2
Phenomena
transport
Who
.
.
.
A
SWITCHED
OUT
THE
ABSORBER
STRIPPER ?
MODULE 11
Introduction
MASS
TO
TRANSFER
FOR
OBJECTIVES
To learn the concept of the mass transfer coefficient and the
Sherwood number, and to apply it to fluid flow in a tube with a
known wall concentration.
LEARNING OUTCOMES
1. To explain the meaning of the mass transfer coefficient (and all its various forms), the
Sherwood number, and the Schmidt number.
2. To use Raoult's law to determine equilibrium mole fractions across an interface.
3. To explain the Chilton-Colburn Analogy between the friction factor, Nusselt number, and
Sherwood number.
4. To model a falling film evaporator (also called a wetted wall evaporator), which is a simple
application of the mass transfer equations to mass transfer in a single domain with a known wall
concentration. (This problem is completely analogous to heat transfer for forced convection in a
pipe with a known wall temperature).
in
Lp
n' AY
AT
=
=
-
-
(
)
h MDL Atzm
t.fi/(TDL)Aycm
HEAT
TRANSFER
MASS
TRANSFER
5. To explain the differences between dilute and concentrated solutions in the mass balance
EXAMPLE
Removing
ABSORBER / STRIPPER
CO2
* ABSORPTION CAN
from
BE
combustion
OPERATION
products
EXOTHERMIC
HIGHLY
ABSORBER AND
ABSORBER
OPERATION
)
(
SCRUBBER
SPECIES
STREAM
TO
A
ABSORBS
THAT
FROM
:
A
types
Two
unit
① Chemical
A
GAS
SIDE
LIQUID
SIDE
A
STRIPPER
7
on
:
( ie
rxn
and
:
amine
Relies
corn
)
ie
(
② physical
ammonia Into
STREAM
)
WATER
A
STRIPPER :
"
STRIPS
"
A
LIQUID
GAS
UNIT
SPECIES
SIDE
SIDE
OPERATION
STREAM
STREAM
THAT
FROM
A
TO
A
OFTEN
USED
TO
REGENERATE
SOLVENT
THE
USED IN
ABSORBER
Applications
GAS
INDUSTRY
•
REFINERIES
DISTILLATION
ABSORPTION
V5
Distillation
SEPARATES
more
or
by
PETROCHEMICAL
chemical
REQUIRES
boiling point
AND
energy
(
change
)
.
CHEMICAL
PAPER
PULP AND
FOOD
transfer
Processing
AIR
SCRUBBING
WASTEWATER TREATMENT
•
on
MASS
COUNTER
SEPARATES Two
COMPONENTS
MORE
SOLUBILITY
OPERATES
points
PHASE
.
ABSORPTION
OR
eguiaolar
is
DIFFUSION
PACKAGING
EXHAUST
species
differences in
of
virtue
Two
DIFFERENCES
Below boiling
mass transfer is
WELL
AND
BASED
unimolecul.AM
.
VAPOR
LIQUID
-
EQUILIBRIUM
Xi8iPsAt=YP
MODIFIED
:
IDEAL
p
Activity
NON
-
RAOULT'S
LAW
(
P
GAS
IDEAL
Low
)
MIXTURE
Coefficient
Psa,- ( )
t
-
A
-
B
]
[ Antoine
EQUATION
Ctt
For
An
ideal mixture
Xi Psat = Yip
Raoult's
LAW
/
ideal
Yi
Xi
=
Trends
gas
PSAT
p
Yip
=)
As
TP
AS
PP
Xi
¥-6
NON IDEAL
-
In
MIXTURE
contact with
idea / GAS
MODELS FOR ACTIVITY
COEFFICIENTS
WILSON
NRTL
's
Henry
UNIFAC
LAW
UNI QUAL
(Ñ¥
MODELS
FOR
EQ
.
OF
.
STATE
IDEAL
VAN
GAS
Peng
Waals
der
Redlich
-
( 2- =L )
-
Kwong
ROBINSON
}
#1
FULL
FORM
OF
VLE
Poynting
p
FACTOR
CLOSE TO
Ñi Yi P
↳ §
ji ✗
)
ioisatpis.AT#p(ViYP-Pis ]
"
=
correction
RT
.
