Page 51 - Distillation theory

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2.3 Geometric Interpretation of Multicomponent Mixture Distillation: Splits 25

Now, if we consider the tangential azeotrope mixture at x 1 = 1 (Fig. 1.2c), then
for x D = 1 the operation line, tangent to a equilibrium curve, should coincide
with the diagonal line (i.e., R min =∞). This makes the production of high-purity
component 1 practically impossible.
If we take the azeotropic mixture (Fig. 1.2d), we see that for points x D and x B
divided by an azeotrope, the distillation process become impossible.

2.3. Geometric Interpretation of Multicomponent Mixture
Distillation: Splits
Geometric interpretation of distillation process of binary mixtures has been deci-
sive in understanding the subject and the basic principles of the distillation units
design development. Geometric interpretation of multicomponent mixtures dis-
tillation is also important for deep insight into the pattern of the multicomponent
mixture distillation and better understanding of the methods of design of the units
used for the separation of these mixtures.
As Chapter 1 introduced, the composition of a ternary (three-component) mix-
ture is symbolized by a point in the concentration triangle, and the composition of
a quaternary mixture is also symbolized by a point in the concentration tetrahe-
dron. The curve of points illustrating the compositions on the distillation column
trays is a trajectory of the distillation process within the composition space. The
regularities of these trajectories arrangement are the essence of the multicompo-
nent mixture distillation general geometric theory forming the foundation for an
optimum design.
Unfortunately, it is impossible to visualize the trajectories of distillation of
mixtures with five or more components. However, it will not prevent us from
investigating the regularities of multicomponent mixture distillation because we
have already observed all these regularities while analyzing the arrangement tra-
jectories of the quaternary mixture distillation.
Let’s go on now with the term split. Under the split for the preset feed compo-
sition x iF , we understand the set of components of each product of separation.
Under the sharp split, we understand such a case when both product points
belong to the boundary elements of the composition space (i.e., each product
contains only a part of the feed components).
As far as the aim of distillation is, more often, the separation of the mixture
into pure components, we are mostly interested in the sharp splits.
The rest of the splits we call the nonsharp splits.
For a three-component ideal mixture (here and further on component 1 is the
lightest, component 2 is the intermediate, and component 3 is the heaviest), an
example of sharp split is 1 : 2, 3 (i.e., x 2D = 0, x 3D = 0, x 1B = 0 − point x iD belongs
to vertex 1, point x iB belongs to side 2-3 of triangle). This split has got an additional
name − direct split (the lightest component is separated from the remaining ones).
For a four-component ideal mixture at K 1 > K 2 > K 3 > K 4 , the direct split
is 1 : 2, 3, 4. The indirect splits of ternary and quaternary mixtures are 1, 2:3 or
1, 2, 3 : 4, respectively.