Challenges in particulate polymerization reactor modeling and optimization: A population balance perspective

Abstract In the present article, recent developments on modeling and optimization of particulate polymerization processes are reviewed. A unified population balance approach is described to follow the time evolution of molecular and morphological polymer properties in batch and continuous polymerization reactors. The numerical methods as well as the computational issues related with the solution of the dynamic population balance equation are critically assessed. The orthogonal collocation on finite elements (OCFE) method and the fixed-pivot technique (FPT) are then applied to a free-radical batch polymerization reactor to calculate the dynamic evolution of the molecular weight distribution (MWD). Moreover, theoretical and experimental results are shown on the dynamic evolution of particle size distribution (PSD) in a suspension polymerization reactor. Recent advances in on-line monitoring of “polymer quality” are briefly discussed in the context of available hardware and software sensors. The problem of real-time optimization of polymerization processes under parametric uncertainty is also examined. Finally, new issues related with the modeling, numerical solution and control of multidimensional population balance equations are conferred.

[1]  R. K. Mutha and,et al.  A New Multirate-Measurement-Based Estimator: Emulsion Copolymerization Batch Reactor Case Study , 1997 .

[2]  Costas Kiparissides,et al.  Generalized model for prediction of the steady-state drop size distributions in batch stirred vessels , 1989 .

[3]  Alexander Penlidis,et al.  STATE ESTIMATION FOR POLYMERIZATION REACTORS , 1986 .

[4]  Hidetaka Tobita,et al.  Molecular Weight Distribution in Free-Radical Polymerization with Chain-Length-Dependent Bimolecular Termination. 2. Emulsion Polymerization , 1995 .

[5]  Andrew Klein,et al.  Dynamic modeling and state estimation for an emulsion copolymerization reactor , 1989 .

[6]  José Carlos Pinto,et al.  A survey of advanced control of polymerization reactors , 1996 .

[7]  Paulo L.C. Lage,et al.  A numerical method for solving the transient multidimensional population balance equation using an Euler–Lagrange formulation , 2003 .

[8]  E. G. Chatzi,et al.  Dynamic simulation of bimodal drop size distributions in low-coalescence batch dispersion systems , 1992 .

[9]  Peter Deuflhard,et al.  Computational treatment of polyreaction kinetics by orthogonal polynomials of a discrete variable , 1989, IMPACT Comput. Sci. Eng..

[10]  Stelios Rigopoulos,et al.  Finite‐element scheme for solution of the dynamic population balance equation , 2003 .

[11]  Francis J. Doyle,et al.  Open-loop control of particle size distribution in semi-batch emulsion copolymerization using a genetic algorithm , 2002 .

[12]  Alan W. Mahoney,et al.  Population balance modeling. Promise for the future , 2002 .

[13]  Costas Kiparissides,et al.  Part II: Dynamic evolution of the particle size distribution in particulate processes undergoing simultaneous particle nucleation, growth and aggregation , 2005 .

[14]  Jyh-Shyong Chang,et al.  Optimization of Batch Polymerization Reactors Using Neural-Network Rate-Function Models , 2002 .

[15]  Masoud Soroush.  State and parameter estimations and their applications in process control , 1998 .

[16]  J. Klein,et al.  Crystallization and precipitation engineering—I. An efficient method for solving population balance in crystallization with agglomeration , 1988 .

[17]  Costas Kiparissides,et al.  Dynamic optimization of molecular weight distribution using orthogonal collocation on finite elements and fixed pivot methods: An experimental and theoretical investigation , 2006 .

[18]  M. Hounslow,et al.  A discretized population balance for nucleation, growth, and aggregation , 1988 .

[19]  Kalanadh V. S. Sastry,et al.  Discretization procedure for the coalescence equation of particulate processes , 1981 .

[20]  Costas Kiparissides,et al.  Multivariate statistical analysis of mid‐infrared spectra for the online monitoring of 2‐ethylhexyl acrylate/styrene emulsion copolymerization , 2001 .

[21]  M. Hounslow,et al.  Adjustable discretized population balance for growth and aggregation , 1995 .

