Better Carbonation Calculator (hopefully)

[kaljade]

Build a better mousetrap, and the world will beat a path to your door...

If you just want the spreadsheets rather than reading on you can download all of my Carbonation Calculator files here.

Otherwise, thanks for stopping by!

I'll start off by saying I'm NOT a Chemical Engineer (in fact I only heard of Henry's Law about a week ago), so if anyone notices any flaws in the logic of my equations please feel free to pass judgement as I won't be offended and the end goal to build a better mousetrap (or in this case carbonation calculator) will be achieved.

So with the disclaimer and invitation for collaboration out of the way, the background for my motivation is quite simple: all the force carbonation charts/calculators are based at sea level and I live 707 metres (≈2320 feet) above sea level so not particularly accurate. Sure there's the Ray Daniel's guide of "Add 1psi for every 2,000ft. above sea level." but again not very accurate.

So a week ago I set off on a journey of (hopefully) understanding in a brave new world that I was little prepared for.

Along the way I stumbled across this: "CO2 Volumes in beer - Development of formulas which replace the ASBC (Zahm and Nagel) CO2 tables." where the author makes the following statements:

"The source of the ASBC data is not known and difficulty in coming up with more accurate formulas may derive from, for example, measurement, rounding or transcription errors in the table data."

"It should exhibit smooth dependence on temperature and little or no dependence on pressure. If there is any pressure dependence, it too should be smooth. As we will see the table data does show variation with pressure that is not smooth."

The author then goes on to provide three formulae to try to match the results of the ASBC data, the first of which is the following:

This "simple formula" (that's easy for you to say), roughly translates into this in Excel:

=SUM((B4+B5)*(0.01821+(0.090115*(EXP(-(B3-32)/43.11))))-0.003342)

(where B4 is keg pressure and B5 is barometric pressure (both in psi), and B3 is keg temperature in Fahrenheit, so if you substitute '14.695' (sea level) in B5 with your local barometric pressure you'll get a pretty good calculator based on the ASBC CO2 tables)

At this point I decided it was time to find out what the 'Constant Henry Coefficient' was, to try and figure how the author came up with that "simple formula"...

According to Wikipedia:

"In chemistry, Henry's law is a gas law that states that the amount of dissolved gas is proportional to its partial pressure in the gas phase. The proportionality factor is called the Henry's law constant. It was formulated by the English chemist William Henry, who studied the topic in the early 19th century."

That doesn't sound so bad right, how hard could it be? Well it turns out Henry's Law can have many definitions depending on the application and in this scenario (temperature dependence) it looks something like this:

Okay so this is the bit that took me a week to get my head around (or not) until finally I came up with this:

=SUM(((((B4*0.0681)+0.92)/29.41)*(0.0821*(B3+273.15)))*(EXP(2400*((1/(B3+273.15))-(1/298.15)))))

(where B4 is keg pressure in psi and B3 is temperature in Celsius (sorry guys I'm an Aussie), and if you substitute '0.92' with your local barometric pressure in atm you'll get another pretty good calculator based on Henry's Law temperature dependence)

So the last piece in the puzzle was the Barometric formula so that you didn't need to find out what your local barometric pressure in atm was.

The Barometric formula looks like this:

After Henry's Law this was actually easy, so in Excel it looks like this:

=SUM(((288.15/((288.15+(-0.0065)*B5)))^((9.80665*0.0289644)/(8.3144598*(-0.0065)))))

(where B5 is your altitude in metres)

So with this new equation I was able to update my Henry's Law equation to use this as follows:

=SUM(((((B4*0.0681)+B6)/29.41)*(0.0821*(B3+273.15)))*(EXP(2400*((1/(B3+273.15))-(1/298.15)))))

(where B6 is the Barometric formula equation)

So what I've now done for anyone interested in road testing them and providing any feedback is to bundle both metric and imperial versions (with a breakdown of how I came to those equations) on Drive for you to download here.

More information on the above can be located at the following links:

http://www.zahmnagel.com/wp-content/uploads/2017/04/Zahm-Nagel-CO2-in-Beer-Chart.pdf

http://www.wetnewf.org/untitled.html

https://chemengineering.wikispaces.com/Henry's+Law

https://en.wikipedia.org/wiki/Henry's_law#Temperature_dependence

https://en.wikipedia.org/wiki/Barometric_formula

My Carbonation Calculator files

 

[kaljade]

I incorrectly posted this thread about a month ago in the General Beer Discussion forum, so Yooper has kindly moved it here.

