Algebraic Approach to Mass Integration: Composition Intervals & Cascade Diagrams, Slides of Process Engineering

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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 rangingcompositions or many streams

Algebraic Method

No accuracy problems

Can handle many streams easily

Can

be

programmed

and

formulated

as

optimization

problems

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:

R

i k

i

k

k

W

G

y

y

S

C

j k

j

j k

j k

W

L

x

x

Table of Exchangeable Loads (TEL) (Cont’d)

Collective load of the rich streams passing through thek’th interval is:

Collective capacity of the lean streams passing throughthe

k’th interval is:

Algebraic Mass Integration 3:

passes through interval

R

R

k

i k

i

k

W

W

passes through interval

S

S

k

j k

j

k

W

W

Mass Exchange Cascade Diagram (Cont’d)

Algebraic Mass Integration 5:

k

W

k

R

W

k

S



k-



k

Mass Recovered

from Rich

Streams

Mass Transferred

to MSA’s

Residual Mass from

Preceeding Interval

Residual Mass to

Subsequent Interval

Algebraic Mass Integration 6:

Comments

is zero (no rich streams exist above the first interval)

Feasibility is insured when all the

k

's are nonnegative

The

most

negative

k

corresponds

to

the

excess

capacity of the process MSA's in removing the targetedspecies.

After removing the excess capacity of MSA's, one canconstruct a

revised TEL/cascade diagram

in which

the flowrates and/or outlet compositions of the processMSA's have been adjusted.

Example No. 5 1:

Dephenolization of Aqueous Wastes

Same problem as solved in Example No. 2 (Lecture 5)

Composition Interval Diagram (CID)

Interval

Rich Streams

Process MSA’s

R

1

R

2

S

2

S

1

1 2 3 4 5 6 7

0.05000.04740.

0.0120 0.01000.

y

0.02400.02270.

0.0050 0.00400.

0.0068 0.00550.

x

1

x

2

Example No. 5 2:

Sample Calculations

Composition scales

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

2

2 (0.

0.001)

y

x

x

y























2 (0.

0.0474)

3 (0.

0.0199)

R

S

W W

















Example No. 5 4:

Cascade Diagram

0.

0.

0.

0.

0.

0.

0.

0.

0.

- 0.0184 (EXCESS LOAD OF

PROCESS MSA,S)

0.

0.

- 0.

0.0000 0.

0.

0.

**- 0.

• 0.**

1

2 3 4 5 6 7

0.0052 0.

0.

2 3

Interval

Load of Waste Streams

kg phenol/s

Load of Process MSA’s

kg phenol/s

R

1

R

2

R

1

+ R

2

S

2

S

1

S

1

+ S

2

1 2 3 4 5 6 7

Elimination of Excess Capacity

Lower flowrate of S

2

to 2.08 kg/s as

calculated in Example No.

Example No. 5 5:

Revised Table of Exchangeable Loads (TEL)

Interval

Load of Rich Streams

kg phenol/s

Load of Process MSA’s

kg phenol/s

R

1

R

2

R

1

+ R

2

S

2

S

1

S

1

+ S

2

1 2 3 4 5 6 7