Tuesday, November 26, 2013

Calculating ABV for Sour Beers

Yesterday I got into a discussion about what adjustments needed to be made to accurately determine the alcohol content of a sour beer. I’d always assumed that the souring process didn’t have much effect on the standard method, using a formula that takes into account the OG of the wort and the FG of the beer, but I’d never spent any time looking into it.

When we calculate the amount of alcohol in a beer we are judging the relative density of the wort before- and after fermentation. This reduction in density (specific gravity) comes from a couple sources (including yeast biomass growth), but most of it is from the conversion of sugars in the wort to ethanol and carbon dioxide by fermentation. I’d always read that the CO2 escaping into the atmosphere was the main cause of the reduction in density during fermentation.

During a clean fermentation a single molecule of glucose is fermented to create two molecules of CO2 and two molecules of ethanol. So our formula is only valid if one molecule of CO2 produced always means the creation of one molecule of ethanol. Luckily alcoholic fermentation is the same regardless of which brewing yeast (Saccharomyces or Brettanomyces) is responsible. However, these aren’t the only microbes at work in a sour beer.

The production of lactic acid by homofermentative strains of lactic acid bacteria utilizes sugar to make lactic acid and essentially nothing else (no CO2 is produced). This could theoretically lead to a higher FG than otherwise as these sugars would not be available for alcoholic fermentation, but it wouldn’t disrupt the calculation of ABV because these microbes don’t generate carbon dioxide as a byproduct. So our original assumption is still valid.

The heterofermentative production of lactic acid produces 1 molecule of lactic acid, plus 1 molecule each of CO2 and ethanol from each molecule of glucose. As a result you’ll still get the same gravity drop for each unit of alcohol produced. The molecule of lactic acid is incidental, similar to homofermentative lactic acid production.

This spurred a question about what was really causing the gravity of the wort to drop as it is fermented: the loss of CO2, or the addition of ethanol? To get a lower density we either need to decrease the mass, or increase the volume (because density is mass/volume). As I’ve never finished with more beer than the amount of wort I started with, I assumed that the loss of weight to gaseous CO2 made sense.

It turns out that fermentation converts sugar into 51.1% ethanol and 48.9% CO2 by weight (a mol of ethanol weighs 46.07 g, a mol of CO2 weighs 44.01 g). A 20 L batch with an OG of 1.050 weighs 21 kg (water weighs 1 kg/L, this wort is by definition 5% denser than water). If fermentation generated 5% alcohol by volume, this would be 1 L of ethanol (which has a density of .789 kg/L). So .789 kg of ethanol. This means that we've fermented 1.544 kg of sugar, and created .755 kg of CO2 in the process. If the total volume remained constant, we'd have 20 L of beer with a weight of 21-.755 = 20.245 kg, divided by the weight of 20 L of water (20 kg) gives us a gravity of 1.0123.

Plugging those numbers (OG=1.050, FG=1.0123) into an alcohol calculator I get 4.95% ABV. Which is almost exactly what we'd expect given that 5% ABV was one of the conditions I specified. This indicates that most the gravity lost is in fact a result of CO2 leaving the beer.

However, it brings up an interesting question, if we are creating 1 L of alcohol, why don’t we see a volume increase as a result of fermentation? When you add rum to a Coke, it certainly seems like it would have the same effect on the volume as adding an equal amount of water. It turns out that when you mix equal parts water and ethanol the volume increases only 1.92 fold. So we’ll only get 92% of the increase from adding the ethanol, .92 L in this case (close enough that we don’t notice a difference mixing spirits with water-based drinks).

If we simply added the same 1 L of pure ethanol to our 20 L of 1.050 wort, we'd have a resulting density of ((.789*1)+(1.05*20))/20.92 = 1.042. So the addition of alcohol is not itself enough to account for much of the drop in gravity we see during fermentation.

In a fermentation we aren’t just adding alcohol, so we’d also need to consider the reduction in volume from the sugar that is fermented (1.544 kg in our case - the sum of the CO2 and ethanol created by our hypothetical fermentation). I couldn’t find similar numbers for maltose, so I’ll treat this sugar as if it were sucrose. When you dissolve sucrose in water, approximately 54% of the volume is added to the volume of the solution. Sucrose weighs about .869 kg/L, so our 1.544 kg of sucrose would take up 1.778 L dry, the loss of which from the wort would result in a .960 L decrease in its volume).

