Page 289 - Academic Press Encyclopedia of Physical Science and Technology 3rd Chemical Engineering

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Encyclopedia of Physical Science and Technology EN006C-252 June 27, 2001 14:15

Fluid Mixing 89

chemical reaction requirements for both small and large
tanks.
Some processes are governed by the maximum impeller
zone shear rate. For example, the dispersion of a pig-
ment in a paint depends upon the maximum impeller zone
shear rate for the ultimate minimum particle size. How-
ever, when constant tip speed is used to maintain this, the
other geometric variables must be changed to maintain a
reasonable blend time, even though process results on full
scale will probably take much longer than those on small
scale.
Two aspects of scaleup frequently arise. One is building
a model based on pilot plant studies that develop an under-
FIGURE 16 Typical dimensionless process correlation of blend standing of the process variables for an existing full-scale
number θ N versus Reynolds number. mixing installation. The other is taking a new process and
studying it in the pilot plant in such a way that pertinent
dimensionless group around the process result. For exam- scaleup variables are worked out for a new mixing instal-
ple, including polymerization yield, including productiv- lation.
ity of a fermentation process, or incorporating the rate of There are a few principles of scaleup that can indicate
absorption of flue gas into caustic does not allow a dimen- what approach to take in either case. Using geometric sim-
sionless type of process grouping. Thus, it is not practical ilarity, the macroscale variables can be summarized as fol-
to deal with dimensionless numbers when we do not have lows:
the ability to write a dimensionless group around the mix-
ing process result. Blend and circulation times in the large tank will be
There are as many potential scaleup parameters as there much longer than in the small tank.
are individual process mixing results. However, we can Maximum impeller zone shear rate will be higher in
make some generalizations which are very helpful in deal- the larger tank, but the average impeller zone shear
ing with actual mixing problems, but for reliable scaleup, rate will be lower; therefore, there will be a much
some experimental verification of the scaleup method to greater variation in shear rates in a full-scale tank than
be used is desirable. in a pilot unit.
For example, it is found that the mass transfer coeffi- Reynolds numbers in the large tank will be higher,
cient, K G a, for gas–liquid processes, is mostly a function typically on the order of 5–25 times higher than those
of the linear superficial gas velocity and the power per unit in a small tank.
volume with the constant D/T ratio for various size tanks. Large tanks tend to develop a recirculation pattern
This is because the integrated volumetric mass transfer co- from the impeller through the tank pack to the
efficient over the entire tank can be quite similar in large impeller. This results in a behavior similar to that for a
and small tanks even though the individual bubble size, number of tanks in a series. The net result is that the
interfacial area, and mass transfer coefficient can vary at mean circulation time is increased over what would be
specific points within the small and large tanks. predicted from the impeller pumping capacity. This
It has also been observed that suspension and blend- also increases the standard deviation of the circulation
ing of slurries operating in the hindered settling range times around the mean.
(such as with particle sizes on the order of 100 mesh or Heat transfer is normally much more demanding on a
smaller) tend to show a decreasing power per unit volume large scale. The introduction of helical coils, vertical
on scaleup. When this relationship is used, the blend time tubes, or other heat transfer devices causes an
for the large tank is much longer than it is for the small increased tendency for areas of low recirculation to
tank. Blend time is not a major factor in a large slurry hold- exist.
ing tank in the minerals processing industry, and there- In gas-liquid systems, the tendency for an increase in
fore, that factor is not an important one to maintain on the gas superficial velocity upon scaleup can further
scaleup. increase the overall circulation time.
For homogeneous chemical reactions, most of the effect
of the mixer occurs at the microscale level. Microscale What about the microscale phenomena? These are de-
mixing is largely a function of the power per unit volume, pendent primarily on the energy dissipation per unit vol-
and maintaining equal power per unit volume gives similar ume, although they must also be concerned about the