Reactor and Product Optimization via Raman Fiber Optics Monitoring: Application to Polymer‐Based Proppants

A setup to characterize polymerization kinetics of polymer‐based proppants produced in an industrial batch reactor by suspension polymerization is presented. A microscale reactor is designed to mimic temperature and pressure conditions of the industrial counterpart. Raman spectroscopy is used to follow the consumption of vinyl bonds of the styrene monomer and the crosslinker via disappearance of the peak at 1632 cm^‐1. Raman data from the microscale reactor are remotely obtained via a fiber optics system. Reaction progress by any generic formulation can be safely followed up to conversions of 90%, well beyond the gel point. Reaction rates are used to define feasible temperature–time profiles for the industrial reactor. In parallel, bulk and suspension polymerizations are carried out under those temperature–time profiles in a 3 L laboratory reactor to produce proppants formulations with the geometry required to perform product characterization, mainly focused on the thermal and mechanical response of the polymer particles. Overall, the whole setup allows optimization of proppant formulations and the cost of their processes of production.     

Effects of Monomer Flow Rate,Flow Configuration,and Reactor Geometry on the Rate of Plasma Polymerization

The effects of flow rate on the plasma polymerization of ethylene in an rf discharge were investigated using both a tubular and a bell-jar-type of reactor. Both reactors contained parallel plate internal electrodes. Experiments with the tubular reactor showed that both the total thickness of the deposit and its distribution in the axial direction were strong functions of the flow rate. At low flow rates the polymer thickness decreased in the flow direction, while at high flow rates the polymer thickness increased. Each of these observations is explained by a simple model of plasma polymerization. Using the bell-jar reactor, different monomer flow distribution configurations were tested to determine their effect on the distribution of polymer thickness. It was found that distribution or diffusion of the monomer inflow provided a more uniform film.     

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.     

Modeling Free Radical Ethylene Polymerization with Multifunctional Comonomers in Tubular Reactors: Influence on Microstructural LDPE Properties

Summary: A kinetic model is developed to predict the effect of multi-functional comonomers in the high-pressure polymerization of ethylene in industrial tubular reactors. Two different modified acrylate based comonomers were tested in the simulation for their influence on molecular-weight distribution and branching densities. A comparison of both methods shows their potential to be used in an industrial process.     

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.     

Applied Thermodynamics for Process Modeling in Catalytic Gas Phase Olefin Polymerization Reactors

The Sanchez–Lacombe Equation of State (SL EoS) is used to model the solubility of different industrial alkane penetrants in polyethylene to explain the importance of considering different diluents for different processes, and the impact that this choice can have on operating conditions, especially for the production of linear low density polyethylene (LLDPE). Extension of this approach to ternary (ethylene/penetrant/LLDPE) systems shows the effect of composition of penetrant/ethylene mixtures on the solubility of such mixtures in LLDPE and swelling of the polymer phase at conditions of industrial relevance. This analysis reveals that using a constant polymer density instead of that predicted by the SL EoS can result in erroneous calculations of the particle size distribution developments in an olefin polymerization reactor.     

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.     

Kinetic study of gas phase olefin polymerization with a TiCl4/MgCl2 catalyst. II. Kinetic parameter estimation and model building

Monomer transport and polymerization kinetics are two key phenomena in olefin polymerization with heterogeneous transition metal catalysts. To have a better understanding of these interrelated kinetics and diffusion phenomena, a quantitative calculation of the monomer diffusion directly from experimental study is essential. In this work, a novel temperature-perturbation technique is developed to systematically study the kinetic and diffusion limitations in catalyzed gas phase olefin polymerization. A physical model of the particle growth mechanism as well as its mathematical representation is presented and the diffusion limitations occurring in the system at high temperature are characterized and quantitatively analyzed. Finally, the practical implications of the results of this study on the operation of industrial scale polyolefin reactors are examined. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 2075-2096, 1997     

Ab initio Emulsion Polymerization by RAFT (Reversible Addition–Fragmentation Chain Transfer) through the Addition of Cyclodextrins