1
USUAU]
unless
Pis
really
k.ge
to ;SAT Fugacity
;
fog ity
for
i
AT
T ,P
in
Coeff
=
.
mixture
( Accounts For non ideality
of gas mixture)
-
coeff
i
for
.
in
pure
gas AT
SAT
T AND p
Inch
.
-_§*()dp
Two
FILM
Theory
f
/
VAPOR LIQUID
stagnant stagnant
film
gas film
being
ya
or
BULK
pa
GAS
Yai
•
bulk
TO
liquid
@
transported
from
¥
LIQUID
species
A is
INTERFACE
Kai
bulk
•
•
XA
LIQUID
1
*
GAS
BULK
•
> ✗
DIRECTION
mass
OF
TRANSFER
or
CA
*
In
stagnant
the
☒ at
↳
f)
=
-
Total
FILM
(go , ☐ A→
FLUX
MOLAR
constant
diffusion
in
A
gas
LIQUID
01¥
=
molar
-
MOLAR
→
Diffusion
211A
G- ✗a)
2X
moving Away
A
of
A
from
moving
Film
concentration
Got DA
Flux
OF
gas
in
gag
2X
INTERFACE
→
of
2¥
stagnant Total
the
↳
OF
concentration
MOLAR
( 1- Ya)
TOWARDS
In
GAS
chemepedia.org
in
constant
in
liquid
INTERFACE
of
liquid
OF
A
the
liquid
A
total
mover
←
FLUX
of
WORD
ON
*
g- a
NOTATIONS
jA*
=
-
XA(Ea*t0IB* )
t
A
In
Equimolar
counter diffusion
OI #
=
-
0IB*
oIE=j¥
In
diffusion
through
A
STAGNANT
B
§a*=jA*tXaIa*
In
dilute
conditions
Ia*=ja*
,
✗a → 0
AND
( Ipf )
-0
OI #
=
-
CTOT DA
211A
G- ✗a)
2X
>
As
Enhancement
§A*=jA*=
✗A → 0
-
FACTOR
Got Da 211A
2x
P
We
do
know
not
this
value
Introduce
mass
transfer
coefficient
jA*=
Kd ( Ca
Sh=
KID
-
=
Da
•
where
Ki
has
D
is
)
f(
Re ,
dimensions
A
is
Da
CA ,i
Is
Sc
of
=
conditions
dilute
)
,
CORRELATION
/time
tenth
length
diffusion coefficient
Sc = Schmidt number
Sh
for
Yp
characteristic
the
prime designation
* The
Sherwood Number
=
=
of
A
PIMDA
Convector
.
enhanced
mass
transfer to
mass
transfer
purely diffusive
Relationship
between
'
Kc
AND
Kc
ki-kw-a.it
in
For
* NOTE :
dilute
The
conditions
prime
Perry's
convention
HANDBOOK
SEPARATIONS
AND
Kiki
Is
OPPOSITE
TEXT Book
-
consistent with
YOUR
Correlations
Nusselt
FOR
Sherwood
NUMBER
THE
HEAT TRANSFER
=
2 to
FROM
MASS TRANSFER
-
MARSHALL
FROM A
0.5
-
-
SPHERE
A
.GRe°"pp%
RANZ
Sh
OFTEN
ARE
SIMILAR
VERY
No
AND
NUMBER
THE
BOTH
21-0.552 Re Sc
CORRELATION
Sphere
13
'
Froessling CORRELATION
}
To first
order
:
Chilton COLBURN
-
J
tf
FACTOR
Nu
ANALOGY
=
up, ,
Sh_
µ ,,
SHORT
jA*
REVIEW
is
eguimolar
pure
COUNTER DIFFUSION
jA*
Kd @
A
=
-
CA ,i
SHERWOOD
)
Sh= KID / DA
§A*= KC (CA Ca ;)
-
→
,
More
flux
general
through
NUMBER IS
DEFINED
WITH
REGARDS
TO
relationship
A
Ri
for
STAGNANT
FILM
BUT
OIF
Kc
=
'
G- ✗
In
dilute
(
CA CA
-
;)
where
① "A) i. im= ÉiD
in aC- Kai )
A
a
limit
,
C- a)
✗
im
=
1
AND
IF ki (Ca Ca ;)
-
-
CO
-
CURRENT
WETTED
WALL
( LIQUID
FILM
COCORRENT →
V5
.
