Inferential closed-loop control of particle size distribution for styrene emulsion polymerization

In this work, a new control strategy for controlling the particle size distribution (PSD) in emulsion polymerization has been proposed. It is shown that the desired PSD can be achieved by controlling the free surfactant concentration which in turn can be done by manipulating the surfactant feed rate. Simulation results show that the closed-loop control of free surfactant concentration results in a better control of PSD compared to open-loop control strategy, in presence of model mismatch and disturbances. Since the on-line measuring of ionic free surfactant concentration is difficult, conductivity which is related to it is measured instead and used for control purposes. The closed-loop control of conductivity also results in a better control of PSD compared to open-loop control strategy, but its performance is not as good as controlling free surfactant concentration in presence of model mismatch.     

Optimal operating strategies for emulsion terpolymerisation

Optimal control policies for emulsion terpolymerisation of styrene, methyl methacrylate (MMA) and methyl acrylate (MA) were determined in a semi-batch reactor using the multi-objective dynamic optimisation method. A comprehensive dynamic model was used for the design of optimal control. The control vector parameterisation (CVP) approach was implemented for constrained optimisation for emulsion terpolymerisation reactors. The feed rates of styrene, MMA, MA, surfactant and initiator, and the temperature of the reactor were used as manipulating variables to produce terpolymers of desired composition, molecular weight distribution (MWD) and particle size distribution (PSD). The particle size polydispersity index (PSPI), molecular weight polydispersity index (MWPI) and the overall terpolymer composition ratios were incorporated in the objective functions to optimise the PSD, MWD and terpolymer composition, respectively. The optimised operational policies were validated with experiments via one stirred tank polymerisation reactor.     

Operation of semi-batch emulsion polymerisation reactors: Modelling, validation and effect of operating conditions

A detailed dynamic model was developed for a styrene emulsion polymerisation semi-batch reactor to predict the evolution of the product particle size distribution (PSD) and molecular weight distribution (MWD) over the entire range of monomer conversion. A system exhibiting zero-one kinetics was employed, with the model comprising a set of rigorously developed population balance equations to predict monomer conversion, PSD and MWD. The modelling equations included diffusion-controlled kinetics at high monomer conversion where the transition from the zero-one regime to a pseudo-bulk regime occurs. The model predictions were found to be in good agreement with experimental results. Both particle growth and the PSD were found to be strongly affected by the monomer feedrate. Reactor temperature had a major influence on the MWD which was, however, insensitive to changes in the monomer feedrate. These findings were confirmed experimentally. As a result, it seems reasonable to propose that the use of the monomer feedrate to control the PSD and the reactor temperature to control the MWD are appropriate in practical situations. Consequently, an optimal monomer feed trajectory was developed off-line (using the validated reactor simulation) and verified experimentally by producing a polymer with specific PSD characteristics.     

On-line multi-variable predictive control of molar mass and particle size distributions in free-radical emulsion copolymerization

A multi-variable model predictive control (MPC) was formulated to solve control problems associated with a combination of regulation and targeting desired set-points. We investigated the simultaneous control of key polymer properties: the particle size (PSD) and molecular weight distribution (MWD) by manipulating the flow rates of the monomers (styrene, MMA), surfactant, initiator and the temperature of the reactor. A multi-input-multi-output (MIMO) formulation was constructed for the constrained optimal control problem to maximize the width of the PSD (with M_n at a constant set-point), and to maximize the average molar mass. The strategy developed within a gPROMS-API-DCS environment allowed real-time implementation of model-based control of the process. The optimal control problem was implemented via an interface to a dynamic optimization code. Major improvements in process operation and polymer property control resulted on the implementation of our multi-variable MPC algorithm. The manipulation of the four flow rates and the temperature increased the degree of freedom in the system and achieved tighter PSD and MWD control. The on-line performance of MPC for MWD and PSD control was found to be satisfactory.     

