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.

In the present study, the Sanchez−Lacombe equation of state (i.e., SL EOS) was employed to calculate the solubilities of α-olefins in polyolefins over a wide range of pressures and temperatures. The characteristic parameters (i.e., P*, T*, and ρ*) of the pure components, appearing in the Sanchez−Lacombe EOS, were estimated using a molecular dynamic procedure (MD). For all binary systems examined, a single binary parameter, k ij , accounting for the interactions between the penetrant molecules and the polymer chains was used to fit model predictions to available solubility measurements. The value of the binary interaction parameter was found to depend on the type of the penetrant molecules, the comonomer type in the ethylene copolymers, and the polymer crystallinity as well as the selected experimental conditions (i.e., temperature and pressure). The theoretically calculated solubilities were found to be in excellent agreement with the corresponding experimentally measured values, demonstrating the capability of the SL EOS to predict the solubility of α-olefins in semicrystalline polyolefins.

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