Comments, suggestions, criticisms are most welcome.

 

[ajdelange]

The first simple formula

V = (P + 14.695)*( 0.01821 + 0.09011*EXP(-(T-32)/43.11) ) - 0.003342

is simple in the sense that it says

amount_of_dissolved_gas = absolute_pressure*Henry_coefficient - small_constant.

It is also simple relative to the other formulae in the paper.

This is a statement of the Henry law i.e. that the amount of a species dissolved in a liquid is equal to a constant (which depends on temperature) times the partial pressure of the gas over the solution. The paper asks the question "Does the Zahm and Nagel/ASBC tabulated data follow the Henry law?" Fig 3.1 plots the ratio of tabulated volume to tabulated pressure vs pressure for individual temperature. At each temperature the ratio would be constant if the table data were consistent with the Henry law. As that figure shows it is above 60 °F but is not completely so below that temperature. But if we take the average ratio for each line we wind up with a set of ratios vs temperature data which appears to be exponentially related to temperature. Indeed the exponential function ( 0.01821 + 0.09011*EXP(-(T-32)/43.11) ) fits these data very well and so we can approximate the full table by multiplying the approximate ratio (Henry coefficient) by ( 0.01821 + 0.09011*EXP(-(T-32)/43.11) ). If we do this and compute the average error over the range of tabulated P and T in the table we find the average error to be 0.003342 Vol. We can make the average error 0 by subtracting that amount from the estimate and thus we have
V = (P + 14.695)*( 0.01821 + 0.09011*EXP(-(T-32)/43.11) ) - 0.003342
as our estimate of the dissolved volumes. The errors in estimates computed with this formula are of 0 mean, as just discussed. The rms dis-
agreement between the table data and the formula is 0.01 volume with a peak error of -0.044 volumes (at 37 F and 19
psig where the dissolved level is 3.27 volumes). Thus thus simple formula is pretty good.

It translates into Excel as

= (B4 + 14.695)*( 0.01821 + 0.09011*EXP(-(B5 -32)/43.11) ) - 0.003342

where P is in B4 and T is in B5. No need for the SUM function. =SUM(1) returns 1 but so does = 1.

Thus there is no need to compute the Henry coefficient as a function of temperature. It is built into the table. It is, of course, interesting to see how the Henry coefficient values implied by the table compare to Henry coefficient values for water as a function of temperature and that is shown in Fig 3.3. The formula you posted as the Henry law is not the Henry law but rather the formula for calculating the Henry coefficient at T given that you know it at T0 and have the enthalpy of solvation number. The Henry law, in this context, is V = K*P where K is the Henry coefficient.

To convert the gas volume at STP to another temperature and pressure you can assume it is an ideal gas which, given the probable accuracy of the table, in doubtless justified from the ideal gas law V = RT/P. P is the absolute pressure and can be obtained from the ICAO Standard Atmosphere table (which you can compute yourself if you want to) or the current weather report.

Finally I'll comment that 'good' in the context of this paper means that the approximation formula matches the ASBC table data closely. The performance of the simplest formula yields a peak error of 0.044 volumes. I don't think that's significant in terms of describing the level of carbonation of beer. Do you? If so you can try some of the polynomial fits but they are much more complex and the peak error is only improved to 0.03 volumes. If this is still too much for you then you should probably use the tables rather than try to calculate values from a formula.

 

[kaljade]

The first simple formula

V = (P + 14.695)*( 0.01821 + 0.09011*EXP(-(T-32)/43.11) ) - 0.003342

is simple in the sense that it says

amount_of_dissolved_gas = absolute_pressure*Henry_coefficient - small_constant.

It is also simple relative to the other formulae in the paper.

