I am going to describe what we mean by segregated flow in a chemical reactor and
discuss how it effects conversion, because depending on what assumptions we make about
mixing on a local scale, micro mixing, we
can end up with different conversions, different
calculations of conversion for the same reactor. So first we need to define what I mean by complete
segregation. Complete segregation referring
to molecules in the same age group, in other words
molecules that enter together, and they are going to spend one minute, for example, in the
reactor, will stay together for
that minute and leave, and these are small
packets of molecules and they do not get diluted by mixing with other packets. So how much reaction
occurs in a given packet depends on the residence time of that packet and of course for an ideal
or real reactor we have some sort of residence time distribution that we then use to look
at how these packets react, and how much time they have to react. So an example that might
make it easier to visualize these packets
that are small on a macro scale but contain
many molecules. This is as if we had laminar flow of a viscous fluid in a tubular reactor
or if we had two immiscible liquids. For example
that we are reacting in a CSTR. Such as a
polymerization reactor. So I have tried to
schematically represent that here of the green
circles representing one of the fluids and
then the rest is the continuous phase that
represents the other fluid. This is how some
types of emulsion polymerization would be carried out.
So these green dots, which are small and I
have just exaggerated the scale here just
for visualization. These green dots then do
not mix with each other and how much of a
reaction occurs in a given packet of molecules
is a function of what is the residence time
distribution. How long does a given packet
of green molecules if you like, spend in the
reactor. Well the way me might model this if we want to assume we have complete
segregation, we want to create a mathematical model, is to think of the reactor as consisting
of a larger numbers of plug flow reactors
in parallel. So this again is the schematic
representation were I have just drawn a few
plug flow reactors, but if you think of these
as a small number representation of a very large
number of plug flow reactors where the different
lengths correspond to different residence
times. Then lengths for a given reactor we
would obtain from a measurement of residence
time distribution, and then we could calculate
the conversion or the concentration leaving
the reactor for each of these plug flow reactors
assuming they are just ideal plug flow reactors.
In contrast to segregated flow we have complete
mixing and complete mixing will give us a
different conversion, for example, for the same
residence time distribution from segregated
flow. So the difference depends on what's
the order of the reaction. So for example
if I have a rate of reaction for component
A, and n equals two, then segregated flow will give a higher conversion, in contrast to micro
mixing. If I have order n equals one, now it is the
same. It does not matter which model we're
going to get the same conversion, and we can
help visualize this. So first if we want to
be more general n greater than one then segregated
has the higher conversion, likewise n less
than one micro mixing is going to have the higher conversion. So if we wanted to visualize this
we could look at just 2 elements of fluid.
One the concentration C1, the other the concentration
of C2, and for segregated the average rate for a packet, we have 2 packets, would be
the rate constant, concentration of the first
packet squared, likewise for the second,
divided by 2. For a mixing, and again this
is micro mixing, it would be the rate constant times
the average concentration, because we are
going to think of mixing these together and
then having the reaction. Of course this we can expand, and I will expand the k over four, C1 squared
plus C2 squared plus 2 C1 C2. If I want to make a
comparison I could, for the segregated flow, multiply
the top and the bottom by two. So I have k over four, C1 squared plus C2 squared
plus C1 squared plus C2 squared, and so
if we want to compare now these two. Of course
this term is the same in both, but if we
have the second order reaction like we are looking at here, then C1 squared plus C2 squared is greater
than 2 C1 C2. This would then mean that we have the higher rate for segregation flow, and the
easiest way to understand and think about
this is to just put some numbers in, for example,
if this was 5 squared and this is 2 squared, That's 29,
on the right side 2 times 5 times 2 is 20 and so we have
a higher rate for the case of segregated flow.
The fact that we have different rates and
therefore different conversions in a reactor
depending on whether we assume segregated or
mixing. Then this means the residence time
distribution is not sufficient for us to determine
conversion in a reactor. So if we have a non-ideal
reactor and measure the residence time distribution,
we could have the same residence time distribution for different combinations, for different types
of reactors, same residence time distribution,
but different conversions, and a good example
is CSTR in plug flow reactor in series. So
if I have a CSTR first and then a plug flow
reactor, compared to plug flow reactor and
a CSTR these have the same residence time
distribution, but for a second order reaction
this system is going to give us the higher
conversion. So the residence time distribution
is not sufficient. We have to know something
about the system. So we start with segregated flow and micro mixing as the two extremes of what sort of
conversion we might get.
