Page 251 - Distillation theory

P1: JPJ/FFX P2: JMT/FFX QC: FCH/FFX T1: FCH
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7.2 Distillation Trajectories of Finite Columns 225

2,3,4
1
R
2
Reg w,r = Reg (N − S − N ), and segment [x f ] is located at separatrix sharp
−
+
att
r
r
r
1 1
1
1
split region Reg sh,R (separatrix S − N ). Similarly, at the indirect split S ≡ N −
+
sep,s s s s s
2,3,4
2
and S ≡ N + (Fig. 7.2b). Therefore, at the indirect split, segment [x f ] is located
r r
1,2,3
4
inside the working trajectory bundle of the bottom section Reg R = Reg (N −
−
w,s att s
4 4
2
+
S − N ) and segment [x f −1 ] is located at separatrix sharp split region Reg sh,R
s s sep,r
1
(separatrix S − N ). 1,2,3
+
r
r
For splits with one distributed component, the summary dimensionality of sep-
2
1
1
2
aratrix sharp split regions Reg sh,R (S − S − N ) and Reg sh,R (S − S − N )is
+
+
sep,r
s
r
r
r
s
sep,s
s
smaller by one than that for splits without distributed components (see Chapter
5). This leads to the decrease by one of the dimensionality of the set of intersec-
tion points of these separatrix bundles and, correspondingly, to the decrease of
sh sh
the dimensionality of sets of the points {x f −1 } and {x f } . Therefore, these sets
lin lin
of points at reflux larger than minimum have zero dimensionality; that is for split
1,2 : 2,3,4, they are the following points: point (x f −1 ) sh is located in separatrix
lin
3,4
sh
1
2
region Reg R (S − S − N ) lin , and point (x f ) , is located in separatrix region
+
sep,r r r r lin
1 1,2
1
2
Reg R (S − S − N ) lin (Fig. 7.3).
+
sep,s s s s
2,3,4
x D
2
x F
x B
x
f−1
x f
1 4
+
N s
3
3,4 1
Figure 7.3. Section regions Reg R and Reg R and possi-
sep,r sep,s
1,2 2,3,4
ble composition points (x f −1 ) and (x f ) in feed cross-section
for the split 1,2 : 2,3,4 with a distributed component. Recti-
fying separatrix sharp split region is shaded.