Transcript Slide 1

Mass Integration
CHEN 4470 – Process Design Practice
Dr. Mario Richard Eden
Department of Chemical Engineering
Auburn University
Lecture No. 9 – Synthesis of Mass Exchange Networks II
February 7, 2013
The Pinch Diagram 1:6
•
Amount of Mass Transferred by Rich Streams
M R i  G i ( y is  y it )
, i  1, 2 , ...., N R
Mass
Exchanged
R2
MR2
MR1
R1
y1t y2t
y1s
y2s
y
The Pinch Diagram 2:6
•
Constructing Rich Composite using Superposition
Mass
Exchanged
MR2
R2
MR1
R1
y1t y2t
y1s
y2s
y
The Pinch Diagram 3:6
•
Amount of Mass Accepted by Process MSA’s
M S j  LCj ( x tj  x sj )
, j  1, 2, ...., N SP
Mass
Exchanged
S2
MS2
MS1
S1
y
x1s
x2s
y  b1
1
m1
y  b2
x2 
2
m2
x1 
x1t
x2t
The Pinch Diagram 4:6
•
Constructing Lean Composite using Superposition
Mass
Exchanged
S2
MS2
MS1
S1
y
x1s
x2s
y  b1
1
m1
y  b2
x2 
2
m2
x1 
x1t
x2t
The Pinch Diagram 5:6
•
Constructing the Pinch Diagram
–
Plot the two composite curves on the same diagram
Mass
Exchanged
Pinch Point
Move the lean
composite vertically
until the entire
stream exists above
the rich composite.
The point closest to
the rich composite is
the Pinch.
Lean Composite
Stream
Pinch
Point
Load to be
Removed
by External
MSA’s
Excess Capacity
of Process MSA’s
Integrated
Mass Exchange
Rich Composite
Stream
y
y  b1
1
m1
y  b2
x2 
2
m2
x1 
The Pinch Diagram 6:6
•
Decomposing the Synthesis Problem
–
•
Above the Pinch
–
–
•
Creates two subregions, i.e. a rich end and a lean end
Mass exchange between rich and lean process streams
No external MSA’s required
Below the Pinch
–
–
Both process and external MSA’s are used
If mass is transferred across the pinch, the lean
composite moves upward, thus:
DON’T TRANSFER MASS ACROSS THE PINCH!
Example No. 2 1:17
•
Dephenolization of Aqueous Wastes
To regeneration &
To final
recycle
finishing
S1 S2 S3 S4
Light Gases
Waste
Gas Oil
Deashing
and
Demetallization
Atmospheric
R1
Gas
Oil
Distillation
Stripping
Steam
Waste
Lube Oil
Deashing
and
Demetallization
R2
R1
Mass
Exchange
Network
S1
Gas
Oil
R2
Air S5
Vacuum
Distillation
Lube Oil
To phenol
condensation
S5
Ion Exchange
Resin S4
Dewaxing
and
Deasphalting
Activated
Carbon S3
Stripping
Steam
Lube Oil S2
Example No. 2 2:17
•
Rich Stream Data
Flowrate
Gi, kg/s
Supply
Composition
yis
Target
Composition
yit
R1
Condensate
from first
stripper
2
0.050
0.010
R2
Condensate
from second
stripper
1
0.030
0.006
Stream
•
Description
Candidate MSA’s
–
–
Two process MSA’s
Three external MSA’s
Example No. 2 3:17
•
Process MSA Data
Stream
•
Description
Upper Bound on
Supply
Target
Flowrate
Composition,
Composition,
Ljc, kg/s
xjs
xjt
S1
Gas oil
5
0.005
0.015
S2
lube oil
3
0.010
0.030
External MSA’s
–
–
–
Absorption using activated carbon (S3)
Ion exchange using a polymeric resin (S4)
Stripping using air (S5)
Example No. 2 4:17
•
Equilibrium Data
–
General equation for transferring phenol to the j’th lean
stream
y  mj  xj
–
 m1  2.00
 m  1.53
 2
,  m3  0.02
 m  0.09
 4
 m5  0.04
Minimum allowable composition difference
 j  0.001 kgkg phenol
M SA
, i  1, 2, 3, 4, 5
Example No. 2 5:17
•
The Pinch Diagram
0.140
Mass Exchanged,
kg phenol/s
0.120
0.1224
Excess Capacity
of Process MSA’s
0.1040
0.100
0.0184 kg phenol/s
Rich
Composite
Stream
0.060
Pinch Point
Load to be
0.040 Removed by
External MSA’s
y = 0.0168
x1 = 0.0074
x2 = 0.0100
0.1224 – 0.1040
=
Lean
Composite
Stream
0.080
Excess Capacity of
Process MSA’s
Pinch
Point
0.020
0.0124
0.000
0.000
0.010
0.004
0.0055
0.020
0.0168
0.030
0.040
0.050
y
0.009
0.0074
0.014
0.019
0.0024
x1
0.0186
0.0251
0.0317
x2
0.0121
0.0100
External MSA
Load
0.0124 kg phenol/s
Example No. 2 6:17
•