COUNTER
FALLING
IS
FILM
CURRENT
EVAPORATOR
PURE , ONE COMPONENT
←
)
COUNTER
CURRENT
PURE
LIQUID A
IN
"
#
to
OVERALL A
mo--µµqqñAiñµ•qn
"
BALANCE
MOLE
-0--7
B.
4k$ µfMM
:<
Bfg
r=Mfs*
COLUMN
'
nain
☒
Bg
,
rigas
ya
IDEAL GAS FLOW
-
Ñiioyoot
B
hat 'n☐
:
in
-
-
)
of
ña=¥jañB
inatriis
✓
v
d-
hug
.in
A AND
HEIGHT
Faze
=
PHASE ( Consists
GAS
GG
,
ÑA in
-
,
µ
Hey
Bg
ÑA out
"
nB( YANK
'
YAN
1-
"
-
Jain
1-
.in Imig
iniiq
)=
gain
-
,
out
PURE
LIQUID A
IN
#
*
MOLE
BALANCE
ON
A
T-e-GOINGINTOGASPHASE-oo-n-agqq.ir?A.iII
,••By^
! Inti!
BMMf Mf
i
Hi
;µf
Bowl
Mlf
,
2a
•
ñ
•
ria.out-na.in =ff(Ea*.ñ)dA
CONTROL
COLUMN
SURFACE
HEIGHT
where
HGqic.Hq v.is/(oIa*.in)da--
r=Gs*ii i"µ-_←
*
ifs
IDEAL GAS FLOW
(
)*kc[Catt) Cai
D- is
-
dz
L
'
na out
-
,
n' a. in
Cai ftp.dz
(4-17)
-11-(13-28) Joke
-
=
Assumptions : ①
8
<<
D
② A is always dilute
③ Pressure
pgµ=yi=PP
the
TEMPERATURE
Do
change Appreciably
is constant
g.
n' A. out
AND
in
-
n' a. in
=
#
[
D) ohki
NOT
that
so
CALZ)
gas
-
CA
,
CA ,i
;]
dz
phase
n' A. out
-
n' A. in
=
#
[
D) Iki
CALZ)
✓
-
dz
To
;]
difference
is not
constant
through
column
HEIGHT
TD Ki [G- G) Cai]
integrate
we
describe
A
choose
,
dz
-
=
To
CA
to
this
dina
-
a
NEED
A
Common
VARIABLE
We
gas phase
mole fraction basis ( Ja)
in
the
.
will
GAS
PHASE :
ÑA
f Generally
t
in .B
AS
Ya
na
nat 'nB
Layer
=
* ÑB
YA
1-
YA
djnAz-
=
his DJA
2¥
For
ideal
a)
IN
TERMS
OF
YA
"
gas
¥
LHSÉRHS
IRMEN ,
A.
CA =
It
STAGNANT
"
CTOT
YA
can BE
partition
.
