Internal Column Balances
Feed tray
V
L
V
L
F
Feed Equation:
y = -{(L - L)/(V - V)}x + Fzf/(V-V)
y = -(Lf/Vf)x + (F/Vf)zf
y = {q/(q-1)}x + zf/(1-q)
q = (L-L)/F = (H-hf)/(H-h)
Example 19: Find the value of q and draw the feed line for a feed
containing 0.4 pentane and 0.6 toluene:
(a) the feed is a saturated liquid,
(b) the feed contains 0.5 fraction of vapor,
(c) the feed was superheated so that each mole of feed
vaporizes 10 moles of liquid,
(d) the feed was subcooled so that each mole of feed
condenses 2 moles of vapor.
Example 19: Find the value of q and draw the feed line for a feed
containing 0.4 pentane and 0.6 toluene:
(a) the feed is a saturated liquid,
(b) the feed contains 0.5 fraction of vapor,
(c) the feed was superheated so that each mole of feed
vaporizes 10 moles of liquid,
(d) the feed was subcooled so that each mole of feed
condenses 2 moles of vapor.
Example 20: The distillation column shown in the figure below was
used for the separation of 0.4 mole fraction pentane in toluene. The
desired distillate and bottom products are 0.1 and 0.9, respectively.
The feed enters the column as a superheated vapor that vaporizes 2
moles of liquid per mole of feed.
Condenser
QC
D, xD= 0.9, hD
Reflux ratio = L0/D
= 3 Rmin
Q=0 (a) What is q-value of the feed? Plot the
F, z, hf
10 Kmole/min,
0.4
superheated vapor
(n)
feed line.
(b) What is the minimum reflux ratio for
the separation?
(c) If the column reflux was operated at 3
Rmin, where is the optimum feed-plate
location?
Reboiler
QR
B, xB= 0.1, hB
Boilup ratio = Vn+1/D
(d) What is the boil-up ratio needed for the separation?
(e) How many equilibrium stages is needed to accomplish the desired separation?
(f) How much distillate and bottom are produced if the feed rate is 10 kmole/min?
(g) What is the minimum number of trays needed for achieve the desired separation?
Example 21: The distillation column shown in the figure below was
used for the separation of 0.25 mole pentane from heptane. The
desired distillate and bottom products are 0.05 and 0.95, respectively.
The vapor flowrate in the enriching and stripping sections of the
column are 2 D and 3B, respectively.
Condenser
QC
D, yD= 0.95, hD
Reflux ratio = L0/D
Q=0 (a) What are the flowrates of distillate and
F, z, hf
1 Kmole/min,
0.25
(n)
bottom?
(b) What is the (L/V)enriching and plot the
top operating line?
(c) Express the the operation reflux ratio, R
as n Rmin
Reboiler
QR
B, xB= 0.05, hB
Boilup ratio = Vn+1/D
(d) What is the boil-up ratio? Plot the bottom operating line.
(e) Is the feed subcooled, saturated liquid, mixture, saturated vapor or superheated
vapor?
(f) How many equilibrium stages is needed to accomplish the desired separation?
(g) Where is the optimum location of the feed plate?
Example 22: A stripping column shown in the figure below was used
to remove oil from contaminated water. The water leaving the bottom
must be at least 99.7 % pure. The VLE data is plotted in the figure
below.
D, yD= 0.6, hD
F, z, hf
15 Kmole/min,
0.10
Q=0 (a) Derive the top and bottom operating
equation for the stripping column.
(b) Plot the top and bottom operating line
(c) Plot the feed line and determine the qvalue of the feed.
(n)
Reboiler
QR
B, xB= 0.003, hB
Boilup ratio = Vn+1/D = 4
(d) What are the allowable feed in a stripping section i.e., subcooled, saturated liquid,
mixture, saturated vapor and superheated vapor? and why?
(e) Determine the number of stages needed for the separation.
(f) What is the minimum reflux ratio for this separation column?
Example 23: Crude oil could be extracted from sand found in Canadian
province of Saskatchewan. Steam is used in the extraction process and the
oil-water mixture is send through a series of distillation column. The final
column known as the dehydrating column is employed for removing the
final traces of water from the crude to meet the industrial maximum
tolerance level of 0.01 mole fraction water. Instead of a condenser
saturated liquid water was used directly as coolant. This arrangement has
the added benefit of diluting the oil that remains in the water recovered at
the distillate. The water from the distillate is then sent to settling tank to
remove the final traces of oil before discharge.
D, yD= 0.8, hD
C, xc, hc
(a) Derive the top operating equation for
dehydration column.
(b) Derive the bottom operating equation
Q=0 (c) Derive the feed equation
(d) Plot the respective top and bottom
operating line as well as the feedline
F, z, hf
75 Kmole/min,
0.20, 25 % vapor
(n)
Reboiler
QR
B, xB= 0.01, hB
Boilup ratio = Vn+1/D = 3
(e) Determine the number of stages needed for the separation and the optimum
feed plate location if the total tray efficiency is 0.25.
Example 24: 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 0.10 and 0.95,
respectively. The feed enters the column as a superheated vapor that
vaporizes 2 moles of liquid 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,
0.4
superheated vapor
feed line.
(b) What will happen if the feed condition
changes from superheated to sat. vapor to
sat. liquid and subcooled liquid.
(n)
Reboiler
QR
B, xB= 0.1, hB
Boilup ratio = Vn+1/D
(c) What is the minimum reflux ratio?
(d) What is the minimum number of plates?
Column Efficiency
Overall Column Efficiency
Eo = Nequil/Nactual
Murphree Efficiency
EMV =
actual change in vapor
change in vapor for equilibrium stage
=
yj - yj+1
yj* - yj+1