A two-fluid model for the numerical simulation of industrial scale olefin polymerization fluidized bed reactors is presented. However, a fully resolved simulation of industrial scale reactor is still nearly unfeasible. We, therefore, use sub-grid models (Schneiderbauer and Pirker, 2014) for the interphase drag and the solids stresses to account for the effect of the small unresolved structures on large resolved scales when using coarse grids. The sub-grid correction for the drag force is modified to consider the wide particle size distribution of high density polyethylene (HDPE). Furthermore, the sub-grid modification for the solids stresses is adapted to include the rheological properties of the polymer. On the one hand, the presented model is validated in the case of the coarse grid simulation of lab-scale bubbling fluidized bed by comparing bed expansion, bubble size and bubble rise velocities with experimental data. On the other hand, the model is applied to the coarse grid simulation of an industrial scale fluidized bed - moving bed reactor assembly. The numerical results demonstrate that our model reveals fairly good agreement with experimental data of average bed voidage, bubble diameters and bubble rise velocities. Finally, the impact of a barrier gas injection is studied, which is aimed to separate the fluidization gas from the gas in the moving bed reactor. (C) 2014 Elsevier B.V. All rights reserved.