Shifted composite curves

Not all heat recovery problems have a Pinch. Sometimes only hot or cold utility is required. Figure 10.20a illustrates a typical situation. Initially (right case), the analysis indicates a pinched problem with both hot and cold utilities. By lowering AT the cold composite curve shifts to the left up to a position where there is no need for hot utility. The value of AT, when this situation occurs is called threshold. Lowering AT below the threshold leads to the need of a second cold utility, this time at the hot end. Similarly,... 

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.

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 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 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 6.30 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 ...

Establish the heat integration potential of simple columns. Introduce heat recovery between reboilers, intermediate reboilers, condensers, intermediate condensers, and other process streams. Shift the distillation column pressures to allow integration, where possible, using the grand composite curve to assess the heat integration potential. 

One further point needs to be noted regarding the construction of the site composite curves. The temperatures are shifted over and above the shift included in the construction of the grand composite curve. The original hot and cold streams are shifted by ATmin/2 to produce the grand composite curve. Site composite curves are shifted by an additional ATmin/2 to give a total AT shift of ATmin, as illustrated in Figure 23.2913. If different values of ATmin apply to different processes, then each set of process data is given its individual shift in A Tmin before the steams are combined in the construction of the site composite curves. The concept of individual shifts for A Tmin was discussed in Chapter 16. 

Figure 24.19 Temperature-shifted cooling water composite curve. (From Kim J-K and Smith R, 2001, Chem Eng Sci, 56 3641, reproduced by permission of Elsevier Ltd.)...

The raw curves for //, i and /.to as well as a composite curve formed by shifting data for the two runs by the amount indicated by the arrows are shown in Fig. 10.3. The combined curve provides information over the combined range of particle numbers, N, covered by the two runs. Note that by keeping one-dimensional histograms for N we are restricted to combining runs of the same temperature, while the more general form (10.14) allows combination of runs at different temperatures. 

Plasticizer and Copolymerization change the glass transition temperature as discussed in Chapter 1. Plasticixers have little effect on Copolymerization can change although less strongly than 7 x. As a result, the basic modulus-temperature and modulus-time curves are shifted as shown in Figure 8 for different compositions. The shift in the modulus-temperature curve is essentially the same as the shift in TK. The shift in the modulus-time curve includes this plus the effect of any change in ()jr... 

The cloud point curves of the epoxy monomer/PEI blend and BPACY monomer/PEI blend exhibited an upper critical solution temperature (UCST) behavior, whereas partially cured epoxy/PEI blend and BPACY/PEI blend showed bimodal UCST curves with two critical compositions, ft is attributed to the fact that, at lower conversion, thermoset resin has a bimodal distribution of molecular weight in which unreacted thermoset monomer and partially reacted thermoset dimer or trimer exist simultaneously. The rubber/epoxy systems that shows bimodal UCST behavior have been reported in previous papers [40,46]. Figure 3.7 shows the cloud point curve of epoxy/PEI system. With the increase in conversion (molecular weight) of epoxy resin, the bimodal UCST curve shifts to higher temperature region. 

As demonstrated by means of residue curve analysis, selective mass transfer through a membrane has a significant effect on the location of the singular points of a batch reactive separation process. The singular points are shifted, and thereby the topology of the residue curve maps can change dramatically. Depending on the structure of the matrix of effective membrane mass transfer coefficients, the attainable product compositions are shifted to a desired or to an undesired direction. 

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