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     

基于计算流体力学的气相烯烃聚合反应器模拟综述

气相聚合过程以流化床为核心反应器,其混合、传递和化学反应过程规律对工艺研发具有指导意义。计算流体力学是一种模拟流体流动的方法,可节省大量人力和物力并提供更全面的反应过程信息,在气固流态化领域得到广泛应用。基于计算流体力学的流态化模拟的难点在于如何建立能够恰当描述颗粒团聚过程的曳力模型,关于热量传递甚至聚合反应过程的模拟工作都是基于此发生的。随着计算机运算能力的提高,研究工业尺度的流化床反应器以及由粒径分布而带来的传递过程的影响可能成为模型广度及深度发展的方向。     

Modeling bubble column reactor with the volume of fluid approach: Comparison of surface tension models

This work aims at comparing surface tension models in VOF (Volume of Fluid) modeling and investigating the effects of gas distributor and gas velocity. Hydrodynamics of a continuous chain of bubbles inside a bubble column reactor was simulated. The grid independence study was first conducted and a grid size of 1.0 mm was adopted in order to minimize the computing time without compromising the accuracy of the results. The predictions were validated by comparing the experimental studies reported in the literature. It was found that all surface tension models can describe the bubble rise and bubble plume in a column with slight deviations.     

Effect of operating parameters inside circulating fluidized bed reactor riser with ring baffles using CFD simulation and experimental design analysis

The effect of the operating parameters on the system hydrodynamics and mixing inside two circulating fluidized bed reactor (CFBR) risers with different ring baffle configurations were investigated using computational fluid dynamics simulations and a 2⁴ factorial experimental design analysis. The operating parameters varied were the gas inlet velocity, and the mass flux, diameter and density of the solid particles, while the response variables were the standard deviation of the solid volume fraction (SVF) in the radial direction (SDSVF-RD) and the average SVF (ASVF). The results from the two CFBR risers with different ring baffle configurations showed a similar trend. The operating parameters that significantly affected the ASVF in both modified CFBR risers were the inlet gas velocity and solid particle mass flux, while those that significantly affected the SDSVF-RD were the inlet gas velocity and the inlet gas velocity–solid particle diameter–solid particle density interaction. For these systems, the lowest and highest ASVF was approximately 0.07 and 0.20, respectively, while the lowest and highest SDSVF-RD was 0.01 and 0.04, respectively. The low variability of the solid particle distribution and the high solid particle concentration will be suitable for chemical reactions. All the obtained results could be explained in terms of the system hydrodynamics. Finally, regression models to predict the mean solid particle concentration and variability of solid particle distribution in the system were obtained.     

Implementation of the quadrature method of moments in CFD codes for aggregation-breakage problems

In this work the quadrature method of moments (QMOM) is implemented in a commercial computational fluid dynamics (CFD) code (FLUENT) for modeling simultaneous aggregation and breakage. Turbulent and Brownian aggregation kernels are considered in combination with different breakage kernels (power law and exponential) and various daughter distribution functions (symmetric, erosion, uniform). CFD predictions are compared with experimental data taken from other work in the literature and conclusions about CPU time required for the simulations and the advantages of this approach are drawn.     

Multi-scale product property model of polypropylene produced in a FBR: From chemical process engineering to product engineering

A multi-scale product model has been built to characterize the polypropylene (PP) formation dynamics in a catalytic FBR. For the first time, the gas–solid flow field, the morphological and molecular properties of particles, as well as their dynamics can be simultaneously obtained by solving the unique model that couples a CFD model, a population balance model (PBM) and moment equations. The quantitative relationships between the operating conditions and the multi-scale particle properties have been further established. The results demonstrate that the product model can be used to guide a multi-scale generalization of the polymer product from chemical process to product engineering.     

稳态反应模型在气相聚乙烯反应器中的应用

通过对气相流化床聚乙烯工艺稳态反应模型的应用进行分析，讨论了中间控制参数温度、氢气乙烯摩尔比、共聚单体乙烯摩尔比、催化剂产率等输入变量对反应器输出变量树脂性能－熔体流动指数（MI）的影响。选择工业实例，对系统出现波动后人工调控MI与利用稳态反应模型的计算机调控MI的过程分别进行了计算，并对2种调控过程进行了比较，证明了稳态反应模型在工业质量控制中的优越性。     

Hydrodynamic modelling of binary mixture in a gas bubbling fluidized bed using the kinetic theory of granular flow

A multi-fluid Eularian CFD model with closure relationships according to the kinetic theory of granular flow has been applied to study the motions of particles in the gas bubbling fluidized bed with the binary mixtures. The mutual interactions between the gas and particles and the collisions among particles were taken into account. Simulated results shown that the hydrodynamics of gas bubbling fluidized bed related with the distribution of particle sizes and the amount of energy dissipated in particle-particle interaction. In order to obtain realistic bed dynamics from fundamental hydrodynamic models, it is important to correctly take the effect of particle size distribution and energy dissipation due to non-ideal particle-particle interactions into account.     

A coupled population balance model and CFD approach for the simulation of mixing issues in lab‐scale and industrial bioreactors

Lab‐scale (70 L) and industrial scale (70 m³) aerated fermenters are simulated using a commercial computational fluid dynamics code. The model combines an Euler‐Euler approach for the two‐phase flow, a population balance model for biological adaptation to concentration gradients, and a kinetic model for biological reactions. Scale‐up at constant volumetric mass transfer coefficient is performed, leading to concentration gradients at the large scale. The results show that for a given concentration field and a given circulation time t_c, the population (physiological) state depends on the characteristic time of biological adaptation T_a. The population specific growth rate (T_a?t_c) is found independent of the spatial location and closely related to the volume average concentration. Oppositely, the population specific uptake rate (T_a～t_c) is spatially heterogeneous. The resulting local disequilibria between the uptake rate and the growth rate provide an explanation for the decreased performances of poorly macromixed industrial bioreactors. © 2013 American Institute of Chemical Engineers AIChE J, 60: 27–40, 2014     

Two phase mathematical model for a bio-trickling reactor for the production of ultra low sulfur diesel (ULSD) from deeply hydrodesulfurized diesel

A trickle bed reactor (TBR) having a diameter of 0.066 m and a height of 0.6 m has been used for the bio-desulfurization of hydrotreated diesel fraction having sulfur concentration in the range of 200–540 ppm. Rhodococcus sp. (NCIM 2891, Pune) has been used to degrade the residual organo-sulfur compounds present in deeply hydrodesulfurized diesel. The microorganisms have been immobilized on the packing material prior to desulfurization within the trickle bed reactor. The volumetric flow rate and hence, the substrate loading rate have been used as the parameters. Sulfur reduction within the range of 84–95% has been achieved. To avoid the excess accumulation of the biomass within the reactor, backwashing technique is incorporated. For such desulfurization, batch studies have been conducted in Erlenmeyer flasks maintaining the concentration of diesel in the range of 0–100% in a diesel supplemented sulfur-free aqueous medium. The concentration of biomass with time has been monitored using dry cell weight method. The concentration of sulfur has been determined by “trace sulfur in petroleum distillate by nickel reduction” (UOP 357-80) method. From the growth curve, it is observed that the system follows uninhibited Monod type model within the range of substrate studied. A systematic and programmed investigation has been carried out to determine the growth kinetic parameters, namely maximum specific growth rate, saturation constant K_s and yield coefficient Y_X/S. A deterministic mathematical model for the TBR has been developed using judicious assumptions to predict its performance characteristics.