How long to force carb: The calculator

[damoninja]

Hi everyone,

I've scoured around looking for a utility that calculates approximately how long it will take you to carbonate your beer at a specific temperature and pressure.

I managed to find plenty of resources which listed just pressure and temp, managed to find one which did calculations at 40 PSI only, which is OK for some things... So I had a bit of spare time and made one in excel. I've taken some trusted commonly referenced resources and worked out what the differentials and exponents are within a reasonable margin.

You can input the style of beer you're brewing and it will give you an idea of how long it should take to carbonate and gives a (good?) guide of the range you'll hit over time.

It's new so it might have some bugs or need some improvement, download it and let me know what you reckon and how it compares to your experiences and knowledge.

I can't upload it because it's a macro enabled excel file (a few basic functions) so I've dropped it in my google drive

Here is the link to it

 

[damoninja]

h34r: reserved h34r:

 

[BKBrews]

Mate, I have no idea about this stuff, so if that's accurate then I think it is very, very good. I was wondering how I would do all of this when I set my keezer up, but it looks like if I set my temp at 2 degrees and leave it at 10psi (serving pressure for all of my kegs) for 12 - 14 days, it will be ready to go at 2.4 volumes.

 

[BrewedCrudeandBitter]

As a terrible brewer who only just kegged a beer for the first time a couple of weeks ago this is incredibly helpful.

 

[pcqypcqy]

Nicely done. Time is a factor that's often missing from these things, and is obviously the most important variable. I wonder how much goes into the calculation of the rate at which the gas dissolves given the other variables. Seems to me that a first principles calculation would be reasonably straight forward. But then I'm a structural engineer and a not a chemist, so I'm sure there's more to it.

I've been thinking of putting something like this together, so you've saved me the effort.

 

[damoninja]

As far as accuracy goes - I've used this well known chart to get the total CO2 numbers for given PSI, I did edit it somewhat as that chart does have errors in it *gasp* it looks like it was entered manually so there are some typos or duplicates, I've used calculations for all mine.

For time, I used a combination of things, but the main source was some spreadsheet I found that calculated time required to carb at 40PSI at a specific temperature, I was able to break down how much CO2 would be dissolved per day and adjust.

The potential room for error is - there are some assumptions... such as absorption rates over time being linear which is almost certainly not the case toward the end of carbonation, that's really the main thing which may make it less accurate... the biggest pitfall of this is likely at higher levels where it may actually carbonate faster in an inverse slope opposed to linear.

If anyone has any insights here please feel free to critique

 

[Droopy Brew]

Looks like it has the makings of a very useful tool mate well done.

Do you intend to create a drop down box for beer style? At the moment it is only Pale ale which I assume is there for test work.

 

[pcqypcqy]

As far as accuracy goes - I've used this well known chart to get the total CO2 numbers for given PSI, I did edit it somewhat as that chart does have errors in it *gasp* it looks like it was entered manually so there are some typos or duplicates, I've used calculations for all mine.

For time, I used a combination of things, but the main source was some spreadsheet I found that calculated time required to carb at 40PSI at a specific temperature, I was able to break down how much CO2 would be dissolved per day and adjust.

The potential room for error is - there are some assumptions... such as absorption rates over time being linear which is almost certainly not the case toward the end of carbonation, that's really the main thing which may make it less accurate... the biggest pitfall of this is likely at higher levels where it may actually carbonate faster in an inverse slope opposed to linear.

If anyone has any insights here please feel free to critique

The rate is almost certainly proportional to the difference between the applied pressure (i.e. regulator setting) and the volumes already dissolved. Things only flow when there is a difference in pressure, and as this difference drops so does the flow rate.

Your spreadsheet is locked, so I can't see how the calculations are done, but you should be able to use the dissolved pressure from the previous time step as an input for the next time step to account for this.

 

[damoninja]

That's is a drop down already, there's something like 90 styles or you can go to the bottom and give a specific number if you want

 

[damoninja]

The rate is almost certainly proportional to the difference between the applied pressure (i.e. regulator setting) and the volumes already dissolved. Things only flow when there is a difference in pressure, and as this difference drops so does the flow rate.

Your spreadsheet is locked, so I can't see how the calculations are done, but you should be able to use the dissolved pressure from the previous time step as an input for the next time step to account for this.

