2015 cn3132 ii lecture 01 mass transfer models
DESCRIPTION
mass transfer in adsorption and stripping and extraction process. Two film theory plus unimolecular and equimolecular counter diffusionTRANSCRIPT
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2015 Sem 1 CN3132
Separation Processes (II)
Lecture 01:
Mass Transfer Models
Dr. ZHAO Dan
Department of Chemical and Biomolecular Engineering
4 Engineering Drive 4, Blk E5, #02-16
Tel: (65) 6516 4679
Wankat 3rd: 15.1; 15.2.1; 15.2.4; 15.3.1; 15.3.2
Treybal: Chapter 2
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Course Outline
Mass Transfer (Lecture 01-03, week 1) Models for mass transfer Two-film theory Individual and overall mass transfer coefficients
Rate Based Method (Lecture 04-09, week 2-3) Transfer units concepts in rate-based design Application of rate-based design for continuous contact operation of
absorption and distillation Design of packed column
Humidification (Lecture 10-14, week 4-5) Humidity, adiabatic saturation, wet bulb temperature Humidification and dehumidification processes Psychrometric chart Design of cooling tower
Adsorption (Lecture 15-17, week 5-6) Definitions Sorbent types Isotherms
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Schedules
Lectures As usual, Monday 9:00-10:35am; Thursday 9:00-9:45am, LT6
Tutorials As usual, totally 5 tutorials, starting next week (12 Oct 2015)
Consultation Fridays 14:00-16:00pm in my office (E5-02-16)
Appointment on other days
IVLE, Webcast, E-mail
Midterm Test Time: Thursday, 12 Nov 2015, 9:00-9:45am (be seated at 8:45am)
Venue: LT7
Coverage: Lectures 01-17
Open-book test
Bring in calculators and stationery
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Recap
Design Concept for Separation Equilibrium
Gibbs phase rule: F = C P + 2
Relative volatility
Flash Distillation Equilibrium line
Operating line
Graphical solution
Multi-Component Flash Distillation Trial and error
Binary Multi-Stage Distillation Top/Bottom operating line
Feed line
q
McCabe-Thiele method
Number of stages
Fenske equation
Optimum feed location
Minimum reflux ratio
Binary Absorption and Stripping Equilibrium line
Operating line
Mole fraction vs. mole ratio
Kremser equation
Min L/G ratio (absorption)
Max L/G ratio (stripping)
Multi-Component Absorption Identify the key component
Extraction (Immiscible Systems) Analogy to stripping
Extraction (Partially Miscible) Triangular diagrams
Mixing point
Inverse lever-arm rule
Equilibrium line
Operable range of feed composition
Correlation curve
Hunter-Nash method
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Learning Outcomes of Lecture 01
Understand the limitation of tray-number calculation in designing and evaluating packed column
Describe the expression and physical meaning of Ficks 1st Law of Diffusion
Estimate Fickian binary gas and liquid diffusivities
Identify the difference between equimolar counterdiffusion (EMD) and unimolecular diffusion (UMD)
Apply EMD and UMD under various cases
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Thermodynamics vs. Kinetics
(Equilibrium vs. Rate)
Thermodynamics: all about if
Kinetics: all about how
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Staged Column vs. Packed Column
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Mass Transfer
When a system contains two or more components whose concentrations vary from point to point, there is a natural tendency for mass to be transferred, minimizing the concentration differences within a system. The transport of one constituent from a region of higher concentration to that of a lower concentration is called mass transfer.
