Page 177 - Distillation theory

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5.6 Conditions of Section Trajectories Joining and Methods 151

V
r y f-1
a) L r x f-1 f-1
L F x F
V s f y'
f
(L +L ) x
F r f
L s f x'
V s y f+1
x f+1
L s f+1
Figure 5.29. Models of feed tray: (a) first mixing
then attain equilibrium, and (b) mixing and attain
equilibrium simultaneously.
V r y f-1
L r x f-1
f-1
b)
V s f y
L F x F
f
(L +L )x fr
F
V s y f+1
x f+1
L s f+1

5.6.2. Conditions of Section Trajectories Joining

As we saw in the previous sections, at the increase of the parameter (L/V) r in
top section and of the parameter (V/L) s in bottom section trajectory bundles of
sections Reg R and Reg R increase, filling up bigger and bigger parts of con-
w,r w,s
centration simple. Along with that the increase of the parameter (L/V) r leads to
the certain increase of the parameter (V/L) s in accordance with the equations of
material and thermal balance of the column at given x D and x B .
At some value of parameter (L/V) min , trajectory bundles of sections Reg r and
r
Reg s adjoin each other by their boundary elements – separatrix min-reflux re-
min,R 2 2 min,R 2
+
+
gions Reg sep,r ≡ (S ⇒ N , shortly S − N ) and Reg sep,s ≡ (S ⇒ N , shortly
+
s
s
r
r
r
r
2
S − N ), mostly remote from product points x D and x B , if one uses for determi-
+
s
s
nation of (L/V) min the model in Fig. 5.29b, or if validity of condition (Eq. [5.18]) is
r
achieved between some points of these boundary elements, if one uses the model
in Fig. 5.29a. At this value of the parameter (L/V) min , the distillation process
r
becomes feasible in infinite column at set product compositions. Such distillation
mode is called the mode of minimum reflux. It follows from the analysis of bun-
2
2
dle dimensionality S − N and S − N that, at separation without distributed
+
+
r r s s
components, points x f −1 and x f can be located in these bundles only at one value
of the parameter (L/V) r .
Really, the split without distributed components 1, 2 ... k : k + 1, ... n the dimen-
2
+
sionalityofthebundle S − N isequalto(n−k−1)anddimensionalityofbundle
r r
2
+
S − N is equal (k − 1) (see section 5.5). Therefore, total dimensionality of those
s s
bundles is equal to (n − 2) at dimensionality of concentration simplex (n − 1).