Page 36 - Coulson Richardson's Chemical Engineering Vol.6 Chemical Engineering Design 4th Edition

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INTRODUCTION TO DESIGN
need to calculate the degrees of freedom in a formal way. He will usually have intuitive
feel for the problem, and can change the calculation procedure, and select the design
variables, as he works through the design. He will know by experience if the problem is
correctly specified. A computer, however, has no intuition, and for computer-aided design
calculations it is essential to ensure that the necessary number of variables is specified to
define the problem correctly. For complex processes the number of variables and relating
equations will be very large, and the calculation of the degrees of freedom very involved.
Kwauk (1956) has shown how the degrees of freedom can be calculated for separation
processes by building up the complex unit from simpler units. Smith (1963) uses Kwauk’s
method, and illustrates how the idea of “degrees of freedom” can be used in the design
of separation processes.

1.9.2. Selection of design variables
In setting out to solve a design problem the designer has to decide which variables are to
be chosen as “design variables”; the ones he will manipulate to produce the best design.
The choice of design variables is important; careful selection can simplify the design
calculations. This can be illustrated by considering the choice of design variables for a
simple binary flash distillation.
For a flash distillation the total degrees of freedom was shown to be (C C 4), so for
two components N d D 6. If the feed stream flow, composition, temperature and pressure
are fixed by upstream conditions, then the number of design variables will be:
0
N D 6 C C 2 D 6 4 D 2
d
So the designer is free to select two variables from the remaining variables in order to
proceed with the calculation of the outlet stream compositions and flows.
If he selects the still pressure (which for a binary system will determine the vapour
liquid equilibrium relationship) and one outlet stream flow-rate, then the outlet compo-
sitions can be calculated by simultaneous solution of the mass balance and equilibrium
relationships (equations). A graphical method for the simultaneous solution is given in
Volume 2, Chapter 11.
However, if he selects an outlet stream composition (say the liquid stream) instead of
a flow-rate, then the simultaneous solution of the mass balance and v l e relationships
would not be necessary. The stream compositions could be calculated by the following
step-by-step (sequential) procedure:
1. Specifying P determines the v l e relationship (equilibrium) curve from experi-
mental data.
2. Knowing the outlet liquid composition, the outlet vapour composition can be calcu-
lated from the v l e relationship.
3. Knowing the feed and outlet compositions, and the feed flow-rate, the outlet stream
flows can be calculated from a material balance.
4. An enthalpy balance then gives the heat input required.

The need for simultaneous solution of the design equations implies that there is a
recycle of information. Choice of an outlet stream composition as a design variable in