Increased Reactor Performance versus Reactor Safety Aspects in Acrylate Copolymerization

The aim of reducing cycle times of semibatch‐polymerization processes requires systematic investigations of the kinetics, careful adjustment of the desired polymer properties, proper thermal reactor design and reliable reactor safety assessment [1]. As a concrete example, a semibatch‐copolymerization was carefully examined with respect to four different aspects. Thermo‐kinetics of the reaction were investigated with isoperibolic reaction calorimetry and GC. In order to obtain reliable values for the overall heat transfer coefficient of the production scale reactor, cooling experiments were carried out with solvent and final copolymer solution as reactor content. For consistent reactor safety assessment additional investigations are necessary including case studies of breakdown incidences. These simulations were performed with a mathematical model based on the GC data and experimental vapor pressure curves. As a result of these calculations, a reduction of reaction time from 10 to 6 hours was possible. To convert into practice, it must be ensured that even in this shortened time a product of the same quality is produced.     

Modeling of “living” free‐radical polymerization processes. I. Batch,semibatch, and continuous tank reactors

A comprehensive mathematical model is developed for “living” free‐radical polymerization carried out in tank reactors and provides a tool for the study of process development and design issues. The model is validated using experimental data for nitroxide‐mediated styrene polymerization and atom transfer radical copolymerization of styrene and n‐butyl acrylate. Simulations show that the presence of reversible capping reactions between growing and dormant polymer chains should boost initiation efficiency when using free nitroxide in conjunction with conventional initiator and also increase the effectiveness of thermal initiation. A study shows the effects of the value of the capping equilibrium constant and capping reaction rate constants for both nitroxide‐mediated styrene polymerization (using alkoxyamine as polymer chain seeds) and atom transfer radical polymerization of n‐butyl acrylate (using methyl 2‐bromopropionate as chain extension seeds). Also the effect of introducing additional conventional initiator into atom transfer radical polymerization of n‐butyl acrylate is studied. It is found that the characteristics of long chain growth are determined by the fast exchange of radicals between growing and dormant polymer chains. Polymerization results in batch, semibatch, and a series of continuous tank reactors are analyzed. The simulations also show that a semibatch reactor is most flexible for the preparation of polymers with controlled architecture. For continuous tank reactors, the residence time distribution has a significant effect on the development of chain architecture. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 1630–1662, 2002     

Tendency modeling of semibatch reactors for optimization and control

Significant economical benefits can be derived from the optimal operation of semibatch reactors even when the detailed understanding of the chemical kinetics is not at hand. To realize these economical benefits a general adaptive optimal control strategy is needed that properly accounts for the lack of detailed knowledge and the great variety of semibatch processes and at the same time takes advantage of the plant data collected during the process operation.In the present paper a novel approach is introduced for the systematic development of approximate reaction networks that are the basis of the reactor model. Other simple kinetic models can be postulated on intuitive grounds. All such networks lump the known species as reactants, product and byproduct and along with a set of mass and energy balances for semibatch reactors constitute the tendency model.This modeling approach is applied to a complex kinetic network containing 20 parameters which is accurately approximated by two simple tendency models that have either 4 or 6 parameters related to the kinetic constants. Estimation of these parameters shows the accuracy of the derived models to be very satisfactory.     

Property evaluation and control in a semibatch MMA/MA solution copolymerization reactor

This article deals with the property control of polymer product in a semibatch MMA/MA copolymerization reactor by applying the extended Kalman filter (EKF) based nonlinear model predictive control (MPC). In addition to the feeding of the more reactive monomer, the solvent is continuously supplied so as to maintain the viscosity of the reaction mixture within a reasonable range. This measure then provides favorable conditions not only for the on-line estimation with the EKF but also for the performance of the EKF based nonlinear MPC. Indeed, the improved performance of the state estimator is confirmed by experiment under isothermal and nonisothermal conditions over a prolonged reaction time. On the basis of the estimated state, the EKF based nonlinear MPC is implemented to the semibatch reactor to produce copolymers with desired properties. The experimental results clearly demonstrate the superiority of the present control strategy compared to the result of our previous work obtained without having additional feed of solvent.     

