Page 144 - Distillation theory

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118 Distillation Trajectories and Conditions of Mixture Separability

sections adjoin to the feed cross-section (trajectories of both sections intersect
each other in the feed point and section working regions have stable node N +
r
+
and N in the feed point x F ). At the increase of reflux number, the product points
s
x D and x B come nearer to the boundary elements of concentration simplex (to
the sides of concentration triangle in Fig. 5.3 or to the faces of concentration
tetrahedron in Fig. 5.4).
Later, the process can develop in different ways, depending on the chosen value
of D/F: (1) both product points x D and x B at R = R 1 can simultaneously reach the
lim
boundary elements of concentration simplex (such a split was called a transitional
one [Fidkowski, Doherty, & Malone, 1993] and a preferable one ([Stichlmair et al.,
1993]); (2) the top product point x D at R = R 1 can reach the boundary element
lim
of concentration simplex, and the bottom product point x B at the same time stays
inside it (such a split was called a direct one); (3) the bottom product point x B at
R = R 1 can reach the boundary element of concentration simplex, and the top
lim
product point x D at the same time stays inside it (such a split was called an indirect
one).
Designating withdrawal at preferable separation D pr ,at D < D pr there is a
direct separation and at D > D pr there is an indirect separation.
At D = D pr and at R = R 1 in both sections, there are two zones of constant
lim
concentrations – in the feed point x F and in the trajectory tear-off points of sections
t
x from the boundary elements of concentration simplex. For a three-component
mixture there is a transition from the first class of fractioning right away into the
third class, omitting the second class. At further increase of reflux number, the
product compositions do not change any more.
At D < D pr and R = R 1 in the top section, there are two zones of constant
lim
concentrations: in feed point x F and in trajectory tear-off point from the boundary
element of concentration simplex and in the bottom section there is one zone in
1
feed point x F .At D > D pr and R = R , on the contrary, in the bottom section
lim
there are two zones of constant concentration and in the top the section there is
one zone. In both cases there is a transition from the first class of fractioning to
the second one (i.e., in one of the sections, zone of constant concentrations in feed
cross-section disappears, and in the other section, the zone is preserved, but the
composition in it starts to change with the change of R).
At further increase of R at direct separation, top product point x D begins to
move along side 1-2 to vertex 1 till component 1 will be completely in top prod-
uct. After that, further movement of product points x D and x B is stopped (i.e.,
the third class of fractioning ensues). At indirect separation, bottom product
point x B moves to vertex 3 till component 3 will be entirely in bottom prod-
t
uct. At the second class of fractioning, trajectory tear-off point x of one of the
sections is not changed and, for mixtures with constant relative volatilities, part
t
+
of trajectory of this section x ≡ S → N is also not changed (Stichlmair et al.,
1993).
Depending on the parameter D/F for three-component mixtures at the transi-
tion to the third class of fractioning, the following splits are feasible: (1) 1 : 1,2,3;
(2) 1 : 2,3; (3) 1,2 : 2,3; (4) 1,2 : 3; (5) 1,2,3 : 3. For four-component mixtures the