Optimal nonlinear control of an industrial emulsion polymerization reactor

International audienceIn this paper, the modelling, dynamic optimization and nonlinear control of an industrial emulsion polymerization reactor producing poly-vinyl acetate (PVAc) are proposed. The reaction is modeled as a two-phase system composed of an aqueous phase and a particle phase according to the model described in our previous work (Gil et al., 2014). The case study corresponds to an industrial reactor operated at a chemical company in Bogotá (Colom-bia). An industrial scale reactor (11 m 3 of capacity) is simulated. Three different dynamic optimization problems are solved from the more simplistic (only one control variable: reactor temperature) to the more complex (three control variables: reactor temperature, initiator flow rate and monomer flow rate) in order to minimize the reaction time. The results show that it is possible to minimize the reaction time while some polymer desired qualities (conversion, molecular weight and solids content) satisfy defined constraints. The optimal temperature profile and optimal feed policies of the monomer and initiator, obtained in a dynamic optimization step, are used as optimal set points for reactor control. A nonlinear geometric controller based on input/output linearization is implemented for temperature control

Optimization Studies Of Batch Polymerization For Polystyrene Process

Polymerization is a chemical reaction process of monomer molecules to form a polymer chain. In the polymer industry, batch polymerization reactors are used extensively to manufacture a variety of polymers of numerous grades. Batch process is well suited for low-volume products and for products with numerous grades (as in specialty polymers. However, this process may require higher operation cost because it can achieve high conversion with long batch time. The operation is unsteady-state where the composition and temperature always change with time. Optimum operating conditions are very important for the polymerization process in order to achieve the objective function in the process. In this study, the optimization technique using mathematical models was implemented to obtain those optimum operating conditions. The dynamic optimization problem was solved using an orthogonal collocation method where the differential variables were fully discretized. Collocation method is one of the methods that can be used to solve dynamic optimization. In the case of solving the dynamic optimization problems, collocation formulae can be used to transform the ordinary differential equations into algebraic equations. In this study, the optimization of optimal temperature generations in batch process of polystyrene was investigated theoretically

Optimal control of particle size distribution in semi-batch emulsion polymerisation

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CONTROL OF KEY POLYMER PROPERTIES VIA REVERSIBLE ADDITION-FRAGMENTATION CHAIN TRANSFER IN EMULSION POLYMERIZATION

