Reactor Modeling of Gas‐Phase Polymerization of Ethylene

A model is developed for evaluating the performance of industrial‐scale gas‐phase polyethylene production reactors. This model is able to predict the properties of the produced polymer for both linear low‐density and high‐density polyethylene grades. A pseudo‐homogeneous state was assumed in the fluidized bed reactor based on negligible heat and mass transfer resistances between the bubble and emulsion phases. The nonideal flow pattern in the fluidized bed reactor was described by the tanks‐in‐series model based on the information obtained in the literature. The kinetic model used in this work allows to predict the properties of the produced polymer. The presented model was compared with the actual data in terms of melt index and density and it was shown that there is a good agreement between the actual and calculated properties of the polymer. New correlations were developed to predict the melt index and density of polyethylene based on the operating conditions of the reactor and composition of the reactants in feed.     

气相法聚乙烯冷凝模式操作的模拟研究(Ⅰ) 反应器运行状态的分析

建立了气相法聚乙烯冷凝模式操作反应器的两相模型 .模型涉及气泡相和乳化相中的热量和质量守衡、乳相和泡相之间的热量传递和质量传递、乳相中的聚合反应以及乳相中粒子的停留时间分布等 .通过模型研究了常规操作和冷凝操作时操作变量和反应器运行状态变量之间的关系 .模型模拟结果与工业的常规操作和冷凝操作数据符合较好 .得到了冷凝操作时时空收率、低温区域、聚合物灰分等的变化规律以及催化剂特性对冷凝操作的影响规律 .提出了适合于冷凝操作的催化剂类型     

Fluidized‐bed reactor modeling for polyethylene production

Gas‐phase technology for polyethylene production has been widely used by industries around the world. A good model for the reactor fluid dynamics is essential to properly set the operating conditions of the fluidized‐bed reactor. The fluidized‐bed model developed in this work is based on a steady‐state model, incorporating interactions between separate bubble, emulsion gas phase, and emulsion solid polymer particles. The model is capable not only of computing temperature and concentration gradients for bubble and emulsion phases, calculating polymer particle mean diameter throughout the bed and polyethylene production rate, but also of pinpointing the appearance of hot spots and polymer meltdown. The model differs from conventional well‐mixed fluidized‐bed models by assuming that the particles segregate within the bed according to size and weight differences. The model was validated using literature and patent data, presenting good representation of the behavior of the fluidized‐bed reactor used in ethylene polymerization. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 321–332, 2001     

Dynamic modeling of gas phase propylene homopolymerization in fluidized bed reactors

A new model with comprehensive kinetics for propylene homopolymerization in fluidized bed reactors was developed to investigate the effect of mixing, operating conditions, kinetic and hydrodynamic parameters on the reactor performance as well as polymer properties. Presence of the particles in the bubbles and the excess gas in the emulsion phase was considered to improve the two-phase model, thus, considering the polymerization reaction to take place in both the bubble and emulsion phases. It was shown that in the practical range of superficial gas velocity and catalyst feed rate, the ratio of produced polymer in the bubble phase to the total production rate is roughly between 10% and 13%, which is a substantial amount and cannot be ignored. Simulation studies were carried out to compare the results of the improved two-phase, conventional well-mixed and constant bubble size models. The improved two-phase and well mixed models predicted a narrower and safer window at the same running conditions compared with the constant bubble size model. The improved two-phase model showed close dynamic behavior to the conventional models at the beginning of polymerization, but starts to diverge with the evolution of time.     

Two‐Phase Sequential Simulation of a Fluidized Bed Reformer

A two‐phase flow model is adapted in order to predict the performance of a fluidized bed reformer using the sequential modular simulator. Since there are physical and chemical phenomena interacting in the reformer, two sub‐models appear to be necessary to describe the overall model. These are the hydrodynamic and reaction sub‐models. The hydrodynamic sub‐model is based on the dynamic two‐phase model and the reaction sub‐model is derived from the literature. In the overall model, the bed is divided into several sections. At each section, the flow of the gas is considered as plug flow through the bubble phase and to be perfectly mixed through the emulsion phase. Two sets of experimental data from the literature at different hydrodynamic regimes were used in order to validate the proposed model. A close agreement was observed between the model predictions and the experimental data. The model proposed in this work may be used as a framework for the development of sophisticated models for non‐ideal reactors inside process simulators.     

