Intermediate sections reversible distillation trajectories location

This allows us to actively influence the location of the pseudoproduct point of the intermediate section in order to maintain sharp separation (i.e., separation at which the intermediate section trajectory ends at some boundary element of the concentration simplex). This is feasible in the case when inside concentration simplex there is one trajectory of reversible distillation for pseudoproduct point x ) that ends at mentioned boundary element, and there is the second trajectory inside this boundary element. To maintain these conditions, pseudoproduct point x j) of the intermediate section should be located at the continuation of the mentioned boundary element, because only in this case can liquid-vapor tie-hues in points of reversible distillation trajectory located in this boundary element he at the lines passing through the pseudoproduct point x jy. We discuss these conditions in Chapter 4. It was shown that in reversible distillation trajectory tear-off point x[ev e from the boundary element the component absent in it should be intermediate at the value of the phase equUibrium coefficient between the components of the top product and of the entrainer rev,D > Kevj > Kev.s)- This condition is the structural condition of reversible distillation trajectory tear-off for the intermediate section. Mode condition of tear-off as for other kinds of sections consists of the fact that in tear-off point the value of the parameter (LfV) should be equal to the value of phase equilibrium coefficient of the component absent at the boundary element in tear-off point of reversible distillation trajectory ((L/V)m =... 

As in that case, to develop a general algorithm of calculation of minimum reflux mode for columns with several feed inputs, we need to understand the location of reversible distillation trajectories of intermediate sections and the structure of trajectory bundles for these sections. 

Location of Reversible Distillation Trajectories of Intermediate Sections... 

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). 

The dimensionality of intermediate section trajectory bundle is equal to n -m + 1, where n is total number of components, and m is summary number of components of top product and entrainer. Pseudoproduct point is located at the continuation of the boundary element, formed by all the components of the top product and entrainer. Reversible distillation trajectories and the stationary points are located at the mentioned pseudoproduct boundary element and at all boundary elements whose dimensionality is bigger by one (at m = n — 1, they are located inside concentration simplex). 

In the stationary points of the trajectory bundle of the intermediate section, the liquid-vapor tie-lines should be directed to pseudoproduct point of this section that is, in the given case, the point of water phase from decanter xli = Such quasistationary point is point qSm, where the calculated trajectory of the intermediate section changes its direction sharply, and the compositions at neighboring trays are very close to each other (quasizones of constant concentrations), and stationary point Af+ that coincides with the point of ternary heteroazeotrope and stationary point N that coincides with the point of binary azeotrope benzene(l)-isopropanol(2). Point Sm is located at reversible distillation trajectory of the intermediate section joining mentioned points N and Its location at this trajectory... 

This result also remains valid for azeotropic mixtures. A necessary condition for exhausting of the some component in the intermediate (extractive) section at reversible distillation consists of the fact that the whole trajectory of intermediate (extractive) section should be located in the region where this component is intermediate in phase equilibrium coefficient (in the region of reversible distillation of the intermediate section Reg J. The segment of the side containing only the component separated as top product and component brought in as an entrainer is a boundary element of this region Reg l. ... 

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. 

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