Splits with distributed component

Besides splits without distributed components, we also discuss splits with one distributed component l,2./c-l,/c /c, /c- -l.n. The significance of these splits is conditioned, first, by the fact that they can be realized for zeotropic mixtures at any product compositions, while at two or more distributed components only product compositions, belonging to some unknown regions of boundary elements of concentration simplex, are feasible. Let s note that for ideal mixtures product composition regions at distribution of several components between products can be determined with the help of the Underwood equation system (see, e.g.. Fig. 5.4). This method can be used approximately for nonideal mixtures. From the practical point of view, splits with one distributed component in a number of cases maintain economy of energy consumption and capital costs (e.g., so-called Pet-lyuk columns, and separation of some azeotropic mixtures [Petlyuk Danilov, 2000]). 

The analysis of dimensionaUty of sections trajectory separatrix bundles shows that for splits with one distributed component trajectory of only one section in the mode of minimum reflux goes through corresponding stationary point or (there is one exception to this rule, it is discussed below). The dimensionality of bundle 5 - A4+ is equal to A - 2, that of bundle — iV+ is equal to n — A — 1. The total dimensionality is equal to n - 3. Therefore, points x/ i and Xf cannot belong simultaneously to minimum reflux bundles at any value of LlV)r. If only one of the composition points at the plate above or below the feed cross-section belongs to bundle 5 - A + and the second point belongs to bundle 5 - 5 - A+, then the total dimensionality of these bundles will become equal n - 2 therefore, such location becomes feasible at unique value oi(LjV)r (i.e., in the mode of minimum reflux). 

At quasisharp separation with one distributed component in the mode of minimum reflux zone of constant concentrations is available only in one of the sections (in that, trajectory of which goes through point 5 ). 

The following cases of location of composition points at plates above and below feed cross-section x/ i and xf. (1) point Xf-i lies in rectifying minimum reflux bundle 5 - A+, and point Xf lies inside the working trajectory bundle of the bottom section (at nonsharp separation) or m separatrix bundle 

At some ratio of amounts of the distributed component in the separation products, there is a transitional split between above-mentioned ones both points 

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Figure 3.2. P roduct points and distillation trajectories under infinite refiux for different number of trays (a) semisharp split, (b) sharp direct split, and (c) split with distributed component. Ideal mixture K > Ki> K/),xd( ),xd(1),xd(3), xb(i), xb(2),(3). product points for different number of trays, xp = const, D/F= const short segments with arrows, conjugated tie-lines hquid-vapor (distillation trajectories under infinite reflux) thick solid lines, lines product composition for different number of trays.

Figure 5.5. ifum as function of Z)/Ffor the mixture described in Hg. 5.4. Segments with arrows, intervals of D/F value for different splits with distributed components. At the conversion take place from one split to another. At the conversion take place from second class of fractionation to third. Points on system axes, D]im/Fand R. ... 

We call such reflux number at which in one of the product one of the components disappears (i.e., at i > i iim in one of the products, the components number is smaller than at i < i iim), a boundary one. We also call such value of withdrawal Dx /F, at which in both products one component disappears at some i iim (i.e., at D = Diim and R > i iim in the top and bottom products, there are number of components smaller by one than at i < i iim), a boundary one. The sharp sphts without distributed components appear at some boundary values of withdrawal. Besides that, for the splits with distributed components there are boundary values of withdrawal, at which reflux number is minimum. Figure 5.5 shows dependence of i iim on D for the above-mentioned example of four-component mixture. It is well seen that at Dum and for the separation modes with distributed components 2 and 3, the reflux number is minimum. 

For splits with distributed components, sharp split regions of two sections are different (Fig. 5.10). Reversible distillation regions Regf and RegJ, which are discussed in Chapter 4, are a particular case of sharp split regions (in this case, component h is absent in overhead and component / is absent in bottom). 

If the split with distributed components is set, then the mentioned trajectory tear-off regions of sections should be boundary elements of two different for the top and bottom sections, but partially overlapping regions of section sharp split (Reg , RegX,Hg.5.10). 

The question about location of points Xf-i and x/ for splits with distributed component is discussed below. 

The algorithm of calculation of minimum reflux mode for splits with distributed component includes the same stages as for intermediate splits without distributed components. 

The rest of heuristic rules are less obvious. The fourth rule sequences with minimum number of columns are preferable. Hence, it follows that splits with distributed components have to be excluded if there are ones without them. Capital costs at minimum number of columns are the smallest. However, energy expenditures in this case are not always the smallest. For zeotropic mixtures, the situation is the same as for azeotropic flowsheets with prefractionator are more profitable sometimes than without it (see Section 8.2). Therefore, the designer has to decide him- or herself if he or she should use this rule at the stage of automatic sequences. 

