An approach for complete molecular weight distribution calculation: Application in ethylene coordination polymerization

The objective of this article is to present an approach to ascertain the molecular weight distribution (MWD) of polymeric systems and its application to an industrial polyethylene reactor. Ascertaining the complete MWD can provide more reliable predictions of polymer end-use properties, as some of them may depend on specific molecular weight ranges, instead of solely on the averages of the distribution. The proposed method is based on differentiation of the cumulative MWD, where the accumulated concentrations, evaluated at a finite number of chain lengths, are considered components in a reaction medium. Therefore, the dimension of the mathematical model may be suited to the desired level of detail on the MWD. The ethylene polymerization in solution with Ziegler-Natta catalyst is taken as a case study because of the lack of studies in this field. The reaction takes place in continuously stirred and tubular reactors. The results show the potential of the proposed approach and its usefulness in ascertaining the whole MWD, which in turn can be used to predict the polymer end-use properties. (c) 2008 Wiley Periodicals, Inc.10942176218

Dynamic Parameter Estimation In Polymerization Process

Mathematic modeling of chemical process is a very useful toll since it allows process knowledge without major investments, as is the case of pilot plants, for example. However, the model must be trustful, allowing predictions to be made in accordance with the process reality. Depending on the process considered, some of the model parameters are unknown, such as kinetic constants, heat capacity and so on. Thus, they must be estimated in order to allow the model to represent the main phenomena taking place in the system. The parameter estimation can be accomplished with experimental studies or using mathematic models, as in the case of this contribution. As a matter of fact, a parameter estimation procedure is an optimization problem: the process model has the same input variables as the real process and thus both output variables should be compared to give an error function which might be minimized. In the optimization problem the decision variables are the parameters to be estimated. The present study take into account an ethylene polymerization process with ZieglerNatta catalyst as a case study, for which real dynamic process data were used. In this process, many kinetic constants and physic parameters, around 30, were unknown and so must be estimated. As it is a dynamic optimization of a complex system, it was necessary to develop a robust optimization procedure based on the use of the Successive Quadratic Programming and the NAG (Numerical Algorithms Group) subroutines were used. The results show that the parameters were successfully estimated, with good agreement between process and model outputs.Faber, R., Li, P., Wozny, G., Sequential Parameter Estimation for Lange-Scale Systems with Multiple Data Sets. 1. Computational Framework (2003) Ind. Eng. Chem. Res, 42, pp. 5850-5860Yoon, W.J., Kim, Y.S., Kim, I.S., Choi, K.Y., Recent Advances in Polymer ReactionEngineering: Modeling and Control of Polymer Properties (2004) Korean J. Chem. Eng, 21 (1), pp. 147-167Sirohi, A.Choi, K. Y. On_Line Parameter Estimation in a Continuous Polymerization Process. Ind. Eng. Chem. Res. v. 35, p. 1332-1343, 1996;Bindlish, R., Rawlings, J.B., Young, R.E., Parameter Estimation for Industrial Polymerization Processes (2003) AICHE J, 49 (8), pp. 2071-2078Embirucu, M., Lima, E.L., Pinto, J.C.P., A Survey of Advanced Control of Polymerization Reactors (1996) Polym. Eng. Sci, 36 (4), pp. 433-447Cozewith, C., Transient Response of Continuous-Flow Stirred-Tank Polymerization Reactors (1988) AICHE J, 34 (2), pp. 272-282Kim, K.J., Choi, K.Y., Continuous Olefin Copolymerization with Soluble Ziegler-Natta Catalysts (1991) AICHE J, 37 (8), pp. 1255-1260Kim, K.J., (1992) AICHE J, 38 (9), p. 1488Embiruçu, M., Lima, E.L., Pinto, J.C., Continuous Soluble Ziegler-Natta Ethylene Polymerizatons in Reactor Trains. I. Mathematical Modeling (2000) J. App. Polym. Sci, 77, pp. 1574-1590CARVALHO, A.B., GLOOR, P.E., HAMIELEC, A.E., A kinetic mathematical model for heterogeneous Ziegler-Natta copolymerization (1989) Polymer, 30, pp. 280-296. , fevXIE, T.Y., McAULEY, K.B., HSU, J.C.C., BACON, D.W., Modeling MolecularWeight Development Of Gas-Phase a-Olefin Copolymerization (1995) AICHE Journal, 41 (5), pp. 1251-1265EMBIRUÇU, Modelagem, M., Estimação e Controle em Reatores Industriais de Polimerização de Eteno em Solução usando Catálise Ziegler-Natta Sol-vel (1998) Tese de Doutorado COPPE/UFR