Optimal operations of semibatch solution polymerization of acrylamide with molecular distribution as constraints

In this work, optimal control profiles of a semibatch solution polymerization of an acrylamide system are investigated for the first time. The control variables are the monomer and initiator feed rates. The objective function is the operating time of each batch. One of the operating constraints is the maximum of the polymerization rate of the reaction, which is important due to the limitation of the heat-removal equipment. The expected number-average molecular weight and molecular weight distribution are also included as constraints in order to guarantee the quality of the products. A nonlinear programming approach developed by Jang and Yang is used for solving the equations. Several simulation and experimental runs show that the operation of this semibatch system is very smooth and conversions are fitted well by the model. The molecular weights and molecular weight distributions of the polymer products are also well controlled. © 1993 John Wiley & Sons, Inc.     

Kinetics and Modeling of Fatty Alcohol Ethoxylation in an Industrial Spray Loop Reactor

The kinetics of the ethoxylation of fatty alcohols catalyzed by potassium hydroxide was studied to obtain the rate constants for modeling of the industrial process. Experimental data obtained in a lab‐scale semibatch autoclave reactor were used to evaluate kinetic and equilibrium parameters. The kinetic model was employed to model the performance of an industrial‐scale spray tower reactor for fatty alcohol ethoxylation. The reactor model considers that mass transfer and reaction occur independently in two distinct zones of the reactor. Good agreement between the model predictions and real data was found. These findings confirm the reliability of the kinetic and reactor model for simulating fatty alcohol ethoxylation processes under industrial conditions.     

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

Batch 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.     

Integrated thermodynamic and kinetic model of homogeneous catalytic N-oxidation processes

The homogeneous phosphotungstic acid catalyzed N-oxidation of alkylpyridines by hydrogen peroxide has important applications in pharmaceutical and fine chemical industries. Current industry practice is to employ a semibatch reactor with gradual dosing of hydrogen peroxide into an alkylpyridine/catalyst solution under isothermal conditions. However, due to lack of understanding of reaction mechanism and thermodynamic behavior, this system is subject to significant risk of flammability, fires and explosions due to hydrogen peroxide decomposition. In this study, we conducted semibatch N-oxidation process in an isothermal reaction calorimeter (RC1) over a wide range of temperature, catalyst amount and oxidizer dosing rates. Reactor pressure, reaction heat generation rate and in situ FTIR spectra of liquid phase species were recorded in real-time during experiments, and final product was quantified using HPLC and GC–MS analytical tools. We developed an integrated thermodynamic and kinetics model of homogeneous N-oxidation reaction based on experimental results and past literature findings. More specifically, Wilson excess Gibbs model was employed to estimate activity coefficients of highly nonideal liquid mixture. We found ideal gas law was satisfactory in calculating incondensable oxygen pressure. First principle reaction mechanism and kinetics parameters of (a) catalytic N-oxidation reaction; (b) catalytic hydrogen peroxide decomposition reaction; (c) noncatalytic N-oxidation reaction; (d) noncatalytic hydrogen peroxide decomposition reaction was derived based on experimental findings of this study and past literature. The proposed integrated thermodynamic model and kinetics model successfully predicted highly nonlinear reactor pressure, species concentration and reaction enthalpy generation rate profile of homogenous catalytic N-oxidation and H₂O₂ decomposition reaction. The optimal reactions conditions with maximum N-oxide product yield and minimum reactor pressure and catalyst usage was theoretically identified and further verified by experiments. The obtained model can be used for inherently safer reactor design and applied to other homogeneous tungstic acid catalytic hydrogen peroxide oxidation processes.     

