Modeling of the Suspension Polymerization Process Using a Particle Population Balance

Chen, Zhong; Pauer, Werner; Moritz, Hans‐Ulrich; Prüß, Jan; Warnecke, Hans‐Joachim

doi:10.1002/(sici)1521-4125(199907)22:7<609::aid-ceat609>3.0.co;2-y

Cited by 15 publications

(7 citation statements)

References 5 publications

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“…A PBM developed in this study for describing the time evolution of the particles/droplets size distribution of dispersed phase is described as follows

\frac{\partial n false(v, t false)}{\partial t} + \frac{\partial}{\partial v} false[G (v) n (v, t) false] = E false(v, t false) - D false(v, t false)

where, n(v,t) is the number density function, G ( v ) n ( v,t ) means the particle flux due to particle growth, and E ( v,t ) and D ( v,t ) denote birth and death rate functions of breakage and coalescence, respectively. They can be written as follows

\begin{matrix} left \\ E false(v, t false) = \int_{v}^{\infty} β (u, v) υ (u) s (u) n (u, t) d u \\ + \int_{0}^{v / 2} κ (v - u, u) n (v - u, t) n (u, t) d u \end{matrix}

D false(v, t false) = n false(v, t false) \int_{0}^{\infty} κ (v, u) n (u, t) d u

…”

Section: Model Developmentsmentioning

confidence: 99%

“…Additionally, the largely increased viscosity will also affect these phenomena. Thus, breakage and coalescence rates are calculated based on frequency and Maxwellian efficiency and the modifications by Chen et al as follows

s false(v false) = k_{b} \exp (- \frac{k_{c} σ {false(1 + ϕ false)}^{2}}{ρ_{normald} v^{5 / 9} ε^{2 / 3}} - \frac{k_{v} μ_{normald} false(1 + ϕ false)}{ρ_{normald} v^{4 / 9} ε^{1 / 3}})

κ false(v, u false) = α_{b} \exp (- \frac{α_{c} μ_{normald} ρ_{normald} ε}{σ^{2} {false(1 + ϕ false)}^{3}} {(\frac{d_{v} d_{u}}{d_{v} + d_{u}})}^{4})

In addition, the functions, υ ( u ) and β ( u,v ) represent the number and distribution of daughter droplets formed by breakage events, respectively. Herein, it is assumed that the daughter droplet size distribution conforms to the normal distribution.…”

Section: Model Developmentsmentioning

confidence: 99%

“…Due to its huge advantages in avoiding the two main problems (i.e., the highly exothermic reactions, the large increase in viscosity), suspension polymerization is one of the most important technologies applied in the polymerization industry. A key consideration in designing a suspension polymerization is to achieve such that desired molecular microstructure and droplet/particle size distribution (PSD) of polymers are satisfied.…”

Section: Introductionmentioning

confidence: 99%

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Modeling of the Methyl Methacrylate Atom Transfer Radical Suspension Polymerization Process: Polymerization and Particle Kinetics

Xie

Luo

2016

Macro Reaction Engineering

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increase in viscosity), [15] suspension polymerization is one of the most important technologies applied in the poly merization industry. A key consideration in designing a suspension polymerization is to achieve such that desired molecular microstructure and droplet/particle size dis tribution (PSD) of polymers are satisfied. The number average molecular weight (M n ) and polydispersity index (PDI), as the most basic performance indices of polymer affecting the polymer enduse properties, are mainly determined by polymerization kinetics, and the PSD can control some key aspects of operation including suspen sion stability and productivity. Hence, there is a growing demand for studying suspension polymerization kinetics and its droplet/particle kinetics.For a suspension polymerization, two characteristic phases, i.e., the aqueous phase and the dispersed phase, are present. If the dissolved monomer in the aqueous phase is ignored, the polymerization process occurring at the suspension droplets will be considered as a bulk one.In this work, a mathematical model is developed to characterize the batch atom transfer rad ical suspension polymerization (batch suspension ATRP). For the first time, the morphological and molecular properties of particles, as well as their dynamics in methyl methacrylate ATRP can be simultaneously simulated by solving the model that consists of ATRP kinetic equations, moment equations, a phase equilibrium equation for calculating equilibrium monomer dis tributions in various phases, and a particle population balance model. The proposed model is verified using the open experimental data. Based on the verified model, two key operating factors including the ratios of monomer to initiator and water to monomer are studied in order to investigate the batch suspension ATRP kinetics. In addition, the model is also used to predict the droplet/par ticle size distribution. The effects of breakage rate, coales cence rate, and agitation speed on the droplet volume density distribution and the Sauter mean diameter are discussed in details. The simulated results demonstrate that the coupled model can describe the batch suspension ATRP kinetics and its droplet kinetics.

