%ABV-fluid to %ABV-vapour: which data or model?

[Kareltje]

Some three months ago, before I found this forum, I wanted a formula to find the %ABV of vapour from the %ABV of a fluid. I needed it for a model and it seemed easier to find a formula to calculate than to make a program to look it up in a list.
I found a list of percentages that seemd quite reliable, but I forgot to write down the source, so the source is unknown. From the corresponding data, %ABV-fluid (x) and %ABV-vapour (y), I made a list y/x. Later I found that this ratio is called K. Plotting K against x showed a graph that looked like a hyperbole, so I tried to find a hyperbolic relation.

K = B + C/(x+A) and then: y = K.x

After some trying I found some values for A, B and C that gave a fit of y from a given x within 0,5 % of the found %ABV-vapour. That is: from x = 10 %ABV to x = 65 %ABV. (A=5.514; B=0.09; C=83.645)
For 0 < x < 10 and for 60 < x < 95 I found some extra tuning, also within 0,5 %.

But then, strolling on HomeDistiller, I found a set of data, given by Edwin Croissant, of a mr Brau:
http://homedistiller.org/forum/viewtopi ... =1&t=57940

Out of curiosity I tried to find values for A, B and C that were valid for this set and indeed I found them: A=6.802; B=-0.035; C=94.507. Valid for 7 % < x < 60, but this time I did not bother to find corrections for x < 7 or x > 60. Because values lower then 7 % are not readable or reliable anyway and who in his right mind would start a run with more than 40 %ABV in the boiler?

Also on the forum I found the formulas of Snowman, to calculate the boiling temparature from the %ABV-fluid and also the % ABV-vapour from the boiling temperature. Combining these gave the %ABV-vapour from the %ABV-fluid.
http://homedistiller.org/forum/viewtopi ... 8&start=60

Then I found the calculations on the part Calc of the HomeDistiller-Calculations page.

And the most recent addition is a set of numbers on page 95 of a handbook for the making of palinka of 1986.
http://www.palinkafozo100literes.hu/Dr. ... afozes.pdf" onclick="window.open(this.href);return false;" rel="nofollow

Plotting all these findings gave the next graph:



As we can clearly see, even on this scale, these curves are quite different.
We have 3 graphs that are supposed to be made of experimental data in a laboratorium or in practice: Unknown, Brau and Palinka.
Then Snowman and HD-calc seem to give formulae made by sophisticated programs operated by educated people and based on solid data.
And I made two fitting formulae for the lab-sets, as explained above.

Snowman and HD-calc gave their formulas with constants with 10 or more digits behind the decimal dot. This suggests a very high precision. Useless, if you ask me, for I cannot read my alcoholmeter more precise than 0,5 % or my thermometer within 0,5 °C. And we now see a difference of 5 % ABV between trusted data.
One of the members of the forum gave a formula with a correction for altitude. This set of graphs makes me wonder: is a correction for latitude and longitude needed as well?

But the big question for me is: which set of data and/or which formula to use? And why?
Or should I just do some experiments with my own still and find out for my own particular individual situation?

[Badmotivator]

Wow. This is cool! If I were you I would do three tests using hearts (mostly ethanol, not other junk) diluted to maybe 40, 30, and 20. Take a reading as soon as the hydrometer floats. Those three test points might all fall on one of those lines. That would be nice. They might fall on wildly different lines. Bad news.

A couple of real-world complications make this difficult, of course. 1) ABV is a moving target, both liquid and vapor. 2) we are dealing with alcohol mixed with other volatiles with their own volatilities and specific gravities.

My fores always look like they are very high ABV, but this is a lie. What they really are is low specific gravity.

[Kareltje]

You are right: the truth is in the experiment.

The problem is not measuring the percentage of a fluid, for I simply trust my alcoholmeter. (Even if my thermometer shows 2 degr. too much: 102 C at boiling water!)
I have a column of 50 cm on my kettle which serves as 1,5 or even 2 equivalent trays, depending on slow or fast fire. And even if I were able to put my stillhead directly onto the kettle, it would still be a rough measurement.

For as you correctly stated: both %ABV are floating: the uncertainty theorem is definitely true for distilling. Only a very large kettle and a very small sample could prevent drifting of the measurement.

