Modeling of the propylene polymerization catalyzed by single‐/multi‐active site catalyst: A Monte Carlo study

In the present study, a model is established to describe the propylene polymerization kinetics catalyzed by the typical catalysts with single‐/multi‐active site type in a liquid phase stirred‐tank reactor using the Monte Carlo simulation method, regardless of the mass and heat diffusion effects within the polymer particles. Many kinetic data, including polypropylene yield, concentration transformation of catalyst active sites, number–average molecular weight, etc., are obtained by the model. The simulated kinetic results are found to be in agreement with the reference ones obtained in a population balance model. Furthermore, the comparisons of the kinetic data between the polymerization catalyzed by the catalyst with single‐active site type (typically silica‐supported metallocene) and the catalyst with multi‐active site type (typically MgCl₂‐supported Ziegler‐Natta catalyst) have been studied using the model. Especially, the effects of hydrogen on the polymerization are studied using the model. The studied results show that the theory of catalyst active site can be used to explain the different propylene polymerization kinetics catalyzed by the typical catalyst with single‐/multi‐active site type. In addition, the role of hydrogen in the propylene polymerization needs to be emphasized. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

A CFD‐PBM‐PMLM integrated model for the gas–solid flow fields in fluidized bed polymerization reactors

Although the use of computational fluid dynamics (CFD) model coupled with population balance (CFD‐PBM) is becoming a common approach for simulating gas–solid flows in polydisperse fluidized bed polymerization reactors, a number of issues still remain. One major issue is the absence of modeling the growth of a single polymeric particle. In this work a polymeric multilayer model (PMLM) was applied to describe the growth of a single particle under the intraparticle transfer limitations. The PMLM was solved together with a PBM (i.e. PBM‐PMLM) to predict the dynamic evolution of particle size distribution (PSD). In addition, a CFD model based on the Eulerian‐Eulerian two‐fluid model, coupled with PBM‐PMLM (CFD‐PBM‐PMLM), has been implemented to describe the gas–solid flow field in fluidized bed polymerization reactors. The CFD‐PBM‐PMLM model has been validated by comparing simulation results with some classical experimental data. Five cases including fluid dynamics coupled purely continuous PSD, pure particle growth, pure particle aggregation, pure particle breakage, and flow dynamics coupled with all the above factors were carried out to examine the model. The results showed that the CFD‐PBM‐PMLM model describes well the behavior of the gas–solid flow fields in polydisperse fluidized bed polymerization reactors. The results also showed that the intraparticle mass transfer limitation is an important factor in affecting the reactor flow fields. © 2011 American Institute of Chemical Engineers AIChE J, 58: 1717–1732, 2012     

Multiple active site Monte Carlo model for heterogeneous Ziegler‐Natta propylene polymerization

In this study, the kinetics of propylene polymerization catalyzed with the fourth heterogeneous Ziegler‐Natta catalyst is studied. More than one type of active site is present in the propylene polymerization based on an analysis of the GPC curves. A multiple active site kinetic model (MSmodel) is proposed by using Monte Carlo technique. Good agreements in the polymerization kinetics are achieved for fitting the kinetic profiles with the MSmodel. In addition, the MSmodel is used to describe the dynamic evolutions of the active sites and their effects on the propylene polymerization. The simulated results indicate that different types of active sites have different polymerization kinetics and the site type can affect the propylene polymerization kinetics. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Monte Carlo simulation of gas phase polymerization of 1,3‐butadiene. Part II: Kinetics optimization and confirmation

Studies on the deactivations and initiations of gas phase polymerizations of 1,3‐butadiene have been achieved by Monte Carlo simulation. Initiation and deactivation control the reaction before and after the peak of the polymerization rate, respectively. The influence of polymerization temperature has been studied. Monte Carlo modeling of polymerization kinetics and mechanism was confirmed by the agreement of experimental data and simulation results of polymerizations run with a temporary evacuation of monomer. The balance of catalysts and active chains is established by both initiation and chain transfer reactions with cocatalyst, which causes a ‘pseudo‐stability’ stage. © 2003 Society of Chemical Industry     

Broadening of molecular‐weight distribution in solid‐state polymerization resulting from condensate diffusion