Free radical emulsion polymerization (FRP) is widely adopted in industry due to its applicability to a wide range of monomers. Despite its many benefits and wide spread use, the fast chain growth and the presence of rapid irreversible termination impose limitations with respect to the degree of control in FRP. Furthermore, producing block copolymers and polymers with complex structures via FRP is not feasible. Closer control of macromolecular chain structure and molar mass, using novel polymerization techniques, is required to synthesize and optimize many new polymer products. Reversible addition fragmentation chain transfer (RAFT)-mediated polymerization is a novel controlled living free radical technique used to impart living characters in free radical polymerization. In combination with emulsion polymerization, the process is industrially promising and attractive for the production of tailored polymeric products. It allows for the production of particles with specially-tailored properties, including size, composition, morphology, and molecular weights. The mechanism of RAFT process and the effect of participating groups were discussed with reviews on the previous work on rate retardation. A mathematical model accounting for the effect of concentrations of propagating, intermediate, dormant and dead chains was developed based on their reaction pathways. The model was combined with a chain-length dependent termination model in order to account for the decreased termination rate. The model was validated against experimental data for solution and bulk polymerizations of styrene. The role of the intermediate radical and the effect of RAFT agent on the chain length dependent termination rate were addressed theoretically. The developed kinetic model was used with validated kinetic parameters to assess the observed retardation in solution polymerization of styrene with high active RAFT agent (cumyl dithiobenzoate). The fragmentation rate coefficient was used as a model parameter, and a value equal to 6×104 s-1 was found to provide a good agreement with the experimental data. The model predictions indicated that the observed retardation could be attributed to the cross termination of the intermediate radical and, to some extent, to the RAFT effect on increasing the average termination rate coefficient. The model predictions showed that to preserve the living nature of RAFT polymerization, a low initiator concentration is recommended. In line with the experimental data, model simulations revealed that the intermediate radical prefers fragmentation in the direction of the reactant. The application of RAFT process has also been extended to emulsion polymerization of styrene. A comprehensive dynamic model for batch and semi-batch emulsion polymerizations with a reversible addition-fragmentation chain transfer process was developed. To account for the integration of the RAFT process, new modifications were added to the kinetics of zero-one emulsion polymerization. The developed model was designed to predict key polymer properties such as: average particle size, conversion, particle size distribution (PSD), and molecular weight distribution (MWD) and its averages. The model was checked for emulsion polymerization processes of styrene with O-ethylxanthyl ethyl propionate as a RAFT based transfer agent. By using the model to investigate the effect of RAFT agent on the polymerization attributes, it was found that the rate of polymerization and the average size of the latex particles decreased with increasing amount of RAFT agent. It was also found that the molecular weight distribution could be controlled, as it is strongly influenced by the presence of the RAFT based transfer agent. The effects of RAFT agent, surfactant (SDS), initiator (KPS) and temperature were further investigated under semi-batch conditions. Monomer conversion, MWD and PSD were found to be strongly affected by monomer feed rate. With semi-batch mode, Mn and increased with increasing monomer flow rate. Initiator concentration had a significant effect on PSD. The results suggest that living polymerization can be approached by operating under semi-batch conditions where a linear growth of polymer molecular weight with conversion was obtained. The lack of online instrumentation was the main reason for developing our calorimetry-based soft-sensor. The rate of polymerization, which is proportional to the heat of reaction, was estimated and integrated to obtain the overall monomer conversion. The calorimetric model developed was found to be capable of estimating polymer molecular weight via simultaneous estimation of monomer and RAFT agent concentrations. The model was validated with batch and semi-batch emulsion polymerization of styrene with and without RAFT agent. The results show good agreement between measured conversion profiles by calorimetry with those measured by the gravimetric technique. Additionally, the number average molecular weight results measured by SEC (GPC) with double detections compare well with those calculated by the calorimetric model. Application of the offline dynamic optimisation to the emulsion polymerization process of styrene was investigated for the PSD, MWD and monomer conversion. The optimal profiles obtained were then validated experimentally and a good agreement was obtained. The gained knowledge has been further applied to produce polymeric particles containing block copolymers. First, methyl acrylate, butyl acrylate and styrene were polymerized separately to produce the first block. Subsequently, the produced homopolymer attached with xanthate was chain-extended with another monomer to produce block copolymer under batch conditions. Due to the formation of new particles during the second stage batch polymerization, homopolymer was formed and the block copolymer produced was not of high purity. The process was further optimized by operating under semi-batch conditions. The choice of block sequence was found to be important in reducing the influence of terminated chains on the distributions of polymer obtained. It has been found that polymerizing styrene first followed by the high active acrylate monomers resulted in purer block copolymer with low polydispersity confirmed by GPC and H-NMR analysis