Molecular weight distribution in low-density polyethylene polymerization; impact of scission mechanisms in the case of a tubular reactor

It has been shown that scission kinetics strongly affects the molecular weight distribution (MWD) of low-density polyethylene (ldPE) in a continuous stirred tank reactor (CSTR). The present paper focuses on the effects of different chemical scission mechanisms, linear and topological scission, as well as mechanical scission on MWD in batch and tubular reactors. In contrast to the CSTR, a batch reactor MWD does not show bimodalities or long tails. The tubular reactor was modeled as an industrially representative system with four initiator injection points and a proper ‘cocktail’ of different initiators. Calculated MWD was compared to one experimentally determined with SEC-MALLS for a commercial tubular product and fair agreement was found. Typically, these MWDs are broad, but not bimodal. Sensitivity studies were performed as to scission kinetics and the effect of chain transfer agent (CTA). Both batch and tubular reactor were observed to be less sensitive to scission kinetics than a CSTR. In addition, alternative CTA injection strategies (downstream positions) were tested. These showed interesting behavior leading to very broad and bimodal MWD. The model allows following the MWD broadening along the tube. We conclude that batch and tubular ldPE reactors lead to completely different MWD behavior than a CSTR and that it is possible to manipulate it to a great extent.     

丁二烯气相聚合产物分子量分布和粒径分布模型研究

对非均相催化的丁二烯气相聚合,基于聚合物多层模型,考虑催化剂颗粒间活性位初始浓度和粒径分布对聚合物分子量分布和粒径分布的影响,建立了聚合物分子量分布和粒径分布的数学模型。模拟了反应温度、催化剂颗粒间活性位初始浓度和粒径分布等因素的影响,结果表明。随着温度升高,聚合物颗粒平均粒径变小,粒径分布变窄,聚合物分子量变小,分子量分布变宽;催化剂颗粒间的活性组分负载越均匀,聚合物分子量越大,分子量分布和粒径分布越窄;随着催化剂平均粒径变大,聚合物分子量变小,分子量分布变宽,不存在催化剂颗粒粒径分布和聚合物颗粒粒径分布间的复制现象。模型模拟结果与实验结果吻合较好,可用于预测丁二烯气相聚合产物的分子量、分子量分布和粒径分布。     

High‐Solid‐Content Emulsions of PVC: Scale‐Down of an Industrial Process for Enhanced Understanding of Particle Formation Part 3: Production of Bimodal Latexes

A scale‐down study of an industrial reactor for the production of polyvinyl chloride (PVC) via an emulsion polymerization process was carried out in order to understand the cause of batch‐to‐batch variations in product quality. The results in Part 2 of this series of papers indicated that a large excess of base is required to control the particle size distribution (PSD) of the seed process. Here, it is demonstrated that the flow rate of the initiator and the second‐stage surfactant are the most important parameters for PSD control. Altering the time point at which the initiator and surfactant are injected allows controlling the relative volume fractions of large and small particles.     

Modelling and simulation of polymerisation processes

In order to model the effects of uneven spatial distribution of components and temperature a computational fluid dynamics (CFD) model has been developed for a living polymerisation reaction in a tubular reactor. The low moments of the molecular weight distribution (MWD) and the dispersiry index of the product as well as the more usual spatial concentration of species and temperature have been calculated. The modelling and simulation work was carried out using the CFD code PHOENICS version 2.1 on Pentium PCs. Additionally, a novel algorithm is described which makes the design of reactor control strategies more tractable by providing a very rapid route to a qualitative approximation of the MWD of products from living polymerisation processes. Numerically simulated data generated using this new procedure are compared with slower but more rigorous approaches to the same problem. The examples cover living polymerisations in an isothermal batch reactor, a steady-state continuous stirred tank reactor (CSTR) and feed-perturbed CSTR. It is demonstrated that, although the novel algorithm comprises only four differential equations, it provides the essential information concerning the position and relative intensity of the peak(s) in a MWD plot needed for the design of reactor control strategies for the production of tailored MWDs.     

