Separations quasisharp

Figure 5.18. The tangential pinch in rectifying section for the acetone(l)-benzene(2)- chloroform(3) mixture for the split 1,3 2 (a) sharp separation (the tangential-pinch region Regj g not shaded), (b) quasisharp separation. 1, 2, 3, different values of L/V and different iso-f 2 lines (thin hues) SN, saddle-node point.

If sharp separation is feasible, then product points at real separation can be located as much as one wants close to vertexes or sides of concentration triangle. We call such separation quasisharp one. If sharp separation is not feasible (i.e., at supposed sharp separation product point does not get into possible product segment Reg or Reg ), neither is quasisharp separation. In this case, only nonsharp separation is feasible, for that there is some minimum feasible content of admixture component or components. We call the separation at minimum feasible content of admixture component or components f/te best non-sharp one. 

Figure 5.20. The trajectories of rectifying section for quasisharp separation of the ideal mixture. (L/Vjs = 1, (L/V)2 > (L/V)2 > (L/V)i, the region between the reversible-distillation trajectory and the distillation trajectory underinflnite reflux is shaded. qS, quasistationary point.

At nonsharp separation tear-off point is absent because it is located outside the concentration simplex. However, for practical purposes, it is expedient to examine the separation, close to sharp one, which assumes the content of admixture components in products to be small (quasisharp separation). With this approach, one can examine the same stationary points 5. . . A+, as for the corresponding absolutely sharp separation, bearing in mind, that trajectories of quasisharp process go not through the stationary points themselves, but close to them (through quasistationary points). That allows to use the theory of sharp separation trajectories bundles for the solution of practical tasks, for which distillation process cannot be absolutely sharp (i.e., besides product components, each product contains also admixture components). 

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. 

At quasisharp separation with one distributed component in the mode of minimum reflux zone of constant concentrations is available only in one of the sections (in that, trajectory of which goes through point 5 ). 

At quasisharp separation, possible product composition regions Rego and RegB grow at the decrease of purity of the products. Boundaries found for sharp separation deliberately ensure possible splits for quasisharp separation, but, if it is necessary, the widened boundaries for the set purity can be found. 

Figure 6.14 shows trajectories of the intermediate section for separation 1 1, 2 3 at different modes. Pseudoproduct points ( > — Dj+D) is located at side 1-2, and joining of the intermediate and bottom sections in the mode of minimum reflux goes on in the same way as for the simple column at indirect split. Trajectory of the intermediate section r tears off from side 1-2 in point Sn, and point of side product xd can coincide with point Sn (Fig. 6.14a) or lie at segment 1 - Sri (Fig. 6.14b). The first of these two modes is optimal because the best separation between top and side products (the mode of the best separation) is achieved at this mode. Zones of constant concentrations in the top and intermediate sections arise in point Sri = AC2- Therefore, in the mode of minimum reflux in the intermediate section, there are two zones of constant concentrations. At the reflux bigger than minimum, point 5 1 moves to vertex 2 and at i = oo this point reaches it (i.e., at i = 00, pure component 2 can be obtained in the infinite column as a side product). Therefore, for the colunuis with side withdrawals of the products, the mode of the best separation under minimum reflux corresponds to joining of sections in points 5 1 and of the trajectory bundle of the intermediate section (at sharp separation) or in its vicinity (at quasisharp separation). The trajectory of the column with a side product at minimum reflux at best separation may be described as follows ...

Minimum reflux mode is determined by the conditions of joining of trajectories of two sections adjacent to the feed cross-section. Therefore, the interconnected parameters (L/V) " and (V/L) " are determined initially for these two sections. Compositions in points x and x g are calculated preliminarily for these sections at set requirements to compositions of all the products at the conditions of sharp or quasisharp separation in each section. Minimum reflux mode is calculated in the same way as for the simple column that separates initial raw materials into products of compositions x jy and x g. Liquid and vapor flow rates for the other sections are calculated at the obtained values of (L/V) " and (L/L)f" with the help of material balance equations (strictly speaking, with the help of equations of material and thermal balance). 

Section trajectories at quasisharp and nonsharp separation and at reflux bigger than minimum are examined below. At quasisharp separation, each product of the column contains, besides the product components itself, small amounts of impurity components, mostly of the key nonproduct component. The purpose of separation is to obtain in each product a prescribed set of product components at a prescribed summary concentration of impurity components. 

Sj - and to the product boundary elements of the concentration simplex (i.e., with respect to the boundary elements in the vicinity of which the product points are located). We note that at quasisharp separation stationary points 5 and 5/ are absent inside the concentration simplex (they are located outside it close to the product boundary elements), but there are separatrix bundles 3QdRegJ (5/ - 5 - N/). These separatrix bundles iso-... 

Similarly, for the bottom section, the ends of segment [xf]f are (xf)f and (x f Yun- Point (xf )f corresponds to point (x )) and point (x )Jj corresponds to point (x5 i)to (Fig. 7.1c). In the first case at quasisharp separation, there is an infinite number of trays in the top section and the smallest number in the bottom section, and vice versa in the second case. 

The smallest summary number of trays of two sections at quasisharp separation corresponds to some middle location of points (x/ i)Jj and xf)f. Such compositions in the feed cross-section are optimal. 

Specifying Step 4 is to be taken a few times to ensure the set precision. The column trajectory at quasisharp separation, with the calculation finished, may be presented as follows ... 

At reflux bigger than minimum and at quasisharp separation with distributed component at the set distribution of this component among the products, there is the only one composition at the first tray above the feed cross-section expressed by point X/-1 in the vicinity of separatrix sharp spht region Re p (5/ - - N ) and the only one composition at the first tray below the feed cross-section expressed by point Xf in the vicinity of separatrix sharp split region Reg p - N )- The less sharp is separation the farther from separatrix sharp split trajectory bundles of the sections the composition points in the feed cross-section are located. 

At calculation by method tray by tray from the ends of the column for quasisharp separation, the calculation section trajectories are attracted to separatrix line - 5. At direct and indirect spUts, calculation tray by tray should be carried out in the upward or downward direction correspondingly. 

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