2. Heat Exchange Network Optimization by Thermal Pinch Analysis
Tier II: Case Studies
Section 2:
Heat Exchange Network Optimization by Thermal Pinch Analysis

3. Optimization Problems
There are many different types of optimization problems
It is important to recognize that an optimization problem exists even if it does not immediately or easily lend itself to one of the previously described analytical methods of optimization
Sometimes an alternative method that is more case specific must be used

4. Optimization Problems
A common example of one of these problems is the optimization of a heat exchange network
Without knowing what the maximum possible network integration is, and the minimum possible heating and cooling utilities required, it can be very difficult to design an optimized heat exchange network

5. Optimization of Utility Use in a Heat Exchange Network
Heating and cooling utilities consumption can be treated as an optimization problem
The goal is to minimize the amount of heating and cooling utilities being used by optimizing the heat exchange network
A different method will be used for this type of optimization than what was seen previously

6. Constraints
Total heating (QH) and total cooling (QC) used will still need to be minimized according to a set of constraints
These constraints are:
The target temperature of individual streams
The minimum approach temperature in a heat exchanger

7. Constraints Objective function: Constraints: Minimize QH + QC
T2i = ai , T1i = bi
t1i = ci , t2i = di
DTmin = k

8. Minimum Approach Temperature
T1 – hot out
T2 – hot in
t1 – cold in
t2 – cold out oC T1 t2 T2 t1
Minimum approach
temperature

9. Minimum Approach Temperature
To get the outlet temperature of one stream closer to the inlet temperature of the other stream, exchanger area must be increased, increasing capital cost
Decreased exchanger area means decreased capital cost, but increased utilities cost to make up for lost heat exchange capacity

10. Using Minimum Approach Temperature to Tradeoff Capital vs
Using Minimum Approach Temperature to Tradeoff Capital vs. Operating Costs
This graph demonstrates the tradeoff between capital and operating costs – a decrease in one is met with an increase in the other

11. Minimum Approach Temperature
The optimum exchanger size exists where the total annualized cost is minimized
This typically will correspond to a minimum approach temperature, DTmin of about 10oC
This DTmin = 10oC is a rule of thumb – it can change depending on the fluid service and the type of heat exchanger employed

12. Minimum Approach Temperature
Thermal Equilibrium
T = t
Practical Feasibility
T = t + DTmin
This must be included in the coming analysis

13. Graphical Method – Thermal Pinch Analysis
To optimize a heat exchange network, an example of the graphical method to determine the thermal pinch point will first be examined
The same example will then be solved using the algebraic method for comparison

14. Stream Data
Using the stream supply and target temperatures, the enthalpy change of each stream must be calculated
Enthalpy change:
DH = FiCpi(T2i – T1i) = HHi
= FiCpi(t2i – t1i) = HCi
FiCpi = flow rate x specific heat (kW/K)

15. Stream Data Hot Stream FiCpi Supply (oC) Target (oC) Enthalpy Change
(kW/oC)
T2i
T1i
HHi, (kW) H1
400
340
260
32000 H2
350
360
14000 H3
300
450
380
21000
Cold Stream
t1i
t2i
HCi, (kW) C1
250
240
290
12500 C2
30000 C3
22500

16. Stream Data
Stream data is then plotted as a series of straight line segments in order of ascending temperature
Each consecutive segment begins at the enthalpy level where the previous segment finished
A “hot” stream is any that must be cooled, while a “cold” stream is any that must be heated, regardless of supply temperature

17. Hot Streams

18. Cold Streams

19. Composite Stream Curves
Next the composite curves of the hot and cold streams must be constructed
These composite curves represent the total amount of heat to be removed from the hot streams and the total amount of heat that must be added to the cold streams to reach the target stream temperatures

20. Hot Composite Stream Construction

21. Hot Composite Stream Construction

22. Cold Composite Stream Construction

23. Cold Composite Stream Construction

24. Optimizing the Heat Exchange Network
The cold composite stream must now be superimposed over the hot composite stream to perform the thermal pinch analysis
This will give the minimum amount of utilities required to reach the target states
Note how the temperature axis is shifted for the cold composite stream to account for the minimum approach temperature

25. No Heat Integration Cold composite stream Hot composite stream
240
Cold composite stream
Total hot utility required
QH,max = 65,000 kW
Total cold utility required
Hot composite stream
QC,max = 67,000 kW
QC + QH = 132,000 kW

