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。     

Polymerization of olefins through heterogeneous catalysis. VI. Effect of particle heat and mass transfer on polymerization behavior and polymer properties

The multigrain model for polymerization of olefins over solid catalysts is used to predict kinetic behavior, molecular weights, and polydispersities. The effects of intraparticle and external boundary layer transport resistance on the kinetic behavior and polymer properties are explored. Means for the experimental detection of intraparticle diffusion resistance are suggested. The importance of catalyst physical properties, such as the porosity, and the catalyst loading is illustrated through simulation. Finally, the hypotheses of diffusion resistance and site heterogeneity as explanations for the broad molecular weight distributions of olefin polymers are critically evaluated, and molecular weight distribution control in industrial catalysts is discussed.     

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。     

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 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.     

Evolution to similarity solutions for polymerization and depolymerization with microwave radiation

The kinetics of polymerization and depolymerization are critical in understanding the stability and characterization of polymers. The kinetics of simultaneous polymerization and degradation of poly(methyl methacrylate) have been investigated by varying the initiator concentration and monomer concentration under the influence of microwave energy. Microwave radiation initially polymerizes the monomer, then degrades the resulting polymer and the polymer attains an equilibrium molecular weight distribution with a polydispersity of two. To understand more fully the kinetics, the molecular weight distribution (MWD) is represented as a gamma distribution; the random degradation rate coefficient is assumed to vary linearly with molecular weight and the polymerization rate coefficient is assumed to be independent of molecular weight. The change of the MWD with time is studied by continuous distribution kinetics; the solutions obtained depict the change of the average molecular weight, polydispersity and the gamma distribution parameters with time. Experimental data indicate that reaction rates are enhanced by microwave radiation and the MWD approaches a similarity solution within 10 min for all the investigated cases. The model satisfactorily predicts the change of the MWD with time. © 2001 Society of Chemical Industry     

Rate and molecular weight distribution modeling of syndiospecific styrene polymerization over silica-supported metallocene catalyst

The kinetics of syndiospecific polymerization of styrene over silica-supported Cp^∗Ti(OCH₃)₃/MAO catalyst has been investigated through experimentation and theoretical modeling. At low monomer concentrations, the polymerization rate increases almost linearly with monomer conversion, but the reaction rate becomes independent of monomer concentration at high bulk phase monomer concentrations. A kinetic model that incorporates the monomer partition effect between the solid and the liquid phases has been proposed. The model simulations show that the observed non-linear kinetics can be adequately modeled by the monomer partition model. The polymer molecular weight has also been found to increase with the monomer concentration and the polymer molecular weight distribution (MWD) is quite broad, suggesting that the catalytic behavior deviates from the single site catalytic polymerization model. The MWD broadening is modeled by a two-site kinetic model and a good agreement between the model and the experimental data has been obtained.     

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     

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.     

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     

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     

Effect of Polymer Growth Rate and Diffusion Resistance on the Behavior of Industrial Polyethylene Fluidized Bed Reactor

The two‐phase model developed for the UNIPOL polyethylene process is improved by introducing polymer diffusion resistance, this means modelling of polyethylene fluidized bed reactors has been examined on two levels, at small scale of individual polymer particle, and macroscale of the whole reactor. The model utilizes the multigrain model that accounts for the reaction rate at catalyst surface to explore the static and dynamic bifurcation behavior of the fluidized bed catalytic reactor. Detailed bifurcation diagrams are developed and analyzed for the effect of polymer growth factor and Thiele modulus (the significance of the porous medium transport resistance is characterized by Thiele modulus) on reactor dense phase monomer concentration and reactor temperature as well as polyethylene production rate and reactor single pass conversion for the safe temperature region. The observations reveal that significant diffusion resistance to monomer transport exists, and this can mask the intrinsic rate constants of the catalyst. The investigation of polymer growth factor indicates that, the nascent stage of polymerization is highly gas phase diffusion influenced. Intraparticle temperature gradients would appear to be negligible under most normal operating conditions.     

