CHEN 4470 – Process Design Practice

Dr. Mario Richard EdenDepartment of Chemical Engineering

Auburn University

Lecture No. 11 – Algebraic Mass Integration Techniques

February 19, 2013

Mass Integration

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

RichStreams

Process MSA’sx y b m1 1 1 1

( ) / x y b m2 2 2 2 ( ) / x y b mNsp Nsp Nsp Nsp

( ) /

1

2

3

4

5

6

7

8

9

10

.

.

.Nint

y1s R1

y1t

y2s

yNRs

y2t

yNRt

R2

RNR

x1t

x1s

S1

S2

x2t

x2s

xNspt

xNsps

SNsp

Number of intervals

Nint ≤ 2(NR+NSP) – 1

Equality is when no arrow heads or tails coincide!

• Table of Exchangeable Loads (TEL)– Exchangeable load of the i‘’th rich stream

passing through the k’th interval is:

– Exchangeable capacity of the j’th process MSA which passes through the k’th interval is calculated as:

Algebraic Mass Integration 2:7

, 1( )Ri k i k kW G y y

, , 1 ,( )S Cj k j j k j kW L x x

• Table of Exchangeable Loads (TEL) (Cont’d)– Collective load of the rich streams passing

through the k’th interval is:

– Collective capacity of the lean streams passing through the k’th interval is:

Algebraic Mass Integration 3:7

, passes through interval

R Rk i k

i k

W W

, passes through interval

S Sk j k

j k

W W

• 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

Algebraic Mass Integration 4:7

1R Sk k k kW W

• Mass Exchange Cascade Diagram (Cont’d)

Algebraic Mass Integration 5:7

kWkR Wk

S

k-1

k

Mass Recoveredfrom Rich

Streams

Mass Transferredto MSA’s

Residual Mass fromPreceeding Interval

Residual Mass toSubsequent Interval

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 mass-exchange 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)

Example No. 5 2:6

• Sample Calculations– Composition scales

– Interval loads (rich in first interval, lean in second)

1

1

0.0050.005 0.001 0.024

2

0.015 2 (0.015 0.001) 0.032

y x

x y

1,1

2,2

2 (0.0500 0.0474) 0.0052

3 (0.0300 0.0199) 0.0303

R

S

W

W

Example No. 5 3:6

• Table of Exchangeable Loads (TEL)

IntervalLoad of Waste Streams

kg phenol/sLoad of Process MSA’s

kg phenol/s

R1R2 R1 + R2

S2S1 S1 + S2

1

2

3

4

5

6

7

0.0052 - 0.0052 - - -

0.0308 - 0.0308 - 0.0303 0.0303

0.0040 - 0.0040 0.0050 0.0039 0.0089

0.0264 0.0132 0.0396 0.0330 0.0258 0.0588

0.0096 0.0048 0.0144 0.0120 - 0.0120

0.0040 0.0020 0.0060 - - -

- 0.0040 0.0040 - - -

Example No. 5 4:6

• Cascade Diagram

0.0000

0.00000.0052

0.0308 0.0303

0.0040 0.0089

0.0396 0.0588

- 0.0184 (EXCESS LOAD OF PROCESS MSA,S)

0.0144 0.0120

- 0.0160

0.0000

0.00000.0040

0.0060

- 0.0060

- 0.0100

1

2

3

4

5

6

7

0.0052

0.0057

0.0008

2

3

IntervalLoad of Waste Streams

kg phenol/sLoad of Process MSA’s

kg phenol/s

R1R2 R1 + R2

S2S1 S1 + S2

1

2

3

4

5

6

7

0.0052 - 0.0052 - - -

0.0308 - 0.0308 - 0.0303 0.0303

0.0040 - 0.0040 0.0050 0.0039 0.0089

0.0264 0.0132 0.0396 0.0330 0.0258 0.0588

0.0096 0.0048 0.0144 0.0120 - 0.0120

0.0040 0.0020 0.0060 - - -

- 0.0040 0.0040 - - -

Elimination of Excess Capacity

Lower flowrate of S2 to 2.08 kg/s as calculated in Example No.2

Example No. 5 5:6

• Revised Table of Exchangeable Loads (TEL)

IntervalLoad of Rich Streams

kg phenol/sLoad of Process MSA’s

kg phenol/s

R1R2 R1 + R2

S2S1 S1 + S2

1

2

3

4

5

6

7

0.0052 - 0.0052 - - -

0.0308 - 0.0303 - 0.0210 0.0210

0.0040 - 0.0040 0.0050 0.0027 0.0077

0.0264 0.0132 0.0396 0.0330 0.0179 0.0509

0.0096 0.0048 0.0144 0.0120 - 0.0120

0.0040 0.0020 0.0060 - - -

- 0.0040 0.0040 - - -

Example No. 5 6:6

• Revised Cascade Diagram

IntervalLoad of Rich Streams

kg phenol/sLoad of Process MSA’s

kg phenol/s

R1R2 R1 + R2

S2S1 S1 + S2

1

2

3

4

5

6

7

0.0052 - 0.0052 - - -

0.0308 - 0.0303 - 0.0210 0.0210

0.0040 - 0.0040 0.0050 0.0027 0.0077

0.0264 0.0132 0.0396 0.0330 0.0179 0.0509

0.0096 0.0048 0.0144 0.0120 - 0.0120

0.0040 0.0020 0.0060 - - -

- 0.0040 0.0040 - - -

1

2

3

4

5

6

7

0.0000

0.00000.0052

0.0052

0.0308 0.0210

0.0150

0.0040

0.0113

0.0077

0.0396 0.0588

0.0000 (PINCH POINT)

0.0144 0.0120

0.0024

0.0000

0.00000.0040

0.0060

0.0124

0.0084

Comments

Pinch point is between intervals 4 and 5.

Load to be removed by externals:0.0124 kg/s

• Q&A Session with Consultant – February 21– Cancelled due to conflicts

• Next Lecture – February 26– Advanced Column Design and Reactive

Distillation– Reboiler Selection and Design– Design of Overhead Condensers and Air Cooled

HX

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