Fun mash calc

[beekgeek]

Fun if you have a degree in thermodynamics maybe, but I'm having a harder time figuring this one out and wondering if anybody wants to try their hand:

I'm brewing a witbier this weekend and will be doing a separate protein rest for flaked wheat, oats and a small portion of pilsner malt. I'd like to then add this to an infusion mash for the rest of the malt. (Last batch I took all the grain through a protein rest and then up to saccharification rest temp, and I think my head stability suffered for it).

The thing that's throwing me off is the starting temperature of the protein rest portion -- I know that if I dough into that base with the rest of the pilsner malt I'm going to need to adjust my strike water temps for the infusion mash portion.

Details for a batch that will end up at 11 gallons post boil:

Protein rest portion:
9.25 lbs flaked (unmalted) wheat
1.75 lbs flaked oats
2 lbs pilsner malt

From BeerSmith, I calculate that I would add 16.25 qts of water at 134F to the 13lbs of grain to bring it to target 122F (based on starting mash tun and grain temp of 64F and a mash thickness of 1.25qt/lb).

Infusion rest base:
8 lbs pilsner malt
1.25 lbs wheat malt
.5 lbs Munich malt

If I was just working with the infusion rest malt, I'd add ~12.2 qts of water at 167F to the 9.75 lbs of grain to get it up to 154F (again assuming mash tun and grain starting at 64F).

But if I'm adding the second grain bill to the protein rest, presumably I'm going to need it hotter (with perhaps more water) to get the whole thing to 154. I'm mashing in a Coleman chest and while I can probably do some kind of decoction mash to heat it up, ideally I'd like to hit my target temps right out of the gate.

Any help on figuring this out would be awesome. Thanks.

 

[dcp27]

If I just calculated it right, at those volumes I think you'd need it to be 197F

Total volume * desired temp = volume 1 * temp 1 + volume 2 * temp 2
((16.25+12.2) * 154F - 16.25*134) / 12.2

Edit: sorry, thats without the adjustment for the newly added grain. you'd probably need ~10F hotter than that

 

[beerkrump]

dcp27, you're missing the 13° required to heat the second grain addition. That would bump the temp to 210°.

beekgeek, this is how I'd do it. Add your second batch of grains, 10 qts of boiling water, stir, and give it five minutes to equalize and see where you are. Make adjustments as needed.

 

[beekgeek]

dcp27 / beerkrump: Thanks for replies. I like the suggestion to start with 10qts of boiling water and adjust. I think it'll be alright even if I overshoot my target a little.

I know I'm probably overthinking this, but for future planning, I'm playing with the formula you've got here dcp27. I'm wondering if the volumes need to include grain as well as water. (I could be confusing volume and mass here). So for arguments sake ...

Somewhere I've got it that a kg of grain occupies roughly .652 litres of volume (or .31 qts per lb). By extension my 13lbs in first portion would occupy ~4 qts, and the 9.75lbs would be another 3qts. Playing with your formula:

(35.45 qts water and grain * 154 F) = (Protein rest: 20.25 qts water and grain * 122 F) + (Infusion mash: 15.2 qts water and grain * x temp)

5,459.3 = 2,470.5 + (15.2 * x)
x = 2,988.8 / 15.2 = 196 F (the number you came up with originally).

Beerkrump, how did you come up with the additional 13 F to heat second grain addition?

Thanks guys. Feel free to bow out if this exercise becomes too tedious.

 

[beerkrump]

Your original post 167° to get to 154°.

 

[beerkrump]

I forgot that there is also going to be some heat lost to bringing you mash tun up to temp.

 

[beekgeek]

Your original post 167° to get to 154°.

Right!

 

[dcp27]

so the modified equation of mine you did runs into the same problem. that 196F is with the grains already in, so the water would need that extra 13F to get you there

 

[a10t2]

I don't imagine you could be too far off if you just assume that the grains and water in the protein-rest portion retain their respective specific heat capacities, despite being mixed. That's 1.6 J/g°C for malt, and 4.2 J/g°C for water.

1.6*5910 (grain) + 4.2*15400 (water) + 1.6*4430 (new grain) = 81.2 kJ/°C

And you want to raise that 17.8°C, so you need to infuse 1445 kJ of energy. To do that using 12.2 qt (11.5 L) of water:

1445 kJ = 4.2 kJ/kg°C * 11.5 kg * (T - 67.8)°C

Solving for T gives 97.7°C, or 208°F.

Sorry about the SI units. I don't know that I'd be comfortable doing this in American units, and I don't have the constants memorized anyway.

 

[beekgeek]

a10t2, I'll admit I had to do some Googling and some SI conversions to get my brain around some of the math here, but I feel I've got a much better handle on heat capacity calculations now. So thanks for that excellent response.

The only nuance I'm still trying to figure out -- and may be included above -- is that the new grain going to the sacch. rest will be starting at 64F (a 32°C differential from the mash portion sitting at 122°F -- if you'll forgive the mixed temp scales). I'm guessing your calculation assumes the 81.2 kJ/°C is all at 50°C (122F).

Would it be right to say that I need to infuse an additional 227 kJ (=1.6*4430*32) of energy plus the 1445 kJ to bring the whole thing up to my sacch rest temp? 227+1445 = 1672 kJ = 4.2 kJ/kg°C * 11.5 kg * (T - 67.8)°C. Hence T = 102.4°C = 216°F (which in fact may be hard to achieve). Or done another way: 1672 kJ = 4.2 kJ/kg°C * kg water * (100 - 67.8)°C. In which case I'd need 12.36 L of boiling water. Have I totally fluffed this up?

Appreciate everyone's help so far!

 

[a10t2]

You're right, I did miss that. Your math checks out now.

One thing I'd suggest is to assume that when you add "boiling" water it's actually a few degrees off of a boil by the time it gets into the tun. Unless I do that I under-shoot my infusion targets pretty consistently. Since you're at sea level, I'd use ~13.2 L of boiling water, which should get you on target assuming it goes into the mash at 98°C.

 

[beekgeek]

Great. Good tip on the additional boiling water. I'm very happy to have a better handle on the calculations behind this. Thanks a lot!