丁二烯气相聚合产物分子量分布和粒径分布模型研究

对非均相催化的丁二烯气相聚合,基于聚合物多层模型,考虑催化剂颗粒间活性位初始浓度和粒径分布对聚合物分子量分布和粒径分布的影响,建立了聚合物分子量分布和粒径分布的数学模型。模拟了反应温度、催化剂颗粒间活性位初始浓度和粒径分布等因素的影响,结果表明。随着温度升高,聚合物颗粒平均粒径变小,粒径分布变窄,聚合物分子量变小,分子量分布变宽;催化剂颗粒间的活性组分负载越均匀,聚合物分子量越大,分子量分布和粒径分布越窄;随着催化剂平均粒径变大,聚合物分子量变小,分子量分布变宽,不存在催化剂颗粒粒径分布和聚合物颗粒粒径分布间的复制现象。模型模拟结果与实验结果吻合较好,可用于预测丁二烯气相聚合产物的分子量、分子量分布和粒径分布。     

Gas‐phase polymerization of butadiene. Data acquisition using minireactor technology and particle modeling

Minireactor technology has been used for kinetic studies on polymerization kinetics, phase equilibrium, and mass transfer on a very small scale. There is a nonlinear influence of temperature and pressure on the polymerization rate. The phase equilibrium can be described by a Flory–Huggins approach, with a temperature‐dependent interaction parameter. The diffusion coefficient seems to be slightly pressure dependent, and the temperature dependence can be described with an Arrhenius equation. A simple formal kinetic scheme with formation of active sites, chain propagation, chain transfer to cocatalyst, and deactivation of active sites has been applied. This kinetic scheme was implemented in two different models; they are, a particle model taking into account mass transfer and a simple chemical model with no mass transfer. In principle, both models describe the experimental results for rate and molecular weight distribution equally well, with rate constants of the same magnitude. Molecular weight distributions calculated by the chemical model are narrower. However, the chemical model gives no explanation for the experimental observed rate dependence on catalyst particle size. With increasing catalyst activity, the differences between both models become more significant and the particle model becomes more and more important. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 270–279, 2003     

Modeling of molecular weight distribution of propylene slurry phase polymerization on supported metallocene catalysts

A mathematical model of the molecular weight distribution (MWD) based on a particle growth model and the kinetic scheme is developed to simulate the MWD of the slurry phase propylene polymerization on a silica-supported metallocene catalyst by means of the equations of moments. The model is used to predict molecular weight distribution, including the number-average molecular weight, the weight-average molecular weight, and the polydispersity index. The results show that the mass transfer has great influence on the polymerization reaction, and it can broaden the MWD especially; moreover, the MWD can be evaluated by simulation; the average molecular weight increases as pressure or temperature, and MWD shifts to long chain lengths as the effective diffusion coefficient increasing thought the influence is not remarkable; furthermore, the MWD's simulation results are calculated, which fit greatly with the experimental data.     

Population balance modeling for a continuous gas phase olefin polymerization reactor

Steady-state population balance models have been developed for a continuous flow gas phase olefin polymerization process with both uniform sized and log-normally size distributed high activity catalyst feeds. For the calculation of polymer properties such as molecular weight averages and weight fraction of comonomers in the copolymer, a multigrain solid core model was used with an assumption that intraparticle monomer mass transfer resistance is negligibly small. The multigrain solid core model was incorporated into the population balance model and the effects of feed catalyst particle size distribution and catalyst deactivation parameters on the polymer production rate, polymer particle size distribution, and polymer properties were investigated. It is observed for deactivating catalyst that the polymer particle size distribution tends to be narrower with a reduced amount of large polymer particles. For the catalyst with nonuniform site deactivation, polymer particles of different sizes exhibit different molecular weight and copolymer composition. © 1994 John Wiley & Sons, Inc.     

