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.     

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.     

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.     

High Molecular Weight Polystyrene Obtained by Cationic Emulsion Polymerization Catalyzed by Imidazolium‐Based Ionic Liquid

The ionic liquid 1‐n‐butyl‐3‐methylimidazolium heptachlorodiferrate (BMI.Fe₂Cl₇) is efficiently used as catalyst in the cationic emulsion polymerization of styrene. The effect of different reaction temperatures, surfactant, and ionic liquid concentrations on polymer properties as molecular weight distribution and particle size is evaluated. High weight average molecular weights, above 1000 kDa, are achieved at 70% of conversion in 100 nm polystyrene particles formed mainly by micellar nucleation. Particle sizes and molecular weights increase with the decrease of the amount of surfactant. Even at low concentrations, BMI.Fe₂Cl₇/styrene molar ratio equal to 1/1000, the ionic liquid proves to be efficient for the emulsion polymerization of styrene, and lower ionic liquid concentrations lead to the formation of longer polymer chains.     

Emulsion polymerization of styrene in a single continuous stirred-tank reactor

The effects of mean residence time, initiation rate, and emulsifier concentration on particle formation, particle growth, and polymerization rate are examined for the emulsion polymerization of styrene in a completely mixed continuous stirred-tank reactor. Experimental measurements of number of particles, particle size distribution, polymerization rate, and molecular weights are compared with theoretical predictions. A theoretical model which incorporates Stockmayer's modification of the Smith-Ewart theory into the particle growth equation allows reasonably accurate prediction of polymerization rate, particle formation rate, and particle size distribution. Agreement between experimental measurements of number-average and weight-average molecular weights and a theory based on Smith-Ewart case 2 kinetics is also reasonable.     

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.     

High Xylose Yields from Dilute Acid Pretreatment of Corn Stover Under Process-Relevant Conditions

Pretreatment experiments were carried out to demonstrate high xylose yields at high solids loadings in two different batch pretreatment reactors under process-relevant conditions. Corn stover was pretreated with dilute sulfuric acid using a 4-l Steam Digester and a 4-l stirred ZipperClave® reactor. Solids were loaded at 45% dry matter (wt/wt) after sulfuric acid catalyst impregnation using nominal particle sizes of either 6 or 18 mm. Pretreatment was carried out at temperatures between 180 and 200 °C at residence times of either 90 or 105 s. Results demonstrate an ability to achieve high xylose yields (>80%) over a range of pretreatment conditions, with performance showing little dependence on particle size or pretreatment reactor type. The high xylose yields are attributed to effective catalyst impregnation and rapid rates of heat transfer during pretreatment.     

Microfluidic synthesis of colloidal silica

We demonstrate the design, fabrication, and operation of microfluidic chemical reactors for the synthesis of colloidal silica particles. Two reactor configurations are examined: laminar flow reactors and segmented flow reactors. We analyze particle sizes and size distributions and examine their change with varying linear flow velocity and mean residence time. Laminar flow reactors are affected by axial dispersion at high linear velocities, thus leading to wide particle size distributions under these conditions. Gas is used to create a segmented flow, consisting liquid plugs separated by inert gas bubbles. The internal recirculation created in the liquid plugs generates mixing, which eliminates the axial dispersion effects associated with laminar flow reactors and produces a narrow size distribution of silica nanoparticles.     

Crosslinking Kinetics: Partitioning According to Number of Crosslinks

Summary: To mathematically describe crosslinking kinetics for polymers, we have proposed a novel method that accounts for the number of crosslinks, that is, partitioning according to number of crosslinks (PANC). By contrast, the well‐known method of numerical fractionation tracks generations of crosslinked molecules, defined to include a range of crosslinks. The proposed crosslinking kinetics yield a population balance model that provides moments and hence measurable average properties such as number average molecular weight and weight average molecular weight, polydispersity and average crosslink number. The gel points for batch and continuous‐flow stirred‐tank reactors are derived. Because the usual closure methods do not yield satisfactory convergence, new representations for post‐gelation moments are proposed. The results realistically show how the moments change with time in the post‐gel region.

The average number of crosslinks in the bulk and sol versus time in a batch reactor; the gel point is the dashed line.     

