Page 69 - Distillation theory

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3.2 Distillation Trajectories of Finite and Infinite Columns 43

residue curves bundles inside the concentration space is different, as can be seen
in Figs. 3.1b and 3.1c.
Taking into consideration the aforesaid, sections of Chapter 1 referring to re-
sidue curves bundles, to the structural elements of these bundles, and to the matrix
description of the concentration space structure are completely valid regarding
distillation trajectories under the infinite reflux.
In literature, several different terms for distillation regions at the infinite reflux
are used: simple distillation regions, basic regions of distillation, and regions of
closed distillation. We use a longer but more exact term – distillation region at the
infinite reflux (for the sake of briefness, we sometimes use just distillation region −
∞
Reg ).

3.3. Distillation Trajectories of Finite and Infinite Columns at Set
Feed Composition

3.3.1. Dimensionality of Product Composition Regions for Finite
and Infinite Columns

From Eq. (3.2) and the equation of material balance of the column, a simple
mathematic model follows:

(1) (2) (N)
x D = x B K K ... K (i = 1, 2 ... n) (3.3)
i i i
(i = 1, 2 ... n) (3.4)
x D (D/F) + x B (1 − D/F) = z F
From the system of Eqs. (3.3) ÷ (3.4), it follows that at a given feed composition
z F and at a fixed field of phase equilibrium coefficients, K i = f i (T, P, x 1 ,... x n )
separation products compositions x D and x B depend on only two parameters –
relative withdrawal of one of the products D/F and amount of theoretical plates N.
At infinite reflux, the location of feeding plate does not influence the compositions
of distillation products nor profile of concentrations. This is quite understandable –
the external flow coming to the feeding plate is infinitely small in comparison with
internal flows in the column.
Let’s assume at the beginning that for a set composition of feeding z F unique
distillation products compositions x D and x B (uniqueness of stationary state) cor-
respond to one set of parameters D/F and N. This assumption is not always carried
into effect (see Section 3.7), but in the majority of cases it is. If it is fulfilled, at all
feasible values of parameters D/F and N, all the points x D (and also x B ) form in
the concentration simplex of any dimensionality a two dimensional region (possi-
ble product composition regions at fixed feeding composition are two dimensional
because the coordinates of points of these regions depend on two parameters). In
particular, for three-component mixtures this region is part of the concentration
triangle.
Obviously, at a finite number of stages, the distillation trajectory under the
infinite reflux should lie in one of the c-lines and cannot pass through a stationary
point of the concentration simplex, start or end in it. At the infinite number of