Polymerization Reactor Research Articles

Nonlinear second order plus time delay model identification and nonlinear PID controller tuning based on extended linearization method

PID control systems based on the first order plus time delay model (FOPTD), which approximate the full system dynamics, are well-accepted for a wide range of linear processes. While such controllers can be applied to overdamped nonlinear processes, they often experience excessive overshoots and oscillations for general nonlinear processes. To overcome this limitation, we propose a novel method to design a nonlinear PID controller based on the second order plus time delay (SOPTD) model. The system nonlinearity requires parameter adjustments of the linearized model across operational ranges. Hence, in this work, it is handled by the extended linearization method (ELM), ensuring local stability under the assumptions of slow and small changes in operating points. Importantly, the model achieves global input-to-output stability even without the above constraints, provided there are no structural and parametric errors. The resulting nonlinear SOPTD model can describe changes in process gain and two time constants as the operation point varies. We demonstrate the applicability of our approach with a polymerization reactor simulation and liquid-level control experiments.

Hot Spot Induced Thermal Runaway Map for Polymerization Reactors

AbstractLow‐Density Polyethylene (LDPE) reactors have the potential for rupture because of thermal runaway from auto‐accelerating chemistry. Pockets of unmixed, highly reactive, LDPE constituents, called hot spots, are often generated by conditions within the reactor and are the main source of thermal runaway. Because of this, there is a need to define thresholds of hot spot conditions that produce runaway. Computational Fluid Dynamics is used to study an isolated LDPE sphere with varying initial temperature, initial catalyst concentration, and volume to determine which combinations promote thermal runaway. It is found that increasing both initial temperature and initial catalyst concentration increased thermal runaway likelihood, while, counter‐intuitively, hot spot volume has no effect. An LDPE runaway map is provided to quantify the combinations that result in safe reactor operation. This allows manufacturers to make more informed control actions and to determine safe reactor conditions based on local mixture composition and temperature alone.

A hybrid predictive modeling approach for catalyzed polymerization reactors

Polymerization reactions are characterized by complex, nonlinear behaviors that pose significant challenges for conventional modeling techniques. Accurate and reliable models are crucial for advancing material science and enabling technological innovations across various industries. Conventional first-principles models often fall short in capturing the intricate dynamics of polymeric systems, leading to limitations in predictive accuracy. In this work, we propose a novel hybrid modeling approach that combines a conventional first-principles model with the strengths of a data-driven multi-layer perceptron (MLP) model and also a linear regression (LR) model to enhance the predictability of polymerization processes. Utilizing this hybrid approach significantly reduces the mean absolute error for predicting the concentrations of main reagents by 84% and 86%, respectively, in experiments with significantly deviant outcomes. Our results indicate that the model is capable of predicting the concentrations of both the main and side products with a maximum error margin of 3.5%.

Distributed optical fiber sensors for real-time tracking of fouling buildup for tubular continuous polymerization reactors

Early online fouling detection is expected to be a real step forward in the operation of continuous tubular reactors. As an online technology, the Rayleigh backscatter based Distributed Optical Fiber Sensor (DOFS) technology was evaluated with respect to temperature measurement resolution, reproducibility and the best online calibration method. Different coatings and terminations were characterized for emulsion polymerization reactors. Commercially available sensors with acrylate primary coatings, dual acrylate coatings, and polyimide coatings were all compared with each other. It is shown that the presence of a secondary coating significantly alters sensor behaviour. Sensors with only a primary coating showed a temperature resolution of 0.1 °C. Online calibration for temperature readout was carried out and validation tested on segments of fiber integrated in a 3D-printed reactor channel (diameter 1.5 mm). Acrylate coated sensors showed a deviation of 20 % for the calibration coefficients when inside the reactor channel compared to the online calibration, leading to errors in temperature measurement. Polyimide coated sensors showed a deviation of just 0.6 % in this validation test, demonstrating good capabilities for online calibration with accurate temperature measurements. The possibility of spatial and temporal monitoring of fouling buildup through a heat exchanging wall equipped with DOFS was evaluated.

