Effect of reactor residence time distribution on the size distribution of polymer particles made with heterogeneous Ziegler-Natta and supported metallocene catalysts. A generic mathematical model

A generic mathematical model for analyzing the effect of ideal and non-ideal reactor residence time distributions on the size distribution of polymer particles produced with heterogeneous Ziegler-Natta and supported metallocene catalysts was developed. It was shown that the residence time distribution in polymerization reactors can have a significant effect on the size distribution of polymer particles and this can lead to imperfect replication of the catalyst particle size distribution.     

Modeling and analysis of high‐impact poly(propylene) production processes, 1. Effect of chemical poisoning on particle size distribution and gel formation

This work presents a simple model for a two‐stage process of high impact poly(propylene) (HIPP) production. The model predicts the bivariate distribution of particle size and polymer composition. It takes into account the effect of chemical poisoning on gel particle formation. The result shows that poisoning the solid catalyst is not an effective method for gel reduction. A better approach is to saturate the polymer particles with a co‐catalyst in reactor 1 and poison the co‐catalyst in reactor 2. It is also shown that the residence time distribution (RTD) of reactor 1 has a strong effect on the gel particle formation. A continuous reactor with narrow RTD is advantageous for gel reduction. The model provides some guidance for the analysis and design of the HIPP production process.     

The Effect of Residence Time Distribution on the Slurry‐Phase Catalytic Ethylene Polymerization: An Experimental and Computational Study

This work is focused on the development and validation of a model accounting for the impact of the reactor residence time distribution in well‐stirred slurry‐phase catalytic polymerization of ethylene. Particle growth and morphology are described through the Multigrain model, adopting a two‐site model for the catalyst and a conventional kinetic scheme. Particle size distribution and polymer properties (average molecular weights and polydispersity) are computed as a function of particle size through a segregated model, assuming that neither breakage nor aggregation occur. Reactors are modeled by means of fundamental mass conservation equations. The model is applied to a system constituted by a series of two ideal continuous stirred tank reactors, where the synthesis of polyethylene with bimodal molecular weight distribution is performed, employing the initial catalyst size distribution as the only adjustable parameter. The model provides insights at the single particle scale for each specific size, thus highlighting the inhomogeneity which arises from the synergic effects of chemical kinetics and residence time distributions in both reactors. The satisfactory agreement between model results and experimental data, in terms of particle size distribution and average molecular weights, confirmed the suitability of the model and underlying assumptions.     

Size evolution of gold nanoparticles in a millifluidic reactor

The size evolution of gold nanoparticles in a millifluidic reactor is investigated using spatially resolved transmission electron microscopy (TEM). The experimental data is supported by numerical simulations, carried out to study the residence-time distribution (RTD) of tracers that have the same properties as Au ions. Size and size distribution of the particles within the channels are influenced by the mixing zones as well as the RTD. However, the Au nanoparticles obtained show a broader size distribution even at the shortest investigated residence time of 3.53 s, indicating that in addition to surface growth reaction kinetics also plays an important role. The comparison of time resolved particle growth within the millifluidic channel with flask-based reactions reveals that the particle size can be controlled better within millifluidic channels. Overall, the results indicate potential opportunities to utilize easy to fabricate millifluidic reactors for the synthesis of nanoparticles, as well as as for carrying out time resolved kinetic studies.     

Simulating cumulative distributions under transient conditions in well-mixed,continuous and batch polymerization reactors

Instantaneous property methods are applied to the simulation of cumulative distributions of polymer chain architecture in well-mixed, continuous and batch reactors. We show how cumulative distributions can be simulated under transient conditions using a general convolution integral and suitable output from a dynamic reactor simulation package such as POLYRED^TM. We also show how the state equations that describe a polymerizing system can be augmented for direct simulation of these distributions. Examples of the impact of catalyst kinetics, reactor operating policies, and process upsets on the molecular weight distribution of bimodal high molecular weight polyethylene produced in well-mixed, stirred-bed gas-phase reactors are simulated for a binary transition-metal catalyst system.     

