Oh boy, here we go!! Brining has become a rather contentious subject around here, with some declaring it's a worthless exercise and others claiming they'd never cook anything without brining.
According to those who know more than I, in order to obtain FULL PENETRATION on a pork butt, it would take 7-10 days.
A 24 hour brine will get you approx. 1" of penetration, which it has been speculated (by me) is enough of a protective barrier to prevent the butt's own moisture from migrating out during the cooking process. As I have yet to do the required testing to prove or disprove my theory, it's still anybody's guess.
Pork butt is pretty forgiving, so no matter what you do it's pretty hard to screw up.
Welcome to the forum and let us know how the pork butt turns out.