Looking for Headspace vs Beer CO2 Calculation

[MMP126]

I finally found the time to put together a spreadsheet for OpenCalc that answers VikeMan's question. Just input your vessel volume, your liquid volume and the current temperature and manometer pressure and you'll have values for:

-carbonation level
-gas density in head space and beer
-total CO2
-head space and beer CO2

As an added bonus it will automatically tabulate the same values for temperatures between 0°C and 25°C in 1°C increments so that you can see how they would change assuming the vessel is sealed and no further fermentation takes place. This will answer the often-asked question, "Why does my beer become more carbonated in my unitank when I cold-crash?" and if you can measure the above mentioned four paramenters with some accuracy it will also tell you by exactly how much given an initial and a final temperature. Enjoy.

P.S. All units are metric. Deal with it...

Cool! From the look of your sheet, my math worked out too!!

 

[VikeMan]

@doug293cz I just worked through your formulae. They seem to be in fairly close agreement with @MMP126's. Thanks to you both again!

Next I'll check out @Vale71's sheet. Thanks for that!

 

[Jayjay1976]

This thread makes me feel inadequate. You guys truly are the cool kids of HBT.

 

[Vale71]

Added a "Pressure" column to the table that lets you see at a glance how pressure in your vessel will change with temperature once the new equilibrium is reached.

 

[VikeMan]

Looking more closely, I note that with @MMP126's method, the ratio of CO2 mass between beer and headspace is slightly sensitive to volumes of CO2, where @doug293cz's is not. Peeking ahead at @Vale71's sheet (Thanks!), I see that his is also not.

The answers are all withing spitting distance of each other, but I wonder about the ratio changing (or not). My intuition says it probably shouldn't. Any comments?

 

[VikeMan]

OK, so I put together a little excel calculator that tries to answer the question of how much priming sugar to use in a keg as compared to bottles, given beer and headspace volume inputs for each, as well as volumes of CO2, temperature at packaging, and ultimate storage temperature. I used @doug293cz's CO2 mass formulae for a good bit of this.

I'm attaching it in case anyone, especially but not limited to @doug293cz, wants to have a look and sanity check. Thanks to @MMP126, @doug293cz, and @Vale71 for all their contributions to the thread!

Note: the Headspace Volume input values in the calculator are completely made up. I need to make some accurate measurements to fill in representative "default" volumes. If it turns out the headspace is pretty much the same in both cases, the calculator itself will have turned out to be a waste of time, but I have learned some things in the process, and there's a thread with some great information in it for posterity.

 

[doug293cz]

Found a couple of typos in my original analysis. These have been corrected in the post.

Brew on

 

[VikeMan]

The keg vs. bottle priming debate is very near and dear to me. I have asked in every forum I have seen the "use half as much sugar in a keg vs. bottling," what is the scientific or empirical basis for this. Never gotten a plausible answer. A full (5 gal in "5" gal keg) keg and a 12 oz bottle have almost the same headspace to beer volume ratio: ~6%. I measured both myself, using weight to determine volume of water.

Do you happen to have your keg volume measurements handy? I just measured a bottle, but I don't have a large scale accurate enough to do this with a keg.

FWIW, my standard LHBS "12 oz" bottle measured thus...
Beer (water, with empty headspace): 12.24 fluid ounces
Headspace: 0.57 fluid ounces
(determined by weighing empty bottle, full bottle, and bottle with headspace displaced/ejected with a closed bottling wand, and doing the math)

I'm betting a lot of folks assume that a typical wand displaced headspace is bigger.

 

[doug293cz]

Do you happen to have your keg volume measurements handy? I just measured a bottle, but I don't have a large scale accurate enough to do this with a keg.

FWIW, my standard LHBS "12 oz" bottle measured thus...
Beer (water, with empty headspace): 12.24 fluid ounces
Headspace: 0.57 fluid ounces
(determined by weighing empty bottle, full bottle, and bottle with headspace displaced/ejected with a closed bottling wand, and doing the math)

I'm betting a lot of folks assume that a typical wand displaced headspace is bigger.

Interestingly, I also measured the total volume of a 12 fl oz bottle at 12.81 fl oz.

I measured the total volume of a ball lock corny keg at 5.3 - 5.35 gal.

Brew on

 

[VikeMan]

Interestingly, I also measured the total volume of a 12 fl oz bottle at 12.81 fl oz.

I measured the total volume of a ball lock corny keg at 5.3 - 5.35 gal.

Cool. Thanks Sir!

 

[Vale71]

One more thing you can simulate with the spreadsheet is the drop in pressure you'd get if you were to seal your FV and then cold crash it without attaching a CO2 source and then waiting long enough for beer to start absorbing more than a trivial amount of CO2. Just set the temperature to your fermentation temperature and your manometer pressure to zero.

With 20% headspace cooling from 20°C to 0°C you'd end up with a whopping -0.44 bar of vacuum, more than enough to seriously damage your fermenter. A surprisingly small amount of CO2 has to transfer to the beer for that to happen (unless you brew in the 100bbl range, of course).

 

[VikeMan]

Added a "Pressure" column to the table that lets you see at a glance how pressure in your vessel will change with temperature once the new equilibrium is reached.

@Vale71 I've been playing with your spreadsheet. Pretty cool! When the value in the pressure column (call it "P") goes negative (for lower temps), what does that mean? That the gauge would read zero and that the Actual Pressure (not gauge) in BAR would be something like 1 Atmosphere minus (-1 x P)? Thanks in advance!

 

[Vale71]

That is indeed correct. I've set the formulas to give what a manometer would read, so relative to atmospheric pressure (rounded to 1 bar for simplicity ) and not absolute.