Development of an Unsteady-State Model for Control of Polymer Grade Transitions in Ziegler-Natta Catalyzed Reactor Systems

The dynamics of the activity and polymer growth in Ziegler-Natta catalysts has been well established in the literature. 1 , 2 The corresponding dynamic behaviour of the reactor system is predicted using a segregation model approach and the unsteady state model of residence time distribution previously developed. 3 The model is therefore able to predict reactor performance for a time-varying catalyst flow rate through the reactor, as well as time-varying concentrations of monomer, co-catalyst and chain termination agent. A method of determining grade transition policies by the use of the developed reactor models is then presented. It is demonstrated that the reactor productivity, catalyst efficiency, average chain length and polydispersity can be controlled by the catalyst flow rate and reactor monomer and hydrogen concentrations. The relationship between the required polymer product properties and the system flow rates is determined. Case studies are presented that evaluate various transition strategies for a specific polymer grades.     

Mean residence time of Markov processes for particle transport in fludized bed reactors

A new approach for studying the particle dynamics and RTD (residence time distribution) in processes is to formulate stochastic models. A common question to all models for RTD is whether Danckwerts’ law for mean residence time holds. In this paper we revisit a Markov process that has been proposed by Dehling et al. (1999) as a stochastic model for particle transport in fluidized bed reactors. Under the volumetric flow balance conditions, we deduce different boundary conditions at the entrance and the exit of the reactor, and in both discrete model and continuous model we show that processes satisfy Danckwerts’ law, stating that the mean residence time of particle transport in fluidized bed reactors equals V/v, where V denotes the volume of the reactor occupied by the fluid and v the volumetric inflow rate.     

Dynamic Monte Carlo Simulation of Olefin Polymerization in Stopped-Flow Reactors

Stopped-flow reactors are very useful to estimate olefin polymerization rate constants and to investigate particle morphology development. Because the residence time in these reactors is comparable to the life time of the polymer chains, very narrow molecular weight distributions are obtained and the number average molecular weight is proportional to reactor residence time. In this case, traditional models for olefin polymerization in industrial reactors can not be applied. In this contribution, we derived analytical solutions and performed Monte Carlo simulations to describe the time evolution of the molecular weight distribution of polyolefins made with single- and multiple-site catalysts in stopped-flow reactors.     

A Single-Gallery Model for the In Situ Production of Polyethylene-Clay Nanocomposites

Polyolefin-clay nanocomposites are finding many new applications because of their improved properties, such as high modulus, elevated scratch resistance and low gas permeability. Currently, these composites are produced by melt blending organically modified clay with polyolefins. The most challenging step in this process is the intercalation and exfoliation of the clay to produce a homogenously dispersed phase at the nanoscale. A promising alternative to melt blending is in-situ polymerization, where the polymer is produced between the clay layers in the polymerization reactor. In-situ polymerization of olefins with metallocene catalysts supported on clay can produce nanocomposites using conventional polymerization reactors, provided that the clay can be used as a support for the olefin polymerization catalyst. In this approach, the clay fulfills the functions of catalyst support and dispersed phase in the final nanocomposite. In this work, a mathematical model describing particle growth during in-situ polymerization of ethylene with a metallocene catalyst supported on clay will be discussed. The model expands the approach of the multi-grain model used in heterogeneous olefin polymerization to account for the layered structure of clays.     

Supramolecular Strategies for the Recycling of Homogeneous Catalysts

Supramolecular approaches are increasingly used in the development of homogeneous catalysts and they also provide interesting new tools for the recycling of metal-based catalysts. Various non-covalent interactions have been utilized for the immobilization homogeneous catalysts on soluble and insoluble support. By non-covalent anchoring the supported catalysts obtained can be recovered via (nano-) filtration or such catalytic materials can be used in continuous flow reactors. Specific benefits from the reversibility of catalyst immobilization by non-covalent interactions include the possibility to re-functionalize the support material and the use as “boomerang” type catalyst systems in which the catalyst is captured after a homogeneous reaction. In addition, new reactor design with implemented recycling strategies becomes possible, such as a reverse-flow adsorption reactor (RFA) that combines a homogeneous reactor with selective catalyst adsorption/desorpion. Next to these non-covalent immobilization strategies, supramolecular chemistry can also be used to generate the support, for example by generation of self-assembled gels with catalytic function. Although the stability is a challenging issue, some self-assembled gel materials have been successfully utilized as reusable heterogeneous catalysts. In addition, catalytically active coordination cages, which are frequently used to achieve specific activity or selectivity, can be bound to support by ionic interactions or can be prepared in structured solid materials. These new heterogenized cage materials also have been used successfully as recyclable catalysts.     

