Modelling of heat and mass transfer during the polymerisation of olefins on heterogeneous Ziegler catalysts

The modelling of heat and mass transfer during the gas and slurry phase polymerisation of olefins is examined. It is demonstrated that it might not be necessary in many cases to calculate concentration gradients in the growing catalyst/polymer complex, and that the currently used representation of heat transfer from small, highly active particles using standard chemical engineering correlations might not be accurate.

Close examination of the morphology of catalyst particles shows that it is unlikely that the particles should be treated as a pseudo-homogeneous medium, and in fact the critical length scale for mass transfer is not the particle radius, but is much smaller. Furthermore, computational fluid dynamic simulations of single and interacting particles shows that convection is not the dominant heat transfer mechanism during the critical stages of the reaction.     

Increase in viscosity and its influence on polymerization processes

In the course of polymerization in homogeneous systems, the viscosity of the reaction mass increases by several orders of magnitude. The viscosity increase is affected by reaction conditions, concentration and properties of the formed polymer. Empirical correlations for homogeneous and heterogeneous polymerizations are given. Viscosity significantly affects the polymerization kinetics as well as heat, mass and momentum balances of the polymerization reactor. The influence of viscosity and its increase on conductive heat transfer, stirrer power input and cooling capacity, molecular diffusion and mass transfer coefficients, mixing time and residence time distribution in homogeneous and heterogeneous polymerizations in stirred tank and tubular reactors is reviewed.     

Modeling of transfer phenomena on heterogeneous ziegler catalysts. II. Experimental investigation of intraparticle mass transfer resistance during the polymerization of ethylene in slurry

An experimental investigation of mass transfer limitations on a single batch of high activity, heterogeneous catalysts used in the slurry polymerization of ethylene is presented. The viscosity of the continuous phase was varied, using trace amounts of inert copolymer in order to reduce the monomer diffusivity, and the activity levels were varied using hexene as an activator. These changes were intended to clearly identify situations in which the polymerization becomes mass-transfer-limited due to diffusion resistance in the pores of the catalyst. Increasing the observed activity of the catalyst from approximately 9000 to 40,000 grams of polymer per gram of catalyst per hour (g/g/h) revealed no evidence of mass transfer resistance, even when the diffusivity of the monomer in solution was reduced by a factor of six. Analysis of the molecular weight as a function of particle size supported this conclusion but did suggest that there might be slight chemical differences between large and small particles. © 1996 John Wiley & Sons, Inc.     

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     

Polymerization of olefines through heterogeneous catalysis IV. Modeling of heat and mass transfer resistance in the polymer particle boundary layer

Propylene and ethylene polymerization in liquid and gas media are described by a multigrain particle model. External boundary layer heat and mass transfer effects are investigated for various catalysts and operating conditions. For high-activity catalysts used in slurry, external film mass transfer effects may be significant. For gas-phase polymerization of propylene or ethylene, the model predicts significant particle overheating at short times, which may explain the particle sticking and agglomeration problems sometimes observed in industrial reactors.     

Polymerization of olefins through heterogeneous catalysis. III. Polymer particle modelling with an analysis of intraparticle heat and mass transfer effects

Propylene and ethylene polymerization in liquid and gas media are described by a multigrain particle model. Intraparticle heat and mass transfer effects are investigated for a range of catalyst activities. For slurry polymerization, intraparticle mass transfer effects may be significant at both the macroparticle and microparticle level; however, for normal gas phase polymerization, microparticle mass transfer effects appear more likely to be important. Intraparticle temperature gradients would appear to be negligible under most normal operating conditions.     

Influence of unlimited 3-membered ring cyclization on a multiscale dynamic Monte Carlo/continuum model of drying and curing in sol–gel silica films

The coating process of sol–gel silica films involves multiple length and time scales ranging from molecular to macroscopic. At the molecular scale, cyclization during polymerization is so extensive that it cannot be neglected or treated statistically. Here we present a multiscale model of a 1D sol–gel drying process coupled to a Monte Carlo polymerization model with unlimited cyclization. Because our model allows cyclic and cage–like siloxanes to form, it is better able to predict the silica gelation conversion than any other reported kinetic model. By studying the competition between molecular growth and cyclization, and the competition between mass transfer (drying) and reaction (gelation) on the drying process of the sol–gel silica film, we observe that cyclization delays the gelation, shrinks the molecular size, increases the likelihood of literal skinning, and leads to a molecular structure gradient inside the film. Although for simplicity our model just considers the possibility of forming 3-membered ring, it is the first multiscale model to couple unlimited cyclization in polycondensation with a continuum mass transfer process. Also it is the first model that can predict structure gradients caused by drying in sol–gel silica films.     

