Need help on math for an Eisbock

[DevilNuts]

Greetings!

I've got 6.5 Gallons of what will hopefully be a delicious Eisbock in months to come. OG 1.104. The plan, as I understand it, is once we get to around 1.010 or so, keg the beer and bring it to around 32F, where it will slowly begin to freeze.

Every so often, we will rack the beer into a different keg, leaving behind the water that has frozen and separated off. We will do this until... I dunno... I guess until we feel like it's strong enough?

I'm trying to figure out how to do the math (or even what math to do, for that matter) to determine the adjusted ABV of the newly concentrated beer after freezing.

With each transfer, the volume of beer is going to decrease. The SG of whatever remains will.... what, exactly? Increase? No, that doesn't sound right. Stay the same? How can it, when there's less water? I can't even begin figuring out how this math is supposed to work.

Can anyone point me in the right direction? I am lost in the sauce on this one.

 

[Singletrack]

You don't need SG. You want ABV - alcohol by volume. Volume decreases, but the amount of alcohol stays approximately the same. If ABV is 10% before freezing, then you freeze/remove 20% of the volume as ice, you now have 10 volumes of alcohol in every 80 (100%-20%) volumes of beer, so ABV is 10/80 = 12.5%.

 

[RTL]

To expand on what singletrack said you do want to focus on ABV, not gravity. The equation you are looking for is:

M1*V1 = M2*V2

Where M is mass and V is volume, but you can use ABV for mass. This is the conservation of mass equation, basically just saying that the alcohol is conserved during the transfer. You probably lose some but it should be negligible.

So if you have 6.5 gallons at 10% and you concentrate to 4 gallons you have:

6.5*10 = M2*4

So you solve for M2 to get 16.25%. As far as gravity goes it will change because some of the sugars are going to get stuck in the ice, and the alcohol concentration is increasing. Since the alcohol is less dense than water and you're losing some sugar trying to track your final ABV by taking gravity readings would not work well. However, I think it would be cool to take the gravity readings before and after freeze concentration just for fun, you should be able to approximate how much sugar you lose based on the FG change.

Did you mash low (145F ish) for an extremely long time? I have a hard time believing an 1.104 beer will hit 1.010 unless you had a considerable amount of simple sugar in there. I've gotten 90% ADF on a 1.085 beer after an overnight mash but that's a far cry from 1.104.

Keep us posted I'm interested to hear your results.

 

[porterpounder]

Also, you're going to have to get it colder than 32 F to freeze. With that alcohol content and other things in solution it's probably going to have to go quite a bit colder to start freezing.

 

[DevilNuts]

Thanks for the input! This has really helped me simplify things.

Did you mash low (145F ish) for an extremely long time? I have a hard time believing an 1.104 beer will hit 1.010 unless you had a considerable amount of simple sugar in there. I've gotten 90% ADF on a 1.085 beer after an overnight mash but that's a far cry from 1.104.

Keep us posted I'm interested to hear your results.

Mashed at 149F for about 90 minutes. The beersmith recipe calls for a FG of 1.005, but I never expect to get anywhere near that. 1.010 is about the ceiling of my expectations, and a week into fermentation I repitched a fresh liter of yeast, added new nutrient, and wisked some more air into the wort just to kick it in the pants.

It's been going for a month now. Friday [I thought] the gravity was 1.045, but yesterday I just learned how refractometers really work, so I took a hydro sample and it's sitting at 1.016. I'm going to let it go for another two weeks, and then start my freeze, whatever it's at. (Tastes awesome though, even warm and flat. I can't wait to try the concentrated version with a little heat to it!)

Also, you're going to have to get it colder than 32 F to freeze. With that alcohol content and other things in solution it's probably going to have to go quite a bit colder to start freezing.

I've read that a good way to start is by going 1 degree F below 32 per ABV%. So I'm going to have to decide which ABV calculator I want to trust, and I'll probably end up starting on the warmer side, and cool it gradually until I get the results I'm looking for.

