Three-component mixtures trajectory bundles

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. 

It was shown (Petlyuk, 1986) that the diagram of reversible distillation of any three-component mixture can be forecasted by scanning only the sides of the concentration triangle, defining at each point the values of phase equilibrium coefficients of all the components and using Eqs. (4.19) and (4.20). The latter way defines trajectory tear-off segments Reg or Reg(. y and possible product segments Reg or Reg The node points iV v of the trajectory bundles are determined hypothetically on the basis of the data on the location of azeotropes points and a-points. 

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. 

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. 

Figure 2.4. Trajectory bundles under infinite reflux for (a) three-component ideal and (b) azeotropic mixtures. xd(x) xb(V),xd(2) - a b(2), possible splits solid lines, trajectories dotty line, separatrix under infinite reflux.

In Fig. 2.4b, another example of the trajectory bundles is shown (let s call the picture of trajectory bundles a distillation diagram), but already for a three-component azeotropic mixture acetone(l)-benzene(2)-chloroform(3). 

The analysis of the thermodynamically reversible process of distillation for multicomponent azeotropic mixtures was made considerably later. Restrictions at sharp reversible distillation were revealed (Petlyuk, 1978), and trajectory bundles at sharp and nonsharp reversible distillation of three-component azeotropic mixtures were investigated (Petlyuk, Serafimov, Avet yan, Vinogradova, 1981a, 1981b). 

Let s illustrate the location of trajectory bundles of reversible distillation by the example of three-component acetone(l)-benzene(2)-chloroform(3) mixture with one binary saddle azeotrope with a maximum boiling temperature (Fig. 4.7)... 

Locations of trajectories bundles Regr. of node points of these bundles Nrev, and of possible product segments Reg Wd Regf can be shown in diagrams of three-component azeotropic mixtures sharp reversible distillation for various types of such mixtures (Fig. 4.11). 

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. 

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... 

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