Three-component mixtures columns

If there is a three-component mixture and simple columns are employed, then the decision is between two sequences, as illustrated in Fig. 5.1. The sequence shown in Fig. 5.1a is called the direct sequence, in which the lightest component is taken overhead in each column. The indirect sequence, shown in Fig. 5.16, takes the heaviest component as the bottom product in each column. There may be... 

For a three-component mixture, there are only two alternative sequences. The complexity increases dramatically as the number of components increases. Figure 5.2 shows the alternative sequences for a five-component mixture. Table 5.1 shows the relationship between the number of products and the number of possible sequences for simple columns. ... 

This type of chromatographic development will only be briefly described as it is rarely used and probably is of academic interest only. This method of development can only be effectively employed in a column distribution system. The sample is fed continuously onto the column, usually as a dilute solution in the mobile phase. This is in contrast to displacement development and elution development, where discrete samples are placed on the system and the separation is subsequently processed. Frontal analysis only separates part of the first compound in a relatively pure state, each subsequent component being mixed with those previously eluted. Consider a three component mixture, containing solutes (A), (B) and (C) as a dilute solution in the mobile phase that is fed continuously onto a column. The first component to elute, (A), will be that solute held least strongly in the stationary phase. Then the... 

Figure 13.1 A shows a conventional high performance reversed-phase separation of a three-component mixture of aromatic acid esters obtained with a standard 4.6 mm x 250 mm octadecyl column and methanol water as the eluent. From the view of chromatographic resolution and ruggedness, this is an excellent separation. However, from a practical standpoint, an assay based on this particular separation would not be satisfactory since it wastes large amounts of time between elutions of the individual components.

The checkers attempted chromatography of the three-component mixture on a 150-mmol scale using 55- and 75-mm diameter columns. However, mixed fractions were obtained even with seemingly large differences for the components. 

Tedder and Rudd (1978) present the results of a study of the economics of separating a variety of three component mixtures using a variety of thermally coupled and ordinary columns. Their goal was to expose trends. They show which feed characteristics favor which column structure. 

Figure 6 Distribution of component concentrations as a function of column height during separation of a three-component mixture (a) frontal separation (b) displacement separation.

A single distillation column for separating a three-component mixture into three products is shown below. Are the design variables shown sufficient to specify the problem completely If not, what additional design variable(s) would you select ... 

Figure 21.1. Hypothetical separation of a three-component mixture Component A A Component B Component C O. The dotted area represents the original solvent in the column, which is being displaced during elution.

Figure 21.2. Chromatogram of the three-component mixture of Figure 21.1. to = time for solvent to traverse the column, = retention time of substance B, ty,g = peak basewidth of substance B, h = peak height.

By the structural matrix of the azeotropic mixture concentration space, we will name a square matrix, the columns and lines of which correspond to the stationary points and the elements of which aij = 1, if there is a bond directed from stationary point i to stationary point (a, = 0, if such a bond is missing). For the purpose of obviousness, some examples of three-component mixture structural matrices are shown in Fig. 1.8. 

Figure 2.8. A location ofzones of constant concentration (pinches) in columns for distillation of three-component mixtures under minimum reflux (a) R < (first class of fractionation), (b) < R <...

The location of trajectory bundles and possible product composition segments at reversible distillation of three-component mixtures determines the location of trajectory bundles, and of possible product composition regions of multicomponent mixtures and the locations of trajectory bundles of real adiabatic columns. 

Let s examine a column of sharp reversible distillation with two feedings (Fig. 4.18a) for separation of a three-component mixture (Petlyuk Danilov, 1999). For an intermediate section of such a column, Eq. (4.6) is as follows (F2, upper feeding) ... 

For nonideal three-component mixtures, the methods of calculation of minimum reflux mode was developed in the works (Glanz Stichhnair, 1997 Levy Doherty, 1986). The simplifled method that was offered before for the columns with one feed (Stichlmair, Offers, Potthof, 1993) was developed in the work (Glanz Stichlmair, 1997). 

