Section trajectory bundles defined

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... 

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-... 

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 coordinates of points x/ i and Xf are defined at the second stage in accordance with determined at the first stage type of joining of sections trajectories. If, for example, point x/ i hes in bundle — N+ and point Xf lies in bundle 5/ - - A/, then point x/ i can be found as intersection point of linear man-... 

For four-component mixtures at nim = 3 and at two components in the bottom product (Fig. 6.9b), the conditions of joining in the case of bottom control feed are defined by the dimensionality of trajectory bundles N - Sm(d = 1) and (d = 1) and are similar to those of joining of sections trajectories of two-section column in the mode of minimum reflux at intermediate split (see Section 5.6). Point X/-1 should lie on the separatrix min-reflux region Re (N - Sm) and point Xf should lie on the separatrix min-reflux region Re ( - N ). 

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