This is a statement of the Henry law i.e. that the amount of a species dissolved in a liquid is equal to a constant (which depends on temperature) times the partial pressure of the gas over the solution. The paper asks the question "Does the Zahm and Nagel/ASBC tabulated data follow the Henry law?" Fig 3.1 plots the ratio of tabulated volume to tabulated pressure vs pressure for individual temperature. At each temperature the ratio would be constant if the table data were consistent with the Henry law. As that figure shows it is above 60 °F but is not completely so below that temperature. But if we take the average ratio for each line we wind up with a set of ratios vs temperature data which appears to be exponentially related to temperature. Indeed the exponential function ( 0.01821 + 0.09011*EXP(-(T-32)/43.11) ) fits these data very well and so we can approximate the full table by multiplying the approximate ratio (Henry coefficient) by ( 0.01821 + 0.09011*EXP(-(T-32)/43.11) ). If we do this and compute the average error over the range of tabulated P and T in the table we find the average error to be 0.003342 Vol. We can make the average error 0 by subtracting that amount from the estimate and thus we have
V = (P + 14.695)*( 0.01821 + 0.09011*EXP(-(T-32)/43.11) ) - 0.003342
as our estimate of the dissolved volumes. The errors in estimates computed with this formula are of 0 mean, as just discussed. The rms dis-
agreement between the table data and the formula is 0.01 volume with a peak error of -0.044 volumes (at 37 F and 19
psig where the dissolved level is 3.27 volumes). Thus thus simple formula is pretty good.

It translates into Excel as

= (B4 + 14.695)*( 0.01821 + 0.09011*EXP(-(B5 -32)/43.11) ) - 0.003342

where P is in B4 and T is in B5. No need for the SUM function. =SUM(1) returns 1 but so does = 1.

Thus there is no need to compute the Henry coefficient as a function of temperature. It is built into the table. It is, of course, interesting to see how the Henry coefficient values implied by the table compare to Henry coefficient values for water as a function of temperature and that is shown in Fig 3.3. The formula you posted as the Henry law is not the Henry law but rather the formula for calculating the Henry coefficient at T given that you know it at T0 and have the enthalpy of solvation number. The Henry law, in this context, is V = K*P where K is the Henry coefficient.

To convert the gas volume at STP to another temperature and pressure you can assume it is an ideal gas which, given the probable accuracy of the table, in doubtless justified from the ideal gas law V = RT/P. P is the absolute pressure and can be obtained from the ICAO Standard Atmosphere table (which you can compute yourself if you want to) or the current weather report.

Finally I'll comment that 'good' in the context of this paper means that the approximation formula matches the ASBC table data closely. The performance of the simplest formula yields a peak error of 0.044 volumes. I don't think that's significant in terms of describing the level of carbonation of beer. Do you? If so you can try some of the polynomial fits but they are much more complex and the peak error is only improved to 0.03 volumes. If this is still too much for you then you should probably use the tables rather than try to calculate values from a formula.

Wow, this is exactly the kind of response I was hoping for, and you clearly know a LOT more about this stuff than I do, thank you so much for taking the time to write such a detailed response!

I'd love to work with you to get these formulas more accurate, like I said I'm not even close to an expert in this field and the tables don't work for me due to my altitude.

My main motivation for wanting a formula is so that I can incorporate Volumes of CO2 on my digital tap list display which is php based software, so any additional assistance you could offer would be greatly appreciated.

Cheers,

Kal

 

[ajdelange]

The tables work at any altitude since Henry's law says simply that the concentration of carbon dioxide in the beer is, at a given temperature, the partial pressure of CO2 over the beer times a constant which depends on the temperature. There are, however, two things you must keep in mind if you want to use the tables at altitudes other than sea level. The first is that while the law works on absolute pressure at any altitude the volumes are tabulated against gauge pressure at sea level. Thus to use them you must convert gauge pressure at your altitude to gauge pressure at sea level. To do this first convert your gauge pressure to absolute pressure by adding 13.505 psi (your pressure gauges doubtless read in kPa so you'll have to do the conversion to psi). Now subtract 14.695 to get the gauge pressure at sea level and enter the table with that value. If you want to use the formula change it to V = (P + 13.505)*( 0.01821 + 0.09011*EXP(-(T-32)/43.11) ) - 0.003342 in which P is your gauge reading and 11.709 the reference pressure (psi) at 2320 ft msl. Thus the factor (P + 13.505) is the absolute pressure as a function a a gauge reading at 2320 feet.

