Depends on how much you use it. If its going 24/7, it won't take long to go away at all, then, all you have is the "first fire of the Winter" smell each season.
We have an actual Franklin stove and just priced new wood burners yesterday because I didn't know there was a tax credit for a newly installed woodburner. Make sure you ask your tax person about that if you just bought it.
Once they "season", it will lessen. BUT the odor can/will settle into your fabrics, causing it to linger far longer. Spray with Febreeze.....it will help to remove/neutralize the odors. You may have to use it several days but, it will help.
Hum, when I finish organizing down there I will spray everything down with the pet stuff I have. It takes the smell out of anything! Even smoke smell from a car.