The purpose of this video is to explore the use of the UNIFAC function and the activity
coefficients spreadsheet which I am showing here in order to calculate liquid-liquid phase
equilibrium.
And in order to do this, I'm going to use the UNIFAC LLEA and LLEB spreadsheets.
And this is actually described, I encourage you to look at section 12.6 in the textbook
which is an optional section that we didn't assign but which describes how you'd want
to set up this spreadsheet in order to do liquid-liquid phase equilibrium calculations.
So I went ahead and set up a problem with 2 components and we want to look at whether
these components form difference liquid phases.
The components that I've set up are methanol and hexane and I've gone ahead and looked
up the Antoine coefficients for those and put them in here.
And you can see that the saturation pressure is at 25 degrees C or are correspondingly
calculated, although we won't directly make use of those in this calculation.
We can then specify liquid phase compositions for component alpha in LLEA and component
beta.
You see that I've initially guessed compositions of 10% - 90% and 90% - 10% of the two liquid
phases.
And the spreadsheet calculates the activity coefficients for you.
And what we'll use is in the alpha spreadsheet we'll use this Ki formulation.
We need to make an initial guess of Ki and to do that, we just divide the activity coefficient
for component 1 in the alpha phase by the activity coefficient for component 1 in the
beta phase on the other spreadsheet.
So I just put that into this cell.
And then we do the same thing for component 2.
So gamma 2 sub alpha, gamma 2 sub alpha divided by gamma 2 sub beta.
For X old values that we're going to use in our iteration as is described in section 12.6,
we're just going to set those equal to what we put in for our alpha and beta phases inside
the spreadsheet.
So I just have a straight equality here or should.
Right, so this should be equal to C22 so I need to make this exactly 0.1.
Okay.
And we do the same thing for X in the beta phase.
I just have an equality to the spreadsheet over in the, that describes the beta phase.
And then we just basically go through an iterative procedure that's described int eh textbook
in order see a convergence in the values of X1 alpha and X2 alpha and X1 beta and X2 beta.
And so I've defined these cells exactly as described in Step 3 of section 12.6.
I'll let you read about the equations there, but they're very clearly described in terms
of the spreadsheet and you can pause and look at the cells as I've defined them here if
you want.
Here we just use 1 minus X1-alpha to get X2-alpha.
And then for our X1-beta new we actually multiply our K values times our X1-alpha values for
both cells, as described in the textbook.
And now we basically we'll do an iterative procedure where we'll take our X1 and our
X2 alpha for our alpha phase and we'll paste them in here.
And we have to be sure to paste values.
We do the same thing with the new values for the beta phase, and that requires that we
go over to this other sheet.
And again, be sure to paste the values.
And then we return here.
And the last thing we need to do to complete our iteration is then copy the Ki-new and
paste that special, paste values into the Ki-old.
And now we can see that we have new values for X compared to our previous values.
So our Xi-old was from the first iteration was 0.88.
We initially started with 0.9 and then went to 0.88.
Our new iteration as Xi is 0.87 and we have new values for the beta X's as well.
And we can keep on doing these iterations, so we can take our new guesses, again, just
as we did previously, and plug them in for our new values of X and we will eventually
converge.
I have done this and I end up getting about 84% for the Xi-alpha value and maybe about
18% for the Xi-beta value by the time you go through all of the calculations.
And we just keep repeating that, cutting and pasting, always making sure to paste values
where we plug paste in the Xi-alpha and the Xi-beta and the Ki-new into the Ki-old just
as we've done in the first step in order to converge on the solution.