Juraj Kosek

Dynamics of particle growth and overheating in gas-phase polymerization reactors

The particle overheating is an important problem in the industrial catalytic gas-phase olefin polymerization reactors. It has been first investigated with a pseudo-stationary model of a single polymer particle by Hutchinson and Ray (J. Appl. Poly. Sci. 34 (1987) 657). A systematic study of overheating of polymer particle with models based on Ficks and dusty gas model (DGM) transport described below is conducted by tools of continuation (steady-state) analysis and by dynamic simulations. The consideration of convective flow of species in particle pores driven by pressure gradient due to the change in the number of moles in the course of the polymerization reaction makes the polymer particle in the reaction environment containing only monomer more susceptible to overheating. It is found that an intraparticle mass transport resistance has an important effect on particle overheating. The prediction and discussion of a time-scale of particle overheating under industrial process conditions is coupled with the discussion of the dynamics of particle growth and dynamic changes of catalyst activity.

Multi-scale modelling of growing polymer particles in heterogeneous catalytic reactors

Publisher Summary This chapter discusses the problem of polyolefine particle morphogenesis in a heterogeneous gas or slurry catalytic reactor. A conceptual modeling approach is proposed, allowing for the multiple time- and length-scales on which polymerization processes typically occurs. Models of polymer growth and flow in the pores of a catalyst support, catalyst particle fragmentation, and the evolution of a polymer macro-particle are described as well as physical characteristics of key objects forming the particles. The length-scales involved in a typical heterogeneously catalyzed fluid-bed polymerization reactor. For example, the polymerization kinetics at the molecular level determines the polymer chain-length distribution, tacticity, branching, and composition, which determines the visco-elastic properties of a polymer melt and its melting temperature. The properties of molten and semicrystalline polymer together with the architecture of a catalyst support then determine the catalyst fragmentation mechanism, which in turn affects the structure of a growing polymer macro-particle, thus its heat- and mass-transfer characteristics.

Multi-model approach based on parametric sensitivities – A heuristic approximation for dynamic optimization of semi-batch processes with parametric uncertainties

Abstract Optimal processes often exhibit active path constraints. Parametric uncertainties in the process model might thus lead to constraint violations. A heuristic approach is presented to overcome this challenge. The nominal model is optimized with additional path constraints due to worst-case models. A heuristic method of choosing these models is proposed based on sensitivities of the constraints with respect to the uncertain parameters. The presented approximation does not guarantee robust feasibility, but path constraint violations are less likely to occur compared to the optimization using the nominal model solely. Two case studies are presented: a complex emulsion copolymerization process (DAE with 139 equations) and the penicillin formation (four differential equations and two algebraic equations). The results of both case studies show that, in contrast to the optimization in the nominal case, the multi-model approach does not violate the path constraints for different scenarios of the parametric uncertainty set.

Phase Mappings from Diffusion-Coupled Excitable Chemical Systems

Dynamics of a cascade of two diffusion-coupled excitable units periodically perturbed by pulses applied to the first cell is examined. Firing sequences experimentally found in a chemical system constituted by two coupled stirred cells with the Belousov-Zhabotinskii (BZ) reaction are modelled on two levels. A phase mapping of an abstract piecewise linear excitable two-cell system is derived and its dynamics examined in detail. The functional form of this map combined with local excitation dynamics extracted from a realistic model of the BZ kinetics is used to formulate a semi-empirical model directly applicable to the experimental BZ system. The frequency of firings in the second cell can be either equal to that in the first cell - a complete propagation of the excitation, or smaller - a propagation failure. Complex patterns of transitions between the two dynamic modes found in experiments are well predicted by the semi-empirical model and, surprisingly, by the abstract model as well, pointing to a generic nature of the patterns.

Predictive modeling of ionic permselectivity of porous media

Abstract Transport and separation processes in ionic systems located in the porous medium are investigated. The software for the modeling of the combined electroosmotic, migration, diffusion and pressure driven flow in the spatially 2D or 3D porous medium has been developed. This software allows to determine the mapping from the parametric space of the porous structure and distribution of fixed charge into the space of application properties such as ionic permselectivity or perfusion flow. Software capabilities are illustrated on case studies of systems where the Debye length is either comparable or negligible with respect to the characteristic pore size. The concept of the reconstructed porous medium has been employed to represent the morphology.

Real-time Hybrid Monte Carlo Method for Modelling of 4 Monomer Semi-Batch Emulsion Copolymerization

Abstract Semi-batch polymerization processes are traditionally operated according to rigidly prescribed recipes prohibiting process optimisation and product property adjustment in real time. In this contribution, we focus on the development of computationally efficient model of 4-monomer semi-batch emulsion copolymerization for the use in model-based predictive control (MPC). We implemented a hybrid Monte Carlo approach consisting of two steps. First, the important process-product characteristics (conversion of monomers, reaction mixture temperature) are predicted by deterministic process model based on a set of ODEs; second, copolymer molecular architecture is generated using kinetic Monte Carlo simulation, utilizing state variables pre-calculated by deterministic model. The developed model was validated using various lab-scale recipes describing simultaneous copolymerisation of two hydrophilic and two hydrophobic monomers. Due to efficient implementation and program parallelization, the whole several-hours-long batch can be simulated within a few seconds resulting in a model applicable in MPC as a soft-sensor for the detailed molecular architecture of the produced copolymer.

