Page 183 - Distillation theory

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5.6 Conditions of Section Trajectories Joining and Methods 157

tangential pinch does not become apparent, in spite of the availability of values
L/V maximum along reversible distillation trajectory (Koehler et al., 1991).
At tangential pinch, points x f −1 and x f are located not in minimum reflux
bundles but inside rectifying and stripping bundles, as at a reflux bigger than
the minimum one (see Chapter 7). In the section where tangential pinch takes
place, there is a zone of constant concentrations where the composition at plates
corresponds to the composition in the point of pinch, and the second section is
finite.
The example of tangential pinch for four-component mixture is quasisharp sep-
aration of azeotropic mixture acetone (1)-benzene (2)-chloroform (3)-toluol (4)
of composition x f (0,350; 0,250; 0,150; 0,250) at intermediate split 1,3(2) : 2,4(3)
(admixture components heavy and light key are in brackets correspondingly) at
the following composition the products x D (0,699; 0,001; 0,300, 0) and x B (0; 0,500;
−8
10 ; 0,500). The same top product composition, as in the previous example (Fig.
5.18b) of separation of three-component mixture in the top section, is accepted for
convenience of analysis. In this case, the boundary elements of top section trajec-
tory bundle, located in face 1-2-3, completely coincides with top section trajectory
bundle at separation of previously mentioned three-component mixture.
2,4
2
Figure 5.34 shows rectifying trajectory bundle SN r − S − N ≡ Reg sh,R , ob-
+
r
r
sep,r
1,3
tained by means of calculation. In face 1-2-3, pinch point SN r is stable node for
the trajectories, located closer than it to edge 1-3, and is saddle for the rest of
trajectories.
D
2
F
a)
B r S 2

1 4
+
r N Figure 5.34. (a) The tangential pinch in rec-
x D
tifying section for the acetone(1)-benzene(2)-
SN r
13
chloroform(3)-toluene(4) mixture for the split 1,3 :
3
2,4, and (b) natural projection. Separatrix sharp
2
+
splitregionforrectifyingsection SN r − S − N ≡
r
r
2 2,4
Reg sh,R (shaded).
sep,r
b) r S 2 1,3
SN r
x D
1,3 4
+
r N