From what I remember, the Enterprise was said to have three reactors in the engineering hull at least (The original post and at least one other post in this thread mentioned three reactors -- and in the first post, the alien entity left the ship through the engineering room suggesting all three reactors were in that room)
-- probably all matter/anti-matter reactors it would appear as the energy from those reactors go to the warp-engines and probably power the whole ship (Warp engines are powered by matter/anti-matter reactions and matter/anti-matter is more efficient than fusion or fission)
It was stated at least once about matter and anti-matter being used up in the nacelles. However I'm not sure how this should be interpreted. First of all they were called matter/anti-matter nacelles, not warp-nacelles, second of all it would seem that most of the data points to reactors in the engineering-hull providing their power.
It would be interesting however if the ship had three matter/anti-matter reactors in the main hull for powering the warp-nacelles, nav-deflector, and possibly the whole ship, *and* had a back-up matter/anti-matter reaction chamber in each nacelle to provide some warp capability (say Warp 3.5 or Warp 4.5* instead of the typical Warp 6)
in the event of battle-damage or 2 or more reactors failing (the warp-engines and nav-deflectors both require enormous energy... and the reactors have to power the ship too! If you lost two reactors you might be able to do everything, at least you could run the nav-deflectors, some ship systems and use the fusion reactors in the impulse deck to do anything left over)
. Granted you'd need to still pump matter and anti-matter up into the nacelles, but that can be managed on limited power conditions (and I suppose there's no rule that says you can't have a liquid hydrogen tank, and a bunch of anti-matter tanks up in each nacelles as a on demand reserve)
* - Warp 4.5 is around 91 times the speed of light. That would cover you a light year every four days. However considering in Star Trek, warp factors mean whatever the writers wanted it to be Warp 3.5 sounds like a number that is reasonably low enough, yet "fast" enough by writer standards to "limp around".