26. No Heat Integration
With no heat integration, the amount of energy required to reach the target state is maximized
In this case the total amounts of energy required are:
Cooling utility, QC = 67,000 kW
Heating utility, QH = 65,000 kW
Total utilities = QC + QH = 132,000 kW
Clearly there is room for optimization

27. Partial Heat Integration
By moving the cold composite stream down a bit, a partially integrated heat exchange network is graphically represented
Some heat is transferred from hot streams to cold streams to approach the temperature targets

28. Partial Heat Integration
QC = 52,000 kW
QH = 50,000 kW
Integrated heat exchange 15,000 kW
Total hot utility required
Total cold utility required
Cold composite stream
Hot composite stream
QC + QH = 102,000 kW

29. Partial Heat Integration
This heat exchange network is only partially optimized and already utility consumption is reduced by 30,000 kW
The utilities required are:
Cooling utility, QC = 52,000 kW
Heating utility, QH = 50,000 kW
Total utilities = QC + QH = 102,000 kW
Clearly further integration can provide significant energy savings

30. Optimized Heat Integration
To determine the optimized heat exchange network, the thermal pinch point must be found
This is accomplished by moving the cold composite stream down just until one point on the line meets a point on the hot composite line
This point is the thermal pinch point

31. Optimized Heat Integration
QH,min = 8,500 kW
Cold composite stream
Integrated heat exchange = 56,500 kW
Pinch point
Hot composite stream
QC,min = 10,500 kW
240
QC + QH = 19,000 kW

32. Optimized Heat Integration
The heat exchange network is now fully optimized
Total required utilities are minimized
Minimum cooling utility, QC,min = 10,500 kW
Minimum heating utility, QH,min = 8,500 kW
Minimum total utilities = QC + QH = 19,000 kW
No heat is passed through the pinch point

33. Passing Heat through the Pinch Point
To have an optimized heat exchange network, it is critical that no heat is passed through the thermal pinch point
By passing an amount of heat, a, through the pinch point, an energy penalty of 2a is added to the total utilities requirement
It is very important to maximize integration in a heat exchange network

34. Passing Heat Through the Pinch Point
QH,min
QC,min
QH = QH,min + a
QC = QC,min + a
QH + QC = QH,min + QC,min + 2a

35. Crossing the Pinch Point
It would appear that extra energy can be saved by lowering the cold composite stream line further
This does not work however because it creates a thermodynamically infeasible region
For this to work, heat would have to flow from the cooled hot streams to the heated cold streams - from a cold source to a hot source

36. Crossing the Pinch Point
Cold composite stream
Pinch point
Hot composite stream
Infeasible region

37. Disregarding DTmin
Another tempting error is to disregard the minimum approach temperature
By disregarding a minimum approach temperature, the absolute minimum thermodynamically possible utility requirements are obtained
Although this is thermodynamically possible, it is not practically feasible as it would require an infinitely large heat exchanger area
This would obviously cost far more than the relatively small energy savings are worth

38. Disregarding DTmin
QH,min thermo.
QC,min thermo.
240

39. Algebraic Method
This same problem will now be solved using the algebraic method
This will involve producing a temperature interval diagram, tables of exchangeable heat loads, and cascade diagrams

40. Stream Data From before: Hot Stream FiCpi Supply (oC) Target (oC)
(kW/oC)
T2i
T1i H1
400
340
260 H2
350
360 H3
300
450
380
Cold Stream
t1i
t2i C1
250
240
290 C2 C3

41. Temperature Interval Diagram
The first step is to construct the temperature interval diagram
This diagram shows the starting and finishing temperatures of each stream
An interval begins at a stream’s starting or finishing temperature, and it ends where it encounters the next beginning or finishing temperature of a stream
Draw horizontal lines across the table at each arrow’s head and tail, with the intervals lying between these lines
Note how the cold stream temperature scale is staggered by 10 degrees

42. Temperature Interval Diagram

43. Table of Exchangeable Heat Loads
The next step is to construct tables of exchangeable heat loads for the hot and cold streams
These tables show the amount of energy that must be added or removed from a stream over a particular interval
These energy values are calculated as
DHj,i = FCpjDTi, where DTi is the positive temperature difference across the interval, and j denotes the stream number

