I thought about estimating 65% efficiency for the grain bill and then appropriately mixing first and second runnings if I get better efficiency.
Last weekend I brewed an 11 gal nut brown ale (23 lbs grain). I estimated 73% efficiency. I mashed with 7.75 gals strike water, mashed-out with 4 gals, collected, and sparged with 6.25 gals. I hit my efficiency (well, 75% actually). I hit 1.058 SG (1.057 SG estimated). So I don't have problems extracting the sugars out of 20+ lbs grain with a 90 min boil. But that's just my system.
The other thing you should do is keep a few lbs of DME around so you can adjust, just in case you come in low.
I'm not sure how much of the extract will go into the big beer vs. the small beer, but here goes... Here's my thought process (with some assumptions):
vol into fermenter = 5.5 gal
0.5 gal lost to kettle trub
Postboil volume = 6 gal
1.5 gal/hr lost during the boil
Boil time 1 hr
Preboil volume 7.5 gal
First beer:
So, for an OG of 1.105, that's 105 GU/gal (postboil)
105 GU/gal x 6 gal = 630 total GU for the bigger beer
630 GU divided by 7.5 gal (preboil) = 84 GU/gal.
Your preboil gravity for the big beer needs to be 1.084 and volume 7.5 gallons.
Second beer:
(Not sure what the OG of the second beer will be, but this should be close to your 40% of the extract going into the smaller beer
So, for an OG of 1.045, that's 45 GU/gal (postboil)
45 GU/gal x 6 gal = 270 total GU for the smaller beer
270 GU divided by 7.5 gal (preboil) = 36 GU/gal.
Your preboil gravity for the small beer needs to be 1.036 and volume 7.5 gallons.
The total GU then that you'll need out of the grain for both beers = 630 GU + 270 GU = 900 GU
lbs of grain at 100% efficiency = 900 GU divided by average of 36 GU/lb of grain = 25 lbs of grain.
lbs of grain at 63% efficiency = 25 lbs divided by 0.63 = 39 lbs of grain
Strike water needed = 39 lbs of grain x 1 qt/lb of grain = 39 qts = 9.75 gallons
Does that sound about right? It's probably sorta close, then you can mix the runnings a little if you overshoot the 63% efficiency target.
This whole thing is predicated on getting 63% efficiency total across both beers. However, across both beers efficiency is likely to be substantially higher. Probably close to the 73% achieved for the previous 11 gallon batch. You will definitely not need 39 lbs of grain for these two beers. That is just way overkill.
39 lbs is a lot of grain and it sounds crazy to me too. I've never done a partigyle but was trying to help figure it out. Do you see any flaw in the calculations that you can point out?
BTW (assuming the calculations are correct), if you want to figure for a different efficiency, say 73%, you'd divide the 25 lbs by 0.73 = 34 lbs. The other way to reduce the amount of grain is reduce the gravity of the second beer; if you do that you'd have to recalculate the total GU needed for the second beer and proceed from there.
And you could still mix the runnings some if you overshot your efficiency.
EDIT: Just did a quick recalc for a second beer of 1.035 and you'd need a total of 32 lbs of grain (with 73% efficiency).
I've gotten 5 gallons of 1.118 (first runnings only with 1pound table sugar added)
The overall efficiency for a partigyle will definitely be higher than your typical 5 gallon batch unless the problem is with conversion.
I've gotten 5 gallons of 1.118 (first runnings only with 1pound table sugar added) and 5 gallons of 1.055 out of 28 pounds of maris.
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