A Monte Carlo Method to Quantify the Effect of Reactor Residence Time Distribution on Polyolefins Made with Heterogeneous Catalysts: Part I—Catalyst/Polymer Particle Size Distribution Effects

Polyolefins are commercially produced in continuous reactors that have a broad residence time distribution (RTD). Most of these polymers are made with heterogeneous catalysts that also have a particle size distribution (PSD). These are totally segregated systems, in which the catalyst/polymer particle can be seen as a microreactor operated in semibatch mode, where the reagents (olefins, hydrogen, etc.) are fed continuously to the catalyst/polymer particle, but no polymer particle can leave. The reactor RTD has a large influence on the PSD of the polymer particles leaving the reactor, as well as in polymer microstructure and properties, polymerization yield, and composition of reactor blends. This article proposes a Monte Carlo model that can describe how particle RTD in a single or a series of reactors can affect the PSD of polymer particles made under a variety of operation conditions. It is believed that this is the most flexible model ever proposed to model this phenomenon, and can be easily modified to track all properties of interest during polyolefin production in continuous reactors with heterogeneous catalysts.     

Radiotracer investigation of phosphoric acid and phosphatic fertilizers production process

In the phosphoric acid production process, the time a particle spends inside the chemical reactor (residence time) is of paramount importance to process engineers. Residence time distribution (RTD) gives information on the efficiency of the chemical reactor, on the efficiency of the process, and also the availabilities of the reactive volume for the reaction (active volume vs. dead volume). Traditionally, chemical engineers used chemical tracer to determine the RTD. However, first disadvantage is that the chemical tracer could not allow an online diagnosis: the samples containing chemical tracer have to go to a lab for analysis, second disadvantage is that the chemical tracer is less sensitive than radioactive ones because of its adsorption onto strata or its retention in rocks. Consequently, chemical tracer results are not always precise and cannot convincingly explain the multiple flow-path model. Radioactive tracers are the only tracers capable of measuring the active RTD with high degree of precision and give information on the internal recirculation rate. In this work, we will describe the application of radiotracer method for RTD measurement in the phosphoric acid production process and give results and discussion of each case encountered.     

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.     

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.     

Effect of Alkyl Aluminums on Ethylene Polymerization Reactions with a Cr‐V Bimetallic Catalyst

The effect of introducing various types of alkyl aluminums directly into the catalyst and/or in the polymerization process as cocatalyst on the efficiency of a Cr‐V bimetallic catalyst for ethylene polymerization is systematically investigated. Results indicate that polymerization activity, kinetic behavior, and polymer properties of the Cr‐V catalyst are strongly affected by using alkyl aluminums in different stages of polymerization, due to the different responses and sensitivities of the two metal centers to alkyl aluminum. When employed as cocatalyst, triisobutyl aluminum gives high activity and polyethylene with relatively low molecular weight, while diethylaluminum chloride cocatalyzes the production of ultra‐high molecular weight polyethylene but with very low activity. On the other hand, the pre‐reduction of the bimetallic catalyst by alkyl aluminums has a marked promotion effect on catalyst efficiency. It is suggested that the addition of alkyl aluminum to the catalyst and to the reactor as cocatalyst are more or less equivalent in their effects on the improvement of polymerization activity, but they behave in different ways to affect polymer properties.     

Packed column reactor for continuous atom transfer radical polymerization: Methyl methacrylate polymerization using silica gel supported catalyst

A continuous column reactor packed with silica gel supported CuBr‐HMTETA catalyst has been successfully developed for ATRP of MMA. The reactor had a good catalytic stability up to 100 h. The MMA conversion decreased with an increasing feeding flow rate. The polymerization kinetics was first order with respect to the monomer. The molecular weight increased linearly with conversion, demonstrating the living character. Possible flow back‐mixing and polymer trapping in the pores of silica gel caused some broadening in the molecular weight distribution. This type of packed column reactor is believed to be a significant development for possible commercial exploitation of the ATRP 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.     

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.     

