1. Synthesis of Heat Exchanger Networks
Part 6
Synthesis of Heat Exchanger Networks

2. 6.1 Sequential Synthesis
Minimum Utility Cost

3. Example 1 Fcp (MW/C) Tin (C) Tout H1 1 400 120 H2 2 340 C1 1.5 160 C2
1.3
100
250
Steam: 500 C
Cooling water: 20 – 30 C
Minimum recovery approach temperature (HRAT): 20 C

6. Heat Balances around Temperature Intervals

7. Transshipment Model

8. 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.

9. Index Sets

11. Condensed Transshipment Model

12. Example 2 FCp (MW/K) Tin (K) Tout H1 2.5 400 320 H2 3.8 370 C1 2.0 300
420 C2
HP Steam: 500 K, $80/kW-yr
LP Steam: 380 K, $50/kW-yr
Cooling Water: 300 K, $20/kW-yr
HRAT: 10K

15. Minimum Utility Cost with Constrained Matches
Sequential Synthesis
Minimum Utility Cost with Constrained Matches

17. Basic Ideas

19. 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).

21. Index Sets

23. Expanded Transshipment Model

24. Match Constraints

25. Example 1 Fcp (MW/C) Tin (C) Tout H1 1 400 120 H2 2 340 C1 1.5 160 C2
1.3
100
250
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.

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

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

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

29. Objective Function

30. 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.

31. Heat Balances

32. Logical Constraints

33. Solution

34. Example 1 Fcp (MW/C) Tin (C) Tout H1 1 400 120 H2 2 340 C1 1.5 160 C2
1.3
100
250
Steam: 500 C
Cooling water: 20 – 30 C
Minimum recovery approach temperature (HRAT): 20 C

35. Condensed Transshipment Model

37. MILP (i)

38. MILP (ii)

39. Solution

41. Alternative Solution

42. Solve MILP without Partition

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

44. Automatic Generation of Network Structures
Sequential Synthesis
Automatic Generation of Network Structures

45. 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.

46. Superstructure for one hot stream and two cold streams

47. 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

49. Parameters and Unknowns

50. Objective Function

51. Equality Constraints

52. Inequality Constraints

53. Example 3
Stream
Tin
(K)
Tout
Fcp
(kW/K) h
(kW/m^2K)
Cost
($/kW-yr) H1
440
350 22
2.0 - C1
349
430 20 C2
320
368
7.5
0.67 S1
500
1.0
120 W1
300
Minimum temperature approach = 1 K
Exchanger cost = (Area)^0.83

54. Solution