Removing Excess Capacity of Process MSA’s
–
–
Can be eliminated by lowering the flowrate and/or
outlet compositions of the process MSA’s.
If elected to lower the flowrate of S2 then:
new
j
L
Excess
 t
x j  x sj
new
2
L
Excess
0.0184
 t
 3
 2.08 kg/s
s
x2  x2
0.03  0.01
L
L
old
j
old
2
Example No. 2 7:17
•
Activated Carbon
–
–
–
–
Adsorption isotherm is linear up to mass fraction 0.11
Above 0.11 activated carbon becomes saturated
Thus x3t is taken at 0.11
Corresponding composition on y-scale:
y  0 .0 2 ( 0 .1 1  0 .0 0 1)  0 .0 0 2 2
–
–
–
–
Less than supply compositions of R1 and R2
Thus feasible to transfer phenol from both streams to S3
Less than value of tail end of lean composite
Hence S3 will not eliminate any phenol that can be
removed by the process MSA’s.
Example No. 2 8:17
•
Activated Carbon (Continued)
–
Cost of using activated carbon
(A)
–
C 3  0 .0 5  1 .6 0  2  5  1 0  3  x 3t  0 .0 8  0 .0 1  x 3t
Amount of activated carbon required to remove 1 kg of
phenol can be calculated from a mass balance
(B1) 1 k g p h en o l rem o v ed  L 3 ( x 3t  0 )
kg activated carbon 1
 t
(B2)
kg phenol
x3
Example No. 2 9:17
•
Activated Carbon (Continued)
–
Multiplying equations (A) and (B2) provides the cost of
removing 1 kg of phenol from the waste streams using
activated carbon
0.08
C  t  0.01
x3
r
3
–
Substituting x3t = 0.11 kg phenol/kg activated carbon
into (A) and (B2)
C 3  $ 0 .0 8 1 / k g recircu latin g activ ated carb o n
C 3r  $ 0 .7 3 7 / k g o f rem o v ed p h en o l
Example No. 2 10:17
•
Ion Exchange
C 6 H 5O H  N a O H  C 6 H 5O N a  H 2O
–
Regeneration
–
Cost of using ion exchange
(C)
–
C 4  0 .0 5  3 .8 0  0 .4 6  0 .3 0  x 4t  0 .1 9  0 .1 2 8  x 4t
Amount of activated carbon required to remove 1 kg of
phenol can be calculated from a mass balance
(D1) 1 k g p h en o l rem o v ed  L 4 ( x 4  0 )
t
kg ion exchange resin 1
 t
(D2)
kg phenol
x4
Example No. 2 11:17
•
Ion Exchange (Continued)
–
Multiplying equations (C) and (D2) provides the cost of
removing 1 kg of phenol from the waste streams using
ion exchange
t
(E)
–
–
0.19
C  t  0.128
x4
r
4
The higher the value of x4 ,
the lower the removal cost.
So what is the highest
possible value of x4t that can
be used?
No mass should be transferred across the pinch
Optimum target composition of S4 is the pinch
composition y = 0.0168. Corresponding to:
0.0168
x 
 0.001  0.186
0.09
t
4
Example No. 2 12:17
•
Ion Exchange (Continued)
–
Substituting x4t = 0.186 kg phenol/kg ion exchange
resin into (C) and (E)
C 4  $ 0 .2 1 4 / k g recircu latin g resin
C 4r  $ 1 .1 5 0 / k g o f rem o v ed p h en o l
Example No. 2 13:17
•
Air Stripping
–
Based on the cooling duty of the phenol condensation
unit, the cost of using air stripping is given as:
(F)
–
The outlet composition should be 50% of the Lower
Flammability Limit (LFL) of 5.8 weight%:
x 5t  0 .5  0 .0 5 8  0 .0 2 9
Less than supply
composition of rich streams
and pinch composition.
Corresponding y-scale composition
Thus thermodynamically
feasible!
(G)
–
C 5  $ 0 .0 6 / k g air
y  m 5 ( x 5t   5 )  0 .0 4  (0 .0 2 9  0 .0 0 1)  0 .0 0 1 2
Example No. 2 14:17
•
Air Stripping (Continued)
–
Since it is feasible to use air stripping for the phenol
removal, the removal cost can be calculated
C 5r  $ 2 .0 6 9 / k g o f rem o v ed p h en o l
•
Summary
M SA
Unit Cost ($/kg M SA)
Activated Carbon (S 3 )
0.081
Ion Exchange Resin (S 4 )
0.214
Air S tripping (S 5 )
0.060
Removal Cost ($/kg phenol)
0.737
1.150
2.069
And the winner is Activated Carbon!!!
Example No. 2 15:17
•
Summary (Continued)
–
Flowrate of activated carbon
MS 3
0.0124 kg/s
L3  t

