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Part 6

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  1. Part 6 Synthesis of Heat Exchanger Networks

  2. 6.1 Sequential Synthesis Minimum Utility Cost

  3. Example 1 Steam: 500 C Cooling water: 20 – 30 C Minimum recovery approach temperature (HRAT): 20 C

  4. Heat Balances around Temperature Intervals

  5. Transshipment Model

  6. Remarks • LP for minimum utility consumption leads to the same results as the Problem Table in Pinch method. • The transshipment model can be generalized to consider multiple utilities to minimize total utility cost. • This model can be expanded so as to handle constraints on matches. • This model can also be expanded so as to predict the matches for minimizing the number of units. • We can embed the equations of the transshipment model within an optimization model for synthesizing a process system where the flows of the process streams are unknown.

  7. Index Sets

  8. Condensed Transshipment Model

  9. Example 2 HP Steam: 500 K, $80/kW-yr LP Steam: 380 K, $50/kW-yr Cooling Water: 300 K, $20/kW-yr HRAT: 10K

  10. Sequential Synthesis Minimum Utility Cost with Constrained Matches

  11. Basic Ideas

  12. Heat Exchange Options • Hot stream i and cold stream j are present in interval k (see figure in the previous page). • Cold stream j is present in interval k, but hot stream i is only present at higher temperature interval (see figure in the next page).

  13. Index Sets

  14. Expanded Transshipment Model

  15. Match Constraints

  16. Example 1 Steam: 500 C, $80/kW-yr Cooling water: 20 – 30 C, $20/kW-yr Minimum recovery approach temperature (HRAT): 20 C The match between H1 and C1 is forbidden.

  17. Condensed Transshipment Model The annual utility cost: $9,300,000.

  18. Expanded Transshipment Model Annual Utility Cost: $15,300,000 Heating Utility Load: 120 MW Cooling Utility Load: 285 MW

  19. Sequential Synthesis Prediction of matches for minimizing the unit number

  20. Objective Function

  21. Heat Balances The constraints in the expanded transshipment model can be modified for the present model: • The heat contents of the utility streams are given. • The common index i can be used for hot process and utility streams; The common index j can be used for cold process and utility streams.

  22. Heat Balances

  23. Logical Constraints

  24. Solution

  25. Example 1 Steam: 500 C Cooling water: 20 – 30 C Minimum recovery approach temperature (HRAT): 20 C

  26. Condensed Transshipment Model

  27. MILP (i)

  28. MILP (ii)

  29. Solution

  30. Alternative Solution

  31. Solve MILP without Partition

  32. Only 5 units! One less than the previous two!

  33. Sequential Synthesis Automatic Generation of Network Structures

  34. Basic Ideas • Each exchanger in the superstructure corresponds to a match predicted by the MILP model (with or without pinch partition). Each exchanger will also have as heat load the one predicted by MILP. • The superstructure will contain those stream interconnections among the units that can potentially define all configurations. The stream interconnections will be treated as unknowns that must be determined.

  35. Superstructure for one hot stream and two cold streams

  36. Embedded Alternative Configurations • H1-C1 and H1-C2 in series • H1-C2 and H1-C1 in series • H1-C1 and H1-C2 in parallel • H1-C1 and H1-C2 in parallel with bypass to H1-C2 • H1-C1 and H1-C2 in parallel with bypass to H1-C1

  37. Parameters and Unknowns

  38. Objective Function