In this screencast we are going to be working through an example problem that involves determining
the composition exiting a reactor. This will tie together both material and energy balances
for a reactor involving two reactions occurring simultaneously. A good industrial example
of this is a steamer forming of propane to producing hydrogen gas. So for that process
we have two relevant reactions. First propane that reacts with steam to form carbon monoxide
and hydrogen. Secondly, within the reactor we have the water gas shift reaction, which
takes carbon monoxide reacts it with steam to produce carbon dioxide and more hydrogen.
Where we have a feed stream of propane and stream 9 to 1 mole ratio that enters the reaction
at a temperature of 150 degrees Celsius. The outlet products leave the reactor at 700 degrees
Celsius. Now based on this high excesses of steam that is entering with the propane. We can
ensure a complete consumption of the propane. Now to promote this reaction a heating gas
is used to heat the reactor and catalytic surfaces. Now this gas is fed around the reactor
space at 5 meters cubed per mole of propane that is fed, and enters at 1250 degree
Celsius and leaves at 800 degrees Celsius. The heat capacity of this heating gas is given
as 0.04 kilojoules per mole degree Celsius. Lets Assume for this problem that this reactor
is adiabatic. So based on this information, determine the outlet composition from the
reactor.So the first part of approaching this problem is to draw a schematic of this
process. So we don't need to know for the sake of this what type of reactor is used
or how it is built. So we just represent the reactor of this process as a single box. Now
we know that we have a process stream of propane that is entering. We also have steam that
is entering with the propane, and out of the reactor we have some outlet gas composition.
Now coming around the reactor I am going to draw this as coming in from the top. Is our heating
gas, and exiting is our heating gas. So this is only coming into contact with the reactor
to heat up the catalyst in the reactor itself. It is not interacting with the inside of the
process. Now we need to start filling in information that we know. We want to determining the composition
of this outlet gas. So at this point we can enter our unknowns. So we have 5 flow rates.
I will put n1 through n5 to determine the amount of moles leaving in the outlet gas.
So this is starting to get a little cluttered. I am going to redraw the schematic to make
it a little cleaner to look at. So you get something that looks like the following. So
we are not given any amounts of propane or steam that is entering the process. Or an
amount of gas product that is leaving. The only amount we are given is the 5 meters cubed
per mole of propane that is fed for our heating gas. So we can choose a basis for our process,
and the easiest to do is to choose 1 mole of propane that enters. This automatically tells us that
9 moles of steam will enter along with the propane. It might be useful to convert the
heating gas flow rate. Given up here as 5 meters cubed per mole, into moles. So at high temperatures
and low pressures. The ideal gas law might be an appropriate equation of state to help convert
this into an amount of moles. So using the ideal gas law. We can solve for the amount of moles,
and we are given a pressure of 1 atm, we are given a volume of 5 meters cubed. We will
have to look up our gas constant, which in this case is going to be 8.2 time 10 to the
minus 5 for the units that we are working with, and then our temperature in kelvin is
going to be 1523 kelvin. So when we solve this I get 40 moles of our heating gas that
enters the steam reformer. Now since this enters and is not involved in the reaction.
This is also the exiting amount. So now we have everything written in terms of moles.
So we can start setting up our material balances for this process. Since we have two reactions
we need to choose an appropriate approach. We can choose atomic species balance, molecular species
balance, or the extent of reaction method and when I see two reactions I will typically
go with the extent of reaction method. So for the extent of reaction method. We would
write each species balance using extent of reaction. This case zeta 1 and for the second
reaction zeta 2. So when we write our balances for say propane. We take the amount of moles
that enter in this case we know that 1 mole enters the process, and then we either add
or subtract depending on how it is used or generated in the reactions. So looking at
these two reactions we subtract out the extent of reaction 1, and that is all that happens
for propane, and that is going to leave use with the amount of moles of propane coming
out. So from the problem statement we said that this was equal to 0. So right away we
can solve for the extent of reaction one as 1 mole. So lets do this for water. We
know that 9 moles of steam enter the process. We subtract out 3 times the extent of
reaction 1, and subtract out the extent of reaction 2. This will give us the amount
of moles of water leaving the process, which from our schematic we said was equal to n2. Now completing
this for the other species it looks like the following. So unfortunately we cannot solve for the
extent of reaction 2 because we know nothing else about the material balance or conversion
yields, selectivity, in the reactor. At this point we should set up our energy balances.