Reactor modeling and recipe optimization of polyether polyol processes: Polypropylene glycol

The reactor modeling and recipe optimization of conventional semibatch polyether polyol processes, in particular for the polymerization of propylene oxide to make polypropylene glycol, is addressed. A rigorous mathematical reactor model is first developed to describe the dynamic behavior of the polymerization process based on first‐principles including the mass and population balances, reaction kinetics, and vapor‐liquid equilibria. Next, the obtained differential algebraic model is reformulated by applying a nullspace projection method that results in an equivalent dynamic system with better computational performance. The reactor model is validated against plant data by adjusting model parameters. A dynamic optimization problem is then formulated to optimize the process recipe, where the batch processing time is minimized, given a target product molecular weight as well as other requirements on product quality and process safety. The dynamic optimization problem is translated into a nonlinear program using the simultaneous collocation strategy and further solved with the interior point method to obtain the optimal control profiles. The case study result shows a good match between the model prediction and real plant data, and the optimization approach is able to significantly reduce the batch time by 47%, which indicates great potential for industrial applications. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2515–2529, 2013     

Dynamic optimization of the methylmethacrylate cell‐cast process for plastic sheet production

Traditionally, the methylmethacrylate (MMA) polymerization reaction process for plastic sheet production has been carried out using warming baths. However, it has been observed that the manufactured polymer tends to feature poor homogeneity characteristics measured in terms of properties like molecular weight distribution. Nonhomogeneous polymer properties should be avoided because they give rise to a product with undesired wide quality characteristics. To improve homogeneity properties force‐circulated warm air reactors have been proposed, such reactors are normally operated under isothermal air temperature conditions. However, we demonstrate that dynamic optimal warming temperature profiles lead to a polymer sheet with better homogeneity characteristics, especially when compared against simple isothermal operating policies. In this work, the dynamic optimization of a heating and polymerization reaction process for plastic sheet production in a force‐circulated warm air reactor is addressed. The optimization formulation is based on the dynamic representation of the two‐directional heating and reaction process taking place within the system, and includes kinetic equations for the bulk free radical polymerization reactions of MMA. The mathematical model is cast as a time dependent partial differential equation (PDE) system, the optimal heating profile calculation turns out to be a dynamic optimization problem embedded in a distributed parameter system. A simultaneous optimization approach is selected to solve the dynamic optimization problem. Trough full discretization of all decision variables, a nonlinear programming (NLP) model is obtained and solved by using the IPOPT optimization solver. The results are presented about the dynamic optimization for two plastic sheets of different thickness and compared them against simple operating policies. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Dynamic modeling and experimental evaluation of olefin copolymerization with vanadium‐based catalysts

In this study, we developed a mathematical model for olefin copolymerization using soluble Ziegler–Natta catalysts in a semibatch reactor to predict the reaction rate and polymer characteristics (i.e., molecular weight, polydispersity, and ethylene content) as functions of the reaction parameters (i.e., time, temperature, pressure, concentrations, and so on) accurately. The proposed model differs from others because it considers the olefin copolymerization as a dynamic process and applies double moments for two reactants (ethylene and propylene) in the presence of hydrogen. To establish the model validity, the copolymerization was performed with VOCl₃? Al₂Et₃Cl₃ systems with hydrogen as a molecular weight controlling agent. The dynamic model was able to reproduce the experimental data within experimental accuracy and accurately demonstrated the fundamental importance of the polymerization variables on the final properties of the polymer material in the copolymerization of ethylene and propylene with Al/V ratios of up to 28 before synthesis. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 3101–3110, 2006     

Modeling and analysis of a gas sweeping process for polycarbonate polymerization

This article deals with (1) the development of a mathematical model for the finishing polycarbonate polymerization process with a horizontal, rotating disk‐type reactor with countercurrent gas sweeping and (2) the performance analysis of the reactor system with the model. We propose a model describing a reactor system consisting of two phases in which the byproduct (phenol) is removed from the polymer melt phase to the countercurrently flowing vapor phase to facilitate the forward reaction and, therefore, produce a high molecular weight polymer compatible with the products of commercial grades. The vapor phase is represented by the tanks‐in‐series model, whereas the polymer melt phase is regarded as a plug flow reactor. The major concerns here are the influences of the reactor operating conditions, including the catalyst concentration, reaction temperature, mass‐transfer rate, melt‐phase residence time, and vapor‐phase velocity, on the polymer molecular weight, the melt‐phase concentrations of various components, and the molar fraction of phenol in the vapor phase. To corroborate the validity of the proposed model and investigate the complex phenomena of the process, we have conducted a series of simulation studies with various operating policies, and we compare the performance of the process with the performances of the cocurrent process and the vacuum process. According to the results of this study, this new type of reactor system shows satisfactory performance and is sometimes even better than the conventional high‐ vacuum process. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 1010–1021, 2003     

