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.     

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.     

A Semi‐Microscopic Modeling for Polymer Flow Reactors

Summary: A nonisothermal plug‐flow reactor for ethylene polymerization is reexamined so as to illustrate the principle and effect of a refined, semi‐microscopic modeling. The novel feature of the current simulation is the application of a Monte Carlo scheme to exactly solve the free‐radical polymerization involved, whereas a reptation‐based molecular theory is introduced in a self‐consistent manner to simulate more accurately the reactant fluid viscosity during polymerization. The simulation is shown to capture some in‐depth consequences of reaction‐transport coupling that cannot be revealed by a traditional, macroscopic type of modeling. The principle of a future extension for dealing with more complex flow reactors is briefly discussed.

Comparison of the predicted temperature profile between Monte Carlo‐based simulation and the ones using moment equations together with two different weight distributions is shown with experimental data for LDPE.     

Organic nanoparticles as fragmentable support for Ziegler–Natta catalysts

A fragmentable support material for Ziegler–Natta catalysts is presented based on micrometer‐sized aggregates of polystyrene nanoparticles. Hydroxyl anchoring groups are introduced by copolymerization of hydroxymethylstyrene in emulsion process to immobilize the catalysts. The catalytic activity in ethylene slurry polymerizations is found to be directly correlated to the hydroxyl group content of the supports. Furthermore, the fragmentation behavior of dye‐labeled support aggregates into the initial nanoparticles is demonstrated using laser scanning confocal fluorescence microscopy as a nondestructive method. These supported catalysts fulfill two important design criteria, high fragmentability and high catalyst loading, and produce high‐density polyethylene with medium molecular weight distributions (MWDs = 3–4). These values lie between those obtained using single‐site metallocene‐based (narrow MWD < 3) or inorganic supported multi‐site Ziegler–Natta‐based (broad MWD = 4–12) polymerizations without the need of blending. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 15–22     

Monte Carlo Simulation of Ethylene Copolymers: A Look into the Monomer Sequence Distribution

A comprehensive mathematical model was developed using Monte Carlo simulation to describe the mechanism of ethylene and α-olefin copolymerization. The model studies the polymerization mechanism using coordination catalysts and is able to predict molecular weight and detailed chemical composition distributions. This work is considered to be a useful tool that enables us to understand and described the monomer sequence distribution as a function of chain length in semi-batch polymerization reactors.     

Kinetic behavior of ethylene/1‐hexene copolymerization in slurry and solution reactors

The copolymerization of ethylene and 1‐hexene over a spherical polymer/MgCl₂‐supported TiCl₄ catalyst was studied as a function of the polymerization temperature from 40 to 100 °C in a slurry reactor and from 120 to 200 °C in a solution reactor with triethylaluminum (TEA) as a cocatalyst (1.0–6.8 mmol). The activities increased from 40 to 80 °C and then declined monotonically with increases in the temperature during the slurry and solution polymerizations. The kinetic behavior in the slurry and solution operations was described by the same rate expression. The modeling results indicated that the catalyst had at least two different types of catalytic sites; one site was responsible for the acceleration–decay nature of the activity profiles, whereas the second site resulted in long‐term activity. The apparent activation energy for site activation in the slurry operation was 69.9 kJ/mol; no activation energies for site activation could be estimated for the solution operation because the activation process was essentially instantaneous at the higher temperatures. The activation energies for deactivation were 100.3 kJ/mol for the slurry operation and 31.2 kJ/mol for the solution operation. The responses to TEA were similar for the slurry and solution operations; the rates increased with increasing amounts of TEA between 1.0 and 3.4 mmol and then decreased with larger amounts of TEA. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 2248–2257, 2005     

High pressure ethylene polymerization with a post‐metallocene bis‐phenyl phenoxy catalyst

The use of post‐metallocene bis‐phenylphenoxy catalysts to polymerize ethylene under high ethylene pressures (>25,000 psi) results in some remarkable catalytic properties. The high ethylene pressure produces molar ethylene concentrations in the reactor as much as 40 times higher than in typical low pressure ethylene polymerizations. This high ethylene concentration results in high catalyst efficiency at high temperatures and low reactor residence time, between 180 °C and 240 °C the catalyst efficiency surprisingly increases with increasing temperature, allowing for use of these catalysts at temperatures much higher than can be utilized in the low pressure processes. It has further been demonstrated that under these conditions increasing hydrogen levels up to 0.5 mol% does not significantly affect the polymer molecular weight; however, polymer molecular weight control can be realized with varying reactor temperature. The polymer produced is shown to be high density polyethylene made from a single site catalyst and not free radical initiated low density polymer. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 861–866     

Comparison between the performance of an immobilized impinging jet stream reactor and a slurry impinging jet stream reactor for photocatalytic phenol degradation

A new immobilized photocatalytic impinging jet stream reactor was designed, and the influences of the effective parameters like jet flow rate, TiO₂ coating disc diameter, nozzle-to-disc distance, and initial concentration on phenol removal were investigated. The reactor was also used as a slurry reactor, and degradation efficiencies in both reactors were compared based on their catalyst loading. The results indicated that the slurry reactor has a higher degradation efficiency than the immobilized reactor at the same TiO₂ loading and other operational conditions. The slurry reactor needs to separate and recover the TiO₂ nanoparticles from the reaction medium which increases the overall process complexity and cost, while the immobilized reactor could be reused at least 4times without any significant decrease in removal efficiency. RTD result indicates that the tank in series model (N?=?5) could properly predict the reactors hydrodynamic behavior.     