44. Table of Exchangeable Heat Loads
For the hot streams,

45. Table of Exchangeable Heat Loads
For the cold streams,

46. Cascade Diagrams
Using the information from the heat load tables, the cascade diagrams can now be constructed
These diagrams will be used to determine the pinch point and the minimum heating and cooling utilities required

47. Cascade Diagram
First, the cascade diagram is drawn as it appears at right, with one box for each interval that appeared in the temperature interval diagram

48. Cascade Diagram
Next, the total values from the exchangeable heat load tables are added to the cascade diagram
Hot stream loads enter on the left, cold stream loads exit on the right

49. Cascade Diagram
Now, by subtracting an interval’s cold load from the hot load, and adding the resulting value to the residual from the previous stage we get the residual value for the subsequent stage
ri = HHi – HCi + ri-1
12000
7500
5500
-2500
-8500
-5500
-1500
4500
7) 4000 – 0 – 5500 = -1500
9) 0 – = 2000
4) 7000 – = -2500
8) – – 1500 = 4500
6) – 9000 – 8500 = -5500
2) 3000 – = 7500
3) – = 5500
5) 0 – = -8500
1) – = 12000
2000

50. Thermal Pinch Point
The thermal pinch point occurs at the largest negative number
Pinch Point
The absolute value of this number is now added in at the top to cascade through

51. Revised Cascade Diagram
8500
+ 8500
+ 8500
+ 8500
+ 8500
+ 8500
+ 8500
+ 8500
+ 8500
+ 8500

52. Revised Cascade Diagram
Qmin,heating =
We now have the final revised cascade diagram
It can be seen that by adding additional energy at the top, it will cascade through and also be present at the bottom
Pinch
Point
QH + QC = QH,min + QC,min + 2a !
Qmin,cooling =

53. Optimized Heat Integration
The heat exchange network is now fully optimized
Total required utilities are minimized
Minimum cooling utility, QC,min = 10,500 kW
Minimum heating utility, QH,min = 8,500 kW
Minimum total utilities = QC + QH = 19,000 kW
As expected, these values are the same as obtained by using the graphing method

54. Design Considerations
Some design rules to optimize utility consumption:
Do not pass heat through the pinch point
Do not use cooling utilities at temperatures above the pinch point
Do not use heating utilities at temperatures below the pinch point

55. Constructing the Heat Exchange Network
Now that the pinch analysis has been performed, the heat exchange network can be constructed
It is a good idea to perform the pinch analysis first because it sets the performance goal of an optimized heat exchange network
There is no quick method of reliably determining the minimum number of heat exchangers, but the following method should help to construct the network

56. Constructing the Heat Exchange Network
With QC,min and QH,min known, construct a plot similar to the temperature interval diagram, except instead of arrows, use boxes that have a width representing FCp
The area of these boxes corresponds to the heat exchanged by the stream
Draw a horizontal line across at the pinch point – remember, no heat is to be passed across this point

57. Constructing the Heat Exchange Network

58. Constructing the Heat Exchange Network
Now, add QC,min to the lowest point on the coldest hot stream and determine the resulting T1 and T2 for this exchange. Note that T1, T2, t1, and t2 now do not necessarily correspond to the same values as used earlier and are different for each exchanger
QC,min = FCp(T2 – T1)
Do the same with QH,min, adding it to the highest point on the hottest cold stream
QH,min = FCp(t2 – t1)

59. Constructing the Heat Exchange Network

60. Constructing the Heat Exchange Network
Now, working out from the pinch point, match up streams, remembering not to transfer heat across the pinch point and keeping DTmin in mind
For each matched stream, determine the temperatures that exist for the inlet and outlet of the heat exchanger
Qex = FCp(T2 – T1) = FCp(t2 – t1)
Having the table of stream data including enthalpy change on hand may be helpful for determining the best way to match a stream

61. Matched Streams

62. Heat Exchangers
4 heat exchangers, plus a heater and a cooler are needed to meet the optimum heat exchange requirements of this system

63. Conclusion
There is no quick method that is guaranteed to give the minimum number of heat exchangers required every time
However, by first performing a thermal pinch analysis to determine the maximum heat exchange possibilities, designing an optimum network configuration is made a lot easier

64. References
Dr. El-Halwagi lecture notes