scholarly journals A Mathematical Model for Investigating the Effect of Reaction Temperature and Hydrogen Amount on the Catalyst Yield during Propylene Polymerization

2019 ◽  
Vol 68 (7-8) ◽  
pp. 269-280 ◽  
Author(s):  
Gholam Hossain Varshouee ◽  
Amir Heydarinasab ◽  
Ali Vaziri ◽  
Seyed Mehdi Ghafelebashi Zarand
Keyword(s):  
Mathematical Model ◽  
Reaction Temperature ◽  
Propylene Polymerization ◽  
Process Conditions ◽  
Catalytic Potential ◽  
Natta Catalyst ◽  
Balance Technique ◽  
Laboratory Scale Reactor ◽  
Basic And Applied Research ◽  
New Formulation

In this study, the effect of reaction temperature and hydrogen amount, as the most effective process variables on the Ziegler-Natta catalysts yield during propylene polymerization, was investigated with the aid of a validated mathematical model. The approach applied in this modelling was the <i>polymer moment balance technique</i> (<i>population balance approach</i>) derived from the statistics expected value. The model was coded in MATLAB<sup>®</sup> & Simulink<sup>®</sup>, and then validated by experimental data coming from a laboratory-scale reactor. The main target of this study was to gain considerable insight into Ziegler-Natta catalyst performance against variables change. The model might be applicable for catalyst makers to evaluate and improve their catalysts, and could also be useful for process chemical engineers to easily operate the plant, replace new catalyst, optimise process conditions, generate new formulation for a new grade, and use maximum catalytic potential. Accordingly, the model could be applied in basic and applied research in this field.

scholarly journals Determination of optimal reaction temperature and hydrogen amount for propylene polymerization by a mathematical model

2019 ◽  
Vol 68 (3-4) ◽  
pp. 119-127 ◽  
Author(s):  
Gholam Hossain Varshouee ◽  
Amir Heydarinasab ◽  
Ali Vaziri ◽  
Seyed Mehdi Ghafelebashi Zarand
Keyword(s):  
Reaction Temperature ◽  
Average Molecular Weight ◽  
Propylene Polymerization ◽  
Process Conditions ◽  
Adequate Model ◽  
Natta Catalyst ◽  
Optimal Reaction Temperature ◽  
The Relationship ◽  
Optimal Reaction

Regarding the complexity of Ziegler-Natta catalyst kinetics in polypropylene polymerization, so far, there is no adequate model to determine the best process conditions for predicting average molecular weight and dispersity as the most crucial final 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 final product indices to a certain limit, but afterwards they have harmful effects on the indices.

An enhanced composting process with bioaugmentation: Mathematical modelling and process optimization

2021 ◽  
pp. 0734242X2110337
Author(s):  
Tea Sokač ◽  
Anita Šalić ◽  
Dajana Kučić Grgić ◽  
Monika Šabić Runjavec ◽  
Marijana Vidaković ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Model Simulation ◽  
Process Conditions ◽  
Air Flow Rate ◽  
Optimal Process ◽  
Composting Process ◽  
Different Types ◽  
Adiabatic Reactor ◽  
The Mathematical Model ◽  
Good Agreement

In this paper, two different types of biowaste composting processes were carried out – composting without and with bioaugmentation. All experiments were performed in an adiabatic reactor for 14 days. Composting enhanced with bioaugmentation was the better choice because the thermophilic phase was achieved earlier, making the composting time shorter. Additionally, a higher conversion of substrate (amount of substrate consumed) was also noticed in the process enhanced by bioaugmentation. A mathematical model was developed and process parameters were estimated in order to optimize the composting process. Based on good agreement between experimental data and the mathematical model simulation results, a three-level-four-factor Box-Behnken experimental design was employed to define the optimal process conditions for further studies. It was found that the air flow rate and the mass fraction of the substrate have the most significant effect on the composting process. An improvement of the composting process was achieved after altering the mentioned variables, resulting in shorter composting time and higher conversion of the substrate.

Control of Ziegler–Natta catalyst activity by the structural design of alkoxysilane-based external donors

2020 ◽  
Vol 44 (17) ◽  
pp. 6845-6852 ◽  
Author(s):  
Vikas Khatri ◽  
Usharani Sahoo ◽  
Sukhdeep Kaur ◽  
Rashmi Rani ◽  
Gurmeet Singh ◽  
...  
Keyword(s):  
Structural Design ◽  
Catalyst Activity ◽  
Propylene Polymerization ◽  
Natta Catalyst ◽  
Ziegler Natta Catalyst

Herein, the evaluation of four commercial alkoxysilanes and two laboratory synthesized novel diethoxysilacycloalkanes as external donors towards propylene polymerization has been done.

