Page 135 - Distillation theory

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5.1 Introduction 109

distillation process and the main instrument of approximate design of distillation
unit.
Qualitative leap to the second stage (i.e., to the distillation theory of ideal mul-
ticomponent mixtures) was realized by Underwood (1945, 1946a, 1946b, 1948).
Underwood succeded in obtaining the analytical solution of the system of distil-
lation equations for infinite columns at two important simplifying assumptions –
at constant relative volatilities of the components (i.e., which depend neither on
the temperature nor on mixture composition at distillation column plates) and at
constant internal molar flow rates (i.e., at constant vapor and liquid flow rates at
all plates of a column section). The solution of Underwood is remarkable due to
the fact that it is absolutely rigorous and does not require any plate calculations
within the limits of accepted assumptions.
The solution of Underwood gave impetus to numerous investigations based on
this approach. Part of these works was directed to the creation of geometric inter-
pretation of the results obtained from the solution of the Underwood equations
system. It is impossible without such interpretation to form a true notion of the
general regularities of the distillation process of ideal mixtures. For one-section
columns, geometric analysis of trajectories, stationary points, and separatrixes of
distillation was realized even before the works of Underwood by Hausen (1934,
1935, 1952) on the basis of calculations using the method “tray by tray.”
The works (Franklin & Forsyth, 1953; White, 1953; Vogelpohl, 1964; Petlyuk,
Avet’yan, & Platonov, 1968; Vogelpohl, 1970; Shafir, Petlyuk, & Serafimov, 1984;
Franklin, 1986, 1988a, 1988b), in which the evolution of product and stationary
points in concentration triangles and tetrahedrons for two-section columns at a
given feed composition and variable reflux number was examined, appeared after
the articles of Underwood. Underwood’s method was generalized in the work
(Acrivos & Amundson, 1955) for continuous mixtures (i.e., for mixtures consisting
of components whose properties are changed continuously from one component
to another).
Unfortunately, the method of Underwood cannot be applied to nonideal mix-
tures and even to ideal ones, relative volatilities of the components that depend
on the temperature. Therefore, “tray by tray” method was used for the calculation
of minimum reflux mode for such ideal mixtures (Shiras, Hanson, & Gibson, 1950;
Erbar & Maddox, 1962; McDonough & Holland, 1962; Holland, 1963; Lee, 1974;
Chien, 1978; Tavana & Hanson, 1979) and others.
In the mentioned works, it is suggested that “tray by tray” method should be
used only for the part of the column located between zones of constant concentra-
tions. The special equations, taking into account phase equilibrium between the
meeting vapor and liquid flows, are applied to such zones. Approximations to the
mode of minimum reflux are estimated by means of gradual increase of theoretical
plates number in that part of the column for which “tray by tray” method is used.
The attempts to create a theory and to develop methods of minimum reflux
number calculation for nonideal and azeotropic mixtures began later.
The notion of distillation trajectory bundles at finite reflux and at fixed product
composition, which is important for the further development of the theory, was