 

[porterpounder]

Be careful to watch it carefully as it freezes. Put it in a deep freeze and check it for slushiness every 30-60 mins or so and push it off when it gets nice and slushy. If you just set the temp and wait for it to freeze, the whole thing is going to be a solid block before you know it.

 

[ajdelange]

To begin with the calculations are not as straight forward as one might think. Here's an example. The function dens(p,t) returns the density of an alcohol water solution that is 100*p percent ABW at temperature t). Working at 20 °C if one adds 10 mL of pure ethanol ( 10*dens(1,20) = 7.89239 grams) to 90 cc of water (90*dens(0,20) = 89.8381 grams he has 10*dens(1,20) + 90*dens(0,20)= 97.7305 grams of solution at 10% ABV but the ABW is 10*dens(1,20)/(10*dens(1,20) + 90*dens(0,20)) = 0.0807567 i.e. 8.07% ABV and its density is 0.984621 g/cc so that the volume of the mix is 97.7035/dens(0.0807567,20) = 99.2296. IOW 10 cc of pure alcohol added to 90 cc of pure water does not give 100 mL of solution.

Now let us assume that we can remove 10% of the volume of the mix (9.92296) of the water as ice from this solution. The ABW becomes print 10*dens(1,20)/(10*dens(1,20) + (90-9.92296)*dens(0,20)) = 0.0898646 and the ABV 0.0898646/dens(1,20)= 0.113862. So decreasing the volume by 10% increases the ABV by a factor of 1.14, not a factor of 1.1 as one might expect.

Furthermore, one cannot remove 10% of the volume as just water. Some alcohol will come with it. Think of a Marguerita. The booze and the ice are intermixed with each other and it's going to be the same here. If one weighs the slush removed and determines its alcohol content (by weight) he can then use conservation of weight to determine how much water and alcohol are left in the keg.

 

[RTL]

That's cool. Now do it for the sugar, the protein, the polyphenols, the remaining yeast...

Kidding of course, and I respect the level of detail you went into but there is so much noise in this that the level of precision you are working in is impractical IMO

I like the idea of weighing the removed ice, but you are assuming all that is removed is ice/alcohol. I would also let it melt and measure the volume, then take a hydrometer reading. Then also take a hydrometer reading of the beer after the ice was removed. Thus you could approximate how much sugar was lost and calculate what the new FG (of the beer) should be without that sugar and the removed water. Then based on any deviation from that value approximate what amount of alcohol was lost to the slush. Again this will not be extremely precise since we have to deal with the sugar/water/alcohol/etc. mixture.

Thoughts?

 

[ajdelange]

The whole point being that i don't think there is any math you can do that's going to give a good prediction. I had a fellow contact me once with an Eisbock which he had calculated was 20% ABV and asked me if he could come over and measure it. It turned out to be 17% (I'm not sure i remember those numbers correctlu but it was something like that). He commented that the slush he removed was not white (contained some coloring matter) demonstrating that he was not removing pure water.

 

[DevilNuts]

To begin with the calculations are not as straight forward as one might think. Here's an example. The function dens(p,t) returns the density of an alcohol water solution that is 100*p percent ABW at temperature t). Working at 20 °C if one adds 10 mL of pure ethanol ( 10*dens(1,20) = 7.89239 grams) to 90 cc of water (90*dens(0,20) = 89.8381 grams he has 10*dens(1,20) + 90*dens(0,20)= 97.7305 grams of solution at 10% ABV but the ABW is 10*dens(1,20)/(10*dens(1,20) + 90*dens(0,20)) = 0.0807567 i.e. 8.07% ABV and its density is 0.984621 g/cc so that the volume of the mix is 97.7035/dens(0.0807567,20) = 99.2296. IOW 10 cc of pure alcohol added to 90 cc of pure water does not give 100 mL of solution.

Now let us assume that we can remove 10% of the volume of the mix (9.92296) of the water as ice from this solution. The ABW becomes print 10*dens(1,20)/(10*dens(1,20) + (90-9.92296)*dens(0,20)) = 0.0898646 and the ABV 0.0898646/dens(1,20)= 0.113862. So decreasing the volume by 10% increases the ABV by a factor of 1.14, not a factor of 1.1 as one might expect.<.....mathmathmathmath.....>

haha What details must I post for you to do all of this math for me and just spit out a number? Honestly, just looking at all of that gives me a headache.