So the loss of volume attributed to the destruction of sugar (.96 L) during fermentation completely cancels out the volume gained (.92 L) from the resulting ethanol, which is why we don’t see a noticeable volume increase (or decrease) during fermentation!

When trying to determine the ABV of a sour beer specifically, there are four other factors you might consider.

1. Highly acidic beers are around 1% lactic acid. As the formation of lactic acid doesn’t directly lead to anything entering or leaving the fermentor, we know the mass of the beer will remain constant regardless of how much lactic acid is created. Any change in the beer’s density would purely be the result of a change in the total volume.

1 molecule of glucose goes to create 2 molecules of lactic acid in homofermentative lactic acid production. Glucose has a density of 1.54 g/ml, and a molar mass of 180.16 g/mol. Lactic acid has a density of 1.2 g/ml and a molar mass exactly half that of glucose, 90.08 g/mol (which makes sense). In a 20 L batch of beer, 1% lactic acid by volume, would be 200 mL of lactic acid. The equivalent of 240 g of lactic acid, or 2.66 mol. This would require the fermentation of half that number of glucose molecules, 1.33 mol, which is 155.59 mL.

If we assume glucose behaves similarly to sucrose when dissolved in water, the loss of wort volume attributed to 155.59 mL of glucose converted to lactic acid would be 84.02 mL. I can’t find a number for what happens to volume when you mix lactic acid and water, but even if we assume the entire volume of lactic acid goes to increasing the beer’s volume, we’d be increasing the volume of the beer by 115.98 ml, just .58%. This is the equivalent of causing the 5% ABV calculated to be .03% too high (the larger volume with the same mass would indicate a more substantial reduction in gravity than would have been actually caused by alcoholic fermentation).

2. Acetic acid production by either Acetobacter or Brettanomyces consumes a molecule of ethanol along with a molecule of oxygen. This reduces the alcohol content, but also raises the mass slightly as the oxygen comes from the atmosphere. It seems like without the carbon atom of the CO2 released during fermentation the gravity would rise slightly less than what is lost during fermentation, causing an infinitesimally small over-estimate of the ABV. Acetic acid is legally limited to.15%, so it shouldn’t play a major role anyway (even if flavor wasn't a consideration).

3. Ester formation by Brettanomyces could have a small impact on alcohol content because esters are formed by combining an alcohol with an acid (e.g., ethyl lactate is a combo of ethanol and lactic acid). However, all of these are present in parts per million at the most, making their presence too low to substantially impact ABV calculations.

4. While not specific to sour beers, evaporation from a barrel reduces the amount of both water and ethanol a beer contains. As ethanol has a lower boiling point than water, it would tend to evaporate at a faster rate. The humidity in the room apparently plays a role in the relative evaporation rates as well (higher ambient humidity reduces the evaporation rate of water). At 70% humidity, the loss of alcohol and water is supposedly about equal.

In relation to these various areas, when compared to the errors in calibration and measurement I don't think it is necessary to make special considerations for the ABV calculations of mixed fermentation sour beers. This has been one of those things I spend hours thinking about only to come to the conclusion that I was better off ignoring the whole thing.

That said, this isn't exactly my area of specialty, if anyone sees any issues with my assumptions, data, or math, please let me know! I'm sure I've oversimplified some things, like the sugars, or how a water molecule is added when some polysaccharides are split, but I think I'm close enough to prove the point.


Leonard said...


Another factor that effects the density of the beer is how much carbon dioxide that is dissolved in it.
When maximum amount of carbon dioxide is dissolved into the beer, it contains about 2% CO2.
The density of CO2 is 0,00198 g/cm3 and the density of the beer is approximately 1,0 g/cm3.
0,02 * 0,00198g/cm3 + 0,98 * 1,0 = 0,9800296.
This will lower SG with 2 points, or change the final alcohol-content-calibration with about 5% in your case.
I do not think it is a reasonable assumption that the beer contains 2 vol-% CO2 and to get the most correct value you should probably try to stir out the CO2 from the beer before meassuring the specific density.

Do you know if Peddiococcus ferments sugars like homofermentative or heterofermentative Lactobacillus? It would be interesting to know.

The problem with calculating alcohol content in beer fermented with any form of lactic acid bacteria is that you don't know how much lactic acid that have been produced and how much sugars that have been consumed. Even though the density have not been changed very much, there is still less sugars for the yeast to ferment into alcohol. The sugars that have been consumed is not avaliable for the yeast and can not be transformed into alcohol.