Simulation and study of the flow field in a kettle-type reactor for ethylene polymerization

Abstract Addressing the complexities inherent in the polymerization process for solution method polyethylene production, particularly the challenges in describing the turbulent three-dimensional flow field within the reactor and the precise design of reactor structural parameters, this research leverages computational fluid dynamics (CFD) methods integrated with polymerization reaction kinetics equations. We have formulated User-Defined Functions (UDFs) for a quantitative representation of the polymerization process. Employing the Realizable k-epsilon turbulence model and Sliding Grid (SG) technique, we analyzed the flow dynamics and field distribution within the reactor, elucidating the distribution patterns of temperature, pressure, and concentration fields. A comparative assessment of simulation outcomes against experimental data revealed that the average deviation of the simulated temperature field from actual operating conditions falls within the permissible error range, thereby affirming the simulation model’s validity. Utilizing local sensitivity analysis, we investigated the impact of impeller structural parameters on mixing time and stirring power. Our analysis of the most sensitive structural parameters indicated that impeller diameter and the number of impellers are pivotal in reducing mixing time and stirring power, respectively. Notably, the stirring power escalates with an increase in the number of impellers, while the mixing time exhibits a trend of initial decrease followed by an increase with varying impeller diameters. The methodologies and patterns discerned in this study provide insightful design references for the design and optimization of reactors across different tonnages.

Application of multi-objective neural network algorithm in industrial polymerization reactors for reducing energy cost and maximising productivity

Optimization on an industrial scale is a complex task that involves fine-tuning the performance of large-scale systems and applications to make them more efficient and effective. This process can be challenging due to the increasing volume of work, growing system complexity, and the need to maintain optimal performance. Due to the significant power required for compression and the high costs of reactant materials, optimizing low-density polyethylene (LDPE) production to provide maximum productivity with a reduction of energy cost is required. However, it is not a simple process because the optimization problem of the LDPE tubular reactor consists of conflicting objective functions. Multi-objective neural network algorithm (MONNA) is a metaheuristic optimization method that provides a versatile and robust approach for solving complex, contradictory targets and diverse optimization problems that do not rely on specific mathematical properties of the problem. It is inspired by the structure and information-processing capabilities of biological neural networks. MONNA iteratively proposes solutions, evaluates its performance, and adjusts its approach based on feedback, which avoids complex mathematical formulations. In this work, we implement Multi-objective optimization neural network algorithm (MONNA) in LDPE tubular reactor for maximising productivity, conversion and minimising energy costs with three scenario of problem optimization, i.e. maximising productivity and reducing energy cost for the first problem (P1); increasing conversion and reducing energy costs for the second problem (P2); and increasing productivity and reducing by-products for the third problem (P3). The results show that the highest productivity, highest conversion, and lowest energy are 545.1 mil. RM/year, 0.314, and 0.672 mil. RM/year. The extreme points in the Pareto Front (PF) for various bi-objective situations provide practitioners with helpful information for selecting the best trade-off for the operational strategy. According to their preferences, decision-makers can use the resulting Pareto to decide on the most acceptable alternative. The decision variable plots show that both initiators in the reacting zone highly affected the optimal solution with the opposite action.

Modeling of a solution polymerization reactor operating in semi-batch mode for polymethyl methacrylate production

The severe consequences of thermal runaways, make process optimization of paramount importance for free radical polymerization reactors, in order to maximize in an integrated way their safety and productivity. Generally, this optimization is performed by simulation, for the sake of safety and cost. Today, the literature contains several models of free radical polymerization reactors in general; and methyl methacrylate (MMA) polymerization reactors, in particular. Although, MMA polymerization is commonly performed in semi-batch reactors at industrial level, most of the available models focus on batch reactors; while, the semi-batch reactor models are much scarcer. In this work, a model of a MMA solution polymerization batch reactor was modified in order to generalize it to semi-batch operation. The developed semi-batch model was used here for studying the effect of different operation conditions (feeding flow rate, initiator load, monomer initial load, and reactor temperature) on the quality characteristics of the produced polymer and on the safety and productivity of the polymerization reactor. The developed model can be used to optimize the operation conditions of a semi-batch reactor so that the final product quality meets the application requirements, while maintaining the reactor within its safe-operation envelope, and maximizing its productivity.

Improving Environmental Stress Cracking Resistance of High-Density Polyethylene Grades by Comonomer Addition and Nanocomposite Approach.

