Optimal operating strategies for emulsion terpolymerisation

Optimal control policies for emulsion terpolymerisation of styrene, methyl methacrylate (MMA) and methyl acrylate (MA) were determined in a semi-batch reactor using the multi-objective dynamic optimisation method. A comprehensive dynamic model was used for the design of optimal control. The control vector parameterisation (CVP) approach was implemented for constrained optimisation for emulsion terpolymerisation reactors. The feed rates of styrene, MMA, MA, surfactant and initiator, and the temperature of the reactor were used as manipulating variables to produce terpolymers of desired composition, molecular weight distribution (MWD) and particle size distribution (PSD). The particle size polydispersity index (PSPI), molecular weight polydispersity index (MWPI) and the overall terpolymer composition ratios were incorporated in the objective functions to optimise the PSD, MWD and terpolymer composition, respectively. The optimised operational policies were validated with experiments via one stirred tank polymerisation reactor.     

On-line multi-variable predictive control of molar mass and particle size distributions in free-radical emulsion copolymerization

A multi-variable model predictive control (MPC) was formulated to solve control problems associated with a combination of regulation and targeting desired set-points. We investigated the simultaneous control of key polymer properties: the particle size (PSD) and molecular weight distribution (MWD) by manipulating the flow rates of the monomers (styrene, MMA), surfactant, initiator and the temperature of the reactor. A multi-input-multi-output (MIMO) formulation was constructed for the constrained optimal control problem to maximize the width of the PSD (with M_n at a constant set-point), and to maximize the average molar mass. The strategy developed within a gPROMS-API-DCS environment allowed real-time implementation of model-based control of the process. The optimal control problem was implemented via an interface to a dynamic optimization code. Major improvements in process operation and polymer property control resulted on the implementation of our multi-variable MPC algorithm. The manipulation of the four flow rates and the temperature increased the degree of freedom in the system and achieved tighter PSD and MWD control. The on-line performance of MPC for MWD and PSD control was found to be satisfactory.     

Online inferential product attribute estimation for optimal operation of emulsion terpolymerisation: Application to styrene/MMA/MA

An advanced model for process design and control of emulsion terpolymerisation was developed. A test case of emulsion terpolymerisation of styrene (Sty), methyl methacrylate (MMA) and methyl acrylate (MA) was investigated on state of the art facilities for predicting, optimising and control end-use product properties including global and individual conversions, terpolymer composition, the average particle diameter and concentration, glass transition temperature, molecular weight distribution, the number- and weight-average molecular weights and particle size distribution.The model equations include diffusion-controlled kinetics at high monomer conversions, where transition from a ‘zero-one’ to a ‘pseudo-bulk’ regime occurs. Transport equations are used to describe the system transients for batch and semi-batch processes. The particle evolution is described by population balance equations which comprised a set of integro-partial differential and nonlinear algebraic equations. Backward finite difference approximation method is used to discretise the population equation and converts them from partial differential equations to ordinary differential equations. The model predictions were experimentally validated in the laboratory and were found to be in excellent agreement, thus paving the way for further application of the model.     

Population balance model versus lumped model for emulsion polymerisation: Semi-batch and continuous operation

In this article, a systematic comparison is made of a detailed population balance model of the emulsion polymerisation process that accounts for the dynamic evolution of the entire particle size distribution with a simple model of the process that accounts only for the dynamic evolution of the average particle size and the total particles. Both models account for the underlying mechanisms of the process to the level admissible within their respective frameworks. The predictions of the two models are compared under both batch and continuous operation. The aim is to elucidate the degree of disparity of model predictions for batch operation, and to elucidate the ability of the simple lumped models to predict oscillatory dynamics for continuous operation. The focus is on the comparison of the predictions of important control variables such as solids content (conversion), total particles and average particle size, but also those of important particle phenomena of nucleation, growth and coagulation. It is found that with respect to these lumped control variables, the simple model performs well in matching the detailed model, and hence will be a very valuable tool for the purpose of on-line feedback control. However, the detailed models will be important for distributed control variables such as the entire particle size distribution.     

