Page 184 - Distillation theory

P1: JPJ/FFX P2: FCH/FFX QC: FCH/FFX T1: FCH
0521820928c05 CB644-Petlyuk-v1 June 11, 2004 20:15

158 Distillation Trajectories and Conditions of Mixture Separability

2
In rectifying bundle SN r − S − N , pinch point SN r is an unstable node. At
+
r r
(L/V) r < (L/V) min , there is no top section trajectory tear-off from face 1-2-3
r
r
inside concentration tetrahedron and, at (L/V) = (L/V) min , there is trajectory
r
tear-off and two stationary points appear in face 1-2-3: the pinch point SN r and
2
point S .
r
5.6.5. Splits with Distributed Component
Besides splits without distributed components, we also discuss splits with one dis-
tributed component 1, 2,... k − 1, k : k, k + 1,... n. The significance of these splits
is conditioned, first, by the fact that they can be realized for zeotropic mixtures
at any product compositions, while at two or more distributed components only
product compositions, belonging to some unknown regions of boundary elements
of concentration simplex, are feasible. Let’s note that for ideal mixtures product
composition regions at distribution of several components between products can
be determined with the help of the Underwood equation system (see, e.g., Fig.
5.4). This method can be used approximately for nonideal mixtures. From the
practical point of view, splits with one distributed component in a number of cases
maintain economy of energy consumption and capital costs (e.g., so-called “Pet-
lyuk columns,” and separation of some azeotropic mixtures [Petlyuk & Danilov,
2000]).
The analysis of dimensionality of sections trajectory separatrix bundles shows
that for splits with one distributed component trajectory of only one section in the
2
mode of minimum reflux goes through corresponding stationary point S or S s 2
r
(there is one exception to this rule, it is discussed below). The dimensionality of
2
2
bundle S − N is equal to k − 2, that of bundle S − N is equal to n − k − 1. The
+
+
r
s
r
s
total dimensionality is equal to n − 3. Therefore, points x f −1 and x f cannot belong
simultaneously to minimum reflux bundles at any value of (L/V) r . If only one of
the composition points at the plate above or below the feed cross-section belongs
2
1
2
to bundle S − N + and the second point belongs to bundle S − S − N , then
+
the total dimensionality of these bundles will become equal n − 2; therefore, such
location becomes feasible at unique value of (L/V) r (i.e., in the mode of minimum
reflux).
At quasisharp separation with one distributed component in the mode of mini-
mum reflux zone of constant concentrations is available only in one of the sections
2
(in that, trajectory of which goes through point S ).
The following cases of location of composition points at plates above and
below feed cross-section x f −1 and x f : (1) point x f −1 lies in rectifying mini-
2
mum reflux bundle S − N , and point x f lies inside the working trajectory
+
r r
bundle of the bottom section (at nonsharp separation) or in separatrix bundle
3,4 1
1
2
S − S − N (at sharp separation) – Fig. 5.35a (x f −1 ∈ Reg min,R , x f ∈ Reg sh,R );
+
s
sep,r
s
sep,s
s
1,2 2,3,4
2 +
(2) point x f lies in stripping minimum reflux bundle S − N , and point x f −1
s s
lies inside the working trajectory bundle of the top section (at nonsharp