Copolymerization Reactor Research Articles

Dynamic simulation and operation of a high pressure ethylene-vinyl acetate (EVA) copolymerization autoclave reactor

Polyethylene (PE) is one of the most widely used polymers in chemical industry. In all the PE processes, low density polyethylene (LDPE) process is generally considered as the most profitable segment of the polyethylene business worldwide. There are two basic processes used for the manufacturing of LDPE: autoclave and tubular reactor, where autoclave reactor is often used to produce high-value specialty-type grades including ethylene-vinyl acetate (EVA) copolymer. Depending on different grades of the product, reactor zone temperatures in this autoclave process can be in the range 150–230 °C and pressure in the range of 1500–2000 kg/cm 2. In this paper, dynamic simulation of an industrial EVA copolymerization reactor will be established. Industrial operating condition data of seven product grades with melt index ranging from ones to over four hundred will be used as fitted data to obtain the key kinetic parameters in the model. The predicted outputs of melt index, vinyl acetate wt.% in polymer, and polymer production rate will be compared to plant data. This dynamic model was used in determining the controller tuning constants of the three important zone temperature control loops of the autoclave reactor and was also used for comparative study of various operating policies during grade transition.

Calorimetry for Inferential Conversion Monitoring in Emulsion Copolymerization Reactors

A dynamic model was developed describing emulsion copolymerization of styrene and MMA within a batch/semibatch stirred tank reactor. This model includes the initiation, propagation, transfer and termination steps of the monomers styrene and MMA. It also includes the mass and energy balance equations for the polymeric radicals. Energy balance equations incorporate the heat of reaction, internal and external heat transfer effects, as well as heat losses. The resulting sets of (differential/algebraic) equations were solved for both species concentrations and temperature profiles as functions of time. Experiments were conducted in a laboratory reactor, instrumented with platinum resistance thermal transducers and gravimetric conversion measurement devices. Thermal measurements in conjunction with the energy equations helped estimate monomer conversions as a function of time. The kinetic model predictions of conversion compared well with inferential calorimetric measurements, which were validated using gravimetric data. The experiments were run at variable operational conditions in terms of feed rate, temperature and monomers feed ratio. The calorimetric model was used as a soft sensor for the prediction of the rate of reaction, conversion and molar mass.

DIAGNOSIS OF FAULTS WITH VARYING INTENSITIES USING POSSIBILISTIC CLUSTERING AND FAULT LINES

In this paper, a new approach for fault detection and isolation that is based on the possibilistic clustering algorithm is proposed. Fault detection and isolation (FDI) is shown here to be a pattern classification problem, which can be solved using clustering and classification techniques. The possibilistic clustering approach was proposed to address some of the short comings of the fuzzy c-means (FCM) algorithm. The probabilistic constraint imposed on the membership value in the FCM algorithm is relaxed in the possibilistic clustering algorithm. Because of this relaxation, the possibilistic approach is shown in this paper to give more consistent results in the context of the FDI tasks. The proposed approach addresses the issue of correctly isolating a fault that may occur with varying intensities. The concept of fault lines is introduced, which in conjunction with possibilistic clustering has been effectively used for FDI. Fault signatures that change as a function of the fault intensities are represented as fault lines, which are shown to be useful to classify faults that can manifest with different intensities. The proposed approach has been validated here through simulations involving a co-polymerization reactor simulation.

Improving Impact Poly(propylene) Morphology and Production: Selective Poisoning of Catalyst Surface Sites and the Use of Antistatic Agents

