2015 CN3132 II Lecture 02 Mass Transfer Coefficient

7/23/2019 2015 CN3132 II Lecture 02 Mass Transfer Coefficient

1/17

2015 Sem 1 CN3132Separation Processes (II)

Lecture 02:Mass Transfer Coefficient

Dr. ZHAO Dan

Department of Chemical and Biomolecular Engineering4 Engineering Drive 4, Blk E5, #02-16

Tel: (65) 6516 4679

[email protected]

Wankat 3rd: 15.4; 15.4.1Treybal: Chapter 3
mailto:[email protected]:[email protected]


2/17

2

Review: Concept

Equilibrium vs. rate

Mass transfer

Model 1: molecular movement

Model 2: Ficks law Gas diffusivity

Liquid diffusivity

Diffusion + convection

Equimolar Counterdiffusion (EMD)

Unimolecular Diffusion (UMD)


3/17

3

Review: Equation

AAz AB

dcJ D

dz

BBz BA

dcJ D

dz

3/2 1/2

2

(1/ )AB

tot

T MWD

p

16 1/20

0.6

1.173 10 [ ( )]B BAB

B A

MW TD

V

( )A AA A B ABc dc

N N N Dc dz ( )B BB A B BA

c dcN N N Dc dz

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

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


4/17

Learning Outcomes of Lecture 02

Derive linear driving-force models for EMD and UMD

Practice the conversion of mass transfer coefficient

Describe the expression and physical meaning of Henrys Law

Practice the conversion of Henrys law constant

Understand two-film theory Practice the determination of interfacial compositions for

EMD and UMD

4


5/17

5

Models for Mass Transfer:(3) Linear Driving-Force Model

Flux = (mass-transfer rate)/area= (mass-transfer coefficient) (driving force)

1 2( )A c A AJ k c c

1 2( )A x A AJ k x x

1 2( )

A y A AJ k y y

1 2( )

A p A AJ k p p


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6

Linear Driving-Force Model:Equimolar Counterdiffusion (EMD)

Gases:

Liquids:

'

1 2( )A c A AN k c c ' AB

cDk

'

1 2( )A G A AN k p p ' AB

G

Dk

RT

'

1 2( )A y A AN k y y ' AB

y

cDk

'1 2( )A L A AN k c c

' ABL

Dk

'

1 2( )A x A AN k x x ' AB

x

cDk


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7

Linear Driving-Force Model:Unimolecular Diffusion (UMD)

Gases:

Liquids:

1 2( )A c A AN k c c '

( ) ( )

ABc c

B lm B lm

cD ck kc c

1 2( )A G A AN k p p '

( ) ( )

ABG G

B lm B lm

pD pk k

RT p p

1 2( )A y A AN k y y ' 1

( ) ( )

ABy y

B lm B lm

cDk k

y y

1 2( )A L A AN k c c '

( ) ( )

ABL L

B lm B lm

cD ck kc c

1 2( )A x A AN k x x ' 1

( ) ( )

ABx x

B lm B lm

cDk k

x x


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8

Conversion of Mass Transfer Coefficient

Gases:

Liquids:

' ' '1

( ) ( ) ( )

AB

c y G

B lm B lm B lm

c y G

cD

RTc

k k k cRT RT

c y c p

k k kRT RT p

' ' '

( ) ( )

AB

L L x

L B lm x B lm

cD

k c k k MW

k c k x


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9

Comparison of Three Models

Models Pros Cons

Molecular Movement Intuitive

Good for physical

understanding

Detailed theory is

quite complicated

Hard to apply

Ficks Law Widely accepted

Works well for ideal

systems

Difficult for non-ideal

ternary systems

Linear Driving-Force

Widely used bychemical engineers

Weak theoreticalbackground

May fail where Fickian

model fails


10/17

10

Mass Transfer Between Phases


11/17

11

Henrys Law

"At a constant temperature, the

amount of a given gas that dissolves ina given type and volume of liquid is

directly proportional to the partial

pressure of that gas in equilibrium with

that liquid.

William Henry (1774-1836)

'BB B B B

tot tot

p Hy y x H x

p p

B Bp Hx 0exp( )E

H HRT

pB: partial pressure of B in the vapor

(Pa)

xB: mole fraction of B in the liquid

yB: mole fraction of B in the vapor

ptot: total pressure (Pa)

cB: concentration of B in the liquid

(mol/L)

c: total concentration (mol/L)

H, H, H, H: Henrys law constant

''BB B B B

c Hx p c H c

c c

'''BB B B B

tot tot tot

cH H Hy x c H c

p p c p c


12/17

12

Henrys Law Constants (atm/mole frac.)


13/17

13

Two-Film Theory

At the phase interface, cAiandpAiare in equilibrium

Gas phase Liquid phase

pAbpAi

cAi

cAb

Gas phase Liquid phase

pAbpAi

cAi

cAb

G

L

' '( ) ( ) [EMD]A G Ab Ai L Ai AbN k p p k c c

( )Ai Aic f p

( ) ( ) [UMD]A G Ab Ai L Ai AbN k p p k c c


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Interfacial Compositions (EMD)Gas phase Liquid phase

pAbpAi

cAi

cAbG L

' '( ) ( )A G Ab Ai L Ai AbN k p p k c c

'

'

Ab Ai L

Ab Ai G

p p k

c c k

cA

pA

Equilibrium

curve

pAb

pAi

cAb

cAi


15/17

15

Interfacial Compositions (UMD)

cA

pA

Equilibrium

curve

pAb

pAi

cAb

cAi

( ) ( )A G Ab Ai L Ai AbN k p p k c c

'

'

( )

( )

Ab Ai B lmL L

Ab Ai G G B lm

p p pk k c

c c k k c p

( ) ( )( ) ( )

ln

Ai AbB lm A lm

Ai

Ab

c c c cc c c

c c

c c

( ) ( )( ) ( )

ln

Ab AiB lm A lm

Ab

Ai

p p p pp p p

p p

p p


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16

Example Question (1)

Both vapour A and gas B can be dissolved in water. The

Henrys law constant for vapour A is 0.5 and for gas B is 1.2

atm. For an equal molar mixture of A and B under a total

pressure of 3 atm, which one can reach a higher molar

concentration in water?a) Vapour A

b) Gas B

c) Vapour A equals gas B

d) Can not be determined


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17

Example Question (2)

A mixed gas containing 6% volume fraction of solute A gets in

contact with an aqueous solution containing 0.012 mole

fraction of solute A. The equilibrium relationship of solute A

in gas and water follows Y* = 2.25X. Determine the mass

transfer direction of A.

2015 CN3132 II Lecture 02 Mass Transfer Coefficient

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