I'd like to provide just an introduction to chemical reactor design here by overviewing
some basic, ideal type reactors and indicating some important aspects. So if we look at a
generic reactor where we're feeding, say, two reactants, A and B, and some fraction of them
react and we make products C and D, and we're look at the case where there's two reactions.
So A plus B can form C or A plus 2B can form D. This might be an example of a partial oxidation
or partial hydrogenation reactions. What we're assuming is that this is the desired
product. So a couple of important aspects about chemical reactors. The basic idea is
that you want to take something that is relatively inexpensive and make something that's more
expensive to justify the chemical reactor. What tends to be the overriding factor is
often the selectivity. Namely how often does this desired reaction occur compared to all the
possible reactions. So one way that selectivity would be defined in this case would be the
flow rate. So this is a molar flow rate, moles per minute or hour, for component C divided
by the flow rate for C plus D, so the total products that are formed, what fraction, and it's
often expressed as a percent of course by multiplying by 100. Well the selectivity is
really important because it affects the separation units, how much separation has to be carried
out, and separation is expensive, therefore it affects the cost of the process. It also
affects the cost by the fact that if we make a lot of product from our reactants, we make
a lot of D that we can't use ourself for reasonable prices then we're throwing away
essentially a lot of our reactants. So chemical reactor design is basically looking at a chemical
reactor and then doing mass balances and doing energy balances. Those are certainly the most
important, doesn't mean other things are not also used, but those are the dominating ones.
So to get an introduction we'll just look at some of the typical ideal reactors and
sometimes these are very good approximations to real reactors, sometimes real reactors might
be combinations of ideal reactors on other things. So I've indicated here the four ideal
type reactors that we often look at and that are used on large scale. One is a simple batch
reactor which certainly is a just a scale up of a laboratory beaker for a reaction where
concentration and of course temperature can change with time, so this is not steady state.
We dump in all the material at once and then carry out the reaction, so a closed system.
Continuous-stirred reactors are really quite different. It looks like a batch reactor where
we're continuously adding and removing material and this changes things quite a bit. So one, it
means that it can be run continuously at steady state which means the derivatives with respect to time
are equal to 0. We'll talk a little bit more about that, and then semibatch means a batch reactor
where for example you might add one component like A and then continuously feed in B and
the reaction now again is not at steady state. The other type of steady state reactor
is where we feed in material to a tubular reactor typically and then the reaction proceeds
as the material moves down the reactor. So either the reactor is filled with a catalyst
and that catalyzed the reaction, or the reactor is a lot hotter and that's what gets the reaction started.
Again this is steady state which means that any derivative in respect to T
is equal to 0. So for these three type reactors, we assume that they're uniform spatially. Namely
there's no concentration gradient or temperature gradient across the reactor. That's not the
case for the plug-flow reactor, so the concentration is continuously changing as we move down the reactor.
At a given point it doesn't change with time but it does change with location.
Now when we do these mass and energy balances one of the critical terms that we are going
to use is the rate of reaction and for component A this is the most common form and this is
defined as the rate of formation of component A. And so this means that it has sign notation
if we're using up A, if A is our reactant as in the example above, then r _A is going to
be less than 0. So something important to keep in mind and can sometimes be confusing
is the rate of reaction in general is not equal to the change in concentration with
time. Under special circumstances that could be true but in general it's not true and the
easiest way to visualize this is to look at the CSTR, which stands for continuous-stirred tank
reactor, or the plug-flow reactor, which is often referred to as a PFR. If we look at
these two reactors, the derivatives with respect the time are 0 so this means the derivative
of concentration respect to time at a given location of 0, but the rate of reaction is
certainly not 0 if we've design the reactor correctly, and so this is an important thing
the keep in mind. The rate of reaction instead is going to be some rate constant and some concentration
dependence, maybe C_A^2 or for this particular example with A and B, maybe it's
first order in A and first order in B. The units here are moles reacting per volume,
say per liter per second, but could also be per weight of catalyst instead of per volume.
This is an empirical term where we have to make measurements for the simple case of a first
order reaction then the units of k would be inverse time. For the others the units have
to be such that we have for example mol/L here for C_A and likewise for C_B,
then the units of k are such that units are equal on both sides of the equation. So I've
listed the basic mass balances for a batch reactor where N_A is the number of moles
of A in the reactor, B is the volume, contents of the reactor. And if this is liquid phase
then the left side can be written in terms of concentration and you can see then the
reaction does not depend on the volume of the reactor in terms of what fraction is converted.
For a continuous-stirred tank reactor there is a molar flow rate into the reactor, a molar
flow rate out and again a rate of reaction term. Semibatch in general looks like a CSTR
except that the unsteady state term for the number of moles in the reactor changes with time
and we may only have a flow rate in or we may have a flow rate out. The plug-flow
reactor is quite different. The change in the molar flow rate with cumulative volume
as we move down the reactor, so as we have this plug initially, and finally is our
total volume so the cumulative volume, the rate of reaction is equal to this derivative.
The final term we'll mention here is we often use conversion to determine how much is reacted
and the conversion is the flow rate coming in, the molar flow rate, minus the flow rate
leaving, over the flow rate coming in. This in general is not equal to the concentration
difference. I say in general, but if we have constant mass density, then it is. So the final
thing to mention in this introduction is the amount of reaction that occurs, or our conversion,
will increase if we have longer reaction times. For example a bigger reactor or we leave it
in a reactor longer or typically if we raise the temperature or, since many reactions are
catalytic, if we add more catalyst, we will get more reaction.