CA =
¥
B
AS
liquid
CREATES THE
'
¥
ÑA
not
into
'
=
LONG
does
CONSTANT
A
YA ¥
Got =P
RT
dina
=
-
gz
TDKI [
G- (z)
-
ca,
b
f
;]
yai.PT/oYA.Pp-,nB.dya(-YA)2dz
we
AND
Hence :
already
have
Ya
n'
ASSUMED
P ,T
Are
constant
441
BDYA
az
=
-
IDK
)
ja ]
YAG
'c(¥)[
-
,,
INTEGRATING
AFTER
tips ( ya
,
out
-
YA )
,
in
(ya ya ;)
-
in
=
-
µ
TDL *
,
( ya ya ;)
-
,
em
(Ja Yai ) top (ya ya :/ bottom
=
-
-
-
,
In
A
-
JA i / top
,
(JA JA ,i ) bottom
-
>
RIBLJA
,
out
-
Ja
.ir/---k'y1TDL(YA-JA,i)imlk'y=kc(P
/RT
gai
SUMMARY
7
nB(Ya
'
I
→
his
-
,
our
Aint
-
Ja .in/=-kc(1TDY(YA-YA,i/im
7 VOLUMETRIC
* CAREFUL :
PY
✗ a,i= I
ya.in/- -ki(F,-)1TD4Ya-Ya,i) mtiy- ki(PlRt)- -A%Fa-time
RF ⑨
ÑBR¥=
-
ÑB
FLOW
RATE
ALTERATIVE
¢7 FORM
ÑB ( faint YA.in/---kiGtD4&n--JaiL
-
.
①
SIGNS
⑦
The
ABOVE
CONDITIONS
RELATIONSHIPS
ONLY
ARE
FOR DILUTE
MODULE 11
EXERCISE I
MODULE
:
_←ytg
11 :
EXCERCISE
100Mt min
.
in helium
=
f- IATM
F- 60°C
ID -2cm
I
(YTEOS
out
,
YTEOS in)
-
,
tky ITLLD
)(Yieos,i Yteos)
-2s
-
KIDDIE
-
yteos
2- = 25cm
i
,
=
PSAT
16%1%2
=
yteos
SUFFKEWT
And
__€BBET£m 2×105 scam
41
balance equation
"
( dilute limit )
CONDITION
dilute form
° "
760 TORR
P
Hence
=
,m
of
FOR
mass
Ky
_~
kg
/
How
find
to
Gravity
S ?
[
viscosity of
43
8*s=(¥¥;E
Compare
Di
to
-
Di
25
=
=
100mi
2cm
}
cm
Di -2cm
-
:
2cm
-
4.
Flow
FÉ%☐ [ 0.03 Poise
Ñteos
0.95g / cm
Steos _~ 0.03
driven
03cm
)
=
1.94cm
/ min
=
]
0.003 PAS
0
in helium
(YTEOS
From
Perry's
Shaves
,
out
-
YEÑ= tkjlTLDifyieos.it/teos)em
HANDBOOK :
5- 18
TABLE
] "[p÷a]°
"
"
=
µ
1.94cm
Km Di
DA
=
o.az >
Puti
[
M
'
""
to
Applies
g.
Sh
helium
Kin Di
=
=
o
µ
DA
=
Di
=
1.31
cm
density
p=
'
[ 10130¥ [
02 >
/ s [ Diffusion of
of
viscosity
µ=
✓
.
1.94cm
=
DA
.ozz[pv☐i]°"[÷a]°
=
§ccm)*
=
""
helium
p=
e
of helium
@
IATM
TCH
*
P
273
2*105*(2731-60)
273
o
2)
24
=
]
In
/ Atm ,
T -60°C
-
=
2
.
=
0.8kg /m3
/ ✗ co
Ñ
V=
ITDYY
2.4*105 cm /min
"
=
" "
helium
Teos
F- 60°C
.
"
-
5Pa
=
.
S
" 1-
m/s
Kin Di
=
24
DA
R 'm
=
16
cm
/
Ky
s
by
big
km! Got
'
-_
kj
=
5.9
5.9
^5
PA
-
/
J mole
moles
m2 g
=
'
=
164¥ PIRT
/
in helium
(YTEOS
)
TIDL
(
)
tky
ieosi-YTeosfmisueliumlyteos.at/--ky1TDl
,
out
=
*
(0.02-00) ¢02 yteoso )
/N
/µ(
'
02
0.02
-
yteoqoor
102
0.02
-
)
"☐ t
=
=
Ñ helium
=
1
.
8
Ltcol out
,
Yteos
out
,
=
-
-
0.0088
.
0.02
0.02
kin ITDL
V. Helium
-
JTEOS
,
=
°
.
out
6