Component nonkey

In general, the flow of key components is constant and independent of the sequence, while the flow of nonkey components varies according to the choice of sequence, as illustrated in Fig. 5.8. 

It thus appears that the flow rate of the nonkey components may account for the diflerences between sequences. Essentially, nonkey components have two effects on a separation. They cause... 

A widening of the temperature differences across columns, since light nonkey components cause a decrease in condenser temperature and heavy nonkey components cause an increase in the reboiler temperature. 

Figure 5.8 The overall flow rate of key components is constant for any sequence of simple columns. The overall flow rate of nonkey components varies. (From Smith and Linnhoff, Trans. IChemE, ChERD, 66 195, 1988 reproduced by permission of the Institution of Chemical Engineers.)...

The mechanism by which nonkey components affect a given separation is more complex in practice than the broad arguments presented here. There are complex interrelationships between the volatility of the key and nonkey components, etc. Although the argument presented is thus not rigorous, it is broadly correct. 

It is interesting to note that heuristics 2, 3, and 4 from Sec. 5.2 tend to minimize the flow rate of nonkey components. Heuristic 1 relates to special circumstances when there is a particularly difiicult separation. ... 

Distillation. There is a large inventory of boiling liquid, sometimes under pressure, in a distillation column, both in the base and held up in the column. If a sequence of columns is involved, then, as discussed in Chap. 5, the sequence can be chosen to minimize the inventory of hazardous material. If all materials are equally hazardous, then choosing the sequence that tends to minimize the flow rate of nonkey components also will tend to minimize the inventory. Use of the dividing-wall column shown in Fig. 5.17c will reduce considerably the inventory relative to two simple columns. Dividing-wall columns are inherently safer than conventional arrangements because they lower not only the inventory but also the number of items of equipment and hence lower the potential for leaks. 

The (x, i )), values in Eq. (13-37) are minimum-reflux values, i.e., the overhead concentration that would be produced by the column operating at the minimum reflux with an infinite number of stages. When the light key and the heavy key are adjacent in relative volatihty and the specified spht between them is sharp or the relative volatilities of the other components are not close to those of the two keys, only the two keys will distribute at minimum reflux and the Xi D),n values are easily determined. This is often the case and is the only one considered here. Other cases in which some or all of the nonkey components distribute between distillate and bottom products are discussed in detail by Henley and Seader (op. cit.). 

To solve Equation 9.51, it is necessary to know the values of not only a ,-j and 9 but also x, d. The values of xitD for each component in the distillate in Equation 9.51 are the values at the minimum reflux and are unknown. Rigorous solution of the Underwood Equations, without assumptions of component distribution, thus requires Equation 9.50 to be solved for (NC — 1) values of 9 lying between the values of atj of the different components. Equation 9.51 is then written (NC -1) times to give a set of equations in which the unknowns are Rmin and (NC -2) values of xi D for the nonkey components. These equations can then be solved simultaneously. In this way, in addition to the calculation of Rmi , the Underwood Equations can also be used to estimate the distribution of nonkey components at minimum reflux conditions from a specification of the key component separation. This is analogous to the use of the Fenske Equation to determine the distribution at total reflux. Although there is often not too much difference between the estimates at total and minimum reflux, the true distribution is more likely to be between the two estimates. 

Heuristic 1. Separations where the relative volatility of the key components is close to unity or that exhibit azeotropic behavior should be performed in the absence of nonkey components. In other words, do the most difficult separation last. 

If the design problem in the absence of significant constraints can be decoupled in this way, there must be some mechanism behind this. Take two different sequences for the separation of a four-component mixture, Figure 21.103. Summing the feed flowrates of the key components (see Chapter 9) to each column in the sequence, the total flowrate is the same in both cases, Figure 21.10. However, the flow of nonkey components is different, Figure 21.10. 

The mechanism by which nonkey components affect a given separation is more complex in practice than the broad arguments presented here. There are complex interrelationships between the volatility of the key and nonkey components, and so on. Also, it is often the case that the distillations system has constraints to prevent certain heat integration opportunities. Such constraints will often present themselves as constraints over which the pressure of the distillation columns will operate. For example, it is often the case that the maximum pressure of a distillation column is restricted to avoid decomposition of material in the reboiler. This is especially the case when reboiling high molar mass material. Distillation of high molar mass material is often constrained to operate under vacuum conditions. Clearly, if the pressure of the distillation column is constrained, then this restricts the heat integration opportunities. Another factor that can create... 

The six sequencing heuristics are formulated to reduce the separation load on downstream columns, favoring easier separations early and difficult separations in the absence of nonkey components. If only two products are to be derived from a mixture and all of the components in one product are more volatile than all of the components in the other product, then the next split should divide the mixture into the two products. The presence of hazardous or corrosive materials can gready increase costs, and such components should be removed as early as possible. The most plentiful product in a mixture should be removed (if it can be) with one separation and if the relative volatility is favorable. Direct sequences, ie, removing a light product as distillate, generally are favored over indirect sequences, ie, removing a heavy product as bottoms. If no product dominates the feed composition, then separations that yield approximately equimolar splits are favored. Only if no other heuristic applies should the easiest separation be performed next. 

The lower bounds on the recoveries were set to 0.85 on the grounds that a number of simulations performed showed that to avoid the distribution of nonkey components it was necessary to keep the recoveries of the key components greater than or equal to 0.85. 

Figure 2.3 Estimate splits of nonkey components in a multicomponent distillation.

The d/b ratio plot is frequently non-linear, but should be smooth iSec, 2,3.8), The prime cause of bumps is a poor estimate of relative volatility. If a refined estimate (sse Sec, 3.2,1 for estimating guidelines) does not improve things, the bump may reflect anomalies or a need to relocate a feed, The d/b plot gives a measure of how relocating the feed point affects the nonkey component split,... 

Figure 2,23 Application of dlb plots to examine nonkey component distribution in products, Depropanizer example. 20 theoretical stages, = 1.40.

A component is said to be distributed (or distributing) at minimum reflux if it appears both in the distillate and the bottoms at minimum reflux. Usually, nonkeys are nondistributed (or nondistributing), that is, at minimum reflux the heavy nonkeys are totally contained in the bottoms and the light nonkeys in the distillate. A nonkey component may be distributed if... 

Application of Underwood s equation to systems containing distributed nonkey components is as follows ... 

Treat the mole fraction of each distributed nonkey component in the distillate as an unknown. Write Eq. (3.11) fbr each value of B calculated above. (L/Z ) is also unknown. Solve the equations simultaneously to get the mole fraction of each distributed component in the distillate and L/D)min. In the above example, there are five values of 0 and therefore five equations. There are also five unknowns—the mole fractions of DKl, DK2, DKS, and DK4 in the distillate, and (L/D)mjn. 

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