Page 137 - Distillation theory

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5.2 Calculation of Distillation at Minimum Reflux for Ideal Mixtures 111

The approximate method of calculation of the minimum reflux mode for three-
component mixtures at the absence of “tangential pinch” was suggested in the
work (Stichlmair, Offers, & Potthoff, 1993).
Thepreviouslyenumeratedmethodsofcalculationoftheminimumrefluxmode
for nonideal zeotropic and azeotropic mixtures have considerable defects: (1)
they presuppose preliminary setting of possible separation product compositions,
which is a complicated independent task for azeotropic mixtures; (2) they embrace
only three- and four-component mixtures or only special splits; and (3) they do
not take into consideration the leap of concentrations in feed cross-section.
In practice, the enumerated calculation methods are hardly used when design-
ing distillation units because of these defects. Calculation of the minimum reflux
mode is not conducted at all, and the working reflux number and number of plates
in the sections are chosen, as a rule, arbitrarily, based on the designer’s intuition
and experience, which can lead to considerable overstating of separation costs.
To overcome these defects, it was necessary to apply the conception of sharp
separation and to develop the theory of distillation trajectory tear-off from the
boundary elements of concentration simplex at sharp separation (Petlyuk, Vino-
gradova, & Serafimov, 1984; Petlyuk, 1998) and also to develop the geometric
theory of section trajectories joining in feed cross-section in the mode of min-
imum reflux that does not contain simplifications and embraces mixtures with
any number of components and any splits (Petlyuk & Danilov, 1998; Petlyuk &
Danilov, 1999b; Petlyuk & Danilov, 2001a; Petlyuk & Danilov, 2001b).
The significance of the methods, based on the geometric distillation theory,
consists in their universality, rigor, and reliability. To obtain the result, it is not
necessary to set any estimation parameters and possible separation product com-
positions; minimum reflux number for these compositions and distillation trajec-
tory at this reflux number are defined in the process of this calculation.
The geometric distillation theory also allowed the development of the general
methods of separation flowsheets synthesis for azeotropic mixtures and design
calculation of simple and complex distillation columns, which is examined in the
chapters to follow.
This chapter answers two fundamental questions of the conceptual designing
of distillation units:

1. How to determine which sharp splits of any multicomponent mixture are
feasible?
2. How to determine which minimum energy is necessary for the separation
of any multicomponent mixture at any feasible split?

5.2. Calculation of Distillation at Minimum Reflux for Ideal Mixtures
A number of regularities of the minimum reflux mode are common for the ideal,
nonideal, and even azeotropic mixtures. Among these regularities is the follow-
ing: each section trajectory at minimum reflux and at sharp separation is partially