Mixing Patterns and Residence
Time Predictions
G. S. DAWKINS, Associate Professor of Chemical Engineering
Rice University
Houston,   Texas
During the past ten years there has been a number of articles published, mainly in the chemical engineering journals, that deal with the problem of mixing in
chemical reactors. Danckwerts (1) has defined residence time distributions for
reactor systems which can be experimentally determined using tracer on frequency
response techniques.
The best single reference on the effects of non-ideal mixing is Levenspiel's
new book, Chemical Reaction Engineering (2). He devotes two excellent chapters
to this important topic and works out a number of example problems.
Also many excellent articles have appeared in Chemical Engineering Science
during the past 10 years (3-18).
Mixing patterns are important since, when they are known, the effect of non-
ideality in mixing can be predicted if the kinetics of the reaction are understood.
The knowledge of mixing patterns has been used to determine reactor design, agi -
tation requirements, and the effect of deviations from ideal models.
Models which are based on ideal flow patterns are always a bit in error since,
in practice, no flow pattern conforms exactly to a given model.
RESIDENCE TIME DISTRIBUTION
Several residence time distribution functions for a flow system have been defined by Danckwerts (1). If one of these functions is known the age distribution
for the reactor can be obtained as well as the value of an average reactor residence
time.
Generally, for a reactor the actual flow pattern lies somewhere between that
of a plug flow reactor and a backmixed reactor. A plug flow reactor may be defined as a reactor in which each element of incoming feed passes through the reactor with the same residence time. A pipe reactor, in which there is no axial
dispersion of intermixing, would be a plug flow reactor. At the other extreme is
the backmixed reactor. Here it is assumed that as soon as the feed enters it is instantaneously mixed with all the material in the reactor. A stirred tank reactor
with a high degree of agitation approaches this model. In a backmixed reactor at
steady state the effluent concentration remains constant and is identical with the
concentration throughout the reactor.
The following distributions were defined by Danckwerts:
Internal Age Distribution, I
I is defined as the fraction of material in the reactor between the age of
Q and 0 + d9, where Q is in dimensionless time units. Since at any one time the
total fraction of material in the reactor must equal unity, the following relationship holds:
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