Page 470 - Advanced thermodynamics for engineers

19.5 STEP 3: HEAT CASCADING 461

Q Hot streams mC Q
135 2 130 85 85 70 3.0 45

52.5 4 120 85 85 75 C 55 1.5 45
30 MJ/h
110 106.3
70 H 80 80 50 1 2.0 60
7.5 MJ/h 52.5 MJ/h 45 MJ/h 15 MJ/h
115 113.8 80
140 H 3 4.0
5 MJ/h 135 MJ/h
Cold streams
FIGURE 19.18
Hot and cold streams with pinch.

It is now necessary to break the problem at the pinch, and this results in Fig. 19.18, which is the
equivalent of Fig. 19.9 for the first example.
Now the problem can be analysed, bearing in mind the restrictions imposed by the pinch point. This
means that cooling to the utility stream is not allowable above the pinch, and hence the only transfer
can be with the hot utility above the pinch. It is now necessary, as far as possible, to match the hot and
cold streams above the pinch.

1. Consider stream 2 is matched with stream 1, and stream 4 is matched with stream 3. Then stream
2 can transfer 70 MJ/h to stream 1, and enable stream 1 to achieve its target temperature,
while reducing its temperature to 106.7 C. Also stream 4 can transfer its energy to stream 3,

and this will raise the temperature of stream 3 to 93.1 C. This shows that there is not sufficient

energy available in these streams to achieve the target temperatures. The reason for this being
an unsuitable approach is because the heat capacity flowrate for stream 1 above the pinch is
greater than that of the cold stream above the pinch. Since both streams have the same
temperature at the pinch point, then the high temperature of the cold stream would have to
be higher than that of the hot stream to achieve an energy balance: this would result in an
impossible heat transfer situation. Hence, for the result to be possible

mC cold mC hot (19.4)
above the pinch point.
2. If the alternative match is used, viz., stream 2 matched to stream 3, and stream 4 matched to
stream 1, then the answer shown in Fig. 19.19 is obtained. The heat transfers are shown on the
diagram. It can be seen that it is not possible to match the hot and cold streams either above or
below the pinch. This means that utility heat transfers are required from the hot utility above the
pinch, and heat transfers to the cold utility are required below the pinch. This proposal does obey
inequality Eqn (19.4), and is hence acceptable.
3. It can be seen that, above the pinch point, energy has to be added to the system from the hot
utility. This obeys the rules proposed above, and the total energy added is 12.5 MJ/h, which is in
agreement with the value calculated in Fig. 19.16.