A Monte Carlo Method to Quantify the Effect of Reactor Residence Time Distribution on Polyolefins Made with Heterogeneous Catalysts: Part I—Catalyst/Polymer Particle Size Distribution Effects

This work is focused on the development and validation of a model accounting for the impact of the reactor residence time distribution in well‐stirred slurry‐phase catalytic polymerization of ethylene. Particle growth and morphology are described through the Multigrain model, adopting a two‐site model for the catalyst and a conventional kinetic scheme. Particle size distribution and polymer properties (average molecular weights and polydispersity) are computed as a function of particle size through a segregated model, assuming that neither breakage nor aggregation occur. Reactors are modeled by means of fundamental mass conservation equations. The model is applied to a system constituted by a series of two ideal continuous stirred tank reactors, where the synthesis of polyethylene with bimodal molecular weight distribution is performed, employing the initial catalyst size distribution as the only adjustable parameter. The model provides insights at the single particle scale for each specific size, thus highlighting the inhomogeneity which arises from the synergic effects of chemical kinetics and residence time distributions in both reactors. The satisfactory agreement between model results and experimental data, in terms of particle size distribution and average molecular weights, confirmed the suitability of the model and underlying assumptions.

Section: Introductionmentioning

confidence: 99%

The Effect of Residence Time Distribution on the Slurry‐Phase Catalytic Ethylene Polymerization: An Experimental and Computational Study

Casalini

Visscher

Tamaddoni

et al. 2018

“…One of the limitations of this approach is its high computation time, since Monte Carlo simulations rely on large sample sizes (in the order of millions of particles) to get statistically valid results . To complicate matters a little further, the simulation time to solve the PMLM for a single particle depends on the residence time of the particle in the reactor.…”

Section: Resultsmentioning

confidence: 99%

“…For example, in a fluidized bed reactor, smaller particles are likely to stay longer, while larger particles are likely to stay shorter times in the reactor. Following our previous work, a biased sampling method was applied to handle this phenomenon, wherein a weighting factor ( w ) proportional to the size of the particle and to the mean size of the population was used to increase ( D pi < D p, mean ) or decrease ( D pi > D p, mean ) the polymerization time of a given particle. Figure 23 shows the simulation results for polymer PSD and MWD wherein a biased sampling method ( w = 0.5) on the particle residence time was adopted, as well as intraparticle mass transfer resistances.…”

Section: Resultsmentioning

confidence: 99%

“…In a previous publication of this series, we demonstrated how a Monte Carlo model could relate the PSD of the polymer population to the catalyst PSD, as a function of reactor RTD and polymerization kinetics . We showed that the proposed Monte Carlo model was extremely versatile, being able to predict polymer PSD in reactor systems with any arbitrary RTD for catalyst particles having any PSD shape.…”

Section: Introductionmentioning

confidence: 94%

“…These previous models required the solution of simultaneous differential‐integral equations and assumed an average catalyst particle diameter, instead of a catalyst PSD. None of these models could handle complex polymerization kinetics, catalyst particle nonuniformities, and reactor RTDs or catalyst PSDs of unusual shapes effectively …”

Section: Introductionmentioning

confidence: 99%

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A Monte Carlo Method to Quantify the Effect of Reactor Residence Time Distribution on Polyolefins Made with Heterogeneous Catalysts: Part IV—Intraparticle Transfer Resistance Effects

Liu

Soares

2018

Self Cite

An integrated Monte Carlo/polymeric multilayer model (MC/PMLM) is developed to predict the polymer particle size distribution (PSD) and microstructures of polyolefins made with heterogeneous catalysts under intraparticle mass transfer limitations. The Monte Carlo model is used to randomly sample particle sizes and residence times from the catalyst PSD and reactor residence time distribution (RTD), respectively, while the polymeric multilayer model is used to describe single‐particle growth considering intraparticle mass transfer resistances. The effect of reactor RTD, catalyst PSD, and polymerization kinetics on polymer PSD and polymer properties is systematically investigated with the MC/PMLM for the first time. The results show that intraparticle mass transfer limitations under various operating conditions may affect polymer PSD and polymer properties. In addition, due to the versatility of the Monte Carlo approach, the proposed MC/PMLM is adequate to describe complex cases, such as reactor systems with arbitrary RTD and catalyst particles having any PSD.

A Monte Carlo Method to Quantify the Effect of Reactor Residence Time Distribution on Polyolefins Made with Heterogeneous Catalysts: Part II ‐ Packing Density Effects

Romero

Soares

2018

Self Cite

The sphere packing problem consists on arranging spheres, of different or same radii, on a 3D container without overlapping them. The ratio of the volume occupied by the spheres to the total volume of the container is called packing density. The goal of the sphere packing problem is to find the arrangement that maximizes the packing density. When the spheres are packed randomly, the arrangement is referred to as a random loose packing. If the container is shaken afterward, the arrangement is called random close packing.Several approaches exist to model random packing. Two of them are the collective rearrangement [2][3][4][5] and the sequential deposition [6][7][8][9][10][11][12] methods. In the collective rearrangement method, the spheres are randomly placed in a container and allowed to overlap. In a subsequent step, the spheres are moved and/or reduced in size until the overlap drops to an acceptable threshold. In the sequential deposition method, on the other hand, the spheres are dropped one by one in a container following the gravitational law until they find a stable position. This approach is also known as drop and roll algorithm.In this work, we have implemented a drop and roll algorithm as described by Zhou et al. [7] The algorithm consists in the following steps:• An incoming sphere, is randomly positioned at the top of the container. • The incoming sphere is dropped in small increments down the container. • The dropping stops once the incoming sphere touches the floor of the container or hits another sphere. • If the incoming sphere touches the floor of the container, its position is considered stable, and the algorithm starts positioning a new incoming sphere. • If the incoming sphere touches another sphere, it rolls on the stationary sphere until it hits the floor (and becomes stable), or hits a second sphere. • If the incoming sphere hits a second stationary sphere, it rolls again until it either becomes stable by hitting the floor or a third sphere. • When the incoming sphere hits a third sphere, the stability criteria is evaluated to determine if the incoming sphere becomes stable. If not, the incoming sphere will continue rolling but now on the pair of spheres, or on the sphere with the steepest contact angle. Monte Carlo ModelThe residence time distribution of reactors used to produce polyolefins commercially has a significant impact on many of their properties. This effect often goes unnoticed, since the concept of reactor residence time is often poorly understood even among chemical engineers. In the first part of this series of articles, it is shown how the reactor residence time distribution has a marked impact on the particle size distribution of polyolefin particles using a new Monte Carlo model. In this article, the Monte Carlo model is combined with a drop and roll algorithm to predict how reactor residence time distribution affects the packing density of the polyolefin particles.