Page 214 - Distillation theory

P1: FCH/FFX P2: FCH/FFX QC: FCH/FFX T1: FCH
0521820928c06 CB644-Petlyuk-v1 June 11, 2004 20:17

188 Distillation Trajectories in Infinite Complex Columns and Complexes

Conditions 1 ÷ 3 are necessary for the fact that at big enough values of param-
eters (L/V) r ,(L/V) m , and (L/V) s , in each of the three sections, trajectory bundles
of these sections arise. Condition 4 maintains the potential feasibility of joining of
these trajectory bundles. Therefore, the conditions (1 ÷ 4) are necessary ones of
mixture separability in a three-section column. These conditions not valid; sharp
separation with obtaining set products is unfeasible.

6.5.2. Three-Component Mixtures
For the mixture acetone(1)-water(2)-methanol(3) (the entrainer is water, see Fig.
6.8) these four conditions are valid: (1) at side 1-2 there is intermediate section
3
t
trajectory tear-off region Reg , where K 1 > K 3 > K 2 (the segment [α 13 , 2]); (2)
e
1,2
vertex 1 is the unstable node N at side 1-2 (region Reg 1:2 ) (i.e., it can be the top
−
sh,r
r
2
−
product point x D = N ≡ Reg at separation of the mixture 1,2 [K 1 > K 2 ]); (3) the
r
D
1 1
whole side 2-3 is bottom product segment Reg for the mixture 1,2,3 (K 1 > K 3 >
B
2,3 1,2:3
K 2 ); and (4) intermediate section sharp split region Reg (region K 1 > K 3 >
sh,e
1:3,2
K 2 ) coincides with the bottom section sharp split region Reg and intersects the
sh,s
top section sharp split region Reg 1:2 at side 1-2 (the whole side 1-2).
sh,r
We now examine the conditions of joining of sections trajectories at a set flow
rate of entrainer (i.e., at set value of the parameter E/D) for a three-component
mixture in the mode of minimum reflux. Each of two feeds can be the control
one, and the intermediate section trajectory in the mode of minimum reflux in
both cases should pass through the saddle point S m because this trajectory passes
through the node point N not only in the mode of minimum reflux, but also
+
m
at reflux bigger than minimum (point N arises at the boundary element of the
+
m
concentration simplex because the extractive distillation under consideration is
sharp).
Therefore, point x f −1 (composition at the tray of the intermediate section that is
higher than the feed cross-section) in the mode of minimum reflux should lie on the
−
separatrix N − S m (Fig. 6.10). If it turns out that point x f −1 is outside the working
m
3
trajectory bundle of the intermediate section Reg R [(L/V) m < (L/V) min ] then,
w,e m
1,2
as this figure shows, the trajectory of the intermediate sections deviates into the
side opposite to point N .Atareflux bigger than minimum [(L/V) m > (L/V) min ],
+
m
m
point x f −1 gets inside the working trajectory bundle of the intermediate section
and the trajectory of this section does not pass through point S m . Figure 6.10 shows
the case when the bottom feed is the control one. In this case, point x f (composition
at the tray of the bottom section that is lower than the feed cross-section) should
coincide with point N . Along with that, the condition of material balance should
+
s
be valid in the feed cross-section:
L m x f −1 + L F x F = L s x f , where (6.4)
L m + L F = L s (6.5)