Online model-based control of an emulsion terpolymerisation process

A multivariable constrained model predictive control was formulated and implemented to control online an emulsion terpolymerisation process. A generic multilayer control architecture for real-time implementation of optimal control policies for particulate processes was also developed. The methodology was implemented within a multi-tiered software environment for real-time implementation of model-based control strategies. A full mechanistic dynamic model for emulsion terpolymerisation, developed in our previous work, is used as a real-time soft-sensor and incorporated within the MPC strategy. The simultaneous control of key polymer properties such as the particle size distribution (PSD), average molecular weight (Mn) and terpolymer composition were investigated using case studies involving manipulation of flow rates of monomers (styrene, MMA, MA), surfactant and initiator, and the reactor temperature. Although some offsets were observed with a degree of model mismatch, the experimental results agreed well with predictions.     

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.     

Measurement methods of particle size distribution in emulsion polymerization

The particle size distribution of polymer always develops in emulsion polymerization systems, and certain key phenomena/mechanisms as well as properties of the final product are significantly affected by this distribution. This review mainly focuses on the measurement methods of particle size distribution rather than average particle size during the emulsion polymerization process, including the existing off-line, on-line, and in-line measurement methods. Moreover, the principle, resolution, performance, advantages, and drawbacks of various methods for evaluating particle size distribution are contrasted and illustrated. Besides, several possible development directions or solutions of the in-line measurement technology are explored     

Open-loop control of particle size distribution in semi-batch emulsion copolymerization using a genetic algorithm

The open-loop generation of an optimal feed profile to attain a target particle size distribution (PSD) in the semi-batch emulsion co-polymerization of vinyl acetate and butyl acrylate is described. A nominal model of the process based on population balancing is utilized for this purpose. A Genetic Algorithm is employed as the optimization strategy. The optimal recipes generated in these studies are implemented on an experimental emulsion polymerization reactor. The end-point PSD obtained in these experiments closely matches the target in spite of the model uncertainties and process disturbances. Examination of the evolution of the PSD up to the end point provides useful information for feedback control strategies.     

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.     

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.     

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     

Modelling particle size distributions and secondary particle formation in emulsion polymerisation

An extensive model is given for the particle size distribution (PSD), particle number, particle size and amount of secondary nucleation in emulsion polymerisations. This incorporates what are thought to be all of the complex competing processes: aqueous phase kinetics for all radical species arising from both initiator and from exit (desorption), radical balance inside the particles, particle formation by both micellar and homogeneous nucleation mechanisms, and coagulation (the rate of which is obtained using the Healy–Hogg extension of DLVO theory). The predictions of the model are compared to extensive experimental results on rates, time evolution of the particle size distribution, and relative amounts of secondary nucleation, for styrene initiated by persulfate with sodium dodecyl sulfate and with sodium dihexyl sulfosuccinate as surfactants. For this system values of almost all of the many parameters needed for the model are available from independent measurements, and thus no significant parameter adjustment is plausible. Accord with experiment is imperfect but quite acceptable, supporting the validity of the various mechanisms in the model. Effects such as the experimental variation of particle number with ionic strength, as well as calculated coagulation rate coefficients as functions of particle size, suggest that coagulation of precursor (i.e., newly-formed) particles is a significant effect, even above the cmc. The modelling also suggests why secondary nucleation occurs readily in systems stabilised with polymeric surfactant.     

Reduced-order methodologies for feedback control of particle size distribution in semi-batch emulsion copolymerization

Within-batch feedback control strategies are developed for the regulation of the particle size distribution (PSD) in a semibatch vinyl acetate (VAc)/butyl acrylate (BuA) emulsion copolymerization system. These strategies are also applicable for regulation of distributions in other particulate systems governed by population balances. In the first strategy, PID controllers are employed for regulating nucleation and growth events through tracking the nominal trajectories of total number of particles and the solids content by manipulating the feed-rates of the more reactive monomer, BuA, and the surfactant. The second control strategy is based on tracking nominal trajectories of the moments of the distribution with a quadratic dynamic matrix controller (QDMC). To determine the appropriate number of moments to describe the PSD during various stages of a nominal batch, a maximum-entropy approach is utilized. In the final and most complex approach, a nonlinear model predictive controller is designed utilizing the detailed population balance model of the system. The ill-conditioning resulting from the high-dimensionality of the resulting dynamical system is removed by principal component analysis (PCA)-based model order reduction and a multi-rate estimator is designed to compensate for the measurement delay associated with the PSD measurements.     

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.     

基于差分进化算法的多变量预测控制在蒸馏装置上的应用

差分进化算法(DE)具有全局寻优、搜索效率高等优点,本文提出了一种基于DE的多变量预测控制算法,利用DE求解最优控制律,与对象的模型类型无关,能通用于线性模型和非线性模型。采用单值预测减小计算量,并对传统的性能指标函数加以改进,使动态控制和优化有机地结合在一起。通过在蒸馏装置常压部分上的仿真验证,实现了整个蒸馏装置的产品质量闭环控制,并实现了卡边优化,验证了算法的有效性和可行性。     

Estimation of particle size distributions from focused beam reflectance measurements based on an optical model