Modeling and Simulation of Ethylene and 1-Butene Copolymerization in Solution with a Ziegler-Natta Catalyst

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)A comprehensive mathematical model for the ethylene/1-butene polymerization in solution with Ziegler-Natta catalyst is developed. The process comprises a series of continuously stirred and tubular reactors in which polyethylene resins with different properties may be produced. The mechanistic model considers the moments of the bivariant molecular weight distribution in order to ascertain the average molecular weight and polydispersity. The polymer quality is verified through the melt index, density and stress exponent, which is a measure of the polydispersity. The model developed investigates the stationary and dynamic behavior of the process following step changes in feed conditions. It allows for the prediction of non-linear and inverse responses, encouraging the use of the model for optimization and control purposes.o TEXTO COMPLETO DESTE ARTIGO, ESTARÁ DISPONÍVEL À PARTIR DE AGOSTO DE 2015.8Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)FAPESB (Fundacao de Amparo a Pesquisa do Estado da Bahia)FINEP (Financiadora de Estudos e Projetos)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

Modeling And Simulation Of Ethylene And 1-butene Copolymerization In Solution With Ziegler-natta Catalyst

Polyethylene (PE) is a thermoplastic polymer widely used throughout the world due to its versatile physical and chemical properties; even in a single polymerization process, a wide variety of PE resins can be produced, depending on process operation conditions. A mathematic model is a very useful tool in project developments and control studies, since it allows the process knowledge without major investments. The ethylene/1-butene copolymerization in solution with Ziegler-Natta catalyst in a series of Plug Flow Reactor (PFR) and Continuous Stirred Tank Reactor (CSTR) was taken as case study due to its versatility. Some simulation results correlating process input variables with reactor performance and polymer properties are also presented here, showing the mathematic model potential.CARVALHO, A.B., GLOOR, P.E., HAMIELEC, A.E., A kinetic mathematical model for heterogeneous Ziegler-Natta copolymerization (1989) Polymer, 30, pp. 280-296. , fevCHOI, K.Y., RAY, W.H., The Dynamic Behaviour of Fluidized Bed Reactors for Solid Catalyzed Gas Phase Olefin polymerization (1985) Chem. Eng. Sci, 40 (12), pp. 2261-2279COZEWITH, C., Transient Response of Continuous-Flow Stirred-Tank Polymerization Reactors (1988) AICHE Journal, 34 (2), pp. 272-282. , fevDUSSEAULT, J.J.A., HSU, C.C., MgCl2 Supported Ziegler-Natta Catalysts for Olefin Polymerization: Basic Structure, Mechanism and Kinetic Behaviour (1993) J. Macromol. Sci. Rev., Macromol. Chem. Phys, 33 C, p. 103apud Xie, T. YMcAuley, K. B.Hsu, J.C. C.Bacon, D. W. Gas-Phase Ethylene Polimerization: Production Process, Polymer Properties, and Reactor Modeling. Industrial Engineering Chemical Research, V.33, p. 449-479, 1993;EMBIRUÇU, Modelagem, M., Estimação e Controle em Reatores Industriais de Polimerização de Eteno em Solução usando Catálise Ziegler-Natta Solúvel (1998) Tese de Doutorado COPPE/UFRJEMBIRUÇU, M., LIMA, E.L., PINTO, J.C., Continuous Soluble Ziegler-Natta Ethylene Polymerizatons in Reactor Trains. I. Mathematical Modeling (2000) Journal of Applied Polymer Science, 77, pp. 1574-1590. , janHINCHLIFFE, M., MONTAGUE, G., WILLIS, M., BURKE, A., Hybrid Approach to Modeling an Industrial Polyethylene Process (2003) AICHE Journal, 49 (12), pp. 3127-3137KIM, K. J.CHOI, K. Y. Continuous Olefin Copolymerization with Soluble Ziegler-Natta Catalysts. AICHE Journal, v. 37, n. 8, p. 1255-1260, agost. 1991;KIM, K. J. e CHOI, K. Y. Errata, AIChE Journal, v. 38, n. 9, p. 1488, 1992;MCAULEY, K. B.MACGREGOR, J.F.HAMIELEC, A. E. A Kinetic Model for Industrial Gas-Phase Polyethylene Copolymerization. AICHE Journal, v. 36, n. 6, p. 837-850, jun. 1990;XIE, T.Y., McAULEY, K.B., HSU, J.C.C., BACON, D.W., Modeling Molecular-Weight Development Of Gas-Phase a-Olefin Copolymerization (1995) AICHE Journal, 41 (5), pp. 1251-126

Development Of Dynamic Models And Predictive Control By Fuzzy Logic For Polymerization Processes