A novel process to produce homo‐ and copolymers by RAFT polymerization in emulsion is presented. It is known that RAFT‐controlled radical polymerization can be conducted in emulsion polymerization without disturbing the radical segregation characteristic of this process, thus leading to polymerization rates identical to those encountered in the corresponding nonliving systems. However, RAFT agents are often characterized by very low water solubility and, therefore, they diffuse very slowly from the monomer droplets, where they are initially solubilized, to the reaction loci, i.e., the polymer particles. Accordingly, when used in emulsion polymerization, they are practically excluded from the reaction. In this work, we show that cyclodextrins, well‐known for their ability to form water‐soluble complexes with hydrophobic molecules, facilitate the transport across the H₂O phase of the RAFT agent to the polymer particles. Accordingly, chains grow through the entire process in a controlled way. This leads to the production of low‐polydispersity polymers with well‐defined structure and end functionalities as well as to the possibility of synthesizing block copolymers by a radical mechanism.     

Novel Industrial Application of Miniemulsion Polymerization – Use of Alkali Soluble Resin as Surfactant in Miniemulsion Polymerization

Nowadays, the great versatility of the miniemulsion polymerization technique to synthesize novel and high value added materials attracts great interest from both the academic and the industrial community. Recently, a novel process based on the use of alkali soluble resin (ASR) as sole surfactant in miniemulsion polymerization for high solids content latexes has been disclosed. This new technology opens a vast field for the production of high performance latexes for industrial applications, as well as an interesting topic for future academic research. This work presents the key factors influencing the use of ASR in aqueous polymer dispersions, highlighting the differences in terms of types and concentrations of ASR used in conventional and miniemulsion polymerization. The effects of type of initiator, ASR concentration and type, as well as solids content on the miniemulsion polymerization of styrene and acrylic monomers are presented.     

Case studies with mathematical modeling of free-radical multi-component bulk/solution polymerizations: Part 2

In Part 2 of this series of two extensive overviews of multi-component polymerization case studies, we again present mathematical modeling results with experimental confirmations. Part 2 represents a refinement and expansion of the detailed and extensive mathematical model presented in Part 1 for free-radical, bulk and/or solution multi-component polymerizations. The expansion is mainly with respect to depropagation, thus making the model more fluent at elevated polymerization temperatures and, in parallel, with additional features as backbiting (with systems involving butyl acrylate). The model considers up to six monomers (unique in the literature), for either batch or semi-batch reactor modes. As the simulator database contains several monomers, initiators, solvents, chain transfer agents and inhibitors, all tested over a wide range of polymerization conditions, from data in both academic and industrial laboratories, several hundred combinations of ingredients can be modeled. The many outputs generated by the model include conversion, molecular weight, polymer composition, branching indicators, sequence length, as well as many other polymerization characteristics related to both production rate and polymer quality. Although the only literature data found to date contain a maximum of four monomers, model predictions for homo-, co-, ter- and tetra-polymerizations show reasonable agreement against the data at both regular and elevated temperatures. With these expansions, this model is directed towards becoming a complete free-radical polymerization tool for training and educational uses both in industry and academia.     

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.     

A Self‐Supporting Strategy for Gas‐Phase and Slurry‐Phase Ethylene Polymerization using Late‐Transition‐Metal Catalysts

The polyolefin industry is dominated by gas‐phase and slurry‐phase polymerization using heterogeneous catalysts. In contrast, academic research is focused on homogeneous systems, especially for late‐transition‐metal catalysts. The heterogenization of homogeneous catalysts is a general strategy to provide catalyst solutions for existing industrial polyolefin synthesis. Herein, we report an alternative, potentially general strategy for using homogeneous late‐transition‐metal catalysts in gas‐phase and slurry‐phase polymerization. In this self‐supporting strategy, catalysts with moderate chain‐walking capabilities produced porous polymer supports during gas‐phase ethylene polymerization. Chain walking, in which the metal center can move up and down the polymer chain during polymerization, ensures that the metal center can travel along the polymer chain to find suitable sites for ethylene enchainment. This strategy enables simple heterogenization of catalysts on solid supports for slurry‐phase polymerization. Most importantly, various branched ultra‐high‐molecular‐weight polyethylenes can be prepared under various polymerization conditions with proper catalyst selection.     

