Copolymerization Reactor Research Articles

CFD modeling of the ethylene–vinyl acetate copolymerization autoclave reactor: Effects of comonomer ratio on reactor dynamics and copolymer properties

Computational fluid dynamics (CFD) modeling of an industrial ethylene–vinyl acetate autoclave copolymerization reactor was conducted to evaluate the effects of comonomer ratios on reactor dynamics and product properties, including the molecular weight distribution (MWD), and copolymer composition. To accurately predict the MWD of copolymer chains under highly nonideal mixing conditions at a reduced computational cost, the CFD-multicompartment model and probability generating function (PGF) transform were applied. The effectiveness of the developed model was validated by the satisfactorily consistent plant data and simulated results. The model revealed that an increase in the vinyl acetate (VA) content significantly decreased the temperature, promoting combinational termination and chain transfer to polymer reaction for a broad copolymer MWD. The pseudo-kinetic-based analysis showed that VA was consumed more slowly than ethylene, resulting in its lower value in the copolymer composition than that of the comonomer ratios. However, despite nonideal mixing, the copolymer composition was maintained to be uniform for the copolymers produced over the entire reactor volume. In conclusion, the proposed model can be used to understand the governing behaviors of copolymerization under nonideal mixing conditions, design commercial copolymerization reactors, and predict copolymer product qualities.

Calculation of Copolymer Component Composition near Interface

A mathematical description of interconnected processes of mass transfer and chemical conversion in a copolymerization reactor is given. Two cases are investigated: simultaneous transfer of two monomers from a gas to a liquid with chemical reaction in the liquid (for example, copolymerization of ethylene and propylene in ethylene-propylene synthetic rubber production) and copolymerization in a liquid near a solid surface (for example, copolymerization of isobutylene and isoprene in butyl rubber production). The dependence of the component composition of the copolymer on the diffusion resistance to the transfer of monomers near the interface is established.

LPV model development and control of a solution copolymerization reactor

In this paper, linear parameter-varying (LPV) control is considered for a solution copolymerization reactor, which takes into account the time-varying nature of the parameters of the process. The nonlinear model of the process is first converted to an exact LPV model representation in the state-space form that has a large number of scheduling variables and hence is not appropriate for control design purposes due to the complexity of the LPV control synthesis problem. To reduce such complexity, two approaches are proposed in this paper. First, an approximate LPV representation with only one scheduling variable is obtained by means of a parameter set mapping (PSM). The second approach is based on reformulating the nonlinear model so that it provides an LPV model with a fewer number of scheduling parameters but preserves the same input–output behavior. Moreover, in the implementation of the LPV controllers synthesized with the derived models, the unmeasurable scheduling variables are estimated by an extended Kalman filter. Simulation results using the nonlinear model of the copolymerization reactor are provided in order to illustrate the performance of the proposed controllers in reducing the convergence time and the control effort.

Optimization of styrene acrylonitrile random bulk copolymerization reactors

Bulk polymerization of random styrene-acrylonitrile (SAN) copolymer using AIBN initiator, in nonisothermal batch reactors is optimized using single and multiple objective functions. The objectives are selected from among: minimization of the reaction time, maximization of the overall monomer conversion, and maximization of the number average molecular weight of the product. Constraints are used for the mole fraction of styrene in the copolymer produced (so as to produce copolymer having desired properties), and on the permissible range of temperature in the reactor. Pareto optimal solutions are obtained for some sample 2- and 3-objective optimization problems. The optimization toolbox of MATLAB with genetic algorithm as the solver is used. Different points in the Pareto set are associated with different optimal temperature histories, a few of which are provided. POLYM. ENG. SCI., 55:2377–2387, 2015. © 2015 Society of Plastics Engineers

Linear Parameter-Varying Control of a Copolymerization Reactor

This paper demonstrates the application of the linear parameter-varying (LPV) framework to control a copolymerization reactor. An LPV model representation is first developed for a nonlinear model of the process. The LPV model complexity in terms of the model order and the number of scheduling variables is then reduced by truncating those system states that have insignificant direct influence on the input-output behavior of the system and do not directly appear in the output equations of the model. It is important to note that these truncated states are still preserved in the reduced model by affecting the scheduling parameters and hence enabling the representation of the input-output map. Using the derived model, a linear fractional transformation (LFT) based LPV controller synthesis approach is used to synthesize a controller for the process. Simulation based studies of the closed-loop behavior of the system regulated by the designed LPV controller demonstrate that the LPV controller solution outperforms a model predicative control designed previously for this system in terms of the achieved control performance and the online computational effort.

