Page 114 - Distillation theory

P1: FCH/FFX P2: FCH/FFX QC: FCH/FFX T1: FCH
0521832772c04 CB644-Petlyuk-v1 June 11, 2004 17:49

88 Trajectories of Thermodynamically Reversible Distillation

In Fig. 4.9a, there are two trajectories tear-off points x t of the reversible
rev
(2)
distillation trajectory for any points x D of the possible product segment Reg
D
at side 1-2. For point x D located at the end of the possible product composition
segment, both these trajectories tear-off points x t coincide with each other, but
rev
the length of the trajectory inside the concentration triangle becomes equal to
zero. The segment from vertex 1 to point α 23 is trajectory tear-off segment Reg t(2) .
rev,r
At the same figure at side 1-3 from point α 23 to vertex 3, there is a segment of
trajectories tear-off Reg t(2) and possible product composition segment Reg (2)
rev,r D
coincides with side 1-3. Along with that, for any point x D there is one trajectory
t
tear-off point x .
rev

4.3.4. Necessary Condition of Sharp Reversible Distillation

It follows from the aforesaid that sharp separation in a reversible distillation
column is feasible only if the liquid–vapor tie-line of feeding is directed to the
(n−1)
possible product composition region Reg at the boundary element C n−1 of
D
(n−1)
the concentration simplex and from region Reg at other boundary element
B
C n−1 .
In other words, for sharp separation in a two-section column it is necessary that
the feed point belongs to the intersection of true bundles of reversible distillation
trajectories of the two sections x F ∈ (Reg rev,r • Reg rev,s ) (Fig. 4.10). The reversible

2 2
x x
a) α 23 B b) α 23 B
x F
x F α
α 13 13

x D
1 α 23 13 3 1 x D α 23 13 3
2

x
c) α 23 B

x F α 13

x D
1 α 23 13 3
Figure 4.10. Sharp reversible section trajectories of acetone(1)-
benzene(2)-chloroform(3) mixture for two-section columns: (a) split
1,2 : 2,3, x F ∈ (Reg 3 rev,r • Reg 1 rev,s ); (b) split 1,3 : 2,3, x F ∈ (Reg 2 rev,r •
Reg 1 rev,s ); and (c) split 1 : 2,3, x F ∈ (Reg 2=3 • Reg 1 rev,s ) and x F ∈ α 23 .
rev,r