Optimal Control of Batch MMA Polymerization with Specified Time,Monomer Conversion,and Average Polymer Molecular Weights

Summary: In this paper, the optimal control policies are determined for the free-radical polymerization of methyl methacrylate (MMA) in a non-isothermal batch reactor. The temperature of the fluid inside reactor-jacket is used as the control function to realize four different optimal control objectives. Each objective is formulated to optimize a given variable simultaneously specifying another. The first two objectives target the maximization of monomer conversion in a specified operation time, and the minimization of operation time for a specified, final monomer conversion. The last two objectives target the maximization of monomer conversion for specified, final number- and weight-average polymer molecular weights. The realization of these objectives is expected to be very useful for the batch production of polymers. To meet the specification of an optimization variable other than time, the differential model of batch process is expressed and utilized in the range of specified variable. Equations are provided for Jacobian evaluations to help in the accurate solution of process model. A genetic algorithms-based optimal control method is applied to realize the four optimal control objectives. The results of this application show considerable improvements in the performance of batch MMA polymerization.

     

Multi-objective dynamic optimization of semi-batch polymerization processes

An improved evolutionary algorithm is proposed to perform multi-objective dynamic optimization of a semi-batch styrene polymerization process. The target is to determine the optimal feeding trajectories and the reactor operating temperature, which maximize the monomer conversion rate and minimize the initiator residue concentration in the final product. The optimization problem has been formulated as a multi-objective mixed-integer nonlinear problem (MOMINLP). The proposed approach allows the effective computation of the optimal operating strategies for the production of polymers with the average molecular weight and the polydispersity index required.     

Experimental and Modeling Investigation of Radical Homopolymerization of 2‐(Methacryloyloxyethyl) Trimethylammonium Chloride in Aqueous Solution

The radical homopolymerization kinetics of 2‐(methacryloyloxyethyl) trimethylammonium chloride (TMAEMC) in aqueous solution is investigated across a wide range of initial monomer contents (5–35 wt%), ionic strengths, and pH levels using an in‐situ NMR technique to track monomer consumption over the complete conversion range. Molar mass distributions (MMD) of the final homopolymers are also examined, with additional batch and semi‐batch experiments conducted in a stirred vessel. The rates of monomer conversion and polymer MMDs are dependent on initial monomer content but almost entirely independent of pH and the presence of salts, with some acceleration of rate observed for low monomer levels at very high salt concentration. To aid with the interpretation of these results, the conductivity and counterion activity of monomer and polymer mixtures are measured to determine the extent of electrostatic interactions at various levels of conversion. These results are combined with recently reported measurements of TMAEMC homopropagation kinetics to develop a TMAEMC homopolymerization model that captures the systematic decrease in rates of monomer conversion observed with increased initial monomer content during batch polymerization as well as provides a good representation of semi‐batch polymerization.     

Emulsion polymerization of styrene. I. Review of experimental data and digital simulation

Isothermal emulsion polymerization at 60°C of styrene in a batch reactor were studied by using sodium lauryl sulfate as surfactant and potassium persulfate as initiator source. The concentrations of surfactant and initiator were varied during the runs. The polymerization evolution was followed as samples were taken at regular intervals. These emulsion samples were analyzed for monomer conversion, rate of polymerization, as well as for the size and the size distribution of the particles. The molecular weight and molecular weight distribution were obtained by gel permeation chromatography. Our study showed that fresh nucleation takes place even at high conversion, causing a continuous shifting toward broadening of particle size distribution. Contrary to the theory of Smith and Ewart, which assumes a constant number of particles during interval II of the polymerization reaction, our digital simulation of the reaction presents better experimental results with a variable number of particles, and indicates that the Hui–Hamielec model for termination constant k_t as function of conversion is not applicable under our working conditions.     

Kinetic modeling of two-step RAFT process for the production of novel fluorosilicone triblock copolymers

Well-defined poly(dimethylsiloxane)-b-poly(2,2,3,3,4,4,4-heptafluorobutylmethacryl-ate-b-poly(styrene) (PDMS-b-PHFBMA-b-PS) triblock copolymers were prepared by two-step reversible addition-fragmentation chain transfer (RAFT) polymerization. A comprehensive mathematical model for the two-step RAFT polymerization in a batch reactor was presented using the method of moments. The model described molecular weight, monomer conversion and polydispersity index as a function of polymerization time. Good agreements in the polymerization kinetics were achieved for fitting the kinetic profiles with the suggested model. In addition, the model was used to predict the effects of initiator concentration, chain transfer agent concentration and monomer concentration on the two-step RAFT polymerization kinetics. The simulated results showed that for the two-step RAFT polymerizations, the effects initiator concentration, chain transfer agent concentration and monomer concentration are identical and the influence degrees are different yet.     

