Pinch problem

Figure 6.13 Threshold problems are turned into a pinch problem when additional utilities are added.

Rgura 7.2 To target the number of units for pinched problems, the streams above and below the pinch must be counted separately, with the appropriate utilities included. 

Figure 16.10 shows another threshold problem that requires only hot utility. This problem is different in characteristic from the one in Fig. 16.9. Now the minimum temperature difference is in the middle of the problem, causing a pseudopinch. The best strategy to deal with this type of threshold problem is to treat it as a pinched problem. For the problem in Fig. 16.10, the problem is divided into two parts at the pseudopinch, and the pinch design method is followed. The only complication in applying the pinch design method for such problems is that one-half of the problem (the cold end in Fig. 16.10) will not feature the flexibility offered by matching against utility.

Figure 16.10 Some threshold problems must be treated as pinched problems requiring essential matches at both the no-utility end and the pinch.

A. R. Ciric and C. A. Floudas. Application of the simultaneous match-network optimization approach to the pseudo-pinch problem. Comp. Chem. Eng., 14 241,1990. 

Another above-pinch problem is shown in Fig. 18A. This time, there is one hot stream and there are two cold streams. Thus, as far as the number of streams is concerned, there should be no need to split a stream. However, the CP inequality also needs to be satisfied above the pinch the hot stream, with a CP of 0.5, requires a cold stream with a greater CP. Neither of the two cold streams in Fig. 18A is large enough to satisfy the CP inequality. The design problem can be solved by splitting the hot stream into two branches, as shown in Fig. 18B. Splitting arbitrarily into two branches with a CP of 0.3 and 0.2 allows... 

Not all heat recovery problems have a Pinch. Sometimes only hot or cold utility is required. Figure 10.20a illustrates a typical situation. Initially (right case), the analysis indicates a pinched problem with both hot and cold utilities. By lowering AT the cold composite curve shifts to the left up to a position where there is no need for hot utility. The value of AT, when this situation occurs is called threshold. Lowering AT below the threshold leads to the need of a second cold utility, this time at the hot end. Similarly,... 

Consider now the possibility of transferring heat between these two systems (see Fig. 6.76). Figure 6.76 shows that it is possible to transfer heat from hot streams above the pinch to cold streams below. The pinch temperature for hot streams for the problem is 150°C, and that for cold streams is 140°C. Transfer of heat from above the pinch to below as shown in Fig. 6.76 transfers heat from hot streams with a temperature of 150°C or greater into cold streams with a temperature of 140°C or less. This is clearly possible. By contrast. Fig. 6.7c shows that transfer from hot streams below the pinch to cold streams above is not possible. Such transfer requires heat being transferred from hot streams with a temperature of 150°C or less into cold streams with a temperature of 140°C or greater. This is clearly not possible (without violating the ATmin constraint). 

Not all problems have a pinch to divide the process into two parts. Consider the composite curves in Fig. 6.10a. At this setting, both steam and cooling water are required. As the composite curves are moved closer together, both the steam and cooling water requirements decrease until the setting shown in Fig. 6.106 results. At this setting, the composite curves are in alignment at the hot end,... 

It is interesting to note that threshold problems are quite common in practice, and although they do not have a process pinch, pinches... 

Figure 6.30 shows the grand composite curve plotted from the problem table cascade in Fig. 6.186. The starting point for the flue gas is an actual temperature of 1800 C, which corresponds to a shifl ed temperature of (1800 — 25) = mS C on the grand composite curve. The flue gas profile is not restricted above the pinch and can be cooled to pinch temperature corresponding to a shifted temperature of 145 C before venting to the atmosphere. The actual stack temperature is thus 145 + 25= 170°C. This is just above the acid dew point of 160 C. Now calculate the fuel consumption ...

This is a useful result, since if the network is assumed to be loop-free and has a single component, the minimum number of units can be predicted simply by knowing the number of streams. If the problem does not have a pinch, then Eq. (7.2) predicts the minimum number of units. If the problem has a pinch, then Eq. (7.2) is applied on each side of the pinch separately ... 