Dynamic optimization of a copolymerization reactor using tabu search

A novel multistage dynamic optimization strategy based on meta-heuristic tabu search (TS) is proposed and evaluated through sequential and simultaneous implementation procedures by applying it to a semi-batch styrene–acrylonitrile (SAN) copolymerization reactor. The adaptive memory and responsive exploration features of TS are exploited to design the dynamic optimization strategy and compute the optimal control policies for temperature and monomer addition rate so as to achieve the desired product quality parameters expressed in terms of single and multiple objectives. The dynamic optimization results of TS sequential and TS simultaneous implementation strategies are analyzed and compared with those of a conventional optimization technique based on iterative dynamic programming (IDP). The simulation results demonstrate the usefulness of TS for optimal control of transient dynamic systems.

Analysis of optimal operation of a fed-batch emulsion copolymerization reactor used for production of particles with core–shell morphology

In this paper dynamic optimization of a lab-scale semi-batch emulsion copolymerization reactor for styrene and butyl acrylate in the presence of a chain transfer agent (CTA) is studied. The mathematical model of the process, previously developed and experimentally validated, is used to predict the glass transition temperature of produced polymer, the number and weight average molecular weights, the monomers global conversion, the particle size distribution, and the amount of residual monomers. The model is implemented within gPROMS environment for modeling and optimization. It is desired to compute feed rate profiles of pre-emulsioned monomers, inhibitor and CTA that will allow the production of polymer particles with prescribed core–shell morphology with high productivity. The results obtained for different operating conditions and various additional product specifications are presented. The resulting feeding profiles are analyzed from the perspective of the nature of emulsion polymerization process and some interesting conclusions are drawn.

Multistage dynamic optimization of a copolymerization reactor using differential evolution

ABSTRACTA multistage dynamic optimization methodology with sequential implementation procedure is proposed, and the evolutionary optimizing features of differential evolution (DE) are exploited to implement the methodology for optimal control of a semi‐batch copolymerization reactor. DE is designed and implemented to determine the optimal control policies for monomer addition rate and reactor temperature to produce a polymer with the desired copolymer composition and molecular weight distribution. Further, a similar multistage dynamic optimization strategy based on iterative dynamic programming is used for optimal control of copolymerization reactor and to compare with DE. The results show the effectiveness of the DE‐based multistage dynamic optimization strategy in determining the optimal control policies that yield the desired polymer product characteristics. © 2013 Curtin University of Technology and John Wiley & Sons, Ltd.

Multicriteria dynamic optimization of an emulsion copolymerization reactor

Abstract A multicriteria optimization approach based on an evolutionary algorithm has been developed to determine the optimal control policy for a fed-batch emulsion copolymerization reactor, particularly for styrene and butyl acrylate in the presence of n-C12 mercaptan as chain transfer agent. The process model was elaborated and validated experimentally in order to predict the global monomer conversion, the number and weight average molecular weights, the particle size distribution and the residual monomers mass fraction. The process objectives were to produce core–shell particles (hard core and smooth shell) with specific end-use properties and high productivity. This has been achieved by the maximization of the monomers overall conversion at the end of the process and the minimization of the error between the glass transition temperature and a designed profile subject to a set of operational constraints. The nondominated Pareto solutions obtained were ranked according to a decision making aid method based on a decision maker preferences and experience using multi-attribute utility theory. Finally, the best solution was implemented experimentally.

Two Phase Dynamic Model for Gas Phase Propylene Copolymerization in Fluidized Bed Reactor

A two-phase model is proposed for describing the dynamics of a fluidized bed reactor used for polypropylene production. In the proposed model, the fluidized bed is divided into an emulsion phase and bubble phase where the bubble phase flow pattern is assumed to be plug flow and the emulsion phase is considered to be perfectly mixed. Similar previous models consider the reaction in the emulsion phase only. In this work the contribution of reaction in the bubble phase is considered and its effect on the overall polypropylene production is investigated. The kinetic model combined with hydrodynamic model in order to develop a comprehensive model for gas-phase propylene copolymerization reactor. Simulation profiles of the proposed model were compared with those of well mixed model for the emulsion phase temperature. The simulated temperature profile showed a lower rate of change compared to the previously reported models due to lower polymerization rate. Model simulation showed that about 13% of the produced polymer comes from the bubble phase and this considerable amount of polymerization in the bubbles should not be neglected in any modeling attempt.

