In this research, a CFD algorithm for simulation of fluidized bed polymerization reactors is described. In order to properly model the evolution of a polydisperse solid phase, population balance equation (PBE) must be solved along with other transport equations. A novel approach---DQMOM is applied to polydisperse fluidized bed to simulate particle aggregation and breakage in the reactors. Two different aggregation and breakage kernels are tested and the performance of the DQMOM approximation with different numbers of nodes are compared. Results show that the approach is very effective in modeling solid segregation and elutriation and in tracking the evolution of the PSD, even though it requires only a small number of scalars. After successfully developed DQMOM-multi-fluid CFD model, the multi-fluid model is validated with available experiments and discrete particle simulation (DPS). The results show good agreements with experiment data for binary system and DPS reults, and the simulations can describe segregation and mixing behavior in the fluidized bed;After the model development and validation, 2D and 3D simulations are conducted for a pilot-scale polymerization fluidized bed at operating conditions. Significant differences are observed between 2D and 3D simulations. The results shows that, for an industrial-scale fluidized bed, only 3D simulations are able to match the statics (bed height and pressure drop) and the dynamics (pressure power spectra) properties of the bed. The residence time for a polyethylene pilot reactor is on the order of hours, and the time scale for the fluid dynamics in the bed is on the seconds. It is impossible to run a three-dimensional simulation for hours using current CFD codes. Due to the time scale problem, a chemical reaction engineering model based on the age of particles is combined with multi-fluid model to initialize the fluidized bed to a steady state. Direct quadrature method of moments (DQMOM) is used to simulate the particle size distribution in the bed. The hot spots in the fluidized bed are also investigated using CFD simulations.