Three-component mixtures concentration simplex

At D = Dpr and at i = R in both sections, there are two zones of constant concentrations - in the feed point Xf and in the trajectory tear-off points of sections x from the boundary elements of concentration simplex. For a three-component mixture there is a transition from the first class of fractioning right away into the third class, omitting the second class. At further increase of reflux number, the product compositions do not change any more. 

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). 

We now examine the conditions of joining of sections trajectories at a set flow rate of entrainer (i.e., at set value of the parameter E/D) for a three-component mixture in the mode of minimum reflux. Each of two feeds can be the control one, and the intermediate section trajectory in the mode of minimum reflux in both cases should pass through the saddle point Sm because this trajectory passes through the node point not only in the mode of minimum reflux, but also at reflux bigger than minimum (point arises at the boundary element of the concentration simplex because the extractive distillation under consideration is sharp). 

Chemical system with three isomers (A) coordinates in balance triangle (simplex) (B) levels of the Gibbs free energy C (C) domain of inaccessibility in the vicinity of Aq point X, Y, and Z denote two-component mixtures with equal concentrations (ct/2) of both components ... 

Figure 1.1. Concentration simplexes (a) for binary mixtures, (b, c) for three-component mixtnres. and (d) for four-component mixtnres. xi,X2,xs,X4, concentrations of components.

Azeotropic mixtures can almost never be separated completely into pure components in the sequence of columns without recycles at R = oo and N = oo. The set of products of such a system of columns almost always contains not only pure components, but also azeotropes (pseudocomponents). Mixtures, for which concentration simplex contains only one distillation region, are an exception. For three-component azeotropic mixtures, the only phase diagrams of such type are the diagram shown at Fig. 3.10b and antipodal it. Such a mixture can be separated into two columns and into pure components. Two variants of flowsheet with direct 1 2,3 or indirect 1,2 3 split in the first column are feasible. 

Let s examine two constituent parts of section distillation trajectory at the example of sharp preferable split of three-component ideal mixture (Fig. 5.6a) the part located in the boundary element (the side of concentration triangle), and the part located inside concentration simplex (triangle). There is a trajectory tear-off point from the boundary element x between these two parts. 

Determination of coordinates of ends of segments Reg, Reg, RegJ of trajectory tear-off of top, bottom, and intermediate section at edges of concentration simplex C at separation of initial mixture and of all its constituents with number of components k from three to (n-1). 

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