My heads are mostly a bit lower in % then the first sample. ?? I do not really worry about the cogeners, for these come in promilles rather than percentages.

[Kareltje]

In the meantime I found another formula, which I like even better.
See Binous & Al Harthi: http://faculty.kfupm.edu.sa/CHE/binoush ... harthi.pdf" onclick="window.open(this.href);return false;" rel="nofollow
They work at the King Fahd University of Petroleum and Minerals. (sic!) Among other things they study a binary mixture with a positive azeotrope, like ethanol-water.
In formula 9 they give a representation of the VLE-data for this binary mixture with a postive azeotrope:

y = {a.x / (1 + (a-1).x)} + b.x.(1-x)

in which y is the molefraction of ethanol in the vapour and x is the molefraction of ethanol in the fluid. It appears that a = 9.88722 and b = -1.0023. In figure 9 we can see that the fit is not perfect, but still satisfying.

Assuming that this formula for this binary mixture with a positive azeotrope will work for our spirited distillates as well, I tried it for calculating %ABV-fluid from %ABV-vapour. To avoid confusion I replaced a and b by p and q and added an r.
Then we get 10.1, 10.2 and 10.3:

y = K.x (10.1)

K = {p / (1 + (p-1).x/100)} + q.(r-x/100) (10.2)

y = {p.x / (1 + (p-1).x/100)} + q.x.(r-x/100) (10.3)

In which y is %ABV in the vapour resulting from x, the %ABV in the fluid.
My first test was with the dataset of Herminio Brau as given Edwin Croissant. This resulted in p = 13.2466, q = - 4.02 and r = 1.08324 (decimal point) and this graph. Close fitting, less than 0,5 %ABV difference between 4 and 69 %ABV in the fluid and less than 1 % between 2,5 and 93 %ABV! It misses the positive azeotrope.
Sorry, both azeotropes. But, hips, burp, one more drink over here, who gives a damn?



Just for fun I plotted both parts of the formula seperate and instantly I liked it. The first part shows a extinction or satisfying form, the second looks a bit like the curve of the density of mixtures of ethanol and water. Apparently the clinging together makes it more difficult to separate the vapour in the middle of the range.



In my spreadsheet it is fun to play with the values of p and q and see how the curves move around.

Of course I tried this formula with other datasets, like the one on HD-Calc and from Palinka. I tried to minimize the sum of all differences^2 between the datasets and the models, which resulted in three sets of constants.

...........Brau.........HD-Calc.....Palinka
p........ 13.2466......11.86.......11.6
q.........- 0.402.......- 0.44.......- 0.5308
r..........1.08324......1.08564....1.08

By playing around with this constants and seeing the model react one can find the best fit for the relevant part.

I really like this model very much!

But this still is no answer to my original question: which dataset to use when and why?

[Maritimer]

Hi Kareltje,

I was playing around with that k value a couple of years ago and found a formula similar to yours:
http://homedistiller.org/forum/viewtopi ... 0#p7132582 . I had just started using Mathematica back then; it is still my passion these days.

Here is the Brau data:

Cornell and Montonna OCR.pdf

(29.12 KiB) Downloaded 170 times

Check out this post: http://homedistiller.org/forum/viewtopi ... e#p7254371 . Again, Edwin comes to the rescue with some amazing data.

I have tons of analyses of ethanol/water data in Mathematica format--graphs, formulas, etc. If you are interested in mathematics, a computer algebra system will allow you to explore the mysteries of alcohol in ways you might not have even conceived.

M

[Kareltje]

Nice links, thanks.
I wil sit and study them.

About the Cornell and Montana data-set: I have seen it before, but I do not understand them.
What is the first line: {{0, 0, 0, 0, 100., 212., 0, 0, 0, 0}, ? What do these figures mean?

Edit: Ah, its starts to make some sense: The fifth one is the temperature in C.
This will be a nice puzzle.

[Maritimer]

Hi Kareltje,

I'm always trying to get anyone who likes math to try Mathematica. You can get a free trial here: https://www.wolfram.com/mathematica/" onclick="window.open(this.href);return false;" rel="nofollow . I can send you some interesting distilling 'notebooks'. It costs about $225, if you wait for the specials, or $150/year: https://www.wolfram.com/mathematica/pri ... hp?desktop" onclick="window.open(this.href);return false;" rel="nofollow . The home version is complete, not a watered-down version. (Sorry if I sound like an evangelical!)