 0.1127 kg/s
s
x3  x3
0.11  0
–
Minimum Operating Cost
MOC 
$0.081
kg activated carbon

Ahead of design!!!
0.1127 kg activated carbon
s
s 8760 hr
 3600
hr  yr
MOC  $288  10 3 / yr
MOC 
$0.737
kg phenol removed
removed 3600 s 8760 hr
 0.0124 kg phenol
 hr  yr
s
MOC  $288  10 3 / yr
Example No. 2 16:17
•
Trading Off Fixed Vs. Operating Cost
–
–
Minimum allowable composition differences can be used
to trade off fixed vs. operating cost.
When waste streams are mixed, the number of mass
exchangers and, consequently, fixed cost decrease. On
the other hand, mixing various waste streams normally
increases the MOC of the system
–
Waste stream data for mixing of waste streams
Stream
Rmixed
Description
Flowrate
Gi , kg/s
Mixed R1 and R2
3
Supply
Composition
(mass fraction)
yis
0.0433
Target Composition
(mass fraction)
yi t
0.0087
Example No. 2 17:17
•
Trading Off Fixed Vs. Operating Cost (Continued)
–
New Pinch Diagram for mixed waste streams
0.140
Mass Exchanged,
kg phenol/s
0.120
0.1224
Excess Capacity
of Process MSA’s
0.1040
Values Obtained
0.100
Lean
Composite
Stream
0.080
Pinch location as well
as external MSA load is
unchanged, i.e. so is
the MOC.
Rich
Composite
Stream
0.060
Load to be
0.040 Removed by
External MSA’s
Pinch
Point
0.020
0.0124
0.000
0.000
0.0087
0.004
0.0055
MOC = $288,000/yr
0.020
0.0168
0.030
0.040
0.0433
0.050
y
0.009
0.0074
0.014
0.019
0.0024
x1
0.0186
0.0251
0.0317
x2
0.0121
Screening External MSA’s 1:3
•
Questions
–
–
•
How do we screen candidate external MSA’s?
Is the cost of each MSA ($/kg recirculating MSA) a
proper screening criterion?
Example - Refinery Hydrogen Removal
–
–
–
–
Need to remove 10 kg H2/hr from refinery gasses
Two candidate MSA’s
Absorption on sand (Cost $10-4 /kg sand)
Absorption on activated carbon (Cost $1.0 /kg carbon)
Screening External MSA’s 2:3
•
Example - Refinery Hydrogen Removal (Cont’d)
–
1 kg of sand can remove 10-9 kg of H2
L sand
MS sand
10 kg/hr
10
 t


10
kg sand/hr
s
9
x sand  x sand 10  0
C o st sa n d  1 0  4 $ / k g sa n d  1 0 1 0 k g sa n d /h r  $ 1 0 6 /h r
–
1 kg of activated carbon can remove 0.1 kg of H2
Lcarbon
MS carbon
10 kg/hr
 t