A popular in situ particle characterization technique, which can be applied without dilution, is the focused beam reflectance measurement (FBRM^®). The FBRM probe measures a chord length distribution (CLD) which is different from a particle size distribution (PSD). In order to compare results obtained by an FBRM probe with other measurement technologies such as laser diffraction, it is necessary to reconstruct the PSD from a measured CLD. For this reconstruction a measurement model and an inversion procedure are required. Most FBRM models presented in the literature assume that an FBRM records a geometric chord which can be deduced from a two-dimensional projection of the particle silhouette. In previous work [Kail, N., Briesen, H., Marquardt, W., 2008. Analysis of FBRM measurements by means of a 3D optical model. Powder Technology 185 (3), 211-222] it has been demonstrated that FBRM data show significant deviations from this geometric model. Consequently, an estimation of a PSD using such a geometric FBRM model will fail. A novel FBRM model is developed in this work. This model imitates the chord discrimination algorithm used in a Lasentec D600L FBRM system and takes the intensity profile of the laser beam and the optical aperture of the probe into account. The model is ideally suited for the estimation of a PSD from a measured CLD using a sequential, linear inversion routine, as proposed in this work. The novel FBRM model and the inversion procedure are evaluated using small, mono-disperse polystyrene beads, large ion-exchanger beads, and α-lactose-monohydrate particles. The applicability of the FBRM for PSD measurements is discussed on the basis of these results.     

Modeling axial distributions of adsorbent particle size and local voidage in expanded bed

Axial distribution of adsorbent particle as well as local voidage variation is very important and fundamental for the predicting and understanding of adsorptive performance in expanded bed adsorption. Based on the analysis of bed expansion and fluid hydrodynamic behaviors, a model was developed to predict the mean particle size and local voidage variations with the axial bed height under various operation conditions in expanded bed. Experimental measurements of particle size and local voidage changes with bed height were conducted in a modified glass column of inner diameter with sampling ports. Experimental data obtained in this work and in the literature with Streamline SP, Streamline Phenyl and Streamline quartz base matrix particles in the columns of inner diameters 20-, were used to verify the model prediction. The results were in good agreement with the experimental data.     

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.     

Feedback controllability assessment and control of particle size distribution in emulsion polymerisation

In this article, the importance of particle size distribution (PSD) control as a means for the inferential control of the rheology of emulsion polymers is illustrated. A controllability assessment is presented to illustrate the attainability or otherwise of bimodal PSD using feedback control through a consideration of the process mechanisms—measurement limitations and process constraints that prevent the implementation of feedback corrections. The suitability of a batch-to-batch iterative feedback PSD control is demonstrated, which could act in addition to any in-batch feedback control, the latter being less feasible in certain cases, as argued in this article. A detailed population balance model is used for the batch-to-batch control, which simplifies model update and feedback correction.     

Control of a solution copolymerization reactor using multi-model predictive control

We study the control of a solution copolymerization reactor using a model predictive control algorithm based on multiple piecewise linear models. The control algorithm is a receding horizon scheme with a quasi-infinite horizon objective function which has finite and infinite horizon cost components and uses multiple linear models in its predictions. The finite horizon cost consists of free input variables that direct the system towards a terminal region which contains the desired operating point. The infinite horizon cost has an upper bound and takes the system to the final operating point. Simulation results on an industrial scale methyl methacrylate vinyl acetate solution copolymerization reactor model demonstrate the ability of the algorithm to rapidly transition the process between different operating points.     

Predictive control of particle size distribution in particulate processes

In this work, we focus on the development and application of predictive-based strategies for control of particle size distribution (PSD) in continuous and batch particulate processes described by population balance models (PBMs). The control algorithms are designed on the basis of reduced-order models, utilize measurements of principle moments of the PSD, and are tailored to address different control objectives for the continuous and batch processes. For continuous particulate processes, we develop a hybrid predictive control strategy to stabilize a continuous crystallizer at an open-loop unstable steady-state. The hybrid predictive control strategy employs logic-based switching between model predictive control (MPC) and a fall-back bounded controller with a well-defined stability region. The strategy is shown to provide a safety net for the implementation of MPC algorithms with guaranteed stability closed-loop region. For batch particulate processes, the control objective is to achieve a final PSD with desired characteristics subject to both manipulated input and product quality constraints. An optimization-based predictive control strategy that incorporates these constraints explicitly in the controller design is formulated and applied to a seeded batch crystallizer. The strategy is shown to be able to reduce the total volume of the fines by 13.4% compared to a linear cooling strategy, and is shown to be robust with respect to modeling errors.     

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.     

丙烯酸-马来酸水相共聚合过程中的粒径变化研究

以氧化-还原引发剂Na2 S2O8/Na2S2O5引发丙烯酸-马来酸的水相共聚合,用激光光散射粒径分析仪对共聚合过程中的粒径变化进行了研究.结果表明,体系的平均粒径受聚合物链增长和聚合物链间聚结的影响,随着反应进行而增大.通过分析粒径曲线发现,在加料反应阶段,粒径在100 nm以下的粒子始终保持一定数量,同时周期性地形成粒径在100 nm以上的粒子.     

Investigation into the effect of carboxylic acid monomer on particle nucleation and growth in emulsifier-free emulsion copolymerization of styrene-butadiene-acrylic acid

Latexes of carboxylated styrene-butadiene rubber were prepared via batch emulsion copolymerization with different amounts of acrylic acid in the absence of emulsifier. The effect of acid monomer was investigated in the particle formation and growth. It was observed that the amount of acrylic acid strongly affected the particle formation. The number of particles and thus polymerization rate increased with increasing of the acid content. There was no significant difference in the polymerization rate per particle in all experiments. The results show that in this case particle growth process is less dependent on the acrylic acid amount in comparison with its influence on nucleation stage and then particle number. Several parameters such as polymerization rate and number of latex particle per unit volume of the aqueous phase were calculated. Attempt was made to evaluate the average number of growing chain per particle. Also average particle diameter of the above carboxylated SBR latexes was obtained through some calculations from the direct measurement of average particle diameter in the swollen state by light scattering technique for the first time.