Seeded semicontinuous emulsion copolymerization of methyl methacrylate,butyl acrylate,and phosphonated methacrylates: Kinetics and morphology

A series of methyl methacrylate, butyl acrylate, and phosphonated methacrylate (MAPHOS) copolymers were prepared by seeded semicontinuous emulsion polymerization under monomer‐starved conditions by varying the amount and nature of phosphonated methacrylates (diester, monoacid, and diacid). The effects on the kinetics, molecular weight distribution, and particle size distribution were investigated. The molecular weights and particle growth were affected by the amount of acidic MAPHOS in the recipe. Secondary nucleation occurred above a critical concentration of acidic MAPHOS (5 wt %). Characterization of the latices by elemental analysis provided information on the phosphonic acid location and showed that phosphonic oligomers were formed in the aqueous phase. Particle size data and electrophoretic behavior of the latex afforded a discussion on the particle surface morphology. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2469–2480, 2003     

Emulsion polymerization. IV. Experimental verification of the theory based on slow termination rate within latex particles

A large body of data shows that the time dependence of conversion fits the equation P = At² + Bt in the interval where, according to the Smith-Ewart model, the relationship should be linear. For latexes of very small particle size the Smith-Ewart linear relationship (P = Bt) is often observed, and for latexes of very large particle size the conversion was found to be proportional to t². The experimental value of parameter B was in good agreement with independent theoretical predictions. From A and B the ratio between termination and propagation constants was calculated and was in the 5–200 range. Independent estimates of this ratio give the same order of magnitude. These independent estimates are from the literature and are obtained from the increase in conversion rate at catalyst post-addition during emulsion polymerization or from emulsion polymerization initiated by intermittent irradiation or from homogeneous polymerization in the presence of inert polymers of high viscosity. The conversion–time curves describing the whole conversion process generally have sigmoid shape. The molecular weight is often found to pass through a maximum as the conversion increases. In one experiment this maximum coincided with the calculated maximum in the average number of radicals per particle Q. The variation of experimental molecular weights with conversion accurately followed the theoretical predictions. The deviation from the Smith-Ewart model was often significant. The value of Q was not 0.5, as the Smith-Ewart model requires it to be, but often reached values much larger, as large as 10. The particle size distribution broadened with increasing conversion and became increasingly skew. Numerous data taken from the literature are in good quantitative or qualitative agreement with the theory proposed in Part III and for these data the observed deviations from the Smith-Ewart theory are readily explainable. The new data obtained with styrene, n-butyl methacrylate, and methyl methacrylate are also in quantitative agreement with the new theory. One experiment involving methyl methacrylate is analyzed in great detail. The variation of time, of Q, of molecular weight, of average particle size, and of particle size distribution with conversion are reported. The molecular weight distribution is also calculated from the conversion dependence of molecular weight.     

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.     

Design of Nonlinear Model‐Based Control Using Bifurcation Analysis for Solution Polymerizations Carried Out in Lumped‐Distributed Reactors

In order to implement nonlinear control, nonlinear system identification must be performed, however, there are open questions concerning this field of process control, for example, experimental planning, model structure selection, parameter estimation, and validation. Therefore, the study of nonlinear model identification is a relevant unsolved problem that needs to be handled for nonlinear control synthesis. This paper presents the use of bifurcation theory, dynamic and stability analysis for nonlinear identification, and control of polymerization reactors. Peroxide‐initiated styrene‐solution polymerization reactors (lumped‐distributed) are investigated: batch, continuous stirred‐tank reactor (CSTR), and tubular reactors. Open and closed loop analyses are carried out using jacket temperature and weight average molecular weight setpoints as the bifurcation parameters. Phenomenological mathematical models, neural network nonlinear models, and an experimental data from a polymerization unit are employed for validating the proposed methodology in order to implement confident nonlinear controllers.     

Enzyme reactors in unsegmented flow injection analysis

The design of immobilized-enzyme reactors for use in flow injection analysis is discussed. The reactors should be optimized for a short residence time and a very high (> 99.9%) conversion of substrate to products. Selection of carrier and immobilization method is important in order to increase the amount of active enzyme per unit volume. The effeciency of the reactor can be increased by decreasing the particle size in packed-bed reactors and the radius of open tubular reactors. The maximum inherent rate constant that can be obtained under optimal conditions is estimated for a number of enzymes of analytical interest; it is shown that with high rate constants and small particle diamters, residence times less than seconds can be obtained. Some applications of immobilized-enzyme reactors in flow systems are reviewed.     