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“…A PBM developed in this study for describing the time evolution of the particles/droplets size distribution of dispersed phase is described as follows

\frac{\partial n false(v, t false)}{\partial t} + \frac{\partial}{\partial v} false[G (v) n (v, t) false] = E false(v, t false) - D false(v, t false)

\begin{matrix} left \\ E false(v, t false) = \int_{v}^{\infty} β (u, v) υ (u) s (u) n (u, t) d u \\ + \int_{0}^{v / 2} κ (v - u, u) n (v - u, t) n (u, t) d u \end{matrix}

D false(v, t false) = n false(v, t false) \int_{0}^{\infty} κ (v, u) n (u, t) d u

…”

Section: Model Developmentsmentioning

confidence: 99%

s false(v false) = k_{b} \exp (- \frac{k_{c} σ {false(1 + ϕ false)}^{2}}{ρ_{normald} v^{5 / 9} ε^{2 / 3}} - \frac{k_{v} μ_{normald} false(1 + ϕ false)}{ρ_{normald} v^{4 / 9} ε^{1 / 3}})

κ false(v, u false) = α_{b} \exp (- \frac{α_{c} μ_{normald} ρ_{normald} ε}{σ^{2} {false(1 + ϕ false)}^{3}} {(\frac{d_{v} d_{u}}{d_{v} + d_{u}})}^{4})

Section: Model Developmentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modeling of the Methyl Methacrylate Atom Transfer Radical Suspension Polymerization Process: Polymerization and Particle Kinetics

Xie

Luo

2016

Macro Reaction Engineering

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show abstract

“…The particle size distribution of the particles produced in batch suspension polymerization was calculated using a population balance model [13][14][15][16] .…”

Section: Introductionmentioning

confidence: 99%

Study of Some Variables Affecting Particle Size and Particle Size Distribution of Suspension Polymerization of Methyl Methacrylate

Abu‐Ayana¹,

Mohsen²

2005

Polymer-Plastics Technology and Engineering

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A laboratory reactor was designed and constructed to study the effect of both speed of agitation and a concentration of suspension stabilizer on particle size and particle size distribution during the suspension polymerization of methyl methacrylate. It was concluded that the average particle size of the prepared polymer powder is directly proportional to the speed of agitation and is inversely proportional to the stabilizer concentration. New empirical equations correlating the average particle size and the particle size distribution (PSD) were derived from the study.

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“…To the best of authors' knowledge, no past papers report the direct identification of the kinetics of particle-particle interactions during suspension polymerization, due to limitations in in-situ sensors for measuring particle size distributions (PSDs) and because solving the population balance equations for the droplet/particle size distribution was considered as being too computationally expensive [4]. The parameter estimation algorithm in this study integrates two in-situ PSD sensors with a high resolution simulation algorithm, which enables the first direct identification of the kinetics of particle dynamics in suspension polymerization.…”

Section: Introductionmentioning

confidence: 99%

Identification of particle-particle interactions in suspension polymerization reactors

Hukkanen

Braatz

Proceedings of the 2005, American Control Conference, 2005.

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Suspension polymerization is commonly used to produce micron-sized (10-1000 µm) polymer beads, in which the final particle size distribution is an important end-use property. This paper presents an integrated approach for the modeling, simulation, and parameter estimation of particleparticle dynamics during suspension polymerization. This approach integrates in situ particle size measurement with a high resolution finite volume algorithm to estimate the kinetics of particle-particle interactions while accounting for polymerization kinetics and viscoelastic effects. The resulting simulation model is sufficiently computationally efficient to enable the numerical solution of optimal control problems based on first-principles models of suspension polymerization.

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Modeling of the Suspension Polymerization Process Using a Particle Population Balance

Cited by 15 publications

References 5 publications

Modeling of the Methyl Methacrylate Atom Transfer Radical Suspension Polymerization Process: Polymerization and Particle Kinetics

Modeling of the Methyl Methacrylate Atom Transfer Radical Suspension Polymerization Process: Polymerization and Particle Kinetics

Study of Some Variables Affecting Particle Size and Particle Size Distribution of Suspension Polymerization of Methyl Methacrylate

Identification of particle-particle interactions in suspension polymerization reactors

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