AbstractSummary: Selective poisoning has been studied as a means of improving the morphology and rheological properties of high‐impact poly(propylene) copolymer particles. Two different methods of poisoning the catalyst surface in order to avoid the accumulation of ethylene‐propylene rubber (EPR) without influencing the reaction kinetics were tested: a slurry‐phase poisoning step using ethylene glycol dimethyl ether between the homopolymerisation and copolymerisation reaction steps; and direct poisoning via the use of a commercial antistatic agent during the gas‐phase copolymerisation reactor. It was observed that both methods eliminated the formation of rubber on the particle surface without noticeably influencing the kinetics. On the other hand, the use of the products directly in the gas‐phase reaction also contributed to the reduction of static electricity. It can be concluded from these experiments that industrial antistatic agents derive at least part of their effect from poisoning of the active sites on the surface of the catalyst. Furthermore, it appears that in the case of the catalyst used in this study, EPR does not appear to flow out of the growing particles. Most of the EPR found at the surface of the particles is formed close to it.SEM images of hiPP and GLYM001.imageSEM images of hiPP and GLYM001.

Modeling and Sensitivity Analysis of Particle Size Distribution and Chain Length Distribution in a Semibatch Emulsion Copolymerization Reactor

AbstractSummary: A comprehensive model is developed to predict the relationship between the particle size distribution and molecular weights of particles in an emulsion copolymerization reactor. A full population balance equation is used for the particle size distribution and extended to the model for the molecular properties using a continuous reactor approach. The numerical prediction clearly distinguishes the characteristics of molecular properties of particles by homogeneous nucleation from those by micellar nucleation with the dependence on the particle size. Sensitivity analysis of the proposed model under a variety of conditions shows that the compartmentalized feature of the emulsion system should be considered for better prediction of molecular properties, and provides information on the manipulated variables and lumped parameters which effectively decompose the correlation of both properties. Finally, a control strategy utilizing a lumped parameters tracking method is suggested for the regulation of both the particle size distribution and molecular properties.Time evolution of number‐averaged molecular weights in the element under base conditions.magnified imageTime evolution of number‐averaged molecular weights in the element under base conditions.

Modeling and Analysis of Ethylene/Norbornene Copolymerization with ansa-Zirconocene/Methylaluminoxane Catalysts in a Continuous Polymerization Reactor

The kinetics of ethylene/norbornene copolymerization with rac-Et(1-indenyl)2ZrCl2 (1) and [2,2‘-Me(1,3-Me2Cp)2]ZrCl2 (2) catalysts with modified methylaluminoxane are analyzed through experimentation and theoretical modeling. These catalysts show that the rate of norbornene incorporation into the copolymer is strongly catalyst dependent. For example, while catalyst 1 shows a decreasing polymerization rate with an increase in the norbornene concentration, catalyst 2 shows a monotonically increasing polymerization rate with an increase in the norbornene concentration for a norbornene/ethylene mole ratio up to 50 in the bulk liquid phase. Both terminal and penultimate models are developed to describe the rate process with these catalysts. It is shown that for both catalyst systems the penultimate model yields a more accurate description of the copolymerization kinetics than the terminal model. The penultimate model has also been applied to a continuous copolymerization reactor system with catalyst 2. The copolymerization was also carried out in a continuous stirred tank reactor. The model simulation results and the experimental data of norbornene conversion, solid content, and glass transition temperature profiles obtained from a laboratory-scale continuous reactor operation have been compared. Interestingly, the model simulations show that the ethylene concentration in the bulk liquid phase is much lower than the saturated ethylene concentration, suggesting that mass-transfer resistance might be present for the ethylene gas in reaching the catalytic sites in the liquid phase.

Dynamic optimization of a semi-batch reactor for polyurethane production

In this work, the dynamic optimization of a polyurethane copolymerization reactor is addressed. A kinetic–probabilistic model is used to describe the nonlinear step-growth polymerization of a mixture of low- and high-molecular-weight diols, and a low-molecular-weight diisocyanate. The dynamic optimization formulation gives rise to a highly complex and nonlinear differential–algebraic equation (DAE) system. The DAE optimization problem is solved using a simultaneous approach (SDO) wherein the differential and algebraic variables are fully discretized leading to a large-scale nonlinear programming (NLP) problem. The main reactor operation process control objective is the maximization of the molecular weight distribution (MWD) under a desired batch time, subject to a large set of operational constraints, while simultaneously avoiding the formation of polymer network (gel molecule). Typically, polyurethane formation is carried out using batch reactors. However, batch operation leads to attain relatively low MWD values and, if the process is not efficiently operated, there is always the possibility of obtaining a polymer network. In this work, it was found that process operation is greatly enhanced by the semi-batch addition of 1,4-butanediol and diamine, and the manipulation of the reactor temperature profile, allowing to obtain high molecular weights while avoiding the onset of the gelation point.

