Strategy for Validating a Population Balance Model of a Batch Crystallization Process Using Particle Size Distribution from Image-based Sensor

Particle size distribution and number of ice crystals have a great influence on the flow and heat transfer performance of ice slurry. A population balance model (PBM) containing population and mass balances has been built to simulate numerically the development of ice particle size distribution during adiabatic ice slurry storage. The model assumes a homogeneously mixed and long-term storage tank in which the effect of breakage and aggregation between ice crystals was considered. For solving the population balance equations (PBEs) in the PBM, a semi-discrete finite volume scheme was applied. Finally, the effect of breakage and aggregation on development of ice particle size distribution was analyzed respectively. The results show that both breakage and aggregation are the two important effects on the particle size distribution and evolution of ice particle during storage, but they have opposite effect on the development of ice crystal size. In storage, breakage and aggregation have almost equivalent effect in the initial phase, but aggregation has dominant effect at last. The PBM results are in good agreement with experimental results by Pronk et al. [Effect of long-term ice slurry storage on crystal size distribution, 5th Workshop on Ice Slurries of the IIR (2002), pp. 151–160]. Therefore, the PBM presented in this paper is able to predict the development of particle size distribution during ice slurry storage.

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Milling Studies in an Impact Crusher I: Kinetics Modelling Based on Population Balance Modelling

Minerals ◽

10.3390/min11050470 ◽

2021 ◽

Vol 11 (5) ◽

pp. 470

Author(s):

Ngonidzashe Chimwani ◽

Murray M. Bwalya

Keyword(s):

Particle Size ◽

Size Distribution ◽

Population Balance ◽

Impeller Speed ◽

Balance Model ◽

Population Balance Model ◽

Particle Sizes ◽

Product Size ◽

Kinetics Modelling ◽

Vertical Impact

A number of experiments were conducted on a laboratory batch impact crusher to investigate the effects of particle size and impeller speed on grinding rate and product size distribution. The experiments involved feeding a fixed mass of particles through a funnel into the crusher up to four times, and monitoring the grinding achieved with each pass. The duration of each pass was approximately 20 s; thus, this amounted to a total time of 1 min and 20 s of grinding for four passes. The population balance model (PBM) was then used to describe the breakage process, and its effectiveness as a tool for describing the breakage process in the vertical impact crusher is assessed. It was observed that low impeller speeds require longer crushing time to break the particles significantly whilst for higher speeds, longer crushing time is not desirable as grinding rate sharply decreases as the crushing time increases, hence the process becomes inefficient. Results also showed that larger particle sizes require shorter breakage time whilst smaller feed particles require longer breakage time.

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Advantages of Utilizing Population Balance Modeling of Crystallization Processes for Particle Size Distribution Prediction of an Active Pharmaceutical Ingredient

Processes ◽

10.3390/pr7060355 ◽

2019 ◽

Vol 7 (6) ◽

pp. 355

Author(s):

Tamar Rosenbaum ◽

Li Tan ◽

Joshua Engstrom

Keyword(s):

Particle Size ◽

Particle Size Distribution ◽

Size Distribution ◽

Process Parameters ◽

Crystallization Process ◽

Population Balance ◽

Active Pharmaceutical Ingredient ◽

Population Balance Modeling ◽

The Impact

Active pharmaceutical ingredient (API) particle size distribution is important for both downstream processing operations and in vivo performance. Crystallization process parameters and reactor configuration are important in controlling API particle size distribution (PSD). Given the large number of parameters and the scale-dependence of many parameters, it can be difficult to design a scalable crystallization process that delivers a target PSD. Population balance modeling is a useful tool for understanding crystallization kinetics, which are primarily scale-independent, predicting PSD, and studying the impact of process parameters on PSD. Although population balance modeling (PBM) does have certain limitations, such as scale dependency of secondary nucleation, and is currently limited in commercial software packages to one particle dimension, which has difficulty in predicting PSD for high aspect ratio morphologies, there is still much to be gained from applying PBM in API crystallization processes.

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