Simulating product size distribution of an industrial scale VertiMill® using a time-based population balance model

2018 ◽  
Vol 127 ◽  
pp. 312-317 ◽  
Author(s):  
Maruf Hasan ◽  
Sam Palaniandy ◽  
Marko Hilden ◽  
Malcolm Powell
Keyword(s):  
Size Distribution ◽  
Population Balance ◽  
Industrial Scale ◽  
Balance Model ◽  
Population Balance Model ◽  
Product Size

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

Minerals ◽  
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.

Modeling of the formation kinetics and size distribution evolution of II–VI quantum dots

2017 ◽  
Vol 2 (4) ◽  
pp. 567-576 ◽  
Author(s):  
Stefano Lazzari ◽  
Milad Abolhasani ◽  
Klavs F. Jensen
Keyword(s):  
Quantum Dots ◽  
Size Distribution ◽  
Semiconductor Nanocrystals ◽  
Population Balance ◽  
Nanocrystal Size ◽  
Balance Model ◽  
Population Balance Model ◽  
Formation Kinetics

A population balance model describes the formation of II–VI semiconductor nanocrystals and predicts experimentally observed properties of the nanocrystal size distribution.

scholarly journals A numerical study on the estimation of the stable size distribution for a cell population balance model

2018 ◽  
Vol 41 (8) ◽  
pp. 2894-2905 ◽  
Author(s):  
Luis M. Abia ◽  
Óscar Angulo ◽  
Juan Carlos López-Marcos ◽  
Miguel Ángel López-Marcos
Keyword(s):  
Size Distribution ◽  
Cell Population ◽  
Numerical Study ◽  
Population Balance ◽  
Balance Model ◽  
Population Balance Model ◽  
A Cell ◽  
Stable Size Distribution

scholarly journals Simulation of Floc Size Distribution in Flocculation of Activated Sludge Using Population Balance Model with Modified Expressions for the Aggregation and Breakage

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Zhenliang Li ◽  
Peili Lu ◽  
Daijun Zhang ◽  
Fuzhong Song
Keyword(s):  
Activated Sludge ◽  
Size Distribution ◽  
Velocity Gradient ◽  
Population Balance ◽  
Balance Model ◽  
Population Balance Model ◽  
Collision Efficiency ◽  
Volume Percentage ◽  
Floc Size ◽  
Breakage Rate

The floc size distribution of activated sludge was simulated successfully by population balance model in the previous study (Population Balance Model and Calibration Method for Simulating the Time Evolution of Floc Size Distribution of Activated Sludge Flocculation. Desalination and Water Treatment, 67, 41-50). However, nonignorable errors exist in the simulation for the volume percentage of large flocs. This paper describes the application of a modified population balance model in the simulation of the time evolution of floc size distribution in activated sludge flocculation process under shear-induced conditions. It was found that the application of modified size dependent collision efficiency, modified breakage rate expression by assuming a maximum value, and binominal daughter-particles distribution function could improve the population balance model for activated sludge flocculation and successfully predict the dynamic changes in volume percentage distribution and mean floc size of activated sludge under different shear conditions. The results demonstrate that the maximum breakage rate was independent on the velocity gradient, and both the collision efficiency and breakage rate coefficient show a power-law relationship with the average velocity gradient; the former decreases while the latter increases with the rise of the average velocity gradient. These findings would help to understand the dynamics of activated sludge flocculation.

scholarly journals Dynamic simulation of industrial-scale gibbsite crystallization circuit

2021 ◽  
Vol 247 ◽  
pp. 88-101
Author(s):  
Vladimir Golubev ◽  
Tatyana Litvinova
Keyword(s):  
Aluminum Hydroxide ◽  
Population Balance ◽  
Industrial Scale ◽  
Balance Model ◽  
Population Balance Model ◽  
Precipitation Process ◽  
Oscillatory Process ◽  
Quality Of Control ◽  
Cyclic Changes

Population balance model is crucial for improving the method of aluminum hydroxide massive crystallization and enhancing the quality of control over industrial precipitation trains. This paper presents the updated population balance model, which can be used for simulation of industrial-scale precipitation. Processes of birth-and-spread and particle breakage are considered integral parts of the precipitation process along with secondary nucleation, growth and agglomeration of particles. The conceptual difference of the proposed system of equations is its ability to reproduce the oscillatory process that occurs in precipitation circuits as a result of cyclic changes in the quality of the seed surface. It is demonstrated that self-oscillations can occur in the system without any external influence. The updated model is adjusted and verified using historical industrial data. The simulation of seed-recycle precipitation circuit showed an exact correspondence between the calculated dynamic pattern of changes in particle size distribution of aluminum hydroxide and the actual data.

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