Modeling and analysis of a slurry reactor system for heterogeneous olefin polymerization: The effects of hydrogen concentration and initial catalyst size

This article deals with the development of a model for the polymerization process using a Ziegler‐Natta catalyst in a slurry reactor system. Employed here is the hierarchical model describing the entire reactor system that is subcategoried by the gas bubble phase, the continuous gas phase, the liquid phase, the solid polymer particle, and the surface of catalyst where chemical reaction occurs. The concept of the multigrain model (MGM) is introduced to describe the growth of polymer particle from the original catalyst particle. We also adopt the concept of multiple active sites to elucidate the broad molecular weight distribution (MWD). The major concern here is the effects of the hydrogen concentration and the size of the initial catalyst on the performance of the polymerization reactor. It is demonstrated that the hydrogen gas can be used for the purpose of controlling not only the molecular weight but the molecular weight distribution (MWD) of the polymer. In addition, the relationship between the molecular weight and the concentration of hydrogen gas is investigated. The size of the initial catalyst is found to exercise a significant influence on the morphology of the resultant polymer particle. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 79: 2480–2493, 2001     

铬钒双金属催化剂乙烯聚合反应动力学模型化

双金属催化剂可催化乙烯聚合在单个反应器内制备双峰聚乙烯。考察了新型Cr-iV双金属催化剂及相应的单金属S-2和iV催化剂在不同实验条件下的乙烯均聚反应动力学。通过对Cr-iV催化剂聚合产物分子量分布曲线的解析发现铬钒活性中心之间存在相互作用,铬中心活性受到抑制,钒中心活性得到增强;聚合温度基本不改变铬钒活性中心生成的聚合物的质量分数。采用简化的单中心乙烯均聚动力学模型分别描述铬钒双活性中心的动力学行为,结合双金属催化剂的聚合实验结果确定了各个活性中心的动力学参数。相比单金属催化剂,Cr-iV催化剂中铬活性中心链增长速率常数降低,说明其聚合活性降低;而钒活性中心链失活速率常数减小,稳定性增强,活性提高。     

Einfluß des stofftransportes bei der polymerisation von äthylen und 1-okten mit Ziegler-Katalysatoren

The polymerization of ethylene and 1-octene with supported Ziegler-catalysts was investigated with regard to the influence of mass transport of monomers on the kinetics, molecular weight and molecular weight distribution. In the case of the polymerization of ethylene, it was found that for certain conditions of reaction the mass transport of ethylene can influence the kinetics of polymerization respectively the catalyst efficiency strongly. The molecular weight and molecular weight distribution of the polyethylene formed are practically not affected by the conversion as well as particle size of catalyst and polymer. The molecular weight distribution however is affected by the concentration of the catalyst. The polymerization process of ethylene in suspension is distinguished by chemical and physical processes. A continuous chain initiation, for example, is based on the continuous reduction of the catalyst particles to small pieces during the course of polymerization. An apparent chain termination respectively catalyst deactivation can occur when catalyst particles are encapsulated within the growing polymer particles. The polymerization of 1 -octene for similar conditions of reaction gave polymers which were solved completely in the system used. The molecular weight distribution of the polymer formed nevertheless was very broad. This indicates that the mass transport of the monomers through the solid phase of polymer cannot be the main reason for the broad molecular weight distribution of the polymers which are produced by heterogeneous Ziegler-catalysts in suspension.     

The production of high efficiency Ziegler–Natta catalyst with dual active sites nature using cyclohexyl chloride as promoter with super activity and produced superior polyethylene with controllable molecular weight distribution

In the previous studies, the several halocarbons (HC) were tested as promoters for a Ti-based Ziegler–Natta (ZN) catalyst at different polymerization conditions. The Results showed that chloro cyclohexane has the best operation in catalyst activity, polymer particle size growth, hydrogen responsibility and wax reduction too. For the first time in this study, the effect of Al/Ti ratio on the optimum HC/Ti ratio has been considered and the results showed that the optimum HC/Ti ratio depends on the Al/Ti ratio directly. In the optimum HC/Ti ratio, the catalyst activity and hydrogen responsibility ratio of the catalyst increase up to 125 and 55% respectively. The acceptable growth of polymer powder up to 46%, lower flow rate ratio (FRR) up to 19% and decrease of wax amount up to 12%, completed the promotion results. Furthermore, in the next part of this study and as key note, a little dose of halocarbon was used in the catalyst preparation to produce the special catalysts with dual active sites. In the catalyst preparation, the concentration of each active sites depends on the halocarbon amount and it can control the molecular weight distribution of the produced polyethylene; because each active sites have different response to hydrogen. The halocarbon based catalysts showed the remarkable effect on the catalyst activity, the molecular weight and especially molecular weight distribution (MWD). The flow rate ratio and MWD could be increased up to 77 and 88% respectively as the main result of halocarbon addition during the catalyst preparation.     