A kinetic model for the solid‐state polymerization of poly(bisphenol A carbonate) in a single particle has been developed and used to investigate the broadening of molecular‐weight distribution as a result of slow condensate diffusion. The model is based on melt‐phase transesterification kinetics and Fickian diffusion of phenol, the condensate, in the amorphous regions of the semicrystalline particle. Model predictions compare favorably to experimental data. When diffusion is slow compared to reaction, a condensate concentration gradient is established. This gradient induces a molecular‐weight gradient, which results in a broadened overall molecular‐weight distribution with an overall polydispersity above the theoretical limit for homogenous step‐growth polymerization. As the mass transfer resistance inside the particle is decreased, the average molecular weight increases faster with time, and the overall polydispersity decreases. A stoichiometric imbalance of end groups decreases the obtainable molecular weight but mitigates the deleterious effects of slow condensate diffusion. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 79: 928–943, 2001     

Modeling of fractionation in CRYSTAF using Monte Carlo simulation of crystallizable sequence lengths: Ethylene/1‐octene copolymers synthesized with single‐site–type catalysts

Monte Carlo simulation was used to model the fractionation process in crystallization analysis fractionation (CRYSTAF). Five poly(ethylene/1‐octene) samples synthesized with a single‐site–type catalyst were used to verify the simulation results. It was proposed that the fractionation mechanism be controlled by the crystallization of the longest ethylene sequence in each chain. Good agreement between experimental and simulation results verified the validity of the proposed fractionation mechanism. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 2200–2206, 2001     

Dynamic Monte Carlo Simulation of Atom‐Transfer Radical Polymerization

Summary: A dynamic Monte Carlo model was developed to simulate atom‐transfer radical polymerization (ATRP). The algorithm used to describe the polymerization includes activation, deactivation, propagation, chain transfer, and termination by combination and disproportionation reactions. Model probabilities are calculated from polymerization kinetic parameters and reactor conditions. The model was used to predict monomer conversion, average molecular weight, polydispersity and the complete molecular weight distribution at any polymerization time or monomer conversion. The model was validated with experimental results for styrene polymerization and compared with simulation results from a mathematical model that uses population balances and the method of moments. The simulations agree well with experimental and theoretical results reported in the literature. We also investigated the control volume size and number of iterations to reduce computation time while keeping an acceptable noise level in the Monte Carlo results.

Comparison of the chain length distribution of polystyrene made with ATRP and conventional free radical (CFR) polymerization at 50% conversion. The initiator to monomer ratios are 1:100 (ATRP left peak), 1:500 (ATRP right peak), and 1:1000 (CFR).     

High‐molecular‐weight polyacrylonitrile by atom transfer radical polymerization

A single‐pot atom transfer radical polymerization was used for the first time to successfully synthesize polyacrylonitrile with a molecular weight higher than 80,000 and a narrow polydispersity as low as 1.18. This was achieved with CuBr/isophthalic acid as the catalyst, 2‐bromopropionitrile as the initiator, and N,N‐dimethylformamide as the solvent. The effects of the solvent on the polymerization of acrylonitrile were also investigated. The induction period was shorter in N,N‐dimethylformamide than in propylene carbonate and toluene, and the rate of the polymerization in N,N‐dimethylformamide was fastest. The molecular weight of polyacrylonitrile agreed reasonably well with the theoretical molecular weight in N,N‐dimethylformamide. When chlorine was used in either the initiator or the catalyst, the rate of polymerization showed a trend of decreasing, and the molecular weight deviated from the theoretical predication significantly. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 3372–3376, 2006     

丙烯聚合建模研究:扩散作用的影响

提出了均匀分布多粒模型 (UMGM) ,用于研究单个聚丙烯粒子的增长过程。在不考虑催化剂多活性中心和失活的情况下 ,扩散作用能够在较大范围内解释丙烯聚合过程中分子量分布以及反应速率的变化。分析了扩散系数、催化剂的活性以及催化剂颗粒大小对反应的影响。仿真结果表明 ,扩散作用对高活性催化剂的影响更加显著 ,并且与催化剂粒子的大小有密切关系。本模型能够方便地扩展到多活性中心以及采用更加复杂的微观反应动力学方程 .与其他单粒子模型相比 ,UMGM模型参数物理意义明确 ,计算速度快 ,为工业反应器的建模和优化奠定了基础。     

Combined single particle growth and population balance modeling in stereoregular polymerization of styrene

