Specific Gravity vs. Time

[ThreeSheets]

Hello all,

Just wondering if anybody has seen or plotted a graph of specific gravity over time during primary fermentation before.

Quite interested to see if it directly relates to the exponential growth of yeast and co2 expulsion etc. I'd also be interested to know how it varies between beers, ciders and wines of different predicted ABV.

Cheers!

 

[Good Ed]

Each yeast works at a different rate

 

[EskiBrew]

I once wondered about using a TDS (total dissolved solids) sensor to continuously monitor the amount of sugar in a fermenting brew but I'm pretty sure that sugar is not terribly conductive so the TDS reading would not vary significatly. I'd guess therefore the only way to graph it would be to regularly sample using a refratometer and then plot :hmm:

 

[ThreeSheets]

I'd imagine someone in Psychrometry might be able to help you with that.

There's plenty of information on brewing but I can never seem to find any graphs of trends etc. If I had the equipment I'd quite like to put my brew on an electric scale and connect it up to LabVIEW with the weight initially zero'd so you could see the variation in weight. Anyone tried anything like that?

 

[EskiBrew]

I put this question to our Twitter followers and @mjmdavis has come back with some useful info - I'll repost here for those without Twitter accounts (and for those that do use Twitter, be sure to follow us @thbFORUM).

@thbFORUM you put it on a scale

@mjmdavis thanks for the suggestion - have you tried it, got any data we can have a look at?

@thbFORUM I'll have to pull out the chemistry books for that. Never had a scale big enough for a whole batch.

@mjmdavis hmmm good point - the resolution of the scales would have to be pretty damn good to detect the small changes...

@thbFORUM according to my calculations, if you assume perfect fermentation of sucrose, for every 1g of ethanol, 0.96g of CO2 is given off

@thbFORUM but that assumes only sucrose, no evaporation, doesn't account for yeast growth etc...

@thbFORUM given that assumption, 10L of 3% abw beer would create about 288g of CO2. A gram scale or even a 10g scale should work.

@mjmdavis great stuff - so you are saying that the example brew will get lighter by 288g - ignoring evaporation

@thbFORUM that is what I estimate, bear in mind that I am not a chemist. The point was that the amount of CO2 released should be measurable

Come and join the conversation or post here :thumb:

 

[mjmdavis]

Hi,

I'm mjmdavis, I'll post my equations on here in a bit.

I would be interested to see anyone trying this.

-edit:
Here we go with the back of the envelope calculations.

Assuming perfect fermentation of sucrose to ethanol, I threw this together.
Sucrose to Ethanol goes a little like this:

water sucrose ethanol carbon dioxide
H20 + C12H22O11 -> 4 C2H5OH + 4 CO2

Given that the molar mass of ethanol is about 46g/mol and that of carbon dioxide is 44g/mol, one can derive the proportion of ethanol to carbon dioxide:

44/46 = 0.96

This means that for every gram of alcohol you get 0.96 grams of CO2.

Given this, if we brew a beer with 300g of alcohol, we know that 288g of CO2 will be also be created, hence the 10L beer with 3% ABW losing 288g in brewing statement.

Now, in reality, there are probably other things going on during fermentation. If there is dissolved oxygen in the wort you might, depending on your yeast, get aerobic respiration leading to more CO2 and no alcohol:

water sucrose oxygen ethanol carbon dioxide
H20 + C12H22O11 + 12 O2 -> 12 CO2 + 12 H2O

As you can see, there is a lot more CO2 produced here which could really throw off any estimates made.

Once again, I am Engineer, not a Chemist, this is A-Level chemistry that I am putting to good use :-)

 

[EskiBrew]

Thanks for droping in and posting :clap:

 

[mjmdavis]

It's a pleasure.

I have updated the above post with some of the working for people to examine / check. The take home is that the weight of CO2 is indeed appreciable and should be quantifiable if you have a gram accurate scale or a 10 gram accurate scale.

-edit to clarify 1 or 10 gram as opposed to 1/10th gram.

 

[Windy]

For the last 14 days, my latest brew has been fermenting at 23 degrees C in a room which has been at a fairly constant 16 degrees C, only heated by the fermentation. The fact that the temperature remains constant suggests that the SG vs Time graph will be a fairly straight line through the main part of fermentation...

Any idea how much heat is given off during fermentation? Must be quite a few Watts to maintain the 7 degree difference between barrel and room.


Although I have a 1/10th gram scale, it won't take a 26 Kg barrel!

 

[mjmdavis]

Just to clarify, you should be able to see the difference on a 10L batch with a 1 or 10 gram scale. 1/10th would be overkill. I have amended my post to clarify this.

As for the watts given out by your brew, I would have to hit the books again. I don't have the bonding energies of the relevant molecules on hand. You would also need to take into consideration airflow in the room, the geometry of the barrel and the material the barrel is made of (including colour). With that information you could make an estimate as to the reaction rate based on the temperature difference between the room and the barrel.

I might have some time to look at this next weekend if anyone is interested.

 

[Windy]

Just to clarify, you should be able to see the difference on a 10L batch with a 1 or 10 gram scale. 1/10th would be overkill. I have amended my post to clarify this.

As for the watts given out by your brew, I would have to hit the books again. I don't have the bonding energies of the relevant molecules on hand. You would also need to take into consideration airflow in the room, the geometry of the barrel and the material the barrel is made of (including colour). With that information you could make an estimate as to the reaction rate based on the temperature difference between the room and the barrel.

