Page 29 - Distillation theory

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1.3 Phase Equilibrium of Binary Mixtures 3

the distillation column):

(1.3)
Fx iF = Dx iD + Bx iB
(1.4)
(D + B)x iF = Dx iD + Bx iB
D(x iF − x iD ) = B(x iB − x iF ) (1.5)
Equation (1.5) represents the so-called lever rule: points x iF , x iD , and x iB are
located on one straight line, and the lengths of the segments [x iF , x iD ] and [x iB ,
x iF ] are inversely proportional to the flow rates D and B (Fig. 1.1b). Mixture
with a component number n ≥ 5 cannot be represented clearly. However, we will
apply the terms simplex of dimensionality (n − 1) for a concentration space of
n-component mixture C n , hyperfaces C n−1 of this simplex for (n − 1)-component
constituents of this mixture, etc.

1.3. Phase Equilibrium of Binary Mixtures

An equilibrium between liquid and vapor is usually described as follows:
y i = K i x i (1.6)
where y i and x i are equilibrium compositions of vapor and liquid, respectively,
and K i is the liquid–vapor phase equilibrium coefficient.
To understand the mutual behavior of the components depending on the degree
of the mixture’s nonideality caused by the difference in the components’ molecu-
lar properties, it is better to use graphs y 1 − x 1 , T − x 1 , T − y 1 , K 1 − x 1 , and K 2 − x 1
(Fig. 1.2). In Fig. 1.2, the degree of nonideality increases from a to h: a is an ideal
mixture, b is a nonideal mixture with an inflection on the curve y 1 − x 1 (a and b
are zeotropic mixtures), c is a mixture with a so-called tangential azeotrope (curve
y 1 − x 1 touches the diagonal in the point x 1 = 1), d is an azeotropic mixture with
minimum temperature, e is a mixture with a so-called inner tangential azeotrope,
f is a mixture with two azeotropes, g is a heteroazeotropic mixture, and h is an
azeotropic mixture with two liquid phases. Azeotrope is a binary or multicompo-
nent mixture composition for which the values of phase equilibrium coefficients
for all components are equal to one:

K i Az = 1 (i = 1, 2,... n) (1.7)
Heteroazeotrope is an overall composition of a mixture with two liquid phases
for which the values of the overall coefficients of phase equilibrium for all com-
ponents are equal to one:
K Haz = 1 (i = 1, 2,... n) (1.8)
ov,i
(1) (2)
where K ov,i = y i /x ov,i , x ov,i = x a + x i (1 − a), a is the portion of the first liq-
i
(1) (2)
uid phase in the whole liquid, and x and x are the concentrations of the ith
i i
component in first and second liquid phases correspondingly.
In this book, we will see that the previously discussed features are of great
importance. Even b case results in serious abnormalities of the distillation process.