Fluidized beds (FB) reactors are widely used in the polymerization industry due to their superior heat- and mass-transfer characteristics. Nevertheless, problems associated with local overheating of polymer particles and excessive agglomeration leading to FB reactors defluidization still persist and limit the range of operating temperatures that can be safely achieved in plant-scale reactors. Many people have been worked on the modeling of FB polymerization reactors, and quite a few models are available in the open literature, such as the well-mixed model developed by McAuley, Talbot, and Harris (1994), the constant bubble size model (Choi and Ray, 1985) and the heterogeneous three phase model (Fernandes and Lona, 2002). Most these research works focus on the kinetic aspects, but from industrial viewpoint, the behavior of FB reactors should be modeled by considering the particle and fluid dynamics in the reactor. Computational fluid dynamics (CFD) is a powerful tool for understanding the effect of fluid dynamics on chemical reactor performance. For single-phase flows, CFD models for turbulent reacting flows are now well understood and routinely applied to investigate complex flows with detailed chemistry. For multiphase flows, the state-of-the-art in CFD models is changing rapidly and it is now possible to predict reasonably well the flow characteristics of gas-solid FB reactors with mono-dispersed, non-cohesive solids. This thesis is organized into seven chapters. In Chapter 2, an overview of fluidized bed polymerization reactors is given, and a simplified two-site kinetic mechanism are discussed. Some basic theories used in our work are given in detail in Chapter 3. First, the governing equations and other constitutive equations for the multi-fluid model are summarized, and the kinetic theory for describing the solid stress tensor is discussed. The detailed derivation of DQMOM for the population balance equation is given as the second section. In this section, monovariate population balance, bivariate population balance, aggregation and breakage equation and DQMOM-Multi-Fluid model are described. In the last section of Chapter 3, numerical methods involved in the multi-fluid model and time-splitting method are presented. Chapter 4 is based on a paper about application of DQMOM to polydisperse gas-solid fluidized beds. Results for a constant aggregation and breakage kernel and a kernel developed from kinetic theory are shown. The effect of the aggregation success factor and the fragment distribution function are investigated. Chapter 5 shows the work on validation of mixing and segregation phenomena in gas-solid fluidized beds with a binary mixture or a continuous size distribution. The simulation results are compared with available experiment data and discrete-particle simulation. Chapter 6 presents the project with Univation Technologies on CFD simulation of a Polyethylene pilot-scale FB reactor, The fluid dynamics, mass/heat transfer and particle size distribution are investigated through CFD simulation and validated with available experimental data. The conclusions of this study and future work are discussed in Chapter 7.