The second twist in all this is that the concentration of dissolved CO2 is expressed in terms of the volume of the gas that would be extracted from a unit volume of beer, dried and cooled to 0° C at sea level on a standard day (STP). It is not the volume of gas that we would actually collect undried at room temperature (21 °C) in the middle of a Bermuda high (summer time high pressure systems that effect the east coast of the US) at sea level. It is not the volume of gas you would collect, undried and uncooled at 2320 ft either. We don't worry about this at sea level and so we wonder why you are worried about it at 2320 ft. We don't worry about it because volumes at STP is just a convenient way of describing the amount of gas in the beer. One volume is the same amount of gas (by weight) whether the beer is in Bathurst or Paramatta. If you were to collect it in Bathurst it would, of course, take up a larger volume than it would in Paramatta but you aren't going to collect it. What you really want to know is how much is in the beer. If you prefer you can calculate the weight of CO2. Since 1 liter of CO2 at 0° C and 1 atmosphere (STP) weighs 1.9771 grams, the number of volumes from the table or formula multiplied by this is the number of grams of CO2 in a liter of beer. This removes consideration of the difference between STP and current room temperature and pressure.

As I noted in the previous post I don't think you are going to find a formula which fits the tabulated data better than the first formula in the paper unless you want to go to a spline (which would give exact values at each tabulated temperature and pressure with an interpolation in between) but the complexity of that is not justified by the improved 'accuracy'.

Keep in mind in thinking about all this that the thing that determines how much dissolved CO2 you compute depends on the reading of you CO2 pressure gauge. A brand new class B Bourdon tube gauge is typically speced at ± 2%. The rms accuracy of the simple formula is 0.01 Vol. and the peak error 0.044 Vol. At the two volume level that's half a percent for the rms and 2.2% for the peak. The pressure gauge that has sat in your cold room for 5 years or been kicked around on your CO2 bottles isn't going to read that accurately. Thus a better fit to the table (which, of course, demonstrably contains errors of its own) isn't really justified.

I'd say just do the adjustment to the gauge pressure readings for your altitude and Bob's your uncle.

 

[kaljade]

The tables work at any altitude since Henry's law says simply that the concentration of carbon dioxide in the beer is, at a given temperature, the partial pressure of CO2 over the beer times a constant which depends on the temperature. There are, however, two things you must keep in mind if you want to use the tables at altitudes other than sea level. The first is that while the law works on absolute pressure at any altitude the volumes are tabulated against gauge pressure at sea level. Thus to use them you must convert gauge pressure at your altitude to gauge pressure at sea level. To do this first convert your gauge pressure to absolute pressure by adding 13.505 psi (your pressure gauges doubtless read in kPa so you'll have to do the conversion to psi). Now subtract 14.695 to get the gauge pressure at sea level and enter the table with that value. If you want to use the formula change it to V = (P + 13.505)*( 0.01821 + 0.09011*EXP(-(T-32)/43.11) ) - 0.003342 in which P is your gauge reading and 11.709 the reference pressure (psi) at 2320 ft msl. Thus the factor (P + 13.505) is the absolute pressure as a function a a gauge reading at 2320 feet.

The second twist in all this is that the concentration of dissolved CO2 is expressed in terms of the volume of the gas that would be extracted from a unit volume of beer, dried and cooled to 0° C at sea level on a standard day (STP). It is not the volume of gas that we would actually collect undried at room temperature (21 °C) in the middle of a Bermuda high (summer time high pressure systems that effect the east coast of the US) at sea level. It is not the volume of gas you would collect, undried and uncooled at 2320 ft either. We don't worry about this at sea level and so we wonder why you are worried about it at 2320 ft. We don't worry about it because volumes at STP is just a convenient way of describing the amount of gas in the beer. One volume is the same amount of gas (by weight) whether the beer is in Bathurst or Paramatta. If you were to collect it in Bathurst it would, of course, take up a larger volume than it would in Paramatta but you aren't going to collect it. What you really want to know is how much is in the beer. If you prefer you can calculate the weight of CO2. Since 1 liter of CO2 at 0° C and 1 atmosphere (STP) weighs 1.9771 grams, the number of volumes from the table or formula multiplied by this is the number of grams of CO2 in a liter of beer. This removes consideration of the difference between STP and current room temperature and pressure.

