Page 75 - Distillation theory

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3.3 Distillation Trajectories of Finite and Infinite Columns 49

2 x D(1) =x D(2)
a)

x F()2
x F(1)

1 3 Figure 3.7. (a) Product simplexes Reg simp for ternary
x B(1) 13 x B(2)
azeotropic mixture (shaded), and (b) two-column se-
quence (product points – 2,13,1 for feed point x F(1) or
b) 13 2,13,3 for feed point x F(2) ).
2

1,2,3

1,3 1 or 3

both product points in the other one (x D(2) ∈ Reg ∞ and x B(2) ∈ Reg , but x F /∈
∞
Reg ; Fig. 3.6b). This property was noted in the works (Balashov, Grishunin, &
∞
Serafimov, 1970; Balashov, Grishunin, & Serafimov, 1984; Balashov & Serafimov,
1984). For example, in Fig. 3.6a there is shaded triangle to the right from separatrix
2-13 filled with possible bottom points x B , while the feed point x F lies to the left
of this separatrix.
This property allowed to propose sequences of columns with recycles (Balashov
et al., 1970; Balashov & Serafimov, 1984; Balashov et al., 1984). Recently, much
attention is devoted to such sequences (Laroche et al., 1992).
Figure 3.6a shows that at R =∞ and N =∞ for the type of azeotropic mixtures
under consideration, there is only one sharp split 2 : 1, 3 regardless of the feed
point location. However, if the point x F lies to the left of straight line 2-13, then
the bottom product point appears at the segment 1-13, otherwise, at the segment
13-3 (Fig. 3.7a). Correspondingly, in the second column, the bottom product will
be component 1 or 3. Thus, at sharp separation of such azeotropic mixture in
each column, the set of column sequence products depends only on the feed point
location relative to the straight line 2-13.
Further, we call triangles 1-2-13 and 3-2-13 product simplexes Reg simp . This
notion has great significance for separation flowsheets synthesis, because for a
feed point x F located inside the product simplex one can get all the compo-
nents and azeotropes that are vertexes of this simplex in a sequence of (n − 1)
columns.
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 =∞ and at the given
feed compositions x F .