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

chezhao@nus.edu.sg

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

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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