Mathematical Modeling of Acrylonitrile-Butadiene Emulsion Copolymerization: Model Development and Validation

This paper presents a mechanistic model for the production of nitrile-butadiene rubber (NBR). The mathematical dynamic model was developed in order to simulate the industrial production of NBR via emulsion copolymerization of acrylonitrile (AN) and butadiene (Bd) in batch, continuous and trains of continuous reactors. For this reason, the model was constructed in a parsimonious manner to avoid complex and time-consuming computations that typically result when modeling details of specific aspects of micro/macro scale emulsion polymerization phenomena (i.e., full molecular weight and particle size distributions, detailed species phase-partitioning, etc.). Thus, the model provides average properties for typical emulsion characteristics, such as monomer conversion, copolymer composition, number- and weight-average molecular weights, tri- and tetra-functional branching frequencies, and the number and average size of polymer latex particles. The proposed model is an extension of a previous model developed by our group, and allows for the dynamic modeling of different reactor types and configurations. Model comparisons are made between limited literature data for batch operation, while representative simulation profiles are shown for a reactor train.     

Multi‐Objective Optimization of Semi‐Batch Copolymerization Reactors Using Adaptations of Genetic Algorithm

Summary: The polymerization of styrene‐acrylonitrile (SAN) random copolymers in semi‐batch reactors is optimized using multiple objective functions that are often conflicting and non‐commensurate in nature. These include the average composition of the copolymer product, its number‐average molecular weight, its polydispersity index, and the conversion of monomers attained in the reactor. Two decision/control variables are used, namely, the rate of continuous addition of a monomer‐solvent‐initiator mixture (having a specified and fixed composition) and the history of the temperature in the reactor. The elitist non‐dominated sorting genetic algorithm, NSGA‐II, is adapted and used for decision variables that are functions of time (trajectory optimization). This robust, AI (artificial intelligence)‐based technique, enables the solution of far more complex optimization problems than those reported in the literature. A set of several non‐dominating (equally good) Pareto optimal solutions was obtained. These provide insights into the conflicting nature of the objective functions. An engineer (decision maker) can then use his judgment (often intuitive) to choose the preferred solution from among these possibilities.

Pareto set of optimal solutions and some corresponding state variables for a Reference Problem.     

Continuous reaction system to investigate the dispersion polymerization of vinyl monomers in supercritical carbon dioxide

A laboratory‐scale continuous reaction system using a stirred tank reactor was assembled in our laboratory to study the dispersion polymerization of vinyl monomers in supercritical carbon dioxide (scCO₂). The apparatus was equipped with a suitable downstream separation section to collect solid particles entrained in the effluent stream from the reactor, whose monomer concentration could be measured online with a gas chromatograph. The dispersion polymerization of methyl methacrylate in scCO₂ was selected as a model process to be investigated in the apparatus. The experiments were performed at 65 °C and 25 MPa with 2,2′‐azobisisobutyronitrile as the initiator and a reactive polysiloxane macromonomer as a surfactant to investigate the effect of the mean residence time of the reaction mixture on the monomer conversion, polymerization rate, polymer molecular weight, and particle size distribution. The results were compared with those obtained in batch polymerizations carried out under similar operative conditions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4122–4135, 2006     

Dynamic Optimization of Molecular Weight Distribution Using Orthogonal Collocation on Finite Elements and Fixed Pivot Methods: An Experimental and Theoretical Investigation

In the present study, two numerical methods, namely the orthogonal collocation on finite elements and the fixed pivot technique, are employed to calculate the MWD in an MMA free‐radical batch suspension polymerization reactor operating up to very high conversions (e.g., ≥95%). The theoretical MWD predictions are directly compared with experimentally measured MWDs, obtained from a pilot‐scale batch MMA suspension polymerization reactor. It is shown that there is a very good agreement between model predictions and experimental measurements on both monomer conversion and MWD. Subsequently, two different time‐optimal temperature trajectories are calculated to obtain a polymer having either a narrow or a bimodal MWD in minimum batch time. The calculated time optimal trajectories are then applied, as set point temperature changes, to a pilot plant batch polymerization reactor. It is shown that the measured MWDs are in very good agreement with the off‐line calculated optimal MWDs.

