  The accretion of a phantom fluid with non-zero chemical potential by black
holes is discussed with basis on the Generalized Second Law of thermodynamics.
For phantom fluids with positive temperature and negative chemical potential we
demonstrate that the accretion process is possible, and that the condition
guaranteeing the positiveness of the phantom fluid entropy coincides with the
one required by Generalized Second Law. In particular, this result provides a
complementary confirmation that cosmological phantom fluids do not need to have
negative temperatures.