The aim of this paper is to determine the effect of polymer density, correlated to the comonomer content, and nanosilica addition on the mechanical and Environmental Stress Cracking Resistance (ESCR) characteristics of high-density polyethylene (HDPE). In this regard, five HDPE samples with similar Melt Flow Index (MFI) and molar mass but various densities were acquired from a petrochemical plant. Two polymerization reactors work in series and differ only in the amount of 1-buene comonomer fed to the second reactor. To ascertain the microstructure of the studied samples, GPC and SSA (successive self-nucleation and annealing) analyses were accomplished. All samples resulted having similar characteristics but slightly various SCB/1000 C=7.26-9.74 (SCB=Short Chain Branching). Consequently, meanwhile studied HDPEs reveal similar notched impact and stress at yield values, the tensile modulus, stress-at-break, and elongation-at-break tend to demonstrate different results with the SCB content. More significantly, ESCR characteristic varied considerably with SCB/1000 C extent, so that higher amount of SCB acknowledged advanced ESCR. Notably, blending HDPE sample containing higher amount of SCB/1000 C, with 3 wt.% of chemically modified nanosilica enhanced ESCR characteristic by 40 %. DFT (Density Functional Theory) calculations unveiled the role of the comonomer, quantitatively by binding energies and qualitatively by Non Covalent Interaction (NCI) plots.

Reinforcement learning for the optimization and online control of emulsion polymerization reactors: Particle morphology

Online control of emulsion polymerization reactors is challenging due to the complex nature of the polymerization process, which causes difficulties not only for online measurement, but also for real-time prediction and optimization of future trajectories. In this work, the use of reinforcement learning (RL) to overcome these challenges is explored for the case of online control of particle morphology. It is shown in silico that assuming knowledge of the system dynamics in the form of a mathematical model, reinforcement learning can be used to train a neural network that can select optimal control actions in real-time to target a desired final polymer product. Moreover, it is shown that a second neural network model can be utilized as a state estimator to allow for full online control of particle morphology, which cannot be directly measured online. This work highlights the potential of machine learning for optimization and control in challenging polymerization systems.

Surrogate-model-based optimization of a nonideal polymerization reactor for producing tailored molecular weight distribution

The optimization of polymerization reactors with nonideal mixing has been greatly hindered by a tremendous computation burden. In this study, a global optimization framework to integrate full MWD calculations and detailed reactor dynamics with nonideal mixing behaviors was developed by reducing the considerable computation time required for implementing full MWD. A combination of surrogate-model-based optimization and a computational fluid dynamics (CFD)-compartment reactor model was applied to produce the desired MWD in a nonideal reactor. A neural network (NN) surrogate model was trained using 3,000 MWD data produced from the mechanistic reactor model. The results showed that the model successfully described asymmetric MWD with bimodality resulting from the nonideal mixing behaviors in the reactor. The surrogate model was used to construct operation maps for the asymmetry and bimodality factors, with SHapley Additive exPlanations (SHAP) values showing that the flow rate of the chain transfer agent had the largest impact on the asymmetry factor, whereas temperature significantly influenced the bimodality factor. Finally, the optimization strategy based on the asymmetric and bimodality factors successfully determined operating conditions to produce four tailored MWDs, reported in actual polymerization reactors with R scores of 0.988–0.997.

A New Approach in Lipase-Octyl-Agarose Biocatalysis of 2-Arylpropionic Acid Derivatives.

The use of lipase immobilized on an octyl-agarose support to obtain the optically pure enantiomers of chiral drugs in reactions carried out in organic solvents is a great challenge for chemical and pharmaceutical sciences. Therefore, it is extremely important to develop optimal procedures to achieve a high enantioselectivity of the biocatalysts in the organic medium. Our paper describes a new approach to biocatalysis performed in an organic solvent with the use of CALB-octyl-agarose support including the application of a polypropylene reactor, an appropriate buffer for immobilization (Tris base-pH 9, 100 mM), a drying step, and then the storage of immobilized lipases in a climatic chamber or a refrigerator. An immobilized lipase B from Candida antarctica (CALB) was used in the kinetic resolution of (R,S)-flurbiprofen by enantioselective esterification with methanol, reaching a high enantiomeric excess (eep = 89.6 ± 2.0%). As part of the immobilization optimization, the influence of different buffers was investigated. The effect of the reactor material and the reaction medium on the lipase activity was also studied. Moreover, the stability of the immobilized lipases: lipase from Candida rugosa (CRL) and CALB during storage in various temperature and humidity conditions (climatic chamber and refrigerator) was tested. The application of the immobilized CALB in a polypropylene reactor allowed for receiving over 9-fold higher conversion values compared to the results achieved when conducting the reaction in a glass reactor, as well as approximately 30-fold higher conversion values in comparison with free lipase. The good stability of the CALB-octyl-agarose support was demonstrated. After 7 days of storage in a climatic chamber or refrigerator (with protection from humidity) approximately 60% higher conversion values were obtained compared to the results observed for the immobilized form that had not been stored. The new approach involving the application of the CALB-octyl-agarose support for reactions performed in organic solvents indicates a significant role of the polymer reactor material being used in achieving high catalytic activity.

