Number of heat exchangers in network

Zinin Minimum number of heat exchangers in network —... 

Step (i) was proved in Appendix A of Floudas et al. (1986), and hence the minimum number of matches predicted by the MILP transshipment model can always be represented with an equal number of heat exchanger units in a feasible HEN network. 

Note also that the set of constraints (A)-(G) exhibit the nice feature of linearity in the continuous and binary variables. Furthermore, the flow rates do not participate in the formulation at all and hence there is a reduction in the number of continuous variables by the number of flowrates. The penalty that we pay for this desirable feature is threefold (i) we introduce more binary variables since we have possible process matches that are equal to the number of stages times the actual number of potential matches, (ii) we deal with a simplified set of alternatives that excludes a number of desirable structures, and (iii) we need to solve an NLP suboptimization problem to determine the flow rates of the split streams and possible reduce the number of heat exchangers if the resulting network exhibits splitting of the streams. 

One can easily predict the likely least number of heat exchangers required in this network. 

If loops are presents in the network then the number of heat exchangers is given by the formula ... 

In summary, six heat exchangers is the minimum for this network when it is required that the hot and cold utilities be minimized as well. As discussed in Section 10.4, the minimum number of heat exchangers for this system is five, which can be achieved either by breaking heat loops, usually at the price of exceeding the MER targets, or by stream splitting. ... 

In a more general result, Douglas (1988) shows that the minimum number of heat exchangers is also dependent on the number of independent networks, Nnw that is, the number of sub-networks consisting of linked paths between the connected streams ... 

The temperature-interval method can also be used to produce grand composite curves, which show the variation of heat supply and demand in a system. These diagrams enable engineers to minimize the expensive utilities, network area, and number of heat exchanger units. 

The final heat-exchanger network is shown in Figure 15.8. The exchangers are represented by single circles, with fluid flowing through both sides. This network has the minimum number of heat exchangers. 

To this point, it has been assumed that the log-mean tenperature correction factor, F, for all exchangers is the same and equal to 0.8. The reason that F is not assumed to be equal to unity is that, for heat exchangers in most practical applications, the flows of the hot and cold streams are never purely countercurrent. The most common type of heat exchanger in use in the chemical process industries is the shell-and-tube (S T) type. These units are typically made as multiples of the basic 1-shell pass, 2-tube pass (1-2) design. When estimating the fixed capital investment associated with the purchase and installation of the heat-exchanger network, the number of 1-2 S T exchangers is needed in addition to the total surface area of the network. 

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