Modeling and Sensitivity Analysis of Particle Size Distribution and Chain Length Distribution in a Semibatch Emulsion Copolymerization Reactor

Summary: A comprehensive model is developed to predict the relationship between the particle size distribution and molecular weights of particles in an emulsion copolymerization reactor. A full population balance equation is used for the particle size distribution and extended to the model for the molecular properties using a continuous reactor approach. The numerical prediction clearly distinguishes the characteristics of molecular properties of particles by homogeneous nucleation from those by micellar nucleation with the dependence on the particle size. Sensitivity analysis of the proposed model under a variety of conditions shows that the compartmentalized feature of the emulsion system should be considered for better prediction of molecular properties, and provides information on the manipulated variables and lumped parameters which effectively decompose the correlation of both properties. Finally, a control strategy utilizing a lumped parameters tracking method is suggested for the regulation of both the particle size distribution and molecular properties.

Time evolution of number‐averaged molecular weights in the element under base conditions.     

Development of an Integrated Framework for Multiscale,Multiphase Modeling of Industrial Slurry‐Phase Reactors for Polyethylene Production

A framework based on the Monte Carlo/random‐pore polymeric flow model is proposed to simulate both single‐particle and continuous slurry reactor industrial polymerizations. The Sanchez–Lacombe equation of state describes the distributions of components in the different phases of these systems. The developed process model is applied to describe heterogeneously catalyzed polymerizations of ethylene in n‐hexane diluent with or without 1‐hexene as a comonomer, but the proposed methodology is applicable to any ethylene/1‐olefin copolymerization in slurry reactors. In addition to the effects of catalyst particle size and reactor residence time distributions, the proposed hybrid model is used to investigate the impact of several catalyst characteristics under different process conditions on polymer yield and microstructure. Particular attention is paid to the catalyst fragmentation process and active center distribution through the particle. These simulations demonstrate the versatility and thoroughness of combining Monte Carlo simulation with single‐particle models to analyze and predict the behavior of commercial polyolefin reactors.     

Mathematical Modeling of Acrylonitrile-Butadiene Emulsion Copolymerization: Model Development and Validation

This paper presents a mechanistic model for the production of nitrile-butadiene rubber (NBR). The mathematical dynamic model was developed in order to simulate the industrial production of NBR via emulsion copolymerization of acrylonitrile (AN) and butadiene (Bd) in batch, continuous and trains of continuous reactors. For this reason, the model was constructed in a parsimonious manner to avoid complex and time-consuming computations that typically result when modeling details of specific aspects of micro/macro scale emulsion polymerization phenomena (i.e., full molecular weight and particle size distributions, detailed species phase-partitioning, etc.). Thus, the model provides average properties for typical emulsion characteristics, such as monomer conversion, copolymer composition, number- and weight-average molecular weights, tri- and tetra-functional branching frequencies, and the number and average size of polymer latex particles. The proposed model is an extension of a previous model developed by our group, and allows for the dynamic modeling of different reactor types and configurations. Model comparisons are made between limited literature data for batch operation, while representative simulation profiles are shown for a reactor train.     

X-ray microtomography studies of nascent polyolefin particles polymerized over magnesium chloride-supported catalysts

Drastic changes occur during the initial stages of the α-olefin polymerization over heterogeneous catalysts. Fragmentation of the support takes place as polymer is formed at the active sites within the voids of the support/catalyst. Magnesium chloride-supported titanium catalyst/polymer particles have been analyzed employing high-resolution computed microtomography (CMT) using synchrotron radiation at Brookhaven National Laboratory. The changes in morphology, the spatial distribution of the support/catalyst fragments, porosity, and polymer distribution in single growing polypropylene and polyethylene particles have been studied. These studies documented considerable macroporosity ( > 2 μm in size) within the growing catalyst/support/polymer particles. The largest pores may be due to agglomeration of smaller subparticles. Our results confirm that the initial fragmentation of the support proceeds readily and uniformly to yield a multi-grain growth of subparticle agglomerates. The support/catalyst fragments appear to be distributed relatively uniformly within the growing polymer particle. The surface of the subparticle agglomerates is accessible through the void-space between growing catalyst/particle grains. This may facilitate monomer transport to the activate sites through the polymer/catalyst particles. © 1993 John Wiley & Sons, Inc.     

