Does anyone have an approximation to the amount of dissolved CO2 in beer as a function of CO2 partial pressure, temperature, and pH? I don't want an online calculator, but the actual formula for the approximation.
Formula for dissolved CO2
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TipsyDragon
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OP
OP
Although it doesn't explicitly state it, it looks like they use a quadratic approximation which is:
3.0378 - .050062 * T + .00026555 * T^2
...where T is degrees F. This is ok I guess. But, usually quadratic approximations are only best-fit lines and not the actual approximation from physical laws, and I expect an exponential-like formula for this.
TipsyDragon
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from the sound of your question it sounded more like you where asking about force carbing a keg. the equation for that is:
-16.6999 - 0.0101059 * T+0.00116512 * T ^2+0.173354 * T * Vol +4.24267 * Vol - 0.0684226 * Vol ^2
where T is degrees F and Vol is volumes of CO2 you want. but i do agree that that is just a best fit equation.
-16.6999 - 0.0101059 * T+0.00116512 * T ^2+0.173354 * T * Vol +4.24267 * Vol - 0.0684226 * Vol ^2
where T is degrees F and Vol is volumes of CO2 you want. but i do agree that that is just a best fit equation.
john from dc
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well, this isn't a complete answer to your question but henry's law is a start. for a given solute (co2) and liquid, the ratio between pressure and co2 concentration is constant at a given temperature.
as for calculating that constant, there seem to be a few different methods but all that i've found are essentially approximations. i haven't seen any that are derived explicitly from first principles. but this is pretty common in chemistry and physics.
i remember as an undergrad being surprised to learn that much of what we "know" boils down to: observe a phenomenon, write an equation that describes it. there are a lot of "whys" that just aren't explained. at first it was pretty disillusioning, but i now see those unresolved questions as job security
as for calculating that constant, there seem to be a few different methods but all that i've found are essentially approximations. i haven't seen any that are derived explicitly from first principles. but this is pretty common in chemistry and physics.
i remember as an undergrad being surprised to learn that much of what we "know" boils down to: observe a phenomenon, write an equation that describes it. there are a lot of "whys" that just aren't explained. at first it was pretty disillusioning, but i now see those unresolved questions as job security
Know this is an ancient post but as I just coded a little device that does calculations for dissolved CO2 here are the formulas that I use (Based on Zahm Nagels chart)
Temp - Formula
30 F 0,1097936017X+1,7052941176
31 F 0,1074406605x+1,6720915033
32 F 0,104747162x+1,640575163
33 F 0,1033436533x+1,6015686275
34 F 0,1015583075x+1,5679738562
35 F 0,0993498452x+1,5345098039
36 F 0,0970588235x+1,5018300654
37 F 0,0960887513x+1,4599346405
38 F 0,0945201238x+1,4303921569
39 F 0,0932817337x+1,3988235294
40 F 0,0912693498x+1,3762745098
41 F 0,0905572755x+1,3391503268
42 F 0,0898555212x+1,3047058824
43 F 0,0882352941x+1,2817647059
44 F 0,0864602683x+1,2608496732
45 F 0,0850773994x+1,2362091503
46 F 0,0845820433x+1,1998039216
47 F 0,08308856553x+1,1756862745
48 F 0,0819195046x+1,1506535948
49 F 0,080505676x+1,1313071895
50 F 0,0798348813x+1,1015686275
x is the pressure in PSI
Temp - Formula
30 F 0,1097936017X+1,7052941176
31 F 0,1074406605x+1,6720915033
32 F 0,104747162x+1,640575163
33 F 0,1033436533x+1,6015686275
34 F 0,1015583075x+1,5679738562
35 F 0,0993498452x+1,5345098039
36 F 0,0970588235x+1,5018300654
37 F 0,0960887513x+1,4599346405
38 F 0,0945201238x+1,4303921569
39 F 0,0932817337x+1,3988235294
40 F 0,0912693498x+1,3762745098
41 F 0,0905572755x+1,3391503268
42 F 0,0898555212x+1,3047058824
43 F 0,0882352941x+1,2817647059
44 F 0,0864602683x+1,2608496732
45 F 0,0850773994x+1,2362091503
46 F 0,0845820433x+1,1998039216
47 F 0,08308856553x+1,1756862745
48 F 0,0819195046x+1,1506535948
49 F 0,080505676x+1,1313071895
50 F 0,0798348813x+1,1015686275
x is the pressure in PSI
This is indeed an old thread. Nonetheless, taking the ASBC chart (Zahm - Nagle chart is taken from the ASBC MOA) as gospel the most robust fit is probably
V = (P + 14.695)*(0.01821 + 0.090115*exp( (32-T)/43.11) ) - 0.003342
Where V is in vol/vol, P is in psig and T in Fahrenheit. The rms disagreement between the table and what this formula computes is 0.01 V/V and the largest disagreement is -0.044 V/V at 37 °F and 19 psig where the dissolved level is 3.27 volumes.