Halbkontinuierliche Emulsionspolymerisation von Vinylidenfluorid

The various properties of polyvinylidene fluoride enable a wide range of applications from automotive industry to medicine. The semibatch emulsion polymerization of vinylidene fluoride was investigated. To achieve efficient monomer incorporation into the reaction mixture, e.g., stirring speed and reaction pressure were varied. Iodine transfer polymerizations were carried out in the presence of perfluorinated alkyl iodides serving as chain transfer agents to yield narrow molar mass distributions. The size of the latex particles was determined from dynamic light scattering measurements and field emission scanning electron microscopy.     

Modeling of the sheet‐molding process for poly(methyl methacrylate)

The sheet‐molding process for the production of poly(methyl methacrylate) (PMMA) involves an isothermal batch reactor followed by polymerization in a mold (the latter is referred to as a “sheet reactor”). The temperature at the outer walls of the mold varies with time. In addition, due to finite rates of heat transfer in the viscous reaction mass, spatial temperature gradients are present inside the mold. Further, the volume of the reaction mass also decreases with polymerization. These several physicochemical phenomena are incorporated into the model developed for this process. It was found that the monomer conversion attains high values of near‐unity in most of the inner region in the mold. This is because of the high temperatures there, since the heat generated due to the exothermicity of the polymerization cannot be removed fast enough. However, the temperature of the mold walls has to be increased in the later stages of polymerization so that the material near the outer edges can also attain high conversions of about 98%. This would give PMMA sheets having excellent mechanical strength. The effects of important operating (decision) variables were studied and it was observed that the heat‐transfer resistance in the mold influences the spatial distribution of the temperature, which, in turn, influences the various properties (e.g., monomer conversion, number‐average molecular weight, and polydispersity index) of the product significantly. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 1951–1971, 2001     

Heat and mass transfer in calcination of limestone particles

The heat and mass‐transfer phenomena occurring during the calcination of limestone particles was studied by means of modeling. The applicability of two modeling methods for calcination was compared under different conditions. An unsteady numerical particle model with mass, momentum, energy balance, and shrinking core models were chosen for the study. The influence of different phenomena (chemical kinetics, advective and diffusive mass transfer, and heat transfer) in different conditions was evaluated with the aid of dimensionless parameters, and their relative importance was shown in a regime chart. Especially, the significance of advection was studied and its importance in high CO₂ concentration was observed. Local temperatures inside the particle were obtained by solving a dynamic energy balance in each particle layer including calcination reaction energy and conduction heat transfer. Noticeable temperature differences between constant ambient conditions and the particle were observed. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2563–2572, 2012     

松木屑颗粒热解过程中的热/质传递规律

为探索在固定床反应器中有机固废颗粒热解过程中的热量、质量传递机理,本研究从颗粒尺度上对有机固废松木屑颗粒热解过程建模分析,模型中考虑了焦油的二次裂解反应及挥发分在颗粒孔隙中的质量、动量传递过程,并采用达西定律模拟了挥发分在颗粒孔隙内的流动现象,对颗粒热解过程的吸热反应以及挥发分逸出时的对流换热对颗粒温度的影响进行考察。基于两步反应动力学模型,探讨了不同颗粒尺寸、热解温度对有机固废松木屑颗粒热解过程的影响。结果表明,热解吸热反应和挥发分的对流换热阻碍了热量向颗粒中心的传递,延长了颗粒达到均温的时间;松木屑颗粒热解时,颗粒内会存在明显的温度梯度,在颗粒表面主要受化学反应动力学限制,在颗粒内部则主要受热量传递过程限制。此外,热解温度越低,粒径越大,颗粒内部的传热阻力越大。松木屑颗粒完全热解所需时间会随着颗粒粒径的增大而增加,但当颗粒粒径在10mm以上时,随着颗粒粒径的增大,颗粒完全热解所需时间的增量要大于10mm以下颗粒。     

