A core-annulus multicompartment pseudo-2D two-bubble class model accounting for gas and slurry recirculation and coupled with catalyst sedimentation/advection/dispersion/lateral exchange balance equations for monodispersed and polydispersed solid particle systems was proposed to study the hydrodynamics of slurry bubble column facing solids accumulation in the reactor. The distribution of bubbles was represented by a bimodal two-class distribution: large and small bubbles. The model was coupled with a Prandtl-Nikuradse mixing length shear turbulence model or Sato bubble-induced and shear turbulence model to obtain the radial slurry velocity profile. A criterion for setting the onset of particles accumulation in the slurry bubble column was established. In solids polydispersed feeds, the influence of operating conditions (column diameter and height, solids feed mass flux and concentration, particle size distribution, gas velocity, and liquid viscosity) on the threshold particle size corresponding to the onset of particles accumulation in the reactor was analyzed systematically.