Splits sharp

Repeat the calculation from Example 4.2 with actual phase equilibrium data in the phase split instead of assuming a sharp split. 

The temperature of the phase split is well above the critical temperatures of both hydrogen and methane, leading to large K values. On the other hand, the K values of the benzene, toluene, and diphenyl are very low, and hence the assumption of a sharp split in Example 4.2 was a good one. 

Remark 2 The separators are sharp and simple distillation columns (i.e., sharp splits of light and heavy key components without distribution of component in both the distillate and bottoms one feed and two products). The operating conditions of the distillation columns (i.e., pressure, temperature, reflux ratio) are fixed at nominal values. Hence, heat integration options are not considered, and the hot and cold utilities are directly used for heating and cooling requirements, respectively. 

The remaining gas mixture now has the composition nitrogen 3.7 mol%, oxygen 1.0 mol%, methane 47.9 mol%, C02 47.4 mol%. The third heuristic in Table 3.1 applies try to match the products. The appropriate selector is sharp split . Table 3.8 present lists of characteristic properties. Potential methods are absorption, cryogenic distillation, molecular sieving, membranes and equilibrium adsorption. 

Table 3.8 Ranked list of properties for sharp split-separation selector.

The impurities can be grouped into two categories lights (water, cyclohexene, cyclohexadiene) and heavies (phenol, dicyclohexyl-ether, cyclohexenyl- cyclohexanone). To limit their amount, the conversion is kept around 80% with a selectivity of about 98%. The hot reactor effluent is cooled in countercurrent with the feed in FEHE, and finally for phase separation in the heat exchanger (E-2) at 33 °C. The simple flash (S-2) can ensure a sharp split between hydrogen, recycled to hydrogenation reactor, and a liquid phase sent to separation. 

We first need to assess how many different sequences we might actually invent for this problem. Using only simple columns, we can construct the alternative sequences shown in Fig. 8, where each column does a fairly sharp split between adjacent key species. As we can see, there are 14 sequences. The third sequence has two binary separations at the end for it in this tree of alternatives. Note that both are required, so only one sequence results in the counting. 

In general, we will try simple distillation but, when we do, we often discover that significant amounts of almost all of the species show up in either or both of the distillate and bottoms products, no matter how we run the column. The inability to effect sharp splits gives rise to the recycling of streams within the separation process itself—something we did not require earlier when we looked at the separation of ideally behaving mixtures. 

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. 

One important issue that still needs attention is the objective function. It is intuitively obvious that if a separation cost is not associated with it, we will usually end up getting near-complete separations of products, and hence complete conversions to the extent possible within stoichiometric constraints. Thus the AR in concentration space can easily be the entire stoichiometric space. Unfortunately, it is difficult to get an accurate representation for the separation cost, e.specially when sharp splits are not enforced. Here, we present a simple cost model by assuming that the variable cost of separation is determined by two factors, namely, the difficulty of separation and the mass flow rate through the separator. 

If the split fractions 7a = 7b = 7c. we have only a splitting operation without any separation. Otherwise, there is a relative separation between two adjacent components in the mixture and we define Ita 7bI as a measure of the intensity of separation between these two components. When 7a 7b = 7b 7c 0. we have only a splitting operation among these components, and the cost of separation is identically zero however, if 7a 7b = I, we have a sharp split between components A and B. Any intermediate degree of separation could then be modeled by complete sharp split separation followed by mixing in order to achieve the desired composition. 

Here, y is the binary variable associated with the separation of components m and n, such that if y = 0, then = 0 and if y = I, then < I. The second term models the intensity of separation, where the cost coefficient p for unit separation between two adjacent components m and n reflects the difficulty of separation between m and n. Q is the net flow through the separation network. The above formulation gives us an exact representation when we have sharp splits between adjacent components. As we mentioned earlier, nonsharp splits can be modeled by sharp splits followed by mixing, and an upper bound on the separation costs can be derived by enforcing A7 = 1 whenever = 1 (i.e., by assuming sharp splits) while a lower bound on the separation cost... 

Assuming a four component mixture and simple two product splits. Fig. 1 shows all possible separation sequences into the pure components under the assumption of sharp splits. If the number of components is increased, an exponential growth of the number of sequences is observed (Fig. 2, sequences). This behaviour is well known [6] and can be described by... 

In essence, we are then making a sharp split between hexane... 

Generally there is also a pinch in the stripping section of the tower. For sharp splits, the temperature at this second pinch will be the same. We can then derive a second equation like (103) by performing our balances about the bottom n stages of the column to obtain a second equation. 

Figure 20.2 Rotational tunneling spectra for the closely related series of complexes M(H2)(CO)3(PR3)2 where M = Mo and R = Cy (top) and M = W and R = Cy (middle) or Pr (bottom). Note the change in energy scale between top and middle figures and the high sensitivity of the spectra to changes in metal and minor changes in phosphine ligand. The sharp splitting in the peaks in the lower spectrum is believed to be due to the disordered phosphine in the crystal structure (see Fig. 20.1).

The next step is a secondary decomposition of the separation problem of each subsystem by means of so-called selectors . These designate groups of separation methods capable of splitting the initial mixture in sub-mixtures by a procedure that generates a separation sequence. For example, LSM can operate on two selectors zeotropic and azeotropic separations. GSM can operate on three selectors enrichment, purification, and sharp split. 

Thus, a mixture of six components can be separated in 42 different sequences. If a first sharp split may isolate 2 mixtures each of 3 components, then the number of sequences diminish to 1+2x2=5. Note that the decision to remove only one component reduees considerably the number of alternatives. Consequently, we need... 

The separation achieved by distillation in this example is considerably different from the separation achieved by absorption in Example 12.8. Although the overhead total exit vapor flow rates are approximately the same (530 Ibmole/hr) in this example and in Example 12.8, a reasonably sharp split between ethane and propane occurs for distillation, while the absorber allows appreciable quantities of both ethane and propane to appear in the overhead exit vapor and the bottoms exit liquid. If the absorbent rate in Example 12.8 is doubled, the recovery of propane in the bottoms exit liquid approaches 100%, but more than 50% of the ethane also appears in the bottoms exit liquid. 

A sequence may be simple as in Fig. 14.1 or complex as in Fig. 14.2. It is simple if each separator performs a relatively sharp split between two key components and if neither products nor energy is recycled between separators. In this chapter, methods for the synthesis of simple sequences containing simple separators are presented. 

Prior to the development of Tolliver and McCune s procedure (402, 403), Boyd (58, 59) applied an almost identical analysis to a benzene-toluene fractionator performing a sharp split. The results of this analysis are shown in Fig. 18.5. Figure 18.5o is analogous to Fig. 18.3 the only difference is that Boyd used product impurity as the parameter instead of DIF. Since the impurity level is related to the DIF ratio via the component balance equation, the two techniques are essentially identical. 

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