Welcome and glad you joined.
Not sure, but i believe most built in battery mods use a Li Po chemical based battery.
I see some advertisers claim a duel Li Po internal configuration, whatever that means.
For LI Po info:
http://thedronegirl.com/2015/02/07/15-things-every-lipo-battery-user-should-know/
Since you want to go to 40-50w, you will deplete the 2K mAh cell in pretty short order w/o charging. Could look at these sites for over 50 w mods:
Ecig Mods with Built-In Batteries:
Best Vape Mods 2016 — Reviews, Guide and More
Might want to read through this:
http://..................com/thread...safely-be-used-in-a-vapor-shark-rdna30.11656/
I'm guessing you want a plugged in mod for every day use and the capability of being portable if need be. You are at such a high wattage use that internal battery design may not be the way to go portability wise.
You might have to bite the bullet and go with the expense (chargers,wraps, batteries, meter, etc) of carrying around sets of external batteries for a non internal battery box mod.