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.     

Electrostatics and gas phase fluidized bed polymerization reactor wall sheeting

Reduction of electrostatic charge accumulation in fluidized bed polymerization reactors can reduce the frequency of reactor wall sheeting incidents and decrease the cost of operating fluidized bed polymerization reactors. The accumulation of excess electrostatic charge in fluidized bed polymerization reactors causes the fluidized polymer particles to adhere to the reactor wall and form wall sheets. Reactor wall sheets are described in order to characterize the problem. Electrostatic forces are compared to other forces influencing fluidization, such as drag forces and van der Waals forces. Literature values of measured particle electrostatic charges are compared to the maximum theoretical values predicted by Gauss’ law applied to the particles and to the entire fluidized bed. Electrostatic charge mitigation techniques are reviewed and future research areas are suggested based on the theoretical analysis and identified knowledge gaps.     

Characterization of dynamic behaviour of the continuous phase in liquid fluidized bed

The dynamic behaviour of the continuous phase in liquid solid fluidized bed is characterized through velocity measurements by laser anemometry at the top of the bed. The experiments were conducted using glass particles of 2, 4 and 8 mm diameter fluidized by water. The root mean square (RMS) of axial velocity fluctuations presents a maximum value at porosity around 0.7 and increases with particle diameter. When compared to the fixed bed situation, we observe an enhancement of the agitation probably due to the added mass effect which plays the role of a turbulence promoter. The spectra analysis of the velocity time series has revealed a specific spectral dynamic of liquid fluidized bed for the higher frequency range which does neither follow strictly the Kolmogorov law nor a Brownian process power law. A time frequency-scale decomposition combined to an autocorrelation analysis of velocity signal was pertinent to capture the impact of porosity waves and cooperative movements of particles on the liquid phase dynamic, and to characterize these coherent structures by low frequency scales (below 1 Hz). The results compare well with the available data obtained directly from void propagation studies by light transmission techniques. Moreover, the high frequency scales have been found random and linked to the small scale movements of the particles. We have shown, when possible, the similarity of behaviour between the liquid and the dispersed phase dynamics through the comparison of some characteristics.     

Encapsulation of nanoparticles by polymerization compounding in a gas/solid fluidized bed reactor

For the first time, a fluidized bed reactor was used for encapsulating nanoparticles by the polymerization compounding approach using Ziegler–Natta catalysts. The polymerization reaction was carried out using a solvent-free process in a gas-phase reactor. This direct gas–solid reaction greatly simplified collecting the particles of interest after polymerization because none of the extra steps often found in encapsulation processes, such as filtering and drying, were performed in this work. The grafting of the catalyst to the original surface of particles was confirmed by X-ray photoelectron spectroscopy. Micrographs obtained by transmission electron microscopy confirmed the presence of a thin layer of polymer, in the order of a few nanometers, around the particles. The thickness of this coating was affected by the operating conditions of the process. The characterization of the modified particles with electron microscopy also revealed that zirconia nanoparticles tend to be coated in an agglomerated state, whereas aluminum particles were mostly individually encapsulated by the polymer. In addition, the effects of temperature and pressure were studied on the encapsulation process and a kinetic analysis was presented based on the available models in the literature. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Minimum fluidization velocity and gas holdup in gas–liquid–solid fluidized bed reactors

Experiments were performed to study the hydrodynamics of a cocurrent three‐phase fluidized bed with liquid as continuous phase. Based on the 209 experimental data (with four liquid systems and five different particles) along with 115 literature data from six different sources on minimum fluidization velocity, a unique correlation for the estimation of minimum fluidization velocity in two‐phase (u_g = 0) as well as in three‐phase systems is developed. A data bank consisting of 1420 experimental measurements for the fractional gas phase holdup data with a wide range of variables is used for developing empirical correlations. Separate correlations are developed for two flow regimes observed in this present work. The proposed correlations are more accurate and simpler to use. © 2002 Society of Chemical Industry     

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.     

A new model for bubbling fluidized bed reactors

Various mathematical models have been proposed in the past for estimating the conversions of reactant gases in fluidized bed reactors. A new mathematical model is being proposed in this paper that gives relatively better results compared to the prevailing models for bubbling fluidized bed reactors utilizing Geldart B particles. The new model is named as JSR (Jain, Sathiyamoorthy, Rao) model and it is a modified version of bubble assemblage model of Kato and Wen (1969). This paper discusses the development of JSR model and its verification by using data from chemical engineering literature on fluidization and also experimental data from hydrochlorination of silicon in a fluidized bed reactor. The new model is tested for five processes having operating temperatures from 130 °C to 450 °C, operating velocities from 0.019 m s⁻¹ to 0.19 m s⁻¹ and solid particle sizes from 65 to 325 mesh.     