Molecular‐Weight‐Distribution Modelling of Radical Polymerization in Batch and Continuous Reactors with Transfer to Polymer Leading to Gel Formation

Full chain‐length distribution (CLD) modelling applying the Galerkin finite‐element method^[1] (FEM) to polymerization reactors featuring a certain degree of gel formation is confronted with extremely long computation times. The paper describes a new method to predict CLDs for systems where gel formation may occur. The new concept is to model a part of the CLD up to a cut‐off length L, while satisfying the full set of population balances. With transfer to polymer as the mechanism responsible for gelation, this gives rise to a closure problem, which has been solved by assuming the dead CLD beyond L to be represented by a part of a Flory distribution. The method could be proved to work by performing simulations and comparing cut‐off CLDs to full CLDs for non‐gelling systems and comparing results for different L for systems with gelation. The model is demonstrated for polymerization reactors, the batch reactor and the continuous stirred‐tank reactor (CSTR), with either disproportionation or recombination termination. Reliable results are obtained for systems with moderate gel formation. Comparing these results to those from moment models including balance equations up to the fourth moment, a number of interesting differences have been found.     

Mathematical Modeling of the Long‐Chain Branch Structure of Polyolefins Made with Two Metallocene Catalysts: An Algebraic Solution

A mathematical model was developed to describe the populations of polymer chains containing different numbers of long‐chain branches (LCBs) made with a combination of two single‐site catalysts. One of the catalysts produces only linear chains (linear‐catalyst) and the other produces linear and long‐branched chains (LCB‐catalyst). The model shows that when the selectivity for macromer formation of the linear‐catalyst is the same as that of the LCB‐catalyst, it is not possible to maximize the number of LCB per chain, even though the number of LCB per 1 000 carbon atoms (C) can be maximized. On the other hand, if the selectivity for macromer formation of the linear‐catalyst is higher than that of the LCB‐catalyst, both LCB/1 000 C and LCB/chain pass through maxima when varying the fraction of the linear‐catalyst in the reactor. More importantly, polymer populations with different numbers of LCB per chain will reach their maximum values at different ratios of linear‐catalyst to LCB‐catalyst, thus permitting the maximization of individual polymer populations in the mixture.     

Polyethylene with Reverse Co‐monomer Incorporation: From an Industrial Serendipitous Discovery to Fundamental Understanding

A triethylaluminium(TEAl)‐modified Phillips ethylene polymerisation Cr/Ti/SiO₂ catalyst has been developed with two distinct active regions positioned respectively in the inner core and outer shell of the catalyst particle. DRIFTS, EPR, UV‐Vis‐NIR DRS, STXM, SEM‐EDX and GPC‐IR studies revealed that the catalyst produces simultaneously two different polymers, i.e., low molecular weight linear‐chain polyethylene in the Ti‐abundant catalyst particle shell and high molecular weight short‐chain branched polyethylene in the Ti‐scarce catalyst particle core. Co‐monomers for the short‐chain branched polymer were generated in situ within the TEAl‐impregnated confined space of the Ti‐scarce catalyst particle core in close proximity to the active sites that produced the high molecular weight polymer. These results demonstrate that the catalyst particle architecture directly affects polymer composition, offering the perspective of making high‐performance polyethylene from a single reactor system using this modified Phillips catalyst.     

Effect of 1‐hexene comonomer on polyethylene particle growth and copolymer chemical composition distribution

An investigation of the polymer particle growth characteristics and polymer molecular weight and composition distributions in ethylene homopolymerization and ethylene/1‐hexene copolymerization has been carried out with a catalyst comprising a zirconocene and methylaluminoxane immobilized on a silica support. The presence of 1‐hexene leads to higher productivity and easier fragmentation of the support during particle growth. Crystallization analysis fractionation and gel permeation chromatography analysis of ethylene/1‐hexene copolymers prepared at different polymerization times reveals a broadening of the chemical composition distribution with increasing polymerization time as a result of the gradual formation of a relatively high‐molecular‐weight, ethylene‐rich fraction. The results are indicative of significant monomer diffusion effects in both homopolymerization and copolymerization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2883–2890, 2006     

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.     

Concerning the Deactivation of Cobalt(III)‐Based Porphyrin and Salen Catalysts in Epoxide/CO2 Copolymerization