RIGOROUS MODELING OF A HIGH PRESSURE ETHYLENE-VINYL ACETATE (EVA) COPOLYMERIZATION AUTOCLAVE REACTOR

Polyethylene (PE) is one of the most widely used polymers in chemical industry. In all the PE processes, high-pressure autoclave process is generally considered as the most profitable segment of the polyethylene business worldwide in recent years. Depending on different grades of the product, reactor zone temperatures in this autoclave process can be in the range 150-230°C and pressure in the range of 1500-2000kg/cm2. In this paper, rigorous dynamic model of an industrial ethylene and vinyl acetate (EVA) copolymerization reactor will be established. Industrial operating condition data of seven product grades with melt index ranging from ones to over four hundred will be used as fitted or test data to obtain the key kinetic parameters in the model. The predicted outputs of melt index, vinyl acetate wt. % in polymer, and polymer production rate will be compared to plant data.

A Simple and Robust Method of Tuning PID Controllers for Integrator/Dead Time Processes

A simple method is proposed for PID controller settings for an integrating plus dead-time system and a stable FOPTD system with an integrator. The method is based on matching the coefficients of corresponding powers of s, s2, s3 in the numerator to α1, α2, and α2 times that in the denominator of the closed-loop transfer function, respectively, for the servo problem. Here α1 and α2 are tuning parameters, and α1 is greater than 1. It is found by simulation on various transfer function models that the use of α2 = 0.6α1 gives good results. The robustness of the controller is evaluated theoretically by Kharitonov’s theorem. The method is used to design a PID controller for an isothermal continuous copolymerization reactor, and the performance of the controller designed by the present method is compared with a modified gain margin method (Luyben, 1996). The method is extended to design a PID controller for a stable FOPTD system with an integrator. The performance of the method is better than the method proposed by Zhang et al. (1999) for the servo problem, and it is superior to their method for the regulatory problem.

Development and Implementation of a High-Performance Sensor System for an Industrial Polymer Reactor

Because of increasingly stringent demands on product quality, process measurements of high precision, accuracy, and reliability are required in many processes where process variables are traditionally difficult to measure. In many applications, several different measurements of certain key process variables are available from various sources, including on-line analyzers, lab analyses, inferential measurements, and models of all types. Because these individual sensors often differ significantly in terms of their static and dynamic characteristics, precision, accuracy, sampling rate, measurement time delay, etc., in practice, only one of them is utilized for process monitoring and control purposes; the other sensor measurements are ignored. However, significantly improved estimates of the process variables can be obtained by utilizing all of the available sensor information simultaneously, i.e., by combining (fusing) these dissimilar measurements into a single estimate in a robust and fault-tolerant fashion. There is evidence that such sensor fusion operations are integral to the operation of biological control systems, and it is from one of these systems (the blood pressure control system) that we have drawn inspiration for developing the technique discussed in this article. A sensor fusion approach is developed using stochastic systems theory (in particular, Kalman filtering). The advantages of using multiple, redundant sensors, as well as the potential improvements achievable by combining delayed or multirate sensor information with that of a single nominal sensor, are then quantified. Robustness is achieved by augmenting the nominal technique with failure detection, classification, and compensation schemes, based on statistical hypothesis testing. The performance of the techniques is demonstrated on an actual plant application in which improved feed composition estimates are obtained for an industrial ethylene copolymerization reactor.

