Transcript Document 7339060

Other Sources of Enthalpy Data
Riedel Equation
DHn/RTn = 1.092(InPc - 1,013)
0.930 - (Tn/Tc)
Watson Equation
DH2 = (1 - T2/Tc)
DH1
(1 - T1/Tc)
0.38
Specific heats
tabulated (see Appendix of thermodynamic textbook)
and graphical data
Example 14b: Calculate QC using Riedel and Watson Equations.
What would be the value of QC if the distillate subcools liquid to
30°C?
Specific Heats of Liquids
Specific Heats of Gases
Internal Column Balances
Enriching section of the column
V1
L0
D, xD
hD
V1
L0
(1)
V2
L1
(j)
Vj+1
Lj
D, xD
hD
Example 14c: What is the composition and enthalpy of vapor entering
and leaving the first tray of the distillation column shown in example 14a.
V1
L0
(1)
V2
L1
D, xD = 0.6
R=3
External Column Balances
Stripping section of the column
Vk
(n)
Vn+1
Lk-1
(k)
Ln
B, xB
hB
(n)
Vn+1
Ln
B, xB
hB
Lewis Method
Lewis observed that for a distillation column:
enriching section
L1 = L2 ….. = Lj = L is constant
V1 = V2 ….. = Vj = V is constant
stripping section
L1 = L2 ….. = Lk = L is constant
V1 = V2 ….. = Vk = V is constant
but
L  L and V  V
Important assumptions in distillation column calculation:
(1) column is adiabatic
(2) specific heat << latent heat
(3) latent heat (l) is constant independent of concentration
this means one mole of condensed vapor will
evaporate 1 mole of liquid
(4) saturated liquid and vapor lines in H-x-y diagram are
parallel
Lewis Method
Vi, yi
(i)
Vi+1, yi+1
Equilibrium relation
y = Kx
L i , xi
Operating equation
rectifying section
yj+1 = (L/V)xj + (1-L/V)xD
stripping section
yk = (L/V)xj - (L/V-1)xB
Example 15: What is the composition and enthalpy of vapor entering
and leaving tray 1-5 of the distillation column shown below.
V1
L0
(1)
(2)
(3)
(4)
(5)
V6
L5
D, xD = 0.6
hD, R = 3
VLE Data
y(ethanol mass frac.)
105
100
95
90
85
80
75
0
0.2
0.4
0.6
0.8
1
x(ethanol mass frac.)
y(ethanol mass frac.)
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
x(ethanol mass frac.)
1
External Column Balances
McCabe-Thiele Method
y(ethanol mass frac.)
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
x(ethanol mass frac.)
y(ethanol mass frac.)
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
x(ethanol mass frac.)
1
Example 16: What is the composition and enthalpy of vapor entering
and leaving tray 4-9 plus the reboiler for the distillation column shown
below.
V4
L3
(4)
(9)
V10
L9
B, xB = 0.05
hB, boilup ratio = 1
VLE Data
y(ethanol mass frac.)
105
100
95
90
85
80
75
0
0.2
0.4
0.6
0.8
1
x(ethanol mass frac.)
y(ethanol mass frac.)
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
x(ethanol mass frac.)
1
McCabe-Thiele Method
y(ethanol mass frac.)
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
x(ethanol mass frac.)
y(ethanol mass frac.)
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
x(ethanol mass frac.)
1
Example 17: A mixture of pentane and toluene was distilled in
a distillation column. An analysis of the enriching section is needed
to determine whether the column is performing to specification.
partial condenser
V1
L0
(1)
Please determine the composition of liquid
and vapor streams leaving each stages for
(a) a = 2 and 3.5 with R = 2,
(b) a = 3.5 with R = 1 and 4
(2)
(3)
V4
D, yD = 0.9
hD, R = 2
L3
McCabe-Thiele Method
y (mole frac. pentane)
1
a =2
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
x (mole frac. pentane)
y (mole frac. pentane)
1
a =3.5
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
x (mole frac. pentane)
0.8
1
McCabe-Thiele Method
y (mole frac. pentane)
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. pentane)
y (mole frac. pentane)
1
a =3.5
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
x (mole frac. pentane)
0.8
1
Total and Minimum Reflux
Total Reflux
D = 0,
L0 = V1,
R = L0/D = 
L/V = L0/V1 = 1
Minimum Reflux
D = maximum,
L0 = minimum allowable,
a =3.5
y (mole frac. pentane)
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
x (mole frac. pentane)
0.8
1
Example 18: Analysis of the stripping section of the distillation column
for pentane-toluene separation must be conducted to determine the liquid
and vapor compositions leaving each distillation trays.
(a) using a total reboiler,
(b) using a partial reboiler.
V6
L5
(6)
(9)
V10
L9
B, xB = 0.10
hB, boilup ratio = 2
McCabe-Thiele Method
y (mole frac. pentane)
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. pentane)
y (mole frac. pentane)
1
a =3.5
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
x (mole frac. pentane)
0.8
1
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.
McCabe-Thiele Method
y (mole frac. pentane)
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. pentane)
y (mole frac. pentane)
1
a =3.5
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
x (mole frac. pentane)
0.8
1
McCabe-Thiele Method
y (mole frac. pentane)
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. pentane)
y (mole frac. pentane)
1
a =3.5
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
x (mole frac. pentane)
0.8
1
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?
McCabe-Thiele Method
y (mole frac. pentane)
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. pentane)
y (mole frac. pentane)
1
a =3.5
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
x (mole frac. pentane)
0.8
1
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
saturated liquid
(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= 0.1, 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?
McCabe-Thiele Method
y (mole frac. pentane)
1
a =2
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
x (mole frac. pentane)
y (mole frac. pentane)
1
a =2
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
x (mole frac. pentane)
0.8
1
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= 0.1, 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?
McCabe-Thiele Method
y (mole frac. pentane)
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. pentane)
y (mole frac. pentane)
1
a =3.5
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
x (mole frac. pentane)
0.8
1
McCabe-Thiele Method
y (mole frac. pentane)
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. pentane)
y (mole frac. pentane)
1
a =3.5
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
x (mole frac. pentane)
0.8
1
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.
McCabe-Thiele Method
y (mole frac. pentane)
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. pentane)
y (mole frac. pentane)
1
a =3.5
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
x (mole frac. pentane)
0.8
1
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?
McCabe-Thiele Method
y (mole frac. pentane)
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. pentane)
y (mole frac. pentane)
1
a =3.5
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
x (mole frac. pentane)
0.8
1
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
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
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