Functioning as active catalysts for propylene oxide (PO) and carbon dioxide copolymerization, cobalt(III)‐based salen and porphyrin complexes have drawn great attention owing to their readily modifiable nature and promising catalytic behavior, such as high selectivity for the copolymer formation and good regioselectivity with respect to the polymer microstructure. Both cobalt(III)–salen and porphyrin catalysts have been found to undergo reduction reactions to their corresponding catalytically inactive cobalt(II) species in the presence of propylene oxide, as evidenced by UV/Vis and NMR spectroscopies and X‐ray crystallography (for cobalt(II)–salen). Further investigations on a TPPCoCl (TPP=tetraphenylporphyrin) and NaOMe system reveal that such a catalyst reduction is attributed to the presence of alkoxide anions. Kinetic studies of the redox reaction of TPPCoCl with NaOMe suggests a pseudo‐first order in cobalt(III)–porphyrin. The addition of a co‐catalyst, namely bis(triphenylphosphine)iminium chloride (PPNCl), into the reaction system of cobalt(III)–salen/porphyrin and PO shows no direct stabilizing effect. However, the results of PO/CO₂ copolymerization by cobalt(III)–salen/porphyrin with PPNCl suggest a suppressed catalyst reduction. This phenomenon is explained by a rapid transformation of the alkoxide into the carbonate chain end in the course of the polymer formation, greatly shortening the lifetime of the autoreducible PO‐ring‐opening intermediates, cobalt(III)–salen/porphyrin alkoxides.     

Pd nanoparticles dispersed on solid supports: synthesis,characterization and catalytic activity on selective hydrogenation of olefins in aqueous media

Two types of Pd nanoparticle catalysts were prepared having 2–4 nm particle size using silica gel and porous polymer beads as solid supports. 2‐Pyridinecarboxaldehyde ligand was anchored on commercially available 3‐aminopropyl‐functionalized silica gel followed by Pd metal dispersion. Bead‐shaped cross‐linked poly(4‐vinylpyridine‐co‐styrene) gel was prepared by an emulsifier‐free emulsion polymerization of 4‐vinylpyridine, styrene and divinylbenzene in the presence of ammonium persulfate and subsequently dispersing the Pd metal on the synthesized polymer. These catalysts were characterized by SEM, TEM and ICP techiniques with respect to appearance, size and possible leaching out, respectively. Furthermore, the reactivity of these catalysts was tested on hydrogenation of various α,β‐unsaturated carbonyl compounds using aqueous solvent under a hydrogen balloon (1 atm). The results showed that the Pd dispersed on silica was a more efficient catalyst than Pd dispersed on polymer and the former could be recycled more than 10 times without considerable loss in activity. Copyright © 2010 John Wiley & Sons, Ltd.     

Organic solvent‐free catalytic hydrogenation of diene‐based polymer nanoparticles in latex form. Part II. Kinetic analysis and mechanistic study

The central challenge that has limited the development of catalytic hydrogenation of diene‐based polymer latex (i.e., latex hydrogenation) in large‐scale production pertains to how to accomplish the optimal interplay of accelerating the hydrogenation rate, decreasing the required quantity of catalyst, and eliminating the need for an organic solvent. Here, we attempt to overcome this dilemma through decreasing the dimensions of the polymer substrate (such as below 20 nm) used in the hydrogenation process. Very small diene‐based polymer nanoparticles were synthesized and then used as the substrates for the subsequent latex hydrogenation. The effects of particle size, temperature, and catalyst concentration on the hydrogenation rate were fully investigated. An apparent first‐order kinetic model was proposed to describe the rate of hydrogen uptake with respect to the concentration of the olefinic substrate (C?C). Mass transfer of both the hydrogen and catalyst involved in this solid (polymer)–liquid (water)–gas (hydrogen) three‐phase latex system is discussed. The competitive coordination of the catalyst between the C?C and acrylonitrile units within the copolymer was elucidated. It was found that (1) using very small diene‐based polymer nanoparticles as the substrate, the hydrogenation rate of polymer latex can be increased vastly to achieve a high conversion of 95% while a quite low level of catalyst loading is required; (2) this latex hydrogenation process was completely free of organic solvent and no cross‐linking was found; (3) the mass transfer of hydrogen is not a rate‐determining step in the present hydrogenation reactions; (4) the catalyst was dispersed homogeneously within the polymer nanoparticles; (5) for the reaction that has reached about 95 mol % conversion, the kinetic study shows that the reaction is chemically controlled with an apparent activation energy of 100–110 kJ/mol; (6) the strong coordination of C[tbond]N to the catalytically active species RhH₂Cl(PPh₃)₂ imposed a negative effect on the hydrogenation activity. The present research provides a comprehensive study to appreciate the underlying chemistry of latex hydrogenation of diene‐based polymer nanoparticles and more importantly shows great promise toward the commercialization of a “green” catalytic hydrogenation operation of a diene‐based polymer latex in industry. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Modelling non-homogeneous flow and residence time distribution in a single-screw extruder by means of Markov chains

Non-homogeneous velocity distribution of the flow in the channel of a single-screw extruder is taken into account by a new model developed on the basis of the Markov chains. This model allows calculating the Residence Time Distribution (RTD) as well as the influence of the operating conditions on the process at any velocity distribution in the channel. It has been used to represent experimental results on mass flow rate and RTD previously obtained by extrusion of an acrylic polymer, Eudragit E100, at different temperatures and screw rotation speeds. The diffusion coefficient is the only adjusting parameter of the model. It was shown that it does not depend on the screw rotation speed and a correlation between this diffusion coefficient and the barrel temperature was found. The model provides global understanding of the transport kinetics of the flowing material through the extruder according to its behaviour and better describes the progress of the polymer flow all along the barrel from the hopper to the die.     