Yeah I get you - I think that will be a V2 enhancement while I figure out the best way to work this out... the source I used to determine amount of CO2 per absorbed per hour was linear so I kept things this way.

It's semi complicated, but I've used the linear hourly volume of CO2 dissolved at 40PSI (for the temp chosen), divided by 40 and multiplied by the PSI that's been entered. Then apply that hourly until it reaches the max, once it's reached max it no longer increases.

So the way it currently is removing the previous amount dissolved amount would totally negate the next number, or making it based on the previous value alone would make it an infinite curve and never reach the actual target (maybe doesn't matter when we're only talking a few weeks though).

Edit: I reread what you meant and reckon I get you... say if I'm set to 10PSI, and at X hour, 10% of the max potential 2.6 vols has been absorbed, I want to deduct 10% of my pressure... so I'll only absorb 90% of what I did in the last interval... Hmmmmmmmm!

Agree though I need to make that component proportional in some way and certainly plan to

 

[pcqypcqy]

A very rough way of doing it is to assume that it takes 2 weeks for any (reasonable) beer to get carbonated using a set and forget method. You can then work out the linear rate over this time, and then come up with a factor based on the volumes already dissolved and those left to dissolve to simulate the fact that an asymptotic curve is steeper at the start (i.e. faster rate of dissolution) and flatter at the end (slower rate).

Have a look at the attached sheet for an example.

I came up with an initial steepness factor of 6 times the linear rate to give a relatively stable pressure by the end of two weeks.

This sheet only mimics the asymptotic nature of the problem though, the target volume, assumed time to get there, etc are all static values.

What I'd really like is a calculator that can predict for a given time period, temperature and regulator setting, how many volumes will have dissolved in that time - i.e. not the equilibrium volume but a time dependent one. Then, you can come up with a force carb regime where you set to say 20 psi for 4 days (or as many pressure/time steps as you want) and get close to your target volume. I'm going to do some reading on the chemistry involved and try to come up with a calc in excel that mimics this process from first principles. I might then do some measurements maybe (somehow, haven't thought this through) to calibrate it.

View attachment carbonation over time.xlsx

 

[moonhead]

Nice work, I like the simplicity and immediate feedback on the chart.

Next step is to get some kind of accuracy with the CO2 pressure I'm putting into my kegs.

 

[peteru]

Does the size of the area where gas meets liquid play a significant role in the rate of carbonation? For example, upright keg vs keg on it's side, or 4L (tall) vs 5L (wide) mini-kegs.

 

[pcqypcqy]

Does the size of the area where gas meets liquid play a significant role in the rate of carbonation? For example, upright keg vs keg on it's side, or 4L (tall) vs 5L (wide) mini-kegs.

You are right, the instantaneous rate would have to depend on the area. The long term rate would also depend on the volume of beer you are carbonating.

 

[mckenry]

That's great. Can you do one with a carb stone? Typically a day is all it takes to reach equilibrium. So, much faster than absorbing from headspace. Would be nice to know exactly though and I think you're the man [emoji12]

 

[damoninja]

Does the size of the area where gas meets liquid play a significant role in the rate of carbonation? For example, upright keg vs keg on it's side, or 4L (tall) vs 5L (wide) mini-kegs.

Yes but I've written in the notes it's for carbing a normal old 19L keg too many variables to consider.

That's great. Can you do one with a carb stone? Typically a day is all it takes to reach equilibrium. So, much faster than absorbing from headspace. Would be nice to know exactly though and I think you're the man [emoji12]

If someone has something that says what the absorption rate is versus not having a carb stone I could probably add that in, assume it would basically be a multiplier...

 

[damoninja]

A very rough way of doing it is to assume that it takes 2 weeks for any (reasonable) beer to get carbonated using a set and forget method. You can then work out the linear rate over this time, and then come up with a factor based on the volumes already dissolved and those left to dissolve to simulate the fact that an asymptotic curve is steeper at the start (i.e. faster rate of dissolution) and flatter at the end (slower rate).

Have a look at the attached sheet for an example.

I came up with an initial steepness factor of 6 times the linear rate to give a relatively stable pressure by the end of two weeks.

