Page 244 - Distillation theory

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7

Trajectories of the Finite Columns and Their

Design Calculation

7.1. Introduction
In this chapter, we turn from infinite columns to real finite columns. On the ba-
sis of the analysis performed previously for infinite columns, we determine the
regularities of location of finite columns trajectories in the concentration simplex
and, in particular, the regularities of joining of finite column section trajectories.
This will allow us to develop simple and reliable algorithms of distillation design
calculation.
Designing distillation columns is particularly important because of the great ex-
penditures of energy for mixture separation. Simplified empirical methods were
first used for designing. The method of Underwood–Fenske–Gilliland (calcula-
tion of minimum reflux number according to Underwood method [1948], calcu-
lation of minimum trays number according to Fenske method [1932], and usage
of the empirical correlation of Gilliland [1940] for the transition from the infinite
number of trays and from the infinite reflux to their finite calculation values) is
among them. A big number of other approximate methods that could produce
mistakes of unforeseen magnitude, especially for nonideal mixtures, were also
introduced.
Therefore, two rigorous in the limits of conception of theoretical step of sep-
aration (Sorel, 1893) algorithms of distillation columns calculation – Lewis and
Matheson method (1932) and Thiele and Geddes method (1933) – were intro-
duced already in the 1930s. The first of them is based on traywise grouping of the
equations describing distillation process (phase equilibrium equations, equations
of material and thermal balance), the second one is based on componentwise
grouping of these equations. Both methods presuppose a fixed number of trays
in the column, and for this reason they are not design ones. Both methods are
iterative and do not guarantee the solution of the task (i.e., ensuring of equation
system validity with sufficient precision). These methods were widely adopted in
practice and developed in various modifications only with the advent of computers
in the end of the 1950s. The componentwise methods are most widely practised in
modern program systems for simulating calculation of chemical engineering units.

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