Is it french oak, american oak, hungarian oak? Different types of oak give different flavors. I wouldn't use it in the porter. It would be overwhelming of the malts. Let the porter be malty and roasty as it should be.
Save the oak bourbon combo for a big imperial stout or barley wine style ale.
If you want to give the porter a unique flavor from wood then try using some spruce tips or redwood tips. The redwood or spruce tips contain resinous terpenes much like hops, but provide a different mouthfeel.
Personally I love spruce tips. They add spice and a level of chewiness on the mouth. A couple of sprigs added to the secondary for a few weeks will do. I like to add them to the boil.
Good luck. I think overwhelming bourbon characteristics hinder everything the maltsters have done for beer. If you want to drink a bourbon then get a bottle of pappy van winkle. It's not cheap but it's the kind of bourbon you deserve to enjoy once in awhile.
It's just so overwhelming stupid that mainstream publications are promoting bourbon oaked beers as high end esoteric products when they are unbalanced hoppy messes.
If you want to try the pinnacle of beer made with wood from a spirits barrel try the JW Lee's Harvest ale aged in Calvado's barrels. Such a malty hoppy heavenly treat.