Distillation trajectory bundle

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 ... 

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. 

Such a set of trajectories for which not more than one trajectory passes through each nonsingular point is convenient for understanding as a distillation trajectory bundle. This notion is different for various modes of distillation because the number of parameters influencing the location of the trajectories is different. 

The region of reversible distillation can contain one or several reversible distillation trajectory bundles (lines of stationarity). Some of these bundles can be true some of them can be fictitious. Fictitious bundles always have two node points and true ones have one node point or no node point. 

Let s examine the analysis of structure of reversible distillation trajectory bundles at the concrete example of four-component mixture acetone(l)-benzene(2)-chloroform(3)-toluene(4). At the beginning, the segments of the components order Regff at the edges of the concentration tetrahedron are defined by means of scanning and calculation of the values Ki (Fig. 4.13a). The corresponding regions of components order Reg in the tetrahedron are shown in Fig. 4.13b and in its faces - in Fig. 4.14. The whole face 1-2-3, where the component 4 that is absent... 

The notion of distillation trajectory bundles at Unite reflux and at fixed product composition, which is important for the further development of the theory, was... 

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. 

It is seen from Fig. 5.2 that the distillation trajectory bundle of the one-section column fills up some triangle Regf, the vertexes of which are the stationary points. Some of these stationary points are located inside the concentration triangle and the rest of them outside it (i.e., they are of theoretical nature). The triangle filled up with trajectory bundle is called distillation triangle. 

The analogous situation arises in the case if reversible distillation trajectory bundle does not have node points. For the mixture under consideration, such reversible distillation trajectories are available for the top product points, located... 

So far, discussing distillation trajectories and their bundles, we proceeded from the fact, that separation stages are equilibrium ( theoretical plates). In real separation process at plates of distillation columns equilibrium is not achieved and the degree of nonequilibrium is different for different components. That leads to decrease of difference between compositions at neighboring plates and to change of curvature of distillation trajectories (Castillo Towler, 1998), but does not influence the location of stationary points of distillation trajectory bundles because in the vicinity of stationary points equilibrium and nonequilibrium trajectories behave equally. Therefore, implemented above analysis of the structure and of evolution of section trajectory bundles is also valid for nonequilibrium trajectory bundles. 

Petlyuk, F. B., Danilov, R. Yu. (2001b). Theory of Distillation Trajectory Bundles and Its Application to the Optimal Design of Separation Units Distillation Trajectory Bundles at Finite Reflux. Trans IChemE, 79, Part A, 733-46. 

This situation is explained by the fact that the above-described algorithms do not take into consideration the regularities of location of distillation trajectory bundles in the concentration space. 

Trajectory Bundles Under Infinite Reflux Distillation Diagrams... 

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). 

Knowledge about the regularities of the trajectory bundles arrangement under the finite reflux provides an opportunity to develop the reliable and fast-acting algorithm to fulfill design calculations of distillation to determine the required number of trays for each section. 

Generally speaking, for the first and second fractionation classes under the minimum reflux mode, the points of compositions in the zones of constant concentrations (i.e., stationary points of the trajectory bundles) should be arranged at the trajectories of reversible distillation built for the product points. It follows from the conditions of the material balance and the phase equilibrium in the zones of constant concentrations. Figure 2.11b illustrates the partially reversible process (it is reversible in the colunm parts that are from the constant concentration zones for the minimum reflux mode up to the column ends). 

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. 

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. 

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. 

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). 

As far as stationary points of trajectory bundles of distillation at finite reflux lay on trajectories of reversible distillation, these trajectories were also called the lines of stationarity (pinch lines, lines of fixed points) (Serafimov, Timofeev, Balashov, 1973a, 1973b). These lines were used to deal with important applied tasks connected with ordinary and extractive distillation under the condition of finite... 

Significance of reversible distillation theory consists in its application for analysis of evolution of trajectory bundles of real adiabatic distillation at any splits. Numerous practical applications of this theory concern creation of optimum separation flowsheets determination of optimum separation modes, which are close to the mode of minimum reflux and thermodynamic improvement of distillation processes by means of optimum intermediate input and output of heat. 

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)... 

In other words, for sharp separation in a two-section column it is necessary that the feed point belongs to the intersection of true bundles of reversible distillation trajectories of the two sections Xf e (Regrev.r Reg v. ) (Fig. 4.10). The reversible... 

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). 

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. 

Trajectories Bundles of Reversible Distillation for Multicomponent Mixtures 93... 

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. 

Nrev of the trajectory bundle at different pseudoproduct points. The location of point and of the whole trajectory of extractive reversible distillation depends on that of the pseudoproduct point x (i.e., on the ratio E/F between the flow rates of the entrainer and the main feeding). Changing the parameter E/F, we get the trajectory bundle of extractive reversible distillation that, for an ideal mixture, fills up the whole concentration triangle. 

Let s examine now the structure of trajectory bundles of sharp reversible distillation for the intermediate (extractive) section of the column with two feedings at separation of different types of azeotropic mixtures, the way we did it for the top and the bottom sections (Fig. 4.21). While composing these diagrams, we used, just as we did before, the data on the phase equilibrium coefficients of present and absent components at the sides of the concentration triangle and the general regularities of the location of the trajectory bundles of sharp reversible distillation. 

I. Define the main notions (1) region of reversible distillation of top Reg g bottom Reg -e, and intermediate sections Reg g (2) regions of trajectory tear-off Reg and Reg (3) region of possible product points of sharp reversible distillation Reg, Reg, and Reg and (4) node of trajectory bundle of reversible distillation Nrev-... 

Can trajectory bundle of reversible distillation go outside the boundaries of distillation region Reg°° ... 

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