M

[Kareltje]

Hi Kareltje,

I'm always trying to get anyone who likes math to try Mathematica. You can get a free trial here: https://www.wolfram.com/mathematica/" onclick="window.open(this.href);return false;" rel="nofollow . I can send you some interesting distilling 'notebooks'. It costs about $225, if you wait for the specials, or $150/year: https://www.wolfram.com/mathematica/pri ... hp?desktop" onclick="window.open(this.href);return false;" rel="nofollow . The home version is complete, not a watered-down version. (Sorry if I sound like an evangelical!)

M

I took a look, but I am not as much interested in doing math, but more in understanding ethanol-water-mixtures and the distilling and condensation of them.
To me the formulas of Mathematica as given above look more like a transformation into another system: every function can be written not only as y = f(x) but also as y = the sum from i = 1 to ?? of ( a constant Ci times x to a ascending power x^i ).
This can be very useful, but is not what I am looking for.

I now am looking for a reliable set of experimental data of %ABV in fluid and the %ABV in the corresponding vapour (at sealevel). As stated before: I have found at least three sets of seemingly reliable sets, but they differ and do not state the air pressure of gravity strength at which they were measured.
I can find or make models to describe the sets, but did not find a way to decide between them.

[Kareltje]

Nice links, thanks.
I wil sit and study them.

About the Cornell and Montana data-set: I have seen it before, but I do not understand them.
What is the first line: {{0, 0, 0, 0, 100., 212., 0, 0, 0, 0}, ? What do these figures mean?

Edit: Ah, its starts to make some sense: The fifth one is the temperature in C.
This will be a nice puzzle.

The sixth one is degrees Fahrenheit. In the columns before these two are the percentages of the fluid, in the columns after these are the corresponding percentages of the vapour. But are they real measurments or interpolations? And why the differences between columns? Temperature? Pressure?

[wiifm]

http://136.145.83.33:8000/jspui/browse? ... Herminio+M" onclick="window.open(this.href);return false;" rel="nofollow. Technical paper 19 provides Brau's experimental data.

[Maritimer]

Hi Kareltje,

You can also download the Brau paper here: http://136.145.83.33:8000/jspui/bitstre ... .%2019.pdf" onclick="window.open(this.href);return false;" rel="nofollow .
The source for a lot of papers is flyingdutchman. Search his posts for lots of goodies. Edwin's On the Conversion of Alcohol http://homedistiller.org/forum/viewtopi ... 5#p7254371 is an eye-opener.

In the discussion at the start of the Brau paper, he explains that the original units are ABW, at 20 degrees C and 60 degrees F.

When the Brau data is plotted, you'll find a bump at around 25 %ABV. I suspect that two data sets have been combined. I have some smoothed data if you want. Using my OCRed data, you can explore the complete Brau data in your spreadsheet.

The more-than-10-place numbers you see in the polynomial approximations are necessary when high powers are used. They are not an indication of experimental accuracy; they are a result of the least-squares algorithms.

As for which data to use, Brau and Organisation Internationale de Métrologie Légale: Recommendation No 22: Alcoholmetry “ International alcoholometric tables" which you can find here: http://zd2.chem.uni.wroc.pl/pliki/alcohm.pdf" onclick="window.open(this.href);return false;" rel="nofollow .

The monster function that the International alcoholometric tables reduces to is in the same post referred to above: http://homedistiller.org/forum/viewtopi ... 5#p7254371 . If you can get this into your spreadsheet, you'll be on your way to exciting alcoholic explorations!

M

[Kareltje]

http://136.145.83.33:8000/jspui/browse? ... Herminio+M. Technical paper 19 provides Brau's experimental data.

Downloading now. Thanks.
It will take some time to read. But on first glance it seems to be what I asked for.
And there are some other interesting studies accompanying it. 60 years old and still going strong!!

