Page 50 - Distillation theory

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24 Basic Concepts of Distillation

Let’s transform Eq. (2.1), dividing all its members by V − D and taking into
account that V = L+ D and L/D = R:

(2.5)
y j−1 = [R/(R + 1)]x j + [1/(R + 1)]x D
While deriving the Eq. (2.5), we omitted index i, as for the binary mixture the
concentration of one component defines the composition. Besides, we omitted
index j for V and L flows, accepting their constancy along the section lengths.
Equation (2.5) represents the material balance equation and is called an oper-
ating line equation.
If we make x j = x D substitution in Eq. (2.5), we get y D = x D . This means that
at x = x D , the operation line crosses the diagonal line. Operation line has a tangent
of slope angle to the axis of abscissas R/R + 1. It allows us to draw the operating
lines of sections (e.g., they are given for liquid feed in Fig. 2.2a).
The steps drawn between the section operating lines and the equilibrium curve
illustrate the compositions on the trays: points on the operating lines correspond
according to Eq. (2.5) to the composition of liquid from the jth tray, which meets
the composition of vapor from the tray below and points on the equilibrium curve
correspond to the compositions of liquid and vapor leaving the jth tray. Figure 2.2a
allows a number of important conclusions:

1. The operating line of rectifying section has two ultimate positions: it
may coincide with the diagonal line when R =∞; it may be in a point
x j = x F reach the equilibrium curve as it is shown in Fig. 2.2a (line 3 corre-
sponds to minimum reflux R = R min ).
2. When R =∞ (infinite reflux mode), the number of theoretical trays is
minimum, i.e., n = n min (the steps between the equilibrium curve and the
diagonal line are the largest ones).
3. When R = R min (minimum reflux mode), the number of stages is infinite
(in the feed point, the step between stages becomes equal to zero − this is
an area of constant concentrations or pinch).
4. With the reflux increasing, the number of trays decreases.

For multicomponent mixtures, the regularities are more complex. But as a rule,
there is some minimum R-value at which the number of stages is infinite, and the
required number of trays decreases when the R-value increases.

2.2.2. Influences of Nonideality

Now let’s see how the nonideality of binary mixtures influences the distillation
process (Fig. 2.2b).
From Fig. 2.2b it is clear that, in this particular case, the infinite number of
steps and, respectively, the area of constant concentrations appear in the point of
tangency of the top section operation line to the equilibrium curve (this point is in-
dicated as x pinch ), but not in the feed point. Such an area of constant concentrations
is called a tangential pinch.