Now looking at our processes again. We know a certain amount of energy is transferred
from the heating gas to the reactor. We know that the reactor is adiabatic. We also know
we can look or determine the enthalpy of each of our species entering or exiting. Thus
we can use the energy balance to help solve our unknown material balance. So the most common
approach in doing this is using an enthalpy table. Here I have an enthalpy tables with
our mole amounts from our material balances. So I have simplified them in some cases. So
what we want to do in using this table is to track the enthalpy and the amount of each
species that we have that is entering and exiting the process. So we need to determine
this specific enthalpy of each species at the inlet conditions as well as the outlet
condition, but to do this we first need to choose appropriate references. In this problem we
can use the heat of formation method, and add the sensible heat change from the reference
state to account for the enthalpy of the compound. Fortunately for these more common ones like
carbon monoxide carbon dioxide, hydrogen, and water we can look up in tables. In this
case I am going to use the references of the standard elements. So carbon at a solid state,
hydrogen as a gas, and oxygen as a gas at 25 degree Celsius, 1 atm. Now we are also
going to use the heating gas at the lower temperature. In this case 800 Celsius. That
means for our heating gas the specific enthalpy at the outlet will be equal to 0, since that
is our reference state. So to determine the specific enthalpy of any of these species
using the heat of formation method and the sensible heat change we use the following
calculation. So specific heat is just going to be equal to the heat of formation of that
compound at the reference state plus our sensible heat change. So in this case our reference
is 25 degrees to whatever temperature we are looking at. Is going to be the specific heat
of that molecule while we are at the temperature range we are looking at. For both the heating gas and propane we will use this
formula, since we are given the heating gas heat capacity in the problem statement we can look up that
for propane in a table, but for the other species I will use tables. So let
me show you one example of interpolating a table we might get for one of the
other compounds. For instance in this case steam. If I look at the up the enthalpy of
steam. I might find in the table the specific enthalpy given a reference state for steam
at 100 degrees and 200 degrees, but we have steam entering at 150 degrees Celsius. Now
the heat of formation of steam given this reference state is -241.83 kilojoules per
mole. So how do we use these together to determine the enthalpy for our inlet temperature? So we are going
to interpolate 150 degree Celsius between these two temperature and you can refer to
other screencast on interpolating, but when we do that, and in this case it's not too hard, we
get 4.28 kJ/mol so this means that the enthalpy of steam for our inlet condition of 150 degrees
is -241.83 plus 4.28. This is going to give us -237.56 kJ/mol. So now this value will
go in our table. So repeating this processe for other compounds for both the inlet temperature
and the outlet temperature we get the following enthalpy table. So now all the hard work
has really been done.This point we are solving for the extent of reaction 2, and we can do
that because we know the reactor is adiabatic, and therefore we can write our overall energy
balance for this setup. So our overall energy balance can be written as the sum of enthalpy
leaving, So the mole amount times the specific enthalpy associated with that compound. Subtracting
out what is entering the process, and this has to be equal to zero because it's adiabatic.
So now I prefer to do this in Excel. So I can quickly goal-seek an appropriate value
for the extent of reaction 2. I get my excel table set up similarly. So here I have my
enthalpy table with the appropriate values in each of the spaces, and then I can use
this equation up above. The sum of the product of the two arrays of what is leaving the reactor
minus what is coming in. This has to be equal to 0. Now in this case I don't currently have
it equal to 0. So I can goal-seek to determine what value my extent of reaction is to satisfy
this equation. As you can see I get an extent of reaction for for the second reaction that
is pretty much equal too 2. So using the extent of reaction equal to 2, I plug that in to our
enthalpy tables and I get the amounts leaving our reactor. So finding the composition leaving
is as easy as dividing each specific amount by the total. For instance water in this
case is 25 mole percent of the total hydrogen is 56.3 mole percent. Hope this gives you
a good example of combining both material and energy balances together to solve for an
unknown stream parameter.