Three-component mixtures section trajectories

Figure 4.11. Sharp reversible section diagrams of some structures of three-component mixtures. 1,3.4a,..., classification according to Gurikov (1958). Double line, possible composition of overhead product Reg thick solid line, possible composition of bottom product Reg dotted lines with arrows, reversible section trajectories 123,132,312. regions of component order Reg dotty lines, separatrixes thin hues, a-lines.

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. 

Structure and Evolution of Section Trajectory Bundles for Three-Component Mixtures... 

To understand the structure of section trajectory bundles for multicomponent mixtures and their evolution with the increase of reflux number, let s examine first three-component mixtures, basing on the regularities of distillation trajectory tear-off at finite reflux and the regularities of location of reversible distillation trajectories. 

Evolution of Section Trajectory Bundies for Three-Component Mixture 139... 

General regularities of the evolutions of sections trajectory bundles, discussed in the previous section for three-component mixtures, are valid also for the mixtures with bugger number of components. Figure 5.23 shows evolution of top section trajectory bundle at separation of four-component ideal mixture, when the product is pure component (i.e., at direct split) Ki > K2 > >... 

The example of tangential pinch for four-component mixture is quasisharp separation of azeotropic mixture acetone (l)-benzene (2)-chloroform (3)-toluol (4) of composition Xf (0,350 0,250 0,150 0,250) at intermediate split 1,3(2) 2,4(3) (admixture components heavy and light key are in brackets correspondingly) at the following composition the products xd (0,699 0,001 0,300,0) and xb (0 0,500 10 0,500). The same top product composition, as in the previous example (Fig. 5.18b) of separation of three-component mixture in the top section, is accepted for convenience of analysis. In this case, the boundary elements of top section trajectory bundle, located in face 1-2-3, completely coincides with top section trajectory bundle at separation of previously mentioned three-component mixture. 

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). 

We now examine the four-component mixture for = 2 (Fig. 6.9a). The conditions of joining of section trajectories at a set flow rate of the entrainer in the mode of minimum reflux in the cases of top or bottom control feed do not differ from the conditions for three-component mixtures discussed above. In the case of bottom... 

Numerous works (Levy, Van Dongen, Doherty, 1985 Levy Doherty, 1986 Julka Doherty, 1990) in which distillation trajectory bundles of three-and four-component mixtures for two sections of distillation column were used at hxed product compositions and at different values of reflux (vapor) number, are of great importance. They defined the conditions of two section trajectories joining in the feed cross-sections of the column in the mode of minimum reflux, and they developed the methods of this mode calculation for some splits. 

Availability of these conditions allowed Underwood (1948) to obtain general solution, connecting separation product compositions at minimum reflux with the mode parameters (e.g., with Vr and U ). Even before (Hausen, 1934,1935), distillation trajectories of the ideal mixtures in the one-section columns (Fig. 5.1a) were investigated by means of calculation, and it was shown that the part of distillation trajectory located inside the concentration triangle is rectilinear for the ideal mixture (Fig. 5.1b). Later, linearity of distillation trajectories of three-component ideal mixtures at sharp separation was rigorously proved (Levy et al, 1985). 

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. 

This develops the general algorithm of calculation of minimum reflux mode for the columns with two feed inputs at distillation of nonideal zeotropic and azeotropic mixtures with any number of components. The same way as for the columns with one feed, the coordinates of stationary points of three-section trajectory bundles are defined at the beginning at different values of the parameter (L/V)r. Besides that, for the intermediate section proper values of the system of distillation differential equations are determined for both stationary points from the values of phase equihbrium coefficients. From these proper values, one finds which of the stationary points is the saddle one Sm, and states the direction of proper vectors for the saddle point. The directions of the proper vectors obtain linear equations describing linearized boundary elements of the working trajectory bundle of the intermediate section. We note that, for sharp separation in the top and bottom sections, there is no necessity to determine the proper vectors of stationary points in order to obtain linear equations describing boundary elements of their trajectory bundles, because to obtain these linear equations it is sufficient to have... 

To analyze variants of autoextractive distillation with one-component entrainer and one-component top product, it is sufficient to examine edges of concentration pentahedron one of the components of the edge should be the entrainer, and the other one should be the top product. The rest of the components absent at the edge should have intermediate volatilities. The segments Re of trajectory tear-off of intermediate section at separation of three- and four-component constituents of five-component mixture are marked out in Fig. 8.20 at edges that do not contain binary azeotropes. As one can see in this figure, one can separate all three-component constituents and some of the four-component constituents of five-component mixture under consideration by means of autoextractive distillation with one-component entrainer and top product, but it is impossible to separate five-component mixtures itself this way. 

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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