Computational Fluid Dynamics Study of a Styrene Polymerization Reactor

The computational fluid dynamics (CFD) approach was adopted to simulate benzoyl peroxide (BPO)‐initiated styrene polymerization in a laboratory‐scale continuous stirred‐tank reactor (CSTR). The CFD results revealed the effects of non‐homogeneity and the short‐circuiting of the unreacted styrene and initiator on the reactor performance. The study also investigated the effects of the impeller speed and the residence time on the conversion and the flow behavior of the system. The CFD simulation showed that intense mixing remained confined to a small region near the impeller. With increasing impeller speed, it was found that the perfectly mixed region near the impeller expanded, thus reducing non‐homogeneity. Different contours were generated and exhibited the effect of the mixing parameters on the propagation rate and styrene conversion. The monomer and initiator conversions predicted with the CFD model were compared to those obtained with a CSTR model. The CFD model accounts for the non‐ideality behavior of the polymerization reactor, and hence conversion predictions are more realistic.     

Modeling of molecular weight and copolymer composition distributions for ethylene-propylene solution copolymerization

A comprehensive computational fluid dynamics (CFD) model was developed to investigate spatial distributions of molecular weight distribution (MWD) and copolymer composition distribution (CCD) for ethylene-propylene (EPM) copolymers in a bubble column reactor. The CFD approach incorporated Euler–Euler two-fluid model, copolymerization kinetics, and copolymer microstructural distribution model together by user-defined functions for ethylene-propylene heterogeneous copolymerization process. MWD and CCD distributions were calculated by introducing Flory's distribution and Stockmayer's distribution, respectively. CFD model results were validated with literature data. The multiphase hydrodynamics, interphase mass transfer, spatial–temporal variations of MWD and CCD distributions were analyzed. Both distributions are wider at the inlet of reactor for the inefficient mixing, but narrower at the outlet due to fully developed flow and polymerization. This model is beneficial to the improvement of polymer products and process control in industrial EPM reactor.     

Three-dimensional CFD model of the temperature field for a pilot-plant tubular loop polymerization reactor

A three-dimensional (3D) computational fluid dynamics (CFD) model, using an Eulerian-Eulerian two-fluid model which incorporates the kinetic theory of granular flow, the energy balance and heat transfer equations, was developed to describe the steady-state liquid-solid two-phase flow in a loop propylene polymerization reactor composing of loop and axial flow pump. The entire temperature field in the reactor was calculated by the model. The predicted pressure gradient data were found to agree well with the classical calculated data. Furthermore, the model was used to investigate the influences of the circulation flow velocity, the slurry concentration, the solid particle size and the cool water temperature on the temperature field in the reactor. The simulation results showed that the whole loop can be divided into four sections. In addition, the simulation results also showed that the continuous stirred-tank reactor (CSTR) assumption is invalid for the entire field in the loop reactor.     

一种连续流反应器内射流耦合搅拌流的混合特性

连续式搅拌反应器采用连续化工艺,可以保证生产过程的连续性,相较于传统反应器而言,连续式反应器内流场更复杂,进料口射流对于流场的影响较为明显。对传统的双层搅拌桨结构的微波反应釜进行连续化改造,基于计算流体力学CFD(Computational Fluid Dynamics)方法对不同射流方案下反应器内醇油混合液的流动及混合特性进行了数值模拟,得到反应器内混合液的流动特性和混合时间特征。结果表明：射流通过直接影响射流区的流场和改变反应器内的循环涡流位置间接影响全局流动;射流方向对于反应器内流型影响更大,逆时针射流时反应器内的速度梯度大,流体之间的剪切作用更强,混合性能最佳,相较于传统的间歇式搅拌反应器,混合时间缩短了33%。     

A coupled CFD-population balance approach for nanoparticle synthesis in turbulent reacting flows

This paper investigates the first part of a two-stage methodology for the detailed fully coupled modelling of nanoparticle formation in turbulent reacting flows. We use a projected fields (PF) method to approximate the joint composition probability density function (PDF) transport equation that describes the evolution of the nanoparticles. The method combines detailed chemistry and the method of moments with interpolative closure (MoMIC) population balance model in a commercial computational fluid dynamics (CFD) code. We show details of the implementation and present an extensive set of numerical experiments and validation. We consider the example of the chloride process for the industrial synthesis of titania. We show good agreement with experimental data and present fully coupled detailed chemistry CFD simulations of nanoparticle formation in a representative ‘slot’ reactor geometry. The simulations show that inception occurs in a mixing zone near the reactor inlets. Most of the nanoparticle mass is due to surface growth downstream of the mixing zone with a narrower size distribution occurring in the regions of higher surface growth. The predicted temperature and particle properties are compared to a perfect mixing case. The implications for the second part of the methodology, where it is proposed to post-process the data using a more detailed particle model, are discussed critically.     