As I noted in the previous post I don't think you are going to find a formula which fits the tabulated data better than the first formula in the paper unless you want to go to a spline (which would give exact values at each tabulated temperature and pressure with an interpolation in between) but the complexity of that is not justified by the improved 'accuracy'.

Keep in mind in thinking about all this that the thing that determines how much dissolved CO2 you compute depends on the reading of you CO2 pressure gauge. A brand new class B Bourdon tube gauge is typically speced at ± 2%. The rms accuracy of the simple formula is 0.01 Vol. and the peak error 0.044 Vol. At the two volume level that's half a percent for the rms and 2.2% for the peak. The pressure gauge that has sat in your cold room for 5 years or been kicked around on your CO2 bottles isn't going to read that accurately. Thus a better fit to the table (which, of course, demonstrably contains errors of its own) isn't really justified.

I'd say just do the adjustment to the gauge pressure readings for your altitude and Bob's your uncle.

I thank you once again for your thoughtful and informative response, I really do appreciate the time you've taken to explain what is something clearly very complex to a layperson like myself.

I accept that the accuracy of the calculations is not justified considering the accuracy of pressure gauges that we are using in most instances and this is only a hobby for me so it doesn't actually need to be as accurate as I am aiming for.

I also agree that the first formula in the paper you published is going to give me the closest match to the tabulated data, my question was more about creating a formula that is "truer" to Henry's Law than the Zahm and Nagel table which you yourself stated "demonstrably contains errors of its own".

I understand that the purpose of your paper was to formularize the Zahm and Nagel table so in no way am I criticizing your work (quite the opposite in fact), I am extremely impressed with it and really appreciate the opportunity to discuss this with someone as accomplished as yourself.

Thanks again for taking the time, and I hope to discuss this (and hopefully other ideas) with you some more.

Cheers,

Kal

 

[ajdelange]

I also agree that the first formula in the paper you published is going to give me the closest match to the tabulated data,

At the tail end of the paper I model the pressure dependence of the Henry coefficient (remember that there isn't supposed to be any) into account. This reduced the peak error to 0.03 vol but the rms error wasn't improved relative to the simple formula. Given the pressure gauge situation the additional complexity of the more sophisticated estimator is not warranted.

my question was more about creating a formula that is "truer" to Henry's Law than the Zahm and Nagel table which you yourself stated "demonstrably contains errors of its own".

The ASBC (Zahm and Nagel apparently got it from them) table is a wealth of measurement data on real beer (of specific gravity 1.015). Henry's law is exceeding simple. It is a simple matter to compute dissolved CO2 if you know the Henry coefficient for the beer you are interested in and you don't. The van't Hoff equation only tells us what the rate of change of the Henry coefficient (its log really) is with temperature but you must have a value at some temperature in order to use it whch whichyou van only do if yiuy habe the enthalpy of solution of CO2. These data are available for water and a comparison between water and the table data is given in the paper. They are close but not the same.

The table represents a set of measurements you cannot practically make yourself. As it represents measurements it carries some measurement errors such as instrument precision and perhaps even bias errors. These are unavoidable and are responsible for things like the zig-zag features in the constant temperature curves. Thus it is not likely that you will be able to come up with anything better than the ASBC data and cannot, therefore, expect to be able to develop a formula better than those that fit the ASBC data.

Thanks again for taking the time, and I hope to discuss this (and hopefully other ideas) with you some more.

I'll be here.

 

[kaljade]

At the tail end of the paper I model the pressure dependence of the Henry coefficient (remember that there isn't supposed to be any) into account. This reduced the peak error to 0.03 vol but the rms error wasn't improved relative to the simple formula. Given the pressure gauge situation the additional complexity of the more sophisticated estimator is not warranted.

The ASBC (Zahm and Nagel apparently got it from them) table is a wealth of measurement data on real beer (of specific gravity 1.015). Henry's law is exceeding simple. It is a simple matter to compute dissolved CO2 if you know the Henry coefficient for the beer you are interested in and you don't. The van't Hoff equation only tells us what the rate of change of the Henry coefficient (its log really) is with temperature but you must have a value at some temperature in order to use it whch whichyou van only do if yiuy habe the enthalpy of solution of CO2. These data are available for water and a comparison between water and the table data is given in the paper. They are close but not the same.