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Models for Mass Transfer:
(1) Molecular Movement
All molecules move and collide because of thermal energy
Molecular collisions result in mass transfer by diffusion
Molecules tend to distribute throughout the volume available
At equilibrium there is an equal number of density
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For a binary mixture of A and B,
JAz: molecular flux of A in B along z direction [mole/(m
2s)]
DAB: molecular diffusivity (m2/s)
dcA/dz: concentration gradient of A along z direction (mole/m4)
Minus sign: diffusion direction is opposite to concentration gradient
Models for Mass Transfer:
(2) Ficks 1st Law of Diffusion
AAz AB
dcJ D
dz BBz BA
dcJ D
dz
Adolf Eugen Fick (1829-1901)
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Other Forms of Ficks Law
c: mixture concentration (mole/m3)
xA: mole fraction of A
R: ideal gas constant 8.314 [J/(Kmol)]
T: temperature (K)
dpA/dz: pressure gradient of A along z direction (Pa/m)
AAz AB
dxJ cD
dz BBz BA
dxJ cD
dz
AB AAz
D dpJ
RT dz BA BBz
D dpJ
RT dz
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Fickian Binary Gas Diffusivities
DAB: molecular diffusivity (m2/s)
T: temperature (K)
MW: average molecular weight
ptot: total absolute pressure (Pa)
: average diameter of the spherical molecules ()
3/2 1/2
2
(1/ )AB
tot
T MWD
p
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Fickian Binary Liquid Diffusivities
16 1/20
0.6
1.173 10 [ ( )]B BAB
B A
MW TD
V
DAB: molecular diffusivity (m2/s)
B: solvent interaction parameter
MWB: molecular weight of B
T: temperature (K)
B: solvent viscosity (Pas)
VA: molar volume of solute (m3/kmol)
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Convection vs. Diffusion
For a binary mixture of A and B, the fluxes relative to the fixed position for each components can be derived as:
NA: flux of A
NB: flux of B
cA: concentration of A
cB: concentration of B
c: total concentration
( )A AA A B ABc dc
N N N Dc dz
( )B BB A B BAc dc
N N N Dc dz
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Equimolar Counterdiffusion (EMD)
In equimolar counterdiffusion, the molar fluxes or A and B are equal, but opposite in direction, and the total pressure is constant throughout, so N=NA+NB=0
A A AB AA Az AB AB
dc dx D dpN J D cD
dz dz RT dz
2 2 2 2
1 1 1 1
A A A
A A A
z c x p
AB AB ABA A A
A A Az c x p
D cD Ddz dc dx dp
N N RTN
1 2 1 2 1 2
2 1 2 1 2 1
( ) ( ) ( )
( ) ( )
AB A A AB A A AB A AA
D c c cD x x D p pN
z z z z RT z z
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Constant Molar Overflow (CMO) in Distillation
The heat of vaporization per mole is constant
Within each section the liquid and the vapor flow rates remain constant in the whole section
EMD applies
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Unimolecular Diffusion (UMD) (1)
Steady-state diffusion of A through stagnant B, so NB=0
Ammonia
+
Air
Water
A A A A AB AA A AB A A AB A
c dc dx p D dpN N D x N cD N
c dz dz p RT dz
2 2 2 2
1 1 1 11
A A A
A A A
z c x p
AB A AB A AB A
A A A A A Az c x p
cD dc cD dx pD dpdz
N c c N x RTN p p
2 2 2
2 1 1 2 1 1 2 1 1
1ln ln ln
( ) ( ) 1 ( )
AB A AB A AB AA
A A A
cD c c cD x pD p pN
z z c c z z x RT z z p p
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Unimolecular Diffusion (UMD) (2)
logarithmic mean:
2 1 1 2
2 2
1 1
2 1 1 2
2 2
1 1
2 1 1 2
2 2
1 1
( , )
ln
( ) ( )( )
ln ln
(1 ) (1 )(1 )
1 1ln ln
1 1
( ) ( )( )
ln ln
lm
A A A AA lm
A A
A A
A A A AA lm
A A
A A
A A A AA lm
A A
A A
y xM x y
y
x
c c c c c cc c
c c c c
c c c c
x x x xx
x x
x x
p p p p p pp p
p p p p
p p p p
1 2 1 2 1 2
2 1 2 1 2 1
( ) ( ) ( )1 [UMD]
( ) ( ) (1 ) ( ) ( )
AB A A AB A A AB A AA
A lm A lm A lm
D c c cD x x D p pc pN
z z c c z z x RT z z p p
1 2 1 2 1 2
2 1 2 1 2 1
( ) ( ) ( ) [EMD]
( ) ( ) ( )
AB A A AB A A AB A AA
D c c cD x x D p pN
z z z z RT z z
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Example Question (1)
Compare the binary Fickian diffusivity of methanol vapour in N2 (equal mol) at 50 C 1 atm versus that of ethanol vapour in N2 (equal mol) at 30 C 1 atm. Molecular weight is 28.00 g/mol for N2, 32.04 g/mol for methanol, and 46.07 g/mol for ethanol. Molecular kinetic diameter is 3.640 for N2, 3.626 for methanol, and 4.530 for ethanol. a) The diffusivity of methanol is higher
b) The diffusivity of ethanol is higher
c) The diffusivity of methanol equals that of ethanol
d) Can not be determined
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Example Question (2)
Oxygen (A) is diffusing through carbon dioxide (B) under steady-state conditions, with the CO2 non-diffusing. The total pressure is 1 x 105 Pa, and the temperature is 0 C. The diffusion path is 2.0 mm. The partial pressures of oxygen at the 2 ends are 13,000 and 6,500 Pa respectively. The diffusivity of the mixture is 1.87 x 10-5 m2/s. Calculate the molar flux of O2 in the mixture. Given R = 8.314 [J/(Kmol)]
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