Page 79 - Distillation theory

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

3.4 Rule for the Checkup of Azeotropic Mixtures Separability 53

2
a)
D x ) 1 ( ≡ N D + ) 1 (
12 23
x D(2)
x F −
) 2 ( B x ≡ N ) 2 ( B
Figure 3.10. Condition of connectedness for two
1 3 structures of three-component mixtures: (a) 8c,
+ − x B(1)
N D ) 2 ( ;N ) 1 ( B (b) 4b. 8c and 4b − classification according to
Gurikov (1958). Thick lines with arrows, bonds
and c-lines; N , stable node of distillate boundary
+
+ − − D
2 N D ) 3 ( ;N B ) 1 ( ;N ) 2 ( B element Reg ∞ ; N , unstable node of bot-
−
bound,D B
b) tom boundary element Reg ∞ ; x D(1) : x B(1) ,
bound,B
x D(2) : x B(2) , x D(3) : x B(3) , possible splits.
x B(1)
x D(3)
x B(2)
x F ≡ +
D x ) 2 ( N D ) 2 (
1 13 3
) 3 ( B x ≡ N − ) 3 ( B D x ) 1 ( ≡ N D + ) 1 (

One of three parts of trajectory can transform into nodal or saddle point of
concentration simplex.

3.4.2. Application of the Rule of Connectedness
Relatively simple examined examples allow formulation of the general rule
(Petlyuk et al., 1977), with which the product points should comply at R =∞
+
and N =∞ at sharp separation: (1) the stable node N of the top product bound-
D
ary element Reg D and the unstable node N − of the bottom product boundary
B
element Reg D should coincide (N ≡ N ) or should be connected with each other
+
−
D
B
−
by the bond (N → N ) or chain of bonds in direction to the bottom product; and
+
D
B
(2) the product points and the feed point should meet the conditions of material
balance.
For the sake of briefness, we call the first of these conditions the term of con-
nectedness. It has general nature – it can be applied to mixtures with any number
of components and azeotropes. Moreover, the term of connectedness embraces
not only sharp splits, when the product points lie in the boundary elements of
the concentration simplex, but also the semisharp and nonsharp splits, when the
product points lie in the boundary elements of the distillation region.
+
−
+
−
In Fig. 3.11, three constituent parts (x D → N , N → N , and N → x B )of
D D B B
n-component mixture distillation trajectory at R =∞ and N =∞ are shown. The
term of connectedness establishes mutual location of distillation products feasible
points at R =∞ and N =∞. Together with conditions of material balance, the