Page 189 - Distillation theory

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5.7 Necessary and Sufficient Conditions of Separability of Mixtures 163

product regions. At this condition and at the sufficient for trajectory tear-off values
of parameters L/V in the top section and V/L in the bottom section, the trajectory
bundles of the sections arise inside the concentration simplex.
We saw in the previous section that these conditions are not sufficient for
separation in two-section column.
The process of separation becomes possible only if trajectory bundles of the
sections become sufficiently big for the fact that the conditions of sections joining
could be valid (i.e., that the material balance would be valid in feed cross-section
of the column between the certain trajectory points of the sections).
For splits without distributed components and with one distributed component,
the conditions of joining can always be valid at sufficiently large values of param-
eters L/V and V/L in the top and bottom sections, respectively, if the sizes of
trajectory bundles unlimitedly grow at the increase of these parameters.
But we saw in Section 5.4 that the values of parameters L/V and V/L and the
sizes of trajectory bundles of adiabatic columns sections are limited, if for product
point there are two reversible distillation trajectory tear-off points. Therefore,
necessary conditions of separability in adiabatic columns can be insufficient if
for one or for both product points there are two reversible distillation trajectory
1
tear-off points from boundary elements to which points S belong. In these cases,
to check separability it is necessary to verify whether corresponding separatrix
sections trajectory bundles join at the maximum possible value of the parameter
L/V or V/L.

5.7.2. Nonadiabatic Columns

Usage of nonadiabatic columns (i.e., column with intermediate at height inputs
or outputs of heat), broadens conditions of separability of mixtures, having two
reversible distillation trajectory tear-off points. If, for example, heat is brought and
drawnoffinfeedcross-section(Fig.5.36),asitwasofferedinthework(Poellman&
Blass, 1994), then it is possible in one of the sections of the column, where there is
limitation at the value of the parameter L/V or V/L, to keep the corresponding
allowed value of this parameter, and joining of trajectories of the sections can
be maintained at the expense of increase of vapor and liquid flows in the second
section (Petlyuk & Danilov, 1998). In a more general case, when there are limita-
tions of the values of the parameters L/V and V/L in both sections, it is possible
to use intermediate inputs and outputs of heat in the middle cross-sections of both
sections.
However, in some cases, even usage of nonadiabatic columns does not maintain
separability. These are the cases, when reversible distillation trajectories for both
product points do not have node points. In these cases, section trajectory bun-
dles not only of adiabatic, but also of nonadiabatic columns, are limited because
reversible distillation trajectories at which section trajectory bundles stationary
point lie are located in limited parts of concentration space, adjacent to prod-
uct boundary elements (see Fig. 5.17b for x D ). To check whether it is possible to
separate the mixture of this kind into a set product, it is necessary to examine
2
2
2
2
+
the bundles S − N and S − N for points S and S , the most remote along
+
r r s s r s