Dynamic Behavior of Industrial Gas Phase Fluidized Bed Polyethylene Reactors under PI Control

A mathematical model describing the UNIPOL process for the production of polyethylene in the gas phase using a Ziegler‐Natta catalyst in a bubbling fluidized bed is used to analyze the major processes determining the behavior and performance of these industrially important units. The investigation shows that both static bifurcation (multiplicity of the steady states) as well as dynamic bifurcation (stable/unstable periodic attractors) behavior cover wide regions of the design and operating parameter domain. A conventional proportional‐integral (PI) control policy is suggested to stabilize the behavior of the system. The control philosophy covers both aspects of stabilizing unstable steady states as well as compensating for external disturbances. It is shown that for some controller configurations and set points the controlled process can go through a period doubling sequence leading to chaotic strange attractors. The industrial implications of the phenomena discovered for both the open loop (uncontrolled) as well the closed‐loop (controlled) systems are analyzed.     

Chaotic Behavior of Industrial Fluidized‐Bed Reactors for Polyethylene Production

Recent theories of bifurcation and chaos are used to analyze the dynamic behavior of the UNIPOL process for the production of polyethylene in the gas phase using the Ziegler‐Natta catalyst. Dynamic behavior covers wide regions of the design and operating parameters domain of this industrially important unit. A conventional proportional‐integral (PI) controller was implemented to stabilize the desired operating point on the unstable steady‐state branch. The presence of the PI controller stabilized the desired unstable steady‐state regions to a certain range of catalyst injection rate, by contrast, it is found out that the controlled process can go through a period doubling sequence leading to chaotic strange attractors. The practical implications of this analysis can be very serious, since chaos is shown to exist right near the desired operating point where high polyethylene production rates can be achieved     

Bifurcation Analysis of the Fluidized Bed Polyethylene Reactor with Internal Cooler

A mathematical model has been developed to simulate a gas‐phase ethylene polymerization reactor with internal cooler. The model was analyzed to determine the effects of reactor operating conditions on dynamics and stability. The reactor model employed assumed that both the gas and polymer phase in the reactor are well mixed. Comparing the present model to one with external heat exchanger confirms that, in either form, gas‐phase polyethylene reactors are prone to show unstable steady states, limit cycles and excursions toward unacceptably high temperature steady states. It was also observed that, with internal cooler, minor design changes in the cooler area available for heat transfer and in the inlet temperature of the coolant have a significant effect on the low stable steady state range of catalyst feed rates. With internal cooler, the suitable operating range increased with the increase in the area available for heat transfer. This effect is insignificant in the case of a reactor with external heat exchanger. Manipulating the reactor coolant inlet temperature and/or gas velocity can increase the stability range in the reactor with internal cooler as against one with external heat exchanger.     

Total Solution of the Gibilaro and Rowe Model for a Segregating Fluidized Bed

This study re‐examines the one‐dimensional equilibrium model of Gibilaro and Rowe (1974) for a segregating gas fluidized bed. The model was based on volumetric jetsam concentration and divided the bed contents into bulk and wake phases, taking account of bulk and wake flux, segregation, exchange between the bulk and wake phases, and axial mixing. Due to the complex nature of the model and its unstable solution, the lack of computing power at the time prevented the authors from doing little more than the analytical solutions to specific cases of this model. This paper provides a numerical total solution and allows the effect of the respective parameters to be compared for the first time. There is also a comparison with experimental results, which showed a reasonable agreement.     

Synthesis of High‐Quality,Double‐Walled Carbon Nanotubes in a Fluidized Bed Reactor

Double‐walled carbon nanotubes (DWCNTs) were synthesized in a packed bed reactor (PBR) and a fluidized bed reactor (FBR) by cracking CH₄ on a Fe/MgO catalyst. It is observed that the dominant carbon product changes drastically from DWCNTs to multi‐walled CNTs along the axial direction of PBR. The studies indicated that the high concentration of H₂ from the high conversion of CH₄ causes the quick reduction and sintering of the iron catalyst and inhibits the nucleation of DWCNTs. Based on these results, the batch or continuous feeding mode of small amounts of catalyst was adopted in a FBR to maintain a high space velocity of CH₄ and to inhibit the negative effect of excess H₂. Finally, a DWCNT product with a specific surface area of 950 m²/g and a purity of 98 %, was obtained.     