Locations of reversible distillation trajectories depends on position of pseudoproduct point (i.e., on compositions and on flow rates of feeds and of separation products, as is seen from Eq. [6.3]). Difference from the top and bottom sections appears, when the pseudoproduct point of the intermediate section is located outside the concentration simplex (i.e., if concentrations of some components x j)i obtained from Eq. [6.3], are smaller than zero or bigger than one), which in particular takes place, if concentration of admixture components in separation products are small components (i.e., at sharp separation in the whole column). The location of reversible distillation trajectories of the intermediate sections at x j i < 0 or x, > 1 differs in principle from location of ones for top and bottom sections, as is seen from Fig. 6.3 for ideal three-component mixture (Ki > K2 > K3) and from Fig. 6.4 for ideal four-component mixture (Ki > K2 > K3 > K4). 

For three-component mixtures, these kinds of complexes can be easily obtained from three splits of three-component mixture in the first in motion column of the... 

Later, these columns were independently rediscovered (Petlyuk, Platonov, Slavinskii, 1965 Platonov, Petlyuk, Zhvanetskiy, 1970) on the basis of theoretical analysis of thermodynamically reversible distillation because this distillation complex by its configuration coincides with the sequence of thermodynamically reversible distillation of three-component mixture (see Chapter 4), but in contrast to this sequence it contains regular adiabatic columns. The peculiarities of Petlyuk columns for multicomponent mixtures are (1) total number of sections is n(n - 1) instead of 2(n - 1) in regular separation sequences (2) it is sufficient to have one reboiler and one condenser (3) the lightest and the heaviest components are the key components in each two-section constituent of the complex and (4) n components of a set purity are products. 

The main purpose of design calculation is to determine necessary tray numbers for all sections at fixed values of mode parameters. At design calculation, one takes into consideration the equality of compositions at the tray of output of the side product obtained at the calculation of the second and third columns. Each two-section column entering into a Petlyuk column is calculated with the help of algorithms described before for two-section columns. The algorithm of calculation for splits with a distributed component is used for the first column, the algorithms for the direct and the indirect sphts are used for the second, and the third columns at separation of a three-component mixture, respectively. At separation of multicomponent mixtures, the algorithms for intermediate separation are used. 

For azeotropic mixtures, the main difficulty of the solution of the task of synthesis consists not in the multiplicity of feasible sequences of columns and complexes but in the necessity for the determination of feasible splits in each potential column or in the complex. The questions of synthesis of separation flowsheets for azeotropic mixtures were investigated in a great number of works. But these works mainly concern three-component mixtures and splits at infinite reflux. In a small number of works, mixtures with a larger number of components are considered however, in these works, the discussion is limited to the identification of splits at infinite reflux and linear boundaries between distillation regions Reg° . Yet, it is important to identify all feasible splits, not only the spUts feasible in simple columns at infinite reflux and at linear boundaries between distillation regions. It is important, in particular, to identify the spUts feasible in simple columns at finite reflux and curvilinear boundaries between distillation regions and also the splits feasible only in three-section columns of extractive distillation. 

Such an approach was used in the works (Petlyuk Platonov, 1965 Petlyuk, Platonov, Slavinskii, 1965) and in more detail in Agrawal and Fidkowski (1998, 1999). In the latter works the comparison not only of sequences of simple columns, but also of distillation complexes, was made for three-component mixtures. Capital costs can differ considerably for such separation flowsheets, but in this case it is not important because energy expenditures greatly exceed capital ones. 

Some examples of separation of three-component mixtures using curvature of separarix fines are described in Chapter 3. Examples of the application of entrainers forming heteroazeotropes and of columns with decanters for het-eroazeotropic and heteroextractive distillation are given in Chapter 6. 

The economics of the various methods that are employed to sequence multicomponent columns have been studied. For example, the separation of three-, four-, and five-component mixtures has been considered (44) where the heuristics (rules of thumb) developed by earlier investigators were examined and an economic analysis of various methods of sequencing the columns was made. The study of sequencing of multicomponent columns is part of a broader field, process synthesis, which attempts to formalize and develop strategies for the optimum overall process (45) (see Separation systems synthesis). 

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