relaxation technique.pdf

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ENERGY RELAXATIONNETWORKS

By Siti Shawalliah Idris

CPE 633 PROCESS ENGINEERING II



Energy relaxation is a name coined for theprocedure of allowing the energy usage toincrease in exchange for at least one of thefollowing effects :

a reduction in area

A reduction in the heat exchangers

A reduction in complexity (typically less splitting)

Energy Relaxation



Energy Relaxation

This procedure has as goal to increase heating utility and inexchange reduce the number of units.



Energy Relaxation

LOOP: A loop is a circuit through the network that

starts at one exchanger and ends in the same

exchanger

PATH: A path is a circuit through the network that starts at a heater and ends at a cooler



175 0C CP=0.010

C

280

CP=0.040 65 0C

155 0C 20 0C CP=0.020

1 H

1840

360

500 0 40 C

C2 CP=0.015 1120C

520

560

(*) Heat exchanger loads arein kW

C

H2

125 0C H1

Energy Relaxation

Illustration of a loop



125 0C 175 0C FCp=0.010 C

280

FCp=0.040

65 0C

0 20 C 155 0C FCp=0.020 H

36

0

1

1840 500 FCp=0.015

0 40 C

112 0C 560 520

(*) Heat exchanger loads arein kW

C2

C

H2

H1

Energy Relaxation

Illustration of a path



125 0C 175 0C

C

280

65 0C

155 0C 20 0C

H

1840

500 360

0 40

C

-X 520 +X 560

If one wants to eliminate one exchanger: X=500. Note that Xcould have beennegative, but we chose the smallest possible inabsolute value.

C2

+X

C1

H2

-X

112 0C

H1

Energy Relaxation

Procedure: Find a loop and move around the heat from heatexchanger to exchanger until one exchanger is eliminated



0 45 C 175 0C C

65 0C 280 0 65 C

65 0C

155 0C 20 0C 1 H

2340 360 0 112 C 0 40 C

60 1020

108 0C

This exchangeris in

violation of the

minimum

a roach

C2

C

H2

H1

Energy Relaxation

Result: Notice that there is an infeasible match!



0 175 C C

65 0C 280

0 65 C

65 0C

0 1550C

20 C H

2340 360 0 C 0 40 C

60 1020

1080C

Thevalue

of X needed to restore feasibilityis X=795

-X +X

C2

-X

112

C1

+X

H2

+X

H1

ENERGY RELAXATION

Use a path to move heat around to restore feasibility45 C



•

0 0 175 C 45 C C

65 0C 1075

65 C 0

65 0C

0 155 0C 20 C H

1545

112 C 1155

0 0 40 C

855 225

55 0C

C2

C1

H2

H1

Final Network



Thank you for your attention



Energy Relaxation Technique

Working Example



Energy relaxation technique

Remove the smallest heat recovery unit from the network by exploiting the degree offreedom in a loop.

Recalculate the network temperatures and identify any violationsof the Tmin = 10oCconstraint.

Restore the original Tmin = 10oC throughout the network by exploiting a utility path.



Maximum Energy Recovery Design

Identify the degrees of freedom for network optimisation

A

A

1

2

4

6

42oC

90o

C

160 oC

B

B

C

C

C

100o

C

140 oC

150 oCH

D

D

HP

H

3

100 oC

80 oC

80 oC

525o

C79 oC

25 oC

75 oC 40 oC

C

450

0

2100

160

00705

0

192

5

166

70

433

0

242

5

Tmin =o



A

A

1

2

4

6

42oC

90 oC160 oC

B

B

C

C

C

100 oC

140 oC

150o

CH

D

D

H

3

100 oC

80 oC

80o

C

525 oC79 oC

25 oC

75 oC 40 oC

C

450

0

210

0

160

00705

0

192

5

16670

433

0

242

5



Solution

A

A

1

2

4

6

42oC

90o

C

160 oC

B

B

C

C

C

100o

C

140 oC

150 oCH

D

D

HP

H

3

100 oC

80 oC

80 oC

525o

C

79 oC

25 oC

75 oC 40 oC

C

450

0

2100

160

00705

0

192

5

166

70

433

0

242

5

Loop



1 A

A

1

2

4

6

42oC

90o

C

160 oC

B

B

C

C

C

100o

C

140 oC

150 oCH

D

D

H

3

100 oC

80 oC

80 oC

525o

C

79 oC

25 oC

75 oC 40 oC

C

450

0

210

0

160

00705

0

192

5

166

70

433

0

242

5

Loop



A

A

1

2

4

6

42oC

90o

C

160 oC

B

B

C

C

C

100o

C

140 oC

150 oCH

D

D

H

3

100 oC

80 oC

80 oC

525o

C

79 oC

25 oC

75 oC 40 oC

C

450

0

210

0

160

00705

0

192

5

166

70

433

0

242

5

Utility path 1

Utility path 2



A

A

1

2

4

6

42oC

90o

C

160 oC

B

B

C

C

C

100o

C

140 oC

150 oCH

D

D

HP

H

3

100 oC

80 oC

80 oC525

o

C

79 oC

25 oC

75 oC 40 oC

C

4500

+X

2100

+X

160

007050

-X

1925 -

X

166

70

433

0

242

5

Loop

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