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

2. 6.1 Sequential Synthesis
Minimum Utility Cost

3. Example 1 H1 1
400
120 H2 2
340 C1
1.5
160 C2
1.3
100
250

5. Incidence Matrix of Directed Graph

6. Material Balance Around a Node

7. Minimum Cost Flow Problem

8. Transshipment Problem
The transportation problem is a special case of the minimum cost flow problem, corresponding to a network with arcs going only from supply to demand nodes.
The more general problem allows for arbitrary network configuration, so that flow from a supply node may progress through several intermediate nodes before reaching its destination.
The more general problem is often termed the transshipment problem.

10. Heat Balances around Temperature Intervals (Warehouses)

11. Transshipment Model
Total utility consumption rate
LP problem

12. 60 30
123
225

13. Index Sets

15. Condensed Transshipment Model
Total utility cost
Known

16. Remarks

17. Example 2 (The transshipment model can be generalized to consider multiple utilities to minimize total utility cost.)
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

18. HP steam
500K
380K

20. Minimum Utility Cost with Constrained Matches
Sequential Synthesis
Minimum Utility Cost with Constrained Matches
(The transshipment model can be expanded so as to handle constraints on matches.)

21. Example 1 H1 1
400
120 H2 2
340 C1
1.5
160 C2
1.3
100
250

23. Expanded heat cascade!

24. Basic Ideas

25. Two Possible Heat-Exchange Options
Hot stream i and cold stream j are both present in interval k.
Cold stream j is present in interval k, but hot stream i is only present at higher temperature interval.

26. Hot stream i and cold stream j are both present in interval k

27. Cold stream j is present in interval 3, but hot stream i is only present at interval 2

28. Index Sets

30. Expanded Transshipment Model

31. Match Constraints

32. Modified Example 1 H1 1
400
120 H2 2
340 C1
1.5
160 C2
1.3
100
250

33. 60 30
123
225

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

35. Expanded heat cascade!

36. Expanded Transshipment Model

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

38. Prediction of optimal matches for minimizing the unit number in HEN
Sequential Synthesis
Prediction of optimal matches for minimizing the unit number in HEN

39. Objective Function
q=1,2,….,NP+1

40. 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.

41. Expanded Transshipment Model

42. Modification of Expanded Transshipment Model

43. Heat Balances

44. Logical Constraints

45. Solution

46. 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

47. Condensed Transshipment Model

48. Pinch

49. MILP (i)

50. MILP (ii)

51. Solution

52. Manual Synthesis

53. Alternative Solution

54. Solve MILP without Partition

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

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

57. Basic Ideas of Superstructure
Each exchanger in HEN corresponds to a match predicted by the MILP model (with or without pinch partition).
Each exchanger in HEN should also have as heat duty the one predicted by MILP.
The superstructure will contain the stream interconnections among the aforementioned exchangers that can potentially define all configurations.
The flow rates and temperatures of stream interconnections in superstructure will be treated as unknowns that must be determined.

58. Example 3
Stream
Tin
(K)
Tout
Fcp
(kW/K)
Heat Load
(kW) h
(kW/m^2K)
Cost
($/kW-yr) H1
440
350 22
1980
2.0 - C1
349
430 20
1620 C2
320
368
7.5
360
0.67 S1
500
1.0
120 W1
300

59. Step 1 & Step 2

60. Superstructure for hot stream H1

61. 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

63. Parameters and Unknowns

64. Equality Constraints

65. Inequality Constraints

66. Objective Function

67. Solution