Control Of Polymerization Reactor Research Articles

A robustly model predictive control strategy applied in the control of a simulated industrial polyethylene polymerization process

This work investigates the quality control problem of polyethylene grades produced in an industrial polymerization plant. The plant is represented by a phenomenological model previously validated using industrial data. Three advanced control strategies were developed in order to propose strategies capable of dealing with different grades of products. A stability guaranteed [IHMPC (Infinite Horizon Model Predictive Control)] technique and a robust stabilized [RIHMPC (Robust IHMPC)] technique were designed and compared with a conventional MPC. The results show that RIHMPC outperformed the other techniques, providing smoother and faster grade transitions and setpoint tracking. This result provides a significative contribution, since no report of application of RIHMPC on polymerization plants was found. The RHIMPC controller seems to be a promising option for other polymerization reactor control problems in which the diversity of resins produced, coupled with the nonlinear characteristic of the system, lend themselves to the use of different linear models.

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

AbstractIn 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.

Online Optimal Feedback Control of Polymerization Reactors: Application to Polymerization of Acrylamide–Water–Potassium Persulfate (KPS) System

This paper deals with the design and implementation of optimal real-time control strategies for controlling polymerization reactors in free radical polymerization processes. A multiobjective optimization problem is first formulated to determine optimal trajectories for a range of target products. A tailor-made control module is then formulated and implemented in python for controlling the weight-average molar mass (Mw) to robustly achieve the desired polymer molar mass distribution (MMD). Multiple control case studies are discussed and applied to force the system along the optimal targets. Performance of the controller is evaluated in each case using Automatic Continuous Online Monitoring of Polymerization reactions (ACOMP). Results are provided through investigations into the free radical polymerization of the acrylamide in water using potassium persulfate (KPS) as an initiator.

Sensitivity Compensating Control: Data-driven model based adaptive approach

A novel Sensitivity Compensating Control (SCC) approach is proposed in a data-driven model based platform and combined with an Extended External Reset Feedback (EERF) method to handle sensitivity, input saturation, and accurate process model requirement problems associated with application of Generic Model Control (GMC). Two versions of Adaptive GMC (AGMC) are proposed using linear-in-parameters time-series models with time-varying parameters for higher relative degree systems, and are used in the formulation of SCC and EERF approaches. The steps involved in the proposed approach consist of defining a new process, control law and set point such that the determined control action drives the original process to its desired set point. The performance of the proposed control algorithms is illustrated by application to a benchmark multi-product polymerization reactor control challenge problem. The proposed approaches are applicable to chemical engineering systems exhibiting input sensitivity.

Lagrangean heuristic for the scheduling and control of polymerization reactors

AbstractA decomposition technique is applied to address the simultaneous scheduling and optimal control problem of multigrade polymerization reactors. The simultaneous scheduling and control (SSC) problem is reformulated using Lagrangean decomposition as presented by Guignard and Kim. The resulting model is decomposed into scheduling and control subproblems, and solved using a heuristic approach used before by Van den Heever et al. in a different kind of problem. The methodology is tested using a methyl methacrylate (MMA) polymerization system, and the high impact polystyrene (HIPS) polymerization system, with one continuous stirred‐tank reactor (CSTR), and with a complete HIPS polymerization plant composed of a train of seven CSTRs. In these case studies, different polymer grades are produced using the same equipment in a cyclic schedule. The results of the heuristic decomposition technique are compared against those obtained by solving the problem without decomposition, whenever both solutions were available. The presence of a duality gap for the decomposed solution is observed as expected when integer variables and other nonconvexities are present. Computational times in the first two examples were lower for the decomposition heuristic than for the direct solution in full space, and the optimal solutions found were slightly better. The example related to the full scale HIPS plant was only solvable using the decomposition heuristic. © 2007 American Institute of Chemical Engineers AIChE J, 2008

Temperature Control of a Bench‐Scale Batch Polymerization Reactor for Polystyrene Production

AbstractBatch polymerization reactors commonly use optimal temperature control as the strategic operation parameter. This strategy allows for better operability and a more economic process. The main objective of the batch polymerization reactor control is to obtain acceptable product quality. Direct measurement of polymer quality is rarely achievable, which makes the online control of the reactor difficult. Temperature is the most controllable operational variable in the polymer reactor, which is seen to have a direct effect on the polymer properties. Temperature is chosen as the set point by using either the isothermal temperature or optimal temperature trajectory. Online control of the optimal temperature profile of a bench‐scale batch polymerization reactor was experimentally investigated in this study. The temperature trajectory was used as the target for controllers to follow. The time‐profile temperature was obtained with the objective of obtaining the desired conversion and number‐average chain length within the minimum time. Two advanced controls of fuzzy logic control and generic model control were applied to the polymer reactor. A comparison of the controllers reveals that both performed better than conventional controllers.

