The ESB FG range is usually given as 1.010 to 1.016, so let's assume 1.012 and do a simulation.
To get 5.5 ABV with an FG of 1.012 requires an OG of 1.054 (used
this calculator and adjusted OG until I got the target ABV.) Additional assumptions are you want 5.5 gal to the fermenter for each batch, your boil-off for each batch is 1.25 gal, your typical conversion efficiency is 95%, your typical grain absorption is 0.10 gal/lb, you will do a single batch sparge, and have equal boil volumes for the two beers.
If we assume 0.5 gal trub loss going from BK to fermenter, then we need a post-boil volume of 6.0 gal, and pre-boil volume needs to be 7.25 gal. The pre-boil SG needs to be:
Pre-boil SG = 1 + (1.054 - 1) * 6.0 / 7.25 = 1.0447
I will now use
my spreadsheet here to perform some unnatural acts to get to the answer of how much grain is needed, and what the pre-boil SG and OG will be for the gyle.
The results indicate that a straight partigyle, without blending the first and second running worts won't work well for the gyle. You would mash 12.09 lb of grain in 8.46 gal of water, and recover 7.25 gal of 1.0447 SG pre-boil wort. You would then batch (dunk) sparge the spent grains in 7.25 gal of water, and recover 7.25 gal (you don't lose any to grain absorption as the grain is already saturated) of 1.009 SG pre-boil wort for the gyle - not very useful. OG for the gyle would be:
Gyle OG = 1 + (1.009 -1) * 7.25 / 6 = 1.011
If this wort attenuated 75%, the FG would be about 1.003, for an ABV of only ~1%
If you want to look at calculating for a wort blending partigyle, let me know. Would like to know
your values for conversion efficiency, grain absorption rate, boil-off, kettle trub loss, and to-fermenter volumes for each batch, in order to make the calculations better fit your process.
Brew on