I might have some time to look at this next weekend if anyone is interested.

The amount of energy given out will be the same as the amount generated and will not be affected by the colour of the barrel etc... I think there are too many factors involved to use the temperature difference to calculate the reaction rate, but the fact that it is a constant difference must tell us about the shape of the graph.

Even with a 10L brew my 1g resolution kitchen scales don't come close to coping with the weight and taking regular samples doesn't seem a good idea - it's going to take some special scales to use weight.

 

[mjmdavis]

I think that it should be relatively easy to find some scales that offer the kind of performance required. A quick google brought this up (removed for being spammy)

They seem to offer something with a 30kg limit and 1g accuracy.

If you are brewing 30L of beer though, you might be able to use digital bathroom scales. 30L of 3.3% abw beer should give off about a kilo of CO2 which might be readable on such devices. It's funny how the weight of a gas is not at all intuitive, it seems crazy that a kilo of CO2 could be let off by a relatively small amount of beer.

As for the temperature thing, yes, the amount of energy given of is the same as is generated. Conservation of Energy etc. You cannot however estimate the energy released by your brew until you know the rate at which it radiates heat. Your barrel is stuck at 23 degrees, you room is 16. These two pieces of information are not in themselves enough to make the estimate.

Brewing in a thermos would give rise to a higher temperature than brewing in a dark metallic pot. Your brew has reached a thermal equlibrium (not getting hotter nor cooling down). The amount of energy it radiates is the same as is being generated by the yeast. Without knowing one you cannot derive the other.

Thermal dissipation is something that is estimated all the time in industry. It's a fairly well understood problem and good approximations can be made. :thumb:

 

[mjmdavis]

Thinking about it, if you measured mass change and thermal output you could probably come up with a decent estimate of the size of your active yeast culture as well as your specific gravity. Might make for an interesting project.

 

[jarenault]

@thbFORUM but that assumes only sucrose, no evaporation, doesn't account for yeast growth etc...

The yeast break down all of the fermentable disaccharides to glucose and/or fructose (both have the same molecular formula - they're isomers) before fermentation. So it all works out stoichiometrically the same, more or less (fructose metabolism is slightly less efficient).
Evaporation would certainly need to be controlled for (perhaps by splitting the batch, and pitching no yeast into your control batch while noting the weight of yeast you added to the experimental sample).
Yeast growth doesn't matter, as the yeast are growing out of the medium they are living in (the wort). The mass of the wort reduces as the mass of yeast increases, but the net mass is the same before we account for fermentation, which is what we want to measure anyway. So the reproduction of the yeast is zero sum for our purposes.

 

[jarenault]

Some of the CO2 produced will also dissolve in the wort. It will only release CO2 into the atmosphere once the wort has reached it's CO2 capacity for its pressure.

 

[mjmdavis]

Yeast growth doesn't matter, as the yeast are growing out of the medium they are living in (the wort). The mass of the wort reduces as the mass of yeast increases, but the net mass is the same before we account for fermentation, which is what we want to measure anyway. So the reproduction of the yeast is zero sum for our purposes.

Yes, with the yeast growth I was referring to a different calculation where I was trying to estimate the amount of alcohol / CO2 for a given amount of sucrose. That might be a much trickier problem.

As for the CO2, if we are brewing in a vessel with gas trap on the top we can assume the Partial Pressure of CO2 to be atmospheric pressure. If you then assume the solubility to be the same as for water you can work out how big an effect this has. Around 1.5g CO2 per kg of water at 24C.

 

[jarenault]

Pressure in the vessel will be slightly higher than atmospheric pressure. Might make negligible odds though.

 

[mjmdavis]

That range can be worked out by the head and density of the liquid in your air trap ;-)

 

[ThreeSheets]

Thanks for your comments, I think we can tackle it quite simply from a mechanical point of view as opposed to looking to hard at the chemistry:

If we know the diameter of our airlock and the path the carbon dioxide before it expels through the liquid inside the airlock. Every time this "bubbles" (I'll call it the fermentation time period) we can divide this by the path the co2 moves through: This way we can find the volumetric flow rate per cycle. Knowing the density of carbon dioxide (among other gases that are produced) we can work out the mass flow rate, integrating once we can find the mass expelled per cycle.

Total mass expelled over time (kg)=density of expelled fluid (M/L^3)*cross section of airlock (L^2)*length the expulsion travelled the through airlock (L)*fermentation frequency (T^-1)*time taken from beginning(T)

To work out the specific gravity over time we must deduct the total mass expelled over time divided by the volume of the brew from the starting gravity.

SO IN SHORT: We need record how the fermentation time period changes in a fixed temperature environment so we can model see the change in density. The only way I can think of doing this is using a recording device in a closed noise environment then getting processing software to work out all of the time periods.

If anyone would like a schematic diagram of this I can draw one.

 

[bobba]

I'll have a crack at this nut.

You have a rough idea of how well the fermentation is going by the frequency of the bubbles in the air lock.

Given an airlock with constant trap height (or water content), it would be possible to plot the rate by programming a low power listening device such as a mobile phoneto recognise the sound of a bubble. Video observation should be possible but more complicated and hence power hungry. If anyone wants me to write one, they will have to make it worth my while by promoting it so I can put it on my CV, I daren't ask for money, but I seem to spend all my time making money, at an alarming slow rate :-/

Maybe I should be more interested in the yeast growth, since that likes making bread too ;-)