Building a new system to brew 15G batches. Can I get away with having both the HLT and MT being 15G and the boil being 20G?
There are mash tun size calculators out there, but if you want to do the calculations yourself...
Grain occupies about .08 gallons per pound of space when mixed with water.
Let's say you're mashing 12 pounds of grain.
12*.08 = .96 gallons of space for the grain.
And let's say you're mashing at 1.25 quarts per pound of grain.
12 pounds of grain * 1.25 quarts per pound = 15 quarts of water.
Divide that number by 4 to get gallons (4 quarts in a gallon), so you'd have 3.75 gallons of water.
.96 gallons of grain + 3.75 gallons of water = about 4.75 gallons needed for your mash tun (not including dead space and about 2% expansion due to heating the mash from room temp to typical mashing temps).
At 1.25 quarts per gallon, 38 pounds of grain would take up 14.92 gallons.
At 1.5 quarts per gallon, 32.5 pounds of grain would take up 14.79 gallons.
That's a lot of grain for a homebrewed batch of beer.
But in a more direct answer to your question:
Let's say you want 15 gallons of beer in kegs.
You lose about .5 gallons per carboy, so you need 16.5 gallons of wort per batch.
Let's say you can realistically use up to 36 pounds of grain in your mash tun. At 1.25 quarts per pound, that would take up about 14.13 gallons, which would give you some extra room for deadspace, water expansion due to heating the water up to about 150°, and some room for stirring without making an incredible mess of your brew stand.
36 pounds of pale malt 2-row at 75% brewhouse efficiency for a 16.5 gallon batch of beer should give you a beer around 1.061 OG (I'm not even gonna lay out the math for THAT one).
So yeah, you could make 15 gallons of moderately-high OG beer with a 15 gallon MLT, if you have a decent brewhouse efficiency. If you want to brew big beers, then you're probably going to have to stick to 10 gallon batches.