Minimum number of exchangers

This will not necessarily be the optimum design for the network. The optimum design will be that which gives the lowest total annual costs taking into account the capital cost of the system, in addition to the utility and other operating costs. The number of exchangers in the network, and their size, will determine the capital cost. 

To find the optimum design it will be necessary to cost a number of alternative designs, seeking a compromise between the capital costs, determined by the number and size of the exchangers, and the utility costs, determined by the heat recovery achieved. 

For simple networks Holmann (1971) has shown that the minimum number of exchangers is given by  

For complex networks a more general expression is needed to determine the minimum number of exchangers  

S = the number of independent branches (subsets) that exist in the network. 

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Minimum Number of Exchangers. The fewest number of matches or exchangers that are requited in a network can be developed as a limit. The number needed, is generally one less than the total number of streams, S (process and utiUty), involved in the network ... 

Synthesis of MENs with Minimum Number of Exchangers... 

In order to demonstrate the applicability of the foregoing feasibility criteria, we now revisit the dephenolization case study. As has been discussed earlier, the synthesis ought to start at the pinch and proceed in two directions the rich and the lean ends. Let s begin with the rich end of the problem. Above the pinch, we have two waste streams and two MSAs. Hence, minimum number of exchangers above the pinch can be calculated according to Eq. (5.7b) as... 

If the HEN has more than the minimum number of exchangers (say nv more than the minimum) and nT variable target temperatures, then nv + nT of the intermediate stream temperatures and heater loads can be chosen as control variables. Stream split fractions are always available as control variables. These variables are adjusted to try to make the HEN feasible for the assumed, fixed values of the uncertain supply temperatures and flow rates. The HEN is feasible if and only if s 0. 

Figure 10.26 HEN with minimum number of exchangers to meet MER target at = ATth, = 50°C in Example 10.13.

Figure 15.5 Calculation of Minimum Number of Exchangers for Example 15.2...

Below the Pinch. The same method is used to calculate the minimum number of exchangers below the pinch. The diagrams for above and below the pinch are shown in Figure 15.5. and from this it can be seen that five exchangers are required above the pinch and three below the pinch, or a total of eight heat exchangers for the entire network. 

For systems without a pinch, the same approach for the minimum number of exchangers as described above can be used, but the problem no longer needs to be split into two parts. For the case considered here, assuming that the problem did not have a pinch (and hence only one utility is required) and that Equation 15.1 is applicable, we get... 

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