Ethylene polymerization over supported titanium‐magnesium catalysts: Effect of polymerization parameters on the molecular weight distribution of polyethylene

The data on the effects of polymerization duration, cocatalyst, and monomer concentrations upon ethylene polymerization in the absence of hydrogen, and the effect of an additional chain transfer agent (hydrogen) on the molecular weight (MW), molecular weight distribution (MWD), and content of vinyl terminal groups for polyethylene (PE) produced over the supported titanium‐magnesium catalyst (TMC) are obtained. The effects of these parameters on nonuniformity of active sites for different chain transfer reactions are analyzed by deconvolution of the experimental MWD curves into Flory components. It has been shown that the polymer MW grows, the MWD becomes narrower and the content of vinyl terminal groups in PE increases with increasing polymerization duration. It is assumed to occur due to the reduction of the rate of chain transfer with AlEt₃ with increasing polymerization duration. The polydispersity of PE is found to rise with increasing AlEt₃ concentration and decreasing monomer concentration due to the emergence of additional low molecular weight Flory components. The ratios of the individual rate constants of chain transfer with AlEt₃, monomer and hydrogen to the propagation rate constant have been calculated. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

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。     

Copolymerization of ethylene/α‐olefins using bis(2‐phenylindenyl)zirconium dichloride metallocene catalyst: structural study of comonomer distribution

Catalysts have a major role in the polymerization of olefins and exert their influence in three ways: (1) polymerization behaviour, including polymerization activity and kinetics; (2) polymer particle morphology, including bulk density, particle size, particle size distribution and particle shape; and (3) polymer microstructure, including molecular weight regulation, chemical composition distribution and short‐ and long‐chain branching. By tailoring the catalyst structure, such as the creation of a bridge or introducing a substituent on the ligand, metallocene catalysts can play a major role in the achievement of desirable properties. Kinetic profiles of the metallocene catalyst used in this study showed decay‐type behaviour for copolymerization of ethylene/α‐olefins. It was observed that increasing the comonomer ratio in the feedstock affected physical properties such as reducing the melting temperature, crystallinity, density and molecular weight of the copolymers. It was also observed that the heterogeneity of the chemical composition distribution and the physical properties were enhanced as the comonomer molecular weight was increased. In particular, 2‐phenyl substitution on the indenyl ring reduced somewhat the melting point of the copolymers. In addition, the copolymer produced using bis(2‐phenylindenyl)zirconium dichloride (bis(2‐PhInd)ZrCl₂) catalyst exhibited a narrower distribution of lamellae (0.3–0.9 nm) than the polymer produced using bisindenylzirconium dichloride catalyst (0.5–3.6 nm). The results obtained indicate that the bis(2‐PhInd)ZrCl₂ catalyst showed a good comonomer incorporation ability. The heterogeneity of the chemical composition distribution and the physical properties were influenced by the type of comonomer and type of substituent in the catalyst. Copyright © 2010 Society of Chemical Industry     

Polymer chain extension in semibatch emulsion polymerization with RAFT‐based transfer agent: The influence of reaction conditions on polymerization rate and product properties

