Different heat loads are shown in Table 1.16

Table 1.16 Cooling and heating above and below 23.5°C pinch point.

From Table 1.16, mathematically with reference to the Fig 1.37 we can infer that for a pinch point of 23.5°C, we require external heating load of 130.35kW and cooling load of 202.35kW above and below the pinch point respectively.
The process integration is now as follows:
Above pinch point, stream 1 and 3 exchanges 168.3 kW heat, stream 2 and stream 4 exchanges 181.35kw. Below pinch point, stream 2 and stream 3 exchange 168 kW heat. Stream 3 and 4 are to be externally heated with (224-168.3 = 55.7 kW) and (256-181.35 = 74.65 kW) respectively to meet the deficit /demand of 130.35 kW. Similarly, stream 1 and 3 are to be cooled externally with 161.7 kW and (208.65-168 = 40.65 kW) heat exchangers respectively to meet the demand of 202.35 kW.

Possible processes are shown in Fig. 1.38.

Fig 1.38 Possible plant to heat and cool four fluid streams for a minimum 23.5°C temperature difference.

The following rules should be followed in process integration

1. Do not transfer heat from one fluid to another across the pinch point
2. No external heating below pinch point
3. No external cooling above the pinch point
4. A heat exchanger should operate on one side of the pinch, either taking a heat supply from below the pinch, or rejecting heat to a fluid above the pinch
5. A heat pump should operate across the pinch from a cold stream below the pinch to a hot stream above the pinch.

Summary:

1. Exergy is the maximum work potential of a system
2. Exergy transfer with heat, work and mass
3. For an isolated system exergy always decreases
4. Exergy remains constant in a reversible process

Anything that generate entropy is responsible for decrease of exergy