Distillation trajectories

In this section we wish to look in more detail at the nonideal behavior of mixtures of a given set of species. We shall start by examining residue and distillation trajectory plots that show the vaporAiquid behavior of mixtures when... 

The ethanol column (C-1) has practically only stripping zone. Fig. 9.31-left shows composition profile both for liquid and vapour phase. The examination of the composition profiles highlights the role of the entrainer. In the zone close to the top the benzene extracts the ethanol in the liquid phase, and as a result increases the volatility of water, so that on lower stages the water is completely removed. In the lower part practically only the binary ethanol/benzene remains. The distillation trajectory starts from the ternary azeotrope, goes along the ethanol/ benzene saddle and terminates in the ethanol vertex. Because the boiling point of the azeotrope ethanol-water is close to the pure ethanol, the profile could easily jump to the ethanol/water azeotrope. Consequently, the design and operation of the column (C-1) is very sensitive. 

The system [Eq. (2.1) (2.4)] may be solved only by iteration, and the solution is not always immediately obtained, so it requires a high degree of initial approximation. As a result of the system [Eq. (2.1) (2.4)] solution at the preset number of theoretical trays in each section, we get not only the compositions of products XiD and xib, but also the compositions on all trays Xij and yij - profiles of concentrations along the column length, or distillation trajectories, that come to be the basic subject of this book. 

Just as in the case of the inflnite reflux, the broken lines can be replaced by the continuous curves. The distillation trajectories under the finite reflux, first, are different for two column sections and, second, have the composition points of the corresponding product (xio or xib) as parameters as well as reflux ratio or reboil ratio (RotS). 

In the case of the reflux ratio alteration and conservation of the product composition, the stationary points of trajectory bundle are traveling along the reversible distillation trajectories built for a given product, so the trajectories may be called lines of stationarity. Thus, the analysis of the reversible distillation trajectory arrangement in the concentration simplex is decisive in general geometric theory of distillation. 

Figure 2.13. (a) A heteroazeotropic column with decanter, (b) the distillation trajectory of heteroazeotropic column for separation of benzene(l)-isopropil alcohol(2)-water(3) mixture (benzene-entrainer). xli and xl2, two liquid phases xp, initial feed xp+p, total feed into column region of two liquid phases is shaded. 

Due to the entrainer and the decanter, it is possible to separate binary azeotropic mixture Xf into products xb (almost pure isopropyl alcohol) andx/) (contaminated water), which may be purified easily in the second column. Point xd Fes not on the distillation trajectory but on the liquid-liquid tie line (xd=xi2). 

What is the stationary point of the distillation trajectory bundle ... 

What is the arrangement of the distillation trajectory bundles under infinite and finite reflux modes dependent on ... 

The important advantage of mixture separability analysis for each sharp split consists of the fact that this analysis, as is shown in this and three later chapters, can be realized with the help of simple formalistic rules without calculation of distillation. A spht is feasible if in the concentration space there is trajectory of distillation satisfying the distillation equations for each stage and if this trajectory connects product points. That is why to deduct conditions (rules) of separability it is necessary to study regularities of distillation trajectories location in concentration space. 

The investigation of regularities of distillation trajectories location in infinite columns under infinite reflux is directed to the solution of the task of determination of possible splits. 

Analogy Between Residue Curves and Distillation Trajectories... 

The question of the refiux at which these splits are achievable in real columns and of how, along with that, the distillation trajectory is located in the concentration space is discussed in Chapter 5. Here, we investigate only the splits themselves. 

For azeotropic mixtures, not all the practically interesting splits are feasible at the infinite refiux. However, the sequencing should have the infinite reflux mode as its starting point because these splits are the easiest to realize at finite reflux. That is why we start systematic examination of distillation trajectories with the infinite reflux rate. It is also proved to be correct because the regularities of trajectories locations for this mode are the simplest. 