A mathematical model was developed for batch and semiemulsion polymerizations of styrene in the presence of a xanthate‐based RAFT agent. Zero–one kinetics was employed along with population balance equations to predict monomer conversion, molecular weight (MWD), and particle size (PSD) distributions in the presence of xanthate‐based RAFT agents. The effects of the transfer agent (AR), surfactant, initiator, and temperature were investigated. Monomer conversion, MWD, and PSD were found to be strongly affected by monomer feed rate. The polymerization rate (Rp), number average molecular weight (Mn) and particle size (r) decreased with increasing AR. With increases in surfactant and initiator concentrations Rp increased, whereas with increase in temperature Mn decreased, Rp increased and r increased. In semibatch mode, Mn and r increased with increase in monomer flow rate. By feeding the RAFT agent along with the monomer (F_M/F_AR = N_Mo/N_ARo = 100), Mn attained a constant value proportional to monomer/RAFT molar ratio. The observed retardation in polymerization and growth rates is due to the exit and re‐entry of small radicals. Thus, chain extension was successfully achieved in semibatch mode. The simulations compared well with our experimental data, and the model was able to accurately predict monomer conversion, Mn, MWD, and PSD of polymer products. Our simulations and experimental results show that monomer feed rate is suitable for controlling the PSD, and the initial concentration and the feed rate of AR for controlling the MWD and PSD. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

An approach for complete molecular weight distribution calculation: Application in ethylene coordination polymerization

The objective of this article is to present an approach to ascertain the molecular weight distribution (MWD) of polymeric systems and its application to an industrial polyethylene reactor. Ascertaining the complete MWD can provide more reliable predictions of polymer end‐use properties, as some of them may depend on specific molecular weight ranges, instead of solely on the averages of the distribution. The proposed method is based on differentiation of the cumulative MWD, where the accumulated concentrations, evaluated at a finite number of chain lengths, are considered components in a reaction medium. Therefore, the dimension of the mathematical model may be suited to the desired level of detail on the MWD. The ethylene polymerization in solution with Ziegler–Natta catalyst is taken as a case study because of the lack of studies in this field. The reaction takes place in continuously stirred and tubular reactors. The results show the potential of the proposed approach and its usefulness in ascertaining the whole MWD, which in turn can be used to predict the polymer end‐use properties. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Modeling of molecular weight and copolymer composition distributions for ethylene-propylene solution copolymerization

A comprehensive computational fluid dynamics (CFD) model was developed to investigate spatial distributions of molecular weight distribution (MWD) and copolymer composition distribution (CCD) for ethylene-propylene (EPM) copolymers in a bubble column reactor. The CFD approach incorporated Euler–Euler two-fluid model, copolymerization kinetics, and copolymer microstructural distribution model together by user-defined functions for ethylene-propylene heterogeneous copolymerization process. MWD and CCD distributions were calculated by introducing Flory's distribution and Stockmayer's distribution, respectively. CFD model results were validated with literature data. The multiphase hydrodynamics, interphase mass transfer, spatial–temporal variations of MWD and CCD distributions were analyzed. Both distributions are wider at the inlet of reactor for the inefficient mixing, but narrower at the outlet due to fully developed flow and polymerization. This model is beneficial to the improvement of polymer products and process control in industrial EPM reactor.     

Modeling and simulation of polypropylene particle size distribution in industrial horizontal stirred bed reactors

This work aims at developing a steady-state particle size distribution (PSD) model for predicting the size distribution of polypropylene particles in the outflow streams of propylene gas-phase horizontal stirred bed reactors (HSBR), on the one hand and investigating the effect of the catalyst residence time distribution (RTD) on the polymer PSD, on the other hand. The polymer multilayer model (PMLM) is used to describe the growth of a single particle. Knowing the PSD and RTD of a Ziegler–Natta type of catalyst and polymerization kinetics, this model allows calculating the polymer PSD of propylene polymerization in the HSBRs. The calculated polypropylene PSDs agree well with those obtained from the industrial reactors. The results reveal that both the PSD and the RTD of the catalyst affect the polymer PSD but in different manners. The effect of RTD on the PSD is less significant in the case of a nonuniform size catalyst feed. This model also allows investigating the effects of other process parameters on the polymer PSD under steady-state conditions, including intraparticle mass- and heat-transfer limitations, initial catalyst size, and polymer crystallinity. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Development of a multi-scale, multi-phase, multi-zone dynamic model for the prediction of particle segregation in catalytic olefin polymerization FBRs

