Heuristic

Probably the most common method used for sequence selection for simple distillation columns is heuristic. Many heuristics have been proposed, but they can be summarized by the following four ... 

Heuristic 2 Sequences that remove the lightest components alone one by one in column overheads should be favored. In other words, favor the direct sequence. 

Heuristic 3 A component composing a large fraction of the feed should be removed first. 

Heuristic 4 Favor near-equimolar splits between top and bottom products in individual columns. 

These heuristics are based on observations made in many practical applications. In addition to being restricted to simple columns, the observations are based on no heat integration (i.e., all reboilers and condensers are serviced by utilities). Difficulties can arise when the heuristics are in conflict with each other, as the following example illustrates. 

Example 5.1 Each component for the mixture in Table 5.2 is to he separated into relatively pure products. Use the heuristics to determine sequences which are candidates for further evaluation. 

Heuristic 1 Do D/E split last, since this separation has the smallest relative volatility. 

Heuristic 3 Remove the most plentiful component first ... 

Clearly, the conflicts that have arisen in this problem have not been too helpful in identifying sequences which are candidates for further evaluation. A little more intelligence could be used in apphcation of the heuristics, and they could be ranked in order of... 

It is interesting to note that this is the sequence that would have been obtained had only heuristic 4 been used (favor near-equimolar splits between top and bottom products) throughout. 

Had only one of the four heuristics been used throughout, the rank order for the sequence from each heuristic would have been... 

Heuristic Rank order of sequence from Table 5.4... 

However, it would be extremely dangerous from this one calculation to assume that heuristic 4 is the most important, as the next example shows. 

In Example 5.3, heuristic 4 seemed to be the most important. Had heuristic 4 been used exclusively for this example, the sequence ranked fifth in Table 5.6 would have been obtained. 

Examples 5.3 and 5.4 show that the relative importance of the various heuristics changes between problems. Equation (5.8)... 

It is interesting to note that heuristics 2, 3, and 4 from Sec. 5.2 tend to minimize the flow rate of nonkey components. Heuristic 1 relates to special circumstances when there is a particularly difiicult separation. ... 

Porter, K. E., and Momoh, S. O., Finding the Optimum Sequence of Distillation Columns—An Equation to Replace the Rules of Thumb (Heuristics), Chem. Engg. J., 46 97, 1991. 

The tick-off heuristic. Once the matches around the pinch have been chosen to satisfy the criteria for minimum energy, the design should be continued in such a manner as to keep capital costs to a minimum. One important criterion in the capital cost is the number of units (there are others, of course, which shall be addressed later). Keeping the number of units to a minimum can be achieved using the tick-off heuristic. To tick off a stream, individual units are made as... 

Figure 16.5a shows the matches around the pinch from Fig. 16.4a with their duties maximized to tick-oflF streams. It should be emphasized that the tick-off heuristic is only a heuristic and can occasionally penalize the design. Methods will be developed later which allow such penalties to be identified as the design proceeds. 

Figure 16.6 Sizing the units below the pinch using the tick-off heuristic.

It is in fact the tick-off heuristic that steered the design toward the minimum number of units. The target for the minimum number of units was given by Eq. (7.2) ... 

Before any matches are placed, the target indicates that the number of units needed is equal to the number of streams (including utility streams) minus one. The tick-off heuristic satisfied the heat duty on one stream every time one of the units was used. The stream that has been ticked off is no longer part of the remaining design problem. The tick-off heuristic ensures that having placed a unit (and used up one of our available units), a stream is removed from the problem. Thus Eq. (7.2) is satisfied if eveiy match satisfies the heat duty on a stream or a utility. 

The loads on individual units are determined using the tick-off heuristic to minimize the number of units. Occasionally, the heuristic causes problems. 

Solution Figure 16.8a shows the hot-end design with the CP table. Above the pinch, adjacent to the pinch, CPfjSCPc- The duty on the units has been maximized according to the tick-oflF heuristic. 

The algorithm may calculate an increase in Qnmin and Qcmin- This means that the match is transferring heat across the pinch or that there is some feature of the design that will cause cross-pinch heat transfer if the design was completed. If the match is not transferring heat across the pinch directly, then the increase in utility will result from the match being too big as a result of the tick-off heuristic. 

Figure 16.215 shows an alternative match for stream 1 which also obeys the CP inequality. The tick-off" heuristic also fixes its duty to be 12 MW. The area for this match is 5087 m , and the target for the remaining problem above the pinch is 3788 m . Tlius the match in Fig. 16.216 causes the overall target to be exceeded by 16 m (0.2 percent). This seems to be a better match and therefore is accepted. 

This is a case in which the tick-off" heuristic has caused problems. The match is infeasible, and its duty must be reduced to 6 MW to be feasible without either stream being ticked off (Fig. 16.226). 

This completes the heuristic derivation of the Boltzmann transport equation. Now we trim to Boltzmaim s argument that his equation implies the Clausius fonn of the second law of thennodynamics, namely, that the entropy of an isolated system will increase as the result of any irreversible process taking place in the system. This result is referred to as Boltzmann s H-theorem. 

By extending some previous heuristic proposal [238,239], the phase in the polarized state of a ID solid of macroscopic length L was expressed in [240] as... 

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