There is 23 barrels into the launch bay. Be sure to check the upper levels of the bay, there is several barrels there, and three in "top hangar" sections. There is no barrels into "doored" rooms, as Memorial, or Medic bay. All barrels are in the main space area.
Barrels from the Barrel kicking game, does not count (as you can't kick them outside of the Abyssbar).