Three-component mixtures 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.

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. 

Diagrams of reversible distillation of various types of three-component mixtures can be obtained in various ways with the help of the model of phase equilibrium describing these types of mixtures. It is possible to calculate the trajectory consequently for each chosen product point using Eq. (4.6) (4.13) and increasing step... 

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. 

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. 

Let s note, that distillation trajectory of three-component mixture for the set product point is located between trajectory at infinite reflux (ie., at L/V = 1, and reversible distillation trajectory) (Kiva, 1976 Petlyuk Serafimov, 1983 Wahn-schafft et al, 1992 Castillo, Thong, Towler, 1998). 

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... 

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 scheme of the reversible process is shown in Fig. 2.10a. Figure 2.10b illustrates a trajectory of the reversible distillation for three-component ideal mixture. 

In Figs. 3.10a, b, distillation trajectories at R = oo and A = oo for two types of three-component azeotrope mixtures are shown. 

In Fig. 3.11, three constituent parts xd Nf, Nf Nf, and Nf xb) of n-component mixture distillation trajectory at R = oo and Af = oo are shown. The term of connectedness establishes mutual location of distillation products feasible points at R = 00 and N = oo. Together with conditions of material balance, the... 

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. 

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. 

The analysis carried out before for three- and four-component mixtures completely corresponds to the above-formulated general conditions of trajectories joining for multicomponent mixtures. 

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. 

Schematic DRDs are particularly useful in determining the implications of possibly unknown ternary saddle azeotropes by postulating position 7 at interior positions in the temperature profile. Also note that some combinations of binary azeotropes require the existence of a ternary saddle azeotrope. As an example, consider the system acetone (56.4°C), chloroform (61.2°C), and methanol (64.7°C) at 1-atm pressure. Methanol forms minimum-boiling azeotropes with both acetone (54.6°C) and chloroform (53.5°C), and acetone-chloroform forms a maximum-boiling azeotrope (64.5°C). Experimentally there are no data for maximum- or minimum-boiling ternary azeotropes for this mixture. Assuming no ternary azeotrope, the temperature profile for this system is 461325, which from Table 13-18 is consistent with DRD 040 and DRD 042. However, Table 13-18 also indicates that the pure-component and binary azeotrope data are consistent with three temperature profiles involving a ternary saddle azeotrope, namely, 4671325, 4617325, and 4613725. All three of these temperature profiles correspond to DRD 107. Calculated residue curve trajectories for the acetone-chloroform-methanol system at 1-atm pressure, as...

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... 

In accordance with the structural conditions of trajectory tear-off, three following variants of extractive distillation are feasible for such a mixture (1) the top product is component 1, the entrainer is component 4, and the pseudoproduct point x j) lies in the continuation of edge 1-4 (Fig. 6.9a) (2) the top product is mixture 1,2, the entrainer is component 4, and the pseudoproduct point hes in continuation of face 1-2-4 (Fig. 6.9b) and (3) the top product is component 1, the entrainer is mixture 3,4, and the pseudoproduct point x lies in the continuation of face 1-3-4 (Fig. 6.9c). 2,3... 

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