Preparation of poly(vinyl chloride) latexes using a dual surfactant system: The effect in the particle size distribution

The control of the average particle size and size distribution in the emulsion polymerization of vinyl chloride monomer is an important parameter to determine, not only the latex characteristics, but also the properties of the final dispersion powder in several industrial applications. It is possible to manipulate the particle size distribution (PSD) by applying a mixture of an anionic surfactant‐fatty alcohol before the start of the free radical polymerization. Contrary to the procedures of the miniemulsion and the derivative diffusional swelling techniques, no kind of high shear is applied to the monomer and/or surfactant mixtures. In fact, the concentration and selection of the anionic surfactant, together with the fatty‐alcohol, can play an interesting role on the final PSD of the polymer's particles. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Polymer chain extension in semibatch emulsion polymerization with RAFT‐based transfer agent: The influence of reaction conditions on polymerization rate and product properties

A mathematical model was developed for batch and semiemulsion polymerizations of styrene in the presence of a xanthate‐based RAFT agent. Zero–one kinetics was employed along with population balance equations to predict monomer conversion, molecular weight (MWD), and particle size (PSD) distributions in the presence of xanthate‐based RAFT agents. The effects of the transfer agent (AR), surfactant, initiator, and temperature were investigated. Monomer conversion, MWD, and PSD were found to be strongly affected by monomer feed rate. The polymerization rate (Rp), number average molecular weight (Mn) and particle size (r) decreased with increasing AR. With increases in surfactant and initiator concentrations Rp increased, whereas with increase in temperature Mn decreased, Rp increased and r increased. In semibatch mode, Mn and r increased with increase in monomer flow rate. By feeding the RAFT agent along with the monomer (F_M/F_AR = N_Mo/N_ARo = 100), Mn attained a constant value proportional to monomer/RAFT molar ratio. The observed retardation in polymerization and growth rates is due to the exit and re‐entry of small radicals. Thus, chain extension was successfully achieved in semibatch mode. The simulations compared well with our experimental data, and the model was able to accurately predict monomer conversion, Mn, MWD, and PSD of polymer products. Our simulations and experimental results show that monomer feed rate is suitable for controlling the PSD, and the initial concentration and the feed rate of AR for controlling the MWD and PSD. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Prediction of Polymer Properties in LDPE Reactors

Summary: A new analysis tool is presented that uses the governing kinetic scheme to predict properties of low‐density polyethylene (LDPE) such as the detailed shape of the molecular weight distribution (MWD). A model that captures mixing details of autoclave reactor operation is used to provide a new criterion for the onset of MWD shouldering. Kinetic effects are shown to govern the existence of MWD shoulders in LDPE reactors, even when operation is far from perfectly‐mixed. MWD shoulders occur when the mean reaction environment has a relatively high radical concentration and has a high polymer content, and is at a low temperature. Such conditions maximize long chain formation by polymer transfer and combination‐termination, while limiting chain scission. For imperfectly‐mixed reactors, the blending of polymer‐distributions produced in different spatial locations has a small effect on the composite MWD. However, for adiabatic LDPE autoclaves, imperfect mixing broadens the stable range of mean reactor conditions, and thereby increases the possibility for MWD shouldering.

Polymer MWD produced in an LDPE autoclave reactor by various kinetic mechanisms.     

Particle size distribution in olefin continuous stirred-bed polymerization reactors

The control of polymer particle size and PSD is of industrial importance. Very fine particles pack poorly, thereby limiting reactor capacity, and present a dust explosion hazard. In olefin polymerization, a particle size distribution (PSD) in the polymerization reactor has been derived using population balances. Three reasonable reaction mechanisms for Ziegler-Natta catalysts, i.e., a simple reaction model, an active site reduction model, and a two sites model, have been used to derive the average number of active sites. It was observed that the PSD depends not only on residence time, but also on the reaction mechanism. It was also found that multiple active sites change the PSD slightly. The PSD, however, does not depend on initial catalyst volume.     

