Some BIAB and Sparge questions

I did a partial mash a for my first BIAB and it went good. Now im going to do an AG today and have some questions after my first BIAB. It was also my first time using the turkey fryer i got and i boiled off to around 1.50-1.75 gallons in an hour so i want to start with a pre-boil of 6.75 gallons.

my grain bill is 13.65 lbs. i have a 15lb brew bag and an 8.5 pot and a 4 gallon pot. i mash in the 8.5 gallon pot and heat water up in the 4 gallon pot for sparging.

so i figure 13.65 lbs x 1.5 qts/lb = 5.12 gallons for mash.
for grain absorption i figure 5.12-(13.65 x .125 gallons/lb)= 3.41 gallons from mash.

i need 3.34 gallons from sparge to hit 6.75 gallons and i am limited with my 4 gallon pot. would it be better to sparge 2 times or sparge once and add water to boil to get to 6.75 gal?

if i sparged 2 times i need to figure out how much water to sparge with to get to 6.75 gal. How much water would the grain absorb after mashed? (i used .125 gallons/lb before when dry). last time i heated up 3.75 gallons of water and sparged in bottling bucket that can hold 6 gal plus. ended up having to add top off water to the boil.

also i am not sure what the sparge temp should be, last time i heated to 170 and steep the grain bag. i think i read heat the water to 185 and let it steep for 10 minutes and i also read it should be 170 degrees and steep. what is the correct temp?

thanks

The grain doesn't absorb more water during a sparge. It's already saturated with the original mash water.

Describe what you actually plan to do with the "sparge". Once your mash is done and you've got your sparge water heated in the 4g pot, you...................

i heat up the sparge water in the 4 gallon pot. about 3.5 gallons and then pour into my bottling bucket and transfer the grain bag into the bucket and let it steep for ten minutes then pour that into the 8.5 gal pot from the mash. i use the bucket because it would overflow in the 4 gal pot. i just don't think i will get enough sparge water to get a 6.75 gal boil from a single sparge since i can only use about 3.5 gallons.

That's a good process. Just checking.

If you calculated out that you'll leave about 3.5 gallons in your large pot after removing the grain bag, you'll only need to sparge with about 3.25 gallons because like I said earlier, the grain is already going in saturated and won't hold anymore. Dunking it into 3.25 gallons, then letting it drip, should leave 3.25 gallons of wort in that bucket.

thanks. also what should be the temp of the sparge water. 170 or 185?

You could also to a double sparge if you wanted to, split the sparge water b/w the bucket and the pot. You say "steep" the grain during the sparge process, I think you want to actually stir and mix well w/ the sparge water.

Sparge water should be 180-185. The basic idea is that the grain bed should not exceed 170.