Page 217 - Distillation theory

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

6.5 Conditions of Separability in Extractive Distillation Columns 191

In the case of top control feed x e ≡ N , and point x e−1 should lie on the sep-
+
m
+
aratrix S r − N in face 1-3-4 (Reg sh, R ).
r sep,r
Wenowexaminethegeneralcaseofseparationofamulticomponentmixtureby
means of sharp extractive distillation in a column with two feeds at a set flow rate
of entrainer in the mode of minimum reflux. The conditions of sections joining
are similar to the conditions of sections joining of the two-section column and
depend on the number of components in the product or in the pseudoproduct
of each section (m r , m m , and m s ) (i.e., on the dimensionality of the working and
separatrix bundles of the sections).
Trajectory bundles of bottom and intermediate sections in the mode of mini-
mum reflux should join with each other in the concentration space of dimensional-
ity (n − 1). Therefore, joining is feasible at some value of the parameter (L/V) min
m
if the summary dimensionality of these bundles is equal to (n − 2).
R
The dimensionality of the working region of the intermediate section Reg w,e
(N m − S m − N ), as it is shown in Fig. 6.9, is equal to (n − m m + 1) and that of the
−
+
m
separatrix min-reflux region Reg min,R (N m − − S m ) is smaller by one, that is, (n −
sep,e
m m ).
The dimensionality of the sharp split region of the bottom section Reg sh,R
sep,s
1
2
(S − S − N ), as it is shown in Section 5.6, is equal to (n − m s ), and that of the
+
s s s
2
separatrix min-reflux region Reg min,R (S − N ) is smaller by one, that is, (n − m s −
+
sep,s s s
1) (if m s = n − 1, then this bundle degenerates into point N ).
+
s
Therefore, the conditions of joining of two separatrix min-reflux bundles is as
follows:
2n − m s − m m − 1 = n − 2, (6.8)
and the condition of joining of separatrix min-reflux bundle of one of the sections
and of separatrix sharp split bundle of the second section is as follows:
2n − m s − m m = n − 2 (6.9)
Therefore, if the control feed is the bottom one and Eq. (6.8) is valid, then in
the general case the joining takes place as at the intermediate split in two-section
columns and, in the particular case of m s = n−1, it takes place as at the direct split.
If Eq. (6.9) is valid, then the joining takes place as at the split with one dis-
tributed component in two-section columns.
Finally, if

2n − m s − m m < n − 2, (6.10)
then the joining is similar to that in two-section columns with several distributed
components (i.e., in this case the compositions of the bottom product and of the
pseudoproduct should meet some limitations).
If the control feed is the top one, then the trajectory bundle of the top section
+
should join the stationary point N (i.e., the bundle of zero dimensionality) in
m
the concentration space of dimensionality m m − 1. Therefore, joining is feasible
at some value of the parameter (L/V) min if the dimensionality of the trajectory
m
bundle of the top section Reg sh,R is equal to m m − 2.
sep,r