Modeling of a multizone gas‐phase polyethylene reactor with a cluster‐based approach

A circulating fluidized reactor of polyethylene was modeled with the proper hydrodynamics for a riser and downer and combined with a kinetic model based on the moment equations. The hydrodynamic model was able to predict the profiles of the following parameters through the riser and downer: cluster velocity, bed porosity, concentration of potential active sites, active sites, gas‐phase components, molecular weights, and reactor temperature. It was shown that one could control the monomer consumption and molecular weight, which are crucial in the reactor behavior and production properties, respectively, by setting different operating hydrodynamic conditions, such as the gas velocity in the riser and the solid circulation rate. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Cold flow model and computer simulation studies of a circulating fluidized bed reactor for the oxidative coupling of methane

A circulating fluidized bed configuration has been developed for application in the oxidative coupling process. The configuration comprises a bottom turbulent fluidized bed, wherein the oxidative coupling reaction is conducted, followed by a reduced-diameter top fast bed for catalyst entrainment and hydrocarbon cracking. The hydrodynamic characteristics of this configuration have been investigated in a pilot-plant cold flow unit. Detailed experimental results on the turbulent bed flow structure and the gas phase residence time distribution are presented and discussed. The performanceofthe proposed reactor is analyzed by computer simulation studies based on a published oxidative coupling kinetic model. It is shown that improved hydrocarbon yields can be obtained by optimizing the hydrodynamic structure and the mixing characteristics of the turbulent bed.     

Analysis of volume change effects in a fluidized bed catalytic reactor

A mathematical model based on the concept of an improved bubble assemblage model is developed for calculating the conversion of a reaction system involving a volume change in fluidized beds. The influence of volume change on the hydrodynamic behavior of gas in the bed, such as bubble size variation, superficial gas velocity change, and volume fraction occupied by each phase, is also investigated. It is found that increasing stoichiometric coefficient values results in larger bubble size, higher superficial gas velocities, higher crossflow rate between emulsion phase and bubble phase, and greater volume fraction of bubble phase, but smaller volume fraction occupied by the emulsion phase as well as lower conversions.     

拟泡-乳曳力模型在大型高温费托流化床反应器中的CFD模拟研究

以带冷却盘管的大型高温费托流化床反应器为研究对象,开展三维计算流体力学模拟研究。传统双流体模型基于局部平均的假设,认为单位控制体内气固两相均匀分布,网格尺寸必须足够小才能正确揭示局部非均匀结构的所有细节。采用双流体模型模拟大型工业化流化床装置时,将导致网格数量过于庞大,远超现有计算能力。为提高计算效率的同时不损失模拟精度,提出了基于局部非均匀假设、适用于粗网格的拟泡-乳三相非均匀曳力(PBTD)模型。该模型将流化床分为乳化相气体、乳化相颗粒以及气泡三相,分别建立守恒方程,体现气泡的非均匀特性对气固曳力的影响。乳化相内气固曳力以及气泡相与乳化相内颗粒的曳力分开考虑。采用PBTD模型耦合传质和反应模型,建立基于局部非均匀假设的高温费托合成反应器三维流动-传递-反应模型,包括各相守恒控制方程、气泡尺寸模型、相间物质和动量交换模型、高温费托合成反应动力学模型以及初始和边界条件,预测反应器内的流场和组分浓度分布。研究结果表明:在粗网格条件下,非均匀曳力模型可以预测床层内相含率的分布情况,预测的床层膨胀高度与经验公式计算值接近,偏差为1.2%。反应器出口气体组分的质量分数与试验测量值相近,偏差在1.5%~16.0%。模拟结果证实,基于非均匀假设的PBTD模型适用于模拟工业规模的鼓泡流化床反应器,对其设计开发和工业运行具有指导价值。     

