Page 27 - Distillation theory

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Phase Equilibrium and Its Geometric

Presentation

1.1. Introduction
The process of distillation can be presented as consisting of numerous states of
phase equilibrium between flows of liquid and vapor that have different compo-
sitions. Geometric analysis of the distillation process represented in the so-called
concentration space (C) is the main instrument for understanding its regularities.
That is why, before we start the examination of the existing distillation process
and its geometric interpretation, it is necessary to consider geometric interpreta-
tion, of the phase equilibrium. Numerous methods of calculating phase equilib-
rium are described in many monographs and manuals (see, e.g., Walas [1985]).
We will not repeat these descriptions but instead will examine only represen-
tation of equilibrium states and processes in concentration space.

1.2. Concentration Space
Molar composition of an n-component mixture is presented as an array that holds
molar concentrations of all components:

m i
(1.1)
x i =
m i

x i = 1 (1.2)
where m i is the amount of moles of the component i in the mixture.
Concentration space of an n-component mixture C n is a space in which every
point corresponds to a mixture of definite composition. Dimensionality of concen-
tration space corresponds to the number of concentrations of components that can
be fixed independently.
The (n − 1) concentration for an n-component mixture can be fixed indepen-
dently because concentration of the nth component can be found from Eq. (1.2).
That is why the dimensionality of the concentration space of binary mixture C 2 is
one, of ternary mixture C 3 – two, of four-component mixture C 4 – tree, etc.
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