[22]  D. E. Rosner,et al.  Multivariate Population Balances via Moment and Monte Carlo Simulation Methods: An Important Sol Reaction Engineering Bivariate Example and “Mixed” Moments for the Estimation of Deposition, Scavenging, and Optical Properties for Populations of Nonspherical Suspended Particles , 2003 .

[23]  David S. Soong,et al.  A computer model for the gel effect in free-radical polymerization , 1983 .

[24]  Hyun-Ku Rhee,et al.  Extended Kalman filter-based nonlinear model predictive control for a continuous MMA polymerization reactor , 1999 .

[25]  D. Ramkrishna.  The Status of Population Balances , 1985 .

[26]  Rıdvan Berber.  Methods of model based process control , 1995 .

[27]  J. Thomas,et al.  Fiber optic dynamic light scattering from concentrated dispersions. 3: Particle sizing in concentrates. , 1990, Applied optics.

[28]  Jaleel Valappil,et al.  Accounting for batch reactor uncertainty in the nonlinear MPC of end-use properties , 2003 .

[29]  C. Georgakis,et al.  Nonlinear model predictive control of end-use properties in batch reactors , 2002 .

[30]  C. Georgakis,et al.  Control of emulsion polymerization reactors , 1994 .

[31]  John H. Seinfeld,et al.  Coagulation and growth of a multicomponent aerosol , 1978 .

[32]  Costas Kiparissides,et al.  Toward the Development of a General Framework for Modeling Molecular Weight and Compositional Changes in Free-Radical Copolymerization Reactions , 1992 .

[33]  John F. MacGregor,et al.  State estimation for semi-batch polymerization reactors , 1992 .

[34]  B. Brooks,et al.  Vinyl chloride dispersion with relation to suspension polymerisation , 1996 .

[35]  Piet D. Iedema,et al.  Modeling Molecular Weight and Degree of Branching Distribution of low density Polyethylene , 2000 .

[36]  J. Macgregor,et al.  Composition and Particle Diameter for Styrene/Methyl Methacrylate Copolymer Latex Using UV and NIR Spectroscopy , 1993 .

[37]  Klavs F. Jensen,et al.  Estimation of the molecular weight distribution in batch polymerization , 1988 .

[38]  Juan Baselga,et al.  Fluorescence monitoring of polymerization reaction. A new method for treating fluorescence experimental data , 2002 .

[39]  E. G. Chatzi,et al.  Use of a midrange infrared optical‐fiber probe for the on‐line monitoring of 2‐ethylhexyl acrylate/styrene emulsion copolymerization , 1997 .

[40]  Alan Jones,et al.  Crystallization and precipitation engineering , 2005, Comput. Chem. Eng..

[41]  Costas Kiparissides,et al.  Part III: Dynamic evolution of the particle size distribution in batch and continuous particulate processes: A Galerkin on finite elements approach , 2005 .

[42]  Hassan Hammouri,et al.  Non-linear tracking of glass transition temperatures for free radical emulsion copolymers , 1998 .

[43]  Naoto Ohmura,et al.  Controlling particle size by self-sustained oscillations in continuous emulsion polymerization of vinyl acetate , 1998 .

[44]  MIcHAEL WULKoW,et al.  Adaptive treatment of polyreactions in weighted sequence spaces , 1992, IMPACT Comput. Sci. Eng..

[45]  D. Ramkrishna,et al.  On the solution of population balance equations by discretization - III. Nucleation, growth and aggregation of particles , 1997 .

[46]  Margaritis Kostoglou,et al.  Evolution of aggregate size and fractal dimension during Brownian coagulation , 2001 .

[47]  M. Soroush.  Nonlinear state-observer design with application to reactors , 1997 .

[48]  Jose A. Romagnoli,et al.  Inferential conversion monitoring and control in emulsion polymerisation through calorimetric measurements , 2002 .

[49]  Sami Othman,et al.  On-line monitoring of methyl methacrylate–vinyl acetate emulsion copolymerization , 2000 .

[50]  P. Daoutidis,et al.  Numerical solution of multi-variable cell population balance models. II. Spectral methods , 2001 .

[51]  S. Othman,et al.  A combined hardware/software sensing approach for on-line control of emulsion polymerisation processes , 1998 .

[52]  Babu Joseph,et al.  Control of constrained multivariable nonlinear process using a two-phase approach , 1987 .

