In this screen cast we will work through the derivation for flash tank derivation and show
you how we can use the material balance equations with our phase equilibrium xy diagram to do
our separation calculations.
So let's start with drawing a flash distillation tank.The tank has a feed and we will say that
this is F and out of our flash tank we have a vapor phase that we will call V and we have
a liquid phase which we will call L. And one way that flash distillation occurs is in which
we start with a pressurized vapor feed that is heated and it is flashed adiabatically
across the valve to a lower pressure and it results in creating the vapor phase and having
some remaining liquid phase.
Now if the valve is omitted we could just start with a liquid that is partially vaporized
using the heater or we could start with a vapor that is partially condensed to form
the liquid.
So for our example later I am going to say that we have water and ethylene glycol.
So water being our more volatile component we will start with some feed composition Z
for our water.
We will have some vapor composition of our water in out vapor stream and we will have
some liquid composition, which we will say xH of our liquid steam.
So for our material balances we could write an overall balance which says our feed must
be equal to our vapor and our liquid.
Of course this is for steady state operations.
And this could be done in either in a batch or a continuous manner.
Now our water balance we are going to say that the composition or mole fraction of water
in our feed stream, times our flow rate of our feed, has to be equal to the mole fraction
of the water in the vapor stream times the vapor flow rate plus the mole fraction of
the water in our liquid stream times the flow rate of our liquid stream.
So the first substitution that we are going to make is that we know our liquid flow rate
is going to be equal to our feed minus our vapor.
So we could start getting rid of one of our variables by plugging this into our equation.
So then we could write the following, moving the feed variable to one side.
So now if we want to solve for the mole composition yH we could divide everything by V.
At this point it is just playing around with the arithmetic to get it into a form that
we are going to be more comfortable with.
So I am going to rewrite yH is equal to 1-F/V times our mole fraction xH plus F/V times
our mole fraction of water in the feed, ZH.
This is kind of a dirty trick but we multiply everything here by V/F and the last thing
here, gain solving for y we have it in the form of y=mx+b.
So here is our slope and here is our intercept.
So this is our material balance based on operating lines.
So let's use this with some equilibrium data to help us solve an example problem.
So let's say we have a water ethylene glycol mixture that needs to be separated and we
need to operate at a pressure 30.4 kPa.
So this is the equilibrium data we have collected and plotted on an xy diagram.
So if we start with a feed of water equal to, say, 50% and we vaporize 40% of it using
our flash conditions, what are the compositions of the vapor and liquid streams leaving?
So let's take our operating line and plug in some information that we know.
We know the composition of our feed which has a mole fraction of water of 0.5.
We also know that we vaporize 40% of our feed.
So our vapor flow rate divided by our feed flow rate is going to be 0.4.
So we plug that in to our equation where it is equivalent.
So if we simplify this we get an equation for a line.
So we have a line with the y-intercept through 1.25 and a slope of -1.5.
If we plug in a composition of 0.5 for xH then we get a yH of 0.5.
So we have 1 point that lies on our y=x line.
And now we could draw our line using the slope of -1.5 or the intercept of 1.25.
So since this is our operating line and this is our equilibrium line, where these intersect
is where we have our solution.
So this means that our liquid composition, xH, is going to be about 0.18 and our vapor
composition of water is going to be mole fraction of about 0.9.
Now if you had to determine what temperature we are operating at, you could determine where
these fall on a Txy diagram so that you know the temperature.
So note that we weren't given any information with the flow rates coming in or out, we chose
a basis where we could calculate those.
So you could use this information to double check our material balance to make sure that
is correct.One thing to notice is that the minimum and maximum slope of this operating
line.
When we look at this operating line, if we are at its dew point then we essentially have
all saturated vapor and our ratio would be 1.
And therefore our slope would be zero.
This would give a horizontal line and form this we could thus determine what our vapor
and liquid composition would be.
In this case our liquid composition would be less than 0.05 and our vapor composition
would be 0.5, roughly what we came into the tank with.The same goes if we are at the bubble
point, we would have essentially all liquid.
In that case we get a slope of nearly infinity or a vertical line.
When we are at this condition any vapor that we form will by highly enriched our more volatile
component where as our liquid will be close to whatever our feed composition was going
to be at.
So when we do flash distillation our operating conditions will be between these two limits.
So hopefully this gives you an idea of where we get our operating line for flash distillation
and how you could use that with an xy equilibrium plot to determine some of the calculations
necessary for this separation.