Possible Product Composition Regions

If product point Xd or xp belongs to the possible product point region Reg or Regg, the condition [Eq. (4.19) or (4.20)] is valid in one or two points along the trajectory of reversible distillation located at (n - 1) component boundary element C i of the concentration simplex (i.e., there is one tear-off point xj v of the trajectory or there are two x )- In the last case, right side of the expression [Eq. (4.19) or (4.20)] should have an extremum. 

Therefore, Eqs. (4.19) and (4.20) allow determination of the boundaries of the possible product composition region Reg, or Reg at sharp reversible distillation in (n - l)-component boundary elements C i of the concentration simplex. 

In Fig. 4.9b, there are two tear-off points xA of the reversible distillation trajectory for any point xp of the possible product composition segment Regg at side 

The traj ectory goes from one of these points x one x[l the trajectory goes to = 13 ( xp 

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In Fig. 3.8, bundles of c-lines for some types of azeotrope mixtures are shown and, in Fig. 3.9, possible products compositions regions at R = oo and at the given feed compositions xp. 

It follows from the aforesaid that sharp separation in a reversible distillation column is feasible only if the liquid-vapor tie-line of feeding is directed to the possible product composition region Reg at the boundary element C i of the concentration simplex and from region Reg at other boundary element... 

If the feed point lies on the a-line, a-surface, or a-hypersurface, then the liquid-vapor tie-Une of feeding is directed to some (n — 2)-component boundary element or from some (n — 2)-component boundary element. It along with that the liquid-vapor tie-Une is directed to the possible product composition region at this boundary element or from this region, then the product of reversible distillation section can contain n — 2 components. For example, if the feed point in Fig. 4.10c lies on the 23-Une within the true bundle of bottom section trajectories then the liquid-vapor tie-Une of feeding is directed to vertex 1 [i.e., the component 1 = Reg can be a product of the section (the product contains n — 2 components)]. 

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). 

The location of trajectory bundles and possible product composition segments at reversible distillation of three-component mixtures determines the location of trajectory bundles, and of possible product composition regions of multicomponent mixtures and the locations of trajectory bundles of real adiabatic columns. 

To define the frame of possible product composition regions Reg, or RegB at the edges of concentration simplex, it is enough to determine values of phase equilibrium coefficients in the points of edges for the components present and for the component, which is absent in the product. 

At quasisharp separation, possible product composition regions Rego and RegB grow at the decrease of purity of the products. Boundaries found for sharp separation deliberately ensure possible splits for quasisharp separation, but, if it is necessary, the widened boundaries for the set purity can be found. 

The required information about the distillation boundary is obtained from the pinch distillation boundary (PDB) feasibility test [8]. The information is stored in the reachability matrix, as introduced by Rooks et al. [9], which represents the topology of the residue curve map of the mixture. A feasible set of linear independent products has to be selected, where products can be pure components, azeotropes or a chosen product composition. This set is feasible if all products are part of the same distillation region. The singular points of a distillation region usually provide a good set of possible product compositions. The azeotropes are treated as pseudo-components. 

As we will see in Chapter 3, the distillation region and subregion characterize those possible product compositions that can be produced from the given feedstock composition by distillation under one of the most important modes, in particular, under the infinite reflux mode. 

The main difference between the azeotropic mixtures (and also nonideal zeo-tropic mixtures) and the ideal ones are that, to determine possible sphts of an azeotropic mixture, special analysis is required. The availability of a few distillation regions under the infinite reflux Reg can result in sharp separation becoming completely impossible or in a decrease in sharp splits number. Let s note that for ideal mixtures the fine of possible products compositions atR = ooandiV=oo and set feed composition goes partially inside the concentration simplex and partially along its boundary elements. For azeotropic mixtures, this line can go along the boundary elements of the distillation region (Fig. 3.6a, line 2). 

The application of the superstructure for the separation of azeotropic mixtures requires some modifications. Separation is limited by azeotropes and the corresponding distillation boimdaries, which form distillation regions [7]. For a feasible separation, top and bottom product composition have to be in the same distillation region. Boundary crossing (where the feed and the two product compositions are located in different distillation regions) is possible in the presence of curved distillation boundaries, but is not considered in this work. 

If the bottom product point lies in the possible composition region Regf in... 

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