Page 78 - Distillation theory

P1: JPJ/FFX P2: FCH/FFX QC: VINOD/IYP T1: FCH
0521820928c03 CB644-Petlyuk-v1 June 11, 2004 20:12

52 Trajectories of Distillation in Infinite Columns Under Infinite Reflux

3.4. Rule for the Checkup of Azeotropic Mixtures Separability
at R =∞ and N =∞

3.4.1. Distillation Trajectories Location at R =∞ and N =∞
To deduct the general rule for the checkup of possibility one or another sharp split,
let’s examine peculiarities of sharp distillation trajectories’ location at R =∞ and
N =∞ (Petlyuk, Avet’yan, & Inyaeva, 1977; Petlyuk, 1979; Petlyuk & Serafimov,
1983). In Figs. 3.2b, c, the distillation trajectories location for splits with one dis-
tributed component and without distributed component is shown. In Fig. 3.2c,
distillation trajectory from the top product point, lying on side 1-2 of the concen-
tration triangle, goes along this side (boundary element of the concentration trian-
+
gle Reg ≡ Reg ∞ ) to the stable node N of this side (i.e., to vertex 2). Vertex
D bound,D D
−
2 is, at the same time, a stable node for side 1-2, an unstable node N for side 2-3
B
(Reg ≡ Reg ∞ ), and a saddle point for the concentration triangle. From the
B bound,B
vertex 2, distillation trajectory goes along side 2-3 to the bottom product point. We
+ −
can briefly describe the distillation trajectory as follows: x D → N ≡ N → x B .
B
D
1,2 2 2,3
Thus, the distillation trajectory in this case consists of two parts. The first part
is located in the boundary element Reg ∞ the top product point belongs to;
bound,D
+
it joins the top product point x D with the stable node N of this boundary ele-
D
ment. The second part is located in the boundary element Reg ∞ the bottom
bound,B
product point belongs to – it joins the unstable node N of this boundary ele-
−
B
ment with the bottom product point. In Fig. 3.2b, the top product point coincides
with a boundary element of zero dimensionality – vertex 1. In this case, trajec-
tory consists of the same two parts – the whole side 1-2 and part of the side 2-3
+ −
( x D ≡ N → N → x B ).
B
D
1 2 2,3
Let us examine the case of four-component mixture (Fig. 3.4). Let us consider
the split 1 : 2,3,4. The distillation trajectory goes from vertex 1 ≡ Reg D at edge 1-2,
to vertex 2 and further inside face 2-3-4 ≡ Reg B by c-line to the bottom point x B
+ −
∈ 2-3-4 ( x D ≡ N → N → x B ; Fig. 3.4b). Let us also consider the split 1,2 : 3,4.
B
D
1 2 2,3,4
The distillation trajectory goes from point x D on edge 1-2(x D ∈ 1-2 ≡ Reg D ) along
it to vertex 2, then along the edge 2-3, and further along edge 3-4(3-4 ≡ Reg B )to
+ −
bottom product point x B ∈ 3-4( x D → N → N → x B ; Fig. 3.4c).
D
B
1,2 2 3 3,4
In Figs. 3.10a, b, distillation trajectories at R =∞ and N =∞ for two types of
three-component azeotrope mixtures are shown.
In the splits mentioned, the common rule is valid – the trajectory consists of
three parts located in boundary elements of distillation regions for the top and
bottom products points and in bond or in a few bonds, connecting stable node
−
+
N of the boundary element of top product Reg D and unstable node N of the
D B
boundary element of the bottom product Reg B . In split 13 : 1,2 (Fig. 3.10b), there
x D ≡ N + → N + → N − → x B
are two bonds: ( D(1) D(2) B(1) ). Let us note that split 2,3 :
13 3 2 1,2
1,2 at big R and N numbers for this type of mixture was proposed for separation
of binary azeotropic mixture 1,3 with small amount of entrainer 2 in the work
(Laroche et al., 1992).