Population Balance Models for Pharmaceutical Processes

2016 ◽  
pp. 43-83 ◽  
Author(s):  
Anwesha Chaudhury ◽  
Maitraye Sen ◽  
Dana Barrasso ◽  
Rohit Ramachandran
Keyword(s):  
Population Balance ◽  
Pharmaceutical Processes

scholarly journals An Analysis of Uncertainty Propagation Methods Applied to Breakage Population Balance

Processes ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 255 ◽  
Author(s):  
Satyajeet Bhonsale ◽  
Dries Telen ◽  
Bard Stokbroekx ◽  
Jan Van Impe
Keyword(s):  
Experimental Data ◽  
Polynomial Chaos ◽  
Uncertainty Propagation ◽  
Population Balance ◽  
Balance Model ◽  
Model Parameters ◽  
Sigma Point ◽  
Propagation Methods ◽  
The Given ◽  
Pharmaceutical Processes

In data-driven empirical or hybrid modeling, the experimental data influences the model parameters and thus also the model predictions. The experimental data has some variability due to measurement noise and due to the intrinsic stochastic nature of certain pharmaceutical processes such as aggregation or breakage. To use predictive models, it is imperative that the accuracy of the predictions is known. To this extent, various uncertainty propagation techniques applied to a predictive breakage population balance model are studied. Three uncertainty propagation techniques are studied: linearization, sigma point, and polynomial chaos. These are compared to the uncertainty obtained from Monte Carlo simulations. Linearization performs the worst in the given scenario, while sigma point and polynomial chaos methods have similar performance in terms of accuracy.

A One-Dimensional Combined Multifluid-Population Balance Model for the Simulation of Batch Bubble Columns

2021 ◽  
Author(s):  
Ferdinand Breit ◽  
Adam Mühlbauer ◽  
Erik von Harbou ◽  
Mark W. Hlawitschka ◽  
Hans-Jörg Bart
Keyword(s):  
Population Balance ◽  
Bubble Columns ◽  
Balance Model ◽  
Population Balance Model ◽  
One Dimensional

scholarly journals Special Issue on “Recent Advances in Population Balance Modeling”

Processes ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 122
Author(s):  
Seyed Soheil Mansouri ◽  
Heiko Briesen ◽  
Krist V. Gernaey ◽  
Ingmar Nopens
Keyword(s):  
Population Balance ◽  
Special Issue ◽  
Modeling Framework ◽  
Population Balance Modeling ◽  
Recent Advances

Population Balance Modeling (PBM) is a powerful modeling framework that allows the prediction of the dynamics of distributed properties of a population of individuals at the mesoscale [...]

scholarly journals Population Balance Application in TiO2 Particle Deagglomeration Process Modeling

Energies ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3523
Author(s):  
Radosław Krzosa ◽  
Łukasz Makowski ◽  
Wojciech Orciuch ◽  
Radosław Adamek
Keyword(s):  
Particle Size ◽  
Titanium Dioxide ◽  
Mechanistic Model ◽  
Population Balance ◽  
Tio2 Particle ◽  
Application Process ◽  
Titanium Dioxide Powder ◽  
Dioxide Powder ◽  
Computational Fluid Dynamics Cfd ◽  
Hydrodynamic Stresses

The deagglomeration of titanium-dioxide powder in water suspension performed in a stirring tank was investigated. Owing to the widespread applications of the deagglomeration process and titanium dioxide powder, new, more efficient devices and methods of predicting the process result are highly needed. A brief literature review of the application process, the device used, and process mechanism is presented herein. In the experiments, deagglomeration of the titanium dioxide suspension was performed. The change in particle size distribution in time was investigated for different impeller geometries and rotational speeds. The modification of impeller geometry allowed the improvement of the process of solid particle breakage. In the modelling part, numerical simulations of the chosen impeller geometries were performed using computational-fluid-dynamics (CFD) methods whereby the flow field, hydrodynamic stresses, and other useful parameters were calculated. Finally, based on the simulation results, the population-balance with a mechanistic model of suspension flow was developed. Model predictions of the change in particle size showed good agreement with the experimental data. Using the presented method in the process design allowed the prediction of the product size and the comparison of the efficiency of different impeller geometries.

scholarly journals Study on the regional characteristics during foam flooding by population balance model

2020 ◽  
pp. 014459872098361
Author(s):  
Zhongbao Wu ◽  
Qingjun Du ◽  
Bei Wei ◽  
Jian Hou
Keyword(s):  
Numerical Simulation ◽  
Simulation Model ◽  
Oil Recovery ◽  
Population Balance ◽  
Growth Zone ◽  
Balance Model ◽  
Population Balance Model ◽  
Liquid Ratio ◽  
One Dimensional ◽  
Foam Flooding

Foam flooding is an effective method for enhancing oil recovery in high water-cut reservoirs and unconventional reservoirs. It is a dynamic process that includes foam generation and coalescence when foam flows through porous media. In this study, a foam flooding simulation model was established based on the population balance model. The stabilizing effect of the polymer and the coalescence characteristics when foam encounters oil were considered. The numerical simulation model was fitted and verified through a one-dimensional displacement experiment. The pressure difference across the sand pack in single foam flooding and polymer-enhanced foam flooding both agree well with the simulation results. Based on the numerical simulation, the foam distribution characteristics in different cases were studied. The results show that there are three zones during foam flooding: the foam growth zone, stable zone, and decay zone. These characteristics are mainly influenced by the adsorption of surfactant, the gas–liquid ratio, the injection rate, and the injection scheme. The oil recovery of polymer-enhanced foam flooding is estimated to be 5.85% more than that of single foam flooding. Moreover, the growth zone and decay zone in three dimensions are considerably wider than in the one-dimensional model. In addition, the slug volume influences the oil recovery the most in the foam enhanced foam flooding, followed by the oil viscosity and gas-liquid ratio. The established model can describe the dynamic change process of foam, and can thus track the foam distribution underground and aid in optimization of the injection strategies during foam flooding.

scholarly journals Analytical time-stepping solution of the discretized population balance equation

2020 ◽  
Vol 135 ◽  
pp. 106741
Author(s):  
Mohamed Ali Jama ◽  
Wenli Zhao ◽  
Waqar Ahmad ◽  
Antonio Buffo ◽  
Ville Alopaeus
Keyword(s):  
Balance Equation ◽  
Population Balance ◽  
Population Balance Equation ◽  
Time Stepping ◽  
Analytical Time
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