CFD analysis of turbulence non-homogeneity in mixing vessels: A two-compartment model

A two-compartment model has been developed for calculating the droplet/particle size distribution in suspension polymerization reactors by taking into account the large spatial variations of the turbulent kinetic energy and its dissipation rate in the vessel. The two-compartment model comprised two mixing zones, namely an impeller zone of high local energy dissipation rates and a circulation zone of low kinetic energy. Computational fluid dynamics (CFD) was employed for generating the spatial distribution of energy dissipation rates within an unbaffled mixing vessel agitated by a flat two-blade impeller. A general methodology was developed for extracting, from the results of the CFD simulations, the volume ratio of the impeller over the circulation zone, the ratio of the average turbulent dissipation rates in the two zones, and the exchange flow rate between the two compartments. The effect of agitation rate, continuous phase viscosity, impeller diameter, and mixing vessel scale on the two-compartment model parameters was elucidated. The two-compartment model was then applied to a non-homogeneous liquid-liquid dispersion process to calculate the time evolution of the droplet size distribution in the mixing vessel. An excellent agreement was obtained between theoretical and experimental results on droplet size distributions obtained from a laboratory-scale reactor operated over a wide range of experimental conditions.     

Mixing performance comparison of milliscale continuous high‐shear mixers

Mixing performance of two continuous flow millilitre‐scale reactors (volumes 9.5 mL and 2.5 mL) equipped with rotor‐stator mixers was studied. Cumulative residence time distributions (RTD) were determined experimentally using a step response method. Distributions were measured for both reactors by varying impeller speed and feed flow rate. The mixing effect was determined by measured RTDs. Computational fluid dynamics (CFD) were used to verify that the residence time distribution in the measurement outlet agreed with the outlet flow. The mixing power of both reactors was determined using a calorimetric method. The reactor inlet flow rate was found to affect mixing performance at 1–13 s residence times but the effect of impeller speed could not be noted. Both milliscale reactors are close to an ideal continuous stirred‐tank reactor (CSTR) at the studied impeller speed and flow rate ranges. The specific interfacial area was found to depend on the reactor inlet flow rate at constant impeller speed for the case of copper solvent extraction.

     

Continuous emulsion polymerization of vinyl acetate. Part: II Parameter estimation and simulation studies

Conversion data obtained over a wide range of operation of a continuous latex reactor for vinyl acetate polymerization were used to estimate the unknown kinetic parameters of a transient CSTR reactor model. Conversion-time histories were adequately fitted by models of two levels of sophistication: a comprehensive model which solves for the age distribution function of polymer particles, and a simplified model that neglects the effect of particle size distribution for the case of continuous particle nucleation. These models were then used for simulation and control studies in an attempt to devise a practical control strategy⁽¹¹⁾. The existence of sustained oscillations was investigated by examining the behavior of the state variables in the phase-plane.     

氯化法钛白氧化反应器气体错流混合

氧化反应器是氯化法制取钛白粉的关键设备，混合区的流场设计直接影响反应产品TiO₂颗粒的质量（如粒径和粒径分布）.利用无干扰流场测试技术——粒子图像测速仪（PIV）研究了不同气体错流混合区的结构设计对混合区域流场的影响，考察了气流动量比、射流狭缝宽度以及射流角度对混合区流场的影响.结果表明，较大的气流动量比、窄射流狭缝宽度和接近90°的射流能获得更好的混合区速度分布.进一步利用计算流体力学（CFD）手段对相应的流场进行了模拟，与PIV实验结果吻合很好，验证了模型对冷态流动的预测能力.     

