Pinches

With this rule in mind, divide the process at the pinch as shown in... 

Fig. 6.7a. Above the pinch (in temperature terms), the process is in heat balance with the minimum hot utility Qnmin- Heat is received from hot utility, and no heat is rejected. The process acts as a heat sink. Below the pinch (in temperature terms), the process is in heat balance with the minimum cold utility Qcmin- No heat is received, but heat is rejected to cold utility. The process acts as a heat source.

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). 

In choosing to transfer heat, say XP, from the system above the pinch to the system below the pinch, as shown in Fig. 6.8a, then above the pinch there is a heat deficit of XP. The only way this can... 

Figure 6.7 The composite curves set the energy target and the location of the pinch.

Analogous effects are caused by the inappropriate use of utilities. Utilities are appropriate if they are necessary to satisfy the enthalpy imbalance in that part of the process. Above the pinch in Fig. 6.7a, steam is needed to satisfy the enthalpy imbalance. Figure 6.86 illustrates what happens if inappropriate use of utilities is made and some cooling water is used to cool hot streams above the pinch, say, XP. To satisfy the enthalpy imbalance above the pinch, an import of (Q mjj,+XP) is needed from steam. Overall, (Qcmin+AP) of cooling water is used. ... 

An alternative inappropriate use of utilities involves heating of some of the cold streams below the pinch by steam. Below the pinch, cooling water is needed to satisfy the enthalpy imbalance. Figure... 

In other words, to achieve the energy target set by the composite curves, the designer must not transfer heat across the pinch by... 

Details of how this design was developed in Fig. 6.9 are included in Chap. 16. For now, simply take note that the targets set by the composite curves are achievable in design, providing that the pinch is recognized, there is no transfer of heat ac ss it, and no inappropriate use of utilities occurs. However, insight into the pinch is needed to analyze some of the important decisions still to be made before network design is addressed. 

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,... 

In a situation as shown in Fig. 6.12a, with the optimal AT in at the threshold, then there is no pinch. On the other hand, in a situation as shown in Fig. 6.126, with the optimum above the threshold value, there is a demand for both utilities, and there is a pinch. 

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

In design, the same rules must be obeyed around a utility pinch as around a process pinch. Heat should not be transferred across it by process-to-process transfer, and there should be no inappropriate use of utilities. In Fig. 6.13a this means that the only utility to be used above the utility pinch is steam generation and only cooling water below. In Fig. 6.136 this means that the only utility to be used above... 

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

The overlap in the shifted curves as shown in Fig. 6.15a means that heat transfer is infeasible. At some point this overlap is a maximum. This maximum overlap is added as a hot utility to correct the overlap. The shifted curves now touch at the pinch, as shown in Fig. 6.156. Since the shifted curves just touch, the actual curves are separated by AT ,in at this point (see Fig. 6.156). 

More than 7.5 MW could be added from a hot utility to the first interval, but the objective is to find the minimum hot and cold utility. Thus from Fig. 6.186, QHmin = 7.5MW and Qcmm = 10MW. This corresponds with the values obtained from the composite curves in Fig. 6.5a. One further important piece of information can be deduced from the cascade in Fig. 6.186. The point where the heat flow goes to zero at T = 145°C corresponds to the pinch. Thus the actual hot and cold stream pinch temperatures are 150 and 140°C. Again, this agrees with the result from the composite curves in Fig. 6.5a. 

Example 6.1 The flowsheet for a low-temperature distillation process is shown in Fig. 6.19. Calculate the minimum hot and cold utility requirements and the location of the pinch assuming AT, m = 5°C. 

Finally, the heat cascade is shown in Fig. 6.21. Figure 6.21a shows the cascade with zero hot utility. This leads to negative heat flows, the largest of which is -1.84 MW. Adding 1.84 MW from a hot utility as shown in Fig. 6.216 gives = 1.84 MW, Qcmm = 1-84 MW, hot stream pinch temperature =... 

The point of zero heat flow in the grand composite curve in Fig. 6.24 is the pinch. The open jaws at the top and bottom represent Hmin and Qcmin, respectively. Thus the heat sink above the pinch and heat source below the pinch can be identified as shown in Fig. 

In Fig. 6.27, the flue gas is cooled to pinch temperature before being released to the atmosphere. The heat releaised from the flue gas between pinch and ambient temperature is the stack loss. Thus, in Fig. 6.27, for a given grand composite curve and theoretical flcune temperature, the heat from fuel amd stack loss can be determined. 

In Figs. 6.27 and 6.28, the flue gas is capable of being cooled to pinch temperature before being released to the atmosphere. This is... 

Figure 6.29 Furnace stack temperature can be limited by other factors than pinch temperature.

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 ...

Fundamentally, there are two possible ways to integrate a heat engine exhaust. In Fig. 6.31 the process is represented as a heat sink and heat source separated hy the pinch. Integration of the heat engine across the pinch as shown in Fig. 6.31a is coimterproductive. The process still requires QHmm, and the heat engine performs no... 

Figure 6.31 Heat engine exhaust can be integrated either across or not across the pinch.

Figure 6.33 shows a steam turbine integrated with the process above the pinch. Heat Qhp is taken into the process from high-pressure steam. The balance of the hot utility demand Qlp is taken... 

The process requires (Qup + Qlp) to satisfy its enthalpy imbalance above the pinch. If there were no losses from the boiler, then fuel W would be converted to shaftwork W at 100 percent efficiency. However, the boiler losses Qloss reduce this to below 100 percent conversion. In practice, in addition to the boiler losses, there also can be significant losses from the steam distribution system. Figure 6.336 shows how the grand composite curve can be used to size steam turbine cycles. ... 

As with the steam turbine, if there was no stack loss to the atmosphere (i.e., if Qloss was zero), then W heat would he turned into W shaftwork. The stack losses in Fig. 6.34 reduce the efficiency of conversion of heat to work. The overall efficiency of conversion of heat to power depends on the turbine exhaust profile, the pinch temperature, and the shape of the process grand composite. 

Thus the appropriate placement of heat pumps is that they should be placed across the pinch. Note that the principle needs careful interpretation if there are utility pinches. In such circumstances, heat pump replacement above the process pinch or below it can be economic, providing that the heat pump is placed across a utility pinch. Such considerations are outside the scope of the present text. 

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