Morphogenesis of polyolefin particles in polymerization reactors

Abstract The evolution of the spatially 2D or 3D morphology of porous polymer particles during their growth in the catalytic polymerization of olefins is addressed by the concept of discrete element method (DEM). The polyolefin particle is discretized into number of micro-elements with visco-elastic interactions acting among individual micro-elements. The evolution of this agglomerate of micro-elements is employed in the prediction of particle morphology and in the mapping from the parametric space of the architecture of catalyst particles and reactor conditions into the space of final particle morphologies. First-principles based models of particle morphogenesis can be employed to avoid unwanted phenomena in industrial reactors, e.g., the disintegration of growing polymer particles into fines or the fouling of particles at reactor walls.

Probing Coagulation and Fouling in Colloidal Dispersions with Viscosity Measurements: In Silico Proof of Concept

Colloidal dispersions in a flow can undergo the unwanted processes of coagulation and fouling. Prevention of these processes requires their proper understanding and the ability to monitor their extent. Currently, neither of these requirements is sufficiently fulfilled and this motivates the development of detailed models that capture the nature of the dispersion processes operating at the scale of primary colloidal particles. We model coagulation and fouling in colloidal dispersions using the dynamic discrete element method (DEM), with an interaction model accounting for particles that are elastic, adhesive, and stabilized by electrostatic charge. At the same time, the particles can adhere to the wall. Flow-field computation captures the mutual influence between particles and flow. The model also includes a pair-wise implementation of lubrication forces. The modeling results indicate that viscosity is highly sensitive to the formation of clusters, reflecting not only the larger size of clusters with increasing surface energy, but also the slower kinetics of coagulation in charge-stabilized dispersions. By contrast, viscosity is not sensitive to the attachment of particles to the wall. The mechanism of fouling determined from the simulation results comprises the initial bulk formation of clusters and subsequent dynamic wall attachment and detachment of the clusters. The presented work improves understanding of the dynamic behavior of colloidal dispersions, which is strongly relevant for industrial applications as well as for on-line monitoring and control.

Experimental characterization of triboelectric charging of polyethylene powders

Triboelectric charging causes serious problems in the industrial processing of powders. We focus on the charging of polyethylene (PE) powder particles, whose agglomeration can cause serious economic problems in PE production in fluidized-bed reactors. The cascade method apparatus, i.e., a slide followed by the Faradays pail, was utilized to observe the particle-wall charging of PE particles in friction contact with various materials (glass, aluminium, PE) and allowed us to characterize the charging dynamics. Our results indicate that the evolution of the charge on the particles follows a saturation curve, where the saturated state is represented by maximum (outcome) charge. Such a trend can be conveniently fitted by a function representing the first-order dynamics. We determine the dependency of charging dynamics on various factors, e.g., the humidity, the slide surface roughness and the slide material. Our measurements imply that air humidity influences the charging process substantially more than the choice of the slide material. Moreover, we observe significant charging even in the case of the same materials being in contact. The work contributes to a better understanding of tribocharging and the estimation of charging-related parameters provides the input for the modelling of this complex process.

Discrete element method modeling of the triboelectric charging of polyethylene particles: Can particle size distribution and segregation reduce the charging?

Polyethylene particles of various sizes are present in industrial gas-dispersion reactors and downstream processing units. The contact of the particles with a device wall as well as the mutual particle collisions cause electrons on the particle surface to redistribute in the system. The undesirable triboelectric charging results in several operational problems and safety risks in industrial systems, for example in the fluidized-bed polymerization reactor. We studied the charging of polyethylene particles caused by the particle-particle interactions in gas. Our model employs the Discrete Element Method (DEM) describing the particle dynamics and incorporates the Trapped Electron Approach as the physical basis for the considered charging mechanism. The model predicts the particle charge distribution for systems with various particle size distributions and various level of segregation. Simulation results are in a qualitative agreement with experimental observations of similar particulate systems specifically in two aspects: 1) Big particles tend to gain positive charge and small particles the negative one. 2) The wider the particle size distribution is, the more pronounced is the charging process. Our results suggest that not only the size distribution, but also the effect of the spatial segregation of the polyethylene particles significantly influence the resulting charge distribution generated in the system. The level of particle segregation as well as the particle size distribution of polyethylene particles can be in practice adjusted by the choice of supported catalysts, by the conditions in the fluidized-bed polymerization reactor and by the fluid dynamics. We also attempt to predict how the reactor temperature affects the triboelectric charging of particles.