Page 216 - Distillation theory

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190 Distillation Trajectories in Infinite Complex Columns and Complexes

arises in the cross-section of input of the entrainer. Along with that, the conditions
of material balance should be valid in the cross-section of input of the entrainer:
L r x e−1 + Ex E = L m x e , where (6.6)

L r + E = L m (6.7)

6.5.3. The Four- and Multicomponent Mixtures

We now examine the four-component mixture for m m = 2 (Fig. 6.9a). The condi-
tions of joining of section trajectories at a set flow rate of the entrainer in the mode
of minimum reflux in the cases of top or bottom control feed do not differ from the
conditions for three-component mixtures discussed above. In the case of bottom
control, feed point x f −1 should lie in the separatrix min-reflux region Reg min,R
sep,e
2
−
(N − S 1 − S ) and x f ≡ N . The column trajectory may be put as follows:
+
m m m s
(3) (3) (4) (4) 2(4) (2) (2) (1)
x → x ⇐⇓ x → ⇐⇓ x → x
B → S s f f −1 S m → x e e−1 D
1 1 2,3 2,3 2,3 4 .
Reg Reg t N + Reg min,R Reg min,R Reg t Reg 1 Reg
B s s sep,e sep,e e att D
2,3,4 2,3,4 1,4 1,4 1,4 1
With the top feed for the control one, x e−1 ≡ N and x e ≡ N . The equations of
+
+
r m
material balance (6.4) ÷ (6.7) should be valid in both cases.
For four-component mixtures at m m = 3 and at two components in the bottom
product (Fig. 6.9b), the conditions of joining in the case of bottom control feed are
2
−
defined by the dimensionality of trajectory bundles N − S m (d = 1) and S − N +
m s s
(d = 1) and are similar to those of joining of sections trajectories of two-section
column in the mode of minimum reflux at intermediate split (see Section 5.6).
Point x f−1 should lie on the separatrix min-reflux region Reg min,R (N − S m ) and
−
sep,e m
2
point x f should lie on the separatrix min-reflux region Reg min,R (S − N ).
+
sep,s s s
At top control feed x e−1 ≡ N and x e ≡ N ; that is, point N should lie on the
+
+
+
r m r
continuation of the straight line 4 − N (it follows from Eq. [6.6]).
+
m
It is shown below that such a joining variant of sections trajectories at arbitrary
compositions of the top product and of the pseudoproduct is unfeasible. Joining
is feasible if point x e−1 belongs to working trajectory bundle of top section Reg R
w,r
(S r − N ). In other words, the top feed cannot be the control one.
+
r
Finally, at m m = 3 and at three components in the bottom product (Fig. 6.9c),
with the bottom feed for the control one, the analysis of dimensionality of trajec-
tory bundles of the bottom and the intermediate sections shows that at any value
of the parameter (L/V) m point x f−1 cannot belong to the separatrix min-reflux
+
region Reg min,R (N − S m ) and at the same time cannot x f ≡ N . Only the follow-
−
sep,e m s
−
+
ing variants are feasible: (1) point x f−1 belongs to the bundle N − S m − N and
m m
+
x f ≡ N , or (2) point x f−1 belongs to the separatrix min-reflux region Reg min,R
s sep,e
−
(N − S m ) and point x f belongs to the separatrix sharp split region Reg sh,R (S s −
m sep,s
+
N ). Therefore, in the case under consideration, the conditions of joining of tra-
s
jectories of bottom and intermediate section are similar to the condition of joining
of section trajectories of two-section column in the mode of minimum reflux at
split with one distributed component (see Section 5.6).