Another way of seeing the loss in density is that the sugar is transformed into ethanol, which has a lower density.

It is a very complex procedure and I really like your contribution of summing up the factors when calculating alcohol content of a beer.

The Mad Fermentationist (Mike) said...

Certainly removing CO2 from the beer before taking a gravity reading is important. The bubbles can also form on the hydrometer and throw the reading off even more than your calculation suggests.

Pedio is homofermentative as far as I know, at least the strains used in brewing are.

Yep, but luckily because the readings are accurate we don’t need to worry about how much lactic acid there is. Sour beers tend to be higher alcohol than their clean counterparts (given the same OG) anyway despite the sugars taken away for lactic acid production, as there are still plenty of dextrins to be fermented!

Leonard said...

So you belive that I should meassure OF and FG and calculate the alcohol content as usual?

I don't know if I really get your point with the lactic acid formation. Please correct me if I am wrong here.
Do you mean that the sour beers contain more alcohol than their counterparts, because they have fermented dextrins to a lower FG? and that this weights up for the loss of sugars that have been transformed into lactic acid?

Joe said...

Say you have 5 gallons of 1.030 berliner wort, and then add homofermentive lacto which drops the gravity to 1.020. After adding some sacc, the FG ends up at 1.005. In this case, ABV would be calculated from the 1.020 to 1.005 drop in gravity right? What about if the lacto was heterofermentive? Would ABV now be calculated from the 1.030 to 1.005 drop in gravity? Thanks.

Anonymous said...

This was an awesome post.

I may be misinterpreting it now, but I think these are the answers to the last two questions:

Leonard: In your scenario, if you ignore the fact that there tend to be bugs that can ferment longer sugars in sour beers, and just consider sugar lost to lactic acid production, the only result this will have is to raise the FG. Production of lactic acid can be thought of as turning a fermentable sugar into an unfermentable.

Take Back Pabst: Theoretically if you have a homofermentive lacto strain then the gravity should not drop substantially before you add the sacc. If it does drop, then perhaps the assumption that it was homofermentive lacto was wrong or the assumption that it was the only microbe in the beer is wrong. Depending on which of these assumptions is wrong, you might want to calculate the ABV in different ways (it depends on what metabolic pathway was at work, if it produces a gas, and if it produces alcohol). If it was heterofermentive you would calculate the ABV drop from 1.03 to 1.005.

The Mad Fermentationist (Mike) said...

Exactly. You can completely ignore how much lactic acid there is when calculating the ABV. Just do it as you normally would, based on entering the OG and FG into a formula, no adjustment necessary!

Lactic acid would screw with the calculation for real extract/attenuation, but not apparent. Sour beers would have even less residual carbohydrates than their low FG suggests. I'd also be hesitant to use a refractometer to calculate the final gravity of a sour beer, the correction formulas don't take the lactic acid into account.

Agreed again, substantial gravity drop indiates CO2 is being generated, so either you've got a heterofermentative strain, or a mixed culture. If you boil post-souring, use the gravity post-boil (boiling will remove most of the alcohol in the wort). Otherwise, calculate as you usually would with the OG and FG.

Leonard said...

Okay, I think I get it now =) Thanks both of you!

Russ said...

I asked you this in email at some point, but it seemed a good think to keep associated with this post for all to see.

When you talk about the density, are you strictly considering hydrometer measurements? How about refractometer readings on sour beers? We know that alcohol content requires correction to the refractometer reading during fermentation, so I wonder if things like the various acids would change things too. I keep meaning to compare hydro and refrac readings for my sour beers, but never remember to pull out the hydrometer anymore...

The Mad Fermentationist (Mike) said...

Doubt I had a definitive answer then, but I'd suspect that a refractometer reading of a soured beer would be highly suspect. I'd want to pull a sample large enough to taste anyway!

Russ said...

i'll usually pull a few ounces from each when working on a blend, but that's still not quite enough for a hydro sample. perhaps i'll compare when I pull samples for this year's gueuze blend.

Harold stDacard said...

or you could drink a scientifically controlled amount of x percent clean beer on one day and the same amount of x percent (assumed) sour beer on another (both on an empty stomach, and crash your car on both days at the same time and compare the police Breathalyzer readings.
its science damnit