In this interactive simulation we do a degree of freedom analysis for a distillation process,
and the simulation is set up where we can do analysis around just one part, like the
condenser I've shown here, and that's selected with this button, and the blue values correspond
to unknowns, the mass flow rate and the mass fraction, and the mass fraction here of the
liquid. And so the number of unknowns is listed, the balances, two species balances, and then
the relation from phase equilibrium between this mole fraction of vapor and this liquid
mole fraction that's assumed to be in equilibrium, and for these conditions we've selected the
number of unknowns that says the system can be solved. We have the option of a partial
condenser or a total condenser so that we condense all liquid and means this mass fraction
here would be the same as this mass fraction here if we had a total condenser, and then
the simulation allows us to click new problem and we have different unknowns, so we're solving
a different system. And we can do a balance now around the distillation column, the re-boiler,
or around the whole system, and we'll see how we do that when we look at the interactive
simulation. So here we're looking at the interactive simulation, and we selected the condenser,
we have the option of the column or the re-boiler also, or an overall balance. The blue are
the unknowns, so say mass fraction, vapor coming in, mass flow rate leaving, and then
this mass fraction of the liquid that's condensed. So we have three unknowns. We have two species
balances because we have two components, and we have additional information, vapor/liquid
equilibrium that relates the mass fraction in the vapor to the mass fraction in the liquid,
so this says that we have no degrees of freedom, or in other words this problem can be solved,
and this is what the degree of freedom analysis does is tell us whether we can now sit down
and calculate the unknowns, the blue values. Now if I select a new problem what this does
is create different unknowns. Now the unknowns are the inlet flow rate and the outlet flow
rate, these mole fraction are known. Again this happens to be a solvable case. Now another
problem, a new problem, it's over specified. We have three equations and only two unknowns,
so it's over specified. We can do likewise, we can look at the re-boiler, for these particular
conditions it's over specified. If I go to a new problem now it's solvable. Over specified
again, and let me decrease the number of unknowns and look at a new problem. Solvable for these
conditions. And then over specified for other conditions. Let's look at the, finally an
overall balance, and now this tell's for this problem the unknowns again are blue, change
conditions, let's increase the number of unknowns. Well if I have seven unknowns now our system
is under specified pretty much for all the conditions we could pick, we don't have enough
mass balances to be able to solve for this system. The other option here is to consider
both A and B mass fractions as unknowns, and have additional equations that say the mass
fractions have to add to one, and this is the case where different, basically some people
like to do it one way where they have both mass fractions unknowns, others like to assume
we've already taken into account that the mass fractions add to one, and therefore only have,
for example here one unknown, not two unknowns. And so this degree of freedom analysis is
valuable for understanding systems and how we can do mass balances on them, and depending
on which part we select we can have something that's under specified, or over specified,
or solvable.