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Sequential Framework For HENS

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Sequential Framework For HENS

  1. 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
  2. 2. Our Ultimate Goal <ul><li>Solve Industrial Size Problems </li></ul><ul><ul><li>Defined to involve 30 or more streams </li></ul></ul><ul><li>Include Industrial Realism </li></ul><ul><ul><li>Multiple Utilities </li></ul></ul><ul><ul><li>Constraints in Heat Utilization (Forbidden matches) </li></ul></ul><ul><ul><li>Include different heat exchanger models rather than pure countercurrent </li></ul></ul><ul><ul><li>Relevant and Multiple Cost laws accounting for Exchanger Types, Pressure Ratings and Materials of Construction </li></ul></ul><ul><li>Avoid Heuristics and Simplifications </li></ul><ul><ul><li>No global or fixed Δ Tmin </li></ul></ul><ul><ul><li>No Pinch Decomposition </li></ul></ul><ul><li>Develop Automatic Design Tool </li></ul><ul><ul><li>Allow Significant User Interaction </li></ul></ul><ul><ul><li>Identify ”Global Optimum” </li></ul></ul>
  3. 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. 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
  5. 5. Key Elements of the Framework <ul><li>Initial Values </li></ul><ul><ul><li>Level of Heat Recovery  Pre-optimization </li></ul></ul><ul><ul><li>Absolute minimum number of Units </li></ul></ul><ul><ul><ul><li>MILP Transhipment Model </li></ul></ul></ul><ul><ul><ul><li>HRAT from Pre-optimization, EMAT = 0 </li></ul></ul></ul><ul><li>Core Engine </li></ul><ul><ul><li>Match Selection </li></ul></ul><ul><ul><ul><li>” Vertical” MILP Transportation Model </li></ul></ul></ul><ul><ul><li>Network Generation and Optimization </li></ul></ul><ul><ul><ul><li>Non-convex NLP Model </li></ul></ul></ul><ul><ul><ul><li>” All-inclusive” Stream Superstructure </li></ul></ul></ul>
  6. 6. History of the ”Vertical” Model <ul><li>Original Transhipment Model (Gundersen/Grossmann, 1988) </li></ul><ul><li>Improved Model (Gundersen/Grossmann, 1990) </li></ul><ul><li>Extended Vertical Model (Gundersen et al., 1996) </li></ul><ul><li>Transportation Model (Gundersen et al., 1997) </li></ul>
  7. 7. Vertical Transportation Model Subject to H 1 i H H C 1 j C C m-1 m m+1 n-1 n n+1
  8. 8. EMAT as an Optimizing Variable <ul><li>Choosing EMAT is not straightforward </li></ul><ul><ul><li>EMAT set too low (close to zero) </li></ul></ul><ul><ul><ul><li>non-vertical heat transfer (m=n) will have very small Δ T LM,mn and very large penalties in the objective function </li></ul></ul></ul><ul><ul><li>EMAT set too high (close to HRAT) </li></ul></ul><ul><ul><ul><li>Potentially good HLDs will be excluded from the feasible set of solutions </li></ul></ul></ul><ul><li>Δ T LM,mn is a term included in the objective function and depends explicitly on EMAT </li></ul><ul><ul><li>EMAT is an optimizing variable in this formulation </li></ul></ul><ul><ul><ul><li>Sequential Framework is modified to include a loop for EMAT </li></ul></ul></ul>EMAT comes into play only when there is an extra degree of freedom in the system
  9. 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. 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. 11. Example – Looping to Solution 199,914 A 2.5 8 1 INVESTMENT COST ($) HLD# EMAT (K) U S. No
  12. 12. Example – Looping to Solution Vertical MILP LP NLP Adjust Units MILP U HLD Final Network Q H Q C (EMAT=0) New HLD 1 EMAT Adjust EMAT HRAT 2 3 199,914 A 2.5 8 1 - No Soln. 2.5 8 2 INVESTMENT COST ($) HLD# EMAT (K) U Soln. No
  13. 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 ($) HLD# EMAT (K) U Soln. No
  14. 14. Example – Looping to Solution 199,914 A 5.0 8 3 INVESTMENT COST ($) HLD# EMAT (K) U S. No