     

Optimal control of a two-stage reactor system

Optimal operation policies were investigated for a batch reactor system with two different operation stages. At the end of the first nonisothermal stage one of the reactants was added. Since that moment the reactor was operated isothermally. In each stage behavior of the reactor was described by a set of differential equations. The maximum conversion problem was investigated subject to various operating constraints. Dynamic optimization based on the control vector parametrization was used to find the optimal control profile. Gradients of the resulting nonlinear programming problem were obtained by adjoint method based on the optimal control theory.     

Multiobjective optimization of a free radical bulk polymerization reactor using genetic algorithm

A multiobjective optimization technique has been developed for free radical bulk polymerization reactors using genetic algorithm. The polymerization of methyl methacrylate in a batch reactor has been studied as an example. The two objective functions which are minimized are the total reaction time and the polydispersity index of the polymer product. Simultaneously, end‐point constraints are incorporated to attain desired values of the monomer conversion (x_m) and the number average chain length (μ_n). A nondominated sorting genetic algorithm (NSGA) has been adapted to obtain the optimal control variable (temperature) history. It has been shown that the optimal solution converges to a unique point and no Pareto set is obtained. It has been observed that the optimal solution obtained using the NSGA for multiobjective function optimization compares very well with the solution obtained using the simple genetic algorithm (SGA) for a single objective function optimization problem, in which only the total reaction time is minimized and the two end‐point constraints on x_m and μ_n are satisfied.     

Modeling of L-lactide Polymerization by Reactive Extrusion

The kinetics of L-lactide ring-opening polymerization initiated by stannous octoate and triphenylphosphine was investigated in a batch apparatus (Haake Rheocord Mixer). Based on the experimental data, a kinetic model is developed, considering a coordination-insertion mechanism. Reactive extrusion experiments were further conducted for the same polymerization process, on a co-rotating twin screw extruder. The melted material flow and mixing was described by using the Ludovic® commercial simulator. Based on the developed kinetic model and simulated flow of L-lactide polymerization mixture, a mathematical model of reactive extrusion process is formulated, describing the evolutions of monomer conversion and average molecular weight along the extruder. The model is predicting with a reasonable good accuracy the experimental data.     

Dynamic Monte Carlo Simulation of ATRP with Bifunctional Initiators

A dynamic Monte Carlo model was developed to simulate ATRP with bifunctional initiators in a batch reactor. Model probabilities were calculated from polymerization kinetic parameters and reactor conditions. The model was used to predict monomer conversion, average molecular weight, polydispersity and the complete CLD as a function of polymerization time. The Monte Carlo model was compared with simulation results from a mathematical model that uses population balances and the method of moments. We also compared polymerizations with monofunctional and bifunctional initiators to illustrate some of the advantages of using bifunctional initiators in ATRP. In addition, we used the model to investigate the effect of the control volume and several polymerization conditions on simulation time, monomer conversion, molecular weight averages and CLD. Our results indicate that computational times can be reduced without sacrificing the quality of the results if we run several simulations with small control volumes rather than one single simulation with a large control volume.

     

Kinetics and molecular weights distribution study of neodymium-catalyzed polymerization of 1,3-butadiene

The homopolymerization of 1,3-butadiene in a stirred batch reactor with the catalytic system Nd octoate/diethyl-aluminium chloride/triisobutyl-aluminium in n-heptane was studied. The effect of various reaction conditions on especially high conversion and molecular weight is reported. Polymerization is shown to be first order with respect to both monomer and neodymium. Molecular weights are high and broadly distributed. Chain transfer to triisobutylaluminium is the main factor governing molecular weight development. A mechanism of polymerization is presented with the chain transfer process incorporated. © 1995 John Wiley & Sons, Inc.     