[53]  J. Macgregor,et al.  State estimation for continuous emulsion polymerization , 1991 .

[54]  Costas Kiparissides,et al.  CFD analysis of turbulence non-homogeneity in mixing vessels: A two-compartment model , 2002 .

[55]  Prodromos Daoutidis,et al.  Nonlinear productivity control using a multi-staged cell population balance model , 2002 .

[56]  Jay H. Lee,et al.  Integrated run-to-run and on-line model-based control of particle size distribution for a semi-batch precipitation reactor , 2002 .

[57]  John F. MacGregor,et al.  Optimization of molecular-weight distribution using batch-to-batch adjustments , 1998 .

[58]  Klaas R. Westerterp,et al.  Modeling of free radical polymerization up to high conversion. II. Development of a mathematical model. , 1997 .

[59]  Costas Kiparissides,et al.  A comprehensive model for the calculation of molecular weight–long-chain branching distribution in free-radical polymerizations , 1998 .

[60]  T. Crowley,et al.  Discrete Optimal Control of Molecular Weight Distribution in a Batch Free Radical Polymerization Process , 1997 .

[61]  Gregory J. McRae,et al.  Integrated framework for the numerical solution of multicomponent population balances. 1. Formulation, representation, and growth mechanisms , 2004 .

[62]  François Puel,et al.  Simulation and analysis of industrial crystallization processes through multidimensional population balance equations. Part 2: a study of semi-batch crystallization , 2003 .

[63]  Jay H. Lee,et al.  Receding Horizon Recursive State Estimation , 1993, 1993 American Control Conference.

[64]  Andrew Klein,et al.  An experimental study of adaptive Kalman filtering in emulsion copolymerization , 1991 .

[65]  E. G. Chatzi,et al.  Recent Developments in Hardware Sensors For the On-Line Monitoring of Polymerization Reactions , 1999 .

[66]  David Mautner Himmelblau,et al.  Process Analysis and Simulation. Deterministic Systems , 1968 .

[67]  J. Macgregor,et al.  Control of Particle Size Distributions in Emulsion Semibatch Polymerization Using Mid-Course Correction Policies , 2002 .

[68]  R. C. Everson,et al.  Numerical treatment of the population balance equation using a Spline-Galerkin method , 1994 .

[69]  Jürgen Fuhrmann,et al.  ONLINE OBSERVATION OF EMULSION POLYMERIZATION BY FLUORESCENCE TECHNIQUE , 1999 .

[70]  Margaritis Kostoglou,et al.  EVALUATION OF NUMERICAL METHODS FOR SIMULATING AN EVOLVING PARTICLE SIZE DISTRIBUTION IN GROWTH PROCESSES , 1995 .

[71]  Michael J. Hounslow,et al.  Finite-element methods for steady-state population balance equations , 1998 .

[72]  Costas Kiparissides,et al.  Solution of the Bi-variate dynamic population balance equation in batch particulate systems , 2005 .

[73]  W. Harmon Ray,et al.  Control of systems described by population balance equations—I. Controllability analysis , 1995 .

[74]  Panagiotis D. Christofides,et al.  Nonlinear control of particulate processes , 1999 .

[75]  Doraiswami Ramkrishna,et al.  A new solution to the brownian coagulation equation through the use of root-shifted problem-specific polynomials , 1985 .

[76]  John F. MacGregor,et al.  Industrial experiences with product quality control in semi-batch processes , 2000 .

[77]  David Mautner Himmelblau,et al.  Process analysis and simulation , 1968 .

[78]  Doraiswami Ramkrishna,et al.  Transient solution of the brownian coagulation equation by problem-specific polynomials , 1975 .

[79]  Hyun-Ku Rhee,et al.  Online estimation and control of polymer quality in a copolymerization reactor , 2002 .

[80]  G. Févotte,et al.  Robust on-line measurement of conversion and molecular weight using NIR spectroscopy during solution polymerization , 2002 .

[81]  D. Ramkrishna,et al.  On the solution of population balance equations by discretization—II. A moving pivot technique , 1996 .

[82]  Brian Scarlett,et al.  Population balances for particulate processes - a volume approach. , 2002 .

