Carbonation estimation

[Erik Nilsson]

Hello,

In trying to learn the basics of cidermaking, I made a summary "carbonation chart" which estimates resulting CO2 levels and pressure at different temperatures, amounts of added sugar, SG drop in pet nat, etc.

Would be great to get some input whether this calculation is reasonable!

Chart attached as pdf.

/Best wishes, Erik Nilsson (novice hobby cidermaker)

The steps used to compute data for the plot were essentially:

1. Molar concentration of CO2 was calculated from added sugar.

> CO2_M = ( concentration of sugar / molar mass of sugar ) * 2 * efficiency of fermentation (~0.96)

2. A temperature dependent Henrys constant (kHT) was calculated.

> kHT = ( kH * exp( 2400 * (1/T - 1/T_ref) ) )

3. Resulting pressure was derived at different temperatures.

> Pressure (bar) = CO2_M/kHT

Example of using the chart:

Racking from the fermentation vessel at 20 °C will result in residual CO2 corresponding to about 4 g/L sugar already present in the cider (minus any CO2 lost during racking).

If current SG is 1.001 (1 Oe) and final SG was estimated to 0.008, it means a potential SG drop of 0.003 (3 Oe), which corresponds to 8.5 g/L added sugar.

Summarized:

4 + 8.5 = 12.5 g sugar per litre

This “Pet Nat” gives a carbonation level slightly below a typical cider (~3.5 Bar at 20 °C serving temperature).

If ~9 g/L sugar is then added (= total 21.5 g/L), the cider will be champagne-like in petillance (6 Bar at 20 °C).

Link to chart: https://eeenilsson.github.io/ciderkollen/figures.html

[terryc...@gmail.com]

You have produced an interesting chart, Erik. Being a hobby craft cidermaker, I think it could be a very useful tool. I will leave it for others to address your calculations but at first glance they seem to be O.K. to me. My interest is in the carbonation process.

I bottle at the sugar level (i.e. SG) needed for carbonation and retained sweetness, then pasteurise to stop fermentation where I want it (for example, bottle at 1.010 and pasteurise at gauge pressure of 1.8 bar which is 2.5 volumes of CO2 at 20C). At that point the SG should be around 1.005 or 9g/L of sugar for sweetness). It isn’t very precise or elegant, but it works for me.

I monitor bottle pressure in a test bottle fitted with a pressure gauge and hot waterbath pasteurise at 65C for about 10 minutes, so bottle pressure shouldn't get to much more than 6 bar or 100psi which seems to be an adequate safety margin over the likely burst pressure for bottles. As always PPE is essential.

Your chart could be tailored to help with this task. If you are after some feedback, from a user’s perspective I found there are two aspects that you might like to look into.

Firstly, your RHS pressure scale indicates absolute pressure, whereas the actual gauge pressure will be about a bar (15psi) less than this because of atmospheric pressure (Claude and Andrew had an in-depth discussion on this in May 2021, and it is also reflected in the many on-line carbonation calculators that are based on multiple regression research published in Zymurgy Magazine, Summer 1995). So, a “gauge pressure” scale might be useful (you do have a small gauge pressure notation in red that refers to this near the LHS pressure scale).

Secondly, I note that some bottle pressure limits are shown on the chart. This is a useful guide and no doubt you have found that such information is hard to find. The only manufacturers’ information that I could get was from Visy Glass who suggest that 330ml bottles shouldn’t exceed 4 GV (gas volumes) but they don’t specify temperature.

FYI, following is some pressure information that I have found for 12oz/330ml bottles that you might find useful in assessing bottle pressure limits.

Shanghai Misa Glass quote that China Standard GB4544 pass test for various markets is in the order of 1.8MPa (261psi).

U.S. Dept of Commerce has a Voluntary Standard requiring that pressure in reusable bottles should not exceed 200psi

A 1953 Ohio State University PhD study by Jo Morgan Teague “Stress in Glass Bottles” shows distribution curves for the pressure failure of new (and degraded) 12oz bottles. The mean was in the order of 400psi with the worst-case bottles being 50% of this (i.e. around 200psi). Although glass bottle making technology has no doubt changed in the intervening years, I imagine that the spread is similar. Hopefully bottles have become stronger.

[Erik Nilsson]

Thanks Terry!