Modeling of Volatiles Combustion and Alkali Deposition in a Fluidized Bed Coal Combustor

A simplified kinetic model, coupled with the bed hydrodynamics and a volatile evolution region within the bed, was formulated to predict the extent of gas‐phase combustion in a laboratory‐scale fluidized bed coal combustor (FBC). A close examination has also been made to highlight the relevance of the reducing/oxidizing environment (computed with the present theoretical model) in relation to FBC materials exposed to fireside corrosion at high temperature, under various operating conditions. The model results revealed that, for high‐volatile coals with particle diameters (d_c) of 1–3 mm and sand particle size (d_s) of 0.674 mm, over one third of the original coal volatiles may burn in the freeboard region at bed temperature (T_b) ≤ 850 °C and excess air (XSA) ≤ 10 %. These values, together with the computed equilibrium conversion of alkali chlorides to sulfates, may suggest that sodium and potassium salts present in the vapor phase are likely to accelerate hot corrosion of heat exchange tubes above the bed when an FBC operates at T_b ≤ 840 °C, XSA ≤ 20 %, d_c < 5 mm, d_s < 1 mm, H_s ≤ 0.2 m and U_o < 1 m/s. Conversely, at T_b > 890 °C and XSA > 30 %, high oxidation rates may be present for the in‐bed tubes. At these higher T_b values and XSA < 10 %, a sulfidation mechanism presumably influences the extent of corrosion on the metallic components within the bed.     

The Segregation in the Binary‐Solid Liquid Fluidized Bed

A new mechanism is proposed to interpret the phenomena observed in the liquid fluidization of the binary particle mixture. Two main factors, the bulk density and voidage fluctuation, are considered to determine the position of the layer of particles in the bed. The new model successfully explains the layer inversion phenomenon and mixing‐segregation equilibrium, which is the result of the above two factors acting together. The model also proves that bulk density is a simple and reliable method to predict the inversion velocity by comparison with the experimental results reported in the literature.     

Bubbling and Bed Expansion Behavior Under Vibration in a Gas‐Solid Fluidized Bed

The effect of vibration on the flow patterns and fluidization characteristics including the minimum fluidization velocity (u_mf), the void fraction (ϵ_mf) at u_mf and the bed expansion ratio were examined. The powders used were spherical glass beads and their diameters were 6, 20, 30, 60 and 100μm. For group A powders, the manner in which the vibration affects the bubble formation was examined from the bed expansion ratio and the index of n/4.65. The area of the homogeneous fluidization region was also observed. The homogeneous fluidization region was broadened at a certain vibration strength, where the value of n/4.65 was a minimum. The bubble formation was observed even for 20μm powder (group C), at large vibration strengths and at high gas velocities. Under such conditions, the bed expansion ratio increased suddenly due to bubble formation. The bubbles broke the irregular bed structure, including various properties of agglomerates. Although the channel breakage was dominant flow pattern for group C powders, the bubbles also played an important role in the improvement of the fluidization.     

Reduction of the Volatile Matter Evolution Rate from a Plastic Pellet during Bubbling Fluidized Bed Pyrolysis by Using Porous Bed Material

Rapid volatile matter evolution from high‐volatile fuels such as wastes and biomass is one of problems associated with fluidized bed incinerators and gasifiers. When volatile matter evolves rapidly in the vicinity of the fuel feed point, the mixing of volatile matter with reactant gas is poor, and therefore, unreacted volatile matter is expected to be released from the reactor. In the present work, reduction of the volatile matter evolution rate was attempted by employing porous solids as bed materials instead of nonporous sand. The effect of bed material on the onset of devolatilization was measured by use of a bench‐scale bubbling fluidized bed reactor. Volatile matter capture by the porous solids (capacitance effect) and the heat transfer rate within the bed, both of which affect volatile matter evolution rate, were also measured. Four types of porous solids, both with and without capacitance effect, were employed as the bed material. By employing porous solids without capacitance effect, the contributions of reduced heat transfer rate and capacitance effect to the delay of volatile matter evolution can be evaluated separately. For porous bed materials with a moderate capacitance effect (volatile matter capture of up to 20 %), the delay of the onset of devolatilization, which was measured by detecting the flame combustion of the volatile matter, was explained by the lower heat transfer between the fuel and bed. However, for a porous particle with high capacitance effect (volatile matter capture of 30 %), the capacitance effect also affected the delay of the onset of the flame combustion.     