This sheet only mimics the asymptotic nature of the problem though, the target volume, assumed time to get there, etc are all static values.

What I'd really like is a calculator that can predict for a given time period, temperature and regulator setting, how many volumes will have dissolved in that time - i.e. not the equilibrium volume but a time dependent one. Then, you can come up with a force carb regime where you set to say 20 psi for 4 days (or as many pressure/time steps as you want) and get close to your target volume. I'm going to do some reading on the chemistry involved and try to come up with a calc in excel that mimics this process from first principles. I might then do some measurements maybe (somehow, haven't thought this through) to calibrate it.

Good stuff, that's what I was thinking in a way

Few queries though:

1. Why a slope factor of 6? Very natural number and seems to apply in this instance but wondering if this was just what felt right?
2. Would we expect the absorption rate per interval to be linear with increasing PSI? Eg hr 1 @ 12 PSI = 0.044642857 - does 24 PSI = 0.089285714 (double)?

Either way it's a great idea, seems like something you're enjoying so wouldn't wanna steal the concept but I think the two would go hand in hand and reckon it would be a useful tool to have along side this one, so more than happy for them to live in the same sheet if you wanna collab on it

 

[pcqypcqy]

Good stuff, that's what I was thinking in a way

Few queries though:

1. Why a slope factor of 6? Very natural number and seems to apply in this instance but wondering if this was just what felt right?
2. Would we expect the absorption rate per interval to be linear with increasing PSI? Eg hr 1 @ 12 PSI = 0.044642857 - does 24 PSI = 0.089285714 (double)?

Either way it's a great idea, seems like something you're enjoying so wouldn't wanna steal the concept but I think the two would go hand in hand and reckon it would be a useful tool to have along side this one, so more than happy for them to live in the same sheet if you wanna collab on it

I arrived at 6 by playing around with different values of the initial steepness so that it 'looked right' on the chart, i.e. a quick initial jump in dissolved CO2, with a fairly steady curve by the end of the two weeks. much lower and it will still absorbing co2 at the end, and any higher and it's fully carbonated in a day, neither of which seemed right. But this is all just guess work.

My understanding that is that it would be linearly proportional to difference in pressure, so not quite what you've assumed.

Happy to collaborate, I get a bit of downtime at work at the moment in front of the screen just waiting for things to come in, so I'll be looking at this in more detail in the next few days. I'm also thinking about how to test it, this is my plan so far:

• fill a keg
• apply a certain pressure for a certain time
• unhook the gas, leave it for a day (or longer?) to reach equilibrium
• measure the headspace pressure using a gauge (maybe a pressure gauge with a barb, a short bit of hose, and a gas disconnect)
• record this value,
• reapply pressure for another time step
• repeat

This should give some data points along the way to calibrate the spreadsheet model.

 

[pcqypcqy]

That's great. Can you do one with a carb stone? Typically a day is all it takes to reach equilibrium. So, much faster than absorbing from headspace. Would be nice to know exactly though and I think you're the man [emoji12]

Carb stones work by increasing the surface area between gas and beer. I would hate to think of the calculations involved, might be best to measure it as I've described above.

Though if it only takes a day, then you probably don't need to worry too hard? Unless you're an OCD type like myself who just wants to know...

 

[damoninja]

I arrived at 6 by playing around with different values of the initial steepness so that it 'looked right' on the chart, i.e. a quick initial jump in dissolved CO2, with a fairly steady curve by the end of the two weeks. much lower and it will still absorbing co2 at the end, and any higher and it's fully carbonated in a day, neither of which seemed right. But this is all just guess work.

My understanding that is that it would be linearly proportional to difference in pressure, so not quite what you've assumed.

Happy to collaborate, I get a bit of downtime at work at the moment in front of the screen just waiting for things to come in, so I'll be looking at this in more detail in the next few days. I'm also thinking about how to test it, this is my plan so far:

• fill a keg
• apply a certain pressure for a certain time
• unhook the gas, leave it for a day (or longer?) to reach equilibrium
• measure the headspace pressure using a gauge (maybe a pressure gauge with a barb, a short bit of hose, and a gas disconnect)
• record this value, repeat

This should give some data points along the way to calibrate the spreadsheet model.

Sounding like a plan, certainly seems like a V2 enhancement