Particle Size Distribution and Population Balance

2001 ◽  
Author(s):  
A Mersmann
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Population Balance

POPULATION BALANCE MODEL OF ICE CRYSTALS SIZE DISTRIBUTION DURING ICE SLURRY STORAGE

2014 ◽  
Vol 22 (02) ◽  
pp. 1440001 ◽  
Author(s):  
AIXIANG XU ◽  
ZHIQIANG LIU ◽  
TENGLEI ZHAO ◽  
XIAOXIAO WANG
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Crystal Size ◽  
Population Balance ◽  
Ice Crystals ◽  
Balance Model ◽  
Ice Slurry ◽  
Slurry Storage

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.

scholarly journals Improvement of a 1D Population Balance Model for Twin-Screw Wet Granulation by Using Identifiability Analysis

Pharmaceutics ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 692
Author(s):  
Ana Alejandra Barrera Jiménez ◽  
Daan Van Hauwermeiren ◽  
Michiel Peeters ◽  
Thomas De Beer ◽  
Ingmar Nopens
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Population Balance ◽  
Wet Granulation ◽  
Process Conditions ◽  
Model Parameters ◽  
Modeling Tools ◽  
Identifiability Analysis ◽  
Twin Screw

Recently, the pharmaceutical industry has undergone changes in the production of solid oral dosages from traditional inefficient and expensive batch production to continuous manufacturing. The latest advancements include increased use of continuous twin-screw wet granulation and application of advanced modeling tools such as Population Balance Models (PBMs). However, improved understanding of the physical process within the granulator and improvement of current population balance models are necessary for the continuous production process to be successful in practice. In this study, an existing compartmental one-dimensional PBM of a twin-screw granulation process was improved by altering the original aggregation kernel in the wetting zone as a result of an identifiability analysis. In addition, a strategy was successfully applied to reduce the number of model parameters to be calibrated in both the wetting zone and kneading zones. It was found that the new aggregation kernel in the wetting zone is capable of reproducing the particle size distribution that is experimentally observed at different process conditions as well as different types of formulations, varying in hydrophilicity and API concentration. Finally, it was observed that model parameters could be linked not only to the material properties but also to the liquid to solid ratio, paving the way to create a generic PBM to predict the particle size distribution of a new formulation.

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

Processes ◽  
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.

scholarly journals Local Fixed Pivot Quadrature Method of Moments for Solution of Population Balance Equation

Processes ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 209 ◽  
Author(s):  
Junwei Su ◽  
Wang Le ◽  
Zhaolin Gu ◽  
Chungang Chen
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Method Of Moments ◽  
Balance Equation ◽  
Population Balance ◽  
New Method ◽  
Population Balance Equation ◽  
Test Cases ◽  
Quadrature Method

A local fixed pivot quadrature method of moments (LFPQMOM) is proposed for the solution of the population balance equation (PBE) for the aggregation and breakage process. First, the sectional representation for aggregation and breakage is presented. The continuous summation of the Dirac Delta function is adopted as the discrete form of the continuous particle size distribution in the local section as performed in short time Fourier transformation (STFT) and the moments in local sections are tracked successfully. Numerical simulation of benchmark test cases including aggregation, breakage, and aggregation breakage combined processes demonstrate that the new method could make good predictions for the moments along with particle size distribution without further assumption. The accuracy in the numerical results of the moments is comparable to or higher than the quadrature method of moment (QMOM) in most of the test cases. In theory, any number of moments can be tracked with the new method, but the computational expense can be relatively large due to many scalar equations that may be included.

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