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First Name_______________________
Last Name________________________
Student Number_________________________
University of Toronto
Department of Chemical Engineering and Applied Chemistry
Separation Processes – CHE 311S
Instructor: Prof. Ramin Farnood
MIDTERM EXAM
March 2, 2007
Duration: 1 hr and 30 minutes
1.
2.
3.
4.
Exam is closed book/notes.
Non-programmable calculator, only.
Use available space in your answer book.
Do not separate pages from your answer book.
Q1
Q2
Q3
Total
/15
/20
/25
/60
1
Q1. (15 Marks)
A spherical carbon particle in burning in oxygen environment at 1000 K and 1.013×105 Pa. Particle
radius is ro= 1.5 × 10-3 m.
During the burning process, surface of particle is covered with a layer of CO 2 , i.e. partial pressure of
carbon dioxide PCO2 = 1.013×105 Pa at r = ro . Carbon dioxide diffuses from the surface of particle
to the surrounding oxygen by molecular diffusion. The bulk concentration of CO2 is negligible, i.e.
PCO2 = 0 at r = ∞.
Assuming equimolar counterdiffusion (EMD), find the rate of consumption of carbon, W, in kg/s.
Data: Diffusion coefficient of CO2 in gas: D = 1.032 × 10-4 m2/s.
Molecular mass of carbon:
M = 12
Gas constant
R = 8.314 J/mol.K
2
3
Q2. (20 Marks)
Carbon dioxide is to be absorbed by 4% NaOH solution in an atmospheric packed column using a 2”
plastic random packing, FLEXIRING® #2. Gas flow rate is 658 m3/h and liquid flow rate is 17 m3/h.
Column pressure and temperature are 24 oC and 1 atm, and column diameter is 0.6 m. The inlet
concentration of CO2 is 1 mol % and the desired outlet concentration is 0.1 mol%. Considering that
reaction between CO2 and NaOH is very fast and irreversible (i.e. slope of equilibrium line m =0 )
and assuming dilute solution:
1) Determine the number of overall gas transfer units (N OG).
2) Using the manufacturer’s data for FLEXIRING® #2 (see attached graphs), find HOG and the
required packing height.
3) Estimate the pressure drop per unit height of the packing using the manufacturer’s data. What is
the maximum air flow rate before flooding occurs in the column?
Data: Air density at 24 oC and 1 atm:
Molecular weight of gas:
ρair= 1.195 kg/m3
MG = 29
4
5
98 122 147 171
73
L iq
49
uid
Lo
24
ad
ing
= 0 12
m3
/m 2
.h
6
Q3. (25 Marks)
A mixture of methanol and water is to be separated in trayed distillation tower (Figure A) at 1 atm.
Feed consists of zF= 60% methanol and enters the column as a vapor-liquid mixture at equilibrium.
The amount of vapor in the feed is 30% of the total feed molar flow rate, i.e. VF/F = 0.3. It is
desirable to achieve a methanol concentration of xD= 95 mol% in the distillate and xB= 8 mol% in
the bottoms. Column operates with a total condenser to produce saturated liquid, and a kettle reboiler
to boil up the bottoms. The x-y diagrams are given in the next page.
Assuming constant molar overflow (CMO), and using McCabe-Thiele method determine:
a) the minimum number of theoretical stages, Nmin.
b) the slope of q-line and the minimum reflux ratio, Rmin.
c) the slope of rectifying section operating line, slope of q-line, number theoretical plates, and
optimum feed tray if a reflux ratio of L/D = 3 is used.
d) repeat part (c) if instead of partial reboiler, saturated steam (S) at 1 atm is injected directly to the
column (figure B).
e) the amount of steam (S) required for part (d), if feed rate is 100 kmol/h.
Data: Feed enthalpy:
hF = 16,320 kJ/kmol
Distillate enthalpy
hD = 5,280 kJ/kmol
Bottoms enthalpy
hB = 6,970 kJ/kmol
Enthalpy of steam: hS = 48,170 kJ/kmol
Latent heat of vaporization of Distillate:
ΔHvap, D = 35,500 kJ/kmol
V1
V1
Lo
D, xD
Lo
1
D, xD
1
L V
L V
F, zF
F, zF
L V
L V
N
N
B, xB
S, y = 0
B, xB
(A)
(B)
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Use for part (a)
Use for part (b)
Methanol-Water Equilibrium @ 1 atm
1
0.9
0.9
0.8
0.8
0.7
0.7
y (Methanol)
y (Methanol)
Methanol-Water Equilibrium @ 1 atm
1
0.6
0.5
0.4
0.6
0.5
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
x (Methanol)
0.6
0.7
0.8
0.9
1
0.9
1
x (Methanol)
Use for part (c)
Use for part (d)
Methanol-Water Equilibrium @ 1 atm
Methanol-Water Equilibrium @ 1 atm
1
1
0.9
0.9
0.8
0.8
0.7
0.7
y (Methanol)
y (Methanol)
0.5
0.6
0.5
0.4
0.6
0.5
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
x (Methanol)
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
x (Methanol)
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Formula:
Rectifying section operating line: y 
Stripping section operating line: y 
q- line: y 
N OG 
y L 
H OG 
VB  1
x
x B
VB
VB
z
q
x F
q 1
q 1
yin  y out
y L
y bottom  y top
 y

ln  bottom 
 y

top 

G'
G
G


K y a S K G a P S KY a S
HETP 
A
y
R
x D
R 1
R 1
T
Nt
L
KG
 T  N OG H OG
Molecular diffusion flux:
dc A
dy
 y A N  cD AB A ,
dr
dr
dc A
dy A
N A   D AB
 cD AB
dr
dr
N A  y A N  D AB
Molecular diffusion for EMD or dilute systems:
Concentration of ideal gas:
c
P
RT
Fs  vG  G
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