Fractal analysis of polymer molecular weight distribution: Dynamic scaling

The correctness of the molecular weight distribution (MWD) of a poly(dimethyl diallyl ammonium chloride) type was shown in the frame‐work of the dynamic distribution function of the irreversible aggregation cluster–cluster model. The buildup of a generalized distribution curve confirms the possibility to describe the polymerization processes within the framework of the mentioned model and allows one to predict the kinetics of MWD changes as the function of the initial monomer concentration c₀ and reaction time t. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 2382–2384, 2003     

丁二烯气相聚合过程中的单体吸附效应和本征动力学模型

采用负载型稀土催化剂 ,在搅拌床反应器内进行丁二烯气相聚合动力学的研究 .考察了单体在聚合物小粒子中的吸附效应和单体压力与温度对聚合速率影响 ,在此基础上 ,提出了本体系的本征动力学模型     

Particle size distribution and molecular size distribution of polymers in soap-free emulsion polymerization of styrene

Polystrene (PS) particles, generated from soap-free emulsion polymerization of styrene monomer, water, and potassium persulfate, were investigated by photon correlation spectroscopy (PCS) and TEM. The particle size distribution (PSD) was quite uniform. From the data of PCS, it could be said that lots of particles flocculated in the final stage of reaction. It was also deduced from the molecular weight distribution (MWD), measured by GPC, that, during the early stage of reaction, molecules with low molecular weight (<4000) might exist and the particles were perhaps formed through micellar-type nucleation mechanism. When initiator concentration increased, reaction rate increased but weight average molecular weight, tensile modulus, and elongation decreased. The number density of particles was found to be proportional to 0.49 power of initiator concentration. However, monomer concentration did not seem to have any great effect on all of them above.     

The role of diffusion in the Ziegler polymerization of ethylene

A theoretical and experimental study has been made of the polymerization of ethylene in a slurry reactor using a highly active Ziegler catalyst in the presence of hydrogen. A model of the polymerization system has been set up in which polymerization is assumed to proceed with encapsulation of catalyst subparticles. Allowance is made for an experimentally observed first-order decay in intrinsic catalyst activity. The theoretical prediction of the model for the monomer absorption rate behavior and the molecular weight characteristics of the polymers formed are in agreement with experimental findings. Experimental evidence is presented that in the earliest moments of a polymerization significant amounts of polymer are formed with molecular weights 100 times those in the balance of the polymerization. It is concluded that in this system the polymerization is diffusion controlled throughout the major part of the catalyst lifetime. This diffusion phenomenon, together with the gradual loss of active sites, is of vital importance in determining the molecular weight and molecular weight distribution of the polyethylene product.     

Molecular Weight Distribution of Polystyrene Produced in a Starved Feed Reactor

A starved feed reactor (SFR) is a semi-batch polymerization reactor where initiator and monomer are fed slowly into a fixed amount of solvent. The polymerization is carried out isothermally at elevated temperatures, The added initiator decomposes instantaneously and the added monomer polymerizes immediately. The molecular weight (MW) and molecular weight distribution (MWD) of the product polymer can be effectively controlled by the feed ratio of monomer to initiator. This paper preaeats a study on the MWD of styrene polymerization in a SFR. The MWD model parameters are regressed with experimeatvJ data. Although the solids fraction in the SFR is high (higher than 50%), vlscceity is not too high and the “gel effect“ is weak due to the low molecular weight of the products. It is found that the termination rate constant is a power function of molecular weight, radicals terminate via 100% combination,the thermal iuitiation can be neglrcted even at high reaction temperature studied. And calculated results indicate that in the SFR, the validity of the long chain assumptinn becomes doubted. It appears that other alterative assumption should be found for an improved model.     

Dimethylsilylbis(1‐indenyl) zirconium dichloride/methylaluminoxane catalyst supported on nanosized silica for propylene polymerization

A dimethylsilylene‐bridged metallocene complex, (CH₃)₂Si(Ind)₂ZrCl₂, was supported on a nanosized silica particle, whose surface area was mostly external. The resulting catalyst was used to catalyze the polymerization of propylene to polypropylene. Under identical reaction conditions, a nanosized catalyst exhibited much better polymerization activity than a microsized catalyst. At the optimum polymerization temperature of 55°C, the former had 80% higher activity than the latter. In addition, the nanosized catalyst produced a polymer with a greater molecular weight, a narrower molecular weight distribution, and a higher melting point in comparison with the microsized catalyst. The nanosized catalyst's superiority was ascribed to the higher monomer concentration at its external active sites (which were free from internal diffusion resistance) and was also attributed to its much larger surface area. Electron microscopy results showed that the nanosized catalyst produced polymer particles of similar sizes and shapes, indicating that each nanosized catalyst particle had uniform polymerization activity. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2008