So I'm going to describe briefly an interactive simulation for an isothermal plug flow reactor
that has recycle.
It's a first order reaction in the plug flow reactor.
I present a snapshot of the simulation where we can change the recycle ratio, the reactor
volume, and then we have to solve this by iteration.
So the idea is that we have a recycle ratio, and this recycle ratio is the volumetric flow
rate in the recycle stream, this one here, divided by the volumetric flow rate on the
inlet stream to the system here.
In order to solve this, we use an iteration procedure.
The idea is to solve the differential equation, and maybe the easiest thing to do is first
let me write down important just mass balance, the volumetric flow rate times the concentration,
that's the values here, are due to the fact we're adding up the inlet volumetric flow
rate to the system and the inlet concentration and then the volumetric flow rate in the recycle
stream times the concentration in the recycle stream, which is also the final concentration
which in this case is 0.010.
And so, this reduces to C_0 multiplied by the recycle ratio plus 1 is equal to C_i plus
the recycle ratio, and so this is known, for example it's 0.185, and the recycle ratio
we set up here.
In this case it's 1.
We're going to calculate by solving a differential equation, so essentially what we're doing
is assuming constant volumetric flow rate through the reactor, change in concentration
of reactant with respect to cumulative volume down the reactor, it's a first order reaction
where C is the concentration of reactant.
So the reason this is an iterative procedure, in order to solve the differential equation,
we need this concentration because the initial condition is that C is equal to C_0 at the
inlet, at V=0.
But in order to calculate this C_0, we need C_i, which of course we do know, but we need
the outlet concentration from the reactor which is from solving a differential equation.
Well, for this simple case, we might be able to do it analytically, but if we think of
a more general system, we're going to look at an iteration procedure.
So what we're going to do is say, let's guess this value, C_0, and we're going to guess
by moving the slider.
Use that to solve now the differential equation to get C_f, and then calculate C_i, so essentially
the iteration procedure here is to guess this value, solve the differential equation to
get this value, and then calculate the C_i, and that's what we've done and we get this
value.
It's not the right value, so what we do is now use the slider, and we move this slider
until the C_i matches up with the actual value for C_i.
So now let's go and look at the simulation to see the effect and how to do this interactive
simulation, this, if you like, iterative procedure to solve the mass balance.
So here's the simulation, and we've set a recycle ratio of 2 and fixed the reactor volume,
and we're plotting the concentration in the reactor, but notice that we've guessed a value
for C_0 right here, we've guessed a value, and then calculated what the inlet concentration
would be in order to give us that value of C_0, but it's not our actual inlet concentration
which is represented by the green dot in the green circle.
So if I change the C_0 value, and I'm careful, I can get to a C_0 value that now yields the
correct inlet concentration, so this is a solution to the recycle reactor, and of course
I can look at conditions where the recycle ratio increases quite a bit, and the thing
you'll notice is I have to of course change my feed to the reactor.
So the thing you'll notice is the concentration change from the inlet to the outlet of the
reactor is really small.
We've diluted the inlet concentration quite a bit because of the large recycle ratio,
so this is behaving very much like a continuous stirred tank reactor.
And you can look at the effect of the volume and recycle ratio on the behavior of the system,
where you're going to iterate to match up the arrow with the green dot to get the correct
solution.