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     

CATALYST DEACTIVATION BY PORE PLUGGING AND ACTIVE SITE POISONING MECHANISMS II. PARALLEL POISONING IN BIDISPERSE STRUCTURED CATALYST

A catalyst deactivation model is formulated which includes the combined effects of pore plugging and active site poisoning in bidisperse structured catalyst particles. Intraparticle mass transfer is described by an equation which accounts for the configurational nature of diffusion in the micropores, and poison deposition is assumed to be in accord with a parallel poisoning mechanism. The model is used to explore the effects of macroporosity and micropore size on initial activity and activity maintenance, and model predictions appear to be consistent with observations from a recent coal liquefaction catalyst development program.     

Effects of catalyst fragmentation during propylene polymerization. IV: Comparison between gas phase and bulk polymerization processes

A comparative study of the effects of catalyst fragmentation in the gas phase and bulk polymerization processes in performed. Typical operating conditions for each process are used for the comparison. The monomer concentration in the bulk process is nearly one order of magnitude larger than that in the gas phase process. The energy transfer conditions between the particle and the fluid phase are better in the liquid phase. The rate of mass transfer within the macroparticle at the initial steps of the polymerization is found to be slower in the bulk process than in the gas phase process. In the liquid phase process, fragmentation takes place more slowly. Temperature excursion values are smaller even though the dimensionless monomer concentrations are, in fact, greater because of the higher monomer concentration available in the liquid phase. The final steady rate of reaction and the ultimate catalyst yield reflect this phenomenon. Although the microparticle nucleus size affects both processes, the diffusion control that occurs when the fragments are large affects the gas phase process more intensely. In the bulk process, even at the lowest value reached by the rate of reaction, this is still sufficiently high so as to produce high yields.     

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.     

Catalyst fragmentation during propylene polymerization. III: Bulk polymerization process simulation

Fragmentation of support/catalyst particles during propylene bulk polymerization is analyzed by means of a mathematical model including energy and mass balances, with chemical reaction. The rupture phenomenon is specifically considered by the model and analyzed as it proceeds along time. Model predictions concerning the effects of fragmentation on polymerization are discussed. The influence of mass-transfer resistances at the macroparticle and microparticle level, as well as the microparticle nucleus-size effects over the polymerization process, are analyzed. Macroparticle mass-transfer resistance affects both the rate of fragmentation and temperature excursions. Microparticle nucleus-size exerts a strong influence over the whole polymerization process. A small micronucleus-size produces both a delay in the fragmentation process and a greater value of she final catalyst yield. The effects of major critical parameters are evaluated via model simulation, and the results are discussed. The analysis shows that fragmentation depends on the combined effect of the parameters studied. Modeling of the process considering all parameters simultaneously is the proper way of predicting the fragmentation sequence for a given support/catalyst particle. Crystallinity of the produced polymer affects the rate of fragmentation, either increasing or decreasing the rupture rate depending on macroparticle porosity and compactness. Heat transfer conditions in the liquid-phase system make the temperature runaway problem easy to predict and control, in spite of high polymer yields. The design of “tailor-made” support/catalyst macroparticles in accordance with catalytic activity is necessary in order to obtain high yields and controlled process temperatures.     

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.     

Polymerization of olefins through heterogeneous catalysis—V. Gas-liquid mass transfer limitations in liquid slurry reactors

Many processes for polymerization of olefins employ laboratory, pilot plant, or full-scale liquid-phase polymerization reactors with monomer introduced as a gas. Criteria for the presence of gas-liquid mass transfer resistance in these systems are determined in terms of observed reaction rate or loading of a heterogeneous catalyst of given intrinsic activity. The effects of variables such as reactor size and configuration, temperature, and soluble polymer are also examined. The equilibrium monomer concentrations of ethylene in hexane and propylene in heptane are calculated through a modified Benedict-Webb-Rubin equation, and some calculations for ethylene-propylene mixtures are tabulated. The general methodology for predicting gas-liquid mass transfer resistance is readily extendible to copolymerization systems.     

Experimental study of paddy drying in a vortex chamber

The intensification of interfacial mass, heat, and momentum transfer makes vortex chambers potentially interesting for the efficient drying of paddy, allowing shorter drying times and/or more compact equipment. The presence of a shell introduces particular challenges. Intraparticle diffusion limitations are strong and may reduce the advantage from intensified interfacial mass and heat transfer and the efficiency of air usage. Furthermore, high shear and normal stresses in the fast rotating particle bed may cause damage to the paddy shell, posing problems for transport and storage. With these specific aspects in mind, the use of vortex chambers for paddy drying is experimentally evaluated.     

