Developed Hybrid Model for Propylene Polymerisation at Optimum Reaction Conditions

Advances in Mathematical Modeling of Gas-Phase Olefin Polymerization

Mathematical modeling of olefin polymerization processes has advanced significantly, driven by factors such as the need for higher-quality end products and more environmentally-friendly processes. The modeling studies have had a wide scope, from reactant and catalyst characterization and polymer synthesis to model validation with plant data. This article reviews mathematical models developed for olefin polymerization processes. Coordination and free-radical mechanisms occurring in different types of reactors, such as fluidized bed reactor (FBR), horizontal-stirred-bed reactor (HSBR), vertical-stirred-bed reactor (VSBR), and tubular reactor are reviewed. A guideline for the development of mathematical models of gas-phase olefin polymerization processes is presented.

Optimization of Mechanical and Thermal Properties of iPP and LMPP Blend Fibres by Surface Response Methodology

Optimization of the mechanical and thermal properties of isotactic polypropylene (iPP) homopolymer blended with relatively new low molecular low modulus polypropylene (LMPP) at different blend ratios was carried out via surface response methodology (RSM). Regression equations for the prediction of optimal conditions were achieved considering eight individual parameters: naming, elongation at break, tensile strength and elastic modulus, crystallization temperature (TC), first melting temperatures (TM1), heat fusion (Hf), crystallinity, and melt flow rate (MFR), which were measured as responses for the design of experiment (DOE). The adjusted and predicted correlation coefficient (R²) shows good agreement between the actual and the predicted values. To confirm the optimal values from the response model, supplementary experiments as a performance evaluation were conducted, posing better operational conditions. It has been confirmed that the RSM model was adequate to reflect the predicted optimization. The results suggest that the addition of LMPP into iPP could effectively enhance the functionality and processability of blend fibres if correctly proportioned.

Optimization of Mechanical Properties for Polyoxymethylene/Glass Fiber/Polytetrafluoroethylene Composites Using Response Surface Methodology

This paper investigated the effects of polytetrafluoroethylene (PTFE) micro-particles on mechanical properties of polyoxymethylene (POM) composites. Since PTFE is immiscible with most polymers, the surface was etched using sodium naphthalene salt in tetrahydrofuran to increase its surface energy. The effects of two variables, namely PTFE content and PTFE etch time, on the mechanical properties of the composite were studied. Experiments were designed in accordance to response surface methodology (RSM) using central composite design (CCD). Samples were prepared with different compositions of PTFE (1.7, 4.0, 9.5, 15.0, or 17.3 wt %) at different PTFE etch times (2.9, 5.0, 10.0, 15.0, or 17.1 min). Four mechanical properties of the POM/GF/PTFE composites, that is, strength, stiffness, toughness, and hardness, were characterized as a function of two studied variables. The dependency of these mechanical properties on the PTFE etch conditions was analyzed using analysis of variance (ANOVA). Overall desirability, D global index, was computed based on the combination of these mechanical properties for POM/GF/PTFE composites. The D global index was found to be 87.5%, when PTFE content and PTFE etch time were 6.5% and 10 min, respectively. Good correlation between experimental and RSM models was obtained using normal probability plots.

Multiphasic Reaction Modeling for Polypropylene Production in a Pilot-Scale Catalytic Reactor

In this study, a novel multiphasic model for the calculation of the polypropylene production in a complicated hydrodynamic and the physiochemical environments has been formulated, confirmed and validated. This is a first research attempt that describes the development of the dual-phasic phenomena, the impact of the optimal process conditions on the production rate of polypropylene and the fluidized bed dynamic details which could be concurrently obtained after solving the model coupled with the CFD (computational fluid dynamics) model, the basic mathematical model and the moment equations. Furthermore, we have established the quantitative relationship between the operational condition and the dynamic gas⁻solid behavior in actual reaction environments. Our results state that the proposed model could be applied for generalizing the production rate of the polymer from a chemical procedure to pilot-scale chemical reaction engineering. However, it was assumed that the solids present in the bubble phase and the reactant gas present in the emulsion phase improved the multiphasic model, thus taking into account that the polymerization took place mutually in the emulsion besides the bubble phase. It was observed that with respect to the experimental extent of the superficial gas velocity and the Ziegler-Natta feed rate, the ratio of the polymer produced as compared to the overall rate of production was approximately in the range of 9%⁻11%. This is a significant amount and it should not be ignored. We also carried out the simulation studies for comparing the data of the CFD-dependent dual-phasic model, the emulsion phase model, the dynamic bubble model and the experimental results. It was noted that the improved dual-phasic model and the CFD model were able to predict more constricted and safer windows at similar conditions as compared to the experimental results. Our work is unique, as the integrated developed model is able to offer clearer ideas related to the dynamic bed parameters for the separate phases and is also capable of computing the chemical reaction rate for every phase in the reaction. Our improved mutiphasic model revealed similar dynamic behaviour as the conventional model in the initial stages of the polymerization reaction; however, it diverged as time progressed.