Advanced Control of a Continuous Solution Copolymerization Process

A model‐based predictive control system is designed for a copolymerization reactor. These processes typically have such a high nonlinear dynamic behavior to make practically ineffective the conventional control techniques, still so widespread in process and polymer industries. A predictive controller is adopted in this work, given the success this family of controllers is having in many chemical processes and oil refineries, especially due to their possibility of including bounds on both manipulated and controlled variables. The solution copolymerization of methyl methacrylate with vinyl acetate in a continuous stirred tank reactor is considered as an industrial case study for the analysis of the predictive control robustness in the field of petrochemical and polymer production. Both regulatory and servo problems scenarios are considered to check tangible benefits deriving from model‐based predictive controller implementation.

Development of on-line optimization-based control strategies for a starved-feed semibatch copolymerization reactor

A real-time nonlinear optimization scheme is implemented for the high temperature starved feed semi-batch solution polymerization used to produce acrylic resins for automotive coatings. The system input and state trajectories are determined on-line to minimize a cost function defined in terms of deviation from target molecular weight and composition, and batch time. The performance of the proposed strategy is examined through numerical simulation for several study cases for semibatch butyl methacrylate and styrene (BMA/STY) free radical copolymerization. Results show that polymer quality can be assured in reduced batch time while achieving constraint satisfaction over the entire run.

Plant explosion emphasizes importance of implementing PSM

A few years ago, there was an explosion in a reactor at the XYZ Chemical Company. The reactor was a block copolymerization reactor where butadiene and styrene monomers were added in a semibatch manner. The heat of reaction was removed by means of a refrigeration system. The incident occurred when the reactants were not added in the sequence or quantity required. The resulting runaway reaction overpressurized the reactor system and caused an expansion joint to rupture. The hydrocarbons released formed a vapor cloud that exploded, causing the death of two workers, serious injury to three others, and significant damage to the facility. The contributing causes of the incident include: (a) lack of information about the hazards of the chemicals in the process, (b) lack of information about the equipment in the process and inadequate equipment, (c) inadequate or no PHA, (d) inadequate training, (e) confusing operating procedures, (f) failure to use management of change procedures, (g) failure to perform a prestartup safety review, (h) failure to have an adequate contractor safety program, and (i) failure to investigate previous near misses and incidents and take corrective actions. This article describes this accident, the root causes, and the major plant deficiencies. The following expresses my opinion of the events that led to this explosion as testified to in open court. Others may have different opinions. © 2009 American Institute of Chemical Engineers Process Saf Prog, 2010

Batch‐to‐batch control of characteristic points on the PSD in experimental emulsion polymerization

AbstractAn integrated batch‐to‐batch and in‐batch control algorithm to regulate the endpoint particle size distribution (PSD) in an experimental semibatch emulsion copolymerization reactor is presented. Partial least squares (PLS) models of the process are utilized in a model predictive control (MPC) framework to regulate the PSD. The high dimensionality of the PSD is reduced through the use of a new approach, where the heights and positions of the characteristic points on the distribution are used to represent the whole distribution. This approach enables one to shift control priorities on the positions of the modes of a distribution with respect to the heights of the modes as well as efficiently reducing the dimensionality of the problem. The proposed algorithm is first tested on the simulation of the plant and showed success in regulating the PSD both in set point changes and against persistent disturbances. The experimental validation of the algorithm included two case studies where the controller was found to be effective. © 2008 American Institute of Chemical Engineers AIChE J, 2008

Prediction of Bivariate Molecular Property Distributions in Free-Radical Polymerization Systems Using Monte Carlo and Sectional Grid Methods

An efficient Monte Carlo (MC) algorithm and a two-dimensional fixed pivot technique (2-D FPT) are described for the calculation of the average and distributed molecular properties of polymers in batch free-radical polymerization and copolymerization reactors. Simulations are carried out, under different reactor conditions, to calculate the individual monomer conversions, the leading moments of the 'live' and 'dead' polymer chain length distributions as well as the dynamic evolution of the distributed molecular properties (i.e., molecular weight distribution (MWD), long chain branching distribution (LCBD), copolymer composition distribution (CCD), joint LCB-MW and CC-MW distributions, etc.). The validity of the numerical calculations is examined via a direct comparison of the simulation results, obtained by the two numerical methods, with experimental data on the styrene-methyl methacrylate and vinyl acetate batch free-radical polymerization systems. Additional comparisons between the MC and the 2-D FPT methods are carried out for both polymerization systems, under different polymerization conditions. It is clearly shown that both numerical methods are capable of predicting the distributed molecular, branching and copolymer properties, with high accuracy, up to very high monomer conversions.