Computationally efficient solution of population balance models incorporating nucleation, growth and coagulation: application to emulsion polymerization

A computationally efficient solution technique is presented for population balance models accounting for nucleation, growth and coagulation (aggregation) (with extensions for breakage). In contrast to earlier techniques, this technique is not based on approximating the population balance equation, but is based on employing individual rates of nucleation, growth and coagulation to update the PSD in a hierarchical framework. The method is comprised of two steps. The first step is the calculation of the rates of nucleation, growth and coagulation by solving an appropriate system of equations. This information is then used in the second step to update the PSD. The method effectively decomposes the fast and the slow kinetics, thereby eliminating the stiffness in the solution. In solving the coagulation kernel, a semi-analytical solution strategy is adapted, which substantially reduces the computational requirement, but also ensures the consistency of properties such as the number and mass of particles.     

On the role of an unconventional rigid rodlike cationic surfactant on the styrene emulsion polymerization. Kinetics, particle size and particle size distribution

An unconventional amphiphile (1-[ω-(4′-methoxy-4-biphenylyloxy)octyl]pyridinium bromide, PC8) was used as surfactant in the emulsion polymerization of styrene. At low surfactant concentration (6, 12 or 36 mmol l⁻¹), curves of polymerization rate versus conversion obeyed the typical behavior characterized by intervals I, II and III. However, at high concentration (48 or 72 mmol l⁻¹) the interval II was not observed. The particle size distribution curves showed two families of polymer particles, indicating the participation of at least two mechanisms of particle formation, one being the simple micellar nucleation and the other probably the coagulative nucleation of precursor particles. The latter was considered to occur during the nucleation interval.     

Neural network model-based predictive control of liquid-liquid extraction contactors

The inherent complex nonlinear dynamic characteristics and time varying transients of the liquid-liquid extraction process draw the attention to the application of nonlinear control techniques. In this work, neural network-based control algorithms were applied to control the product compositions of a Scheibel agitated extractor of type I. Model predictive control algorithm was implemented to control the extractor. The extractor hydrodynamics and mass transfer behavior were modeled using the non-equilibrium backflow mixing cell model. It was found that model predictive control is capable of solving the servo control problem efficiently with minimum controller moves. This study will be followed by more work concentrated on using different neural network-based control algorithms for the control of extraction contactors.     

Inferential closed-loop control of particle size distribution for styrene emulsion polymerization

In this work, a new control strategy for controlling the particle size distribution (PSD) in emulsion polymerization has been proposed. It is shown that the desired PSD can be achieved by controlling the free surfactant concentration which in turn can be done by manipulating the surfactant feed rate. Simulation results show that the closed-loop control of free surfactant concentration results in a better control of PSD compared to open-loop control strategy, in presence of model mismatch and disturbances. Since the on-line measuring of ionic free surfactant concentration is difficult, conductivity which is related to it is measured instead and used for control purposes. The closed-loop control of conductivity also results in a better control of PSD compared to open-loop control strategy, but its performance is not as good as controlling free surfactant concentration in presence of model mismatch.     

Measurement based modeling and control of bimodal particle size distribution in batch emulsion polymerization

In this article, a novel modeling approach is proposed for bimodal Particle Size Distribution (PSD) control in batch emulsion polymerization. The modeling approach is based on a behavioral model structure that captures the dynamics of PSD. The parameters of the resulting model can be easily identified using a limited number of experiments. The resulting model can then be incorporated in a simple learning scheme to produce a desired bimodal PSD while compensating for model mismatch and/or physical parameters variations using very simple updating rules. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Operation of semi-batch emulsion polymerisation reactors: Modelling, validation and effect of operating conditions

A detailed dynamic model was developed for a styrene emulsion polymerisation semi-batch reactor to predict the evolution of the product particle size distribution (PSD) and molecular weight distribution (MWD) over the entire range of monomer conversion. A system exhibiting zero-one kinetics was employed, with the model comprising a set of rigorously developed population balance equations to predict monomer conversion, PSD and MWD. The modelling equations included diffusion-controlled kinetics at high monomer conversion where the transition from the zero-one regime to a pseudo-bulk regime occurs. The model predictions were found to be in good agreement with experimental results. Both particle growth and the PSD were found to be strongly affected by the monomer feedrate. Reactor temperature had a major influence on the MWD which was, however, insensitive to changes in the monomer feedrate. These findings were confirmed experimentally. As a result, it seems reasonable to propose that the use of the monomer feedrate to control the PSD and the reactor temperature to control the MWD are appropriate in practical situations. Consequently, an optimal monomer feed trajectory was developed off-line (using the validated reactor simulation) and verified experimentally by producing a polymer with specific PSD characteristics.     