Optimal Temperature−Time Programming in a Batch Copolymerization Reactor

This paper addresses the optimization of a batch copolymerization reactor of styrene and α-methylstyrene. The reactor is equipped with a jacket for heat exchange and, thus, for temperature control. The performance index is the batch period, and the decision variable is the jacket inlet temperature. The constraints involved include the process model, the polymer quality, the final monomer conversion rate, the heating/cooling rate of the reactor and upper and lower bounds of the variables. The optimization method is a direct method with a sequential strategy known as control vector parametrization method. The optimal profiles are determined with great care in terms of treatment and fulfilment of constraints. The results show a substantial improvement with respect to the complete discretization method previously used.

On-Line Particle Size Distribution Control Strategy in an Emulsion Copolymerization Reactor

Model order reduction is applied to a population balance equation (PBE) describing the particle size distribution in an emulsion copolymerization reactor. The reduced order model is used in linear model predictive control. The perfonnance of controllers with different controlled outputs is compared in the presence of two classes of disturbances, one related to the nucleation mechanism and the other affecting the growth rate, to determine the most robust control strategy for the regulation of the distribution at the final time.

Complexity Reduction of Nonlinear Systems for Process Control

While models of high complexity are very useful for simulation and prediction purposes in the process industry, they may not be adequate for controller design. This paper proposes a procedure for model complexity reduction for this specific purpose by combining several nonlinear identification and optimization techniques. The available complex simulation model is used as surrogate plant to generate control relevant input and output trajectories and both an optimization of the input and an iterative nonlinear identification procedure are used. The results are illustrated on a nonlinear exothermic copolymerization reactor example.

Control of Copolymer Properties in a Semibatch Methyl Methacrylate/Methyl Acrylate Copolymerization Reactor by Using a Learning-Based Nonlinear Model Predictive Controller

This paper is concerned with the production of copolymers with uniform copolymer composition and desired weight-average molecular weight by using a learning-based nonlinear model predictive control (NLMPC). For an effective control in a semibatch copolymerization system, the successive linearization method used in NLMPC is modified. The nonlinear model for the copolymerization system is linearized by using the previous batch data within the prediction horizon in such a way that the linear time-varying model is obtained as a function of the increment of the inputs between the two consecutive batches. The learning algorithm is incorporated into the controller by virtue of the model structure, and the effectiveness of the proposed controller is shown by comparison with a conventional nonlinear model predictive controller as well as a linear model-based learning controller. Through the implementation of the controller to a semibatch methyl methacrylate/methyl acrylate copolymerization reactor, it is proven that copolymers with desired properties are produced effectively using the algorithm proposed in this study.

An LMI-Based Constrained MPC Scheme with Time-Varying Terminal Cost

Modelbased Predictive Control (MPC) is a control technique that is widely used in chemical process industry. In the past decade, stability of MPC has been an intensive research area, resulting in the general acceptance of a theoretical MPC stability framework introducing a terminal cost and terminal constraint to the classic MPC formulation. Although guaranteeing stability, issues regarding optimality and feasibilit.y remain. In this paper, an LMI-based constrained MPC scheme for linear systems is introduced which guarantees stability by use of a time-varying terminal cost and terminal constraint. The online calculation of the terminal cost results in improved performance and feasibility compared to MPC schemes with fixed terminal cost. Finally, the technique is illustrated on a copolymerization reactor.

Multi‐Objective Optimization of Semi‐Batch Copolymerization Reactors Using Adaptations of Genetic Algorithm

AbstractSummary: The polymerization of styrene‐acrylonitrile (SAN) random copolymers in semi‐batch reactors is optimized using multiple objective functions that are often conflicting and non‐commensurate in nature. These include the average composition of the copolymer product, its number‐average molecular weight, its polydispersity index, and the conversion of monomers attained in the reactor. Two decision/control variables are used, namely, the rate of continuous addition of a monomer‐solvent‐initiator mixture (having a specified and fixed composition) and the history of the temperature in the reactor. The elitist non‐dominated sorting genetic algorithm, NSGA‐II, is adapted and used for decision variables that are functions of time (trajectory optimization). This robust, AI (artificial intelligence)‐based technique, enables the solution of far more complex optimization problems than those reported in the literature. A set of several non‐dominating (equally good) Pareto optimal solutions was obtained. These provide insights into the conflicting nature of the objective functions. An engineer (decision maker) can then use his judgment (often intuitive) to choose the preferred solution from among these possibilities.Pareto set of optimal solutions and some corresponding state variables for a Reference Problem.imagePareto set of optimal solutions and some corresponding state variables for a Reference Problem.