We turn to the following splits in the first column. Mixtures 1,233 and 1,3,4,5 (bottom products at extractive distillation in first colunm at splits 2 h- 4) can be separated only in the column with one feeding at splits with distributed component. 

Joining condition at minimum reflux for split with distributed component feed cross-section composition point for one column s section must belong to the sep-aratrix min-r ux region and the other to the separatrix sharp distillation region for given product points and reflux ratio and satisfy the material balance in feed cross-section x/ i e andxf e Reg or Xf.i and... 

Finally, the sharp splits include the splits with the components to be distributed 1,2 2,3 (for three-component mixture), and 1,2,3 23,4 13 23,4 1,2,3 3,4 (for four-component mixture). 

At some boundary values of the parameter D/F, at which it is equal to the concentration of the lightest component or to the sum of concentrations of a few light components in the feeding, we have sharp separation without distributed component and at other values of the parameter D/Fv/e have sharp separation with one distributed component. These are sharp splits without distributed components 1 2,3,4 1,2 3,4 1,23 4 (here and further the components of the top product are shown before the colon and those of the bottom product follow the colon). 

Regard-Therefore, for different splits section sharp regions, Reg and Reg are different. For splits without distributed components, sharp split regions of both sections coincide with each other Re J,. = Reg (Fig. 5.9). 

At reflux bigger than minimum and at quasisharp separation with distributed component at the set distribution of this component among the products, there is the only one composition at the first tray above the feed cross-section expressed by point X/-1 in the vicinity of separatrix sharp spht region Re p (5/ - - N ) and the only one composition at the first tray below the feed cross-section expressed by point Xf in the vicinity of separatrix sharp split region Reg p - N )- The less sharp is separation the farther from separatrix sharp split trajectory bundles of the sections the composition points in the feed cross-section are located. 

At intermediate splits and spUts with distributed component calculation, tray by tray calculation should be carried out from the ends of the column. Design calculation of necessary trays number in each section is carried out for the set of values of the summary concentrations of the impurity components at the... 

Besides splits without distributed component, splits with one distributed component can be of great practical importance. Therefore, it is necessary to check which splits of this type are feasible. 

It follows from the analysis made that in a column with one feeding only two splits without distributed components are feasible (1) 2,4 1,3,5 and (2) 1,2,4 3,5. 

A nucleus with / > has a nonspherical charge distribution. It thus possesses a quadrupole moment that interacts with nonspherical components of the total charge distribution of its surroundings. This interaction further splits the ENDOR transitions into 21 lines at frequencies (to first-order)... 

Figure 1.20 Optical absorption of Nag in its ground-state structure D2d. This result from pseudopotential perturbation theory is explained in the main text. The spherical plasmon line at about 2.5 eV (see Figure 1.21) is split into two components which can be understood as follows. The moments of inertia of the structure D2d point to a prolate spheroid within the jellium approximation to the distribution of ions. In such a system there are two collective excitations one at higher frequencies (perpendicular to the axis of symmetry) and one for the motion along the axis of symmetry. Because the motion perpendicular is twofold degenerate its intensity is twice that of the low-frequency motion (with the cluster being statistically oriented in the beam (see [30])...

Often the splits for zeotropic mixtures are ones of sharp separation without distributed components. At practice, these splits are the most widespread because they are the sequences with the smallest number of columns (n - 1 column for n-component mixture, if each component is a purpose product) that correspond to them. 

Splits with the number of distributed components bigger than one at R = 00 and N = oo are impossible (e.g., for four-component mixture, the split 1,2,3 2,3,4 with two distributed components is impossible). 

An example of determination if the feed composition belongs to this or that product simplex, which was formerly depicted in Fig. 3.14a, is shown in Fig. 3.19. Besides the direct and the indirect splits that were shown in Fig. 3.14a, we have three other possible splits an intermediate spht and two sphts with one distributed component. In Fig. 3.19, lines of material balance are shown for all possible sphts of the feed composition under consideration at / = oo and N=oo. 

Splits with one distributed component shown below in brackets are the third one (component 3), the fourth one (component 8), the sixth one (component 8), the seventh one (component 8), and the eighth one (component 8). 

The binary mixture is the separation product of three-component mixture in the case of split with a distributed component (1,2 23), including the case of preferable split and in the case of the top section at indirect separation (1,2 3). 

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