Algorithms for Using Some Models of Gel and Glass Effects in Free-Radical Polymerization of Methyl Methacrylate

The aim of this article is the modeling and simulation of the batch bulk polymerization of methyl methacrylate (MMA). Simple dependencies between the propagation and termination rate constants and monomer conversion for the gel and glass effects are proposed. The empirical parameters in these relations are determined from conversion and molecular-weight experimental data obtained under various reaction conditions (initiator concentration and temperature). Sometimes, different relations were necessary to express the variation of the kinetic constants on conversion subintervals. Thus, these models have been used continuously or discontinuously, as a function of their results. An algorithm for using this model was also established.

The analysis of this model has two aims: (1) to get a good agreement between simulation and experiment; (2) to provide a simple model to be used under different reactor conditions (batch, semibatch, or continuous) or which can be easily handled in polymer engineering studies, such as sensitivity analysis, optimal control, and so forth.     

Melt polymerization of bisphenol‐A and diphenyl carbonate in a semibatch reactor

The effect of thermodynamic phase equilibrium on the kinetics of semibatch melt polycondensation of bisphenol‐A and diphenyl carbonate was studied for the synthesis of polycarbonate. In the melt‐polymerization process, a partial loss of diphenyl carbonate occurs as the reaction by‐product phenol is removed from the reactor. To obtain a high molecular weight polymer under high temperature and low‐pressure conditions, a stoichiometric mol ratio of the two reactive end groups needs to be maintained during the polymerization. In this work, vapor–liquid equilibrium data for a binary mixture of phenol and diphenyl carbonate are reported and they are used in conjunction with the Wilson equation to calculate the exact amounts of diphenyl carbonate and phenol returned from a reflux column to the reactor. A good agreement between the reactor model simulations and the experimental polymerization data was obtained. It was also observed that diphenyl carbonate is quickly consumed during the early stage of polymerization and the fraction of evaporated diphenyl carbonate refluxed to the reactor is essentially constant during this period. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 1253–1266, 2001     

Free-radical polymerizations associated with the trommsdorff effect under semibatch reactor conditions. III. Experimental responses to step changes in initiator concentration

The presence of the diffusion-limited gel or Trommsdorff effect in free-radical polymerizations poses a challenge for the modelling of these reactors. The available models cannot be applied to industrial reactors because of their inability to account for nonisothermal effects and semibatch operations. Recent models have overcome these limitations. These models have already been validated for step changes in temperature. The validity of these models under semibatch reactor conditions has been established in the present investigation. Experiments have been carried out at constant temperatures (50 and 70^°C) and a step change in the initiator concentration from about 15.48 to 100 mol/m³ has been effected during the course of polymerization. Experimental results on monomer conversions and average molecular weights have been found to be in reasonable agreement with model predictions. The present study establishes the applicability of these models for more general semibatch reactor operations, as well as the possibility of model-based optimal control of industrial reactors. © 1996 John Wiley & Sons, Inc.     

Optimal policies for BMA polymerization in nonisothermal batch reactor

In this paper, the optimal policies for bulk polymerization of n‐butyl methacrylate (BMA) are determined in a nonisothermal batch reactor. Four objectives are realized for BMA polymerization based on a detailed process model. The objectives are: (i) maximization of monomer conversion in a specified operation time, (ii) minimization of operation time for a specified, final monomer conversion, (iii) maximization of monomer conversion for a specified, final number average polymer molecular weight, and (iv) maximization of monomer conversion for a specified, final weight average polymer molecular weight. For each objective, the optimal temperature policy of heat‐exchange fluid inside reactor jacket is determined. The temperature of the heat‐exchange fluid is considered as a function of a specified variable. Necessary equations are provided to suitably transform the process model in terms of a specified variable other than time, and to evaluate the elements of Jacobian to help in the accurate solution of the process model. A genetic algorithm‐based optimal control method is applied to realize the objectives. The resulting optimal policies of this application reveal considerable improvements in the batch production of poly(BMA). © 2006 Wiley Periodicals, Inc. J Appl PolymSci 102: 2799–2809, 2006     