Nonlinear model order reduction and control of particle size distribution in a semibatch vinyl acetate/butyl acrylate emulsion copolymerization reactor

This paper addresses the control of the full particle size distribution (PSD) in a semibatch emulsion copolymerization reactor. The numerical approximation of a fundamental population balance model results in a high order system to accurately describe the distribution of particle size; therefore, model order reduction is required. Pseudo random input signals are input to the mechanistic model to generate a data set which covers the reachable region of the system, on the basis of which the transformation matrices are calculated by principal component analysis (PCA). A linear time varying model with reduced order obtained from the transformation matrices is augmented in the prediction equation of linear model predictive control. The performance of the controller is evaluated to drive the particle size distribution at the final time of the batch to the desired distribution in the presence of disturbances.

On the effect of the estimation structure in the functioning of a nonlinear copolymer reactor estimator

In this work, the effect of the estimation structure on the performance and robustness characteristics of a geometric nonlinear estimator is studied for free-radical continuous solution copolymerization reactors where conversion, composition, average molecular weight, solid mass fraction, and production rate are inferred from temperature, density, refractive index, volume, and flowrate measurements. The case study is based on the geometric characterization of the robust detectability property, yielding a set of admissible estimator structures that represent a degree of freedom in the estimator design. The choice of structure determines the estimator reconstruction rate and error propagation mechanism. Measures of estimability (i.e., robust detectability) are introduced to discriminate structures. The estimator functioning results confirm the ones drawn from the structural assessment stage, and yield that the best estimator behavior is attained with a structure different from the nominal detectability structure that underlies the nonlinear fixed-structure EKF and Luenberger techniques employed in previous polymer reactor estimation studies.

Design and Application of Model-on-Demand Predictive Controller to a Semibatch Copolymerization Reactor

This article considers the design of a multivariable model-on-demand predictive controller (MoD-PC) and its application to polymer quality control in a semibatch MMA/MA copolymerization reactor. The MoD-PC is designed by combining the model-on-demand (MoD) framework with the conventional model predictive controller. For this purpose, a local autoregressive exogenous input model is constructed with a small portion of data located in the region of interest at every sample time when a model equation is needed for output prediction. This model equation is then used to calculate the optimal control input sequence. Through the open-loop test, the reaction temperature and free volume are shown to be an adequate choice for the elements of the regressor state vector in the data searching step. The validity of the identified model is corroborated by the prediction method. The results of simulation studies for the regulation and disturbance rejection problems with and without noise demonstrate that, despite the nonlinearity of the system, the MoD-PC is an effective strategy with a low computational load for the production of copolymers with desired properties.

A Practical, Systematic Approach for the Scaling‐Up and Modeling of Industrial Copolymerization Reactors

A systematic methodology for the modeling and engineering analysis of industrial copolymerization reactors is presented. The methodology, especially suited for the scaling‐up from laboratory experiments to pilot plant and industrial reactor level, consists of gradually building models of more complexity in a modular way as more information is obtained from experimental data and/or theoretical considerations. In the first stage, simple models for copolymer composition are written based on the Mayo–Lewis copolymerization equation and empirical copolymerization rate data for different reactor configurations (batch and CSTR) and reactor operations (steady state and some dynamic transients for the CSTR case). This set of models, which use minimal or no data fitting, is shown to be highly predictive. In a second stage, as kinetic information is obtained in the form of an expression for the copolymerization rate, either empirical or mechanistic, the models can be gradually expanded to include a full non‐linear a...