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.

Modelling the activated sludge flocculation process combining laser light diffraction particle sizing and population balance modelling (PBM)

2002 ◽  
Vol 45 (6) ◽  
pp. 41-49 ◽  
Author(s):  
I. Nopens ◽  
C.A. Biggs ◽  
B. De Clercq ◽  
R. Govoreanu ◽  
B.-M. Wilén ◽  
...  
Keyword(s):  
Experimental Data ◽  
Laser Light ◽  
Population Balance ◽  
Light Diffraction ◽  
Balance Model ◽  
Floc Size ◽  
Shear Rates ◽  
Breakage Rate ◽  
On Line ◽  
Floc Size Distributions

A technique based on laser light diffraction is shown to be successful in collecting on-line experimental data. Time series of floc size distributions (FSD) under different shear rates (G) and calcium additions were collected. The steady state mass mean diameter decreased with increasing shear rate G and increased when calcium additions exceeded 8 mg/l. A so-called population balance model (PBM) was used to describe the experimental data. This kind of model describes both aggregation and breakage through birth and death terms. A discretised PBM was used since analytical solutions of the integro-partial differential equations are non-existing. Despite the complexity of the model, only 2 parameters need to be estimated: the aggregation rate and the breakage rate. The model seems, however, to lack flexibility. Also, the description of the floc size distribution (FSD) in time is not accurate.

Flotation efficiency of activated sludge flocs using population balance model in dissolved air flotation

2006 ◽  
Vol 23 (2) ◽  
pp. 271-278 ◽  
Author(s):  
Heung-Joe Jung ◽  
Jae-Wook Lee ◽  
Do-Young Choi ◽  
Seong-Jin Kim ◽  
Dong-Heui Kwak
Keyword(s):  
Activated Sludge ◽  
Population Balance ◽  
Balance Model ◽  
Population Balance Model ◽  
Dissolved Air Flotation ◽  
Sludge Flocs ◽  
Air Flotation ◽  
Dissolved Air

Modelling Flocculated Cell Suspensions using a Population Balance Approach: Applications to Microfiltration

2002 ◽  
Vol 752 ◽  
Author(s):  
S. Ranil Wickramasinghe ◽  
Binbing Han ◽  
Saengchai Akeprathumchai ◽  
Xianghong Qian
Keyword(s):  
Distribution Function ◽  
Size Distribution ◽  
Volume Fraction ◽  
Particle Diameter ◽  
Population Balance ◽  
Balance Model ◽  
Floc Size ◽  
Balance Approach ◽  
Fragment Distribution ◽  
Log Normal

ABSTRACTExperimental results for flocculation of yeast and CHO cells using cationic polyelectrolytes are presented. These results suggest the existence of a self-similar floc size distribution. The experimentally determined floc size distributions have been modelled using a population balance approach. For flocculated yeast suspensions, the variation of the floc volume fraction with dimensionless particle diameter is predicted by the population balance model assuming a binary fragment distribution function. However, for CHO cell flocs, the floc volume fraction is predicted using a log normal fragment distribution function. Since the efficiency of unit operations such as microfiltration may be improved by flocculation of the feed suspension characterization of the particle size distribution is of great importance.

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 Comparison of the Accuracy and Performance of Different Numbers of Classes in Discretised Solution Method for Population Balance Model

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Zhenliang Li ◽  
Zhien Zhou ◽  
Sheng Zhang ◽  
Hongqiang Jiang
Keyword(s):  
Fibonacci Sequence ◽  
Population Balance ◽  
Balance Model ◽  
Population Balance Model ◽  
Collision Efficiency ◽  
Exponential Relationship ◽  
Parameter Ratio ◽  
And Performance ◽  
Number Of Classes ◽  
Geometric Grids

One way of solving population balance model (PBM) in a time efficient way is by means of discretisation of the population property of interest. A computational grid, for example, vi+1=kvi (vi is the volume of particle in class i), could be used to classify the particles in discretisation techniques. However, there are still disagreements in the appropriate number of classes divided by the grids. In this study, the different numbers of classes for solving PBM were compared in terms of accuracy and performance to describe the particle size distribution (PSD) from the flocculation of activated sludge. It is found that the simulated PSDs are similar to the experimental data for all the geometric grids (vi+1:vi≤2), and there is no obvious difference among the values of calibrated parameter, ratio of breakage rate coefficient and collision efficiency, for each velocity gradient. However, the simulation results with less error could be obtained with larger number of classes, and more computational times, which show exponential relationship with the number of classes, are needed. Considering numerical accuracy and efficiency, the classes 35 or a geometric grid with factor 1.6, aligning with the Fibonacci sequence (vi+vi-1≈vi+1), is recommended for the particles in the size range of 5.5~1086 μm.

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