Page 203 - Practical Control Engineering a Guide for Engineers, Managers, and Practitioners

CHAPTER 7

Distributed

Processes

ost of the example processes presented so far have been
lumped. That is, the example processes have been described
Mby one or more ordinary differential equations, each repre-
senting a process element that was relatively self-contained. Further-
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more, each ordinary differential equation described a lump." A
process with dead time does not yield to this lumping" approach
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and can in some ways be considered a distributed process which is
the subject of this chapter.

7-1 The Tubular Energy Exchanger-Steady State
Consider Fig. 7-1 which shows a jacketed tube of length L. A liquid
flows through the inside tube. The jacket contains a fluid, say steam,
from which energy can be transferred to the liquid in the tube. To
describe how this process behaves in steady state, a simple energy
balance can be made, not over the whole tube but over a small but
finite section of the tube. Several assumptions (and idealizations)
must be made about this new process.
1. The steam temperature ~ in the jacket is constant along the
whole length of the tube. The tube length is L. The steam
temperature can vary with time but not space.
2. The tube is cylindrical and has a cross-sectional area of
2
A = trD I 4 where D is the diameter of the inner tube.
3. The liquid flows in the tube as a plug at a speed v. That is,
there is no radial variation in the liquid temperature. There is
axial temperature variation of the liquid due to the heating
effect of the steam in the jacket but there is no axial transfer of
energy by conduction within the fluid. This is equivalent to
saying the radial diffusion of energy is infinite compared to
axial diffusion. The temperature of the flowing liquid
therefore is a function of the axial displacement z, as in T(z).

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