Page 315 - Distillation theory

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8.4 Multicomponent Azeotropic Mixtures: Presynthesis 289

acetone(1)-benzene(2)-chloroform(3)-toluene(4) with one binary azeotrope 13.
ijk(2)
Figure 4.13 shows the segments of identical order of the components Reg ord at
the edges of concentration tetrahedron and the regions of identical order of com-
ijk(4)
ponents Reg ord inside concentration tetrahedron obtained by means of scanning
of phase equilibrium coefficients at the edges.
t(1)
The structural condition of trajectory tear-off determines the vertexes Reg r,s ,
t(2) t(3)
the segments at the edges Reg r,s , and the regions at the faces Reg r,s of the
concentration tetrahedron from points of which the trajectory tear-off into it is
2,3,4
t(1) t
possible (Fig. 5.27a). For the top section, these are Reg r − vertexes 1(Reg ) and
r
1,2,4 3,4 1
t(2)
t
t
3(Reg ) (unstable nodes N ), Reg r − segments at edge 1-2 (Reg ) and at edge
−
r r
3 1,2
2,4 4
t t(3) t
1-3(Reg ), and region Reg r − the whole face 1-2-3(Reg ) (for all these boundary
r r
1,3 1,2,3
elements, the absent components are heavier than present ones). For the bottom
1,2,3
t(1) t t(2)
+
section, these are Reg s − vertex 4(Reg ) (stable node N ), Reg s − the whole
s
1,2 4 1
t t(3) t
edge 2-4(Reg ), and Reg s − the part of face 2-3-4(Reg ) (for all these boundary
s s
2,4 2,3,4
elements, the absent components are lighter than present ones).
(2)
Figure 5.27b shows possible product composition segments Reg at the edges
D,B
of concentration tetrahedron. The whole edge 1-3 is filled up with possible top
2
product points at distillation of three-component constituents 1,2,3(Reg D ) and
4 1,3
1,3,4(Reg D ), and the whole edge 2-4 is filled up with possible bottom product
1,3 1 3
points for mixtures 1,2,4(Reg B ) and 2,3,4(Reg B ). Therefore, these edges are en-
2,4 2,4
tirely filled up with possible points of top and bottom products, respectively, for
2,4 1,3
the whole four-component mixture ([1 − 3] ≡ Reg D ,[2 − 4] ≡ Reg B ). At edge 1-2,
1,3 2,4
there is a small common segment of possible top product compositions for mix-
tures 1,2,3 and 1,2,4. This segment is a possible top product composition segment
3,4
Reg D at distillation of four-component mixture.
1,2
The next step of presynthesis is determination of possible product regions
(3)
Reg in those two-dimensional faces of concentration tetrahedron that contain
D,B
trajectory tear-off regions (i.e., in face 1-2-3 for the top product and in face 2-3-4
(2)
for the bottom product). We have to find contours of these regions Reg
bound,D,B
at the edges of faces 1-2-3, 2-3-4.
In accordance with the described algorithm, we have to examine ternary mix-
tures composed of each edge of these faces and of the component that is absent
at the face (in the given example, only one component is absent: for face 1-2-3,
it is component 4; for face 2-3-4, it is component 1). Therefore, for face 1-2-3, it
4 4
is sufficient to determine possible product segments Reg D ∈ Reg bound,D at edge
4 4 1,2 1,2,3
1-2 in ternary mixture 1,2,4, Reg D ∈ Reg bound,D at edge 1-3 – in ternary mixture
4 4 1,3 1,2,3
1,3,4 and Reg D ∈ Reg bound,D at edge 2-3 – in ternary mixture 2,3,4. Edges 1-2, 1-3,
2,3 1,2,3