Monday, June 20, 2011

Five Gallons At A Time: Natural Carbonation

As your brewing kung fu improves, your calculations for natural carbonation might evolve in a manner such as this:

-Use fixed volumes of sugar and water for all of your beers.
-Adjust the volume of sugar based on your desired CO2 level and beer volume.
-Improve your accuracy by calculating your sugar additions by weight instead of volume.
-Replace the mystical coefficients of various priming sugars with fermentability and solubility values.
-Include vessel headspaces in your "beer volume" because they need to be "carbonated" as well. That's why authors of homebrewing books recommend using less sugar for kegs than bottles.
-Incorporate the relationship between "volumes of CO2" and the mass of CO2 per volume of beer.
-Base your sugar calculations on the fact that a molecule of fermented glucose produces approximately two molecules of CO2.
-Account for the CO2 present in the headspaces of vessels, which depends on whether or not the vessels will be purged with CO2 (for purged vessels, I assume that headspaces have the same initial "volumes of CO2" as the beer).
-If priming with wort, krausen or beer: develop equations that calculate fermentable extract from the original gravity, pitching gravity, expected final gravity, estimated pitching alcohol content and expected final alcohol content of the priming solution. Due to the presence of alcohol, you can't calculate post-fermentation extract from gravity alone.
-Include your priming solution in your beer volume because it also needs to be carbonated.
-If priming with krausen or beer: compensate for the CO2 already present in your priming solution.

If you carbonate with a fixed volume of priming solution, you can run through a series of calculations once. However, if you prime with wort/krausen/beer or you want to make a sugar solution at a specified gravity, you'll have to iterate the calculations because you'll be solving for a variable that you need to know from the outset (priming solution volume). Here's a simplified outline of the process:

-Start with your pre-carbonated beer volume.
-Solve for your required priming solution volume and, if necessary, sugar weight.
-Repeat, but with the priming solution volume from the last step included in your initial beer volume.
-Keep repeating until your iterations converge on a single set of answers.

Spreadsheets are nice for this because you can place each variable in a row and each iteration in a separate column. For the scenarios I've been able to envision, four iterations have been enough. If you'd rather not do the math yourself, you can download my spreadsheet here. As a side note, a lot of these considerations also apply to estimating the alcohol content of a naturally-carbonated beer.

On the off-chance that you're wondering how this came about, I'm planning on brewing a lambic at this year's Madison Homebrewers and Tasters Guild Brewpalooza (click the Calendar link for event info) and blending it with future batches to make gueuze. Stop by if you're interested in watching a turbid mash being performed with the utmost incopetence, smelling two-year-old hops from J.T. Whitney's or laughing at a boil kettle as it tries to imitate a cooledship.

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