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     

Three‐dimensional CFD‐PBM coupled model of the temperature fields in fluidized‐bed polymerization reactors

A three‐dimensional (3‐D) computational fluid dynamics model, coupled with population balance (CFD‐PBM), was developed to describe the gas–solid two‐phase flow in fluidized‐bed polymerization reactors. The model considered the Eulerian–Eulerian two‐fluid model, the kinetic theory of granular flow, the population balance, and heat exchange equations. First, the model was validated by comparing simulation results with the classical calculated data. The entire temperature fields in the reactor were also obtained numerically. Furthermore, two case studies, involving constant solid particle size and constant polymerization heat or evolving particle‐size distribution, polymerization kinetics, and polymerization heat, were designed to identify the model. The results showed that the calculated results in the second case were in good agreement with the reality. Finally, the model of the second case was used to investigate the influences of operational conditions on the temperature field. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

Numerical simulation of liquid-solid two-phase flow in a tubular loop polymerization reactor

Understanding hydrodynamics of tubular loop reactors is crucial in proper scale-up and design of these reactors. Computational fluid dynamics (CFD) models have shown promise in gaining this understanding. In this paper, a three-dimensional (3D) CFD model, using a Eulerian-Eulerian two-fluid model incorporating the kinetic theory of granular flow, was developed to describe the steady-state liquid-solid two-phase flow in a tubular loop propylene polymerization reactor composing of loop and axial flow pump. Corresponding simulations were carried out in the commercial CFD code Fluent. The entire flow field in the loop reactor was calculated by the model. The predicted pressure gradient data were found to agree well with the classical calculated data. Furthermore, the model was used to investigate the influences of the circulation flow velocity and the sold particle size on the solid hold-up. The simulation results showed that the solid hold-up has a relatively uniform distribution in the loop reactor at small particles in volume and high-circulation flow velocities.     

Evaluation of experimental techniques to validate numerical computations of the hydraulics inside a UV bench-scale reactor

Computational fluid dynamics (CFD) is widely used to predict the hydraulics in environmental systems, but the validity of these predictions continues to receive attention. The hydraulics of a UV bench-scale reactor was evaluated by numerical and experimental techniques. Different experimental techniques were used to examine the hydraulics: salt injection to measure the residence time distribution, dye injection to visualize the mixing patterns, and LDA to measure the local velocity profiles. The combination of these measurements techniques provides information in unprecedented detail of the hydraulics inside UV systems. A CFD model with a standard k?ε turbulence model was used for comparison with the experimental results. The main flow patterns were predicted well. The largest differences were found at regions in the reactor where recirculation occurred, for example in the wake region of a lamp. Also, the CFD model predicted a larger mixing over the flow cross-section, resulting in a narrower residence time distribution.     

全混流反应器内流动规律模拟研究

研究了一种接近全混流的小型气固相反应器,可以用于在实验室研究时需要实现全混流接触状态的气固相反应的研究.采用计算流体力学软件(CFD)进行模拟得到最优结构,其结构包括1个圆锥形反应器主体,4个连接在反应器主体底部的进料口,1个连接在反应器主体上部的出料口.气体从4个进料口进入,催化剂在流动过程中从中部掉落,形成气体水平...     

Experimental study and computer simulation of a two-stage continuous polymerization process for the production of methyl methacrylate

The two major problems encountered in industrial liquid-phase addition polymerization are: the heat released by highly exothermic reactions and the great increase in viscosity with conversion. The high rate or heat generation, coupled with the low thermal diffusivity of the reacting system, often lead to thermal runaway. Even with the process kept under marginal control, large temperature variations broaden the product molecular-weight distribution. Temperature control is particularly difficult in the Trommsdorff region, where reaction rate rapidly increases as temperature rises and viscosity builds up. A two-stage process is developed in this work to attack these problems and to achieve continuous operation of poly(methyl methacrylate) bulk polymerization. This process utilizes a continuous stirred-tank reactor (CSTR) as a first-stage prepolymerizer and a spray tower as the second-stage finishing reactor. Use of a CSTR offers good temperature control and product uniformity during the early stages of reaction and eases delivery of the reacting system to the second stage at the desired conversion and molecular-weight level. Spraying the partially polymerized mixture into the tower as fine droplets prior to the onset of gel effect eliminates the problems of transporting, agitating, and mixing a reacting system with a rapidly increasing viscosity. Heat of reaction is efficiently removed by a countercurrent stream of nitrogen in the tower, in direct contact with the falling droplets. The high surface-to-volume ratio of these small droplets facilitates heat transfer, and the problem of heat buildup can be efficiently controlled. Products from the bottom of the tower can then be melt-processed by conventional methods, such as extrusion. Experiments performed in the laboratory have demonstrated the feasibility of this proposed concept. Process optimization was in no way achieved due to serious space and equipment limitations. The process was thus further examined by computer simulation and model parameter sensitivity study. A practical design was recommended based on the model predictions.     

