XF351Lucifa

Possible fuel pump/filter, just cause of black smoke doesn't necesarilly mean overly rich, but is normally. The backfiring on the other hand is a sign of getting lean, what will happen being that the car has adaptive learning is if your fuel pump is cactus and can't pump enough fuel pressure, it will learn around this, pumping peddle etc may cause it to issue black smoke, as will lean if detonating, but overall their is little or no fuel to supply, so once hold at an rpm it won't have the fuel to back it up.

Easy to diagnose without spending lots of $$$$, just take the inlet fuel hose off, which is the larger one leading to the fuel rail, rather than coming from the reg. take it off, put a T fitting in line with it and inlet fuel and run the middle T outlet to a fuel pressure gauge and just see what its doing, if no fuel pressure gauge avail, you can always use an oil pressure gauge (cheap like $20). When full throttle fuel pressure should be near 38psi, at idle around 30, if under these values of about 5 psi there is definetly a fuel pressure prob.