Dynamics of pressurization and blowdown of an adiabatic adsorption bed: 4. Intraparticle diffusion/convection models

The importance of intraparticle mass transfer during pressurization and blowdown steps of PSA processes in an adiabatic adsorption bed was assessed by comparing intraparticle diffusion/ convection and intraparticle diffusion models. Film mass/heat transfer resistances are also considered in the model. The film heat transfer resistance is more important than the heat transfer resistance inside the particle; it can be assumed to be negligible in PSA processes when the temperature variation is not very large, otherwise it leads to serious errors when the adsorption capacity of adsorbents is high and the heat capacity of the system is not high. Intraparticle convection improves the mass transfer inside the particle and leads to faster heat releases into and out of the adsorbents.     

Hydrodynamics and Mass Transfer in Gas‐Liquid‐Solid Circulating Fluidized Beds

Although extensive work has been performed on the hydrodynamics and gas‐liquid mass transfer in conventional three‐phase fluidized beds, relevant documented reports on gas‐liquid‐solid circulating fluidized beds (GLSCFBs) are scarce. In this work, the radial distribution of gas and solid holdups were investigated at two axial positions in a GLSCFB. The results show that gas bubbles and solid particles distribute uniformly in the axial direction but non‐uniformly in the radial direction. The radial non‐uniformity demonstrates a strong factor on the gas‐liquid mass transfer coefficients. A local mass transfer model is proposed to describe the gas‐liquid mass transfer at various radial positions. The local mass transfer coefficients appear to be symmetric about the central line of the riser with a lower value in the wall region. The effects of gas flow rates, particle circulating rates and liquid velocities on gas‐liquid mass transfer have also been investigated.     

Gas‐Liquid Mass Transfer in a Bench‐Scale Trickle Bed Reactor used for Benzene Hydrogenation

The gas‐liquid mass transfer coefficients (MTCs) of a trickle bed reactor used for the study of benzene hydrogenation were investigated. The Ni/Al₂O₃ catalyst bed was diluted with a coarse‐grained inert carborundum (SiC) particle catalyst. Gas‐liquid mass transfer coefficients were estimated by using a heterogeneous model for reactor simulation, incorporating reaction kinetics, vapor‐liquid equilibrium, and catalyst particle internal mass transfer apart from gas‐liquid interface mass transfer. The effects of liquid axial dispersion and the catalyst wetting efficiency are shown to be negligible. Partial external mass transfer coefficients are correlated with gas superficial velocity, and comparison between them and those obtained from experiments conducted on a bed diluted with fine particles is also presented. On both sides of the gas‐liquid interface the hydrogen mass transfer coefficient is higher than the corresponding benzene one and both increase significantly with gas velocity. The gas‐side mass transfer limitations appear to be higher in the case of dilution with fine particles. On the liquid side, the mass transfer resistances are higher in the case of dilution with coarse inerts for gas velocities up to 3 · 10^–2 cm/sec, while for higher gas velocities this was inversed and higher mass transfer limitations were obtained for the beds diluted with fine inerts.     

Effect of partial wetting on liquid/solid mass transfer in trickle bed reactors

The wetting efficiency of liquid trickle flow over a fixed bed reactor has been measured for a wide range of parameters including operating conditions, bed structure and physico-chemistry of liquid/solid phases. This data bank has been used to develop a new correlation for averaged wetting efficiency based on five different non-dimensional numbers. Finally liquid/solid mass transfer has been determined in partial wetting conditions to analyse what are the respective effects of wetting and liquid/gas flow turbulence. These effects appear to be separated: wetting being acting on liquid/solid interfacial area while the liquid/solid mass transfer coefficient is mainly connected to flow turbulence through the interstitial liquid velocity. A correlation has been proposed for liquid/solid mass transfer coefficient at very low liquid flow rate.     

Mass transfer effects in emulsion polymerization systems. I. Diffusional behavior of chain transfer agents in the emulsion polymerization of styrene

On the basis of the so-called two-films theory for mass transfer, a mathematical model for transfer of chain transfer agents from monomer droplets to polymer particles, where chain transfer agent molecules are consumed by the chain transfer reaction, is developed for an emulsion polymerization system. It is shown by the model that the concentration of chain transfer agent in the polymer particles during the polymerization is decreased to a value much less than that which would be attained if thermodynamic equilibrium for chain transfer agent were reached between the polymer particles and the monomer droplets, due mainly to the resistance to transfer of chain transfer agent molecules across the diffusion films at the interface between the monomer droplets and the water phase. The validity and utility of the model developed for predicting the diffusion and consumption rates for chain transfer agent are demonstrated experimentally using five normal aliphatic mercaptans from n-C₇ to n-C₁₂ as chain transfer agents in the seeded emulsion polymerization of styrene. © 1994 John Wiley & Sons, Inc.     