Modeling of Anionic Polymerization of Isoprene in an Industrial Reactor

One of the most important reasons for modeling polymerization processes is to provide a tool for estimating the risks of runaway reactions in polymer industry. This is especially important for batch processes, such as anionic polymerization of isoprene or butadiene. This work presents a theoretical and experimental research of the anionic polymerization of isoprene using cyclohexane as solvent and n‐butyllithium as initiator. In the first part, a phenomenological kinetic expression is obtained that describes the anionic polymerization of isoprene initiated by n‐butyllithium in cyclohexane. In the second, the mass and energy balance equations are solved to model the anionic polymerization of isoprene in a quasi‐adiabatic batch reactor. Adjustment of reactor parameters is made using the data obtained from a laboratory reactor. The proposed model predicts adequately the obtained temperature, pressure, and conversion profiles from this set of experiments. Finally, a mathematical model is developed to predict the behavior for the anionic polymerization of isoprene in an industrial reactor.     

Batch process monitoring and its application to polymerization systems

Slight changes in raw material properties or operating conditions during critical periods of operation of batch and semi-batch polymerization reactors may have a strong influence on reaction mechanism and impact final product quality. Online process monitoring, fault detection, fault diagnosis, and product quality prediction in real-time ensure safe reactor operation and warn operators about excursions from normal operation that may lead to deterioration in product properties. Multivariate statistical process monitoring and quality prediction using multiway principal components analysis and multiway partial least squares have been successful in detecting abnormalities in process operation and product quality. When abnormal process operation is detected, fault diagnosis tools are used to determine the source cause of the deviation. Illustrative case studies are presented via simulated polyvinyl acetate polymerization.     

Simulation of free radical high-pressure copolymerization in a multi-zone autoclave reactor: compartment model investigation

A compartment model is used to describe the complex flow of a high-pressure ethylene copolymerization process in an industrial multi-feed multi-zone autoclave reactor at steady state operation conditions. To capture the imperfect mixing effects due to fresh initiator injection, each zone is considered as a set of three interconnected well mixed CSTRs with recycle streams. Volumes of the reactors and the recycle flow are adjusted to get the best fit with results of steady state well mixed analysis for each zone. Once the temperature and conversion as state variables in each reaction volume are known, the properties of polymer produced in each zone and those of final polymer can be determined. Using a realistic set of kinetic mechanisms, temperature, monomer conversion, molecular weights and short and long chain branching frequencies in each zone and at the exit point of the reactor are estimated. Some of the model results are compared with experimental data obtained for an industrial reactor.     

PREPARATION AND PROPERTIES OF SILICONE-ACRYLATE COPOLYMER LATEX

Silicone-acrylate copolymer latex was prepared through three different polymerization processes, i.e., the batch process, preemulsified monomer addition and the monomer addition process. The results revealed that the monomer addition process is a desirable approach to produce narrow particle size distribution latex with higher polymerization conversion and less amount of coagulum. The effect of silicone content on the glossiness and water absorption of latex film was investigated and the results showed that the glossiness of latex film is improved up to a silicone content of 10% of total monomers, but becomes impaired thereafter, whereas water absorption is reduced accordingly.     

Comparative study of monomer droplet nucleation in the seeded batch and semibatch miniemulsion polymerisation of styrene

Monomer droplet nucleation in the seeded miniemulsion polymerisation of styrene under monomer-flooded and monomer-starved conditions was studied. The miniemulsion feeds were added to the reactor either batchwise or semibatchwise. The droplets preserved longer under flooded conditions. As a result, the batch operation led to a larger number of particles (N_p) than the semibatch operation. For the miniemulsion droplets containing predissolved polymer, the final N_p was independent of the way that the feed was added to the reactor and was equivalent to the number of monomer droplets in the original miniemulsion feed. The size distribution of the final latexes, however, was influenced by the operation type. For the batch operation, the rate of polymerisation (R_p) with the miniemulsion feeds was higher than that with the conventional monomer emulsion feed because of the monomer droplet nucleation. But for the semibatch operation, the opposite was true because of R_p controlled by the rate of monomer diffusion from rather stable miniemulsion droplets to the growing polymer particles.     

Dynamic Monte Carlo Simulation of ATRP in a Batch Reactor

A dynamic MC model was developed to simulate the polymerization kinetics and the detailed microstructure of copolymers made with ATRP in a batch reactor. The model was used to predict monomer conversion, average molecular weight, polydispersity index, and copolymer composition as a function of polymerization time. The model can also predict the distribution of molecular weight, chemical composition, and comonomer sequence length at any polymerization time or comonomer conversion. The simulation was used to explore the effects of rate constants and reactant stoichiometry on the microstructure of chains. Two copolymerization systems were chosen to demonstrate the effect of reactivity ratios and comonomer feed compositions on the final chemical composition distribution.