In the present study, a comprehensive mathematical model is developed to analyze the effects of initial catalyst size, active site concentration, catalyst morphology (e.g., porosity, extent of prepolymerization, etc.), and hydrodynamic conditions on the growth and overheating of highly active Ziegler−Natta catalyst particles (e.g., fresh or prepolymerized) in gas-phase olefin polymerization. The generalized Stefan−Maxwell diffusion equation for porous solids is combined with the mass balances on the various molecular species (i.e., monomer and “live” and “dead” polymer chains) and the energy conservation equation to predict the temporal−spatial evolution of temperature and monomer concentration, as well as the polymerization rate in a single catalyst/polymer particle. To calculate the equilibrium monomer concentration in the amorphous polymer phase, the Sanchez−Lacombe equation of state is employed. It is shown that the evolution of the catalyst/particle morphology greatly affects the internal and external mass- and heat-transfer resistances in the particle and, thus, its growth rate and overheating. The effect of the hydrodynamic flow conditions on particle overheating is analyzed in detail. It is shown that, depending on the particle size, the concentration of solids in the bulk gas phase, and the dissipation rate of the turbulence kinetic energy of the flow field, the Ranz−Marshall correlation can significantly underestimate the value of the heat-transfer coefficient, resulting in an erroneous overestimation of the particle temperature.

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Summary: In the present study, a comprehensive, multi‐scale, mathematical model is developed for the calculation of the distributed properties of polymer particles in a gas phase, catalytic, olefin polymerization, fluidized bed reactor (FBR). At the molecular level, a generalized multi‐site, Ziegler‐Natta, kinetic scheme is employed to predict the evolution of the polymer molecular properties. To calculate the particle growth, and the spatial monomer and temperature profiles in a particle, the random pore, polymeric flow model (RPPFM) is utilized. The RPPFM is solved together with a dynamic, discretized, particle population balance model, to predict the particle size distribution (PSD) in the bed. The overall molecular weight distribution (MWD) in the bed is then calculated by the weighted sum of all individual polymer particle MWDs. The effects of hydrogen concentration, the distribution of catalyst active sites, and the polymer crystallinity, on the evolution of the PSD and MWD in an ethylene‐propylene copolymerization FBR are thoroughly analyzed. It is also shown that under certain operating conditions, the proposed multi‐scale model can predict the formation of bimodal MWDs, produced in multi‐stage reactor configurations (e.g., the Borstar® Process, Spheripol, etc.).Schematic representation of the multi‐scale model.magnified imageSchematic representation of the multi‐scale model.