Mass Integration
CHEN 4470 – Process Design Practice
Dr. Mario Richard Eden
Department of Chemical Engineering
Auburn University
Lecture No. 7 – Overview of Mass Exchange Operations
January 31, 2013
What is a Mass Exchanger?
•
Mass Exchanger
–
A mass exchanger is any direct-contact mass-transfer
unit which employs a Mass Separating Agent (or a
lean phase) to selectively remove certain components
(e.g. pollutants) from a rich phase (e.g. a waste
stream).
–
Absorption, Adsorption, Extraction, Ion Exchange, ….
R ic h (W a s te ) S tre a m
F lo w ra te :G i
In le t C o m p o s itio n : y i in
O u tle t
C o m p o s itio n : y i o u t
M ass Exchanger
L e a n S tre a m (M S A )
F lo w ra te :L j
In le t C o m p o s itio n : x j in
O u tle t
C o m p o s itio n : x j o u t
Equilibrium 1:4
•
Generalized Description
–
The composition of the rich stream (yi) is a function of
the composition of the lean phase (xj)
yi  f j ( x j )
*
•
*
Dilute Systems
–
For some applications the equilibrium functions may be
linearized over the operating range
yi  m j  x j  b j
*
Equilibrium 2:4
•
Special Cases
–
Raoult’s law for absorption
yi 
–
p
0
solute
(T )
PTotal
 xj
*
•
Mole fraction of solute in gas
•
Vapor pressure of solute at T
•
Mole fraction of solute in liquid
•
Total pressure of gas
Henry’s law for stripping
yi  H j  x j
*
Hj 
PTotal
p
0
solute
(T )
y
solubility
i
•
Mole fraction of solute in gas
•
Mole fraction of solute in liquid
•
Henry’s coefficient
•
(T )
Liquid-phase solubility
of the pollutant at
temperature T
Equilibrium 3:4
•
Special Cases
–
Distribution function used in solvent extraction
yi  K j  x j
*
•
•
Solute composition in liquid
•
Solute composition in solvent
•
Distribution coefficient
Interphase Mass Transfer
–
For linear equilibrium the pollutant composition in the
lean phase in equilibrium with yi can be calculated as:
x 
*
j
yi  b j
mj
Equilibrium 4:4
•
Interphase Mass Transfer (Continued)
–
For linear equilibrium the pollutant composition in the
rich phase in equilibrium with xj can be calculated as:
yi  m j  x j  b j
*
•
Rate of Mass Transfer
 K y   yi  y 


*
K

x
 xj 

 x  j
*
i
N pollutant
•
Overall mass transfer
coefficient for rich
phase
•
Overall mass transfer
coefficient for lean
phase
Correlations for estimating overall mass transfer coefficients can be found in McCabe et al.
(1993), Perry and Green (1984), King (1980) and Treybal (1980).
Mass Exchangers – I
•
Multistage Contactors
–
Multistage countercurrent tray column
L ig h t P h a s e O u t
H e a v y P h a s e In
W e ir
D ow ncom er
S h e ll
P e rfo ra te d
P la te (T ra y )
L ig h t P h a s e In
H eavy Phase O ut
1:2
Mass Exchangers – I
•
2:2
Multistage Contactors (Continued)
–
Multistage Mixer-Settler System
MSA
out
W a s te
in
MSA
in
W a s te
out
Modeling – I
•
1:5
Stagewise Columns
–
A generic mass exchanger
R ic h (W a s te ) S tre a m
F lo w ra te :G i
In le t C o m p o s itio n : y i in
O u tle t
C o m p o s itio n : y i o u t
M ass Exchanger
O u tle t
C o m p o s itio n : x j o u t
L e a n S tre a m (M S A )
F lo w ra te :L j
In le t C o m p o s itio n : x j in
–
Schematic of a multistage mass exchanger
y i,1 = y i o u t
y i,2
1
x j,0 = x j in
y i,3
y i,n
n
2
x j,1
y i,n + 1 y i,N -1
x j,2
x j,n .1
N
N -1
x j,n x
j,N -2
y i,N + 1 = y i in
y i,N
x j,N -1
x j,N = x j o u t
Modeling – I
•
2:5
Stagewise Columns (Continued)
–
Operating line (material balance)
y ou t
Gi  yi  yi
in
–
out
  Lj xj  xj
out
in
L
x in

The McCabe-Thiele diagram
y in
O p e ra tin g
L in e
L j /G i
y i in
yi
E q u ilib riu m
L in e
y io u t
x j in
xj
x jo u t
G
x ou t
Modeling – I
•
3:5
Stagewise Columns (Continued)
–
The Kremser equation
•
•
•
Isothermal
Dilute
Linear equilibrium
NTP 

m j Gi
ln  1 

Lj

  yiin  m j x inj  b j
  out
in
y

m
x
 bj
j j
 i
 Lj
ln 
m G
 j i



 m j Gi
 
Lj




Modeling – I
•
4:5
Stagewise Columns (Continued)
–
Other forms of the Kremser equation
NTP 

