INSTRUCTOR: A purge stream is a portion
of a recycle stream that is withdrawn
in order to prevent the build up of a material
that remains entirely in the recycle stream.
Such a situation would result in the accumulation
of the material preventing the system
from ever coming to steady state.
An example of this is an inert species
that since it doesn't react is never consumed.
So, let's look at an example of a system
first without and then with a purge stream.
So we have the reaction to produce ammonia
and this is known as the Haber process.
And here is the pertinent reaction.
So you have a fresh feed containing
stoichiometric amount of the reactants
and inert gas.
This combines with a recycle, forms of feed to the reactor
where you have a fractional conversion of nitrogen.
Then the products enter a separator.
So we have two different units.
The ammonia is removed, the unreacted gases
as well as the inert form the recycle stream.
We have the feed to the reactor
and we need to find the composition of the fresh feed.
So, let's look at a picture of the system.
Since the feed to the reactor
contains a stoichiometric amount
of N, two and H, two
and 20% is the inert,
that'll allows us to solve for each one of those.
So we have six moles per second of H, two,
two moles per second of N, two
and two moles per second of inert.
And so we're given a fractional conversion of the nitrogen.
So let's solve for that over here.
We know that 0.15 is equal to the amount
of nitrogen coming in.
So that's two moles per second
minus the number of moles of N, two coming out
divided by two moles per second.
And so that allows us to solve for the number of moles
of nitrogen coming out
which is equal to 1.7 moles per second.
So we use atomic species balances for hydrogen and nitrogen
to solve for the other two species coming out.
So let's put all of these onto our diagram.
Note that I didn't need to put the species right here
because the ammonia comes off in this stream here
and the rest of these species are recycled.
Note though that the inert is still part of the system.
None of it has been reacted.
So it forms part of the recycle stream.
However, if you note,
because that inert is two moles per second
if we add right here this stream to the fresh feed
that means that no inert can be added.
However, if you take a look right here
in the problem statement it says the fresh feed
has an inert gas in it.
So, that means that the inert
will continue to build up
and the system will not get to steady state.
So let's see what happens if we add a purge to the system.
So the problem stays the same all the way to the separator
but instead in this purge stream,
we're gonna say that 25% of the recycle stream
that exits the separator is going to be removed
as a purge stream.
So now let's put in our quantities.
Note the amount of an N, H, three that exits is the same
but we've split that recycle stream in two portions.
One of which is the purge stream right here
and the other which is now the recycle stream
that meets the fresh feed.
Note that because it's a splitting point right here,
the compositions of both of those streams
have to remain the same.
So, now you can see when we get to the fresh feed right here
that we are able to add an inert every single time
and the system is at steady state.
So hopefully you can see the necessity
of having a purge stream
whenever you have an unreactive species in your system