Packed‐bed reactor for short time gas phase olefin polymerization: Heat transfer study and reactor optimization

A specially conceived packed‐bed stopped flow minireactor (3 mL) suitable for short gas phase catalytic reactions has been used to study the start‐up of ethylene homopolymerization with a supported metallocene catalyst. Focus has been put on the heat transfer characteristics of the supported catalysts and on understanding the relationship between the initial rate and the relative gas/particle velocities and the influence of particle parameters in the packed bed. We performed a comprehensive study on the influence of various physical parameters on the heat transfer regime at start up conditions. The catalyst activity as well as the polymer morphology is shown to be dependent on heat transfer regime. The knowledge thus obtained is applicable to industrial problems like catalyst injection in fluidized beds and helps preventing experimental artifacts due to overheating in following studies. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

气固流化床反应器内多相流CFD的研究进展

流化床反应器因其优良的性能而广泛应用于化工、石油、冶金、农业和环保等诸多领域。传统的过程研究与设计方法需要耗费大量的人力和物力,且产业化周期较长。多相流CFD方法很好地解决了这些问题。随着数值计算方法和计算机软硬件技术的不断发展,多相流CFD方法必将会有更广阔的前景。     

Forced bed mass oscillations in gas–solid fluidized beds

A second-order mechanical vibration model is proposed to explain the oscillation phenomena and pressure fluctuations in gas–solid fluidized beds. Experiments were conducted in a 0.1-m ID gas–solid fluidized bed driven by periodic gas pulses with the frequency varying from 0.2 to 10 Hz. Experimental results indicate that the proposed mechanical vibration model, which considers the pressure fluctuation as the results of the response of the fluidized bed to the external excitation forces related to the bubble behavior in the bed, can reasonably explain the pressure fluctuations of the gas–solid fluidized bed. The behavior of pressure fluctuations is correlated with characteristics of both the bed system and excitation forces.     

Two-phase modeling of a gas phase polyethylene fluidized bed reactor

A two-phase model is proposed for describing the behavior of a fluidized bed reactor used for polyethylene production. In the proposed model, the bed is divided into several sequential sections where flow of the gas is considered to be plug flow through the bubbles and perfectly mixed through the emulsion phase. Polymerization reactions occur not only in the emulsion phase but also in the bubble phase. Voidages of the emulsion and bubble phases are estimated from the dynamic two phase structure hydrodynamic model. The kinetic model employed in this study is based on the moment equations. The hydrodynamic and kinetic models are combined in order to develop a comprehensive model for gas-phase polyethylene reactor. The results of the model are compared with the experimental data in terms of molecular weight distribution and polydispersity of the produced polymer. A good agreement is observed between the model predictions and actual plant data. It has been shown that about 20% of the polymer is produced inside the bubble phase and as such cannot be neglected in modeling such reactors.     

Predictive radiation field modeling for fluidized bed photocatalytic reactors

A predictive model of the radiation distribution for fluidized bed photocatalytic reactors was proposed and solved by means of the Monte Carlo approach coupled with the ray tracing technique. This model considers the interaction between the photocatalytic TiO₂-coated spheres and the photons, taking into account the shadowing effect of the beads, the reflection on the surface of the spheres, and the absorption in the TiO₂ films. This radiation model is completely predictive and does not use any adjustable parameter. Modeling results indicate a strong influence of the bed expansion on the radiation distribution, with the shadowing effect of the beads being the main cause for this dependence. Increasing the bed expansion improves the uniformity of the radiation distribution in the reactor. Nevertheless, an excessively expanded bed would reduce the efficiency of the reactor because the transmittance of the bed increases and a fraction of photons leave the reactor without being absorbed by the TiO₂-coated spheres. The radiation model was evaluated in a laboratory-scale fluidized bed photocatalytic reactor that was designed and built for the elimination of organic pollutants from water streams. TiO₂-coated glass spheres with a diameter of 1.18 mm were used as photocatalyst. The model was validated by comparing the predicted values of the effective transmittance of the bed with experimental results measured under different bed expansions. The performance of the reactor was also assessed experimentally, showing a good efficiency for the photocatalytic degradation of formic acid as a model compound.     

A CFD‐PBM‐PMLM integrated model for the gas–solid flow fields in fluidized bed polymerization reactors

Although the use of computational fluid dynamics (CFD) model coupled with population balance (CFD‐PBM) is becoming a common approach for simulating gas–solid flows in polydisperse fluidized bed polymerization reactors, a number of issues still remain. One major issue is the absence of modeling the growth of a single polymeric particle. In this work a polymeric multilayer model (PMLM) was applied to describe the growth of a single particle under the intraparticle transfer limitations. The PMLM was solved together with a PBM (i.e. PBM‐PMLM) to predict the dynamic evolution of particle size distribution (PSD). In addition, a CFD model based on the Eulerian‐Eulerian two‐fluid model, coupled with PBM‐PMLM (CFD‐PBM‐PMLM), has been implemented to describe the gas–solid flow field in fluidized bed polymerization reactors. The CFD‐PBM‐PMLM model has been validated by comparing simulation results with some classical experimental data. Five cases including fluid dynamics coupled purely continuous PSD, pure particle growth, pure particle aggregation, pure particle breakage, and flow dynamics coupled with all the above factors were carried out to examine the model. The results showed that the CFD‐PBM‐PMLM model describes well the behavior of the gas–solid flow fields in polydisperse fluidized bed polymerization reactors. The results also showed that the intraparticle mass transfer limitation is an important factor in affecting the reactor flow fields. © 2011 American Institute of Chemical Engineers AIChE J, 58: 1717–1732, 2012     

