Stream Matching at the Pinch

to the cold stream that has a heat-capacity flow rate of Q, entering at F , and exiting at F. On the cold end of the heat exchanger, where the temperatures of the hot and cold streams are the lowest, the approach temperature difference is AFj. On the hot end, where the temperatures are the highest, the approach temperature difference is AF2. Carrying out energy balances for the hot and cold streams  

Following the approach introduced by Linnhoff and Hindmarsh (1983), the potential locations for the heat exchangers at the pinch are considered next. When a heat exchanger is positioned on the hot side of the pinch, which is considered first arbitrarily, AF, = AT jn, and Eq. (10.10) becomes  

to assure that AF2 AF j , since Q 0 and the heat-capacity flow rates are positive, it follows that Q Q is a necessary and sufficient condition. That is, for a match to be feasible at the pinch, on the hot side, C , must be satisfied. If two streams are matched at the 

When a heat exchanger is positioned on the cold side of the pinch, AF2 = AF j , and Eq. (10.10) becomes  

In this case, to assure that there are no approach temperature violations (i.e., AFj AF j ), it is necessary and sufficient that C s Q. Note that this condition is just the reverse of that on the hot side of the pinch. These stream-matching rules are now applied to design a HEN for Example 10.1. 

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If the heat capacities of streams are such that it is not possible to make a match at the pinch without violating the minimum temperature difference condition, then the heat capacity can be altered by splitting a stream. Dividing the stream will reduce the mass flow-rates in each leg and hence the heat capacities. This is illustrated in Example 3.16. 

Cannot match stream 1 or 2 with stream 3 at the pinch. 

Similarly, if not enough streams are available to make all of the required matches at the pinch, then streams with large CP can be split to increase the number of streams. 

Can match stream 1 or 2 with stream 3, but neither stream can match with stream 4. This creates a problem, since if we match stream 1 with 3, then stream 2 will not be able to make a match at the pinch. Likewise, if we match stream 2 with 3, then stream 1 will not be able to make a match at the pinch. 

Fig. 14 shows the part of the design below the pinch. In this particular case, because the heat exchanger network is simple, there is only one hot stream and one cold stream below the pinch. The match at the pinch shown in Fig. 14 is seen to be feasible with a hot stream CP of 0.4 matched against a cold stream CP of 0.2. By a reasoning analogous to the arguments for the CP inequality above the pinch, it can be concluded that below the pinch, at the pinch, CPh > CPc for a feasible match. 

The CP inequality for individual matches. Figure 16.2a shows the temperature profile for an individual exchanger at the pinch, above the pinch.Moving away from the pinch, temperature differences must increase. Figure 16.2a shows a match between a hot stream and a cold stream which has a CP smaller than the hot stream. At the pinch, the match starts with a temperature difference equal to The relative slopes of the temperature-enthalpy... 

Figure 16.3 shows the situation below the pinch at the pinch. If a cold stream is matched with a hot stream with a smaller CP, as shown in Fig. 16.3a (i.e., a steeper slope), then the temperature differences become smaller (which is infeasible). If the same cold stream is matched with a hot stream with a larger CP (i.e., a less steep slope), as shown in Fig. 16.36, then temperature differences become larger (which is feasible). Thus, starting with ATmin at the pinch, for temperature differences to increase moving away from the pinch,... 

The CP table. Identification of the essential matches in the region of the pinch is clarified by use of a CP table. In a CP table, the CP values of the hot and cold streams at the pinch are listed in descending order. 

Temperature feasibility requires constraints on the CP values to be satisfied for matches between streams at the pinch. 

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. 

Once again, stream splitting may be required to guarantee that inequality (5.12a) or (5.12b) is realized for each pinch match. It should also be emphasized that the feasibility criteria (Eqs. 5.8 and 5.12) should be fulfilled only at the pinch. Once... 

Applying this condition at the pinch, stream 1 can be matched with stream 4, but not with 3. 

To design the network for maximum energy recovery start at the pinch and match streams following the rules on stream heat capacities for matches adjacent to the pinch. Where a match is made transfer the maximum amount of heat. 

Start at the pinch. The pinch is the most constrained region of the problem. At the pinch, A Tmin exists between all hot and cold streams. As a result, the number of feasible matches in this region is severely restricted. Quite often there... 

Masso and Rudd (1969), Lee, Masso and Rudd (1970) and Pho and Lapidus (1973) start a match with the two stream inlet conditions and exchange all the heat possible, terminating when one stream reaches its target outlet temperature or when a temperature pinch occurs. Ponton and Donaldson (1974), Donaldson, Paterson and Ponton (1976) and Grossmann and Sargent (1978) start a match at the hot end of both streams (or as close to the hot end of the cold stream as possible). The idea is to introduce necessary utilities at their least cost level while exchanging as much heat as possible. Rathore and Powers (1975) do both, getting two alternative matches and obviously many more alternative networks. 

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