Online Monitoring of Polyolefin Particle Growth in Catalytic Olefin Slurry Polymerization by Means of Lasentec Focused Beam Reflectance Measurement (FBRM) and Video Microscopy (PVM) Probes

Polymer particle growth in catalytic ethylene slurry polymerizations with SiO₂‐supported metallocene and post‐metallocene catalysts was monitored online using a Lasentec FBRM probe inserted into the stirred reactor. FBRM enabled the online monitoring of particle numbers and size distributions. Trend analyses provided time‐resolved information on selected variables of the particle growth processes. FBRM was combined with simultaneous ethylene mass flow measurements in order to distinguish between ideal particle growth and more complex growth processes involving particle fragmentation and aggregation. Additional use of a Lasentec PVM video microscopy probe during ethylene polymerization on a MgCl₂‐supported Ziegler catalyst enabled the online visualization of PE particles, complementing the data generated by FBRM online monitoring.

     

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.     

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.     

Polyethylene Made with Combinations of Single‐Site‐Type Catalysts: Monte Carlo Simulation of Long‐Chain Branch Formation

The formation of long‐chain branches (LCBs) during ethylene polymerization with a combination of catalysts was studied by Monte Carlo simulation. The model describes polymerization with a non‐branching catalyst that produces linear macromonomers, and a branching catalyst that produces linear and branched macromonomers. The LCBs are formed when the branching catalyst incorporates a macromonomer. The discussion is based on the three types of chain topology obtained during the synthesis: linear, comb‐branched, or hyperbranched. Simulation results show how the chain length distribution and the number of LCBs change according to the ratio between the two catalysts present in the reactor. The ratio hyperbranched/comb‐branched is defined to evaluate the system composition and the contribution of each catalyst.     

Copolymerization of Ethylene with 1,9‐Decadiene: Part II—Prediction of Molecular Weight Distributions

In the present work, adaptive orthogonal collocation and a Monte Carlo method are used to compute the molecular weight distributions (MWD) of ethylene/1,9‐decadiene copolymers produced with a constrained geometry catalyst. Predictions from each model are compared to each other and to the experimental MWDs, allowing for the evaluation of relative strengths and weaknesses of each mathematical modeling method. Comparisons with experimental results indicate that the rate of macromonomer incorporation in the growing polymer chains decays with the macromonomer radius of gyration. In all cases, the proposed models are able to fit appropriately the available experimental MWDs.     

Ethylene/1‐octene copolymerization studies with in situ supported metallocene catalysts: Effect of polymerization parameters on the catalyst activity and polymer microstructure

Ethylene and 1‐octene copolymerizations were carried out with an in situ supported rac‐[dimethylsilylbis(methylbenzoindenyl)] zirconium dichloride catalyst. In a previous study, it was found that some in situ supported metallocenes produced polyethylene/α‐olefin copolymers with broad and bimodal short chain branching distributions and narrow molecular weight distributions. The ability to produce polyolefins with multimodal microstructural distributions in a single metallocene and a single reactor is attractive for producing polymers with balanced properties with simpler reactor technology. In this study, a factorial experimental design was carried out to examine the effects of the polymerization temperature and ethylene pressure, the presence of hydrogen and an alkylaluminum activator, and the level of the comonomer in the feed on the catalyst activity, short chain branching distribution, and molecular weight distribution of the polymer. The temperature had the most remarkable effect on the polymer microstructure. At high 1‐octene levels, the short chain branching distribution of the copolymer broadened significantly with decreasing temperature. Several factor interactions, including the hydrogen and alkylaluminum concentrations, were also observed, demonstrating the sensitivity of the catalyst to the polymerization conditions. For this catalyst system, the responses to the polymerization conditions are not easily predicted from typical polymerization mechanisms, and several two‐factor interactions seem to play an important role. Given the multiple‐site nature of the catalyst, it has been shown that predicting the polymerization activity and the resulting microstructure of the polymer is a challenging task. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 4426–4451, 2002     

Olefin polymerization using supported metallocene catalysts: development of high activity catalysts for use in slurry and gas phase ethylene polymerizations

