Analysis of four Monte Carlo methods for the solution of population balances in dispersed systems

Zhao, Haibo; Maisels, A.; Matsoukas, Themis; Chen, Zheng

doi:10.1016/j.powtec.2006.12.010

Cited by 129 publications

(98 citation statements)

References 48 publications

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“…where Q is the total number of MC repetitions (Q = 3 in this simple ideal case for comparison with these published data (Zhao et al 2007)); δ…”

Section: Case1 Constant Coagulation Kernelmentioning

confidence: 85%

“…The particle number concentration N (M 0 , the zero-order moment of particle size distribution), particle volume (mass) concentration M (M 1 , the first-order moment of particle size distribution), and the particle size distribution function, which is expressed in terms of P k (the probability of obtaining a cluster obtaining k primary particles), are calculated and compared with the analytical solution (Zhao et al 2007). To this end, the mean standard deviations σ ξ (t) of these parameters ξ (N , M or P k ), obtained by comparison with the analytical solution, are calculated according to:…”

Section: Case1 Constant Coagulation Kernelmentioning

confidence: 99%

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Reducing Statistical Noise and Extending the Size Spectrum by Applying Weighted Simulation Particles in Monte Carlo Simulation of Coagulation

Kruis

Chen

2009

Aerosol Science and Technology

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The direct simulation Monte Carlo (DSMC) method is widely utilized to simulate microscopic dynamic processes in dispersed systems that give rise to the population balance equation. In conventional DSMC approaches, simulation particles are equally weighted, even for broad size distributions where number concentrations in different size intervals are significantly different. The resulting statistical noise and limited size spectrum severely restrict the application of these DSMC methods. This study proposes a new Monte Carlo (MC) method, the differentially weighted timedriven method, which captures the coagulation dynamics in dispersed systems with low noise and is simultaneously able to track the size distribution over the full size range. Key elements of this method include constructing a new jump Markov process based on a new coagulation rule for two differentially weighted simulation particles, and restricting the number of simulation particles in each size interval within prescribed bounds. The method is validated by using an ideal coagulation kernel with a known analytical solution and a real coagulation kernel for which an accurate solution can be found numerically (self-preserving particle size distribution in the continuum regime).

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“…where Q is the total number of MC repetitions (Q = 3 in this simple ideal case for comparison with these published data (Zhao et al 2007)); δ…”

Section: Case1 Constant Coagulation Kernelmentioning

confidence: 85%

Section: Case1 Constant Coagulation Kernelmentioning

confidence: 99%

Reducing Statistical Noise and Extending the Size Spectrum by Applying Weighted Simulation Particles in Monte Carlo Simulation of Coagulation

Kruis

Chen

2009

Aerosol Science and Technology

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“…In timedriven simulations a time step is specified then the simulation implements all possible events within that step [18]. The used MC algorithm is described in this section.…”

Section: Solution By Means Of the Monte Carlo Methodsmentioning

confidence: 99%

“…by means of which the mean temperature of droplet population over the reactor is expressed as (18) while the mean concentration of the k th species over the reactor can be expressed as…”

Section: Tab 1 Free-radical Polymerization Reactions Of Vinyl Chloridementioning

confidence: 99%

Modelling of heat exchange between drops in suspension polymerization of vinyl chloride

Bárkányi

Lakatos

Németh

2012

Per. Pol. Chem. Eng.

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“…Monte Carlo simulation (MCS) has been used as such a method over the past few decades 4,5 . With this approach a large population of particles, perhaps of O (10 9 ) is represented by a small sample, perhaps O(10 3…”

Section: Introductionmentioning

confidence: 99%

Accuracy and optimal sampling in Monte Carlo solution of population balance equations

Hounslow

Reynolds

2015

AIChE Journal

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Analysis of four Monte Carlo methods for the solution of population balances in dispersed systems

Cited by 129 publications

References 48 publications

Reducing Statistical Noise and Extending the Size Spectrum by Applying Weighted Simulation Particles in Monte Carlo Simulation of Coagulation

Reducing Statistical Noise and Extending the Size Spectrum by Applying Weighted Simulation Particles in Monte Carlo Simulation of Coagulation

Modelling of heat exchange between drops in suspension polymerization of vinyl chloride

Accuracy and optimal sampling in Monte Carlo solution of population balance equations

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