## From vapor temperature to vapor abv

Distillation methods and improvements.

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### From vapor temperature to vapor abv

Some time ago I made some functions to convert mole fractions to ABV and back and some functions to calculate the boiling point of an ethanol water mixture and the resulting vapor concentration. It has been asked several times on this forum if there are formula's available to calculate the reverse: from vapor temperature to vapor concentration. Now I have made some functions that do exactly that.

The funny thing with VLE formula's that they are not very accurate. At near vacuum condition they will show an azeotrope that in reality is not there. So my functions are not accurate near vacuum. Experimental data is scarce and mostly beyond pay walls so I cannot check the validity of my functions. So use at your own risk.

Please feel free to pick this apart and if you find errors, and you will, please let me know

The functions can be found in the attached example

Now:

X = mole fraction liquid
Y = mole fraction vapor
T = temperature in Celsius
P = pressure in mmHg
A = Azeotrope

X2T(X, P) Result is T for given X and P
X2Y(X, P, T) Result is Y for given X and P and an optional T
Y2X(X, P) You should get it by now
T2X(T, P, xAzeo) xAzeo is optional
P2XA(P) Result is the mole fraction at the azeotrope
P2TA(P) Result is the temperature at the azeotrope

The optional parameters are calculated if not present, when available it will save some calculation time.

Fro those of you wondering why there is no P2YA(P) I suggest to study some more

The example I made work in LibreOffice 5.0.2.2 and in Open Office 4.
In the example you can enter a minimum barometric pressure, a maximum barometric pressure, a pressure step and a minimum ABV in the sheet named "MAIN". Make sure you leave the last cell you edited by selecting another cell before you click the button "Start".
After clicking the button a new sheet is made and filled like this example:

I made this example to eventually generate a look up table that could be read by an Arduino type micro controller to show the ABV that matches the temperature and barometric pressure. Why a look up table? Some of these routines are rather slow as many iterations are needed to get a result. Try out the example and you will understand why

I hope this is useful for somebody.
Attachments
VLE example.zip
"In all affairs, it’s a healthy thing now and then to hang a question mark on the things you have long taken for granted.”
Bertrand Russell

Edwin Croissant
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### Re: From vapor temperature to vapor abv

Thanks Edwin. I always wanted to build an Android app to do just that but have been too lazy busy with important stuff to figure out the math. Guess I'm out of reasons not to start coding...
Mr98398
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### Re: From vapor temperature to vapor abv

I stumbled upon Technical Paper 19 by Herminio M. Brau some time ago when I was searching for fusel oil behavior. The paper is a compilation of experimental data from Noyes and Warfel from 1901 for the boiling points and Data from Cornell and Montonna from 1933.

There is not much experimental data available that is not behind a pay-wall.
Now I thought that the above equation was accurate, however compared to the expirimental data it is not.

I think that until the forces between the molecules during boiling are fully understood an accurate equation is not possible.

From the Technical Paper 19 I interpolated a table that will give the liquid and vapor ABV for a given temperature. Please note that the original data set for the boiling point consisted of 60 data points and the original data set for the liquid and vapor ABV's consisted of 45 data points.
Attachments
VLE.zip
TXY C-ABV for PDF.pdf
"In all affairs, it’s a healthy thing now and then to hang a question mark on the things you have long taken for granted.”
Bertrand Russell

Edwin Croissant
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### Re: From vapor temperature to vapor abv

Hi Edwin,

A while ago I turned the Cornell and Montonna data into ascii. Here it is, if you or anyone else wants to use it:

Cornell and Montonna OCR.pdf

And here is the original:

true %ABV at temp.pdf

It is in the form of a list of 201 lists. Each of the sublists is one line in the table of data. It has been thoroughly checked.

Thanks for the new data.

M
Maritimer
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### Re: From vapor temperature to vapor abv

What I have always wondered is what the "other components " that we could expect in a wash to be at Vapor temperature at the top of the column? Along with this I have noticed that some washes will have a different "hearts" temperature that is a temperature where the still will run completely stable for the majority (95%) of the run. Is the still producing pure ethanol or has this wash produced something slightly different?

I am aware of the temperature measurement error components and have minimized them or taken these into account.

Is it just barometric pressure on the day or something else.

My examples are washes that would vary from 77.6 to 78.6 (just to be clear these difference's are the stable temperatures from different washes run on different days ) Have I produced something slightly different or is it just in the variables?
sungazer
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### Re: From vapor temperature to vapor abv

Edward , sorry I have little Idea what you are doing here and I can't contribute anything but I see the Graph with the blue and Red lines and it seems very similar to the one that's been bandied around here fore years .