Modelling and simulation of coal gasification process in fluidised bed

A one-dimensional steady state mathematical model and a numerical algorithm have been developed to simulate the coal gasification process in fluidised bed. The model incorporates two phases, the solid and the gas. The gaseous phase participates in the emulsion (with the solid phase) and forms the bubble. The solid phase is composed of carbonaceous material, limestone and/or inert bed material. The model can predict temperature, converted fraction, and particle size distribution for the solid phase. For the gaseous phase, in both emulsion and bubble, it can predict profiles of temperature, gas composition, velocities, and other fluid-dynamic parameters. In the feed zone, a Gaussian distribution for the solid particle size is considered. This distribution changes due to attrition, elutriation, consumption and drag inside the reactor. A system of 29 differential and 10 non-linear equations, derived from the mass, energy and momentum balances for each phase, at any point along the bed height, are solved by the Gear and Adams Method. Experimental data from the Universidad de Antioquia and Universidad Nacional-Medellin have been used to validate the model. Finally, the model can be used to optimise the gasification process by varying several parameters, such as excess of air, particle size distribution, coal type, and geometry of the reactor.     

Simulation of fluidized-bed reactors for catalytic oxidative coupling of methane to C2-hydrocarbons

The “bubble assemblage model” of Kato and Wen was applied to simulate the catalytic oxidative coupling of methane to C₂-hydrocarbons in a fluidized bed reactor. Simulation results were compared to experimental data obtained in a laboratory-scale fluidized bed reactor. To improve the accuracy of predictions, the influence of fluid bed hydrodynamic and kinetic submodels was investigated by applying a sensitivity analysis. It was shown that the most important element in the model is the applied reaction scheme; the consecutive reactions of C₂ hydrocarbons occurring most probably in the gas phase should be considered.     

Methanation in a fluidized bed reactor with high initial CO partial pressure: Part II— Modeling and sensitivity study

A model of a bench-scale methanation reactor was set-up by modifying the classical two-phase model approach and introducing an additional bulk flow from bubble to dense phase to consider the volume contraction of the methanation reaction. The model uses experimentally determined kinetics and hydrodynamic correlations from literature. It was satisfyingly validated by comparing the calculated gas concentration profiles with the experimental data, especially with respect to initial reaction rates and reactor exit concentrations.A sensitivity study with respect to different bubble size correlations, mass transfer rates and considering or neglecting the bulk flow (influence of volume contraction caused by the methanation reaction) was carried out. It showed that the bubble size correlation by Werther and the resulting gas concentration profiles fit the measured data better than the computed gas concentration profiles using the bubble size correlation by Rowe.Neither a variation of the mass transfer coefficient nor neglecting the bulk flow in the fluidized bed model did yield further improvement of the calculated concentration profiles.     

High temperature fluidized bed reactor: measurements,hydrodynamics and simulation

This paper was made possible through the development of a novel high temperature optical fiber probe to study the hydrodynamics of a high temperature fluidized bed reactor. The experimental results show that the hydrodynamic parameters considerably change with bed temperature when fluidizing FCC particles. For a given superficial gas velocity, the average local particle concentration, the dense phase fraction and the particle concentration in the dense phase decrease with increasing bed temperature. As a result of an increase in temperature, the fluidized behavior of the FCC particles progressively shifts from typical Geldart A towards B. Consequently, a modified two-phase model, based on the simple two-phase model, integrating the effects of temperature and superficial gas velocity on the hydrodynamics, is proposed. Simulation of a reactive catalytic system using a conventional simple two-phase model and the modified model is achieved. The predicted reactor performances strongly differ for each model. In the present case, the simple two-phase model underestimates the reactor performance by inadequately accounting for the solid fractions in the bubble and dense phases and their dependence on temperature and superficial gas velocity. This suggests that the hydrodynamic models should take into account the effects of temperature and superficial gas velocity when simulating the performance of a high temperature fluidized bed reactor.     

Modular Simulation of Fluidized Bed Reactors

Simulation of chemical processes involving nonideal reactors is essential for process design, optimization, control and scale‐up. Various industrial process simulation programs are available for chemical process simulation. Most of these programs are being developed based on the sequential modular approach. They contain only standard ideal reactors but provide no module for nonideal reactors, e.g., fluidized bed reactors. In this study, a new model is developed for the simulation of fluidized bed reactors by sequential modular approach. In the proposed model the bed is divided into several serial sections and the flow of the gas is considered as plug flow through the bubbles and perfectly mixed through the emulsion phase. In order to simulate the performance of these reactors, the hydrodynamic and reaction submodels should be integrated together in the medium and facilities provided by industrial simulators to obtain a simulation model. The performance of the proposed simulation model is tested against the experimental data reported in the literature for various gas‐solid systems and a wide range of superficial gas velocities. It is shown that this model provides acceptable results in predicting the performance of the fluidized bed reactors. The results of this study can easily be used by industrial simulators to enhance their abilities to simulate the fluidized bed reactor properly.     

