Engineering task and calculation objective
This module supports the analysis and structuring of heat exchanger networks using the pinch method, based on the VDI Heat Atlas (VDI-Wärmeatlas, 12th edition 2019). Starting from the hot and cold product streams of a process and the additional utilities (heating and cooling media), it determines the energy targets of the network: the minimum required heating duty, the minimum required cooling duty, the minimum necessary number of heat exchangers, and the minimum required heat transfer area.
In practice, this kind of heat integration analysis is needed whenever several streams in a process plant have to be heated and cooled at the same time – for example in refineries, chemical plants, or heat recovery systems. Engineers who want to calculate and optimize a heat exchanger network obtain, from the pinch targets, reliable lower bounds for energy demand and equipment count before a single heat exchanger has been sized.
The central design parameter is the pinch, the minimum allowable temperature difference between hot and cold streams. It governs the trade-off between energy savings (small pinch, large areas) and capital cost (large pinch, small areas).
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Collect stream data: All hot and cold product streams of the process are recorded with their heat capacity flow rates and inlet and outlet temperatures. For this purpose, the module manages the number of cold and hot product streams in the network as well as the current number of material streams.
- Set the pinch: The minimum allowable temperature difference (pinch) is specified as a design parameter. It determines how closely hot and cold streams may approach each other thermally in the network, thereby fixing the location of the pinch point.
- Determine the energy targets: From the composite curves of heat capacity flow rate versus temperature (or the problem table), the minimum required heating duty and the minimum required cooling duty of the process are obtained – i.e., the external utility demand that cannot be undercut even with complete heat integration.
- Determine the minimum number of units: According to the graph-theoretical rule, the maximum required (i.e., minimum necessary) number of heat exchangers follows from the number of participating streams including the utilities. The module compares this number with the actual number of heat exchangers in the network.
- Estimate the area target: From the composite curves and the heat transfer coefficients of the streams, the minimum required heat transfer area of the overall network is estimated. It serves as a benchmark for specific network designs and as a basis for cost estimates.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Number of heat exchangers in the network | nA | - |
| Number of cold product streams in the system | nC | - |
| Number of hot product streams in the system | nH | - |
| Number of additional operating resources | nB | - |
| Max. required number of heat exchangers | n | - |
| Existing number of matter flows | nAS | - |
| Stoffstrom | Stoffstrom | - |
| Stoffstrom | Stoffstrom | - |
| Stoffstrom | Stoffstrom | - |
| Stoffstrom | Stoffstrom | - |
| Stoffstrom | Stoffstrom | - |
| Stoffstrom | Stoffstrom | - |
| Stoffstrom | Stoffstrom | - |
| Stoffstrom | Stoffstrom | - |
| Stoffstrom | Stoffstrom | - |
| Stoffstrom | Stoffstrom | - |
| Stoffstrom | Stoffstrom | °C |
| Stoffstrom | Stoffstrom | °C |
| Stoffstrom | Stoffstrom | °C |
| Stoffstrom | Stoffstrom | °C |
| Stoffstrom | Stoffstrom | °C |
| Stoffstrom | Stoffstrom | °C |
| Stoffstrom | Stoffstrom | °C |
| Stoffstrom | Stoffstrom | °C |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Max. required number of heat exchangers | n | - |
| Stoffstrom | Stoffstrom | - |
| Stoffstrom | Stoffstrom | - |
| Stoffstrom | Stoffstrom | - |
| Stoffstrom | Stoffstrom | - |
| Stoffstrom | Stoffstrom | - |
| Stoffstrom | Stoffstrom | - |
| Stoffstrom | Stoffstrom | - |
| Stoffstrom | Stoffstrom | - |
| Stoffstrom | Stoffstrom | - |
| Stoffstrom | Stoffstrom | - |
| Stoffstrom | Stoffstrom | W |
| Stoffstrom | Stoffstrom | W |
| Stoffstrom | Stoffstrom | W |
| Stoffstrom | Stoffstrom | W |
| Stoffstrom | Stoffstrom | W |
| Stoffstrom | Stoffstrom | W |
| Stoffstrom | Stoffstrom | W |
| Stoffstrom | Stoffstrom | W |
| Stoffstrom | Stoffstrom | W |
| Stoffstrom | Stoffstrom | W |
| 1.Stoffstrom | 1.Stoffstrom | °C |
| 2.Stoffstrom | 2.Stoffstrom | °C |
| 3.Stoffstrom | 3.Stoffstrom | °C |
Worked example
In a process, 3 hot and 4 cold product streams are to be thermally interconnected. As additional utilities, a heating medium (steam) and a cooling medium (cooling water) are available. Find the minimum required number of heat exchangers for a connected network without heat loops.
Given values
| Number of hot product streams | 3 |
| Number of cold product streams | 4 |
| Number of additional utilities | 2 (1 heating, 1 cooling medium) |
Solution
Form the total number of streams
All streams that absorb or release heat enter the count – process streams and utilities:
S = 3 + 4 + 2 = 9
Minimum number of exchangers by the Euler rule
For a connected network without independent heat loops:
Nmin = S − 1 = 9 − 1 = 8
At least 8 heat exchangers (including heaters and coolers) are therefore required. Real designs that strictly observe the pinch may exceed this, because the rule must then be applied separately to the subregions above and below the pinch.
Result
| Minimum number of heat exchangers N_min | 8 |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
What does the pinch point mean physically?
The pinch is the point where the composite curves of the hot and cold streams come closest together – exactly the minimum allowable temperature difference exists there. It divides the process into a heat sink region above and a heat source region below the pinch. The three pinch rules are: no heat transfer across the pinch, no external cooling above the pinch, and no external heating below the pinch. Every violation increases the heating and cooling demand simultaneously by the same amount.
How do I choose a sensible minimum allowable temperature difference?
The choice is an economic trade-off: a small pinch (e.g. 5–10 K) maximizes heat recovery but leads to large heat transfer areas; a large pinch (e.g. 20–40 K) reduces the capital investment but increases utility demand. Typical starting values are 10–20 K for liquid/liquid systems, and rather higher for gas streams or fouling media. Ideally, the value is varied via a cost-targeting calculation (supertargeting).
Why is the minimum number of heat exchangers equal to the number of streams minus one?
This follows from Euler's relation for connected networks: if you connect S streams (process streams plus utilities) without independent heat loops, you need at least S − 1 exchangers. If the count is carried out separately for the regions above and below the pinch, the sum can turn out larger, because individual streams appear in both regions.
Does the targeting calculation replace the design of the individual heat exchangers?
No. Pinch analysis provides lower bounds for the energy demand, equipment count, and area of the overall network, but no detailed design. The individual units must subsequently be sized with the relevant methods of the VDI Heat Atlas (overall heat transfer, pressure drop, type of construction). Real networks usually exceed the theoretical minima due to operating, control, and layout requirements.