离心流化床中强制对流换热的实验研究

对离心流化床干燥器中气体与被干燥颗粒物料之间的强制对流换热进行了实验研究,获得了各主要运行参数对气固换热系数的影响规律,并利用场协同原理分析了对流换热强化的机理. 实验证明,在一定转速范围内,在气流速度方向和热流方向（温度梯度方向）一致时,换热的准则关联式具有Nu＝CRePr的形式. 获得了满足Nu～RePr呈直线关系的Pe(Pe=RePr)数变化范围和临界Pe数,当Pe数大于临界值后,离心流化床中对流换热强度随Pe数增加而增大的趋势会明显减缓并偏离线性区.     

Numerical study on steady and transient mass/heat transfer involving a liquid sphere in simple shear creeping flow

A numerical method is utilized to examine the steady and transient mass/heat transfer processes that involve a neutrally buoyant liquid sphere suspended in simple shear flow at low Reynolds numbers is described. By making use of the known Stokes velocity field, the convection‐diffusion equations are solved in the three‐dimensional spherical coordinates system. For the mass transfer either outside or inside a liquid sphere, Sherwood number Sh approaches an asymptotic value for a given viscosity ratio at sufficiently high Peclet number Pe. In terms of the numerical results obtained in this work, two new correlations are derived to predict Sh at finite Pe for various viscosity ratios. © 2013 American Institute of Chemical Engineers AIChE J, 60: 343–352, 2014     

氯乙烯SET-DT悬浮聚合动力学和成粒过程的相互关系

以碘仿为引发剂、连二亚硫酸钠/碳酸氢钠为催化体系、聚乙烯醇(PVA)和/或纤维素衍生物(MC)为分散体系,进行氯乙烯单电子转移-蜕化链转移(SET-DT)活性自由基悬浮聚合,采用在线示踪气相色谱法和激光粒度分析系统研究分散剂种类和浓度、搅拌转速等对聚合动力学和单体液滴/聚合物颗粒粒径分布的影响。发现在相同搅拌转速下,以MC为分散剂的氯乙烯聚合速率最大,以PVA为分散剂时反应速率最小;分散剂种类固定时,聚合速率随分散剂浓度增大而增大。SET-DT悬浮聚合过程中,水相连二亚硫酸钠分解产生的自由基向单体液滴的扩散速率与液滴粒径分布和皮膜结构有关,因此聚合成粒过程影响聚合动力学。尽管不同条件下的聚合均经历液-液分散、液滴黏并、树脂颗粒稳定(转化率>30%)等成粒阶段,但各阶段的液滴/颗粒平均尺寸随分散体系和搅拌转速的变化而变化,引起聚合速率变化;采用MC为分散剂得到的PVC树脂皮膜少,有利于水相产生的自由基向单体相的扩散,聚合速率大。     

Catalyst fragmentation during propylene polymerization: Part I. The effects of grain size and structure

Fragmentation of support/catalyst particles during propylene polymerization in the gas phase is analyzed via a mathematical model including energy and mass transfer with chemical reaction processes. The rupture phenomenon is considered specifically by the model, and evaluated as it proceeds in time, Two different regions are recognized in the polymerizing particle at fragmentation time: an inner core resembling the original solid support/catalyst structure, and an external set of layers where most of the polymerization occurs. Model predictions concerning the effects of fragmentation on polymerization are discussed. The influence of different degrees of fragmentation on thermal runaways and monomer availability at active sites located inside the support/catalyst/polymer complex is shown. Monomer concentration profiles inside the growing particles are explained in terms of the combined fragmentation-polymerization interaction. Results show a strong influence of catalyst structure on critical phenomena during early polymerization stages, and suggest the possibility of controlling critical parameters via the definition of fragment structure at catalyst preparation time.     