Optimal grade transition and selection of closed-loop controllers in a gas-phase olefin polymerization fluidized bed reactor

To satisfy the diverse product quality specifications required by the broad range of polyolefin applications, polymerization plants are forced to operate under frequent grade transition policies. Commonly, the optimal solution to this problem is based on the minimization of a suitable objective function defined in terms of the changeover time, product quality specifications, process safety constraints and the amount of off-spec polymer, using dynamic optimization methods. However, considering the great impact that a given control structure configuration can have on the process operability and product quality optimization, the time optimal grade transition problem needs to be solved in parallel with the optimal selection of the closed-loop control pairings between the controlled and manipulated variables. In the present study, a mixed integer dynamic optimization approach is applied to a catalytic gas-phase ethylene-1-butene copolymerization fluidized bed reactor (FBR) to calculate both the “best” closed-loop control configuration and the time optimal grade transition policies. The gPROMS/gOPT computational tools for modelling and dynamic optimization, and the GAMS/CPLEX MILP solver are employed for the solution of the combined optimization problem. Simulation results are presented showing the significant quality and economic benefits that can be achieved through the application of the proposed integrated approach to the optimal grade transition problem for a gas-phase polyolefin FBR.     

The effect of pressure on fluidized bed behaviour

The influence of pressure on the behaviour of different particles fluidized by nitrogen was experimentally investigated. The powders used were mostly in Geldart's group B and the pressure was varied in the range 100 to 3500 kPa. The results for bed voidage and gas velocity at both the minimum fluidization and minimum bubbling conditions are compared with results of other authors and are discussed in the light of available correlations.     

Biodegradation of organic compounds in fluidized bed reactors

Biodegradation of organics in fluidized bed reactors was studied experimentally. Both single-substrate and mixed-substrate systems were considered. With the use of a previously developed biofilm model, parameters pertinent to the degradation of mixed-substrate systems and their single substrate system counterparts were evaluated and compared. Two approaches attempted to predict the degradation of a mixed-substrate system. One assumed independent biodegradaion and diffusion of individual substrates while the other used a lumped concentration approach. The latter approach was found to give better agreement with experiments than the former.     

Sequential modular simulation of circulating fluidized bed reactors

Bypassing the mathematical complexity of equation-oriented approaches in predicting the performance of chemical reactors has recently stimulated a significant amount of interest. Among chemical reactors, circulating fluidized bed reactors (CFBRs) have secured an important role in a broad range of applications in energy sectors due to their advantages, including high fluid-solid contact efficiency, uniform temperature, and enhanced heat and mass transfer rates. Accordingly, modelling and predicting the performance of these reactors is of great importance. In this study, a sequence-based model was developed to predict the behaviour of CFBRs. Complex phenomena in CFBRs were mimicked by two sub-models, namely the hydrodynamics module, which addressed the physical changes, and the reaction kinetics module, which described the chemical evolution of species. The performance of the proposed model was validated with a library of catalytic ozone decomposition experimental data in CFBRs. This work introduces a new infrastructure for modelling CFBRs, which may be combined with the current process simulation software, such as Aspen Plus©, for advanced process modelling applications.     

气固脉动流化床混合特性的研究

以小米、硅胶、绿豆等颗粒为实验物料,对脉动流化床的混合特性进行了冷态模拟实验。利用自制的活塞机构对床层中的物料进行取样,用筛分的方法对颗粒在床层中的分布浓度特性进行了分析和研究,探讨了气流速度、颗粒粒径、颗粒密度、脉动频率对物料混合的影响,并利用实验数据对混合/分离模型进行了验证,对颗粒的混合与分离做出了探讨。     

Steady state multiplicity of fluidized bed reactors. The solid-circulation model

A solid circulation model is used to investigate the steady-state multiplicity features of a fluidized bed reactor in which a single, first-order, exothermic reaction occurs. The model predicts that up to five steady-state solutions may exist. Numerical examples seem to indicate that at most two of the states are stable. The temperature profiles computed by the solid-circulation model are similar to those computed by the axial conductivity model. A regular perturbation expansion is used to prove that the axial-conductivity model and the corresponding Danckwerts boundary conditions are a special limiting form of the solid-circulation model attained when the rate of solid exchange between the bubbles and the dense phase is high.