Taguchi Approach and ANOVA in Optimization of the Dissolution of Colemanite in CO2 and SO2- Water Systems

2020 ◽  
Vol 10 (2) ◽  
pp. 88-97
Author(s):  
Zafer Ekinci ◽  
Esref Kurdal ◽  
Meltem Kizilca Coruh
Keyword(s):  
Particle Size ◽  
Reaction Time ◽  
Reaction Temperature ◽  
Gas Flow ◽  
Operating Conditions ◽  
Optimum Operating ◽  
Process Conditions ◽  
Liquid Ratio ◽  
Positive Effects ◽  
Controllable Factors

Background: Turkey is approximately 72% of the world’s boron sources. Colemanite, tincal, ulexite and pandermite are among the most significant in Turkey. Boron compounds and minerals are widely used in many industrial fields. Objective: The main purpose of this study was to investigate the control of impurities in the boric acid production process using colemanite by carrying out the reaction with a mixture of CO2 and SO2 - water, and determining the appropriate process conditions to develop a new process as an alternative to the use of sulfuric acid. Due to worrying environmental problems, intensive studies are being carried out globally to reduce the amount of CO2 and SO2 gases released to the atmosphere. Methods: The Taguchi method is an experimental design method that minimizes the product and process variability by selecting the most appropriate combination of the levels of controllable factors compared to uncontrollable factors. Results: It was evaluated the effects of parameters such as reaction temperature, solid-to liquid ratio, SO2/CO2 gas flow rate, particle size, stirring speed and reaction time. The optimum conditions determined to be reaction temperature of 45°C; a solid–liquid ratio of 0.083 g.mL−1; an SO2/CO2 ratio of 2/2 mL.s−1; a particle size of -0.354+0 .210 mm; a mixing speed of 750 rpm and a reaction time of 20 min. Conclusion: Under optimum operating conditions, 96.8% of colemanite was dissolved. It is thought that the industrial application of this study will have positive effects on the greenhouse effect by contributing to the reduction of CO2 and SO2 emissions that cause global warming.

scholarly journals A MATHEMATICAL MODEL FOR EBOLA EPIDEMIC WITH SELF-PROTECTION MEASURES

2018 ◽  
Vol 26 (01) ◽  
pp. 107-131 ◽  
Author(s):  
T. BERGE ◽  
M. CHAPWANYA ◽  
J. M.-S. LUBUMA ◽  
Y. A. TEREFE
Keyword(s):  
Mathematical Model ◽  
Ebola Virus ◽  
Virus Disease ◽  
Mass Action ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Protection Measures ◽  
Globally Asymptotically Stable ◽  
New Formulation ◽  
Self Protection

A mathematical model presented in Berge T, Lubuma JM-S, Moremedi GM, Morris N Shava RK, A simple mathematical model for Ebola in Africa, J Biol Dyn 11(1): 42–74 (2016) for the transmission dynamics of Ebola virus is extended to incorporate vaccination and change of behavior for self-protection of susceptible individuals. In the new setting, it is shown that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number [Formula: see text] is less than or equal to unity and unstable when [Formula: see text]. In the latter case, the model system admits at least one endemic equilibrium point, which is locally asymptotically stable. Using the parameters relevant to the transmission dynamics of the Ebola virus disease, we give sensitivity analysis of the model. We show that the number of infectious individuals is much smaller than that obtained in the absence of any intervention. In the case of the mass action formulation with vaccination and education, we establish that the number of infectious individuals decreases as the intervention efforts increase. In the new formulation, apart from supporting the theory, numerical simulations of a nonstandard finite difference scheme that we have constructed suggests that the results on the decrease of the number of infectious individuals is valid.

POISONING OF ACTIVE SITES ON ZIEGLER-NATTA CATALYST FOR PROPYLENE POLYMERIZATION

2008 ◽  
Vol 26 (05) ◽  
pp. 547 ◽  
Author(s):  
Kitti Tangjituabun ◽  
Sang Yull Kim ◽  
Yuichi Hiraoka ◽  
Toshiaki Taniike ◽  
Minoru Terano ◽  
...  
Keyword(s):  
Active Sites ◽  
Propylene Polymerization ◽  
Natta Catalyst ◽  
Ziegler Natta Catalyst
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