Continuous precipitation polymerization of acrylic acid in supercritical carbon dioxide: The polymerization rate and the polymer molecular weight

The precipitation polymerization of acrylic acid in supercritical carbon dioxide was studied in a continuous stirred tank reactor with 2,2′‐azobis(2,4‐dimethylvaleronitrile) as the free‐radical initiator. The reactor temperature was between 50 and 90 °C, the pressure was 207 bar, and the average residence time was between 12 and 40 min. The product polymer was a white, dry, fine powder that dissolved in water. A wide range of polymer molecular weights (5–200 kg/mol) was obtained. The effects of the operating variables on the polymerization rate and on the polymer molecular weight were evaluated. The observed kinetics suggested that polymerization took place in both the supercritical fluid and the precipitated polymer particles. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 2546–2555, 2005     

Preparation of polyurethane dispersions by miniemulsion polymerization

With a two‐step miniemulsion polymerization, hydrophobic polyurethane (PU) dispersions were prepared with a cosurfactant, the costabilizer hexadecane (HD) in the oil phase, and sodium dodecyl sulfate (SDS) in the water phase. The first step involved the formation of NCO‐terminated prepolymers between isophorone diisocyanate and poly(propylene glycol) oligomer in toluene. Next, PU dispersions were produced by a miniemulsion method in which an oil phase containing NCO‐terminated prepolymers, HD, the chain extender 1,4‐butanediol (BD), the crosslinking agent trimethylol propane (TMP), and the catalyst dibutyltin dilaurate was dispersed in the water phase containing SDS. The influence of experimental parameters, such as the ultrasonication time, concentrations of SDS and HD, and TMP/BD and NCO/OH equivalent ratios, on the sizes of the miniemulsion droplets and polymer particles, as well as the molecular weights and thermal properties of the PU polymer, was examined. The chemical structure of the produced PU polymer was identified with a Fourier transform infrared spectrometer. The molecular weight distribution and average particle size were measured through gel permeation chromatography and dynamic light scattering, respectively. The thermal stability of the PU polymer was characterized with thermogravimetric analysis. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4870–4881, 2005     

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.     

Experimental Design and Statistical Analysis of AGET ATRP of MMA in Emulsion Polymer Reactor

This study investigates atom transfer radical polymerization (ATRP) of methyl methacrylate (MMA) using activators generated by electron transfer (AGET) as the initiation technique in an emulsion well‐mixed 2L stirred tank reactor. The performance of the AGET ATRP of MMA is analyzed for five key independent variables, namely temperature, catalyst complex (CuBr2/dNbpy), initiator (EBiB), reducing agent (ascorbic acid), and surfactant (Brij 98). The reaction is carried out based on a two‐step polymerization procedure. A resolution 5 fractional factorial design technique is employed to assess the influence of the five independent variables on the monomer conversion, polymer average molecular weights, and polydispersity index (PDI). An input–output model is constructed from the data of 21 designed experimental tests. A statistical analysis of the results shows that the temperature is the most influential variable for the three output process responses. The initiator strongly affects the poly(methyl methacrylate) (PMMA) molecular weights. It is the least important key variable affecting MMA conversion and PDI, and the surfactant is the least one affecting PMMA Mn. On assessing the independent interactions effect, the interactions of temperature‐surfactant on conversion, and temperature‐initiator for PMMA M_n are considered. Process simulation in 3D mapping has demonstrated that model predictions agree well with experimental data.     

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.     

Continuous reaction system to investigate the dispersion polymerization of vinyl monomers in supercritical carbon dioxide

A laboratory‐scale continuous reaction system using a stirred tank reactor was assembled in our laboratory to study the dispersion polymerization of vinyl monomers in supercritical carbon dioxide (scCO₂). The apparatus was equipped with a suitable downstream separation section to collect solid particles entrained in the effluent stream from the reactor, whose monomer concentration could be measured online with a gas chromatograph. The dispersion polymerization of methyl methacrylate in scCO₂ was selected as a model process to be investigated in the apparatus. The experiments were performed at 65 °C and 25 MPa with 2,2′‐azobisisobutyronitrile as the initiator and a reactive polysiloxane macromonomer as a surfactant to investigate the effect of the mean residence time of the reaction mixture on the monomer conversion, polymerization rate, polymer molecular weight, and particle size distribution. The results were compared with those obtained in batch polymerizations carried out under similar operative conditions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4122–4135, 2006