Reaction of hydroxylated silica and alumina supports with methyl aluminoxane in toluene suspension provides chemically modified supports suitable for use in slurry and gas-phase polymerizations of ethylene or propylene on treatment with a variety of metallocene dichloride complexes. In particular, aluminas derived from calcination of sol–gel precursors feature high degrees of surface hydroxylation in comparison with commercially available silica (or even alumina) of similar surface area and total porosity. This feature provides a mechanism for increasing the amount of aluminoxane on the former supports, such that commercially acceptable productivities (>10 kg PE/g support×h) are observed at relatively low, total levels of aluminoxane or other alkylaluminum compounds in slurry or gas-phase polymerizations, respectively. A variety of evidence indicates that leaching of active catalyst from these alumina supports occurs to a minor extent under slurry conditions, particularly at higher temperatures in the presence of additional aluminoxane. At lower temperatures, this does not occur to an appreciable extent but the morphology and bulk density of the polymer formed is unsuitable for use in a gas-phase process. This can be attributed to the method for synthesis of the sol–gel alumina precursor which results in irregular particles with a broad particle size distribution. Copolymerization of ethylene with 1-octene or 1-hexene results in formation of linear, low density, PE with a narrow composition distribution as revealed by temperature rising elution fractionation. These studies indicate that less comonomer is incorporated using these supported metallocene catalysts than their soluble analogues under otherwise identical conditions. Finally, some of the resins prepared under slurry conditions (and to a lesser extent in a gas-phase process), exhibit properties consistent with the presence of low levels of long-chain branching; this feature appears to be reasonably general for a variety of simple metallocene complexes.     

Catalytic Polymerization of Liquid Propylene: Effect of Low‐Yield Hexene Prepolymerization on Kinetics and Morphology

Summary: A Ziegler‐Natta‐catalyst was used in ultra low‐yield slurry prepolymerization followed by liquid propylene (main) polymerizations. Complete catalyst disintegration down to 1.5–2 µm particle size is observed at prepolymerization yields of 10 g per g cat. The initial (main) polymerization rate increased up to 55% and the final average particle diameter can be controlled between 50 and 1 500 µm at main polymerization yields of 20 kg PP per g cat · hr⁻¹. Tension generation within the particle and the absence of a polymer layer explains these results.

Surface SEM. Top: Catalyst surface covered with polyhexene. Bottom: Cracks on catalyst surface after washing with hexane.     

α‐Diamine Nickel Catalysts with Nonplanar Chelate Rings for Ethylene Polymerization

A series of novel α‐diamine nickel complexes, (ArNH‐C(Me)‐(Me)C‐NHAr)NiBr₂, 1 : Ar=2,6‐diisopropylphenyl, 2 : Ar=2,6‐dimethylphenyl, 3 : Ar=phenyl), have been synthesized and characterized. X‐ray crystallographic analysis showed that the coordination geometry of the α‐diamine nickel complexes is markedly different from conventional α‐diimine nickel complexes, and that the chelate ring (N‐C‐C‐N‐Ni) of the α‐diamine nickel complex is significantly distorted. The α‐diamine nickel catalysts also display different steric effects on ethylene polymerization in comparison to the α‐diimine nickel catalyst. Increasing the steric hindrance of the α‐diamine ligand by substitution of the o‐methyl groups with o‐isopropyl groups leads to decreased polymerization activity and molecular weight; however, catalyst thermal stability is significantly enhanced. Living polymerizations of ethylene can be successfully achieved using 1 /Et₂AlCl at 35 °C or 2 /Et₂AlCl at 0 °C. The bulky α‐diamine nickel catalyst 1 with isopropyl substituents can additionally be used to control the branching topology of the obtained polyethylene at the same level of branching density by tuning the reaction temperature and ethylene pressure.     

GPGPU for orbital function evaluation with a new updating scheme

We have accelerated an ab initio quantum Monte Carlo electronic structure calculation using general purpose computing on graphical processing units (GPGPU). The part of the code causing the bottleneck for extended systems is replaced by Compute Unified Device Architecture‐GPGPU subroutine kernels which build up spline basis set expansions of electronic orbital functions at each Monte Carlo step. We have achieved a speedup of a factor of 30 for the bottleneck for a simulation of solid TiO₂ with 1536 electrons. To improve the performance with GPGPU we propose a new updating scheme for Monte Carlo sampling, quasi‐simultaneous updating, which is intermediate between configuration‐by‐configuration updating and the widely used particle‐by‐particle updating. The error in the energy due to by the single precision treatment and the new updating scheme is found to be within the required accuracy of ～10^?3 hartree per primitive cell. © 2012 Wiley Periodicals, Inc.     

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.     

Kinetics of ethylene polymerization reactions with chromium oxide catalysts

Principal kinetic data are presented for ethylene homopolymerization and ethylene/1‐hexene copolymerization reactions with two types of chromium oxide catalyst. The reaction rate of the homopolymerization reaction is first order with respect to ethylene concentration (both for gas‐phase and slurry reactions); its effective activation energy is 10.2 kcal/mol (42.8 kJ/mol). The r₁ value for ethylene/1‐hexene copolymerization reactions with the catalysts is ～30, which places these catalysts in terms of efficiency of α‐olefin copolymerization with ethylene between metallocene catalysts (r₁ ～ 20) and Ti‐based Ziegler‐Natta catalysts (r₁ in the 80–120 range). GPC, DSC, and Crystaf data for ethylene/1‐hexene copolymers of different compositions produced with the catalysts show that the reaction products have broad molecular weight and compositional distributions. A combination of kinetic data and structural data for the copolymers provided detailed information about the frequency of chain transfer reactions for several types of active centers present in the catalysts, their copolymerization efficiency, and stability. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 5315–5329, 2008