Modeling and experimental analysis for syndiospecific polymerization of styrene over silica-supported metallocene catalyst was carried out. A detail model was developed by coupling the single particle growth model (PGM) with particle population balance equation. The model was employed to predict the effects of intraparticle mass transfer limitations and the initial catalyst particle size on the rate of polymerization and the particle size distribution (PSD) of syndiotactic polystyrene (sPS). The single PGM, based on a modified polymeric multigrain model, was first utilized to calculate the single particle growth rate and polymerization rate under intraparticle mass transfer limitations and different initial catalyst particle sizes. Then, the model was solved simultaneously with particle population balance equation to estimate the PSD of sPS under the same limitations. The single PGM results showed a significant radial distribution of styrene concentration across polymer growth. It was further noticed that the diffusion resistance was most intense at the beginning of the polymerization reaction and the effects of polymerization rate were stronger. Moreover, it appeared that increasing the initial catalyst particle size led to lower rate of polymerization. The PSD simulation results revealed that the mass transfer limitation, as well as the initial catalyst particle size made a strong impact on the PSD of sPS. In addition, the simulation results obtained from this model showed good agreement results with experimental data of sPS.     

Phase‐transfer‐agent‐aided polymerization and graft copolymerization of acrylamide

The use of phase‐transfer catalysts, with water‐insoluble initiators, for polymerization and graft copolymerization reactions was explored. The polymerization of a water‐soluble vinyl monomer, acrylamide (AAm), and the graft copolymerization of AAm onto a water‐insoluble polymer backbone, isotactic polypropylene (IPP), with a water‐insoluble initiator, benzoyl peroxide (BPO), and a phase‐transfer catalyst, tetrabutyl ammonium bromide (Bu₄N⁺Br^?), were carried out in a water/xylene binary solvent system. The conversion percentage of AAm into polyacrylamide (PAAm) and the percentage of grafting of AAm onto IPP were determined as functions of various reaction parameters, such as the BPO, AAm, and phase‐transfer‐catalyst concentrations, the amounts of water and xylene in the water/xylene mixture, the time, and the temperature. The graft copolymer, IPP‐g‐PAAm, was characterized with IR spectroscopy and thermogravimetric analysis. By a comparison of the results of the phase‐transfer‐catalyzed graft copolymerization of AAm onto IPP and the preirradiation method, it was observed that the optimum reaction conditions were milder for the phase‐transfer‐catalyst‐aided graft copolymerization. Milder reaction conditions, including the temperature, the time of reaction, and a moderate initiator (BPO), in comparison with high‐energy γ‐rays, led to better quality products, and the reaction proceeded smoothly with high productivity. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 91: 2364–2375, 2004     

How penultimate monomer unit effects and initiator influence ICAR ATRP of n‐butyl acrylate and methyl methacrylate

The relevance of penultimate monomer unit (PMU) effects and the selection of the correct initiator species under typical reversible deactivation radical copolymerization conditions is illustrated, using matrix‐based kinetic Monte Carlo simulations allowing the visualization of all monomer sequences along individual chains. Initiators for continuous activator regeneration atom transfer radical polymerization (ICAR ATRP) is selected as illustrative polymerization technique with n‐butyl acrylate and methyl methacrylate as comonomers, aiming at the synthesis of well‐defined gradient copolymers. Using literature based model parameters, in particular temperature dependent monomer and radical reactivity ratios, it is demonstrated that PMU effects on propagation and ATRP (de)activation cannot be ignored to identify the most suited ICAR ATRP reactants (e.g., tertiary ATRP initiator) and reaction conditions (e.g., feeding rates under fed‐batch conditions). The formulated insights highlight the need for further research on PMU effects on all reaction steps in radical polymerization. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

Monte Carlo Simulation of Propylene Selective Oxidation and Ammoxidation over β-Bi_2Mo_2O_9 Catalyst under Anaerobic Condition

A random walk Monte Carlo(RWMC)simulation model of catalytic particle was established on the basis of the structures of bismuth molybdate catalysts and mechanisms of catalytic reactions with propylene selective oxidation and ammoxidation.The simulation results show that rationality of the RWMC model is proved on the basis of pulse experimental data.One of the most remarkable factors affecting catalytic behavior is the transfer of bulk lattice oxygen,which decides the rate of ammonia-consuming and propylene-consuming.The selectivity of main products reaches the maximum after the reduction of catalysts to a certain degree.It is inferred that catalytic performance improves greatly if the ratio of capacity for dehydrogenation from adsorbed propylene molecule on catalytically active site of molybdenum metal-imido group(Mo=NH)to that on catalytically active site of molybdenum metal-oxo group(Mo=O)becomes much higher.     