CHARACTERIZATION OF TWO-DIRECTIONAL DISPERSED PHASE FLOW THROUGH TIME SERIES ANALYSIS

A catalyst deactivation model is formulated which includes the combined effects of pore plugging and active site poisoning. Intraparticle mass transfer is described by an equation which accounts for the configurational nature of diffusion, and poison deposition is assumed to be in accord with a parallel poisoning mechanism. A computational algorithm is presented for solving the highly nonlinear system equations numerically. The relative extent of deactivation by pore plugging and active site poisoning is determined by a dimensionless parameter, α, and several examples illustrate the effects that this parameter and other system parameters have upon the computed results. The model when combined with laboratory experiments should prove useful in optimizing catalyst pore size.     

MASS TRANSFER EFFECTS IN LIQUEFACTION OF COAL BY SRC-II PROCESS PART II STUDY OF BUBBLE COLUMN REACTORS

The effects of hydrogen mass transfer resistance in large-scale SRC-II bubble column reactors (BCR), over large ranges of process variables, are studied. Due to the interactive effects of mass transfer resistance and gas hold up, the hydrogen consumption or liquid yield in a BCR has a maximum with respect to the specific mixing power. Under normal SRC-II process conditions a superficial gas velocity of about 0.01 m/s represents the optimum with respect to the hydrogen consumption or liquid yield. In general, the product quality requirement rather than the rate of hydrogen consumption determines the minimum specific mixing power requirement. Increase in hydrogen partial pressure can be used to reduce the level of mixing power required to maintain the desired product quality. Interrelations between mass transfer and gas hold effects and the variations in hydrogen concentration in slurry over large ranges of process conditions are also illustrated. This work provides some bases for the selection of reactor dimensions and process conditions for an SRC-II bubble column reactor (BCR).     

MASS TRANSFER EFFECTS IN LIQUEFACTION OF COAL BY SRC-II PROCESS PART II STUDY OF BUBBLE COLUMN REACTORS

The effects of hydrogen mass transfer resistance in large-scale SRC-II bubble column reactors (BCR), over large ranges of process variables, are studied. Due to the interactive effects of mass transfer resistance and gas hold up, the hydrogen consumption or liquid yield in a BCR has a maximum with respect to the specific mixing power. Under normal SRC-II process conditions a superficial gas velocity of about 0.01 m/s represents the optimum with respect to the hydrogen consumption or liquid yield. In general, the product quality requirement rather than the rate of hydrogen consumption determines the minimum specific mixing power requirement. Increase in hydrogen partial pressure can be used to reduce the level of mixing power required to maintain the desired product quality. Interrelations between mass transfer and gas hold effects and the variations in hydrogen concentration in slurry over large ranges of process conditions are also illustrated. This work provides some bases for the selection of reactor dimensions and process conditions for an SRC-II bubble column reactor (BCR).     

淤浆聚合体系乙烯溶解度及传质系数测定

对采用淤浆聚合法聚合生成超高相对分子质量聚乙烯过程中的传质过程进行了研究,考察了压力、温度对平衡溶解度的影响以及搅拌速率和物料对传质系数K_L的影响规律。结果表明：乙烯溶解度随气相中乙烯压力的升高而线性增加,气液平衡关系符合亨利定律;温度升高,气体溶解度减小;搅拌速率增大,相应的传质系数线性增大;加入聚乙烯颗粒会使吸收速率降低,物料量与传质系数基本呈反比例关系。     

Modeling of particle growth and morphology in the gas phase polymerization of butadiene. I. Model and its solution method

An improved multigrain model designed to simulate the polymeric particle growth and morphology in the gas phase polymerization of butadiene was developed. In the model, the effects of intraparticle heat and mass transfers, heat and mass transfer resistances at the particle boundary layer, sorption of 1,3‐butadiene in 1,4‐cis‐polybutadiene, and intrinsic kinetics on the polymeric particle growth and morphology were considered. An improved numerical method was also proposed. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 719–729, 2001     

Modeling of transfer phenomena on heterogeneous Ziegler catalysts: Differences between theory and experiment in olefin polymerization (an introduction)

This article begins by briefly reviewing the more important contributions to the area of modeling heat and mass transfer, and particle growth during the polymerization of olefins on Ziegler–Natta catalysts. It is shown that these models are capable of identifying the critical areas involved in heat and mass transfer, and of modeling polymerizations where the observed activity is less than approximately 5,000 g of polymer per gram of catalyst per hour (g/g/h). However, it is not possible to use these models “as-is” to model more modern catalysts whose activity levels can surpass the 50,000 g/g/h mark because they predict prohibitively large concentration gradients inside the growing particles during slurry polymerizations, and temperature gradients outside the particles during polymerization in the gas phase. An analysis of the mass and heat transfer Peclet numbers (Pe) reveals that certain simplifying assumptions may not always be valid. Pe values in the transition range suggest that convection inside the particles during polymerization in the liquid phase may help to explain why observed mass transfer rates are higher than the predicted rates. In an opposite vein, a Pe analysis shows that conductive heat transfer may play an important role at length scales characteristic of those in the early stages of polymerization. A new mechanism for heat transfer at reduced length scales is proposed. © 1995 John Wiley & Sons, Inc.     

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.