Koopman operator-based multi-model for predictive control

AbstractThis work describes a new model structure developed for prediction in Model Predictive Control (MPC). The model has a multi-model structure in which independent sub-models are employed for the consecutive sampling instants. The model lifts process states into a high-dimensional space in which a linear process description is applied. Depending on the influence of the manipulated variables on lifted states, three general model versions are described and model identification algorithms are derived. As a result of the multi-model structure, model parameters are found analytically from computationally uncomplicated least squares problems using the Extended Dynamic Mode Decomposition algorithm, but the evolution of states over the horizon used in MPC is taken into account. Next, the MPC algorithm for the described model is derived. It requires solving online simple quadratic optimisation tasks. The effectiveness of three considered model configurations and three versions of the lifting functions is examined for a nonlinear DC motor benchmark. Their impact on model accuracy, complexity, possible control accuracy and MPC calculation time is thoroughly discussed. Finally, a more complex polymerisation reactor process is considered to showcase the practical applicability of the presented approach to modelling and MPC.

The hidden secrets of the average number of radicals per particle ([formula omitted]) and their implications in control of emulsion polymerization reactors

Emulsion polymerization is the method of choice to produce waterborne polymers but is susceptible to run-to-run variations. This variability is hard to avoid because on-line measurement of many of the characteristics of interest, in particular the molar mass distribution (MMD) of non-linear polymers, is not possible. This work offers a way to solve this problem. First, it is shown that the average number of radicals per particle (n¯), a value that can easily be obtained from kinetic measurements, contains sufficient information to directly determine the distribution of particles with n radicals. It is then demonstrated that for a given measured MMD, knowledge of the distribution of radicals per particle allows solving the long standing problem of the accurate estimation of the effective termination rate coefficient in emulsion polymerization. Combining this knowledge, it is shown the value of n¯ alone (a value that can be obtained experimentally by calorimetric measurements) can be used to develop a soft sensor able to estimate on-line the molar mass distribution of highly non-linear polymers. This, for the first time, offers the possibility of on-line control of the MMD of non-linear emulsion polymers.

Adaptive Backstepping Fractional-order Nonsingular Terminal Sliding Mode Control of the Continuous Polymerization Reactor

Adaptive Backstepping Fractional-order Nonsingular Terminal Sliding Mode Control of the Continuous Polymerization Reactor

Digital Strategies to Improve Product Quality and Production Efficiency of Fluorinated Polymers: 2. Heat Removal Performance of Reactor with Internal and External Cooling Systems

This work aims to study the heat transfer performance of a sophisticated industrial suspension polymerization reactor, which is distinguished by its complex blade structure and capability in efficient heat removal,...

A combinatorial hollow cathode discharge/plasma polymerization system for silver containing plasma parylene coating

The conventional pyrolysis of parylene coating depends on a high vacuum environment and an expensive solid dimer precursor. Our previous study successfully demonstrated the feasibility of synthesizing plasma parylene (PP) coating using plasma polymerization with a liquid para-xylene precursor. The deposition conditions for plasma polymerization are compatible with the vacuum level of the hollow cathode discharge (HCD). This led to the idea of using an HCD gun as the metal source to incorporate metal into the plasma polymerized films, thereby achieving different coating functions and extending applications, such as active antibacterial purposes. In this study, an HCD gun was installed on the plasma polymerization reactor to synthesize a silver containing plasma parylene (Ag-PP) coating, where the silver HCD tube serves as the in situ source for incorporating silver.The experimental results demonstrate that the quantity of incorporated silver increases linearly with the power delivery level of the HCD device, and its content can be controlled during deposition to form an Ag-PP coating. Microstructural analysis reveals that the incorporated silver exhibits a crystalline and granular structure with a metallic state in the Ag-PP coating. Furthermore, the Ag-PP coating significantly resists both Staphylococcus aureus and Escherichia coli, with an antibacterial activity value exceeding 2.0 after 24 h of plate culture, corresponding to a silver metal ion release of 2–3 ppb. This quantitatively substantiates that the incorporated silver can impart an active antibacterial function to the PP coating for biomedical surface treatment applications.

Model-Based design of a novel process applicable to solution and slurry polymerization with phase change

This work aims on developing a novel process that is applicable to solution and slurry polymerization, which can efficiently control production efficiency, product properties and reactor thermal load through changing the flow ratios of cooled evaporation streams between different reactors. Furthermore, various process routes can be created by varying the destinations of cooled evaporation streams, markedly enhancing the process flexibility. To provide a thorough insight into the characteristics of the developed process, numerical simulations based on coupling the constructed models of polymerization reaction kinetics, thermodynamic properties and reactors are conducted to comprehensively study the impact of various factors (e.g., process routes, pressure, monomer and catalyst concentration, flow rates of cooled evaporation streams in different reactors) on the ethylene/1-octene solution copolymerization system with several stirred reactors connected in series. Some strategies for regulating production efficiency, product properties and reactor heat load of different process routes are obtained.