Optimal operation of ethylene polymerization reactors for tailored molecular weight distribution

This work presents a comprehensive steady‐state model of the high‐pressure ethylene polymerization in a tubular reactor able to calculate the complete molecular weight distribution (MWD). For this purpose, the probability generating function technique is employed. The model is included in an optimization framework, which is used to determine optimal reactor designs and operating conditions for producing a polymer with tailored MWD. Two application examples are presented. The first one involves maximization of conversion to obtain a given MWD, typical of industrial operation. Excellent agreement between the resulting MWD and the target one is achieved with a conversion about 5% higher than the ones commonly reported for this type of reactor. The second example consists in finding the design and operating conditions necessary to produce a polymer with a bimodal MWD. The optimal design for this case involves a split of the initiator, monomer, and modifier feeds between the main stream and two lateral injections. To the best of our knowledge, this is the first work dealing with the optimization of this process in which a tailored shape for the MWD is included. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2007     

Molecular weight distributions in terpolymerization of α‐methylstyrene/styrene/acrylic acid in continuous stirred tank reactor

Free‐radical terpolymerization of α‐methylstyrene/styrene/acrylic acid (AMS/ST/AA) in a continuous stirred tank reactor (CSTR) was studied theoretically and experimentally. A series of reactions were conducted to investigate the effect of the reaction temperature, residence time, solvent contents, initiator concentration, chain‐transfer agent level, and different monomer compositions on the molecular weight distribution (MWD). The mathematical model based on “the instantaneous property method (IPM)” and the pseudokinetic rate constant method was introduced and modified to predict the MWD of the bulk terpolymer produced in a CSTR. The effects of process variables were included in the mathematical model. Extensive comparisons were made between the theoretical results and experimental values. The rate of the free‐radical terpolymerization of AMS/ST/AA was comparatively slow and it was found that the concentration of α‐methylstyrene had a strong influence on the molecular weight and polydispersity of the MWD. This presumably reflected the existence of a normal bimolecular termination rate and a slow propagation rate due to steric hindrances at the doubly substituted vinyl carbon atom or transfer of the allylic hydrogen from the α‐methyl group. Good agreement was obtained between calculated MWD and the experimental one by assuming that the disproportionation termination of free radicals was the dominant chain‐stoppage mechanism. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 79: 479–487, 2001     

Advanced modelling and optimal operating strategy in emulsion copolymerization: Application to styrene/MMA system

A model-based framework for advanced optimal operation of copolymerization processes was developed and tested experimentally in conjunction with a distributed control system (DCS) suitable for industrial application. A test case of emulsion copolymerization of styrene (Sty) and methyl-methacrylate (MMA) was investigated for predicting and optimizing key product properties including molecular weight distribution (MWD), particle size distribution (PSD), copolymer composition and conversion. The model equations include diffusion-controlled kinetics at high monomer conversions, where transition from a ‘zero-one’ to a ‘pseudo-bulk’ regime occurs. The reactor mass and energy balances describe the system transients for batch and semi-batch operations. Population balance equations, describe the particle evolution and comprise sets of integro-partial differential and nonlinear algebraic equations. The models were solved using an efficient numerical scheme suitable for on-line monitoring and control. The model predictions were found to be in good agreement with experimental results for measurements carried out with variable monomer feed rates, variable temperature and variable composition of styrene-MMA, from 25/75 to 75/25 proportions. The manipulation of these variables was found to affect the PSD significantly. The experimental results confirmed the accuracy of our optimization scheme for the desired conversion, MWD and PSD.     

