  The thermodynamic properties of dark energy-dominated universe in the
presence of a black hole are investigated in the general case of a varying
equation-of-state-parameter $w(a)$. We show that all the thermodynamics
quantities are regular at the phantom divide crossing, and particularly the
temperature and the entropy of the dark fluid are always positive definite. We
also study the accretion process of a phantom fluid by black holes and the
conditions required for the validity of the generalized second law of
thermodynamics. As a results we obtain a strictly negative chemical potential
and an equation-of-state parameter $w<-5/3.$