Simultaneous cyclic scheduling and optimal control of polymerization reactors

AbstractThe simultaneous solution of the optimal sequencing and optimal dynamic transitions of two multigrade polymerization continuous stirred‐tank reactors (CSTRs) is presented. The simultaneous formulation leads to a mixed‐integer dynamic optimization (MIDO) problem. The profiles of the state variables during dynamic transitions are discretized using orthogonal collocation on finite elements, transforming the MIDO problem into a mixed‐integer nonlinear programming (MINLP) problem. The objective of this formulation is to maximize the profit of the manufacturing operation, considering polymer sales, inventory costs and transition costs. The transition cost term is determined by the duration of the transition stages and the manipulated variable profile during transitions. Two industrial reaction systems are used to analyze the optimal solution and compare it to other solutions obtained using different methods. Finally, a sensitivity analysis is carried out to describe the impact of changes in certain problem parameters. © 2007 American Institute of Chemical Engineers AIChE J, 2007

A LAGRANGEAN DECOMPOSITION HEURISTIC FOR THE SIMULTANEOUS SCHEDULING AND OPTIMAL CONTROL OF MULTI-GRADE POLYMERIZATION REACTORS

In this work we present the simultaneous scheduling and optimal control of polymerization reactors using a previously proposed MINLP formulation. The problem is then solved in two ways: first by directly using an Outer Approximation technique, and second, by applying a Lagrangean decomposition scheme that allows the independent solution of the scheduling and optimal control problems. However, both subproblems are linked by a set of Lagrangean Multipliers that evolve during an iterative solution process using a subgradient method. During this process the decomposition approach yields an upper bound to the original problem while a lower bound is obtained heuristically based on the solution of the decomposed problem. The methodology is tested on two polymerization processes and compared vs. the solution obtained when the problem is solved directly. In both cases optimal solutions are almost identical while solution times for the larger problem were reduced significantly when using the decomposition approach.

Measurement and control of polymerization reactors

The measurement and control of polymerization reactors is very challenging due to the complexity of the physical mechanisms and polymerization kinetics. In these reactors many important variables, which are related to end-use polymer properties, cannot be measured on-line or can only be measured at low sampling frequencies. Furthermore, end-use polymer properties are related to the entire molecular weight, copolymer composition, sequence length, and branching distributions. This paper surveys the instrumentation technologies, which are of particular interest in polymerization reactors with emphasis on, for example, measurement of viscosity, composition, molecular weight, and particle size. This paper presents a hierarchical approach to the control system design and reviews traditional regulatory techniques as well as advanced control strategies for batch, semibatch, and continuous reactors. These approaches are illustrated by focusing on the control of a commercial multiproduct continuous emulsion polymerization reactor. Finally, the paper captures some of the trends in the polymer industry, which may impact future development in measurement and reactor control.

Monitoring and Control of Polymerization Reactors Using NIR Spectroscopy

: The development and use of microprocessor-based devices improved the speed and reliability of transmission and manipulation of data. More recently, some monitoring techniques were greatly improved by the combination of spectroscopic methods and fiber optics technology, which allow for the in situ and in-line acquisition of process data, consequently allowing for reduction of time delays normally involved with sample preparation. Among them, techniques based on the near infrared spectroscopy (NIRS) have certainly become the most important ones. The main objective of this paper is to review the use of NIR spectroscopy as an alternative technique for polymerization process monitoring and control, presenting and discussing successful applications of NIR spectroscopy as a tool for in situ and in-line monitoring and control of solution, suspension, and emulsion polymerization processes.

