COMPOSITE-CURVE

Composite curves were developed for heat recovery targeting (Linnhoff et al., 1982). The word composite reveals the basic concept behind the composite curves method A system view of the overall heat recovery system. One hot composite stream represents all the hot process streams, while one cold composite stream represents all the cold process streams. In this manner, the problem of assessing a complex heat recovery system involving multiple hot and cold streams is simplified as a problem of two composite streams. In essence, the hot composite stream represents a single process heat source, while the cold composite stream represents a single process heat sink. 

What characteristics should a hot composite stream possess to represent the three hot streams The composite stream should have two features (i) It should go through the exact same temperature ehanges as the three streams do, and (ii) it should have the same total heat load as the summation of the heat loads of three streams. 

The analysis of the heat exchanger network first identifies sources of heat (termed hot streams) and sinks (termed cold streams) from the material and energy balance. Consider first a very simple problem with just one hot stream (heat source) and one cold stream (heat sink). The initial temperature (termed supply temperature), final temperature (termed target temperature) and enthalpy change of both streams are given in Table 16.1. 

Steam is available at 180°C and cooling water at 20°C. Clearly, it is possible to heat the cold stream using steam and cool the hot stream, in Table 16.1, using cooling water. However, this would incur excessive energy cost. It is also incompatible with the goals of sustainable industrial activity, which call for use of the minimum energy consumption. Instead, it is preferable to try to 

The importance of lNTmin is that it sets the relative location of the hot and cold streams in this two-stream problem, and therefore the amount of heat recovery. Setting the value of A Tmin or Qnmm or Qcmin sets the relative location and the amount of heat recovery. 

Stream Type Supply temperature Ts (°C) Target temperature TtC C) AH (MW) Heat capacity flowrate CRfMW-Kr1) 

However, care should be taken not to ignore practical constraints when setting A Tmin. To achieve a small A Tmm in a design requires heat exchangers that exhibit pure countercurrent flow. With shell-and-tube heat exchangers 

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FIgura 6.5 Plotting the hot and cold composite curves together allows the targets for hot and cold utility to be obtained. 

Where the cold composite curve extends beyond the start of the hot composite curve in Fig. 6.5a, heat recovery is not possible, and the cold composite curve must be supplied with an external hot utility such as steam. This represents the target for hot utility (Q niin)- For this problem, with ATn,in = 10°C, Qnmin 7.5 MW. Where the hot composite curve extends beyond the start of the cold composite curve in Fig. 6.5a, heat recovery is again not possible, and the hot composite curve must be supplied with an external cold utility such as cooling water. This represents the target for cold utility (Qcmin)- For this problem, with AT in = 10°C, Qcmm = 10-0 MW. 

Figure 6.6 illustrates what happens to the cost of the system as the relative position of the composite curves is changed over a range of values of AT ir,. When the curves just touch, there is no driving force for heat transfer at one point in the process, which would require an... 

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

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,... 

Figure 6.14 Shifting the composite curves in temperature allows complete heat recovery within temperature intervals.

It is important to note that shifting the curves vertically does not alter the horizontal overlap between the curves. It therefore does not alter the amount by which the cold composite curve extends beyond the start of the hot composite curve at the hot end of the problem and the amount by which the hot composite curve extends beyond the start of the cold composite curve at the cold end. The shift simply removes the problem of ensuring temperature feasibility within temperature intervals. 

This shifting technique can be used to develop a strategy to calculate the energy targets without having to construct composite curves ... 

Figure 6.15 The utility target can be determined from the msiximum overlap between the shifted composite curves.

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. 

The initial setting for the heat cascade in Fig. 6.18a corresponds to the shifted composite curve setting in Fig. 6.15a where there is an overlap. The setting of the heat cascade for zero or positive heat flows in Fig. 6.186 corresponds to the shifted composite curve setting in Fig. 6.156. 

The composite curves are useful in providing conceptual understanding of the process, but the problem table algorithm is a more convenient calculation tool. 

Although the composite curves can be used to set energy targets, they are not a suitable tool for the selection of utilities. The grand composite curve is a more appropriate tool for understanding the interface between the process and the utility system. It is also, as is shown in later chapters, a useful tool for study of the interaction between heat-integrated reactors and separators and the rest of the process. 

The grand composite curve is obtained by plotting the problem table cascade. A typical grand composite curve is shown in Fig. 6.24. It shows the heat flow through the process against temperature. It should be noted that the temperature plotted here is shifted temperature T and not actual temperature. Hot streams are represented ATn,in/2 colder and cold streams AT iJ2 hotter than they are in practice. Thus an allowance for ATj in is built into the construction. 

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. 

Figure 6.24 The grand composite curve shows the utihty requirements in both enthalpy and temperature terms.

The shaded areas in Fig. 6.24, known as pockets, represent areas of additional process-to-process heat transfer. Remember that the profile of the grand composite curve represents residual heating and cooling demands after recovering heat within the shifted temperature intervals in the problem table algorithm. In these pockets in Fig. 6.24, a local surplus of heat in the process is used at temperature differences in excess of AT ,in to satisfy a local deficit. ... 

Figure 6.25a shows the same grand composite curve with two levels of saturated steam used as a hot utility. The steam system in Fig. 6.25a shows the low-pressure steam being desuperheated by injection of boiler feedwater after pressure reduction to maintain saturated conditions. Figure 6.256 shows again the same grand composite curve but with hot oil used as a hot utility. 

Example 6.3 The problem table cascade for the process in Fig. 6.2 is given in Fig. 6.18. Using the grand composite curve ... 

Figure 6.25. The grand composite curve allows alternative utility mixes to be evaluated.

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. 

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 ...

Now let us take a closer look at the two most commonly used heat engines (steam and gas turbines) to see whether they achieve this efficiency in practice. To make a quantitative assessment of any combined heat and power scheme, the grand composite curve should be used and the heat engine exhaust treated like any other utility. 

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. ... 

Using the grand composite curve, the loads and temperatures of... 

As with heat pumping, the grand composite curve is used to assess how much heat from the process needs to be extracted into the refrigeration system and where, if appropriate, the process can... 

Figure 6 9 The grand composite curve can be used to size heat pump cycles. (From Smith and Unnhoff, Trans. IChemE, ChERD, 66 195, 1988 reproduced by permission of the Institution of Chemical Engineers.)...

Figure 7.3 To determine the network area, the balanced composite curves are divided into enthalpy intervals.

Solution First, we must construct the balanced composite curves using the complete set of data from Table 7.1. Figure 7.5 shows the balanced composite curves. Note that the steam has been incorporated within the construction of the hot composite curve to maintain the monotonic nature of composite curves. The same is true of the cooling water in the cold composite curve. Figure 7.5 also shows the curves divided into enthalpy intervals where there is either a... 

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