Page 80 - Distillation theory

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

54 Trajectories of Distillation in Infinite Columns Under Infinite Reflux

D
D
B
i , i ,..., i D i m 1 + i , B + ,..., i B Figure 3.11. Condition of connectedness. Thick
1 2 m m 2 n
lines with arrows – bond, c-lines, indices: D
x x F x
D B and B, distillate and bottom boundary elements
Reg ∞ and Reg ∞ of concentration
bound,D bound,B
D
D
symplex correspondingly; i ÷ i , components
1 m
B
− of distillate; i B ÷ i , components of bottom.
N m+1 n
+ B
N D Product regions are shaded; bottom region is
darker shaded.
term of connectedness determines feasible variants of product points’ location in
concentration simplex (i.e., separation products feasible compositions at any feed
composition). This property of connectedness rule can be used for the solution
sequencing tasks. The rule of connectedness follows from the fact that at N =∞
and R =∞ distillation trajectory should go at boundary elements of trajectory
bundle at the infinite reflux (i.e., at the boundaries of distillation region Reg ∞
bound,D
and Reg ∞ ). At sharp split, these boundary elements should be located at the
bound,B
boundary elements of concentration simplex. But, in the general case, Reg ∞
bound,D
and/orReg ∞ maybelocatedwithintheconcentrationsimplexonseparatrixes,
bound,B
separatingonedistillationregionReg fromtheother.Weexaminesuchexamples
∞
later (see Fig. 3.14). The rule of connectedness holds good in these cases, too.
Let’s examine the application of the rule of connectedness in a few more cases.
At the beginning, the trivial case of impossible separation of the ideal three-
component mixture split 2 : 1,3 (Fig. 3.3) does not meet the rule of connectedness.
+
Really, stable node N of top product region Reg ≡ Reg ∞ is vertex 2 and
D D bound,D
−
unstable node N of the bottom product region Reg ≡ Reg ∞ is vertex 1.
B B bound,B
Bond 1-2 is directed to the top but not to the bottom product.
Let’s examine four-component azeotropic mixture (Fig. 3.12) with one region
↑→ → 2 →→ ↓
of distillation: 12 ⇒ 24 or 12 → 1 → 3 → 23 → 24. Split 1,3 : 2,4 (x D(1) : x B(1) ),
↓→ 4 →↑
according to the rule of connectedness, is possible because the stable node N +
D
of top product boundary element Reg ∞ (vertex 3) is connected with the
bound,D
unstable node N of the bottom product boundary element Reg ∞ (vertex 4):
−
B
bound,B
x D(1) → N + → N − → x B(1)
D(1) B(1) . Here, the points through
Reg ∞ Reg ∞ Reg ∞ Reg ∞
bound,D bound,D bound,B bound,B
which the distillation trajectory goes are given in the upper line, and the boundary
elements they belong to are given in the lower one. However, split x D(2) : x B(2) is
impossible because between points N + and N − there is azeotrope 23 and the
D(2) B(2)
rule of connectedness is not kept.
To determine whether one or another sharp occurs split occurs in the case of
R =∞ and N =∞, it is necessary (1) to define products compositions x D and x B ;
(2) to find the stable node N of the boundary element Reg D to which the point
+
D
x D belongs; (3) to find the unstable node N of the boundary element Reg B ,to
−
B
which point x B belongs; and (4) to establish whether points N and N coincide
−
+
D B
with each other (N ≡ N ), or there is a bond or chain of bonds N → N ,or
−
+
−
+
D B D B
this condition is not kept.