  The large time behavior of the deterministic and stochastic three dimensional
convective Brinkman-Forchheimer (CBF) equations for $r\geq3$ ($r>3$, for any
$\mu$ and $\beta$, and $r=3$ for $2\beta\mu\geq1$), in periodic domains is
carried out in this work. Our first goal is to prove the existence of global
attractors for the 3D deterministic CBF equations. Then, we show the existence
of random attractors for the 3D stochastic CBF equations perturbed by small
additive smooth noise. Finally, we establish the upper semicontinuity of random
attractor for the 3D stochastic CBF equations (stability of attractors), when
the coefficient of random perturbation approaches to zero.