The table represents a set of measurements you cannot practically make yourself. As it represents measurements it carries some measurement errors such as instrument precision and perhaps even bias errors. These are unavoidable and are responsible for things like the zig-zag features in the constant temperature curves. Thus it is not likely that you will be able to come up with anything better than the ASBC data and cannot, therefore, expect to be able to develop a formula better than those that fit the ASBC data.

Okay, you've convinced me (sorry I'm a slow learner), so I've now created a final version of the spreadsheet that I respectfully call the "deLange Carbonation Calculator", in the original directory here.

Please give it a test drive and let me know what you think?

(happy to PM you an unlocked copy if you want to look behind the curtain)

Cheers,

Kal

 

[ajdelange]

I didn't mean to discourage further investigation but rather to make you aware of what the outcome of such investigation is likely to be. But this doesn't mean you should not investigate further. At the very least you will, at the conclusion, know more about physical chemistry than you do now. I have always found knowledge for its own sake to be a good thing. You might, for example, look at calculating volumes in water using available Henry coefficient data for water and then try modifying those calculations to reflect the lower mole fraction of H2O in beer relative to that (100%) in pure water. I have no idea where such an investigation might lead except that the result very probably will not be a formula simpler than the constant Henry coefficient formula in the paper.

 

[kaljade]

I didn't mean to discourage further investigation but rather to make you aware of what the outcome of such investigation is likely to be. But this doesn't mean you should not investigate further. At the very least you will, at the conclusion, know more about physical chemistry than you do now. I have always found knowledge for its own sake to be a good thing. You might, for example, look at calculating volumes in water using available Henry coefficient data for water and then try modifying those calculations to reflect the lower mole fraction of H2O in beer relative to that (100%) in pure water. I have no idea where such an investigation might lead except that the result very probably will not be a formula simpler than the constant Henry coefficient formula in the paper.

It's funny you should say that as I was thinking of finding a way to add Specific Gravity as a variable in the calculations.

One way would be to assume a linear change between the van't Hoff equation for water at 1.000 SG and your equation for the ASBC data for beer at 1.015 SG, or even simpler still would be to set a 5% variance between 1.000 SG and 1.015 SG in accordance with your findings in your paper and extrapolate accordingly.

This of course would not be entirely accurate, but one could argue it would be more accurate than assuming all beers are made equally at 1.015 SG.

What do you think?

Cheers,

Kal

 

[ajdelange]

It passes the common sense test for sure. The problem you will encounter, of course, is that you have no way to check your formula,

 

[kaljade]

The "low hanging fruit" was to implement the 5% variance method (but I'll continue to work on a more accurate method), so it's now in the usual location.

Cheers,

Kal

 

[user 254822]

Okay, you've convinced me (sorry I'm a slow learner), so I've now created a final version of the spreadsheet that I respectfully call the "deLange Carbonation Calculator", in the original directory here.

Please give it a test drive and let me know what you think?

(happy to PM you an unlocked copy if you want to look behind the curtain)

Cheers,

Kal

Hi, I have read your thread and i don´t manage to get my calculation in Excel correct so can you please send the unlocked version to me, so I can see how you have done it and how I can use it in my excel program

 

[kaljade]

Hi, I have read your thread and i don´t manage to get my calculation in Excel correct so can you please send the unlocked version to me, so I can see how you have done it and how I can use it in my excel program

Sure, but first what seems to be the trouble with your calculation?

 

[user 254822]

Sure, but first what seems to be the trouble with your calculation?

I tried to figure out how you have done it and also use the formula you using (in the beginning of this thread) but I would like to have it the opposite way and instead of put in what gauge pressure you want and instead put in Volumes CO2 because I have a table (which many retailers from Sweden using that sells brewing stuff) where my excel looks in that way (and we use bar and *C as well) so tried to recalculate your formula without success. I´m good in excel but doesn´t understand this sciences and how to calculate, I´m more try and error guy.

 

[kaljade]

Hi there, as per the original post in this thread that table is probably not as accurate as may think it is, and this calculator is an excel spreadsheet'ed version of the extensive work done by AJ deLange, which if you read his paper is based on measurements using actual beer (not water which is what most of the other tables getting around are based on).

That said, I'm all for progress, so when I'm back home I send you an unlocked copy to reverse engineer.