Splitting for strength: Manipulating polymerization reactor split ratios to control mechanical and rheological properties in bimodal polyethylene resins

AbstractThis study integrates advanced mathematical modeling and experimental methodologies to investigate the simultaneous impact of modifications in the split ratio and molecular weight (MW) of chains on the rheological and mechanical properties of bimodal polyethylene (BiPE) resins. The outcomes underscored the viability of fine‐tuning the molecular weight distribution (MWD) of a BiPE resin by augmenting the MW of high molecular weight (HMW) chains while simultaneously diminishing their proportion in the final alloy formulation. In addition, the experimental results illuminated the prospect of attaining a targeted melt flow index for the final polymers by elevating the MW of HMW chains alongside an increase in the proportion of low molecular weight chains. Significantly, these adjustments resulted in remarkable enhancements in the shear thinning index and strain hardening modulus of the fabricated resins.

Photo-Catalytic Activity Improvement for Organic Pollutant Removal in Wastewater using Zinc Oxide Quantum Dots: An Experimental and Modeling Study

Photo-catalyst nanoparticles (NPs) find applications in many diverse fields, including environmental remediation, energy conversion, and organic synthesis. By optimizing the nanoparticle's composition, size, morphology, and surface properties, the photo-catalytic performance can be enhanced to develop more efficient and sustainable catalytic systems. This work aligns with this innovative approach and aims to improve the photo-catalytic degradation of Sulfamethoxazole (SMX) through the intensification of the photo-catalyst and the micro-reactor. ZnO-NPs were synthesized using the sol-gel method. Zinc Acetate (Z.A) and sodium hydroxide were used as precursor materials. The resulting ZnO-NPs were characterized for their structure and crystallinity using X-Ray Diffraction (XRD) and the photo-catalytic activity was assessed with a micro-structured polymer reactor. The degradation of SMX through photo-catalysis proceeds through several stages that involve coupled processes, such as the transportation of molecules and chemical reactions. To solve the mathematical equations governing the transport and photocatalytic reaction, COMSOL Multiphysics software was utilized. The characterization results demonstrate the excellent crystallinity and high purity of the synthesized ZnO-NPs, enabling the estimation of the average diameter of the NPs under different synthesis conditions. The grain growth is faster (3.5 hr) at higher temperatures (70, 80, and 90 °C), and slower (4 hr) at lower temperatures (50 and 60°C). The photo-catalytic degradation is significantly more efficient on 16 nm ZnO-NPs than 50 nm ZnO-NPs. At this size, the conversion rate reaches 96%, surpassing the performance of commercial ZnO-NPs, which only degrades 81% of SMX. The conversion rate obtained through simulation is slightly higher than that achieved in the experiments. However, this difference remains negligible, and overall, the model fits well with the experimental data. This validation of the chosen model confirms its reliability and accuracy.

Исследование устойчивости химического реактора полимеризации этилена

The chemical reactor is the main and most complex object in the management of the technological process of polymerization. When designing chemical reactors, it is necessary to select design and operating parameters that will be able to provide the only or most stable state with the specified process characteristics. To study the stability of the ethylene polymerization process in an autoclave reactor with a stirrer, it is necessary to build a mathematical model based on the analysis of the physico-chemical laws of the process and search for the necessary steady-state conditions for the reactor. A solution based on a deterministic mathematical model of ethylene polymerization is proposed. The description of the process of polymer molecule formation, which includes the stages of initiation, growth and chain breakage; the mechanism of chemical kinetics of ethylene polymerization; a system of assumptions to simplify the construction of a mathematical model. The mathematical model of an ethylene polymerization reactor in an autoclave reactor with a stirrer is a system of differential equations. When calculating the static reactor mode, the mathematical description contains a system of nonlinear algebraic equations, the solution of which is implemented using numerical methods. It is noted that chemical reactors can have not one, but several stationary states at the same values of variables and parameters. Knowing the coordinates of the stationary states of the chemical process, you can choose the one that is more preferable from the point of view of productivity or the quality of the products produced. As a result of the simulation, the existence of a single solution under the conditions found that ensure a stable stationary state of the chemical ethylene polymerization reactor is confirmed.