Page 245 - Distillation theory

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7.1 Introduction 219

Among these methods, the modification that was named “inside-out” (Russel,
1983) is the most widely used.
But the existing methods of distillation calculation (simulating methods) are
poorly adapted to designing. They do not answer essential questions, such as: (1)
is the set split feasible? (2) which minimum reflux number is necessary to ensure
the set split? and (3) which numbers of the trays in column sections are sufficient
to ensure the set split?
Therefore, the answers to these questions are being looked for “in the dark,”
setting tray numbers in column sections at random.
The second problem is the convergence of iterative process that is not guaran-
teed but depends on numerous parameters of calculating process, such as those
set by the designer assumed in the initial approximation (estimated) profiles of
vapor and liquid flow rates, profiles of temperature, and components concentra-
tions at theoretical trays. It is usually necessary to make numerous calculations at
different parameters.
If, finally, the designer obtains the result acceptable to his opinion then he does
not know how far he is from the optimal parameters of the column and of the mode
in it. The search for parameters in such conditions turns into a nearly hopeless
task, especially in conditions of time deficit usual to the designing process, and
the application of mathematical optimization methods also does not lead to the
achievement of the goal because of the difficulties caused by the availability of
“local” extremums and discrete variables. This leads to the fact that in practice the
task of designing is not solved optimally (i.e., the expenditures for the separation
unwarrantably grow).
This situation is explained by the fact that the above-described algorithms do
not take into consideration the regularities of location of distillation trajectory
bundles in the concentration space.
The geometric theory of distillation suggests a new approach to the task of its
designing. This approach ensures guaranteed obtaining of optimal design param-
eters without any participation of the designer in the calculation process.
The geometric approach based on calculation of reversible distillation trajecto-
ries, on linearization of separatrix distillation trajectory bundles, and on realization
of calculations by means of the method “tray by tray” required the development of
the theory of joining of sections trajectory bundles at reflux bigger than minimum
for any splits (Petlyuk & Danilov, 2001a, 2001b). Similar approach was applied
before for two splits simplest in calculating aspect – the direct and the indirect
ones (Julka & Doherty, 1990), (Doherty & Melone, 2001). But the algorithms use-
ful for the direct and the indirect splits cannot be used for any intermediate ones
and ones with a distributed component. Limitations of these algorithms are of
fundamental nature (i.e., they are conditioned by the peculiar structure of section
trajectory bundles for the direct and the indirect splits). This fact is discussed later
in this present chapter.
The geometric approach develops methods of conceptual design calculation of
simple and complex distillation columns (i.e., methods of determination of optimal
values of the main process parameters, of the numbers of theoretical trays at