Algorithm for the Number-of-Shells Target

One particularly important property of the relationships for multipass exchangers is illustrated by the two streams shown in Fig. E.l. The problem overall is predicted to require 3.889 shells (4 shells in practice). If the problem is divided arbitrarily into two parts S and T as shown in Fig. El, then part S requires 2.899 and Part T requires 0.990, giving a total of precisely 3.889. It does not matter how many vertical sections the problem is divided into or how big the sections are, the same identical result is obtained, provided fractional (noninteger) numbers of shells are used. When the problem is divided into four arbitrary parts A, B, C, and D (Fig. E.l), adding up the individual shell requirements gives precisely 3.889 again. 

This additive property takes on fundamental practical significance when the problem of setting a target for the number of shells in a network from the composite curves is considered.  

To establish the shells target, the composite curves are first divided into vertical enthalpy intervals as done for the area target algorithm. It was shown in App. B that it is always possible to design a network for an enthalpy interval with (5, -1) matches, with each match having the same temperature profile as the enthalpy interval. 

If such a design is established within an interval, then the number of shells for each match in interval k will be the same. This is so because the number of shells in Eqs. (7.14) to (7.16) depends only on the temperatures of the streams being matched, and since each match within an interval operates with the same temperatures, each match will require the same number of shells. 

It is important to work in fractional numbers of shells (rather than integer) in order to use the additive property for 1-2 shells from one interval to another. If each match in enthalpy interval k requires iV shells using the temperatures of interval k in Eqs. (7.14) to (7.16), then the minimum shells count for the interval is 

---

An algorithm to target the number of shells and network area for networks consisting of 1-2 shells can now be formulated ... 

Algorithm for the Heat Exchanger Network Number of Shells Target... 

A simple algorithm can be developed (see App. E) to target the minimum total number of shells (as a real, i.e., noninteger number) for a stream set based on the temperature distribution of the composite curves. The algorithm starts by dividing the composite... 

---