As for your next post: thank you again.
I already read some articles.
I am still trying to get my head around the concept of %ABV. 50 ml of water plus 50 ml of pure alcohol is supposed to result in about 54 %ABV alcohol. This of course can not be true, as it would also result in 54 % water by volume. So the total would be 108 % of a mixture!
It must be a technique to calculate the amount of alcohol in a given volume of a given strength, more motivated by tax than by science or technical purposes. For indeed: 100 ml of 50 %ABV contains more then 50 ml pure alcohol and more than 50 ml pure water.

Monster function, indeed!

[Maritimer]

Hi Kareltje,

Sorry wiifm, I didn't see your post.

Yes, it's true, water and ethanol don't add up. It's like adding one bucket of rocks to one bucket of water, the total volume is less than two buckets. Maybe not the greatest analogy, but the water and alcohol molecules fit into each other resulting in a smaller total volume.

That's why the experiments were done using weights instead of volume.

The density changes with temperature, too. That's what the monster function calculates--density given alcohol by weight at temperature. From there you can go crazy calculating all sorts of properties of water/ethanol. Combined with Brau you go to vapour.

Edwin's paper is the best introduction to the weirdness.

Atmospheric pressure is another variable that has to be incorporated to get the full picture.

M

[Kareltje]

Hello Maritimer,

I know about the contraction of mixtures of ethanol and water and the energy freed by that: about 6 degr C. And it looks very nice when you pour water in ethanol!
I understand that it makes calculations a bit more complex, but I have some problems understanding the correct way of handling this.
First I wil study the research you linked me to, and of course Edwins paper again.

[Kareltje]

Hello again Maritimer,

I read the Technical Paper nr 19 of Herminio M. Brau and it was exactly what I wanted: sources, discussion of method, discussion about the choices, including arguments.
Only question now is, why a renowned writer of a Hungarian book gives such different data. I can read the numbers he gives in the book, but I can not read the Hungarian. I will ask Paulinka about that.

I found some mistakes in the table in Mathematica-format you gave.
In table 1 of Brau there are notes in the column for the degr. C. They show that the marked temperatures are from a separate source. In the Mathematica-table at some rows, but not all, these notes are added to the temperature.
So, for example, at 29.0 %ABW, the boiling temperature really is 84.86 degr. C, is given as 84.862 , but has become 84.862.

Thanks again for your help!

Edit:
Shame on me: I looked up the table in the book http://www.palinkafozo100literes.hu/Dr. ... afozes.pdf" onclick="window.open(this.href);return false;" rel="nofollow
at page 95 and compared it with the table in Brau. Shame on me: Dr. Solyom Lagos gives the equilibria in %ABW instead of %ABV!! As can easily be seen by the azeotrope!

[Maritimer]

Hi Kareltje,

I used optical character recognition (OCR) to convert the tables to ASCII. Thought I'd caught those reference numbers. There are a couple of real errors in the tables that I've corrected. They were obvious when the data were plotted. (Hope I've uploaded the latest version. Maybe not...)

Glad to hear you're happy with the data. Now, can you load the monster function into your spreadsheet? I'll show you some interesting things you can do with it.

M

[Kareltje]

Hello Maritime,

I just finished typing the data in a spreadsheet, all the time wondering if that could not be done easier.
Looking at the graphs I found only one real mistake: at %ABW 42,5 the corresponding %ABV fluid @ 20 C should'nt be 50.80 but 50.08. The graphs are a bit wobbly, but, as I said before, I can not measure in tenths of percents, so that does not bother me.

And there is the bump between 20 and 22 %ABW, which finds his origin in the data of Noyes & Warfel. I wondered why Brau did not mention it, because he must have seen it after plotting. The only reason I can think of is that he was not really interested in the temperature, but mostly in the liquid-vapour % equilibrium. And because that is my main interest too, I do not mind.

It feels good having reliable data at hand.
I will try the monster formula, but now first I wil take a drink and make something to eat.

To think this research was done mainly by hand! No computer, no spreadsheet, at best a mechanical calculating machine and large sheets of paper.
And no gaschromatograph either!

[Maritimer]

Hi Kareltje,

I should have converted the file to xls. Here is a zipped xls file of the text you have. Sorry, I've only flirted with spreadsheets; I thought it would be easy to convert.

Brau.zip

(13.21 KiB) Downloaded 205 times

M