Investigations of residue curves have been conducted for over 100 years, beginning Ostwald (1900) and Schreinemakers (1901). Later, close correspondence between residue curves (i.e., curves of mixture composition change in time at the open evaporation) and distillation trajectories at infinite refiux (i.e., lines of mixture composition change at the plates of the column from top to bottom) was ascertained. 

For distillation trajectories at the infinite reflux, see Chapter 2 Thormann (1928).]... 

The distillation trajectory under infinite reflux is a line of conjugated liquid-vapor tie-lines, each of which corresponds to one of the column plates, in accordance with Eq. (3.2). In the works (Zharov, 1968 Zharov Serafimov, 1975), the broken line of conjugate hquid-vapor tie-lines is replaced with a continuous c-line, for which the liquid-vapor tie-hues are chords (Fig. 3.1a). At the same time it follows from Eq. (3.1) that the hquid-vapor tie-line is a tangent to the residue curve. Therefore, hquid-vapor tie-line, on the one hand, is a tangent to residue curve and, on the other hand, is a chord of the c-line. This fact determines the similarity and the difference between the residue curves and the c-lines (see Fig. 3.1b). In Fig. 3.1c, it is shown that the distillation trajectory under the infinite reflux (c-hne) crosses the set of residue curves. 

Taking into consideration the aforesaid, sections of Chapter 1 referring to residue curves bundles, to the structural elements of these bundles, and to the matrix description of the concentration space structure are completely valid regarding distillation trajectories under the infinite reflux. 

Distillation Trajectories of Finite and Infinite Columns at Set Feed Composition... 

Obviously, at a flnite number of stages, the distillation trajectory under the infinite reflux should he in one of the c-lines and cannot pass through a stationary point of the concentration simplex, start or end in it. At the infinite number of... 

As far as c-lines cannot cross each other and boundary elements of concentration simplex are filled with their c-lines bundles, c-lines cannot pass from the internal space of the simplex to its boundary element. Therefore, the distillation trajectories at the infinite reflux can lie completely inside the concentration simplex or inside its boundary elements. 

Figure 3.2. P roduct points and distillation trajectories under infinite refiux for different number of trays (a) semisharp split, (b) sharp direct split, and (c) split with distributed component. Ideal mixture K > Ki> K/),xd( ),xd(1),xd(3), xb(i), xb(2),(3). product points for different number of trays, xp = const, D/F= const short segments with arrows, conjugated tie-lines hquid-vapor (distillation trajectories under infinite reflux) thick solid lines, lines product composition for different number of trays.

Thus, the distillation trajectory in this case consists of two parts. The first part is located in the boundary element Reg the top product point belongs to it joins the top product point xd with the stable node of this boundary element. The second part is located in the boundary element Reg bottom product point belongs to - it joins the unstable node of this boundary element with the bottom product point. In Fig. 3.2b, the top product point coincides with a boundary element of zero dimensionality - vertex 1. In this case, trajectory consists of the same two parts - the whole side 1-2 and part of the side 2-3... 

Let us examine the case of four-component mixture (Fig. 3.4). Let us consider the split 1 2,3,4. The distillation trajectory goes from vertex 1 = Regz> at edge 1-2, to vertex 2 and further inside face 2-3-4 = Regs by c-line to the bottom point Xb... 

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... 

Figore 3.19. Example of determiDation whether the feed point (Kg. 3.14a) belongs to the prodnct simplex Regsimp (only the distillation region Reg°° = 12 13 is shown). Material balance lines and distillation trajectories at i =... 

At R = oo and N = oo, distillation trajectories bundles fill up distillation regions Reg°° in concentration simplex limited by node and saddle stationary points (points of components and azeotropes) and by boundary elements of various dimensionality, part of which are located at boundary elements of concentration simplex and part of which are located inside it. 

In addition, the product points should lie on the straight hne passing through the liquid-vapor tie-line of feeding. Hence, it follows that the maximum length of reversible distillation trajectory is achieved at the intersection of this straight line with the hyperfaces of concentration simplex that (hyperfaces) correspond to (n - 1)-component constituents C i of the initial mixture (sharp separation). 

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