  In this paper, we have used the reconstructed DBI-essence dark energy density
to modify the mass accretions of black holes and wormholes. In general, the
black hole mass accretion does not depend on the metric or local Einstein
geometry. That is why we have used a generalized mechanism by reconstructing
the DBI-essence dark energy reconstruction with f(R) gravity. We have used some
particular forms of the scale factor to analyze the accretion phenomena. We
have shown the effect of cosmic evolution in the proper time variation of black
hole mass accretion. Finally, we have studied the validity of energy conditions
and analyzed the type I - IV singularities for our reconstructed model.
