[Luyben] Process Mod.. - Student subdomain for University of Bath

INTRODUmION 3
Since this is a book on control and instrumentation, we might also mention that a
high-level alarm and/or an interlock (a device to shut off the feed if the level gets too
high) should be installed to guarantee that the tank would not spill over. The tragic
accidents at Three Mile Island, Chernobyl, and Bhopal illustrate the need for welldesigned
and well-instrumented plants.
The design of the system would involve an economic balance between the cost
of a taller tank and the cost of a bigger pipe, since the bigger the pipe diameter the
lower is the liquid height. Figure 1.2 shows the curve of !i versus F for a specific
numerical case.
So far we have considered just the traditional steadystate design aspects of
this fluid flow system. Now let us think about what would happen dynamically if we
changed Fe. How will he) and F$) vary with time? Obviously F eventually has to
end up at the new value of F,. We can easily determine from the steadystate design
curve of Fig. 1.2 where h will go at the new steadystate. But what paths will h(,, and
Fgb take to get to their new steadystates?
Figure 1.3 sketches the problem. The question is which curves (1 or 2) represent
the actual paths that F and h will follow. Curves 1 show gradual increases in
h and F to their new steadystate values. However, the paths could follow curves 2
where the liquid height rises above its final steadystate value. This is called
“overshoot.” Clearly, if the peak of the overshoot in h is above the top of the tank,
we would be in trouble.
Our steadystate design calculations tell us nothing about what the dynamic
response to the system will be. They tell us where we will start and where we will
end up but not how we get there. This kind of information is what a study of the
dynamics of the system will reveal. We will return to this system later in the book to
derive a mathematical model of it and to determine its dynamic response quantitatively
by simulation.
Example 1.2. Consider the heat exchanger sketched in Fig. 1.4. An oil stream passes
through the tube side of a tube-in-shell heat exchanger and is heated by condensing
steam on the shell side. The steam condensate leaves through a steam trap (a device