Reduction of Devolatilization Rate of Fuel During Bubbling Fluidized Bed Combustion Using Porous Bed Material

Plastic waste combustion in bubbling fluidized bed combustors (BFBC) is characterized by the rapid devolatilization of the fuel. Noncombusted hydrocarbons are often formed, which have been reported to promote the formation of dioxins. In this work, porous bed material was employed instead of commonly used non‐porous sand to reduce the devolatilization rate. We measured (1) the heat transfer coefficient between an immersed object (brass sphere) and the bed and (2) the time required for the devolatilization of a plastic pellet after dropping it into the bed at 943 K. For porous particles we found a 30 % lower heat transfer coefficient, delayed onset of devolatilization and prolonged devolatilization time, compared with quartz sand. Therefore, porous particles were found to be effective in suppressing the rapid devolatilization of plastic waste.     

Modeling and Characterization of Air Emissions from Laboratory and Industrial Fluidized Beds

A fluidized bed model using several elutriation correlations was developed and tested against an operating fluidized bed used in a Fluidized Catalytic Cracker Unit (FCCU) and a 1:8.5 scale laboratory system. It was found that there was little variation between the emission rates predicted using different elutriation correlations, although the newly developed equations were slightly more accurate for the laboratory‐scale system. Although total emission rates were predicted with reasonable accuracy, the actual volatility and fluctuations seen in real fluidized beds emissions were not predicted. When the model was used to predict particle emission from the industrial FCCU, they preformed poorly, grossly overestimating the actual levels. It was determined that the attrition terms used in emission modeling were inappropriate and that the model preformed better without them, but still overestimated the actual emissions. This overestimation was greater in the industrial system compared with the smaller laboratory system. It was also found that the older elutriation terms were better for predicting industrial emissions compared with those of the smaller scale units.     

A Practical Method to Estimate the Bed Height of a Fluidized Bed of Fine Particles

Knowledge of both dense bed expansion and freeboard solids inventory are required for the determination of bed height in fluidized beds of fine particles, e.g., Fluidized Catalytic Cracking (FCC) catalysts. A more accurate estimation of the solids inventory in the freeboard is achieved based on a modified model for the freeboard particle concentration profile. Using the experimentally determined dense bed expansion and the modified freeboard model, a more practical method with improved accuracy is provided to determine the bed height both in laboratory and industrial fluidized beds of FCC particles. The bed height in a fluidized bed can exhibit different trends as the superficial gas velocity increases, depending on the different characteristics of the dense bed expansion and solids entrainment in the freeboard. The factors that influence the bed height are discussed, showing the complexity of bed height and demonstrating that it is not realistic to determine the bed height by a generalized model that can accurately predict the dense bed expansion and freeboard solids inventory simultaneously. Moreover, a method to determine the bed height, based on axial pressure fluctuation profiles, is proposed in this study for laboratory fluidized beds, which provides improved accuracy compared to observation alone or determining the turning points in the axial pressure profiles, especially in high‐velocity fluidized beds.     

Expansion Behavior of a Binary‐Solid Liquid Fluidized Bed with Large Particle Size Difference

The overall expansion of two dissimilar solid particle species with over a tenfold difference in their size and substantial density difference is investigated here for different compositions of the fluidized bed. Contrary to the widely held notion that the total bed height would be the sum of the heights of the two segregated mono‐component beds, the actual bed heights were, in fact, found to be lower. This volume contraction is found to strongly depend upon the mixing behavior prevailing in the binary‐solid fluidized bed. At the complete mixing of the two solid species, the bed‐contraction versus liquid velocity profile shows a global maximum. As a result, the overall bulk density profiles are similarly affected. Moreover, it is found here that correlations meant for predicting the porosity of the packing of binary particle mixtures can be satisfactorily extended to binary‐solid fluidized beds where solid species differ significantly in size.     