A comprehensive multi-scale, multi-phase, multi-compartment dynamic model is developed to analyze the extent of particle segregation in catalytic, gas-phase ethylene-propylene copolymerization fluidized bed reactors (FBRs). From the numerical solution of the proposed integrated model, the temporal-spatial evolution of the morphological (i.e., particle size distribution, PSD) and molecular (i.e., molecular weight distribution, MWD) polymer properties in a catalytic polymerization FBR can be predicted. In particular, the polymer molecular properties are determined by employing a generalized multi-site, Ziegler-Natta kinetic scheme. To determine the growth of a single catalyst/polymer particle, the random pore polymeric flow model (RPPFM) is utilized. The RPPFM is solved together with a dynamic discretized particle population balance equation (PBE) to calculate the dynamic evolution of PSD in the various compartments of the FBR. Moreover, overall dynamic mass and energy balances are derived in order to assess the dynamic behavior of catalytic gas-phase FBRs. The effects of various fluidized bed operating conditions (e.g., fluidization gas velocity, temperature and catalyst feed rate) on the morphological and molecular distributed polymer properties are thoroughly analyzed.     

Preparation of SBS/poly(styrene–methyl methacrylate) thermoplastic interpenetrating polymer network

SBS as polymer I, poly(styrene–methyl methacrylate) polymerized by atom transfer radical polymerization as polymer II, and a thermoplastic interpenetrating polymer network of SBS/poly(styrene–methyl methacrylate) were prepared by the sequential method. The effects of the polymerization temperature, the composition of the catalyst, the ratio of the monomers studied, and the kinetics at 90°C were also investigated. It was shown that when polymerization was initiated by a BPO/CuCl/bpy (BPO:CuCl:bpy = 1:1:3) system at 90°C, the mass averaged molecular weight of the poly(styrene–methyl methacrylate) increased with monomer conversion, and the polydispersities were kept very low. Fourier transform infrared spectroscopy and gel permeation chromatogram showed that poly(styrene–methyl methacrylate) with low polydispersities had been synthesized. Thus, a thermoplastic interpenetrating polymer network comprised of both narrow molecular‐weight‐distribution components was successfully prepared. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 2007–2011, 2003     

Particle growth modeling of gas phase polymerization of butadiene

Butadiene polymerization in the gas phase is modeled by a polymeric multilayer model. Intraparticle mass and heat transfer effects are studied. The effects of catalyst size and diffusivity of butadiene on the radial profile of monomer concentration in polymeric particles and on the rate of particle growth are significant. Intraparticle temperature gradients do appear to be negligible under normal reaction conditions. External boundary layer heat effects are studied for various operation conditions. The model predicts that there is no significant temperature rise of the polymeric particles, even in the case of large catalyst particles. The effect of deactivation of active sites on the rate of particle growth is also studied. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 64: 203–212, 1997     

用多粒模型模拟丁二烯气相聚合的颗粒增长

Gas phase polymerization of butadiene by neodymium catalyst was modeled. The effects of mass and heat transfer resistances in the external boundary layer and within particles, sorption of butadiene in polybutadiene,and deactivation of active sites on polymer particle growth and morphology were studied. Simulation results show that the effects of intraparticle mass and heat transfer resistances on the growth rate of polymer particles are insignificant, and that there is no significant effect of mass transfer resistance on the morphology of polymer particles.The simulation results were compared with the experimental results.     

Coupled‐single‐particle and Monte Carlo model for propylene polymerization

A coupled‐single‐particle and Monte Carlo model was used to simulate propylene polymerization. To describe the effects of intraparticle transfer resistance on the polymerization kinetics, the polymeric multilayer model (PMLM) was applied. The reaction in each layer of the PMLM was described with the Monte Carlo method. The PMLM was solved together with the Monte Carlo model. Therefore, the model included the factors of the mass‐ and heat‐transfer resistance as well as the stochastic collision nature of the polymerization catalyzed with single‐site‐type/multiple‐site‐type catalysts. The model presented results such as the polymerization dynamics, the physical diffusion effect, and the polymer molecular weight and its distribution. The simulation data were compared with the experimental/actual data and the simulation results from the uniform Monte Carlo model. The results showed that the model was more accurate and offered deeper insight into propylene polymerization within such a microscopic reaction–diffusion system. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011