.... the slush he removed was not white (contained some coloring matter) demonstrating that he was not removing pure water.

Is there any practical way to ensure I am only removing water, or mostly removing water?

 

[ajdelange]

Not that I know of. You could, of course, melt the slush and assay it but if you are willing to do that you could, presumably, just assay the beer.

 

[ten80]

Is there any practical way to ensure I am only removing water, or mostly removing water?

Sort of. The alcohol will become more separated from the water each time you let the beer freeze and partially thaw. So you can put the keg outside (or in fridge), bring it back inside for a few hours, then freeze again, and repeat.

The best way to calculate alcohol, short of an analytical laboratory, is to measure volumes and gravities of the recovered portion of beer and what is left behind. Then use the following dilution formula to solve for your final abv (C3):

(C2*V2)+(C3*V3) = C1*V1

and
C3 = ((C1*V1)-(C2*V2))/V3

C = concentration (ABV)
V = volume

This calculation also works for figuring out the final or initial specific gravity for two mixed worts or beers.

 

[DevilNuts]

So I started trying to freeze the beer this weekend, and it's not as simple as I had thought. I've brought it down to 14F overnight, and I keep moving it around in the carboy to see how thick it's getting. There's a nice slush forming, but it doesn't look like it's actually separating. It's all the same color.

Not sure how I'm going to be able to tell what's beer and what's not when I try to remove the beer. Maybe I'm overthinking this, and I should just turn the carboy upside down and let whatever falls out into the keg be my eisbock.

 

[ClaudiusB]

It's all the same color.

Not sure how I'm going to be able to tell what's beer and what's not when I try to remove the beer. Maybe I'm overthinking this, and I should just turn the carboy upside down and let whatever falls out into the keg be my eisbock.

My steps making an Eisbock
1. I freeze my 5 gallon Doppelbocks in 1 gallon containers for a few days. It's all the same color after freezing.
2. Drain each container into a 3 gallon Corny until the ice is clear.
3. Force carbonate to required level and enjoy

A few pics should give you an idea. I try to recover 2-2.5 gallons.
The bottom container was not completely drained as can be seen in the picture.

 

[Jwin]

I had good luck with an eisPA by just freezing my Speidel and drawing from the spigot. In a wide fermenter, the ice settles to the top.
I use an upright freezer as my keezer, but at the time was using it for a fermentation chamber.
I bottled straight from the fermenter and used carb drops and CBC yeast with great success.
It was a 10g batch that came up short on volume so I kegged 10 and froze the other 3.5.
So, I think using a vessel with a spigot would be advantageous. Would also reduce o2 as your not pouring it.

 

[ClaudiusB]

Would also reduce o2 as your not pouring it.

O2 is always a problem.
In my case the beer is gone after two weeks.
If I would make a lot of Eisbiers I would build a miniature version of a commercial unit.

 

[DevilNuts]

Thanks! I wasn't sure whether to expect the ice to become clear or not, the pics helped.

 

[DevilNuts]

This beer came out wonderful! I ended up freezing it at a5F for about a week, and when it came time to transfer I just purged my keg with CO2 and dumped it in. Not ideal, but it was heavy and I was by myself.

We started with exactly 5 gallons at 12.4%, and froze off to 3.75 gallons, giving us about 16.5%.

The alcohol heat is almost nonexistent for a beer this strong (and young), and the nutty/raisin flavor is nice and balanced. Good head retention. The BJCP guy I showed it to told me I should definitely enter this as a strong scottish ale.

 

[ClaudiusB]

This beer came out wonderful!

Over the weekend I finished a Barrel aged Eis-Mead.
The mead aged for 8-1/2 months in my Scotch barrel I previously used for my Doppelbock.
To get to this point it took close to three years, two years for the mead to be perfect.

 

[DevilNuts]

We've been thinking of doing that with our cherry mead, very cool!