The table data do not exactly conform with what the physics predict and so it is not possible to fit it much better than that though slightly better agreement can be had with a 3rd order polynomial fit. Going to higher orders doesn't gain much and with the polynomial fits one dare not go outside the boundaries of the table (not that one would necessarily want to do that anyway). The exponential form is more robust in this regard.
Polynomial fits and a broader look at the whole subject can be found at
http://www.wetnewf.org/pdfs/Brewing_articles/CO2 Volumes.pdf
V = (P + 14.695)*(0.01821 + 0.090115*exp( (32-T)/43.11) ) - 0.003342
Where V is in vol/vol, P is in psig and T in Fahrenheit. The rms disagreement between the table and what this formula computes is 0.01 V/V and the largest disagreement is -0.044 V/V at 37 °F and 19 psig where the dissolved level is 3.27 volumes.
The table data do not exactly conform with what the physics predict and so it is not possible to fit it much better than that though slightly better agreement can be had with a 3rd order polynomial fit. Going to higher orders doesn't gain much and with the polynomial fits one dare not go outside the boundaries of the table (not that one would necessarily want to do that anyway). The exponential form is more robust in this regard.
Polynomial fits and a broader look at the whole subject can be found at
http://www.wetnewf.org/pdfs/Brewing_articles/CO2 Volumes.pdf
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TuffBunny
Member
Hi DrKarma,
I know, this is an ancient post! Good info is always welcome, if it's useful!
I've been doing a lot of extrapolation from the Zahm Nagle chart for temperatures / pressures out of the range of the chart. Just curious, if you recall, how did you develop your formula?
He's clearly doing linear fits to the Zahm and Nagle (it should be called ASBC) data. Figure 3.1 in the paper referenced in No. 8 verifies that the slopes of the volumes vs pressure lines are largely insensitive to pressure and that the slopes listed in No. 6 are not unreasonable. The pressure dependence is picked up in the exponential form in No. 7.
Meant to comment on pressures outside the table range but forgot. As the figure shows the slope is pretty constant with pressure are insensitive to pressure and thus you can extrapolate beyond the table without too much fear. The term in parentheses in No. 7 that contains the exponential gives the estimated slope.
TuffBunny
Member
Thanks so much for the quick reply! This is very helpful information to me.
A little background on what I'm up to... I've been warm aging (at room temperature) canned beers fermented with various brettanomyces, diastaticus (saison strains identified as having diastatucus genes) and wild yeast strains, checking with a Zahm can piercer, and charting the gravities, pressures, and temperatures, and calculating the volumes of CO2 over a one year period. Needless to say, with some of the yeast strains I'm investigating, CO2 volumes can quickly go way out of range of the values on the ASBC Beer-13 table. When I first started, I was using simple linear extrapolations that seemed reasonable. I finally got to the point where I wanted to get a sanity check on my techniques, reexamine my data, and get some advice from those who understand the math better than me . I'm happy to say that my initial extrapolations are within 2/10ths of a volume, and I don't require more accuracy than that for CO2 volumes. I'm more interested in the increase in pressure, since the work I'm doing is to avoid exploding cans.
TuffBunny
Member
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