Highly Dispersed and Small‐Sized Nickel(II) Hydroxide Co‐Catalyst Prepared by Photodeposition for Hydrogen Production

Photodeposition has been widely used as a mild and efficient synthetic method to deposit co‐catalysts. It is also worth studying how to synthesize non‐noble metal photocatalysts with uniform dispersion. Different synthetic conditions in photodeposition have a certain influence on particle size distribution and photocatalytic activity. Therefore, we designed experiments to prepare the inexpensive composite photocatalyst Ni(OH)₂/g‐C₃N₄ by photodeposition. The Ni(OH)₂ co‐catalysts disperse uniformly with particle sizes of about 10 nm. The photocatalytic hydrogen production rate of Ni(OH)₂/g‐C₃N₄ reached about 19 mmol g^?1 h^?1, with the Ni(OH)₂ deposition amount about 1.57 %. During 16 h stability testing, the rate of hydrogen production did not decrease significantly. The composite catalyst also revealed a good hydrogen production performance under sunlight. The Ni(OH)₂ co‐catalyst enhanced the separation ability of photogenerated carriers, which was proved by surface photovoltage and fluorescence analysis.     

Catalytic reduction of 4‐nitrophenol using silver nanoparticles‐engineered poly(N‐isopropylacrylamide‐co‐acrylamide) hybrid microgels

Nearly monodisperse poly(N ‐isopropylacrylamide‐co ‐acrylamide) [P(NIPAM‐co‐AAm)] microgels were synthesized using precipitation polymerization in aqueous medium. These microgels were used as microreactors to fabricate silver nanoparticles by chemical reduction of silver ions inside the polymer network. The pure and hybrid microgels were characterized using Fourier transform infrared and UV–visible spectroscopies, dynamic light scattering, X‐ray diffraction, thermogravimetric analysis, differential scanning calorimetry and transmission electron microscopy. Results revealed that spherical silver nanoparticles having diameter of 10–20 nm were successfully fabricated in the poly(N ‐isopropylacrylamide‐co ‐acrylamide) microgels with hydrodynamic diameter of 250 ± 50 nm. The uniformly loaded silver nanoparticles were found to be stable for long time due to donor–acceptor interaction between amide groups of polymer network and silver nanoparticles. Catalytic activity of the hybrid system was tested by choosing the catalytic reduction of 4‐nitrophenol as a model reaction under various conditions of catalyst dose and concentration of NaBH₄ at room temperature in aqueous medium to explore the catalytic process. The progress of the reaction was monitored using UV–visible spectrophotometry. The pseudo first‐order kinetic model was employed to evaluate the apparent rate constant of the reaction. It was found that the apparent rate constant increased with increasing catalyst dose due to an increase of surface area as a result of an increase in the number of nanoparticles.     

Metal‐Free Electrocatalyst for Oxygen Reduction: Synthesis‐Controlled Density of Catalytic Centers and Impact on ORR

This work demonstrates a rapid and scalable route for the preparation of N‐doped carbon spheres of 80–120 nm via pyrolysis of polypyrrole as the only carbon and nitrogen source. The resulting porous catalyst has a nitrogen doping level of 6–8 at%. Electrochemical studies show that N‐doped C is very active toward oxygen reduction in alkaline electrolyte and the mechanism of ORR process is controlled by the surface concentration of catalytic active sites that promote either a direct four‐electron or two‐electron process. An interesting observation is that we can generate precursors for the N‐doped carbon with desirable particle size, shape and with the preferential structure (linear polypyrrole from the α? α coupling during slow polymerization or cross‐linked polypyrrole from α? β coupling during fast polymerization) that promotes the formation of favorable catalytic sites for O₂ reduction. The XPS analysis in conjunction with RDE voltammetry highlights the effect of polymer precursor synthesis on the chemical structure and a resulting electrochemical activity of the N‐doped carbon materials.