This work presents the development of a predictive hybrid controller (PHC) based in fuzzy systems for polymerization processes. These reactions have typically a highly non linear dynamic behavior, thus making the performance of controllers based on conventional internal models to be poor or to require a lot of effort in controller tuning. The solution copolymerization of methyl methacrylate and vinyl acetate in a continuous stirred tank reactor is used to illustrate the performance of the proposed controller. It is introduced the development of a methodology for the design of the predictive controller based on functional fuzzy dynamic models of Takagi-Sugeno type. These models present an excellent capacity to represent dynamic data and this feature is explored in the proposed hybrid controller. Moreover, they allow the inclusion of qualitative or operational information of the process. Gaussian membership functions are used for the fuzzy sets and model determination (rules number and model parameters) is obtained from the process database. The treatment of these data for the fuzzy model determination is carried out by means of algorithms of subtractive clustering and least squares. The kinetic parameters and reactor operating conditions are obtained from the literature and a mathematical model is considered as a virtual plant for data generation and process identification. The modeling by the fuzzy approach showed to have a good potential for the processes representation. The PHC controller was compared to the dynamic matrix controller (DMC) to the regulatory and servo problems. The obtained results showed that the proposed control is robust and it requires less computational time than the conventional predictive controllers, being an interesting alternative to attack control problems in complex chemical processes.ABDELAZIM, T., MALIK, O.P., Identification of nonlinear systems by Takagi-Sugeno logic grey box modeling for real-time control (2005) Control Engineering Practice, 13, pp. 1489-1498ALEXANDRIDIS, A.P., SIETTOS, C.I., SARIMVEIS, H.K., BOUDOUVIS, A.G., BAFAS, G.V., Modelling of nonlinear process dynamics using Kohonen's neural networks, fuzzy systems and Chebyshev series (2002) Computers and Chemical Engineering, 26, pp. 479-486CERRADA, M., AGUILAR, J., COLINA, E., TITLI, A., Dynamical membership functions: An approach for adaptive fuzzy modeling (2005) Fuzzy Sets and Systems, 152, pp. 513-533CHEN, B., LIU, X., Reliable control design of fuzzy dynamic systems with time-varying delay (2003) Fuzzy Sets and Systems, pp. 1-26CHIU, S., A cluster estimation method with extension to fuzzy model identification (1994) IEEE, pp. 1240-1245CHIU, S., Method and software for extracting fuzzy classification rules by subtractive clustering (1996) IEEE, pp. 461-465CONGALIDIS, J.P., RICHARDS, J.R., RAY, W.H., Feedforward and feedback control of a solution copolymerization reactor (1989) AIChe Journal, 35 (6), pp. 891-907. , JuneDOUGHERTY, D., COOPER, D.A., Practical Multiple Model Adaptive Strategy for Multivariable Model Predictive Control (2003) Control Engineering Practice, 11, pp. 649-664GUIAMBA, I.R.F., MULHOLLAND, M., Adaptive Linear Dynamic Matrix Control Applied to an Integrating Process (2004) Computers and Chemical Engineering, 28, pp. 2621-2633HABBI, H., ZELMAT, M., BOUAMAMA, B.O., A dynamic fuzzy model for a drum-boiler-turbine system (2003) Automatica, 39, pp. 1213-1219HAERI, M., BEIK, H.Z., Application of Extended DMC for Nonlinear MIMO Systems (2005) Computers and Chemical Engineering, 29, pp. 1867-1874MANER, B.R., DOYLE III, F.J., Polymerization reactor control using autoregressive-plus volterra-based MPC (1997) AIChe Journal, 43 (7), pp. 1763-1784. , JulyPARK, M., RHEE, H., Property Evaluation and Control in a Semibatch MMA/MA Solution Copolymerization Reactor (2003) Chemical Engineering Science, 58, pp. 603-611PASSINO, K.M., YURKOVICH, S., (1998) Fuzzy Control, , Addison-Wesley-Longman, Menlo Park, CARAMASWAMY, S., CUTRIGHT, T.J., QAMMAR, H.K., Control of a Continuous Bioreactor Using Model Predictive Control (2005) Process Biochemistry, 40, pp. 2763-2770ROSS, T.J., (2004) Fuzzy Logic with Engineering Applications, , John Wiley & Sons Ltd, Second EditionSALA, A., GUERRA, T.M., BABUSKA, R., Perspectives of fuzzy systems and control (2005) Fuzzy Sets and Systems, 156, pp. 432-444SANTOS, L.O., AFONSO, P.A., CASTRO, J.A., OLIVEIRA, N.M., BIEGLER, L.T., On-line Implementation of Nonlinear MPC: An Experimental case study (2001) Control Engineering Practice, 9, pp. 847-857SCHNELLE, P.D., ROLLINS, D.L., Industrial Model Predictive Control Technology as Applied to Continuous Polymerization Processes (1998) ISA Transactions, 36 (4), pp. 281-292SILVA, J. E. L. Simulação e Controle Preditivo Linear (com Modelo de Convolução) e Não-Linear (com Modelo Baseado em Redes Neurais Artificiais) de Colunas Recheadas de Absorção com Reação Química. MSc. Thesis, DESQ/FEQ/UNICAMP, Campinas, São Paulo, Brazil, 1997;TAKAGI, T., SUGENO, M., Fuzzy identification of systems and its applications to modeling and Control (1985) IEEE Transactions on Systems, Man, and Cybernetics, 15, pp. 116-133TOLEDO, E.C., Modelagem, V., Simulação e Controle de Reatores Catalíticos de Leito Fixo. DSc. Thesis (1999) DPQ/FEQ/UNICAMP, , Campinas, São Paulo, BrazilZADEH, L., Outline of a new approach to the analysis of complex systems and decision process (1973) IEEE Transactions on Systems, Man, and Cybernetics, 1, pp. 28-4