 100 kg carbon/hr
s
x carbon  x carbon
0.1  0
C o st ca rb o n  1 .0 $ / k g carb o n  1 0 0 k g carb o n /h r  $ 1 0 0 /h r
Screening External MSA’s 3:3
•
Proper Screening Criterion
–
•
Removal cost: $/kg removed of targeted species
Conversion to Removal Cost
–
How to convert from $/kg MSA to $/kg removed?
1 kg of MSA
xs
(xt – xs) kg of targeted species is removed
per kg of the MSA
(3.30) C 
r
j
xt
Cj
x tj  x sj
IMPORTANT!!!
No Process MSA’s 1:2
•
Screening the External MSA’s
If C2r < C1r then eliminate S1 from the problem, as it
is thermodynamically and economically inferior to S2
Mass
Exchanged
If C2r < C3r retain both MSA’s
Rich Composite
Stream
Load to be
Removed by S2
Load to be
Removed
by S3
S1
x 1s
S2
x s2
S3
x s3
x t3
x t2
y
x 1t
y  b1
1
m1
y  b2
x2 
2
m2
x1 
x3 
THERMODYNAMIC FEASIBILITY
y  b3
 3
m3
No Process MSA’s 2:2
•
Constructing the Pinch Diagram
Mass
Exchanged
Pinch
Point
Rich Composite
Stream
Lean
Composite
Stream
S1
x 1s
S2
x s2
S3
x s3
x t3
x t2
y
x 1t
y  b1
1
m1
y  b2
x2 
2
m2
x1 
x3 
y  b3
 3
m3
Example No. 3 1:4
•
Toluene Removal from Wastewater
–
–
–
–
Flowrate of wastestream: G = 10 kg/s
Supply composition of toluene: ys = 500 ppmw
Target composition of toluene: yt = 20 ppmw
Three external MSA’s
•
•
•
Stream
Air (S1) for stripping
Activated carbon (S2) for adsorption
Solvent (S3) for extraction
Uppe r
bound
on flowrate
C
j
L
Supply
composition
Target
composition
(ppmw)
xjs
(ppmw)
kg/s
mj
 j
Cj
ppmw
$/kg
MSA
Removal Cost
C1r = $0.38/kg
xjt
S1

0
19,000
0.0084
6,000
7.2x10-3
C2r = $5.53/kg
S2

100
20,000
0.0012
15,000
0.11
C3r = $43.90/kg
S3

50
2,100
0.0040
10,000
0.09
Example No. 3 2:4
•
Screening the MSA’s
–
S2 and S3 are capable of removing the entire toluene
load. S1 has limited removal capability
0.0050
0.0048
Mass Exchanged,
kg Toluene/s
0.0040
Rich
Stream
0.0030
0.0020
Activated carbon is
less expensive than
the solvent, thus S2
should be used to
remove the
remaining load, i.e.
0.0003 kg/s
Air is least
expensive, thus S1
should be used to
remove all the load
to its right, i.e.
0.0045 kg/s
0.0010
0.0003
0.000
0 20
50
Carbon
100
0
20,000
100
Air
200
19,000
300
400
500 y, ppmw
x1, ppmw
x2, ppmw
Extractant
50
2100
x3, ppmw
Example No. 3 3:4
•
Constructing the Pinch Diagram
0.0050
Mass Exchanged,
kg Toluene/s
0.0048
0.0040
Air
Rich
Stream
0.0030
0.0020 Activated
Carbon
0.0010
0.0003
0.000
0 20
50
0
100 20,000
100
200
19,000
300
400
500 y, ppmw
x1, ppmw
x2, ppmw
Example No. 3 4:4
•
Minimum Operating Cost (MOC) Solution
–
Flowrate of air:
MS1
0.0045 kg/s
L1  t

 0.237 kg air/s
s
6
x1  x1 19, 000  10  0
–
Flowrate of activated carbon:
MS2
0.0003 kg/s
L2  t

 0.015 kg carbon/s
s
6
x 2  x 2 (20, 000  100)  10
–
Assuming 8000 hr/yr:
MOC  0.237 kg/s  $7.2  10  3 /kg  0.015 kg/s  $0.11/kg
MOC  0.00335 $/s  $96,700/yr
Other Business
•
Michelin Information Session – February 12
–
•
Meet in McMillan Auditorium during regular lecture time
Next Lecture – February 14
–
–
Graphical mass integration techniques
SSLW pp. 297-308