Influence of Effective Particle Porosity on Vacuum Fluidized Bed Drying

A series of vacuum fluidized bed drying experiments was carried out employing particles with distinct effective porosities. The experiments showed that decreasing the operating pressure as well as increasing the operating temperature produces higher drying rates in both drying periods. In all cases, the enhancement of the drying rates was found to be more significant in the case of particles with higher effective porosities. It is concluded that lower operating pressures as well as higher operating temperatures help to reduce the formation of air pockets in the pores and postpone the onset of the pendular state, enhancing the capillary action and the drying rates.     

Effect of Polymer Particle Size and Inlet Gas Temperature on Industrial Fluidized Bed Polyethylene Reactors

Static and dynamic bifurcation behaviors dominate the operation of fluidized bed catalytic reactors for the production of polyethylene (UNIPOL Process) and have important implications on the safe operating temperature and polyethylene production rate. The investigations show that the multiplicity of the steady state phenomenon covers a wide range of parameters together with the phenomenon of periodic oscillations with sharply changing amplitudes with a change of the chosen bifurcation parameter. In some cases, the periodic branches terminate through periodic limit point (PLPs), while in other cases it terminates homoclinically. A detailed parameteric investigation using two-parameter continuation diagrams for the loci of static and Hopf bifurcation points as well as one parameter bifurcation diagrams shows that it is possible to increase the productivity of the unit considerably without exceeding the constraints of the polymer melting point. Gas feed temperature, catalyst feed rate, and polymer particle size distribution are important operating parameters in polyethylene fluidized bed reactors. Gas velocity plays a significant role in keeping the fluidized bed bubbling in addition to the fact that it acts as a cooling media by removing excess heat generated from the polymerization reaction. The kinetic behavior of the catalyst and effect of reactor temperature on product properties require, in some cases, operating just below the softening point of the polymer which requires a suitable controller to avoid polymer melting.     

基于CPFD的流化床数值模拟

流化床的数值模拟在流化床结构设计和放大中有着重要作用,目前得到广泛应用的多种基于CFD的数学模型在工业尺度的计算中存在不同缺陷。本文引入一种基于CPFD理论的方法,对射流流化床和鼓泡流化床分别进行了数值模拟,结果显示该方法能够有效模拟大量颗粒的两相流体系,反映颗粒和流体的真实运动状态。     

流化床反应器分布板开孔率计算方法初探

流化床反应器分布板开孔率的确定多基于经验,缺乏理论计算依据。通过流化床反应器研究开发的大量实践,总结归纳了分布板开孔率的几种计算方法,并结合实验对这些方法进行了讨论。     

A Grade Transition Strategy for the Prevention of Melting and Agglomeration of Particles in an Ethylene Polymerization Reactor

To satisfy the diverse product quality specifications required by the broad range of polyethylene applications, polymerization plants are forced to operate under frequent grade transition policies. During the grade transition, the reactor temperature must be kept within the narrow range between the gas dew point and the polymer melting point, otherwise the particles melt or agglomerate inside the reactor. In the present study, a dynamic well‐mixed reactor model is used to develop a grade transition strategy to prevent melting and agglomeration of particles in an ethylene polymerization reactor. The model predicts the conditions under which the temperature of the reactor is outside the allowable range in continuous grade transition. Manipulation of feed flow and cooling water flow rates has shown that the reactor temperature cannot be maintained within the allowable range. Hence, a semi‐continuous grade transition strategy is used for this case so that the temperature is maintained within the allowable range. In addition, several continuous and semi‐continuous grade transition strategies for the production of linear low‐density polyethylene (LLDPE), medium density polyethylene (MDPE), and high‐density polyethylene (HDPE) are compared.