Dynamic Optimization Of A Mma With Vac Copolymerization Reactor

Increasing worldwide market competitiveness and reduced profit margins are pressing chemical and process industries to move towards a predictive control approach, based on first-principles mathematical models, as well as plant dynamic optimization. In this perspective, the paper focuses on the development of a nonlinear model predictive control (NMPC) to manage the copolymerization process of methyl methacrylate (MMA) with vinyl acetate (VAc), consisting of a jacketed continuous stirred tank reactor, a separator, and a recycle loop. This system presents a highly complex behavior, thus making difficult the success of controllers based on linear models. A detailed differential and algebraic mathematical model consists of 53 equations and is implemented in Fortran 90/95 to simulate the plant and setup the NMPC. The numerical solution is performed by using IMSL library. NMPC is proved to be superior to a linear model predictive control approach and appears to hold a considerable promise for such a reactor system. Copyright © 2009, AIDIC Servizi S.r.l.1713831388Bemporad, A., Morari, M., Robust Model Predictive Control: A Survey (1999) Robustness in Identification and Control. Lecture Notes in Control and Information Sciences, 245. , Eds. Garulli A, Tesi A. and Vicino A, Springer, BerlinCongalidis, J.P., Richards, J.R., Ray, W.H., Feedforward and feedback control of a solution copolymerization reactor (1989) AIChE J, 35, pp. 891-907Haeri, M., Beik, H.Z., Application of extended DMC for nonlinear MIMO systems (2005) Comput. Chem. Eng, 29, pp. 1867-1874Lima, N.M.N., Maciel Filho, R., Embiruçu, M., Wolf Maciel, M.R., A cognitive approach to develop dynamic models: Application to polymerization systems (2007) J. Appl. Polym. Sci, 106, pp. 981-992Manenti, F., Rovaglio, M., Integrated multilevel optimization in large-scale poly(ethylene terephthalate) plants (2008) Ind. Eng. Chem. Res, 47, pp. 92-104Maner, B.R., Doyle III, F.J., Polymerization reactor control using autoregressive-plus volterra-based MPC (1997) AIChE J, 43, pp. 1763-1784Özkan, G., Hapoglu, H., Alpbaz, M., Non-linear generalized predictive control of a jacketed well mixed tank as applied to a batch process - a polymerization reaction (2006) Appl. Therm. Eng, 26, pp. 720-726Soroush, M., Kravaris, C., Nonlinear control of a batch polymerization reactor: An experimental study (1992) AIChE J, 38, pp. 1429-144

Optimal operating policies for tailored linear polyethylene resins production

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)In this work, optimal operating policies for the ethylene polymerization in solution with a Ziegler-Natta catalyst in a series of tubular and stirred tank reactors are proposed. The polymer is specified through properties such as melt index, stress exponent and density. Usually such properties are predicted by means of a process model once the operating conditions are specified. However, the computation of appropriate operating conditions to match desired resins properties is a much more difficult and not Yet industrially established task. This problem can be solved through optimization techniques, an efficient alternative to costly pilot plant or production scale tests. A formulation is proposed, where a stationary model of the flowsheet (DAE system) is cost into a multi-stage model with the spatial flow path coordinate as the independent variable. Discontinuities occur at the stage transitions because of model switches and reactants injection. Several studies, involving different polyethylene resin specifications, are carried out to present the high potential and versatility of the suggested procedure. (C) 2008 American Institute of Chemical Engineers.54923462365Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)DAAD (Deutscher Akademischer Austauschdienst)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES