Section trajectory bundles structure

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 turn now to the mixtures with any number of components, and let s discuss general conditions of existence of sections trajectory bundles and their structure. 

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. 

In Chapter 5, to develop a general algorithm of calculation of minimum reflux mode for columns with one feed, we had to understand the location of reversible distillation trajectories and the structure of top and bottom section trajectory bundles. 

We now examine the structure of intermediate section trajectory bundle for four-component mixtures at the example of ideal mixture (ATi > K2 > > K4). 

The general approach to design calculation of extractive distillation columns is similar to the approach applied for two-section columns. We use our notions about the structure of intermediate section trajectory bundles (see Sections 6.4 6.6), about possible compositions at the trays adjacent to the feed cross-section from above and below (see Section 7.2), and about possible directions of calculation... 

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. 

We examine the structure of trajectory bundles of intermediate sections (i.e., location and character of the stationary points of these bundles). 

The analysis carried out above (see Figs. 6.8 and 6.9) allows for a general conclusion about dimensionality, structure, and evolution of trajectory bundles (regions) of intermediate section at sharp extractive distillation for any multicomponent mixtures. 

Before examining minimum reflux mode for complexes with branching of flows, we discuss complex columns with side withdrawals of flows. Side products of such columns cannot be pure components at finite reflux, but the number of components in each side product can differ from the number of components in the other side products, in the initial mixture, and in the top and bottom products. In such complex columns in each section, the number of components at the exit from the section is smaller, than at the entrance. The simplest example of separation is 1 1, 2 3 (Fig. 6.14). In this case, side product 1,2 is withdrawn above feed. Such splits are sharp. We confine oneself to examining of complex columns with sharp splits. The pseudoproduct of each intermediate section of the column with side withdrawals of products is the sum of all the products above (below) the section under consideration, if this section itself is located above (below) feed. For such splits, all the pseudoproduct points of the intermediate sections are located at the boundary elements of concentration simplex. Therefore, the structure of trajectory bundles for the intermediate sections does not differ from the structure of trajectory bundles for the top or bottom sections at sharp separation. 

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. 

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