Page 146 - Distillation theory

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120 Distillation Trajectories and Conditions of Mixture Separability

At nonsharp separation, the stationary points of section working regions,
except the stable node N , are located outside the concentration simplex (the
+
direction of trajectory from the product is accepted). At sharp separation, other
t
stationary points – trajectory tear-off points x from the boundary elements of
concentration simplex – are added to the stable node. These are the saddle points
S and, besides that, if the product point coincides with the vertex corresponding
to the lightest or to the heaviest component, then this point becomes an unstable
−
node N .
These qualitative regularities have a general nature and apply not only to ideal
mixtures, but also to nonideal ones. Only the possibility of analytic solution for the
minimum reflux mode (Underwood equation system) and linearity of separatrixes
R
andofdividingsurfacesandhypersurfacesofsectionregionsReg w,r andReg R are
w,s
specific for ideal mixtures. The latter circumstance was also extended to nonideal
mixtures in a number of approximate methods (Levy et al., 1985; Julka & Doherty,
1990; Stichlmair et al., 1993).

5.3. Trajectory Tear-Off Theory and Necessary Conditions
of Mixture Separability

The task of determining distillation product compositions of ideal mixtures in
infinite column at minimum reflux is discussed in the previous section. The Un-
derwood equation system solves this task for set composition x F and thermal state
of feeding q at two set parameters (e.g., R and D/F or d i and d j ).
For nonideal zeotropic and azeotropic mixtures, the solution of the task of min-
imum reflux mode calculation in such a statement run across the insurmountable
calculating difficulties in the majority of cases.
Thedevelopmentofdistillationtrajectorybundlestheoryatfiniterefluxshowed
that the task of minimum reflux mode calculation for nonideal zeotropic and
azeotropic mixtures can be solved in another statement: at set composition x F and
thermal state q of feeding, it is necessary to determine minimum reflux number
R min for the set product compositions x D and x B of sharp separation and set
permissible concentrations of admixtures in the products.
If the problem is stated in this way, it is necessary to determine what product
compositions x D and x B of sharp separation are feasible at distillation of nonideal
zeotropic and azeotropic mixtures. The theory of distillation trajectory tear-off
from the boundary elements of concentration simplex answers this question.

5.3.1. Conditions of Distillation Trajectory Tear-Off at Sharp Splits

Let’s examine two constituent parts of section distillation trajectory at the example
of sharp preferable split of three-component ideal mixture (Fig. 5.6a): the part
located in the boundary element (the side of concentration triangle), and the part
located inside concentration simplex (triangle). There is a trajectory tear-off point
t
from the boundary element x between these two parts.