Some turbo information and why the HE221w. Feel free to skip or read when you are trying to go to sleep.
Holset turbos have been around since the early 50s. Cummins bought them in 1973. They have manufacturing facilities in USA, Brazil, China, UK and India. As with everything there are fakes out there so make sure you buy a genuine Holset no matter where it's made. Another fun Holset fact, Holset Turbochargers are the only manufacturer that focuses solely on medium to heavy-duty diesel engine turbo technologies.
The HE221W is capable of 320bhp, thats well over the 120bhp of the 13BT.

The good side is it's still a really quick spool up even on small under 2.0L engines. This is a good start. I'm looking for a reliable quick spooling turbo that isn't really pricey.
Choosing your turbo: To figure out what turbo would be a good fit, you can either find what others did, pay others to do it or do maths. I've seen a few upgrades and read a ton of information so I decided to run "the maths" to see if it would fit because I like to learn.
Again, warning boring science learning ahead
First you need to know the air requirement's of your engine. You can figure that by a formula. The 13BT is 120HP and makes max HP at 3400rpm. So we need to figure our how much air it needs at that RPM.
13BT, 3400cc = ~208 cubic inches.
208ci x 3400rpm divided by 3,456 = 205cfm (cubic feet/min)
205 x .80*** efficiency = 164cfm (Volumetric efficiency is a moving target. Lots of factors but generalizing will be close enough)
So at 3400RPM, the 13BT uses 164cfm. Thats assuming 0psi, or basically 1 bar/atmosphere. 1 bar is 14.7psi at sea level. The higher you go up, the lower that pressure is. At 5000' in elevation, it's around 12.2psi.
So what air does the engine use without boost and with different levels of boost.
1:0 would be164cfm at 0psi
2:1 that would be 327cfm at 14.7psi
3:1 would be 492cfm at 29.4psi
the 1:0, 2:0, 3:0 is the pressure ratio. The Pressure Ratio is the
total absolute pressure produced by the turbo divided by the atmospheric pressure (14.7 psi). The total absolute pressure is basically the atmospheric pressure plus the amount of boost we're running/going to run.
I won't be running 30psi, ideally topping around 20ish, so that would be 410cfm at 22psi which is been reported safe by others. So using the formula for pressure ratio at seal level 22psi = 14.7(atmosphere) + 22 (guage reading) divided by 14.7 (atmosphere) to = 2.49 pressure ratio.
So I want a turbo that can do 410cfm at a 2.5 pressure ratio efficiently. Clear as mud?
So now we can look at turbo compressor maps to see if we can match a turbo to the engine.
Continued in next post...