Precipitation polymerization of acrylic acid: Kinetics,viscosity and heat transfer

The free-radical precipitation polymerization of acrylic acid in toluene was studied in an isothermal reaction calorimeter. The polymerization shows an autocatalytic behaviour of the rate of polymerization typical for precipitation polymerizations. The rate of polymerization with respect to conversion can be modeled by taking the volume fraction of the precipitated polymer into consideration. The viscosity of the reaction mixture increases with increasing volume fraction of precipitated polymer. The viscosity runs through a maximum at high conversion. The final viscosity decrease is probably due to shear stress caused aggregation phenomena of the polymer particles. A model is discussed which can describe the increase and decrease of viscosity of the system. By means of reaction calorimetry it is possible to determine the reaction-sided heat transfer coefficient during polymerization. The comparison of the experimentally determined temperature course of the reaction mixture and the temperature course calculated with a coupled model of the polymerization and the calorimeter shows that the heat-transfer characteristic changes instantaneously during a small conversion interval at the very beginning of the polymerization.     

Analysis of styrene polymerization in a continuous flow tubular reactor

A mathematical model has been developed to predict the spatial variations in temperature, velocity and composition which occur during thermal polymerization of styrene in a laminar flow tubular reactor. The resulting computer simulation model is capable of analysing the effects of coupled momentum, heat and mass transfer including system parameter variations and different operational conditions on reactor stability and conversion rate. It was found that a tube of radius up to 2 cm can be unconditionally used for continuous flow polymerization. Above this radius, thermal runaway, flow channelling and steep radial gradients in all principal variables may occur.     

Polymer molecular weight and chain transfer during the photopolymerization of an aliphatic monoacrylate in a smectic liquid crystal

Polymer/liquid crystal (LC) composites offer a unique opportunity to study polymerizations in ordered media, specifically the potential effect mesophase order can have on polymer properties including molecular weight. To develop successful polymer/LC composites for display applications, it is important to understand the effect of mesophase order on polymer molecular weight in order to optimize the electro-optic (EO) properties of the polymer/LC composite. Polymer molecular weight may be influenced in a LC by changes in polymerization rate as LC order is modulated and by chain transfer. This work focuses on the photopolymerization of an aliphatic monoacrylate monomer, decyl acrylate (DA), both in the ordered LC phases of 8CB as well as in isotropic solutions with LC and co-solvent.When DA is polymerized using the LC as the solvent, enhanced polymerization rates and polymer molecular weights are observed in the highly ordered smectic phase compared to the less ordered nematic and isotropic phases. When conducted strictly in an isotropic environment using a co-solvent with increasing 8CB percentages, a dramatic decrease in the polymerization rate and a significant reduction of the polymer molecular weight is observed, implying degradative chain transfer to the LC. NMR results show that this chain transfer is a result of hydrogen abstraction from the liquid crystals, which leads to the reduction in the polymerization rate with increasing 8CB concentration. The most likely site of hydrogen abstraction is from the benzyl hydrogens of the alkyl chain of 8CB. This chain transfer also plays a role for polymerizations performed in the ordered phases of the LC. Chain transfer appears to be less significant when polymerizations are conducted in the smectic phase due to the anti-parallel association of the LC molecules. When polymerizations occur in the less ordered phases, chain transfer dominates leading to a large reduction in polymer molecular weight and polymerization rate.     

A novel fluidized and induction heated microreactor for catalyst testing

The jiggled bed reactor (JBR) is a state‐of‐the‐art batch fluidized microreactor designed and developed to test catalysts for endothermic reactions. The solid particles in the microreactor are mechanically fluidized by agitating the reactor using a linear pneumatic actuator. An external induction field heats up vertical metal wires installed inside the reactor bed to generate heat rapidly and uniformly within the bed of solid particles, while eliminating hot spots and large temperature gradients. Image and signal processing techniques were utilized to investigate how the fluidization dynamics of the solid particles are affected by the amplitude and frequency of the vibrations, and the size distribution and the mass of the particles. The results show that the microreactor is very flexible: operating conditions can be optimized to successfully fluidize any type of catalyst. Heat‐transfer coefficients between heating surfaces and the bed are similar to the coefficients that could be obtained in a well‐bubbling fluidized bed. This confirms the excellent quality of the fluidization achieved with the new JBR. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3107–3122, 2014