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

Abstract

Implementation of a Monte Carlo simulation for the solution of population balance equations requires choice of initial sample number (N 0 ), number of replicates (M) and number of bins for probability distribution reconstruction (n). It is found that Squared

A compartmental CFD‐PBM model of high shear wet granulation

“…Squared Hellinger Distance (SHD) was used to quantify the goodness of fit (Table ), which is defined as where are probability density functions (PDF), describing the frequency of occurrence at size ; is particle size.…”

“…The validation and accuracy of numerical prediction from the compartmental PBM in this study depends on the validation and accuracy of the model set, including both CFD and PBM. Numerically, validation of our Monte Carlo code can be found in our previous publication . Validation of the granulation mechanisms can be found in the granulation literature but specific validation remains more challenging due to the confounding contribution of multiple competing rate processes.…”

“…nucleation, rewetting, layering, coalesce and breakage) are implemented subsequently based on probability of events occurring at specific compartment. In this program, a dynamic allocation of array (DAA) algorithm is used to store and update the properties of particle population changing with time.…”

Reliability Assessment of Bearings Based on Performance Degradation Values under Small Samples

“…That method and fault tree analysis were applied to analysis of the reliability for a wastewater treatment plant [20]. The Monte Carlo simulation was also applied to the solution of the population balance equations, and the accuracy and the optimal sampling in Monte Carlo solutions of the equations have been discussed [21]. A multilevel Monte Carlo method was proposed to estimate the uncertainty in pore-scale and digital rock physics problems [22].…”

Representing spray zone with cross flow as a well-mixed compartment in a high shear granulator

“…There is no mesoscopic model to link microscopic models and macroscopic models (e.g. Population Balance Model [18], [19]) in describing granulation rates, such as nucleation, in a spray zone. The significance of developing mesoscopic models has been addressed by Michaels [20] in particulate systems.…”