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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
Wankat 3rd: 15.4; 15.4.1Treybal: Chapter 3
mailto:[email protected]:[email protected] -
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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)
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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
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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
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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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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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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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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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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
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Mass Transfer Between Phases
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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
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Henrys Law Constants (atm/mole frac.)
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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
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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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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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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.