[83]  John F. MacGregor,et al.  Product Quality Control in Semibatch Reactors Using Midcourse Correction Policies , 1997 .

[84]  Enrique Luis Lima,et al.  Molecular weight distribution in composition controlled emulsion copolymerization , 2000 .

[85]  A. J. Morris,et al.  Online optimizing control of molecular weight properties in batch free-radical polymerization reactors , 2002 .

[86]  Wayne F. Reed,et al.  Online Monitoring of Composition, Sequence Length, and Molecular Weight Distributions during Free Radical Copolymerization, and Subsequent Determination of Reactivity Ratios , 2002 .

[87]  T. Crowley,et al.  Experimental studies on optimal molecular weight distribution control in a batch-free radical polymerization process , 1998 .

[88]  John H. Seinfeld,et al.  Simulation of multicomponent aerosol dynamics , 1992 .

[89]  Gregory J. McRae,et al.  Integrated Framework for the Numerical Solution of Multicomponent Population Balances. 2. The Split Composition Distribution Method , 2004 .

[90]  Chyi Hwang,et al.  A wavelet-Galerkin method for solving population balance equations , 1996 .

[91]  Dominique Bonvin,et al.  Application of Estimation Techniques to Batch Reactors , 1991 .

[92]  J. M. Asua,et al.  Estimation of conversion and copolymer composition in semicontinuous emulsion polymerization using calorimetric data , 1995 .

[93]  Hyun-Ku Rhee,et al.  Molecular Weight Distribution Control in a Batch Polymerization Reactor Using the On-Line Two-Step Method , 1999 .

[94]  C. A. Silebi,et al.  Size Analysis of Simple and Complex Mixtures of Colloids in the Submicrometer Range Using Capillary Hydrodynamic Fractionation , 1991 .

[95]  C. Kiparissides,et al.  Dynamic Optimization of Molecular Weight Distribution Using Orthogonal Collocation on Finite Elements and Fixed Pivot Methods: An Experimental and Theoretical Investigation , 2007 .

[96]  George M Hidy,et al.  On the theory of the coagulation of noninteracting particles in brownian motion , 1965 .

[97]  Costas Kiparissides,et al.  Part I: Dynamic evolution of the particle size distribution in particulate processes undergoing combined particle growth and aggregation , 2004 .

[98]  Adrian Sandu,et al.  A framework for the numerical treatment of aerosol dynamics , 2003 .

[99]  Costas Kiparissides,et al.  Prediction of particle size distribution in suspension polymerization reactors: effect of turbulence nonhomogeneity , 2000 .

[100]  J. Seinfeld,et al.  Simulation of Aerosol Dynamics: A Comparative Review of Algorithms Used in Air Quality Models , 1999 .

[101]  Kenji Ito,et al.  R&D Note: On the Calculation of Molecular Weight Distribution from the Moments Using Laguerre Polynomials , 1993 .

[102]  J. Seinfeld,et al.  Sectional representations for simulating aerosol dynamics , 1980 .

[103]  Margaritis Kostoglou,et al.  Evaluation of Zero Order Methods for Simulating Particle Coagulation , 1994 .

[104]  S. Katz,et al.  Some problems in particle technology: A statistical mechanical formulation , 1964 .

[105]  Timothy J. Crowley,et al.  Calculation of Molecular Weight Distribution from Molecular Weight Moments in Free Radical Polymerization , 1997 .

[106]  Sotiris E. Pratsinis,et al.  A discrete-sectional model for particulate production by gas-phase chemical reaction and aerosol coagulation in the free-molecular regime , 1990 .

[107]  Panagiotis D. Christofides,et al.  Control of nonlinear distributed process systems : Recent developments and challenges , 2001 .

[108]  François Puel,et al.  Simulation and analysis of industrial crystallization processes through multidimensional population balance equations. Part 1: a resolution algorithm based on the method of classes , 2003 .

[109]  Christodoulos Pilinis.  Derivation and numerical solution of the species mass distribution equations for multicomponent particulate systems , 1990 .

[110]  D. E. Rosner,et al.  Bivariate Extension of the Quadrature Method of Moments for Modeling Simultaneous Coagulation and Sintering of Particle Populations. , 2001, Journal of colloid and interface science.