Modeling of branching density and branching distribution in low-density polyethylene polymerization

Low-density polyethylene (ldPE) is a general purpose polymer with various applications. By this reason, many publications can be found on the ldPE polymerization modeling. However, scission reaction and branching distribution are only recently considered in the modeling studies due to difficulties in measurement and computation of scission effect and branchings of polymer. Our previous papers [Kim, D.M., et al., 2004. Molecular weight distribution modeling in low-density polyethylene polymerization; impact of scission mechanisms in the case of CSTR. Chemical Engineering Science 59, 699-718; Kim, D.M., Iedema, P.D., 2004. Molecular weight distribution modeling in low-density polyethylene polymerization; impact of scission mechanisms in the case of a tubular reactor. Chemical Engineering Science, submitted for publication] are concerned with the scission reaction during ldPE polymerization and its effect on molecular weight distribution (MWD) of ldPE for various reactor types. Here we consider branching distributions as a function of chain length for CSTR and tubular reactor processes. To simultaneously deal with chain length and branching distributions, the concept of pseudo-distributions is used, meaning that branching distributions are described by their main moments. The computation results are compared with properties of ldPE samples from a CSTR and a tubular reactor. Number and weight average branchings and branching density increase as chain length increases until the longest chain length. The concentrations of long chain branching (LCB) are close to those of first branching moment in both CSTR and tubular reactor systems. The branching dispersity, a measure for the width of the branching distribution at a certain chain length, has the highest value at shorter chain length and then monotonously decreases approaching to 1.0 as chain length increases. Excellent agreements in branching dispersities between calculation with branching moments and prediction with assumption of binomial distribution for a tubular reactor and CSTR processes show that the branching distribution follows a binomial distribution for both processes.     

Free radical polymerization with long chain branching: continuous polymerization of vinyl acetate in t-butanol

Vinyl acetate was polymerized in a continuous stirred tank reactor (CSTR) at 60°C in t-butanol solution. Mean residence times ranged from 1.35 to 7.2 hr; steady state conversions ranged from 15 to 61%. Molecular weights $\text{M}$_n and $\text{M}$_w were measured and interpreted in terms of a kinetic model developed from batch studies and the state of local mixing in the reactor. Good macroscopic mixing was confirmed by tracer studies and measurements of conversion vs time during the start-up period and at steady state. The molecular weights obtained at high conversions agreed more closely with predictions based upon a locally segregated state than with those based on complete molecular mixing. However, calculations based on agitation and diffusion rates raised serious questions about the validity of the segregation model for this polymerization. Other factors, some chemical and some related to the agitation, may be important, but the problem of predicting molecular structure remains unresolved.     

A numerical study on the effects of acidic catalyst on the polymerization of nylon-6

The effects of acetic acid on the polymerization characteristics of nylon-6 are investigated in a reactor model that consists of a continuous flow stirred tank reactor (CSTR) and a tubular reactor connected in series. Mathematical models for the CSTR and the tubular reactor have been established and solved by numerical methods. In the CSTR, the monomer conversion and the molecular weights are increased as the feed acetic acid concentration is increased. In the tubular reactor, the acid acts as both a catalyst and a modifier for the polymerization reaction. The effects of the feed acetic acid content on the zeroth, first and second moments and the polydispersity index of the polymer have been discussed.     

连续进出料鼓泡流化床颗粒停留时间分布

针对双流化床气化或双床热解气化工艺中鼓泡床反应器的设计,采用脉冲法研究了Geldart B类固体颗粒在连续颗粒进料和出料的矩形流化床内的停留时间分布(RTD),考察了气速、床料高度、粒径、物料流率等操作参数对RTD的影响. 结果表明,物料流率、床料高度、粒径是影响颗粒RTD的主要因素,而气速则是次要因素. 随物料流率和粒径增加,鼓泡床内颗粒流动向平推流靠近;随床料高度增加,物料在床内的混合更加充分,颗粒流动向全混流靠近. 根据实验结果,推荐采用比理想平推流时间低9%~18%计算平均颗粒停留时间.     

对二甲苯氧化反应器非均匀混合模型

对二甲苯氧化是一个复杂的气-液-固三相反应过程。今根据实验测取的对二甲苯氧化反应动力学关系与数据,建立了工业氧化反应器的非均匀混合模型,用以考察气、液相的混合状况及其对反应的影响。模型采用三区串联加区问返混的结构,区间返混参数由工业反应器实测轴向温度分布拟合确定。计算表明,釜内液相混合接近全混、流,而气相氧浓度存在明显的轴向梯度：溶剂蒸发与液相混合相互竞争造成反应器内有一定的温度梯度：氧浓度梯度和温度梯度共同作用使得CO2．CO量增多,燃烧副反应加剧,这其中氧浓度梯度起主要作用。