Free radical solution oligomerization of styrene in a continuous-stirred tank reactor train

For free radical oligomerization of styrene, a scheme for calculating the molecular weight distribution and conversion in a continuous-stirred tank reactor (CSTR) train is developed, which also allows the calculation of molecular weight distribution (MWD) for batch reaction. Calculations show that under conventional or near dead-end condition: (1) increasing initial initiator concentration, reaction time and reaction temperature, and decreasing initial monomer concentration cause P?_n and P?_w to decrease and MWD to narrow; (2) increasing initial initiator concentration, reaction time and reaction temperature, and increasing monomer concentration cause monomer conversion to increase; (3) a single CSTR gives a lower rate of oligomer production, but a narrower MWD than does a batch reactor.     

Feedback controllability assessment and control of particle size distribution in emulsion polymerisation

In this article, the importance of particle size distribution (PSD) control as a means for the inferential control of the rheology of emulsion polymers is illustrated. A controllability assessment is presented to illustrate the attainability or otherwise of bimodal PSD using feedback control through a consideration of the process mechanisms—measurement limitations and process constraints that prevent the implementation of feedback corrections. The suitability of a batch-to-batch iterative feedback PSD control is demonstrated, which could act in addition to any in-batch feedback control, the latter being less feasible in certain cases, as argued in this article. A detailed population balance model is used for the batch-to-batch control, which simplifies model update and feedback correction.     

Modeling of molecular weight and copolymer composition distributions for ethylene-propylene solution copolymerization

A comprehensive computational fluid dynamics (CFD) model was developed to investigate spatial distributions of molecular weight distribution (MWD) and copolymer composition distribution (CCD) for ethylene-propylene (EPM) copolymers in a bubble column reactor. The CFD approach incorporated Euler–Euler two-fluid model, copolymerization kinetics, and copolymer microstructural distribution model together by user-defined functions for ethylene-propylene heterogeneous copolymerization process. MWD and CCD distributions were calculated by introducing Flory's distribution and Stockmayer's distribution, respectively. CFD model results were validated with literature data. The multiphase hydrodynamics, interphase mass transfer, spatial–temporal variations of MWD and CCD distributions were analyzed. Both distributions are wider at the inlet of reactor for the inefficient mixing, but narrower at the outlet due to fully developed flow and polymerization. This model is beneficial to the improvement of polymer products and process control in industrial EPM reactor.     

Model predictive control of a fixed-bed reactor with nonlinear quality inference

A generic model predictive control framework has been proposed for a fixed-bed reactor with exothermic reaction. The proposed framework can conduct nonlinear inferential control of a product concentration together with linear multivariable control of bed temperatures. In addition, the framework can accommodate the multi-rate sampling and analysis delay caused by the product measurement. Performance of the proposed technique has been demonstrated with a non-adiabatic fixed bed reactor model producing maleic anhydride under various operating scenarios.     

Modeling and analysis of a slurry reactor system for heterogeneous olefin polymerization: The effects of hydrogen concentration and initial catalyst size

This article deals with the development of a model for the polymerization process using a Ziegler‐Natta catalyst in a slurry reactor system. Employed here is the hierarchical model describing the entire reactor system that is subcategoried by the gas bubble phase, the continuous gas phase, the liquid phase, the solid polymer particle, and the surface of catalyst where chemical reaction occurs. The concept of the multigrain model (MGM) is introduced to describe the growth of polymer particle from the original catalyst particle. We also adopt the concept of multiple active sites to elucidate the broad molecular weight distribution (MWD). The major concern here is the effects of the hydrogen concentration and the size of the initial catalyst on the performance of the polymerization reactor. It is demonstrated that the hydrogen gas can be used for the purpose of controlling not only the molecular weight but the molecular weight distribution (MWD) of the polymer. In addition, the relationship between the molecular weight and the concentration of hydrogen gas is investigated. The size of the initial catalyst is found to exercise a significant influence on the morphology of the resultant polymer particle. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 79: 2480–2493, 2001