (dc)
Sizing of Distillation Column Diameter
uflood = K [(L - V)/V]0.5 ft/s
(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 [L/V]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.
(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)/3600VAnet ft/s
Sizing of Distillation Column
QC
QR
F, hf
D, xDi
B, xBi
Q = 0
(n)
Partial Reboiler
Total Condenser
zi
R
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.
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
X (ethanol)
Y (
eth
ano
l)
VLE Data
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
X (ethanol)
Y (
eth
ano
l)
Multi-component Flash Distillation
Pb Pc PdPa >>> >
pump
heater
throttlevalve
Tb Tc TdTa ~ <
Liquid productL, xi, hL
Vapor productV, yi, Hv
Tdrum
Pdrum
Q
TF, PF, hF
FeedF, zi,T1, P1
Rachford-Rice Equation
f(V/F) =(Ki-1)zi
1 + (Ki-1)(V/F)i=1
c
= 0
Solution Methods for Rachford-Rice Equation
f(V/F) =(Ki-1)zi
1 + (Ki-1)(V/F)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
Multi-component Flash Distillation
F = 1000 kmole/h
zc3 = 0.3
znC4 = 0.1
znc5 = 0.15
znc6 = 0.45
V, yi
L, xi
T = 50°CP = 200 kPa
Example 26: Determine the amount and composition of the productsleaving the flash distillation shown below.
VLE Data
Multi-component Flash Distillation
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
Example 27: Determine the operating temperature for the flash drum if the composition of propane in the vapor is 0.7.
VLE Data