Lj
ln  1 

m j Gi

 m j Gi
ln 
 L
j

yi  b j
in
out ,*
xj

,*
  xiin  x out
j
  out
out ,*
x

x
j
 j

Li
 
 m j Gi



mj
 Lj

in
 m j x j  b j  m j Gi
y  mjx
in
i
out
yi
out
j
 bj




NTP



Modeling – I
•
5:5
Stagewise Columns (Continued)
–
Number of actual plates
NAP 
–
NTP
o
Stage efficiency can be based on either the rich or the
lean phase. If based on the rich phase, the Kremser
equation can be rewritten as:
NTP 

m j Gi
ln  1 

Lj

  yiin  m j x inj  b j
  out
in
y

m
x
 bj
j j
 i


 ln 1   y


 m j Gi


 L j
 m j Gi
 
Lj




  1 
 





Mass Exchangers – II
•
Differential (Continuous) Contactors
–
Countercurrent packed column
L ig h t
Phase O ut
H eavy
P h a s e In
P a c k in g R e s tra in e r
Random
P a c k in g
S h e ll
P a c k in g
S u p p o rt
H e a v y -P h a s e
R e -D is trib u to r
Random
P a c k in g
L ig h t
P h a s e in
H eavy
Phase O ut
1:3
Mass Exchangers – II
•
2:3
Differential (Continuous) Contactors (Continued)
–
Spray column
L ig h t
Phase O ut
H eavy
P h a s e In
S h e ll
L ig h t
P h a s e In
H eavy
Phase O ut
Mass Exchangers – II
•
3:3
Differential (Continuous) Contactors (Continued)
–
Mechanically agitated mass exchanger
L ig h t P h a s e
Out
M ix e r
H eavy
P h a s e In
S h e ll
L ig h t
P h a s e In
H eavy Phase
Out
Modeling – II
•
Continuous Mass Exchangers
–
Height of a differential contactor
H  HTU y NTU y
yi  yi
in
NTU y 
y
i
y
*
i

H  HTU x NTU x
out
( yi  yi ) log mean
*
 yi  m j x j  b j    y i
in

log mean
out
out
 m j x j  bj 
 yiin  m j x out
 bj 
j
ln  out
 y  m x in  b 
j j
j 
 i
in
Crash Course in Economics 1:5
•
Which Car is Cheaper?
–
Fixed cost: The car itself, i.e. body, engine, tires, etc.
$500
$21,000
Crash Course in Economics 2:5
•
Which Car is Cheaper? (Continued)
–
Annual Operating Cost (AOC): How much to run
and maintain the car.
$ vs. $/year ???
We need to annualize
the fixed cost of the car
$4,000/year
$700/year
Crash Course in Economics 3:5
•
Which Car is Cheaper? (Continued)
–
Annualized Fixed Cost (AFC)
AFC 
Initial Fixed Cost  Salvage or Resale Value
Useful Life Period
–
Total Annualized Cost (TAC)
T AC  A nnualized Fixed C ost  A nnual O perating C ost
Crash Course in Economics 4:5
•
Which Car is Cheaper? (Continued)
Useful Life: 2 Years
Useful Life: 20 Years
Salvage Value: $200
Salvage Value: $1000
AFC = ($500-$200)/2 yr = $150/yr
AFC = ($21,000-$1,000)/20 yr =
$1000/yr
Crash Course in Economics 5:5
•
Which Car is Cheaper? (Continued)


TAC = $4,000 + $250 =
TAC = $1,000 +$700 =
$4,250/yr
$1,700/yr
Minimizing Cost of MENs 1:3
•
Total Annualized Cost of Mass Exchange System
–
–
Fixed cost: Trays, shell, packing, etc.
Operating
cost:
solvent
makeup,
heating/cooling, etc.
TAC  AO C  AFC
•
y
pumping,
P ra c tic a l F e a s ib ility R e g io n
Driving Force
–
–
Minimum allowable composition
difference
Must stay to the left of
equilibrium line

j
E q u ilib riu m
L in e
x * j = (y - b j )/m j

j
P ra c tic a l F e a s ib ility
L in e
xj
Minimizing Cost of MENs 2:3
•
Driving Force (Continued)
–
Minimum allowable composition difference at rich end
of mass exchanger

yi
j
in
O p eratin g
L in e
yi
yi
When the minimum allowable
composition difference εj
increases, then the ratio of
L/G increases.
AOC increases, due to
higher MSA flow
out
E q u ilib riu m
L in e
x j in
x j o u t, m a x x j o u t, *
xj
F ig . 2.9. M in im u m A llo w ab le C o m p o sitio n D ifferen ce at th e
AFC decreases, due to
smaller equipment, e.g.
fewer stages
Minimizing Cost of MENs 3:3
Driving Force (Continued)
Trade-off between
reducing fixed cost and
increasing operating
cost
Composition driving
force, becomes a
optimization variable
7 0 ,0 0 0
6 0 ,0 0 0
TAC
5 0 ,0 0 0
$/ year
•
4 0 ,0 0 0
A n n u a l O p e ra tin g
Cost
3 0 ,0 0 0
2 0 ,0 0 0
A n n u a liz e d
F ix e d C o s t
1 0 ,0 0 0
0
OPTIMUM
0 .0 0 0 0
0 .0 0 1 0
0 .0 0 2 0
0 .0 0 3 0
0 .0 0 4 0
M in im u m A llo w a b le C o m p o s itio n D iffe re n c e ,
0 .0 0 5 0

F ig 2 .1 3 . U sin g M in im u m A llo w a b le C o m p o sitio n D ifferen ce to
T ra d e O ff F ix ed V ersu s O p era tin g C o sts
Other Business
•
Next Lecture – February 5
–
–
Synthesis of mass exchange networks part I
SSLW pp. 297-308