Mass Integration
CHEN 4470 – Process Design Practice
Dr. Mario Richard Eden
Department of Chemical Engineering
Auburn University
Lecture No. 11 – Algebraic Mass Integration Techniques
February 19, 2013
Why an Algebraic Approach?
•
Pinch Diagram
–
–
–
•
Useful tool for representing global transfer of mass
Identifies performance targets, e.g. MOC
Has accuracy problems for problems with wide ranging
compositions or many streams
Algebraic Method
–
–
–
No accuracy problems
Can handle many streams easily
Can be programmed and formulated as optimization
problems
Algebraic Mass Integration 1:7
•
Composition Interval Diagram (CID)
Interval
Rich
Streams
y1
s
Process MSA’s
x1  ( y  b 1 ) / m 1   1
R1
1
x 2  ( y  b 2 ) / m2   2
x1t
2
x2t
3
4
xNspt
y1t
5
xNsps
6
SNsp
7
y2s
8
yNRs
9
10
.
.
.
Nint
xNsp  ( y  bNsp ) / mNsp   Nsp
x1s
R2
RNR
S1
x2s
y2t
yNRt
S2
Number of intervals
Nint ≤ 2(NR+NSP) – 1
Equality is when no arrow
heads or tails coincide!
Algebraic Mass Integration 2:7
•
Table of Exchangeable Loads (TEL)
–
Exchangeable load of the i‘’th rich stream passing
through the k’th interval is:
Wi ,Rk  Gi ( y k 1  y k )
–
Exchangeable capacity of the j’th process MSA which
passes through the k’th interval is calculated as:
W jS, k  LCj ( x j , k 1  x j , k )
Algebraic Mass Integration 3:7
•
Table of Exchangeable Loads (TEL) (Cont’d)
–
Collective load of the rich streams passing through the
k’th interval is:
WkR 

Wi ,Rk
i passes through interval k
–
Collective capacity of the lean streams passing through
the k’th interval is:
WkS 

j passes through interval k
W jS, k
Algebraic Mass Integration 4:7
•
Mass Exchange Cascade Diagram
–
Within each composition interval it is possible to
transfer a certain mass of pollutant from a rich to a lean
stream
–
It is also possible to transfer mass from a rich stream in
an interval to a lean stream in lower interval
–
Component material balance for interval k
W kR   k 1  W kS   k
Algebraic Mass Integration 5:7
•
Mass Exchange Cascade Diagram (Cont’d)
Residual Mass from
Preceeding Interval
 k-1
Mass Recovered
from Rich
Streams
WkR
k
k
Residual Mass to
Subsequent Interval
WkS Mass Transferred
to MSA’s
Algebraic Mass Integration 6:7
•
Comments
–
δ0 is zero (no rich streams exist above the first interval)
–
Feasibility is insured when all the δk's are nonnegative
–
The most negative δk corresponds to the excess
capacity of the process MSA's in removing the targeted
species.
–
After removing the excess capacity of MSA's, one can
construct a revised TEL/cascade diagram in which
the flowrates and/or outlet compositions of the process
MSA's have been adjusted.
Algebraic Mass Integration 7:7
•
Comments (Continued)
–
On the revised cascade diagram the location of
residual mass = zero corresponds to the massexchange pinch composition.
–
Since an overall material balance for the network must
be realized, the residual mass leaving the lowest
composition interval of the revised cascade
diagram must be removed by external MSA's.
Example No. 5 1:6
•
Dephenolization of Aqueous Wastes
–
–
Same problem as solved in Example No. 2 (Lecture 5)
Composition Interval Diagram (CID)
Rich Streams
Interval
R1
1
2
3
4
R2
y
Process MSA’s
x1
x2
0.0500
0.0240
0.0317
0.0474
0.0227
0.0300
0.0320
0.0150
0.0199
0.0300
0.0140
0.0186
0.0168
0.0074
0.0100
0.0120
0.0050
0.0068
0.0100
0.0040
0.0060
0.0020
5
6
7
S1
0.0055
0.0029
S2
Example No. 5 2:6
•
Sample Calculations
–
–
Composition scales
y  0.005

