Optimal control of molecular weight and particle size distributions in a batch suspension polymerization reactor

Koolivand, Abdollah; Shahrokhi, Mohammad; Farahzadi, Hamzeh

doi:10.1007/s13726-019-00737-z

Cited by 6 publications

(3 citation statements)

References 42 publications

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“…Koolivand et al [64] used a population balance model and a kinetic model to represent the particle size distributions and MMD of polystyrene produced in suspension polymerization. The effects of impeller rotation speed, chain transfer agent, initiator and temperature were investigated.…”

Section: Population Balance Modelingmentioning

confidence: 99%

Modeling of Particle Size Distributions in Industrial Poly(vinyl chloride) Suspension Polymerization Reactors

2023

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In the present paper, a mathematical model is built and implemented to describe the trajectories of mass inventories, pressures and polymer properties with emphasis on final particle size distributions of industrial scale poly(vinyl chloride) suspension polymerization reactors. The model comprises the mass balances, statistical moment balances, equilibrium relationships and population balance equations. A discretization scheme is employed to transform the integro-differential equations resulting from the population balance model into a system of differential equations. The obtained results show, for the first time, that classical breakage and coalescence kernels described in the literature can provide very good fittings of actual industrial scale data when coupled with proper parameter estimation procedures, so that the proposed model is able to represent the available operation data with good accuracy at distinct conditions. Particularly, it is also shown that the use of a top condenser for control of the reactor temperature can lead to changes of parameters that control the particle size distributions.

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Section: Population Balance Modelingmentioning

confidence: 99%

Modeling of Particle Size Distributions in Industrial Poly(vinyl chloride) Suspension Polymerization Reactors

2023

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“…[20] To better understand the connection between kinetics and MWD as well as to clarify which theory is correct or more proper, many efforts have been made to simulate MWD. [11,12,16,[18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] Three methods, i.e., moments, Monte Carlo, and solving ordinary differential equations directly, have been developed. [14,16] Among them, the most used is the method of moments because it is not only based on clear reaction mechanism and kinetic equation, but also ratio (RR) of chain propagation to chain transfer can give an impact on the degree of uniformity of chain length.…”

Section: Introductionmentioning

confidence: 99%

Molecular Weight Distribution in Ring‐Opening Polymerization of Propylene Oxide Catalyzed by Double Metal Complex: A Model Simulation

Zhao

Fan

2021

Macro Theory & Simulations

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easy to calculate. Even though this method cannot show out the full MWD curves, it gathers the most important information such as monomer conversion (x), molecular weight (MW), and polydispersity index (PDI). [28] PDI quantifies the width of MWD.The ring-opening polymerization (ROP) of propylene oxide (PO) catalyzed by double metal complex (DMC) is generally considered to have the characteristics of living polymerization. For example, the MW increases with x, and block copolymers with ethylene oxide can be prepared. However, our recent experimental study shows that the MWD of products is not easy to keep very narrow even if the polymerization is carried out in batch or plug flow reactor. [34] According to the polymerization mechanism proposed by Huang et al., [35][36][37] it is generally believed that the chain transfer reaction between active chains and dormant chains is the key to narrow MWD. However, up to now, no one has quantitatively investigated the effect of this chain transfer reaction on the MWD.In this work, a kinetic model involving chain propagation and chain transfer is established; the method of moments is used to simulate PDI as well as x and number-average polymerization degree (Xn) under various reaction conditions. We hope that this work can facilitate the understanding of the polymerization mechanism behind various complex phenomena in the ROP catalyzed by DMC. Modeling Section Polymerization MechanismAs Huang et al. [35][36][37] and Kim et al. [38,39] have reported, ROP of PO catalyzed by DMC consists of induction, chain propagation, and transfer reaction. Herein, only the chain propagation and transfer reaction are considered since they are the main reactions that affect MWD. As shown in Scheme 1, chains with active center can be propagated; meanwhile, the active center can be transferred to dormant chains so that they are activated and propagated. It is the chain transfer between the active chain and dormant chain that results in the more uniform chain growth. Obviously, it can be thought that the instant rate In the present work, method of moments is used to model the molecular weight distribution (MWD) of polypropylene glycol (PPG) produced with ring-opening polymerization of propylene oxide catalyzed by double metal complex (DMC), and an explicit expression about the polydispersity index (PDI) of PPG is obtained. The simulated results indicate that decreasing the initial concentration ratio of monomer to total chains (K 1 ) or increasing the rate constant ratio of chain transfer to propagation (K 2 ) leads to smaller PDI. Reducing the concentration of DMC can induce larger PDI. When the PPG's initial PDI (i.e., PDI of initiator) increases, PDI of the final PPG grows up linearly. However, with the increase of monomer conversion, PDI increases first and then decreases, that is, there is a critical conversion. The possible lack of chain transfer at the beginning of polymerization and the insufficient chain transfer caused by increased K 1 , decreased concentration of catalyst, and decreased...

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“…The integration of mechanistic models and computational techniques allows to simulate and control physical and chemical processes (e.g., suspension polymerization [32]), perform system identification and risk analysis (e.g., pharmaceutical manufacturing [33]), and conduct process and product design. Based on our computational findings, here we pursue the process design objective and propose a new microdevice for the sorting of artificial (e.g., polymer shell capsules) and physiological capsules (e.g., biological cells) based on their size, by utilizing tall trapezoidal microchannels with low base ratios.…”

Section: Introductionmentioning

confidence: 99%

Motion of an Elastic Capsule in a Trapezoidal Microchannel under Stokes Flow Conditions

Koolivand

Dimitrakopoulos

2020

Polymers

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Even though the research interest in the last decades has been mainly focused on the capsule dynamics in cylindrical or rectangular ducts, channels with asymmetric cross-sections may also be desirable especially for capsule migration and sorting. Therefore, in the present study we investigate computationally the motion of an elastic spherical capsule in an isosceles trapezoidal microchannel at low and moderate flow rates under the Stokes regime. The steady-state capsule location is quite close to the location where the single-phase velocity of the surrounding fluid is maximized. Owing to the asymmetry of the trapezoidal channel, the capsule’s steady-state shape is asymmetric while its membrane slowly tank-treads. In addition, our investigation reveals that tall trapezoidal channels with low base ratios produce significant off-center migration for large capsules compared to that for smaller capsules for a given channel length. Thus, we propose a microdevice for the sorting of artificial and physiological capsules based on their size, by utilizing tall trapezoidal microchannels with low base ratios. The proposed sorting microdevice can be readily produced via glass fabrication or as a microfluidic device via micromilling, while the required flow conditions do not cause membrane rupture.

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Optimal control of molecular weight and particle size distributions in a batch suspension polymerization reactor

Cited by 6 publications

References 42 publications

Modeling of Particle Size Distributions in Industrial Poly(vinyl chloride) Suspension Polymerization Reactors

Modeling of Particle Size Distributions in Industrial Poly(vinyl chloride) Suspension Polymerization Reactors

Molecular Weight Distribution in Ring‐Opening Polymerization of Propylene Oxide Catalyzed by Double Metal Complex: A Model Simulation

Motion of an Elastic Capsule in a Trapezoidal Microchannel under Stokes Flow Conditions

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