Constrained model predictive control in ball mill grinding process

Stable control of grinding process is of great importance for improvements of operation efficiency, the recovery of the valuable minerals, and significant reductions of production costs in concentration plants. Decoupled multi-loop PID controllers are usually carried out to manage to eliminate the effects of interactions among the control loops, but they generally become sluggish due to imperfect process models and a close control of the process is usually impossible in real practice. Based on its inherent decoupling scheme, model predictive control (MPC) is employed to handle such highly interacting system. For high quality requirements, a three-input three-output model of the grinding process is constructed. Constrained dynamic matrix control (DMC) is applied in an iron ore concentration plant, and operation of the process close to their optimum operating conditions is achieved. Some practical problems about the application of MPC in grinding process are presented and discussed in detail.     

Hybrid fuzzy model-based predictive control of temperature in a batch reactor

Processes in industry, such as batch reactors, often demonstrate a hybrid and non-linear nature. Model predictive control (MPC) is one of the approaches that can be successfully employed in such cases. However, due to the complexity of these processes, obtaining a suitable model is often a difficult task. In this paper a hybrid fuzzy modelling approach with a compact formulation is introduced. The hybrid system hierarchy is explained and the Takagi–Sugeno fuzzy formulation for the hybrid fuzzy modelling purposes is presented. An efficient method for identifying the hybrid fuzzy model is also proposed.

A MPC algorithm suitable for systems with discrete inputs is treated. The benefits of the MPC algorithm employing the proposed hybrid fuzzy model are verified on a batch-reactor simulation example: a comparison between MPC employing a hybrid linear model and a hybrid fuzzy model was made. We established that the latter approach clearly outperforms the approach where a linear model is used.     

High‐Solid‐Content Emulsions of PVC: Scale‐Down of an Industrial Process for Enhanced Understanding of Particle Formation Part 3: Production of Bimodal Latexes

A scale‐down study of an industrial reactor for the production of polyvinyl chloride (PVC) via an emulsion polymerization process was carried out in order to understand the cause of batch‐to‐batch variations in product quality. The results in Part 2 of this series of papers indicated that a large excess of base is required to control the particle size distribution (PSD) of the seed process. Here, it is demonstrated that the flow rate of the initiator and the second‐stage surfactant are the most important parameters for PSD control. Altering the time point at which the initiator and surfactant are injected allows controlling the relative volume fractions of large and small particles.     

高转化率乳聚丁苯橡胶聚合过程中乳液相对分子质量分布与粒径分布考察

采用中石油吉化分公司乳聚丁苯橡胶高转化率大生产配方,考察了实验室聚合反应釜聚合反应单体转化率随反应时间的变化,采用激光粒度分析仪和凝胶渗透色谱仪测定了聚合反应不同单体转化率的胶乳的粒径分布与分子质量分布,结果表明：胶乳粒径呈正态分布,粒径主要集中分布在0.1μm附近,胶乳的平均粒径随反应时间的延长逐渐增大,但是增加的幅度越来越小;聚合反应时间在11 h前（即转化率小于72%）,胶乳的重均分子质量、Z均分子质量一直增大,而数均分子质量变化无明显规律;而分子质量分布宽度指数随反应的进行变小,表明调整的高转化率配方合成的丁苯橡胶可有效改善聚合生成的胶乳粒径分布。     

High‐Solid‐Content Emulsions of PVC: Scale‐Down of an Industrial Process for Enhanced Understanding of Particle Formation Part 2: Preliminary Analysis of Seed Production

A scale‐down study of an industrial reactor for the production of polyvinyl chloride (PVC) via an emulsion polymerization process was performed in order to understand the source of batch‐to‐batch variations in product quality. In Part 2 of this series of three papers, it is demonstrated that a large excess of base is required to control the particle size distribution of the seed process. Although differences exist between the critical micelle concentration and the surface area occupied by a surfactant molecule for linear and branched isomers of the surfactant sodium dodecyl benzene sulfonate, the characteristics of the molecules from different suppliers were reasonably similar.     

