Page 86 - Distillation theory

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60 Trajectories of Distillation in Infinite Columns Under Infinite Reflux

to substitute such simplex for the simplex with linear boundary elements, which
we call the product simplex Reg simp . Here are the examples of such distillation
subregions:

1. 2 → 13 → 1 and 2 → 13 → 3(2 ⇒ 1 and 2 ⇒ 3) at Fig. 3.6
2. 12 → 23 → 2, 12 → 1 → 3 and 12 → 23 → 3 (12 ⇒ 2 and 12 ⇒ 3) at
Fig. 3.10a
3. 12 → 2 → 23 → 24 (12 ⇒ 24) at Fig. 3.12

Such simplex is analogous to an ideal mixture, components of which correspond
to the stationary points of the simplex (in both cases, we have only one bonds
chain). That is why at sharp separation, when product points lie in boundary ele-
ments of distillation subregion, the set of stationary points (pseudocomponents)
is divided into two subsets of stationary points of the top and bottom products,
just as at separation of ideal mixture, a set of components is divided into two
subsets.
At sharp separation of azeotropic mixture, the key stationary points (key pseu-
docomponents), that is, stationary points that are adjacent in the bonds chain,
play the key components. At separation without distributed pseudocomponents,
the set of stationary points A 1 , A 2 ... A m is divided into two subsets: A 1 , A 2 ... A k
and A k+1 , A k+2 ...A m . These subsets are the boundary elements of distillation
subregion Reg ∞
bound , which the top and bottom product points belong to (Reg D
and Reg B ). Dimensionality of these boundary elements is k − 1 and m − (k + 1),
correspondingly.Thesummarydimensionalityoftheseboundaryelementsisequal
to m + 2.
As far as the stable node of boundary element A 1 , A 2 ...A k (Reg D ) is station-
+
ary point A k (A k ≡ N ) and unstable node of boundary element A k+1 , A k+2 ...A m
D
−
(Reg B ) is stationary point A k+1 (A k+1 ≡ N ) and as far as there is bond A k →
B
A k+1 (A k and A k+1 are adjacent stationary points of one bonds chain), separa-
tion into considered subsets of stationary points meets the rule of connected-
ness (i.e., it is feasible). In exactly the same way, it is possible to show that splits
with one distributed pseudocomponent are feasible. It is noteworthy that the
boundary elements A 1 , A 2 ... A k and A k+1 , A k+2 ...A m are curvilinear, and three
−
constituent parts of the distillation trajectory x D → N → N → x B are also
+
D B
curvilinear.
Thus, if the feed point lies inside some distillation subregion (x F ∈ Reg sub ) to
which the chain of bonds A 1 → A 2 →· · · → A m (where m = n), corresponds, then
at R =∞ and N =∞ the following splits without distributed pseudocomponents are
feasible: (1) A 1 : A 2 , A 3 , ... A m ; (2) A 1 , A 2 : A 3 , ... A m ;...; (m − 1) A 1 , A 2 , ...A m−1 :
A m , and also the following splits with one distributed pseudocomponent: (1) A 1 :
A 1 , A 2 ...A m ; (2) A 1 , A 2 : A 2 , ... A m ;...(m − 1) A 1 , A 2 , ... A m−1 : A m−1 , A m ;(m)
A 1 , A 2 , ...A m−1 , A m : A m .
Let’s call the above-stated method of determination of the set of feasible splits
at R =∞ and N =∞ the method of product simplex.