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In this screencast we will look at performing a degree of freedom analysis on a multiple
unit separation process. Performing a degree of freedom analysis is very important first
stem in analysis a system and determining if the conditions are fully defined. Now imagine
you are being tasked in designing a process to meet certain specifications, and you spent
countless hours trying why you cannot meet those specifications and certain conditions
all to find out that too much information was given and the information did not correlate
correctly, or what if not enough information was provided and you could not fully design
that process. To solve that problem we are going to perform a quick degree of freedom
analysis that could give us this kind of information before any kind of calculation are written
out. So lets loo at the case here for a system. So we have an absorbing column on the left
and a stripping column here on the write. So I have redrawn this processes in a block
flow diagram and labeled known information about the certain processes. The questions
is can we determine the undetermined perimeters. Now one thing about this process you might
have seen is this spent solvent line, and so you know. When we are recycling this adsorbent
at some point we have to dump it, so there might be a valve to control that stream . We
are going to neglect that in our processes. We have our block diagram and our streams.
This is the first place to start given any kind of problem. So to start the degree of
freedom analysis we have to choose an appropriate balance boundary to analysis. Now we can do
a couple of different things here. We can choose to analysis the overall system. So
this would include both units. We would draw our boundary here. Thus we would look at any
streams that crossed that boundary, and forget about any streams within that boundary area.
So this would be our overall process. We can also do a degree of freedom analysis just
around the absorber, or we an do one just around the stripping column. Sometimes it
is important to look at all of them. To determine if there is a good place to start and analysis
multiple units. So lets start with the overall all. So lets start with choosing a basis,
which in this case is given to us. We are told that 100 moles per hour enter into the
absorbing column. If none of the entering or exit streams had a basis, we might be able
to choose one. As long as it didn't change the values that were given to us for other
streams. So to start the degree of freedom analysis we start with writing down our unknowns.
Now we don't know n1. We also don't know n5, nor n6. However we are given all the compositions
for those streams. So those are three unknowns. So then we write the species that are involved.
We have acetone, carbon dioxide, and air. Now why don't we include water. Well we don't
have water coming in or our of our boundary. It is just within it. So we are not looking
at those streams. We just care about what is crossing that boundary. So we have three
species, but here is one thing to take into consideration. Our air over here that is labeled
as n5 is 100 percent air and it leaves at the same flow rate in this stream. So this
isn't independent relationship we can use in our degree of freedom analysis. So we can't
write a molecular species balance for air. So anytime that you have a relationship like
this. It is not independent that it does not help us solve the balances around that boundary
we remove that species from one of the molecular balance species that might help us. So we
have 3 unknowns we take out the two species balances that we could write. We are left
with 1 degree of freedom. So this means that it is under specified we can't solve the material
balances as specified unless we were given some other type of information. So next lets
do a degree of freedom analysis around the absorber. Again looking at the unknowns the
stream coming in is fully defined. We have unknown stream that is leaving. We have an
unknown n2 that is coming in and we also have a stream leaving with flow rates n3 and n4.
We write the species that we might be able to perform a molecular species balance on
we have acetone, carbon dioxide, and water. So again this gives us 4 unknowns 3 species
balances we could write, and we get left over 1 degree of freedom. So we cannot solve the
material balances for the absorbing column. Lastly lets do a degree of freedom analysis
for the stripping column. For our unknowns we have n2, n3, n4, n5, and n6. Again the
compositions are labeled for us were needed. The species that we are looking at for the
stripping column are water, acetone, and air, but again as we mentioned for the overall
balance we cannot do a material balance for air, it is non independent. So we are left
with 5 unknowns and 2 species balances that we can write. That gives us 3 degrees of freedom.
So for this particular processes every degree of freedom analysis we performed says the
system is not fully defined and we cannot solve for any of the unknowns. Since the basis
is provided we cannot assume a different one as one of the variables that might help us.
So we would need some other piece of information to complete this problem. Hence the degree
of freedom analysis is important, since we know realized that we need to dig deeper for
information or assume something else to proceed.