Simulation and optimization of the continuous tower process for styrene polymerization

The continuous tower process, a popular industrial process for the manufacture of polystyrene, was simulated and optimized. A kinetic model for the thermal polymerization of styrene, which takes into account the Trommsdorff effect and the volume change accompanying the reaction, was developed. This was used to formulate model equations for the continuous flow stirred tank reactor (CSTR) and plug flow reactor (several sections) in the tower process. The model can predict monomer conversion, number‐ and weight‐average molecular weights, polydispersity index (PDI), and temperature at various locations in the unit, under specified operating conditions. Multiobjective optimization of this process was also carried out, for which an adaptation of a genetic algorithm (GA) was used. The two objectives were maximization of the final monomer conversion and minimization of the PDI of the product. The conversion in the CSTR was constrained to lie within a desired range, and polymer having a specified value of the number‐average molecular weight was to be produced. The optimal solution was a unique point (no Pareto sets were obtained). The optimal solutions indicated that the tower process is operated under near‐optimal conditions. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 775–788, 2004     

Particle size distribution control in emulsion polymerization

Effects of the operating policies—the initial initiator amount; the initial emulsifier amount; the monomer addition mode: batch or semibatch; and the monomer addition rate under “monomer‐starved conditions” for the control of particle size distribution (PSD)—were studied through a model that simulates batch and semibatch reactor operations in conventional emulsion polymerization. The population balance model incorporates both the nucleation stage and the growth stage. The full PSDs were reported, which have normally been omitted in earlier studies. It was shown through simulations that the broadness of the distributions, both initial (obtained after the end of nucleation) and final (after complete conversion of monomer), can be controlled by the initial initiator amount and the emulsifier amount. The higher initiator amounts and the lower emulsifier amounts favor narrower initial and final distributions. The shape of the initial PSDs and the trends in the average size and range were preserved with subsequent addition of monomer in the batch or in the semibatch mode, although the final PSD was always considerably narrower than that of the initial PSD. The addition of monomer in the semibatch mode gave narrower distribution compared to that of the batch mode, and also, lower monomer addition rates gave narrower distributions (larger average sizes), which was a new result. It was further shown through simulations that, under monomer‐starved conditions, the reaction rate closely matched the monomer feed rate. These conclusions are explained (1) qualitatively—the shorter the length of the nucleation stage and the larger the length of the growth stage (provided the number of particles remains the same), the narrower is the distribution; and (2) mathematically—in terms of the “self‐sharpening” effect. Experimental evidence in favor of the self‐sharpening effect was given by analyzing the experimental particle size distributions in detail. The practical significance of this work was proposed. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 2884–2902, 2004     

Conversion of polyester into heat‐resistant polyamide by reacting with aromatic diamine compound II. Semibatch reaction by nitrogen gas sweeping process

The conversion of poly(ethylene terephthalate) (PET) into heat‐resistant polyamide was carried out in the solid state polycondensation by applying a nitrogen gas sweeping process. The reaction product obtained by the catalyzed and uncatalyzed batch reaction with the specified reaction condition was used as the starting material in the semibatch reaction process. Nitrogen gas was introduced into the reactor to remove a volatile reaction byproduct from the reaction mixture. Effect of the semibatch reaction variables such as temperature, time, and nitrogen gas sweeping rate on the extent of reaction and the heat‐resistant property of polyamide obtained was investigated. A comparison of the extent of reaction in the semibatch reaction process was made between the catalyzed starting material and the uncatalyzed one. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 2223–2232, 2004     

Composition control in emulsion copolymerization. II. Application to binary and ternary systems

The optimal monomer feed policy for producing in a semibatch reactor a given amount of polymer with constant instantaneous composition, in the minimum reaction time and complete monomer depletion, as developed in Part I of this work, has been implemented experimentally. Conversion has been monitored on-line using a densitometer suitably connected to the laboratory reactor. The procedure has been applied to two binary and one ternary systems. The composition of the polymer produced has been characterized through various experimental techniques. The composition control procedure is insensitive to most types of irreproducibilities that arise in batch reactions performed in industrial appli-fjcations. © 1994 John Wiley & Sons, Inc.