The Petlyuk Columns

We examined above Petlyuk columns with preferable split in each colunm -1,2... n -1 23... - Along with such sequence one can use in practice sequences, where each product contains several components. The example of such separation given in the work (Amminudin et al, 2001) is the separation of the mixture of light hydrocarbons consisting of nine components into three products propane fraction, butane fraction, and pentane fraction. In these case, the split of the following type is used in the first column 13,.. k.l k, k + (i.e., 

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Fig. 3. Rearrangement of a conventional distillation sequence into the Petlyuk column...

As mentioned earlier, the Petlyuk column (Figure Ic) poses potential operational problems because of the two directions of the interconnecting vapor... 

In addition to the visual observations of the dynamic responses, a quantitative measure is needed to provide a better comparison. With such an objective, lAE values were evaluated for each closed-loop response. The PUL option shows the lowest lAE value of 5.607 x 10 , while the value for the Petlyuk column turns out to be 2.35 x 10. Therefore, the results of the test indicate that, for the SISO control of the heaviest component of the ternary mixture, the PUL option provides the best dynamic behavior and improves the performance of the Petlyuk column. Such result is consistent with the prediction provided by the SVD analysis. 

The results of the dynamic test for a positive change in the set point of the light component (A) are displayed in Figure 6. For a change in the set point from 0.987 to 0.991, the three systems are shown to be controllable and reach the new value of product composition, although the PUL scheme shows a quicker adjustment. lAE values were also calculated for each response the two best lAE values correspond to the new arrangements 4.20 x 10 for the PUL system, and 6.10 x 10 for the PUV system. The lAE value for the Petlyuk column was 2.35 x 10, which again shows a case in which the dynamic... 

Figure 7 shows the dynamic responses obtained when the set point for the intermediate component was changed from 0.98 to 0.984. One may notice the better response provided by the Petlyuk column in this case, which is faster than the other two systems and without oscillations. When the lAE values were calculated, a remarkable difference in favor of the Petlyuk system was observed 2.87 x 10 for the Petlyuk column, compared to 0.0011 for the PUL system and 0.0017 for the PUV system. The results from this test may seem unexpected, since the new arrangements have been proposed to improve the operation capabilities of the Petlyuk column. The SISO control of the intermediate component, interestingly, seems to conflict with that of the other two components in terms of the preferred choice from dynamic considerations. 

Thermally coupled systems can also be devised for multicomponent mixtures. Sargent and Gaminibandara (Optimization in Action, L. W. C. Dixon, ed.. Academic Press, London, 1976, p. 267) presented a natural extension of the Petlyuk column sequence to multi-component systems. Agrawal [Ind. Eng. Chem. Res., 35,1059 (1996) Trans. Inst. Chem. Eng., 78,454 (2000)] presented a method for generating an even more complete superstructure from which all the... 

In the previous examples, a one-to-one correspondence exists between the units and the tasks (e.g., in Fig. 2 each node performs a particular separation task). It is possible, however, to develop more general superstructure representations in which a one-to-many relationship exists between the units and the tasks. An example of a one-to-many relationship is the superstructure for separation shown in Fig. 6 proposed by Sargent and Gaminibandara (1976), this superstructure accommodates sharp splits and has the Petlyuk column embedded as an alternative design. Note, for instance, that column 1 does not have a prespecified separation task. From this example it is clear that superstructures that have one-to-many relationships between units and tasks tend to be richer in terms of embedded alternatives. On the other hand, the more restricted one-to-one superstructures tend to require simpler MINLP models that are quicker to solve. 

FIGURE 7.2 CS breakdown for the Petlyuk column operating at infinite reflux. 

The second inhnite reflux condition in the Petlyuk column is where CSj and CSe operate at infinite reflux, but we do not specify that CS2-5 operate under these conditions, that is, the vapor and liquid flowrates in 82-5 are finite values and are not equal to each other. Since the overall reflux is infinite, there is still no effect from feed addition or product removal on the column. Therefore, the CS breakdown for this structure is equivalent to the one shown in Figure 7.2. We can again apply the mass balance around the thermally coupled junction at the top of the column as in Equation 7.4. In this case, we again have the condition that Va = La and x = y , but in this case Vb 7 Lb, Vc Lc- Under these conditions, we find that Equation 7.4 reduces to... 

FIGURE 7.13 Five different global FPs for the Petlyuk column, labeled 1 5. 

FIGURE 7.14 Representation of FP transition in space for the Petlyuk column. 

Let us first treat the difference points across the feed stage depicted in Figure 7.15. It is again important to stress that in simple columns, a similar balance can be arrived at, but the net flowrates (A) and difference points are fixed by the product specifications of the column. In the Petlyuk column there is no such requirement... 

As one may expect, it is possible to operate this column under the same product specifications and R i value, but with alternate choices for d>yand d> , which again suggests multiple steady states. Minimum reflux in the Petlyuk column is defined as the lowest value of/ ai which still allows profile intersection, for any choice of v and d> ,. Put in another way, if / ai is decreased any further there will be no d>y d> pair that will result in a feasible design. 

FIGURE 7.26 The application of TTs for pinch and stability analysis in the Petlyuk column. 

Due to the fact that the Kaibel column falls under the same class of column as the Petlyuk column, namely fully thermally coupled columns, much of the design ideas introduced in Petlyuk design are applicable to Kaibel design too. A typical Kaibel column with its associated CS breakdown is shown in Figure 7.41. Here one can see that four products are produced for a certain feed, only requiring the use of a single reboiler and condenser set. 

The immediate consequence of removing an additional sidestream is that an extra CS is created. For the sake of consistency, we have kept the numbering format of CSs the same to that of the Petlyuk column, and simply labeled the additional CS in the Kaibel column as CS7. 

The resemblance between the Petlyuk column and the Kaibel column are quite blatant from a structural point of view. The addition of another sidestream however means that there are now 12 external degrees of freedom, assuming the feed stream is known 16 unknown material flowrates minus 4 independent material balances. This essentially requires that the compositions of each product stream be specified from... 

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