Page 23 - Design and Operation of Heat Exchangers and their Networks

10 Design and operation of heat exchangers and their networks

The lumped parameter model assumes that temperatures of fluid streams
and solid materials (if they are involved) are only functions of the time var-
iable, that is, the fluid and the solid material have an infinite large value of
thermal conductivity, therefore, a uniform temperature distribution,
which greatly simplifies the mathematical model describing the transient
behavior of heat exchangers and is convenient for controller design.
The distributed parameter model takes variations of the temperatures with
both time and space variables into account, which may more closely coin-
cide with the real operation condition than the lumped parameter model.
As pointed out by Pantelides and Barton (1993), the modeling of distrib-
uted parameter systems is of strategic importance for the future evolution
of general-purpose modeling environments.
For both the lumped and distributed parameter systems, the transient
behavior can generally be described mathematically by mixed sets of differ-
ential and algebraic equations. To obtain the transient responses of heat
exchangers, the differential equation systems based on the previously men-
tioned approaches are solved by means of different methods such as the
finite-difference method, finite-volume method, numerical inversion of
the Laplace transform, and numerical inversion of the Fourier transform.
Furthermore, one may derive transient functions to analyze the response
characteristics in the frequency domain.
There are various types of heat exchangers with different constructions
and flow arrangements. Since many variables are involved and a variety of
disturbances might be possible, no general solution can be obtained for the
dynamic simulation of heat exchangers. The solutions for some specific types
of heat exchangers can be found in the literature (Roetzel and Xuan, 1999).
The transient responses to step disturbances are often reported. For deriving
differential equations of transient behavior, different flow patterns may be
used except for the lumped parameter approach that pays no attention to
the flow pattern of the fluid streams in the exchanger. In the distributed
parameter approach, the most common case corresponds to assuming the
plug-flow pattern, which is widely used in the steady-state procedure and
the early phase of dynamic simulation. To account for the possible flow mal-
distribution, the conventional plug-flow model is modified, and the dis-
persed plug-flow model (Roetzel and Xuan, 1992; Xuan and Roetzel,
1993) may be applied to the dynamic simulation of heat exchangers. In this
book, the achievements in those areas are reviewed, and most recent devel-
opments are evaluated.