散式流态化到聚式流态化的混沌识别

散式流态化呈现出一种非常均匀的理想流态化结构 .聚式流态化具有明显的两相结构 .当流型从散式到聚式转变时 ,床层结构发生了变化 .本文在提出用最小二乘法同时计算关联维D2 和K2 熵的计算方法的基础上 ,就A类颗粒在不同气速下的压力波动 ,分析了从散式到聚式转变时所对应的床层结构的变化 ,解释了在不同尺度下两种流型所表现出的不同动力学行为 .以此为基础 ,提出了新的识别流型转变的方法 .     

散式流态化到聚式流态化的混沌识别

散式流态化呈现出一种非常均匀的理想流态化结构 .聚式流态化具有明显的两相结构 .当流型从散式到聚式转变时 ,床层结构发生了变化 .本文在提出用最小二乘法同时计算关联维D2 和K2 熵的计算方法的基础上 ,就A类颗粒在不同气速下的压力波动 ,分析了从散式到聚式转变时所对应的床层结构的变化 ,解释了在不同尺度下两种流型所表现出的不同动力学行为 .以此为基础 ,提出了新的识别流型转变的方法 .     

Modeling a fluidized bed reactor by integrating various scales: Pore,particle, and reactor

This work proposes a novel population-balance based model for a bubbling fluidized bed reactor. This model considers two continuum phases: bubble and emulsion. The evolution of the bubble size distribution was modeled using a population balance, considering both axial and radial motion. This sub-model involves a new mathematical form for the aggregation frequency, which predicts the migration of bubbles from the reactor wall toward the reactor center. Additionally, reacting particles were considered as a Lagrangian phase, which exchanges mass with emulsion phases. For each particle, the variation of the pore size distribution was also considered. The model presented here accurately predicted the experimental data for biochar gasification in a lab-scale bubbling fluidized bed reactor. Finally, the aggregation frequency is shown to serve as a scaling parameter.     

Predictions on bubble and solids movement in laboratory polyethylene fluid beds as visualized by X-ray computer assisted tomography (CAT) scanning

Solid and gas distributions are tomographically quantified as a function of position with high resolution in a series of laboratory fluid beds containing air and polyethylene particles. The resolution used is 0.4 mm by 0.4 mm by 3 mm. The laboratory models are Plexiglas columns of 10 cm in diameter and the settling bed L/D ratios vary between one and three. Large particles (up to 1.5 mm in diameter) of high density polyethylene and linear low density polyethylene are used. The superficial gas velocities vary from the minimum fluidization velocity to 50 cm/s. In this paper, the analysis of fluid bed CAT scanner images is extended to show bubble, emulsion and dense phase distribution. The analysis is also used to determine the bubble diameter and to predict the flow direction of solid particles as well as the velocity of descending solids. The voidage frequency distributions of a bed at different gas flow rates are compared to each other and the voidage threshold values corresponding to gas, emulsion and dense phases are determined. These threshold values are used to prepare ternary images that clearly show the parts of the bed cross-section corresponding to bubble, emulsion and dense phases.     

An unsteady potential flow model of bubble-induced particle motion near a horizontal tube in a fluidized bed

An unsteady hydrodynamic model of bubble-induced particle motion near a horizontal tube immersed in a gas-fluidized bed is proposed. According to the model, a two-dimensional bubble rising past the tube is treated as a moving doublet so that particle motion relative to the bubble is analogous to the potential flow of a gas past a circular cylinder. Also, the condition that particles should not penetrate the tube wall is established using the method of images. The particle velocities induced by the rising bubble are used together with a numerical integration scheme to establish particle trajectories near the tube wall. Results of calculations are shown to compare qualitatively with experimental observations by others. Further calculations illustrate the effect of bubble size upon particle motion in the defluidized cap on the leeward side of the tube.

The proposed model could be used as a basis for estimation of emulsion phase residence time or improved interstitial gas velocity estimates required for heat transfer analyses.