Trajectory Bundles Under Finite Reflux

If all the trajectories coming from the stationary point, in this case, such stationary point is called the unstable node (vertex 1). The stationary point to which the trajectories get in is called the stable node A+ (vertex 3). At last, the stationary point that all trajectories bend around is called a saddle point S (vertex 2). 

In Fig. 2.4b, another example of the trajectory bundles is shown (let s call the picture of trajectory bundles a distillation diagram), but already for a three-component azeotropic mixture acetone(l)-benzene(2)-chloroform(3). 

In this case, we have two trajectory bundles, differing by their unstable nodes and separated from each other with a specific trajectory, which begins not at the unstable node, but in a saddle (azeotrope 13 of maximum temperature) and is called the separatrix. 

To return to Eqs. (2.3) and (2.5) for the rectifying section and to fix x, d and R parameters, we obtain a number of points x, by solving this system from the upper tray. 

The concentration profile of the rectifying section under reflux R and an overhead product composition Xi d will be represented by broken lines, the lengths of which come through points Xij, which are found by means of solving Eqs. (2.3) and (2.5). 

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Figure 2.5. Trajectory bundles under finite reflux of ace-tone(l)-benzene(2)-chloroform(3) azeotropic mixture for (a) rectifying and (b) stripping section. Solid lines with arrows, trajectories solid Une, a-hne dotty hne, separatrix under infinite reflux big circles, stationary points nnder infinite reflux tittle circles, stationary points nnder finite reflnx.

Calculation investigations (Petlyuk, 1978 Petlyuk Vinogradova, 1980 Shafir et al., 1984) determined the conditions under which saddle and saddle-node stationary points of sections trajectory bundles at finite reflux arise inside the concentration simplex, but not only at its boundary elements, promoted the development of this trajectory bundles theory. 

What is the arrangement of the distillation trajectory bundles under infinite and finite reflux modes dependent on ... 

Knowledge about the regularities of the trajectory bundles arrangement under the finite reflux provides an opportunity to develop the reliable and fast-acting algorithm to fulfill design calculations of distillation to determine the required number of trays for each section. 

As far as stationary points of trajectory bundles of distillation at finite reflux lay on trajectories of reversible distillation, these trajectories were also called the lines of stationarity (pinch lines, lines of fixed points) (Serafimov, Timofeev, Balashov, 1973a, 1973b). These lines were used to deal with important applied tasks connected with ordinary and extractive distillation under the condition of finite... 

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. 

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