High‐Solid‐Content Emulsions of PVC: Scale‐Down of an Industrial Process for Enhanced Understanding of Particle Formation Part 1: Introduction and Scale‐Down

A scale‐down study of an industrial reactor for the production of polyvinyl chloride (PVC) via an emulsion polymerization process was carried out in order to understand the source of batch‐to‐batch variations in product quality. In Part 1, an analysis of the plant is presented and the industrial recipe scaled down to a pilot‐scale reactor. In the following Parts 2 and 3 a systematic analysis of the main process parameters revealed that particle generation and stabilization actually occurred in a manner slightly different from what was thought at the production site.     

Maximizing production and polymer quality (MWD and composition) in emulsion polymerization reactors with limited capacity of heat removal

In this work, an on-line control strategy based on reaction calorimetry was used to maximize the production of styrene/n-butyl acrylate latex with desired copolymer composition and molecular weight distribution in reactors with limited capacity of heat removal. For this purpose, nonlinear model-based controllers were used to maximize the production maintaining simultaneously the ratios of each comonomer concentration and of the overall unreacted monomer concentration to chain transfer agent at the required values.     

Optimization-based predictive control of a simulated moving bed process using an identified model

For optimization-based dynamic control of simulated moving bed (SMB) process, a novel control strategy based on process identification, which is an extension of the earlier work (Song et al., 2006a. Identification and predictive control of a simulated moving bed process: purity control. Chemical Engineering Science 61, 1973-1986), is proposed. A linear output prediction model is obtained by the method of subspace identification and used for the dynamic control. The controller is designed for optimizing the production cost while maintaining the specified product purities. For all of these, the average purities over one switching period of the target components in extract and raffinate streams, the reciprocal productivity and the solvent consumption are selected as output variables, while the flow rates in 1, 2, 3 and 4 are chosen as the manipulated variables. The realization of this concept is discussed and assessed on a virtual eight column SMB unit for a system following a bi-Langmuir isotherm. The identified prediction model is proven to be in good agreement with the first principles model considered as the actual SMB process. For typical control objectives encountered in actual operation, i.e., disturbance rejection and set-point tracking, it is shown that the proposed controller exhibits excellent performance, hence it is an effective tool for optimization-based control of SMB process.     

Nonlinear model order reduction and control of particle size distribution in a semibatch vinyl acetate/butyl acrylate emulsion copolymerization reactor

This paper addresses the control of the full particle size distribution (PSD) in a semibatch emulsion copolymerization reactor. The numerical approximation of a fundamental population balance model results in a high order system to accurately describe the distribution of particle size; therefore, model order reduction is required. Pseudo random input signals are input to the mechanistic model to generate a data set which covers the reachable region of the system, on the basis of which the transformation matrices are calculated by principal component analysis (PCA). A linear time varying model with reduced order obtained from the transformation matrices is augmented in the prediction equation of linear model predictive control. The performance of the controller is evaluated to drive the particle size distribution at the final time of the batch to the desired distribution in the presence of disturbances. This paper is dedicated to Professor Hyun-Ku Rhee on the occasion of his retirement from the Seoul National University.     

Robust model predictive control of nonlinear process systems: Handling rate constraints

This work considers the problem of stabilization of control affine nonlinear process systems subject to constraints on the rate of change and magnitude of control inputs in the presence of uncertainty. We first handle rate constraints within a soft constraints framework. A new robust predictive controller formulation that minimizes rate constraint violation while guaranteeing stabilization and input constraint satisfaction from an explicitly characterized stability region is designed. We then derive conditions that allow for guaranteed satisfaction of hard rate constraints. Subsequently, a predictive controller is designed that ensures rate constraints satisfaction when the required conditions are satisfied, relaxing them otherwise to preserve feasibility and robust stability. The implementation of the proposed predictive controllers is illustrated via a chemical reactor example.