  This work is concerned about the asymptotic behavior of the solutions of the
two and three dimensional stochastic convective Brinkman-Forchheimer (SCBF)
equations driven by white noise with nonlinear diffusion terms. We prove the
existence and uniqueness of weak pullback mean random attractors for the 2D
SCBF equations (for $r\geq1$) as well as 3D SCBF equations (for $r>3$, any
$\mu,\beta>0$ and for $r=3$, $2\mu\beta\geq1$) in Bochner spaces, when the
diffusion terms are Lipschitz nonlinear functions. Furthermore, we establish
the existence of weak pullback mean random attractors for a class of locally
monotone stochastic partial differential equations.