However I see quite a distinct kink in both these red and blue curves . Do you now what that's all about and is the familiar curves we see around here a "normalized " version of this

Yummyrum
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### Re: From vapor temperature to vapor abv

Right, interesting stuff.
Getting back into stilling after a few years off.
freaky_cutout
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### Re: From vapor temperature to vapor abv

sungazer wrote:This may not be the correct thread to ask this question so please forgive me. [...] Is it just barometric pressure on the day or something else. My examples are washes that would vary from 77.6 to 78.6 (just to be clear these difference's are the stable temperatures from different washes run on different days )

I think the question is appropriate as the boiling temperature varies with the barometric pressure. The pressure varied from below 980 to above 1020 millibar in a couple of days last week where I live. That is a boiling point change for water from 99.3 to 100.3 °C. So today you can make a combined barometer and thermometer that calculates the ABV for you like this:

This will give you the ABV of the boiler and the ABV of the top of the column. The output reading of the Alcometer (92%) was corrected for temperature (13 °C) ~93.7 % ABV.
I am now working on one that uses a temperature sensor that is accurate within 0.1 °C and can convert to 0.01 °C resolution within 15 milliseconds.

I attached a spreadsheet (warning contains macro's) that can calculate the shift in boiling point and , thanks to Maritimer, compensate your alcometer for temperature using the equation from the Organisation Internationale de Métrologie Légale. I think this is the same equation that is used to correct the alcometer readings for the excise duty.

Yummyrum wrote:Edward , sorry I have little Idea what you are doing here and I can't contribute anything but I see the Graph with the blue and Red lines and it seems very similar to the one that's been bandied around here fore years . However I see quite a distinct kink in both these red and blue curves . Do you now what that's all about and is the familiar curves we see around here a "normalized " version of this

The familiar curve is from an equation that is not very accurate. This graph is based on experimental data. One day I am going to redo Brau's work from 1957 with the computer to see if I get different results.

Maritimer wrote:A while ago I turned the Cornell and Montonna data into ascii. Here it is, if you or anyone else wants to use it:

First pdf is the table from Brau (without the misprints ), second pdf is for correcting an alcometer.
Thank you, thank you very much for making that nasty equation from the Organisation Internationale de Métrologie Légale into a manageable format. The coefficients are not exactly the same but I suspect that the program you used did a simplification. The output matches the table to the last digit as far as I can see.
Attachments
ABV temperature correction en.zip
"In all affairs, it’s a healthy thing now and then to hang a question mark on the things you have long taken for granted.”
Bertrand Russell

Edwin Croissant
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### Re: From vapor temperature to vapor abv

Hi Edwin,

How are you doing your calculations these days?

Any chance to convert you to Mathematica? I've got tons of stuff to share. (That applies to anybody else who is using Mathematica.)

Did you find an error in the coefficients? There were a lot of corrections in the OCR conversion.

M
Maritimer
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### Re: From vapor temperature to vapor abv

Thanks for the information. I can get quite large pressure changes however the average would vary by about 20hpa my weather station has shown from 980 up to 1048. You will need to use a RTD thermometer to be able to go into the sub 0.1 degree resolution. Thermocouples or thermistors just don't have the capacity.

Do you have the formula for barometetric pressure changes to the boiling point of ethanol ? I might make up a bit of a table just so I am more at ease with the number on my thermometer and the product coming over and out.
sungazer
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### Re: From vapor temperature to vapor abv

Sorry to dig out an old post, but I was reading some other threads and is there finally an equation to convert vapor temp to %ABV corrected with a measured pressure ?

cede
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### Re: From vapor temperature to vapor abv

cede wrote:Sorry to dig out an old post, but I was reading some other threads and is there finally an equation to convert vapor temp to %ABV corrected with a measured pressure ?

+1

I need that formula too

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DenisO
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### Re: From vapor temperature to vapor abv

To comment on a old post:
I made a Arduino library for the SMT172 temperature sensor, resolution 0.01 C, conversion time about 20 ms.

In reply to the two recent posts:
I made a eParrot based on the Arduino. I use the Clausius Clapeyron relation to compensate for pressure. Unfortunately I misplaced the conversion of this equation to programming code
You can find the source here: https://github.com/EdwinCroissant
"In all affairs, it’s a healthy thing now and then to hang a question mark on the things you have long taken for granted.”
Bertrand Russell

Edwin Croissant
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### Re: From vapor temperature to vapor abv

cede wrote:Sorry to dig out an old post, but I was reading some other threads and is there finally an equation to convert vapor temp to %ABV corrected with a measured pressure ?

There seems to be a very strange sort of internet etiquette that says you ought not to 'dig out an old post'.

Why the hell not??

Geoff
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