CONTROL OF KEY POLYMER PROPERTIES VIA REVERSIBLE ADDITION-FRAGMENTATION CHAIN TRANSFER IN EMULSION POLYMERIZATION

Free radical emulsion polymerization (FRP) is widely adopted in industry due to its applicability to a wide range of monomers. Despite its many benefits and wide spread use, the fast chain growth and the presence of rapid irreversible termination impose limitations with respect to the degree of control in FRP. Furthermore, producing block copolymers and polymers with complex structures via FRP is not feasible. Closer control of macromolecular chain structure and molar mass, using novel polymerization techniques, is required to synthesize and optimize many new polymer products. Reversible addition fragmentation chain transfer (RAFT)-mediated polymerization is a novel controlled living free radical technique used to impart living characters in free radical polymerization. In combination with emulsion polymerization, the process is industrially promising and attractive for the production of tailored polymeric products. It allows for the production of particles with specially-tailored properties, including size, composition, morphology, and molecular weights. The mechanism of RAFT process and the effect of participating groups were discussed with reviews on the previous work on rate retardation. A mathematical model accounting for the effect of concentrations of propagating, intermediate, dormant and dead chains was developed based on their reaction pathways. The model was combined with a chain-length dependent termination model in order to account for the decreased termination rate. The model was validated against experimental data for solution and bulk polymerizations of styrene. The role of the intermediate radical and the effect of RAFT agent on the chain length dependent termination rate were addressed theoretically. The developed kinetic model was used with validated kinetic parameters to assess the observed retardation in solution polymerization of styrene with high active RAFT agent (cumyl dithiobenzoate). The fragmentation rate coefficient was used as a model parameter, and a value equal to 6×104 s-1 was found to provide a good agreement with the experimental data. The model predictions indicated that the observed retardation could be attributed to the cross termination of the intermediate radical and, to some extent, to the RAFT effect on increasing the average termination rate coefficient. The model predictions showed that to preserve the living nature of RAFT polymerization, a low initiator concentration is recommended. In line with the experimental data, model simulations revealed that the intermediate radical prefers fragmentation in the direction of the reactant. The application of RAFT process has also been extended to emulsion polymerization of styrene. A comprehensive dynamic model for batch and semi-batch emulsion polymerizations with a reversible addition-fragmentation chain transfer process was developed. To account for the integration of the RAFT process, new modifications were added to the kinetics of zero-one emulsion polymerization. The developed model was designed to predict key polymer properties such as: average particle size, conversion, particle size distribution (PSD), and molecular weight distribution (MWD) and its averages. The model was checked for emulsion polymerization processes of styrene with O-ethylxanthyl ethyl propionate as a RAFT based transfer agent. By using the model to investigate the effect of RAFT agent on the polymerization attributes, it was found that the rate of polymerization and the average size of the latex particles decreased with increasing amount of RAFT agent. It was also found that the molecular weight distribution could be controlled, as it is strongly influenced by the presence of the RAFT based transfer agent. The effects of RAFT agent, surfactant (SDS), initiator (KPS) and temperature were further investigated under semi-batch conditions. Monomer conversion, MWD and PSD were found to be strongly affected by monomer feed rate. With semi-batch mode, Mn and increased with increasing monomer flow rate. Initiator concentration had a significant effect on PSD. The results suggest that living polymerization can be approached by operating under semi-batch conditions where a linear growth of polymer molecular weight with conversion was obtained. The lack of online instrumentation was the main reason for developing our calorimetry-based soft-sensor. The rate of polymerization, which is proportional to the heat of reaction, was estimated and integrated to obtain the overall monomer conversion. The calorimetric model developed was found to be capable of estimating polymer molecular weight via simultaneous estimation of monomer and RAFT agent concentrations. The model was validated with batch and semi-batch emulsion polymerization of styrene with and without RAFT agent. The results show good agreement between measured conversion profiles by calorimetry with those measured by the gravimetric technique. Additionally, the number average molecular weight results measured by SEC (GPC) with double detections compare well with those calculated by the calorimetric model. Application of the offline dynamic optimisation to the emulsion polymerization process of styrene was investigated for the PSD, MWD and monomer conversion. The optimal profiles obtained were then validated experimentally and a good agreement was obtained. The gained knowledge has been further applied to produce polymeric particles containing block copolymers. First, methyl acrylate, butyl acrylate and styrene were polymerized separately to produce the first block. Subsequently, the produced homopolymer attached with xanthate was chain-extended with another monomer to produce block copolymer under batch conditions. Due to the formation of new particles during the second stage batch polymerization, homopolymer was formed and the block copolymer produced was not of high purity. The process was further optimized by operating under semi-batch conditions. The choice of block sequence was found to be important in reducing the influence of terminated chains on the distributions of polymer obtained. It has been found that polymerizing styrene first followed by the high active acrylate monomers resulted in purer block copolymer with low polydispersity confirmed by GPC and H-NMR analysis

Modelagem, simulação e analise de desempenho de reatores tubulares de polimerização com deflectores angulares internos