Comparing Long‐Chain Branching Mechanisms for Ethylene Polymerization with Metallocenes and Other Single‐Site Catalysts: What Simulated Microstructures Can Teach Us

Three different long‐chain branch (LCB) formation mechanisms for ethylene polymerization with metallocenes in solution polymerization semi‐batch and continuous stirred‐tank reactors are modeled to predict the microstructure of the resulting polymer. The three mechanisms are terminal branching, C–H bond activation, and intramolecular random incorporation. Selected polymerization parameters are varied to observe how each mechanism affects polymer microstructure. Increasing the ethylene concentration during semi‐batch polymerization reduces the LCB frequency of polymers made with the terminal branching and intramolecular mechanisms, but has no effect on those made with the C–H bond activation mechanism, which disagrees with most previous data published in the literature. The intramolecular mechanism predicts that LCB frequencies hardly depend on polymerization time or ethylene conversion, which also disagrees with the published experimental data for these systems. For continuous polymerization reactors, experimental data relating polydispersity to LCB frequency can be well described with the terminal branching mechanism, but both C–H bond activation and intramolecular models fail to describe this experimental relationship. Therefore, detailed simulations confirm that the terminal branching mechanism is indeed the most likely mechanism for LCB formation when ethylene is polymerized with single‐site coordination catalysts such as metallocenes in solution polymerization reactors.     

Steady State Simulation of Ethylene Polymerization Using Multiple-Site Coordination Catalysts

Summary: Simulation models are important tools for the development and optimization of polymerization processes because they can describe catalyst performance and polymer properties as a function of polymerization kinetics and process conditions. As the polyolefin industry moves towards the production of resins with more complex microstructures, these models become essential for process understanding and product design. A simulation model has been developed for the polymerization of ethylene in a process with n reactors working in series. The model can predict raw material conversions and product properties like the molecular weight distribution (MWD) coupled with short chain branching distribution (SCBD), melt index, density and fluff morphology. Model parameters have been obtained from laboratory data. The model predictions are in good agreement with experimental results.     

Modeling of Ethylene Polymerization Kinetics over Supported Chromium Oxide Catalysts

Summary: Silica supported chromium oxide catalysts have been used for many years to manufacture polyethylene and they still account for more than 50% of world production of high‐density polyethylene. Along with its commercial success, the catalytic mechanism and polymerization kinetics of silica supported chromium oxide catalysts have been the subject of intense research. However, there is a lack of modeling effort for the quantitative prediction of polymerization rate and polymer molecular weight properties. The chromium oxide catalyzed ethylene polymerization is often characterized by the presence of an induction period followed by a steady increase in polymerization rate. The molecular weight distribution is also quite broad. In this paper, a two‐site kinetic model is developed for the modeling of ethylene polymerization over supported chromium oxide catalyst. To model the induction period, it is proposed that divalent chromium sites are deactivated by catalyst poison and the reactivation of the deactivated chromium sites is slow and rate controlling. To model the molecular weight distribution broadening, each active chromium site is assumed to have different monomer chain transfer ability. The experimental data of semibatch liquid slurry polymerization of ethylene is compared with the model simulations and a quite satisfactory agreement has been obtained for the polymerization conditions employed.

Polymerization rates at different reaction temperatures: symbols – data, lines – model simulations.     

Effect of Reaction Conditions and Catalyst Design on the Rheological Properties of Polyolefins Produced in Gas‐Phase Olefin Polymerization Reactors

A model is developed to predict the viscoelastic behavior of polyolefins produced in catalytic polymerization reactors. The approach is based on the solution of different sub‐models (e.g., a kinetic model, a single particle model, a macroscopic reactor model and a rheological model). From the calculated rheological curve, the polymer melt index is determined. The ability of the proposed model to predict the viscoelastic behavior of linear polymer melts quantitatively is examined for the operation of a catalytic olefin polymerization cascade‐loop reactor process. In addition, the transient rheological properties of polyolefins produced in a Ziegler‐Natta gas‐phase olefin polymerization fluidized‐bed reactor are calculated.

     

Modelling of ethanol evaporative losses during batch alcohol fermentation

A general theoretical model to predict evaporative ethanol losses during the industrial process of batch alcohol production by fermentation is suggested. The model takes into account the combined effects of several yield loss factors. It also includes kinetic equations to predict product formation as a basis for calculating evaporative rates.The model has been compared with others reported in the literature and a compilation of experimental data from different discontinuous processes has been used for verification, at both industrial and laboratory levels. The results show the suggested model to yield higher theoretical consistency as well as better adaptability to actual experimental data.