- [John] I'm going to briefly describe how to use an
interactive simulation that leads you
through the steps in the McCabe-Thiele method
for distillation column.
And I've indicated here where you can find this simulation.
So let's look at one snapshot of the simulation.
So simulations plotting the vapor mole fraction,
the more volatile component,
in this case methanol versus
the liquid mole fraction, that component.
This is the X=Y line
as the reference that we use.
The values for this simulation, some are fixed.
ZF to feed is a mole fraction of 0.5.
The value of the liquid,
we collect the distillate where D is the distillate.
Flow rate is set at 0.85
And the value of the bottoms is set at 0.05.
The vapor flow rate
among the liquids, what's returned to the column.
That's for the upper part.
The rectifying part and the lower part,
the vapor notation like that with a line over it.
And the liquid flow rate is like that.
So that means that this is the vapor flow rate
at the bottom part of the column,
the stripping section.
Liquid flow rate, and B is the flow rate of the liquid
that we're collecting out of the bottom.
And then on the plot, the orange line.
This is the mass balance
for the upper part of the column rectifying.
This is the mass balance
for the stripping part of the column.
This is the relation between Y and X
for vapor liquid equilibrium
for this mixture's non-ideal
and details are explained in the simulation.
And then this line, so ZF is here
and XD is here and XB is down here.
And this line's slope is changed by changing the quality.
So if quality is equal to zero,
then that corresponds to a vapor
at its dew point and quality equals one.
So that vapor is liquid at its bubble point
can be greater than one, super cold liquid.
It can be less than zero, super heated vape.
So this is a total condenser
meaning this composition is this,
which is this Y value going in,
in this case it would be Y1,
would also have the same mole fraction as XD.
Well, let's look at the top part of the column.
So let's look at another snapshot
we're going to have some of the stages drawn in.
And you can see, select it here,
the stages that we're going to count,
then we use a slider that steps in increments to count.
And we'll show in the simulation how we
go through each of these steps.
What I want to do here is point out the mass balances.
So let me label things again.
So I've indicated liquid flow rate,
so L is a molar flow rate.
Liquid flow rate's down, vapor flow rate is up,
and D is the distillate flow rate.
If I had to write a mass balance
around this dotted dash purple section,
then what's coming in is Y3 times the molar flow rate.
So mole fraction times the molar flow rate,
number of moles coming into that.
And what's leaving is two places
liquid flow rate going down times X2
plus the distillate flow rate times XD.
Well, I can generalize this and I can rearrange it slightly
by dividing through by the vapor flow rate.
Yn plus 1 equals L over V times Xn
plus D over V times XD.
So this then would be the slope of this line here.
And since, so let's label these again.
L, that's vapor.
So the vapor is L plus D,
which means L over V is less than one.
So the slope is less than one there.
And so this mass balance applies
the upper part of the column
and so we have to satisfy that at these points.
And then equilibrium, so X1, Y1, X2, Y2 leaving a column.
So look at this stage here,
leaving a stage, Y2 is in equilibrium with X2.
Y1 is in equilibrium with X1.
You can see from this mass balance
this point is X1 and Y2,
this is X2 and Y3,
and that's why they fall on the mass balance line.
Let's look at one more snapshot.
Well now I'm doing a balance
in the lower part of the column.
And so again, a balance, this purple area,
and what's coming into the system as defined
by that purple dash line should equal
what's leaving for a more volatile component.
So entering X3 times L with a line over it
and what's leaving is Y4, vapor flow rate,
and then XB times the bottom flow rate.
Well, let me rearrange this.
So, this is a mass balance,
of course I can generalize it for more stages.
This is then the equation for this line
because those points have to fall on X3
and Y4 has to fall on the mass balance line.
Well also notice that because that liquid flow rate coming
into the bottom is split up into vapor
and the bottoms that means that
the slope of this line L over V
must be greater than one as you can see on the plot.
So let's look at the simulation briefly.
So here's the interactive simulation
and the idea is for you to step through.
You notice right now I selected the plot points
and it shows the feed.
There's the distillate, there's the bottoms.
Next step is to draw the operating lines.
And so this is showing the feed.
I can change the quality
and that's going to change the slope
and the diagram on the right shows then
how the feed is distributed.
Partially vaporized feed,
some of it goes into the liquid stream
and some of it goes into the vapor stream.
So by selecting that,
it shows now the slope that we talked
about previously for the operating line.
And then the diagram corresponding to that.
If I select the bottoms, the stripper part,
again shows this mass balance that we derive
and the purple line indicating the slope.
I count stages.
And what it does is the slider
only of course goes to energy values, the first stage.
Second stage where, remember,
we are using this point for X1 and Y1,
phase in equilibrium.
This point is the mass balance that we derive.
This point is also mass balance
and I can step through to get to the bottom.
That's also a stage, the reboiler.
And then it shows where the optimal feed location is
for this particular system.
So very brief, but hopefully gives you an idea
of how to use this interactive simulation.
Change the quality and see how that affects things.