Having decided that no exchanger should have a temperature difference smaller than ATmi, two rules were deduced. If the energy target set by the composite curves (or the problem table algorithm) is to be achieved, there must be no heat transfer across the pinch by... 

Start at the pinch. The pinch is the most constrained region of the problem. At the pinch, exists between all hot and cold... 

Figure 16.4 The CP table for the designs above and below the pinch for the problem from Table 6.2.

Divide the problem at the pinch into separate problems. 

The design for the separate problems is started at the pinch, moving away. 

Example 16.1 The process stream data for a heat recovery network problem are given in Table 16.1. A problem table analysis on these data reveals that the minimum hot utility requirement for the process is 15 MW and the minimum cold utility requirement is 26 MW for a minimum allowable temperature diflFerence of 20°C. The analysis also reveals that the pinch is located at a temperature of 120°C for hot streams and 100°C for cold streams. Design a heat exchanger network for maximum energy recovery in the minimum number of units. 

In Sec. 6.3 it was mentioned that some problems, known as threshold problems, do not have a pinch. They need either hot utility or cold utility but not both. How should the approach be modified to deal with the design of threshold problems ... 

The philosophy in the pinch design method was to start the design where it was most constrained. If the design is pinched, the problem is most constrained at the pinch. If there is no pinch, where is the design most constrained Figure 16.9a shows a threshold problem that requires no hot utility, just cold utility. The most constrained part of this problem is the no-utility end. Tips is where temperature differences are smallest, and there may be constraints, as shown in Fig. 16.96, where the target temperatures on some of the cold... 

If there had been more cold streams than hot streams in the design above the pinch, this would not have created a problem, since hot utility can be used above the pinch. 

By contrast, now consider part of a design below the pinch (Fig. 16.12a). Here, hot utility must not be used, which means that all cold streams must be heated to pinch temperature by heat recovery. There are now three cold streams and two hot streams in Fig. 16.12a. Again, regardless of the CP values, one of the cold streams cannot be heated to pinch temperature without some violation of the constraint. The problem can only be resolved by splitting a hot (a)... 

It is not only the stream number that creates the need to split streams at the pinch. Sometimes the CP inequality criteria [Eqs. (16.1) and (16.2)] CEmnot be met at the pinch without a stream split. Consider the above-pinch part of a problem in Fig. 16.13a. The number of hot streams is less than the number of cold, and hence Eq. (16.3) is satisfied. However, the CP inequality also must be satisfied, i.e., Eq. (16.1). Neither of the two cold streams has a large enough CP. The hot stream can be made smaller by splitting it into two parallel branches (Fig. 16.136). 

Figure 16.14a shows the below-pinch part of a problem. The... 

Clearly, in designs different from those in Figs. 16.13 and 16.14 when streams are split to satisfy the CP inequality, this might create a problem with the number of streams at the pinch such that Eqs. (16.3) and (16.4) are no longer satisfied. This would then require further stream splits to satisfy the stream number criterion. Figure 16.15 presents algorithms for the overall approach. ... 

Example 16.2 A problem table analysis of a petrochemicals process reveals that for a minimum temperature difference of 50°C the process requires 9.2 MW of hot utUity, 6.4 MW of cold utility, and the pinch is located at 550°C... 

The network can now be designed using the pinch design method.The philosophy of the pinch design method is to start at the pinch and move away. At the pinch, the rules for the CP inequality and the number of streams must be obeyed. Above the utility pinch and below the process pinch in Fig. 16.17, there is no problem in applying this philosophy. However, between the two pinches, there is a problem, since designing away from both pinches could lead to a clash where both meet. 

It is rare for there to be two process pinches in a problem. Multiple pinches usually arise from the introduction of additional utilities causing utility pinches. However, cases such as that shown in Fig. 16.18 are not uncommon, where there is, strictly speaking, only one pinch (one place where occurs), but there is a near-pinch. This... 

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. 

The cold-utility target for the problem shown in Fig. 16.22 is 4 MW. If the design is started at the pinch with stream 3, then stream 3 must be split to satisfy the CP inequality (Fig. 16.22a). Matching one of the branches against stream 1 and ticking off stream 1 results in a duty of 8 MW. 

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