Another useful trick to disposing of wood cleanly in a fireplace
(IMHO), is, once a fire is started with some relatively dry wood, to
put a few pieces at a time on end along the inside of the fireplace.
Turn periodically and don't overcook. Remove and replace with other wet
pieces after sufficiently dry.
The smaller the pieces, both in length and cross-section, the more
quickly they dry. So you may want to split & cut further.
(Comments withheld about throwing away good fuelwood in a fireplace-
hard to do for a Yankee.)