Nonlinear Control of Polymerization Reactor by Wiener Predictive Controller Based on One-Step Subspace Identification

A subspace identification algorithm for the Wiener model is reformulated from a control point of view. The linear time-invariant part and the inverse static nonlinear function are simultaneously identified without an iterative procedure, and then the Wiener input/output data-based predictive controller is designed on the basis of the identified model. Through simulation and experimental studies for the multivariate control of polymer properties in a continuous methyl methacrylate (MMA) polymerization reactor, the proposed identification method is validated, and the performance of the designed predictive controller is examined. The Wiener model identified without any iterative procedure is found to predict accurately the output of the polymerization reactor, and the predictive controller designed in this work performs quite satisfactorily for polymer property control in the polymerization reactor.

Monitoring and control of styrene solution polymerization using NIR spectroscopy

AbstractTailored polymer resins are frequently required for a given application. The lack of instruments for in‐line monitoring of polymer quality has long been recognized as an important problem in polymerization reactor control. Using the styrene solution polymerization system as an example, we present the use of near‐infrared (NIR) spectroscopy as an alternative tool for in‐line and in situ monitoring and control of monomer conversion and average molecular weight of polymer resins. By using a Kalman filter state estimator and an accurate first‐principle model, the control loop could be successfully closed to track desired monomer values and average molecular weights. Two process control strategies, one based on the optimal control theory and the other on model predictive control, were implemented both theoretically and experimentally. The experimental results showed that it is feasible to use NIR spectroscopy for the simultaneous control of monomer conversion and polymer average molecular weight. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 1273–1289, 2003

The effect of operational conditions on the performance of batch polymerization reactor control

In this work, the effect of operational conditions on the performance of a controlled batch polymerization reactor was investigated experimentally. The effect of agitation speed on conversion and heat transfer coefficient in free radical chain growth polymerization in this controlled, stirred, jacketed batch reactor was also investigated. The transient response of the polymerization reactor following sequential step changes in agitation speed has been obtained experimentally. The experiments were conducted under optimal loading conditions calculated by using Lagrange’s multiplier method. The reactor temperature was controlled by manipulating the heat input to the reactor. Some correlations are also provided relating the viscosity and the overall heat transfer coefficient to the monomer conversion.

Nonlinear control of polymerization reactor

In this work, nonlinear model based control was applied to the free radical solution polymerization of styrene in a jacketted batch reactor and its performance was examined to reach the required monomer conversion and molecular weight. Optimal temperature profiles for the properties of polymer quality were evaluated using the Hamiltonian optimization method. Total simulation program having mass and energy balances of the jacketed polymerization reactor was used to calculate the optimal trajectories. For control purposes, several experimental and theoretical dynamic studies have been made to observe the validity of simulation program. Experimental and theoretical nonlinear model based control have been investigated to track the temperature at the optimal trajectory Two types of parametric and nonparametric models were evaluated to achieve the temperature control. For this purpose, reaction curve was obtained to calculate the system dynamic matrix as a nonparametric model. In all control work, heat input to the reactor was chosen as a manipulated variable. Nonlinear auto regressive moving average exogenous (NARMAX) giving a relation between heat input and reactor temperature was chosen to represent the system dynamic and this model was used to describe the related control system as a parametric model. NARMAX model parameters were determined by using Levenberg Marquard algorithm. A pseudo random binary sequence (P.R.B.S.) signal was employed to disturb the system. Total simulation program was used to calculate the system and control parameters. Several types and orders were used to construct the NARMAX models. The efficiency and the performance of the nonlinear model based control with the NARMAX model and dynamic matrix were tested to calculate the best model. Nonlinear model based control system was used to control the reactor temperature at desired temperature trajectory experimentally and theoretically. Theoretical simulation results were compared with experimental control data. It was concluded that the control simulation program represents the behavior of the controlled reactor temperature well. In addition, nonlinear model based control keeps the reactor temperature of optimal trajectory satisfactorily.

Optimization and non-linear control of a batch emulsion polymerization reactor

The optimal temperature policy which minimizes the terminal time in a batch emulsion polymerization reactor of styrene and α-methylstyrene was determined by means of orthogonal collocation techniques combined with a general non-linear programming method. The constraints concern the final latex properties and the thermal limitations of the pilot plant. An experimental validation has been realized. The optimal temperature profile was tracked using a non-linear geometric control technique which is particularly adapted to polymerization reactor control. An extended Kalman filter was used to estimate the non-measured state variables. Experimental results showed excellent agreement with predictions for this complex system. A good temperature tracking was observed and the product quality was well predicted and controlled.