Cheers,

Kal

 

[ajdelange]

The formula is easily solved for P in terms of V. Just keep in mind that P + 14.695 is the absolute pressure in psi and so you will need to include a factor which converts kPa gauge to psi gauge. Also note that (T-32) is the Celsius temperature multiplied by 1.8.

 

[kaljade]

As promised here's an unlocked version for you to reverse engineer: deLange Carbonation Calculator (Unlocked Version)

 

[user 254822]

As promised here's an unlocked version for you to reverse engineer: deLange Carbonation Calculator (Unlocked Version)

thanks

 

[rleglise]

Hello!

First, thank you for working on this equation! Reading this thread has been immensely helpful to learn more about gas dissolving dynamics.

Second, sorry for reviving a thread that has been dead for 3 years! At least it's still relevant to someone

Now for the meat:

At my brewery we add carbonation to our packaged beer by 2 methods simultaneously:
1) by force (gas through carb stone @ pressure + temperature + time)
2) with sugar and yeast (aka bottle conditioning)

We do it this way to decrease the amount of O2 in the final package, hoping to extend shelf life for as long as possible. The CO2 added by force helps us to cap on foam and decrease initial TPO. The 2nd fermentation cleans up any O2 that may have been introduced at packaging. We are not the only brewery to do this, but there isn't much literature on it that I've found.

Anyway, we combine both of these carbonation methods together to reach a final target carbonation (usually around 2.7 volumes). We've been using a rather ad-hoc spreadsheet to roughly predict these values...it has worked for most of the time, but we still have yet to get accurate and consistent results based on our targets (diastaticus likes to mess with our numbers too but that's for another thread)

So, I decided to try to re-write our spreadsheet with more accurate data. I ran into problems when I couldn't find an equation that delivers the values from the Zahm and Nagel (ASBC) table. After a bunch of googling, I stumbled upon this thread and your unlocked spreadsheet! Thank you for the hard work you've put in! I intend to expand the spreadsheet and your equations to be more useful for brewers doing mixed carbonation methods.

Once I get it working well, I'll post a link here. In the meantime, if you were able to make any more discoveries in your spreadsheet trials, I'd love to hear about them!

Cheers!

 

[rleglise]

Hello again!

I've got a relatively good working version of the sheet with some new functionality built in. Check it out here: Carbonation Calculator Version 1.0 - Unlocked

I have some of our beers that we make loaded in as presets "White, Blond, IPA" - the sheet can be modified to use anyone else's presets. The "Other" option under beer type allows the user to put in one-time custom values.

Anyway, take a look and let me know what you think. If you have any comments or changes to make to it to get it more accurate, I am all ears. I made a variety of assumptions about the science and built them into the equations so if something doesn't look right, it probably isn't

 

[bkozak@precisionfermentat]

Hopefully, I can reignite this discussion. First a disclaimer . . . unlike Kaljade (who made the first post in this discusiion thread), I am a chemical engineer but not a brewer. However, I am trying to figure out the mechanics that go into a Zahm & Nagel tester. From first principles, I can get reasonable values for both the gas and liquid phase CO2 concentrations as a function of temperature and pressure. (i.e. by using the Ideal gas law, Henry's Law, van'T Hoff equation, etc.) The values I calculate have <10% deviation from the liquid phase concentrations as determined by Equation 2.1 pasted by Kaljade. The Henry's Law constant and van'T entropy term used in my calculations were for CO2 in H2O so the difference may be related to the liquid phase being beer instead of water and Henry's Law only being true at infinite dilution. Also, I did not subtract the vapor pressure of water over the beer from the total pressure.
Anyway, I am trying to predict the values in the Zahm & Nagel table. I assumed - perhaps mistakenly - that when the Z&N tester is unlocked and shaken, it expands to a constant fixed volume. If it did, I could calculate the CO2 present in the liquid phase before shaking and releasing the lock). Since that did not work, my question to this group is how is the expanded volume in Z&N tests determined? My best guess is that the piston operates against a spring, Any help or advice would be appreciated.

 

[Barfield]

For anyone looking to find A.J. deLange's post on the Homebrew Digest website of his ASBC volume approximation formula (in post #5, above), it can be found at the Internet Archive, here:
https://web.archive.org/web/20160819162911/https://hbd.org/hbd/archive/5586.html