Orientadores: Rubens Maciel Filho, Liliane Maria Ferrareso LonaTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia QuimicaResumo: O modelo determinístico e processo homopolimerização na emulsão do estireno são aplicados em reator tubular contínuo sem e com deflectores angulares internos sob condição isotérmica e não isotérmica. Os resultados de modelagem e simulação foram realizados a estado estacionário, modelo unidimensional, coordenada cilíndrica, fluxo pistão laminar completamente desenvolvido, modelo Smith-Ewart para estimar a conversão do monômero, cinética química de Arrhenius corno modelo de velocidade finita laminar para computar a geração química. O objetivo é modelar, simular e analisar o comportamento do reator de homopolimerização na emulsão do estireno com deflectores angulares inclinados internos, e comparar com reator tubular. Os métodos experimental e matemático-dedutivo foram aplicados para obter resultados, por meio de programação computacional, usando Dinâmica de Fluido Computacional através do método de volumes finitos. As seguintes variáveis como temperatura de reação constante e variável, reator tubular sem e com deflectores, temperatura de alimentação, diâmetro de reator, processo adiabático e exotérmico, calor de reação constante e velocidade axial completamente desenvolvida foram investigados. Os efeitos de conversão de monômero, área transversal interna, temperatura axial, concentração do polímero, radicais e iniciador, outros corno densidade de polímero e monômero, perda de carga e queda de pressão foram determinados e simulados. Os produtos foram caracterizados com Número de Partículas (nucleação homogênea e heterogênea), distribuição de peso molecular, tamanho de partículas de polímero e distribuição de viscosidade. Estes resultados foram validados com resultados da literatura sob condição igualou aproximada. Os resultados sob condições não isotérmicas foram melhores que os resultados isotérmicos em termos de caracterização do polímero. Isso mostra que o desenho alternativo proposto (com deflectores) permite obter o polímero com propriedades melhores em termos de número de partículas, distribuição de peso molecular, distribuição do tamanho de partículas e viscosidadeAbstract: Deterministic model and emulsion homopolymerization process of styrene are applied in continuous tubular reactor without and with internal angular baffles under isothermic and no isothermic conditions. The modeling and simulation results were approximate to steady state, one-dimensional model, cylindrical coordinate, fully developed laminar plug flow, Smith-Ewart model to estimate the monomer conversion, Arrhenius chemical kinetics as laminar finite-rate model to compute chemical source. The objective is to model, simulate and to analyze the emulsion homopolymerization reactor performance of styrene with internal-inc1ined angular baffles, and to compare with continuous tubular reactor. The experimental and mathematical-deductive methods were applied to obtain results, by means of computational programming, using Computational Fluid Dynamics (program code), finite volume method. The following variables such as constant and variable reaction temperature, tubular reactor without and with baffles, feed temperature, reactor diameter, adiabatic and exothermic process, constant reaction heat and fully developed axial velocity were investigated. The monomer conversion, internal transversal are a, axial temperature, concentration of polymer, radicals and initiator, others as density of polymer and monomer, head loss and pressure drop effects were determined and simulated. The products were characterized by partic1es number (homogeneous and heterogeneous nuc1eation), molecular weight distribution, polymer partic1es size and polymer viscosity distribution. These results were validated with literature results under same or approximate condition. The results under no isothermic conditions were better than isothermic results in terms of polymer characterization. It is shown that the proposed alternative design (with baffles) allow to obtain the polymer with better properties in terms of number of partic1es, molecular weight distribution, particle size distribution and viscosityDoutoradoDesenvolvimento de Processos QuímicosMestre em Engenharia Químic

Modelamiento, simulación, Optimización dinámica y control de un proceso semibatch de polimerización en emulsión

