Distillation trajectories defined

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... 

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. 

The significance of the methods, based on the geometric distillation theory, consists in their universality, rigor, and reliability. To obtain the result, it is not necessary to set any estimation parameters and possible separation product compositions minimum reflux number for these compositions and distillation trajectory at this reflux number are defined in the process of this calculation. 

To check conditions that possible product point at some k-component boundary element(Cj j, ) should meet, it is necessary (1) for the product point x or xy under exanunation to construct reversible distillation trajectory inside the product boundary element and (2) to define all the first and second (if they are) reversible trajectory tear-off points x[] and x from the product boundary element into all the adjacent (k + l)-component boundary elements. If there is only one reversible distillation trajectory tear-off point into each adjacent boundary element, the point under examination is possible product point and part of reversible distillation trajectory from the most remote from it tear-off point... 

We previously examined the process of reversible distillation for a given feed point. Below we examine trajectories of reversible distillation sections for given product points located at any -component boundary elements Q of the concentration simplex (xd e C or xg e Q). If / < (n - 1), then in the general case such trajectories should consist of two parts the part located in the same -component boundary element where the product point lies and the part located at some (k+ l)-component boundary element adjacent to it. Along with that, the product point should belong to the possible product composition region Reg or Reg for the examined ( )-component boundary element, and the boundaries of this region can be defined with the help of Eqs. (4.19) and (4.20). 

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. 

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-... 

This develops the general algorithm of calculation of minimum reflux mode for the columns with two feed inputs at distillation of nonideal zeotropic and azeotropic mixtures with any number of components. The same way as for the columns with one feed, the coordinates of stationary points of three-section trajectory bundles are defined at the beginning at different values of the parameter (L/V)r. Besides that, for the intermediate section proper values of the system of distillation differential equations are determined for both stationary points from the values of phase equihbrium coefficients. From these proper values, one finds which of the stationary points is the saddle one Sm, and states the direction of proper vectors for the saddle point. The directions of the proper vectors obtain linear equations describing linearized boundary elements of the working trajectory bundle of the intermediate section. We note that, for sharp separation in the top and bottom sections, there is no necessity to determine the proper vectors of stationary points in order to obtain linear equations describing boundary elements of their trajectory bundles, because to obtain these linear equations it is sufficient to have... 

---