Coupled Single‐Particle and Population Balance Modeling for Particle Size Distribution of Poly(propylene) Produced in Loop Reactors

A comprehensive model was developed for the PSD of PP produced in loop reactors. The polymeric multilayer model (PMLM) was first applied to calculate the single particle growth rate under intraparticle transfer limitations. In order to obtain the comprehensive model, the PMLM was solved together with a steady‐state particle population equation to predict the PSD in the loop reactors. The simulated PSD data obtained under steady‐state polymerization conditions agreed with the actual data collected from industrial scale plant. The comprehensive model was also used to predict the effects of some critical factors, including the intraparticle mass and heat transfer limitations, the feed catalyst particle size and the catalyst deactivation, etc., on the PSD.

     

Nanoporous structure of ultrahigh-molecular-weight polyethylene reactor powder

The influence of the catalyst system and synthesis conditions on the morphology and molecular dynamics of reactor (nascent) powders of ultrahigh-molecular-weight PE synthesized over supported Ziegler-Natta catalysts in laboratory reactors was studied by means of electron microscopy and ¹H broadline NMR spectroscopy. For comparison, commercial reactor powders were studied as well. The type of the catalyst system and the temperature of slurry polymerization have a substantial effect on the supermolecular structure of the nascent polymer. The proton NMR spectra of the reactor powders synthesized at low temperatures display a narrow component. An analysis of its behavior at low temperatures and different humidities led to the conclusion that the signal is due to water localized in nanopores of 2–4 nm in size in the nascent polymer. The role of nanopores in the sintering of reactor particles is discussed.     

浆态床用CuO/ZrO2催化剂的完全液相法合成及其对CO加氢的催化性能

 利用完全液相法制备了CuO/ZrO2浆状催化剂,通过X射线衍射、氮气吸附和程序升温还原等方法对催化剂的结构和织构性质进行了研究,并考察了CuO/ZrO2催化剂上CO加氢反应的性能. 结果表明,本方法制备的CuO/ZrO2浆状催化剂具有与传统方法制备的固体催化剂相似的相结构; 利用共沸蒸馏法进行表面处理后, CuO/ZrO2催化剂分散均匀且易于还原; CuO/ZrO2浆状催化剂用于CO加氢反应时,不需另外添加甲醇脱水剂就可以直接合成二甲醚,在473 K时CuO/ZrO2对二甲醚的选择性达到92.1%, 并且在15 d的反应中催化剂呈现出良好的稳定性.     

EMULSION POLYMERIZATION IN A SEED-FED CONTINUOUS STIRRED-TANK REACTOR

A numerical method has been developed to predict the particle size distribution (PSD) of the product latex from a steady-state polydisperse-seeded continuous reactor. Simulations have been carried out for the emulsion polymerization of vinyl chloride based on the experimental conditions reported by Berens(l). The simulation results can be reasonably well fitted to the PSD data published by Berens. The radical desorption constant, k_d, for Berens’ vinyl chloride emulsion polymerization can be estimated by fitting the simulated PSD to experimental measurements. The simulation work presented in this article demonstrates that the combination of mathematical modeling and PSD measurements can be a useful tool in studying radical transport rates and aqueous phase termination phenomena. The simulation results also indicate that the continuum diffusion theory for free radical absorption by the particles leads to a better PSD fit than a model based on equal diffusion rates per unit area.     

Modelling nucleation and particle growth in emulsion copolymerization in continuous loop reactors

A mathematical model for emulsion copolymerization in continuous loop reactors is presented. The flow pattern of the loop reactor can be represented by a loop formed by two tubular reactors with axial dispersion. The mathematical model combines this flow model with the physico-chemical characteristics of the emulsion copolymerization. The outputs of the model are monomer conversion, copolymer composition, particle size distribution and latex viscosity. The model was checked during the redox initiated emulsion copolymerization of vinyl acetate and veova 10 carried out in a completely automated continuous loop reactor.     

Continuous Heterogeneous Photocatalysis in Serial Micro‐Batch Reactors

Solid reagents, leaching catalysts, and heterogeneous photocatalysts are commonly employed in batch processes but are ill‐suited for continuous‐flow chemistry. Heterogeneous catalysts for thermal reactions are typically used in packed‐bed reactors, which cannot be penetrated by light and thus are not suitable for photocatalytic reactions involving solids. We demonstrate that serial micro‐batch reactors (SMBRs) allow for the continuous utilization of solid materials together with liquids and gases in flow. This technology was utilized to develop selective and efficient fluorination reactions using a modified graphitic carbon nitride heterogeneous catalyst instead of costly homogeneous metal polypyridyl complexes. The merger of this inexpensive, recyclable catalyst and the SMBR approach enables sustainable and scalable photocatalysis.