  15. 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 ($) HLD# EMAT (K) U Soln. No
  16. 16. Example – Looping to Solution Vertical MILP LP NLP Adjust Units MILP U HLD Final Network Q H Q C (EMAT=0) New HLD 1 EMAT Adjust EMAT HRAT 2 3 - No Soln. 5.0 8 4 199,914 A 5.0 8 3 - No Soln. 2.5 8 2 199,914 A 2.5 8 1 - No Soln. 7.5 8 5 INVESTMENT COST ($) HLD# EMAT (K) U Soln. No
  17. 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 ($) HLD# EMAT (K) U Soln. No
  18. 18. Example – Looping to Solution 147,861 A 2.5 9 6 INVESTMENT COST ($) HLD# EMAT (K) U S. No
  19. 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 ($) HLD# EMAT (K) U Soln. No
  20. 20. Example – Looping to Solution 151,477 B 2.5 9 7 INVESTMENT COST ($) HLD# EMAT (K) U S. No
  21. 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 ($) HLD# EMAT (K) U Soln. No
  22. 22. Example – Looping to Solution 147,867 A 5.0 9 8 INVESTMENT COST ($) HLD# EMAT (K) U S. No
  23. 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 ($) HLD# EMAT (K) U Soln. No
  24. 24. Example – Looping to Solution 151,508 B 5.0 9 9 INVESTMENT COST ($) HLD# EMAT (K) U S. No
  25. 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 ($) HLD# EMAT (K) U Soln. No
  26. 26. Example – Looping to Solution 149,025 A 7.5 9 10 INVESTMENT COST ($) HLD# EMAT (K) U S. No
  27. 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 ($) HLD# EMAT (K) U Soln. No
  28. 28. Example – Looping to Solution 149,224 B 7.5 9 11 INVESTMENT COST ($) HLD# EMAT (K) U S. No
  29. 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 ($) HLD# EMAT (K) U Soln. No
  30. 30. Example – Looping to Solution 164,381 A 2.5 10 12 INVESTMENT COST ($) HLD# EMAT (K) U S. No
  31. 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 ($) HLD# EMAT (K) U Soln. No
  32. 32. Example – Looping to Solution 167,111 A 5.0 10 13 INVESTMENT COST ($) HLD# EMAT (K) U S. No
  33. 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 ($) HLD# EMAT (K) U Soln. No
  34. 34. Example – Looping to Solution 164,764 A 7.5 10 14 INVESTMENT COST ($) HLD# EMAT (K) U S. No
  35. 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
  36. 36. SeqHENS <ul><li>Excel based user interface for automating the procedure </li></ul><ul><li>User interaction at each step (or loop) </li></ul><ul><li>Initial values for the NLP formulation calculated using heuristics are displayed and can be modified by the user </li></ul><ul><ul><li>Useful for users with good understanding of the problem at hand </li></ul></ul><ul><li>All solution values are tabulated and can be sorted based on utility cost, investment cost or total cost </li></ul>
  37. 37. Concluding Remarks <ul><li>Sequential Framework has many advantages </li></ul><ul><ul><li>Automates the design process </li></ul></ul><ul><ul><li>Allows significant User interaction </li></ul></ul><ul><ul><li>Numerically much easier than MINLPs </li></ul></ul><ul><li>Limiting elements </li></ul><ul><ul><li>NLP model for Network Generation and Optimization </li></ul></ul><ul><ul><ul><li>Enhanced convex estimators are required to ensure global optimum </li></ul></ul></ul><ul><ul><li>MILP Transhipment model for minimum number of units </li></ul></ul><ul><ul><ul><li>Significant improvements required to avoid combinatorial explosion </li></ul></ul></ul><ul><ul><ul><ul><li>One possibility is to use approximation methods to ”fine-tune” the model for exact solutions </li></ul></ul></ul></ul><ul><ul><li>MILP Transportation Model for promising HLDs </li></ul></ul><ul><ul><ul><li>Similar combinatorial problems as the Transhipment model </li></ul></ul></ul>
  38. 38. THANK YOU FOR YOUR ATTENTION

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