Your method is quite interesting and I have considered trying something similar. In fact, that was one reason I wanted to calculate the temperature dependent  pressure. Something similar is described in Andrew Leas book, though he cautions for bottle explosions.

Your starting pressure (2.8 bar, 1.8 gauge @20C) seems to accord with ~4 density points fermentation, though previously dissolved CO2 from fermentation should perhaps add ~1 bar to that. However, according to my estimations you should from 2.8 bar pressure (1.8 gauge, 2.5 volumes) at 20C get a pressure of around 8 Bar (7 gauge) at 65C. Not sure how to explain the slight discrepancy from your measurement of 6 gauge. Maybe the bottle contents wont reach 65C in 10 minutes?

In any case, there seems to be bottles that are safe for 8 bar or more. As you say its difficult to find specifics (the China standard is interesting, but I haven't seen it on bottles here in Europe). I suppose most manufacturers have a relatively large safety margin. I bought some champagne bottles from a retailer who stated a tested pressure of 18 bar for those.

Added a longer "gauge pressure" indicator to the figure, and made some complementary tables for higher temperatures (you can find them here: https://eeenilsson.github.io/ciderkollen/figures.html). Just let me know if there is something else that would be helpful. Do note its just my amateur calculations.

Kind regards, Erik

 

[jeff.k...@gmail.com]

Hey folks,

To contribute a bit to the question of absolute bottle pressure limits, I ran some tests that I reported on here:

https://groups.google.com/g/cider-workshop/c/BQHvpggBocw/m/-hjlyMgDAgAJ

Summary:  for 330 g glass Tosca bottle, the measured rupture (explosion) pressure was between 40-70 bars (around 500-1000 psi).

/Jeff

[terryc...@gmail.com]

Hi Erik

Re the China Standard GB4544, I found that you have to buy it (which I wasn't really interested in doing), however the following web site 
www.misaglass.com/beer-glass-bottle-quality-standards

has a relevant extract and also shows a production line with Heinekin labelled bottles that suggests to me that they are supplying to reputable European customers.

Cheers!

[terryc...@gmail.com]

Re the pressure discrepancy. There really isn't one. I was just using some rough figures from projecting Andrew Lea's Carbonation Table to suggest that 65C for up to then minutes shouldn't create pressure much more thn 100psi which I consider is an adequate safety margin given that the bottles' burst pressure is probably in exces of 250psi and stresses that result in failure are slow to build up in glass. The actual figure at 65C is 7.51bar or 109psi which aligns with your calculation.

When pasteurising, I use a spreadsheet to record the bottle temperature each minute and calculate the cumulative PUs generated. Even though 65C for 10 minutes works fine as a "rule of thumb", I like to know just what I have done for each batch. 

In practice, the 65C bottle temperature (taken by a thermometer in a test bottle) is usually reached in less than 10 minutes because often 7+ minutes is long enough if the bottle starting trmperature is something like 20C. By the time the bottle temperature reaches 65C about 20+PUs have been generated and the bottles are removed from the bath. Time out of the waterbath as the bottles cool to 60C generates another 20 PUs and I find that the total of 40+ PUs is enough. By monitoring time and temperature I usually end up with somewhere between 40 and 55 PUs depending on how diligent I have been with monitoring.

[gareth chapman]

If all you are doing is wanting to prevent re-fermentation, then there is evidence out there that as little as 1 PU  is sufficient  and I can confirm anecdotally that it is true if I ever pasteurise I bring the product up to 60 degrees C and that has never let me down.

A Preliminary Evaluation to Establish Bath Pasteurization Guidelines for Hard Cider - ProQuest

[Erik Nilsson]

Terry, Jeff, and Gareth, thanks or the input!

That's an interesting paper, suggesting very low PU can be sufficient.

For doing pasteurization of capped bottles, it seems to me the major uncertainty lies in estimating carbon dioxide concentrations. Eg a heavy bottle would probably withstand the carbonation level of a typical cider (3.3 volumes CO2) at 65C (~10 bar), but if it is actually carbonated at champagne-level (~5.8 volumes), pressure at 65C would be ~20 bar. This is still lower than  Jeffs bottle test, but its probably wise factoring in uncertainties like exact CO2 content, bottle quality variability etc.

Its also an interesting observation from Terry that the time spend with high pressure affects bottle explosion risk.

Kind regards, Erik

PS. Attaching a pasteurization chart for different time/temp/PUs