Abstract. In this work, modeling, simulation, dynamic optimization and nonlinear control of an industrial emulsion polymerization process to produce poly-vinyl acetate (PVAc) are proposed. The reaction is modeled as a two-phase system composed of an aqueous phase and a particle phase. A detailed model is used to calculate the weight average molecular weight, the number average molecular weight and the dispersity. The moments of the growing and dead chains are used to represent the state of the polymer and to calculate the molecular weight distribution (MWD). The case study corresponds to an industrial reactor operated at a chemical company in Bogot´a. An industrial scale reactor (11 m3 of capacity) is simulated where a semi-batch emulsion polymerization reaction of vinyl acetate is performed. Dynamic optimization problem is solved directly using a Nonlinear Programming solver. Integration of differential equations is made using Runge-Kutta method. Three different optimization problems are solved from the more simplistic (only one control variable : reactor temperature) to the more complex (three control variables : reactor temperature, initiator flowrate and monomer flowrate) in order to minimize the reaction time. A reduction of 25% of the batch time is achieved with respect to the normal operating conditions applied at the company. The results show that is possible to minimize the reaction time while some polymer desired qualities (conversion, molecular weight and solids content) satisfy the defined constraints. A nonlinear geometric control technique by using input/output linearization is adapted to the reactor temperature control. An extended Kalman filter (EKF) is implemented to estimate unmeasured states and it is tested in different cases including a robustness study where model errors are introduced to verify its good performance. After verification of controller performance, some process changes were proposed in order to improve process productivity and polymer quality. Finally, the optimal temperature profile and optimal feed policies of the monomer and initiator, obtained in a dynamic optimization step, are used to provide the optimal set points for the nonlinear control. The results show that the nonlinear controller designed here is appropriate to follow the optimal temperature trajectories calculated previously.Resumen. En este trabajo se aborda el modelamiento, simulación, optimización dinámica y control de un proceso industrial de polimerización en emulsión para producir poli-acetato de vinilo. La reacción se modela como un sistema bifásico compuesto de una fase acuosa y una fase partícula. El peso molecular promedio en número y en peso, y la dispersidad, se calculan con un modelo detallado. Los momentos de las cadenas vivas y muertas de polímero se utilizan para representar el estado del polímero y calcular la distribución de peso molecular (MWD). El caso de estudio corresponde a un reactor industrial operado en una empresa de productos químicos en Bogotá. Se simuló un reactor de escala industrial (11 m3 de capacidad) en el que se lleva a cabo la reacción en semi-lotes de la polimerización en emulsión de acetato de vinilo. El problema de optimización dinámica se resolvió directamente usando un algoritmo de solución de programación no-lineal. La integración del sistema de ecuaciones diferenciales se realizó a través de un método de Runge-Kutta. Tres diferentes problemas de optimización fueron resueltos partiendo del más sencillo (una sola variable de control : temperatura del reactor) al más complejo (tres variables de control : temperatura del reactor, flujo de iniciador y flujo de monómero) con el fin de minimizar el tiempo de reacción. Una reducción del 25% en el tiempo de reacción, con respecto a las condiciones normales de operación aplicadas en la empresa, fue obtenida. Los resultados muestran que es posible minimizar el tiempo de reacción mientras que algunos parámetros de calidad (conversión, peso molecular y contenido de solidos) satisfacen las restricciones impuestas al problema. Una técnica de control geométrico no-lineal usando linearización entrada/salida fue adaptada para el control de temperatura del reactor. Un filtro de Kalman extendido (EKF) se implementó para estimar los estados no medibles y fue probado en diferentes casos, incluyendo un estudio de robustez en el que se introducen errores en el modelo para verificar el buen desempeño del estimador. Después de verificar el desempeño del controlador, se proponen algunos cambios en el proceso para mejorar la productividad y la calidad del polímero que se obtiene. Finalmente, el perfil ´optimo de temperatura los perfiles óptimosRésumé. Dans ce travail, la modélisation, la simulation, l’optimisation dynamique et la commande nonlinéaire d’un procédé industriel de polymérisation en émulsion produisant du polyacétate de vinyle (PVAc) sont étudiées. La réaction est modélisée comme un système à deux phases constitué d’une phase aqueuse et une phase particulaire. Un modèle détaillé est développé pour calculer la masse molaire moyenne en poids, la masse molaire moyenne en nombre et la dispersité. Les moments de chaînes en croissance et terminées sont utilisés pour représenter l’état du polym`ere et pour calculer la distribution de masse molaire (MWD). L’étude de cas correspond à un réacteur industriel fonctionnant dans une entreprise de produits chimiques à Bogotá. Un réacteur à l’échelle industrielle (11 m3 de capacité) est simulé dans lequel une réaction semi-batch de polymérisation en émulsion de l’acétate de vinyle est effectuée. Le problème d’optimisation dynamique est résolu directement en utilisant un solveur de programmation non linéaire. L’intégration des équations différentielles est faite en utilisant la méthode de Runge-Kutta. Trois problémes d’optimisation différents sont résolus, depuis le plus simpliste (une seule variable d’optimisation : la température du réacteur) au plus complexe (trois variables d’optimisation : la température du réacteur, le débit de l’initiateur et le débit du monomére) en vue de minimiser le temps final de réaction. Une réduction de 25% du temps de traitement par batchs est réalisée par rapport aux conditions normales de fonctionnement appliquées dans l’entreprise. Les résultats montrent qu’il est possible de minimiser la durée de réaction alors que certaines qualités de polyméres souhaitées (conversion, masse molaire et contenu en solides) satisfont les contraintes définies. Une technique de commande non linéaire géométrique à l’aide de la linéarisation entrée/sortie est adaptée à la régulation de la température du réacteur. Un filtre Kalman étendu (EKF) est mis en oeuvre pour estimer les états non mesurés et il est testé dans différents cas, dont une étude de robustesse où des erreurs du modèle sont introduites pour vérifier son bon fonctionnement. Après vérification des performances du régulateur, certains changements d’opération du procédé ont été proposés afin d’améliorer la productivit´e du proc´ed´e et la qualit´e du polym`ere. Enfin, le profil de temp´erature optimale et les politiques d’alimentation optimales de d´ebits du monom`ere et de l’amorceur, obtenues dans l’étape d’optimisation dynamique, ont fourni les consignes optimales pour la commande non linéaire. Les résultats montrent que le régulateur non linéaire concu ici convient pour suivre les trajectoires optimales de température calculées précédemment.Doctorad

