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Sequential Framework For HENS
1. Revisiting the Sequential Framework for Near-Optimal Heat Exchanger Network Synthesis Rahul Anantharaman* , Truls Gundersen Dept of Energy & Process Engineering, Norwegian University of Science & Technology Email: rahul.anantharaman@ntnu.no
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3. Illustrating Example References: Example 3 in Colberg, R. D. and Morari M., Area and Capital Cost Targets for Heat Exchanger Network Synthesis with Constrained Matches and Unequal Heat Transfer Coefficients, Computers chem. Engng. Vol. 14, No. 1, 1990 Example 4 in Yee, T. F. and Grossmann I. E., Simulataneous Optimization Models for Heat Integration II. Heat Exchanger Network Synthesis, Computers chem. Engng. Vol. 14, No. 10, 1990 Exchanger cost ($) = 8,600 + 670A 0.83 (A is in m 2 ) 3.50 - - 308 293 CW 3.50 - - 650 650 ST 3.20 427.57 1.690 566 313 C4 0.33 457.62 7.627 386 326 C3 0.25 119.87 0.641 576 389 C2 0.65 832.76 7.179 613 497 C1 3.20 1078.18 6.161 353 528 H3 0.05 296.03 2.931 519 620 H2 1.25 392.08 9.802 586 626 H1 h (kW/m 2 K) ΔH (kW) C p (kW/K) T out (K) T in (K) Stream
4. Our Engine – A Sequential Framework Vertical MILP LP NLP Adjust Units Adjust HRAT MILP U HLD Final Network Q H Q C (EMAT=0) New HLD 1 4 3 EMAT Adjust EMAT 2 Pre- optim. HRAT
9. Example – Initial Values Vertical MILP LP NLP Adjust Units MILP U HLD Final Network Q H Q C (EMAT=0) New HLD 1 EMAT Adjust EMAT HRAT 2 3 HRAT fixed at 20 K Q H = 244.1 kW Q C = 172.6 kW Absolute Minimum Number of Units = 8
10. Example – Looping to Solution Vertical MILP LP NLP Adjust Units MILP U HLD Final Network Q H Q C (EMAT=0) New HLD 1 EMAT Adjust EMAT HRAT 2 3 199,914 A 2.5 8 1 INVESTMENT COST ($) HLD# EMAT (K) U Soln. No
11. Example – Looping to Solution 199,914 A 2.5 8 1 INVESTMENT COST ($) HLD# EMAT (K) U S. No
12. Example – Looping to Solution Vertical MILP LP NLP Adjust Units MILP U HLD Final Network Q H Q C (EMAT=0) New HLD 1 EMAT Adjust EMAT HRAT 2 3 199,914 A 2.5 8 1 - No Soln. 2.5 8 2 INVESTMENT COST ($) HLD# EMAT (K) U Soln. No
13. Example – Looping to Solution Vertical MILP LP NLP Adjust Units MILP U HLD Final Network Q H Q C (EMAT=0) New HLD 1 EMAT Adjust EMAT HRAT 2 3 - No Soln. 2.5 8 2 199,914 A 2.5 8 1 199,914 A 5.0 8 3 INVESTMENT COST ($) HLD# EMAT (K) U Soln. No
14. Example – Looping to Solution 199,914 A 5.0 8 3 INVESTMENT COST ($) HLD# EMAT (K) U S. No
15. Example – Looping to Solution Vertical MILP LP NLP Adjust Units MILP U HLD Final Network Q H Q C (EMAT=0) New HLD 1 EMAT Adjust EMAT HRAT 2 3 199,914 A 5.0 8 3 - No Soln. 2.5 8 2 199,914 A 2.5 8 1 - No Soln. 5.0 8 4 INVESTMENT COST ($) HLD# EMAT (K) U Soln. No
16. Example – Looping to Solution Vertical MILP LP NLP Adjust Units MILP U HLD Final Network Q H Q C (EMAT=0) New HLD 1 EMAT Adjust EMAT HRAT 2 3 - No Soln. 5.0 8 4 199,914 A 5.0 8 3 - No Soln. 2.5 8 2 199,914 A 2.5 8 1 - No Soln. 7.5 8 5 INVESTMENT COST ($) HLD# EMAT (K) U Soln. No
17. Example – Looping to Solution Vertical MILP LP NLP Adjust Units MILP U HLD Final Network Q H Q C (EMAT=0) New HLD 1 EMAT Adjust EMAT HRAT 2 3 : : : : : 147,861 A 2.5 9 6 199,914 A 2.5 8 1 INVESTMENT COST ($) HLD# EMAT (K) U Soln. No
18. Example – Looping to Solution 147,861 A 2.5 9 6 INVESTMENT COST ($) HLD# EMAT (K) U S. No
19. Example – Looping to Solution Vertical MILP LP NLP Adjust Units MILP U HLD Final Network Q H Q C (EMAT=0) New HLD 1 EMAT Adjust EMAT HRAT 2 3 : : : : : 147,861 A 2.5 9 6 199,914 A 2.5 8 1 151,477 B 2.5 9 7 INVESTMENT COST ($) HLD# EMAT (K) U Soln. No
