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For complex networks a more general expression is needed to determine the minimum
number of exchangers: CHEMICAL ENGINEERING
0
0
Z min D N C L S 3.42
0
where L D the number of internal loops present in the network
S D the number of independent branches (subsets) that exist in the network.
A loop exists where a close path can be traced through the network. There is a loop in
the network shown in Figure 3.27. The loop is shown in Figure 3.28. The presence of a
loop indicates that there is scope for reducing the number of exchangers.

B C
1

A D
2

A C D
3
B
4
Pinch

Figure 3.28. Loop in network

For a full discussion of equation 3.42 and its applications see Linnhoff et al. (1979),
and IChemE (1994).
In summary, to seek the optimum design for a network:
1. Start with the design for maximum heat recovery. The number of exchangers needed
will be equal to or less than the number for maximum energy recovery.
2. Identify loops that cross the pinch. The design for maximum heat recovery will
usually contain loops.
3. Starting with the loop with the least heat load, break the loops by adding or
subtracting heat.
4. Check that the speciﬁed minimum temperature difference T min has not been
violated, and revise the design as necessary to restore the T min .
5. Estimate the capital and operating costs, and the total annual cost.
6. Repeat the loop breaking and network revision to ﬁnd the lowest cost design.
7. Consider the safety, operability and maintenance aspects of the proposed design.

Importance of the minimum temperature difference

In a heat exchanger, the heat-transfer area required to transfer a speciﬁed heat load is
inversely proportional to the temperature difference between the streams; see Chapter 12.

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