Feed cross-section possible compositions

The second stage, including the selection of the best reflux numbers and the quantity of column section trays, will be the important one. The geometric distillation theory makes it possible to determine the feasible compositions that are to be in trays above and below the feed cross-section, then make the design calculations of the trajectory of sections and determine the best ratio of section tray numbers. The new algorithms allow for an increase in the design quality and apart from that, they make it possible to lower the separation costs and to practically exclude the human participation in the process of calculation. 

However, numerous questions remained unsolved in these works (1) the methods of prediction of possible product compositions for a given feed composition were absent, which does not allow to calculate minimum reflux mode (2) the methods of calculation were good only for two special splits direct and indirect ones, but these methods were not good for the intermediate splits (3) the peculiarities arising in the case of availability of a-lines, surfaces, and hypersurfaces that are characteristic of nonideal and azeotropic mixtures were not taken into consideration and (4) the sudden change of concentrations in the feed cross-section was not taken into consideration. 

The previously enumerated methods of calculation of the minimum reflux mode for nonideal zeotropic and azeotropic mixtures have considerable defects (1) they presuppose preliminary setting of possible separation product compositions, which is a comphcated independent task for azeotropic mixtures (2) they embrace only three- and four-component mixtures or only special splits and (3) they do not take into consideration the leap of concentrations in feed cross-section. 

Distillation Trajectories of Finite Columns Possible Compositions in Feed Cross Section... 

In general, at intermediate sphts and splits with a distributed component, the calculation from one of the ends of the column for such splits encounters large difficulties. Determination of possible compositions in the feed cross-section of the column is of great importance for overcoming these difficulties. To estimate correctly the limits of change of component concentrations at the trays above and below feed cross-section, this limits have to be determined at sharp separation ([ / i] and [x/] ). 

The intermediate split is chosen as illustrating the most general case of separating multicomponent mixtures. To determine the set of composition points at the first trays above and below the feed cross-section at given reflux larger than minimum, we examine first sharp separation and linear regions Reg p (5r - - N+) and Reg p (5 - 5 - iV+). We designate possible compositions in the feed cross-section at these assumptions (x/ and (xf)f . 

Possible composition segments at the first trays above and below the feed cross-section in the real columns [xf i] and [x/] located at vicinity of curvilinear sepa-ratrix manifolds RegJ (5 f - - N ) and RegJ p (5/ - 5 - iV4+), or inside the working trajectory bundles Reg and Reg , correspond to segments and [xfYl. 

The determination of the end coordinates of possible composition segments in the feed cross-section and [xf]f at the assumption about linearity... 

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... 

The main part of the algorithm is the calculation of section trajectories and the determination of optimal tray numbers in the sections at set two mode parameters. This includes in the the same main stages as at the calculation of two-section columns the calculation of reversible distillation trajectories of the three sections the obtaining of linear equation systems for separatrix bundles of the three sections and for the manifolds, including the boundary elements of these bundles and point xp the determination of coordinates of possible composition segments in the feed cross-section and in that of input of the entrainer the calculation of section trajectories by method tray by tray. ... 

At reflux bigger than minimum and at separation without distributed components for all feasible quasisharp splits - the direct, the indirect, and the intermediate ones-possible compositions at the trays adjacent to the feed cross-section from above x/ i and below x/fill some segments [x/ i] and [x/] located in the vicinity of... 

Possible compositions at the trays adjacent to the feed cross-section from above and below for any splits at the assumption about the linearity of separatrix trajectory bundles and about sharp separation [x/ i], xf or (xf i)f , (xf)f can be determined from purely geometric considerations by means of solution of corresponding systems of linear equations. 

Segment of possible feed cross-section coiii-positions the set of possible of feed cross-section composition points x/ i or X/ at reflux greater then minimum. 

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