0.005
x1 
 0.001  0.024
2
x1  0.015

y  2  (0.015  0.001)  0.032
Interval loads (rich in first interval, lean in second)
W1,1R  2  (0.0500  0.0474)  0.0052
S
W2,2
 3  (0.0300  0.0199)  0.0303
Example No. 5 3:6
•
Table of Exchangeable Loads (TEL)
Load of Waste Streams
kg phenol/s
Interval
Load of Process MSA’s
kg phenol/s
R1
R2
R1 + R2
S1
S2
S1 + S2
1
0.0052
-
0.0052
-
-
-
2
0.0308
-
0.0308
-
0.0303
0.0303
3
0.0040
-
0.0040
0.0050
0.0039
0.0089
4
0.0264
0.0132
0.0396
0.0330
0.0258
0.0588
5
0.0096
0.0048
0.0144
0.0120
-
0.0120
6
0.0040
0.0020
0.0060
-
-
-
7
-
0.0040
0.0040
-
-
-
Example No. 5 4:6
•
Cascade Diagram
Load of Waste Streams
kg phenol/s
Interval
Load of Process MSA’s
kg phenol/s
0.0000
R1
R2
R1 + R2
S1
S2
S1 + S2
1
0.0052
-
0.0052
-
-
-
2
0.0308
-
0.0308
-
0.0303
0.0303
3
0.0040
-
0.0040
0.0050
0.0039
0.0089
4
0.0264
0.0132
0.0396
0.0330
0.0258
0.0588
5
0.0096
0.0048
0.0144
0.0120
-
0.0120
6
0.0040
0.0020
0.0060
-
-
-
7
-
0.0040
0.0040
-
-
-
0.0052
0.0000
1
0.0052
0.0308
0.0303
2
0.0057
0.0040
33
0.0089
0.0008
0.0588
0.0396
4
0.0144
- 0.0184 (EXCESS LOAD OF
PROCESS MSA,S)
5
0.0120
- 0.0160
Elimination of Excess Capacity
Lower flowrate of S2 to 2.08 kg/s as
calculated in Example No.2
0.0060
0.0000
6
- 0.0100
0.0040
0.0000
7
- 0.0060
Example No. 5 5:6
•
Revised Table of Exchangeable Loads (TEL)
Load of Rich Streams
kg phenol/s
Interval
Load of Process MSA’s
kg phenol/s
S1
S2
S1 + S2
0.0052
-
-
-
0.0303
-
0.0210
0.0210
R1
R2
R1 + R2
1
0.0052
-
2
0.0308
-
3
0.0040
-
0.0040
0.0050
0.0027
0.0077
4
0.0264
0.0132
0.0396
0.0330
0.0179
0.0509
5
0.0096
0.0048
0.0144
0.0120
-
0.0120
6
0.0040
0.0020
0.0060
-
-
-
7
-
0.0040
0.0040
-
-
-
Example No. 5 6:6
•
Revised Cascade Diagram
Load of Rich Streams
kg phenol/s
Interval
Load of Process MSA’s
kg phenol/s
0.0000
S1
S2
S1 + S2
0.0052
-
-
-
0.0303
-
R1
R2
R1 + R2
1
0.0052
-
2
0.0308
-
0.0052
0.0052
0.0308
0.0210
0.0000
1
0.0210
0.0210
2
0.0150
3
0.0040
-
0.0040
0.0050
0.0027
0.0077
4
0.0264
0.0132
0.0396
0.0330
0.0179
0.0509
5
0.0096
0.0048
0.0144
0.0120
-
0.0120
6
0.0040
0.0020
0.0060
-
-
-
7
-
0.0040
0.0040
-
-
-
0.0040
0.0113
0.0396
5
0.0120
0.0024
0.0060
0.0000
6
Pinch point is between intervals 4 and 5.
Load to be removed by externals:
0.0124 kg/s
0.0588
4
0.0000 (PINCH POINT)
0.0144
Comments
0.0077
3
0.0084
0.0040
0.0000
7
0.0124
Other Business
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Q&A Session with Consultant – February 21
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Cancelled due to conflicts
Next Lecture – February 26
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Advanced Column Design and Reactive Distillation
Reboiler Selection and Design
Design of Overhead Condensers and Air Cooled HX