绝氧条件下β-Bi2Mo2O9晶相上丙烯氨氧化反应的Monte Carlo模拟研究

A random walk Monte Carlo （RWMC） simulation model of catalytic particle was established on the basis of the structures of bismuth molybdate catalysts and mechanisms of catalytic reactions with propylene selective oxidation and ammoxidation. The simulation results show that rationality of the RWMC model is proved on the basis of pulse experimental data. One of the most remarkable factors affecting catalytic behavior is the transfer of bulk lattice oxygen, which decides the rate of ammonia-consuming and propylene-consuming. The selectivity of main products reaches the maximum after the reduction of catalysts to a certain degree. It is inferred that catalytic performance improves greatly if the ratio of capacity for dehydrogenation from adsorbed propylene molecule on catalytically active site of molybdenum metal-imido group （Mo=NH） to that on catalytically active site of molybdenum metal-oxo group （Mo=O） becomes much higher.     

Monte Carlo Simulation of Kinetics of Ammonia Oxidative Decomposition over the Commercial Propylene Ammoxidation Catalyst (Mo-Bi)

Monte Carlo method is applied to investigate the kinetics of ammonia oxidative decomposition over the commercial propylene ammoxidation catalyst(Mo-Bi). The simulation is quite in agreement with experimental results. Monte Carlo simulation proves that the process of ammonia oxidation decomposition is a two-step reaction.     

Modeling of molecular weight distribution of gas‐phase polymerization of butadiene

A mathematical model of the molecular weight distribution (MWD) based on a multilayer model and an improved intrinsic kinetics model was proposed to simulate the MWD of the gas‐phase polymerization of butadiene with a heterogeneous catalyst. Intrinsic kinetics and heat and mass‐transfer resistances based on the multilayer model of a polymeric particle were considered in the modeling of the MWD. The effects of the reaction conditions, catalyst particle size, mass‐transfer resistance, deactivation of active sites, and transfer of the polymer chain on the molecular weight and MWD were simulated. The results show that the effects of the deactivation of active sites and transfer of the polymer chain on the average molecular weight are significant and that the effect of the catalyst particle size on the MWD is not significant. The simulation results of the molecular weight and MWD are compared with the experimental results. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 88–103, 2003     

Population balance modeling and simulation of liquid–liquid–liquid phase transfer catalyzed synthesis of mandelic acid from benzaldehyde

Mandelic acid has cosmetic, pharmaceutical, and antibacterial activities and is used in urinary antiseptic medicines. An attractive process for the production of mandelic acid is through reaction between benzaldehyde, sodium hydroxide, and chloroform in the presence of polyethylene glycol 4000 as a phase transfer catalyst. The liquid–liquid phase transfer catalyzed (L–L PTC) reaction can be intensified by converting it into three‐liquid phases (L–L–L PTC). We address the modeling of a well‐stirred reactor for the foregoing process, in which organic droplets surrounded by a thin film of catalyst‐rich phase are suspended in the aqueous phase. A population balance model is formulated for the L–L–L PTC reaction and solved by Monte Carlo simulation using interval of quiescence technique. Transport processes and intrinsic reaction kinetics are extracted from the experiments. This population balance model serves to assess and interpret the relative roles of various processes in L–L–L PTC reaction, such as diffusive transport, reaction, and interaction between dispersed phase droplets. The model is expected to be an effective tool for reactor design and scale up. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

丙烯聚合的Monte Carlo模拟(Ⅰ)活性杂质对丙烯聚合的影响

A comprehensive mechanism for propylene polymerization was proposed by considering the effects of main impurities in the material on propylene polymerization. According to the proposed mechanism, Monte Carlo simulation was employed to investigate the polymerization kinetics in order to determine the effects of the main impurities on the polymerization. Significant influences of the main impurities on the rate, number-average degree and controlling capability of hydrogen of the polymerization were analyzed.     

丙烯聚合的Monte Carlo模拟(Ⅰ)活性杂质对丙烯聚合的影响

1 INTRODUCTION Polypropylene is a popular thermoplastic polymer, and produced via bulk polymerization in petroleum chemical industry. The molecular configuration of polypropylene and the characteristics of polymer can be controlled by the catalyst and polymerization method. Furthermore, other factors, such as impurities in the material and polymerization conditions, also influence the industrial production. Catalyst influences the rate and the quality of polymer, is a key factor of the in…