  Motivated by some earlier works \cite{pavon,sadjadi} dealing with the study
of generalized second law (GSL) of thermodynamics for a system comprising of a
Schwarzschild black accreting a test non-self-gravitating fluid namely phantom
energy in FRW universe, we extend them when the entropy of horizons of black
hole and the cosmological undergo quantum corrections. Two types of such
corrections are relevant here including logarithmic and power-law, while both
are motivated from different theoretical backgrounds. We obtain general
mathematical conditions for the validity of GSL in each case. Further we find
that GSL restricts the mass of black hole for accretion of phantom energy. As
such we obtain upper bounds on the mass of black hole above which the black
hole cannot accrete the phantom fluid, otherwise the GSL is violated.
