A dynamic model for ethylene copolymerization in an industrial fluidized-bed reactor (FBR) is developed to describe its behavior and calculate the properties of polyethylene. The presented model considers particle entrainment and polymerization reaction in two phases. Two-site kinetic and hydrodynamic models in combination, provide a comprehensive model for the gas phase fluidized-bed polyethylene production reactor. The governing moment and hydrodynamic differential equations were solved simultaneously and the results compared with a similar work, as well as industrial data. The dynamic model showed accurate results for predicting Polydispersity Index (PDI), Molecular Weight Distribution (MWD), reactor temperature and polymer production rate.
AbstractThis is a detailed review on olefin polymerization models, and the most recent process control approaches used to control these nonlinear systems are presented. Great focus has been given to the various approaches of fluidized-bed reactor (FBR) modeling. Currently, there has yet to be a single model that blends these modeling aspects together into one single formulation. In this article, the classification of models works by looking at their assumption in considering the phases inside the system. Researchers have been unraveling vast information to narrate in detail the relations between various variables that can be found in FBRs. Although it is not difficult to understand about the basics of modeling polymer properties, a gap exists for future researchers to justify in detail the phenomena and reduce the gap between model predictions and the actual data. The various controlling approaches to control these FBRs have also been reviewed and categorized depending on the method they used to control significant parameters of this nonlinear system. The progress that can be expected in this field leads to the creation of more efficient reactors and minimizing waste.
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.
Hexaploid bread wheat (Triticum aestivum L. ssp. aestivum) is assumed to have originated by natural hybridization between cultivated tetraploid Triticum turgidum L. and wild diploid Aegilops tauschii Coss. This scenario is broadly accepted, but very little is known about the ecological aspects of bread wheat evolution. In this study, we examined whether T. turgidum cultivation still is associated with weedy Ae. tauschii in today's Middle Eastern agroecosystems. We surveyed current distributions of T. turgidum and Ae. tauschii in northern Iran and searched for sites where these two species coexist. Ae. tauschii occurred widely in the study area, whereas cultivated T. turgidum had a narrow distribution range. Traditional durum wheat (T. turgidum ssp. durum (Desf.) Husn.) cultivation associated with weedy Ae. tauschii was observed in the Alamut and Deylaman-Barrehsar districts of the central Alborz Mountain region. The results of our field survey showed that the T. turgidum-Ae. tauschii association hypothesized in the theory of bread wheat evolution still exists in the area where bread wheat probably evolved.
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