G. H. VARSHOUEE et al.: Determination of Optimal Reaction Temperature and Hydrogen ..., Kem. Ind. 68 (3-4) (2019) 119–127 119 1 Introduction Polypropylene is nowadays one of the most widely used polyolefns, and its application is strongly infuenced by the fnal product properties. In spite of about sixty years of Ziegler-Natta catalyst use for polypropylene production, the polymerization performance remains ambiguous and hazy due to the complexity of the catalyst kinetics. 1–2 In practice, the polymer application is determined by cer- tain crucial indices, such as the number and weight average molecular weight ( n M & w M ) and dispersity (Đ) as an indi- cator of molecular weight distribution. Since these indices of fnal product properties are highly dependent on the process variables, i.e., reaction temperature and hydro- gen amount in the polymerization system, it is necessary to investigate how the process variables affect these fnal product properties indices. Accordingly, for designing a desired product, a mathematical model could be a worthy replacement for the conventional manner, i.e., experimen- tal by trial and error. There is still a need for a validated mathematical model that would be able to predict these fnal product properties in a proper way. In view of the sig- nifcance of these matters, few researchers have addressed these problems in a comprehensive and clarifed manner, in particular with the aid of a validated mathematical mod- el. However, the gap remains. To understand the behaviour of the polymerization sys- tem, most studies so far have focused on the experimental approach. However, this approach is neither reliable nor applicable since its results are heavily dependent on the test and laboratory conditions. The other constraint of this approach is the type of catalyst used. 3–5 Therefore, these studies have not fulflled the existing gap as defned earlier. In respect of the modelling, Reginato 2 modelled an in- dustrial-scale loop reactor using a non-ideal continuous stirred tank model to explain the industrial process, and compared their simulation results with commercial plant data. Al-haj Ali 3 proposed a generalized model for hydro- gen response based on the dormant site theory in liquid propylene polymerization. His research work was based on only experimental data, and there was no validated mathematical model able to predict the polymerization rate profle and the indices of the fnal product properties simultaneously. Although some other researchers in this feld have carried out their work based on a mathematical model, there re- mains the defned gap, because their models have been es- tablished based on only mathematical calculations without experimental validation. In this context, some studies only tend to focus on loop or fuidized-bed reactors (FBRs), i.e., bulk or gas phase polymerization. 2,6–8 Yang 9 has modelled loop propylene polymerization reactors in bulk media. The model was targeted at commercial reactor variables with- out being attentive to kinetics studies and fnal product properties. Subsequently, another paper was published in- volving modelling of multi-scale polypropylene properties in the FBR reactor. Their modelling approach was moment equations. 10 Like in their in previous work, in 2016 Kim et al. 11 proposed a simulation for liquid polypropylene po- lymerization reactors based on Sheripol technology with- out giving attention to the determination of the vital fnal product properties, such as average molecular weight and polydispersity. Determination of Optimal Reaction Temperature and Hydrogen Amount for Propylene Polymerization by a Mathematical Model DOI: 10.15255/KUI.2018.038 KUI-9/2019 Original scientifc paper Received August 1, 2018 Accepted December 17, 2018 G. H. Varshouee, a A. Heydarinasab, a* A. Vaziri, a and S. M. Ghafelebashi Zarand b This work is licensed under a Creative Commons Attribution 4.0 International License a  Department of Petroleum and Chemical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran b Polymer Group, Research and Technology, National Petrochemical Company, Tehran, Iran Abstract Regarding the complexity of Ziegler-Natta catalyst kinetics in polypropylene polymerization, so far, there is no adequate mod- el to determine the best process conditions for predicting average molecular weight and dispersity as the most crucial fnal product properties index. Consequently, a validated model has been developed which describes the relationship between the kinetic model and the existing gap using the polymer moment balance approach. It was concluded that increasing reaction temperature and hydrogen amount are useful and improve the fnal product indices to a certain limit, but afterwards they have harmful effects on the indices. Keywords Mathematical modelling, propylene polymerization, optimization, population balance, average molecular weight, dispersity * Corresponding author: Assoc. Prof. Amir Heydarinasab Email: a.heidarinasab@srbiau.ac.ir