I'm going to present a brief overview of plug-flow reactors and what are some of their important
properties and why we might use them, and so I've drawn a representation. Essentially
we're going to take a tubular reactor and model it as a plug-flow reactor. So what
we have coming in is a molar flow rate of A, so this is moles per minute for example
and we'll call that F_A0 for the inlet, and then leaving we have a different molar flow
rate because is A is reacted. The way we model this for this change due to reaction
is that we have a plug that's essentially moving through the reactor. It does not interact
with the material in front of it, it does not interact with the material behind it,
but just moves along and so it looks the same as a batch reactor that spends a certain amount
of time and indeed the equations for a plug-flow reactor are equivalent to the equations
for a batch reactor. So it's similar to a batch reactor and what this means is that
each plug has the same history, same temperature and pressure history, and it also means all
molecules spend the same time in the reactor. This is particularly important when we
compare a plug-flow reactor to a CSTR where in a CSTR molecules don't all spend the same
time in the reactor. So when we look at modeling this, we'll use volume as our independent variable
and say volume is 0 at the inlet and at the outlet, volume is the total volume in the reactor.
So the concentration profile, we're going to assume for a plug-flow reactor that we
have no radial gradients. This means no radial gradients in concentration, in temperature
and in velocity, so that means if we look at a plug-flow reactor the velocity near the
wall, same as the velocity here, the same as here and so we have a plug. This is in contrast
to a laminar flow reactor where the velocity would be low near the wall and get bigger
in the center and again lower near the wall in a parabolic flow. It turns out plug-flow
reactors are not a bad approximation to a laminar flow reactor. This is a plug-flow reactor,
this is a laminar. In order to write down the mole balance for a plug-flow reactor, we look
at a differential volume, and we have flow rate in and the flow rate leaving is different
because of reaction and we write a mass balance, accumulation is in minus out plus generation
due to the reaction. We're interested in steady state, so accumulation is 0. We're going to
do a balance on one component, so that's A in this case, in minus out. And the generation
is some rate of reaction in this differential volume so the rate of reaction is per volume,
so we multiply by the differential volume and this simplifies to the change in the molar
flow rate with cumulative volume is r_A where r_A might be k, concentration of
A raised to some power. What we're not going to do is write it this way, because remember
the molar flow rate is the volumetric flow rate times the concentration. This is moles per minute,
volumetric flow rate for example, Liters per minute and concentration in moles per liter.
We're not going to do this because the volumetric flow rate changes. It changes because
the temperature changes, because the pressure changes and because the moles change. Namely,
if A in the gas phase reacts to form 2 mol of B in the gas phase we increase the number
of moles. This changes the time in the reactor. Now there are other ways we can write this
mass balance, the change in the flow rate with respect to z, and I'll just bring the cross
sectional areas so the equation otherwise is the same, or I could write it in terms
of the cumulative amount of catalyst, the weight of catalyst. So I'll write this r_A
prime because now units of mol/min for example, per kg of catalyst on both sides
of the equation. In addition to solving the mass balance we'd also have an equation for
energy balance, an equation for pressure and we could write a mole balance for each of
the species in the plug-flow reactor. So why would we use a plug-flow reactor? So here's
when we use a plug-flow reactor: large quantities of material so we're continuous, and therefore
in large quantities we want to do it continuously at steady state. Certainly has an advantage
if we don't have to worry about maintenance, there's no moving parts. Plug-flow reactors
typically contain catalyst. Now the fact there are no moving parts also means that mixing
can be poor. This maybe a concern depending on the particular process and sometimes we
can get around that by having static mixers in the plug-flow reactor, but certainly the
catalyst causes mixing much more so than a tubular reactor without catalyst. The other
concern is hot spots. Namely as we move down the reactor and the rate gets faster, exothermic
reaction, the temperature increases and we have a potential for thermal runaway, and we
can decrease the potential for this by using smaller diameter tubes and therefore increasing
the heat transfer rate, and a shell and tube system, just like a shell and tube heat exchanger,
with catalyst in the tubes, heat transfer fluid on the shell side is one way that this
is compensated for if we have an exothermic, very exothermic reaction. So this is just
a brief overview of plug-flow reactor and some of the things that are important in
plug-flow reactors when we might use them.