Composite curves enthalpy intervals

Figure 7.3 To determine the network area, the balanced composite curves are divided into enthalpy intervals.

Solution First, we must construct the balanced composite curves using the complete set of data from Table 7.1. Figure 7.5 shows the balanced composite curves. Note that the steam has been incorporated within the construction of the hot composite curve to maintain the monotonic nature of composite curves. The same is true of the cooling water in the cold composite curve. Figure 7.5 also shows the curves divided into enthalpy intervals where there is either a... 

Figure 73 The enthalpy intervals for the balanced composite curves of Example 7.2.

The Fp correction factor for each enthalpy interval depends both on the assumed value of Xp and the temperatures of the interval on the composite curves. It is possible to modify the simple area target formula to obtain the resulting increased overall area A etwork for a network of 1-2 exchangers ... 

Figure 16.26 shows a pair of composite curves divided into enthalpy intervals with a possible superstructure shown for one of the intervals. The structure is created by splitting each hot stream... 

Figure B.l shows a pair of composite curves divided into vertical enthalpy intervals. Also shown in Fig. B.l is a heat exchanger network for one of the enthalpy intervals which will satisfy all the heating and cooling requirements. The network shown in Fig. B.l for the enthalpy interval is in grid diagram form. The network arrangement in Fig. B.l has been placed such that each match experiences the ATlm of the interval. The network also uses the minimum number of matches (S - 1). Such a network can be developed for any interval, providing each match within the interval (1) satisfies completely the enthalpy change of a strearh in the interval and (2) achieves the same ratio of CP values as exists between the composite curves (by stream splitting if necessary).

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. 

The composite curves (including utilities) are divided into enthalpy intervals. The minimum (fractional) number of shells for the temperatures of each interval k is evaluated using Eqs. (D.7) to (D.9). 

As the diagram shows changes in the enthalpy of the streams, it does not matter where a particular curve is plotted on the enthalpy axis as long as the curve runs between the correct temperatures. This means that where more than one stream appears in a temperature interval, the stream heat capacities can be added to give the composite curve shown in Figure 3.21b. 

A simple algorithm can be developed (see Appendix G) 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 curves into enthalpy intervals in the same way as the area target algorithm. 

Note that the A Tmin for the problem must be fixed in order to remain an MILP problem. Fixing A Tmin fixes the composite curves and the temperatures across each enthalpy interval or block. Unfortunately, this would not necessarily lead to the best network, as the initial superstructure was already simplified with many structural options missing. But this can be allowed for by first carrying out the... 

Extending this equation to all enthalpy intervals in the composite curves gives ... 

The composite curves for this problem have already been divided into enthalpy intervals in Figure 17.5. 

The vertical heat transfer between the hot and cold composite curves utilizes as a means of representation the partitioning of enthalpy (Q) into enthalpy intervals El). The partitioning into enthalpy intervals has a number of similarities with the partitioning of temperature intervals presented in section 8.3.1.3, but it has at the same time a number of key differences outlined next. 

The basic idea in this case is to consider all kink points of both the hot and cold composite curves and draw vertical lines at these kink points. These vertical lines define the enthalpy intervals. Note that the list of kink points includes supply and targets of hot and cold streams. To illustrate such an (El) partitioning let us consider the example used in section 8.3.1.2 for which the temperature interval partitioning is depicted in Figure 8.2 of section 8.3.1.3. The (El) partition for this example is shown in Figure 8.11. Note that in this example there are six Els. 

Composite Curve (CC) displays the cumulated enthalpy of all streams, hot or cold, available in a temperature interval between the extreme supply and targets temperatures. The formula to calculate the relation enthalpy-temperature is ... 

The surface area calculation for heat transfer equipment is the most importent part of cost targeting. For simplicity, the area model (Townsend and Linnhoff, 1983a, 1983b) is used to explain how surface area is calculated directly from composite curves. To do this, utilities are added to composite curves to make heat balance between hot and cold composites. Then the balanced composite curves are divided into several enthalpy intervals, and each enthalpy interval must feature straight temperature profiles (Figure 9.11). 

Consider now a portion of the composite enthalpy curve shown in Figure 15.11(bh This curve is made up of two hot streams (1 and 2) and two cold streams (3 and 4). Both the hot streams and both the cold streams have the same temperature change in the interval. However, in general, the enthalpy in either of the hot streams is not the same as the enthalpy in either of the cold streams. Instead, the sum of the enthalpies in the hot streams is equal to that in the two cold streams. This means that different streams cannot be matched in this temperature (enthalpy) interval, because the enthalpy of individual hot and cold streams will be different. However, an estimate of the heat transfer area required to transfer all the energy... 

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