Page 42 - Chemical engineering design

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INTRODUCTION TO DESIGN
benefit. Sub-division, and optimisation of the sub-units rather than the whole, will not
necessarily give the optimum design for the whole process. The optimisation of one unit
may be at the expense of another. For example, it will usually be satisfactory to optimise
the reflux ratio for a fractionating column independently of the rest of the plant; but if the
column is part of a separation stage following a reactor, in which the product is separated
from the unreacted materials, then the design of the column will interact with, and may
well determine, the optimisation of the reactor design.
In this book the discussion of optimisation methods will, of necessity, be limited to a
brief review of the main techniques used in process and equipment design. The extensive
literature on the subject should be consulted for full details of the methods available, and
their application and limitations; see Beightler and Wilde (1967), Beveridge and Schechter
(1970), Stoecker (1989), Rudd and Watson (1968), Edgar and Himmelblau (2001). The
books by Rudd and Watson (1968) and Edgar and Himmelblau (2001) are particularly
recommended to students.

1.10.1. General procedure
When setting out to optimise any system, the first step is clearly to identify the objective:
the criterion to be used to judge the system performance. In engineering design the
objective will invariably be an economic one. For a chemical process, the overall objective
for the operating company will be to maximise profits. This will give rise to sub-objectives,
which the designer will work to achieve. The main sub-objective will usually be to
minimise operating costs. Other sub-objectives may be to reduce investment, maximise
yield, reduce labour requirements, reduce maintenance, operate safely.
When choosing his objectives the designer must keep in mind the overall objective.
Minimising cost per unit of production will not necessarily maximise profits per unit time;
market factors, such as quality and delivery, may determine the best overall strategy.
The second step is to determine the objective function: the system of equations, and
other relationships, which relate the objective with the variables to be manipulated to
optimise the function. If the objective is economic, it will be necessary to express the
objective function in economic terms (costs).
Difficulties will arise in expressing functions that depend on value judgements; for
example, the social benefits and the social costs that arise from pollution.
The third step is to find the values of the variables that give the optimum value of the
objective function (maximum or minimum). The best techniques to be used for this step
will depend on the complexity of the system and on the particular mathematical model
used to represent the system.
A mathematical model represents the design as a set of equations (relationships) and, as
was shown in Section 1.9.1, it will only be possible to optimise the design if the number
of variables exceeds the number of relationships; there is some degree of freedom in the
system.

1.10.2. Simple models

If the objective function can be expressed as a function of one variable (single degree of
freedom) the function can be differentiated, or plotted, to find the maximum or minimum.