Density data for copolymer systems: butyl acrylate/vinyl acetate homo- and copolymerization in ethyl acetate

A study was performed to provide precise density data, badly needed for on-line measurements and control of polymerization reactors, e.g. for densimetry studies. Data was obtained for one copolymer of butyl acrylate/vinyl acetate, the homopolymers of vinyl acetate and butyl acrylate, plus the two monomers and ethyl acetate. In addition, the hypothesis of the linear dependence of the density of the copolymer as a function of the weight fraction of the individual homopolymer density was validated for the system under consideration. Temperature–density data for the monomers and solvent are also provided.

AUTOMATICALLY CONFIGURING RADIAL BASIS FUNCTION NEURAL NETWORKS FOR NONLINEAR INTERNAL MODEL CONTROL*

A nonlinear internal model control (NIMC) strategy based on automatically configuring radial basis function networks (RBFN) is proposed for single-input single-output (SISO) systems of relative degree greater than unity. The automatic configuration and training of the RBFN is carried out employing hierarchically-self-organizing-learning algorithm, which eliminates a predefined network structure, with closed-loop input-output data generated for a series of setpoint changes using PI controller. Simulation studies with automatically configuring RBFN for isothermal polymerization reactor control demonstrate the superior performance of the proposed control strategy with automatically configuring RBFN over PI control for setpoint tracking as well as disturbance rejection.

Control of batch suspension polymerization reactor

The automation and control of polymerization reactors that operate in batches is quite a difficult task. The gel effect and the absence of a stable operational state are factors that determine the need for special control systems. In this study, a methodology is implemented for controlling the operation of a batch polymerization reactor, utilizing an adaptive controller of the type STC (Self Tuning Controller). By utilizing a model of the polymerization process, the necessary operational conditions were determined for producing the polymer within the desired characteristics. Variables of the mean molecular weight type and the polydispersion rate were utilized as polymer quality parameters. Experimental tests in a pilot unit of polystyrene production in suspension, showed the capacity of the STC for controlling this type of reactor. The results also showed that, from the methodology utilized for determining the operational variables, polymers with previously defined characteristics can be produced.

Process Control of Polymerization Reactors: An Industrial Perspective

ABSTRACTPolymerization reactors usually exhibit complex nonlinear dynamic behavior because of the complexity of the physicochemical interactions and the kinetics of the polymerization reactions. In these reactors many important variables, often related to end-use polymer properties, cannot be measured on-line or can only be measured at very low sampling frequencies. Furthermore, end-use polymer properties are usually related to the molecular weight and composition distributions in the polymerization reactor. Finally, the typical industrial polymer reactor is used to manufacture a variety of grades of the same basic product necessitating frequent startups, on-line transitions, and shutdowns.The approaches used by the authors to meet these challenges are illustrated, within the constraints of protecting proprietary information, by focusing on the modeling and control of a commercial multiproduct continuous emulsion copolymerization reactor. The development of fundamental process understanding captured in a ...

Polymerization reactor modeling: A review of recent developments and future directions

Synthetic polymers are produced via a multitude of reaction mechanisms and processes, including addition (e.g. free-radical, ionic, group-transfer, Ziegler-Natta coordination) and step-growth polymerizations. A major objective of polymerization reaction engineering is to understand how the reaction mechanism, the physical transport processes (e.g. mass and heat transfer, mixing), reactor configuration and reactor operating conditions affect the macromolecular architecture (e.g. molar mass, molecular weight distribution, copolymer composition distribution, branching distribution, stereoregularity, etc.) as well as the morphological properties of the polymer product (e.g. particle size distribution, porosity, etc.). As the polymer industry becomes more competitive, polymer manufacturers face increasing pressures for production cost reductions and more stringent “polymer quality” requirements. To achieve these goals one needs to develop comprehensive mathematical models capable of predicting the molecular and morphological properties in terms of reactor configuration and operating conditions. These mathematical representations can be classified into microscale kinetic models, mesoscale physical, transport and thermodynamic models and dynamic reactor ones. The present paper provides an overview of the different polymerization processes and mathematical modeling approaches. It is also addresses the problems related with the computer-aided design, monitoring, optimization and control of polymerization reactors.