Chemical Engineering August 2021 - 28

Cover Story
Time and Length Scales of
Mixing: The Macro Scale
Successfully scaling up a mixing process involves understanding several important timescale
parameters that can impact chemical reactions and equipment performance
R. K. Grenville,
J. J. Giacomelli,
B. A. Boyer and
S. J. Johnson
Philadelphia Mixing
Solutions, An SPX
FLOW Brand
IN BRIEF
MEAN RESIDENCE TIME
VELOCITY AND
CIRCULATION TIME
BLEND TIME
BLENDING AND
CIRCULATION
CIRCULATION VERSUS
BLEND TIME
FINAL THOUGHTS
M
any industrial processes are
defined by rates. For example,
rates of mass and heat transfer,
rates of reaction and rates of
addition to a reactor. Even a batch process
can be described in terms of a rate - the
number of batches to be completed in a
day. If mixing is required to achieve the process
result, then the rate of mixing must
often be related to the process rate. In reaction
engineering, the ratio of mixing rate to
reaction rate is the Damkohler number [1].
It is also useful to consider the inverse of
the rate, which is a timescale. Comparison
of rates or timescales enables an engineer
to determine which is likely to dominate
the process and identify when interactions
are likely to occur. Understanding the role
of mixing and quantification of these rates
often plays an important role in successful
process design and scaleup.
There is a spectrum of scales to consider
depending on the nature of the process in
question. There are five timescales, with associated
length scales, of interest in mixing
processes, which are defined in Table 1.
Note that in this article, the first three timescales,
which take place at the scale of the
vessel, and their associated length scales,
are reviewed.
Mean residence time
Figure 1 shows a
sketch of a continuous
stirred-tank reactor
(CSTR) with volume
V and flowrate Q. The
mean residence time
is defined as the operating
volume of the
vessel divided by the
flowrate through it. It
is the average time
that a packet of fluid
spends in the vessel.
In principle, some
of the entering fluid
26
Scale
1. Mean residence
time (or space time)
3. Blend time
Q, CAO
TRES=V/Q
V, CAO
-rA=kRCAO
Q, CAO
pH
FIGURE 1. A continuous stirred-tank reactor with feedback
pH control is illustrated
will immediately travel to the outlet and
leave, while some will remain in the vessel
for an infinite time. The variation in
these times is described by the residencetime
distribution [2].
This analysis assumes that the vessel
contents are " perfectly back-mixed, " which
means that the composition of the fluid leaving
the vessel (CAo) is equal to the average
composition inside it. In addition, it assumes
that the feed stream entering the vessel is
instantaneously mixed with the contents.
This is a key assumption in the calculation of
TABLE 1. TIME AND LENGTH SCALES IN MIXING
Decription
In a continuous stirred-tank reactor (CSTR), this is simply the operating
volume divided by the flowrate through the vessel.
2. Circulation time This is the time taken, on average, for a packet of fluid to travel from
the impeller, around the vessel and back to the impeller again
This is the time taken for the material added to a vessel to be blended
to a desired degree of homogeneity with all the vessel contents. The
required degree of homogeneity will be determined by a description of
the process, or the process result
4. Meso-mixing
timescale
5. Micro-mixing
timescale
This is associated with the time taken to disperse the feed entering
a semi-batch or continuous reactor and is particularly important in
the understanding of the role of mixing in fast, competitive or parallel
chemical reactions
This is associated with the time taken for the smallest turbulent eddies
to shrink down to the Kolmogorov length scale where they lose
their structural identity and their kinetic energy is dissipated as heat.
This occurs when the Reynolds number of the eddies is unity and the
inertial and viscous stresses are in balance
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Chemical Engineering August 2021

Table of Contents for the Digital Edition of Chemical Engineering August 2021