20. Example – Looping to Solution 151,477 B 2.5 9 7 INVESTMENT COST ($) HLD# EMAT (K) U S. No
21. Example – Looping to Solution Vertical MILP LP NLP Adjust Units MILP U HLD Final Network Q H Q C (EMAT=0) New HLD 1 EMAT Adjust EMAT HRAT 2 3 147,867 A 5.0 9 8 151,477 B 2.5 9 7 : : : : : 147,861 A 2.5 9 6 199,914 A 2.5 8 1 INVESTMENT COST ($) HLD# EMAT (K) U Soln. No
22. Example – Looping to Solution 147,867 A 5.0 9 8 INVESTMENT COST ($) HLD# EMAT (K) U S. No
23. Example – Looping to Solution Vertical MILP LP NLP Adjust Units MILP U HLD Final Network Q H Q C (EMAT=0) New HLD 1 EMAT Adjust EMAT HRAT 2 3 147,867 A 5.0 9 8 151,477 B 2.5 9 7 : : : : : 147,861 A 2.5 9 6 199,914 A 2.5 8 1 151,508 B 5.0 9 9 INVESTMENT COST ($) HLD# EMAT (K) U Soln. No
24. Example – Looping to Solution 151,508 B 5.0 9 9 INVESTMENT COST ($) HLD# EMAT (K) U S. No
25. Example – Looping to Solution Vertical MILP LP NLP Adjust Units MILP U HLD Final Network Q H Q C (EMAT=0) New HLD 1 EMAT Adjust EMAT HRAT 2 3 151,477 B 2.5 9 7 151,508 B 5.0 9 9 147,867 A 5.0 9 8 : : : : : 147,861 A 2.5 9 6 199,914 A 2.5 8 1 149,025 A 7.5 9 10 INVESTMENT COST ($) HLD# EMAT (K) U Soln. No
26. Example – Looping to Solution 149,025 A 7.5 9 10 INVESTMENT COST ($) HLD# EMAT (K) U S. No
27. Example – Looping to Solution Vertical MILP LP NLP Adjust Units MILP U HLD Final Network Q H Q C (EMAT=0) New HLD 1 EMAT Adjust EMAT HRAT 2 3 149,025 A 7.5 9 10 151,477 B 2.5 9 7 151,508 B 5.0 9 9 147,867 A 5.0 9 8 : : : : : 147,861 A 2.5 9 6 199,914 A 2.5 8 1 149,224 B 7.5 9 11 INVESTMENT COST ($) HLD# EMAT (K) U Soln. No
28. Example – Looping to Solution 149,224 B 7.5 9 11 INVESTMENT COST ($) HLD# EMAT (K) U S. No
29. Example – Looping to Solution Vertical MILP LP NLP Adjust Units MILP U HLD Final Network Q H Q C (EMAT=0) New HLD 1 EMAT Adjust EMAT HRAT 2 3 149,224 B 7.5 9 11 151,508 B 5.0 9 9 151,477 B 2.5 9 7 149,025 A 7.5 9 10 164,381 A 2.5 10 12 147,867 A 5.0 9 8 : : : : : 147,861 A 2.5 9 6 199,914 A 2.5 8 1 INVESTMENT COST ($) HLD# EMAT (K) U Soln. No
30. Example – Looping to Solution 164,381 A 2.5 10 12 INVESTMENT COST ($) HLD# EMAT (K) U S. No
31. Example – Looping to Solution Vertical MILP LP NLP Adjust Units MILP U HLD Final Network Q H Q C (EMAT=0) New HLD 1 EMAT Adjust EMAT HRAT 2 3 149,224 B 7.5 9 11 151,508 B 5.0 9 9 151,477 B 2.5 9 7 167,111 A 5.0 10 13 149,025 A 7.5 9 10 164,381 A 2.5 10 12 147,867 A 5.0 9 8 : : : : : 147,861 A 2.5 9 6 199,914 A 2.5 8 1 INVESTMENT COST ($) HLD# EMAT (K) U Soln. No
32. Example – Looping to Solution 167,111 A 5.0 10 13 INVESTMENT COST ($) HLD# EMAT (K) U S. No
33. Example – Looping to Solution Vertical MILP LP NLP Adjust Units MILP U HLD Final Network Q H Q C (EMAT=0) New HLD 1 EMAT Adjust EMAT HRAT 2 3 149,224 B 7.5 9 11 151,508 B 5.0 9 9 151,477 B 2.5 9 7 167,111 A 5.0 10 13 149,025 A 7.5 9 10 164,381 A 2.5 10 12 147,867 A 5.0 9 8 : : : : : 147,861 A 2.5 9 6 199,914 A 2.5 8 1 164,764 A 7.5 10 14 INVESTMENT COST ($) HLD# EMAT (K) U Soln. No
34. Example – Looping to Solution 164,764 A 7.5 10 14 INVESTMENT COST ($) HLD# EMAT (K) U S. No
35. Example - Comparisons MILP optimized w.r.t ”area” NLP optimized w.r.t cost $147,861 189.7 9 Our work Optimized w.r.t. cost $150,998 217.8 9 Yee and Grossmann (1990) Synthesized network by evolution $177,385 188.9 12 Colberg & Morari (1990) Optimized w.r.t area Spaghetti design - 173.6 22 Colberg & Morari (1990) Remarks Cost Area (m 2 ) No of Units
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