You should only need 2-3 pieces about 1-1/2 inch in diameter of smoke wood. Your meat only soaks up the smoke for the first part of the cook until the bark develops so don't worry about it after that. You shouldn't see a lot of smoke, only a very little bit of blue coming out the top for the first couple hours. After that, it is all about getting a nice bark and the right color. Once the rub is set(won't wipe off with a fingernail) and the bark is the right color, I foil it until done.
That said, white (bad smoke) is worse than no smoke at all.
Large Big Green Egg, Cold smokehouse,
UDS with hinged lid, Santa Maria pit
26.75" Weber OTG, Weber Performer, WGA
MAK One Star Pellet Grill, Smokey Joe Gold, Jumbo Joe Gold, Hasty Bake Gourmet
Custom wooden handles for BBQ's made by Marty Leach (oh, that's me)