Análisis del control y optimización de un reactor piloto para producir poliacetato de vinilo

Este trabajo presenta el modelamiento y optimización de la reacción de polimerización de Vinil Acetato (VAc), desarrollado con el objetivo de establecer las condiciones operacionales necesarias para minimizar el tiempo de procesamiento. El sistema se modeló teniendo en cuenta las interacciones fisicoquímicas, energéticas y usando las condiciones de operación que normalmente emplea una empresa de producción de adhesivos en Colombia. Para este modelamiento se utilizó como base un equipo de reacción de 65L ubicado en la Universidad Nacional de Colombia y un reactor de 11m3 ubicado en Preflex S.A. A partir de los resultados de la simulación base, se realizó la optimización de cada modelo, mediante el método de control óptimo, en donde se modificaron los flujos de alimentación de monómero, iniciador y fluido de enfriamiento. Para cada problema de optimización identificado se buscó crear las condiciones operacionales que permitieran reducir el tiempo de este procesamiento. Por otra parte, se analizó numéricamente la controlabilidad del sistema de reacción a escala piloto usando dos estrategias, PID y MPC; ambas presentaron un comportamiento satisfactorio, pero la más recomendada es la estrategia PID debido a su facilidad de implementación. Por último y teniendo en cuenta los resultados previos, se validó experimentalmente el proceso de reacción en un reactor a escala piloto, siguiendo los perfiles de las 3 propiedades medibles: contenido de sólidos, viscosidad y temperatura de proceso. Se encontró que es posible realizar la reducción de tiempo planteada en la optimización, usando agua como fluido refrigerante y mediante un control PID adaptativo, mantener las propiedades físicas del material en los parámetros establecidos, pero cambiando la distribución de tamaños de las partículas.Abstract: Modelling, simulation and optimization of the vinyl acetate polymerization was realized in this paper in order to determine the operating conditions that allows the reaction time minimization. The system has been modeled considering the physicochemical, energy interactions and operating conditions of the industrial reactor from an adhesive production company in Colombia. Polymerization modelling was based on a 65L steel reactor located at the National University of Colombia and a 11m3 reactor located on Preflex S.A. Based on the results of the simulation, an optimization process of each model was carried out, using the optimal control method, where the monomer feed, initiation and cooling fluid were modified. Operational conditions that allows a time process reduction were determined on each optimization problem. On the other hand, the controllability of the system using the PID and MPC control strategies were analyzed, both with a satisfactory performance through time, being the PID strategy more recommended due to its ease of implementation. Finally, the reaction process was experimentally validated in a pilot scale reactor, following the profiles of 3 measurable properties during the process: Solids content, viscosity and process temperature. Pilot scale experimentations show that it is possible to reduce the reaction time using water as coolant, with a dynamic PID control, keeping holding the polymer physical properties, but with a different size particle distribution.Maestrí