[111]  Costas Kiparissides,et al.  Dynamic evolution of PSD in continuous flow processes: A comparative study of fixed and moving grid numerical techniques , 2006 .

[112]  E. Lima,et al.  Dynamic optimization of semicontinuous emulsion copolymerization reactions: composition and molecular weight distribution , 2001 .

[113]  A. Brandolin,et al.  On-Line Particle Size Distribution Measurements for Latex Reactors , 1991 .

[114]  J. Seinfeld,et al.  Numerical solution of the dynamic equation for particulate systems , 1978 .

[115]  Kangtaek Lee,et al.  Solution of the population balance equation using constant-number Monte Carlo , 2002 .

[116]  Klavs F. Jensen,et al.  On‐line molecular weight distribution estimation and control in batch polymerization , 1994 .

[117]  Enrique Luis Lima,et al.  In-line monitoring of weight average molecular weight in solution polymerizations using intrinsic viscosity measurements , 2001 .

[118]  Hidetaka Tobita,et al.  Molecular weight distribution in free radical polymerization with long‐chain branching , 1993 .

[119]  B. Finlayson.  Nonlinear analysis in chemical engineering , 1980 .

[120]  Francis J. Doyle,et al.  Polymer grade transition control using advanced real-time optimization software , 2004 .

[121]  Prodromos Daoutidis,et al.  Numerical solution of multi-variable cell population balance models. III. Finite element methods , 2001 .

[122]  José M. Asua,et al.  Control of Molecular Weight Distribution in Emulsion Polymerization Using On-Line Reaction Calorimetry , 2001 .

[123]  B. Brooks,et al.  Prediction of vinyl chloride drop sizes in stabilised liquid-liquid agitated dispersion , 1996 .

[124]  Costas Kiparissides,et al.  A generalized population balance model for the prediction of particle size distribution in suspension polymerization reactors , 2006 .

[125]  Rainer Bleck,et al.  A fast, approximative method for integrating the stochastic coalescence equation , 1970 .

[126]  C. Kiparissides.  Polymerization reactor modeling: A review of recent developments and future directions , 1996 .

[127]  Francis J. Doyle,et al.  Modeling of particle size distribution in emulsion co-polymerization: comparison with experimental data and parametric sensitivity studies , 2002 .

[128]  Timothy J. Crowley,et al.  Control of copolymer hydrodynamic volume distribution in a semibatch free radical copolymerization process , 1999 .

[129]  John P. Congalidis,et al.  Feedforward and feedback control of a solution copolymerization reactor , 1989 .

[130]  W. Harmon Ray,et al.  Control of semicontinuous emulsion copolymerization reactors , 1997 .

[131]  Efstratios N. Pistikopoulos,et al.  Optimal grade transition and selection of closed-loop controllers in a gas-phase olefin polymerization fluidized bed reactor , 2003 .

[132]  Y. Ozaki,et al.  Comparison of various chemometric evaluation approaches for on-line FT-NIR transmission and FT-MIR/ATR spectroscopic data of methyl methacrylate solution polymerization , 2002 .

[133]  A. Herk,et al.  Measurement of partial conversions during the solution copolymerization of styrene and butyl acrylate using on-line Raman spectroscopy , 2001 .

[134]  J. Leiza,et al.  Simultaneous control of copolymer composition and MWD in emulsion copolymerization , 2001 .

[135]  Ernst Dieter Gilles,et al.  A population model for crystallization processes using two independent particle properties , 2001 .

[136]  Doraiswami Ramkrishna,et al.  Efficient solution of population balance equations with discontinuities by finite elements , 2002 .

[137]  Francis J. Doyle,et al.  Control of particle size distribution described by a population balance model of semibatch emulsion polymerization , 2000 .

[138]  Vanni,et al.  Approximate Population Balance Equations for Aggregation-Breakage Processes. , 2000, Journal of colloid and interface science.

[139]  Francis J. Doyle,et al.  Hybrid model-based approach to batch-to-batch control of particle size distribution in emulsion polymerization , 2003, Comput. Chem. Eng..

[140]  D. Bonvin,et al.  Application of estimation techniques to batch reactors—II. Experimental studies in state and parameter estimation , 1989 .