Matrix Representation of Polymer Chain Size Distributions, 3 – Case Studies for Linear Polymerization Mechanisms at Transient Conditions

AbstractThe mass balance equations used to describe different polymerization systems are represented and analyzed with the help of a general matrix framework previously developed. Some of its properties were presented in previous works and are illustrated here in three examples. The first example regards the dynamics of a copolymerization reactor. It is shown that terminal and penultimate models may predict qualitatively different responses in batch reactions. The second example also regards the dynamics of copolymerization reactions. It is shown how manipulation of initial conditions and monomer feed rates can be used to keep copolymer composition constant throughout the batch. The third example concerns the existence of oscillating chain size distributions when there are multiple monomer insertion steps.magnified image

Dynamic prediction of the bivariate molecular weight–copolymer composition distribution using sectional-grid and stochastic numerical methods

In the present study, a two-dimensional fixed pivot technique (2-D FPT) and an efficient Monte Carlo (MC) algorithm are described for the calculation of the bivariate molecular weight–copolymer composition (MW–CC) distribution in batch free-radical copolymerization reactors. A comprehensive free-volume model is employed to describe the variation of termination and propagation rate constants as well as the variation of the initiator efficiency with respect to the monomer conversion. Simulations are carried out, under different reactor conditions, to calculate the individual monomer conversions, the leading moments of the ‘live’ and ‘dead’ polymer chain length distributions as well as the dynamic evolution of the distributed molecular properties (i.e., molecular weight distribution (MWD), copolymer composition distribution (CCD) and joint MW–CC distribution). The validity of the numerical calculations is examined via a direct comparison of the simulation results, obtained by the two numerical methods, with experimental data on the styrene–methyl methacrylate batch free-radical copolymerization. Additional comparisons between the 2-D FPT and the MC methods are carried out for different polymerization conditions. It is clearly shown that both numerical methods are capable of predicting the distributed molecular and copolymer properties, with high accuracy, up to very high monomer conversions. It is also shown that the proposed dynamic MC algorithm is less computationally demanding than the 2-D FPT.

Multi-rate model predictive control of particle size distribution in a semibatch emulsion copolymerization reactor

A multi-rate model predictive controller algorithm is presented for the in-batch closed-loop control of the full particle size distribution (PSD) in a semibatch emulsion copolymerization system. The lack of frequent measurements of the PSD and the measurement delay of these measurements are addressed through the use of frequent density measurements from which the current conditions of the system are estimated. The high dimensionality of the discretized full PSD is reduced by the use of model order reduction based on principal component analysis. This method effectively reduces the size of the problem while preserving the main characteristics of the population balance system. Disturbances that perturb the surfactant and monomer amounts inside the semibatch vinyl acetate–butyl acrylate reactor are considered to demonstrate the performance of the proposed control algorithm.

Multivariable control of an industrial gas phase copolymerization reactor

Advanced control is used to avoid large temperature offsets for a batch copolymerization gas phase reactor. A nonlinear state-space model is developed to represent the reactor behavior in terms of mass and energy balances. A growth model describes the gas phase copolymerization and includes an activation–deactivation model for the catalyst. The control system includes three manipulated inputs, three controlled outputs and two measurements, temperature and pressure. The strategy combines nonlinear control laws where states are either estimated by extended Kalman filtering or predicted from the kinetic model. This advanced control has been implemented with success on an industrial reactor.

Computer-Aided Model Based Analysis for Design and Operation of a Copolymerization Process

The advances in computer science and computational algorithms for process modelling, process simulation, numerical methods and design/synthesis algorithms, makes it advantageous and helpful to employ computer-aided modelling systems and tools for integrated process analysis. This is illustrated through the study of a copolymerization process, where operational problems due to their complex nonlinear behaviour are usually encountered, indicating thereby, the need for the development of an appropriate process model that can describe the dynamic behaviour over the complete range of conversion. This will allow analysis of the process behaviour, contribute to a better understanding of the polymerization process, help to avoid unsafe conditions of operation, and to develop operational and optimizing control strategies. In this work, through a computer-aided modeling system ICAS-MoT, two first-principles models have been investigated with respect to design and operational issues for solution copolymerization reactors in general, and for the methyl methacrylate/vinyl acetate system in particular. The Model 1 is taken from literature and is commonly used for low conversion region, while the Model 2 has been derived in this work and covers the complete range of conversion. The performances of the two models are compared with respect to the steady state and dynamic behaviour of the polymerization process. The model analyses highlight the influence of the reaction mechanism, the transport phenomena, the process design and conditions of operation on the polymer grade and the production rate.