Understanding the Precipitated Calcium Carbonate Flocculation Mechanism Induced by Starch through Population Balance Modeling

2011 ◽  
Vol 236-238 ◽  
pp. 1250-1255
Author(s):  
Yi Zhou Sang ◽  
Nayef M. Al Saifi ◽  
Peter Englezos
Keyword(s):  
Calcium Carbonate ◽  
Population Balance ◽  
Energy Dissipation Rate ◽  
Balance Model ◽  
Collision Efficiency ◽  
Precipitated Calcium Carbonate ◽  
Population Balance Modeling ◽  
Flocculation Mechanism ◽  
Effects Of Temperature ◽  
Breakage Mechanism

The precipitated calcium carbonate (PCC) flocculation kinetics and floc structures induced by cationic tapioca starch were recorded by the Malvern Mastersizer 2000 (Malvern Instruments Inc, Malvern, UK). Of particular interest, a population balance model for PCC flocculation was employed to extract the flocculation constants, namely collision efficiency, magnitude of energy dissipation rate and restructuring rate. The model made an attempt to take aggregation, breakage and flocs restructuring into account simultaneously to describe the PCC flocculation by aggregation and breakage mechanism. Through a response surface methodology (RSM) involving a central composite design, the effects of temperature, polymer dosage, ionic strength, and shear rate on flocculation parameters were investigated in this paper.

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 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.

scholarly journals Understanding the coagulation mechanism and floc properties induced by Fe(VI) and FeCl3: population balance modeling

2021 ◽  
Author(s):  
Xinliang Liu ◽  
Hailiang Yin ◽  
Jian Zhao ◽  
Ziqi Guo ◽  
Zhen Liu ◽  
...  
Keyword(s):  
Practical Importance ◽  
Population Balance ◽  
Collision Efficiency ◽  
Population Balance Modeling ◽  
Floc Size ◽  
Coagulation Mechanism ◽  
Coagulation Kinetics ◽  
Floc Strength ◽  
Floc Properties ◽  
Positive Effect

Abstract Coagulation kinetics and floc properties are of great fundamental and practical importance in the field of water treatment. To investigate the performance of Fe(VI) and Fe(III) salt on particle coagulation, Malvern Mastersizer 2000 was employed to continuously and simultaneously monitor the kaolin floc size and structure change, and population balance modeling was used to investigate the coagulation mechanism. The results show dosage increase had positive effect on collision efficiency and floc strength and negative effect on restructure rate. Low shear rate resulted in higher collision efficiency and stronger floc. Low water temperature had a pronounced detrimental effect on coagulation kinetics. Temperature increase showed the most significant positive effect on collision efficiency, floc strength and restructure rate. The optimum pH zone for the coagulation was found to be between 6 and 8. Further pH increase lowered the collision efficiency and floc strength and increased the restructure rate. FeCl3 resulted in a larger ratio of the mass to volume of kaolin flocs (compactness) than those induced by ferrate.

scholarly journals Population balance modeling for air–water bubbly flow in a vertical U-bend

2018 ◽  
Vol 10 (4) ◽  
pp. 170-177
Author(s):  
Yichuan Huang ◽  
Hongye Zhu ◽  
Xingtuan Yang ◽  
Jiyuan Tu ◽  
Shengyao Jiang
Keyword(s):  
Tube Wall ◽  
Bubbly Flow ◽  
Population Balance ◽  
Superficial Velocity ◽  
Balance Model ◽  
Outer Side ◽  
Group Model ◽  
Population Balance Modeling ◽  
Buoyant Force ◽  
High Heat Transfer

Bubbly flow in U-bend is widely encountered in two-phase flow systems because of its compactness and high heat transfer coefficient. The modeling of phase distributions, velocity fields, and interfacial area concentration in the U-bend is crucial for the analysis of mass, momentum, and energy transportation processes in the equipment. However, this subject has not received enough attention yet. In this paper, the combination of population balance model and two-fluid model was used in the simulation of air–water bubbly flow in a U-bend with 24 mm inner diameter and 96 mm curvature. The homogeneous multiple size group model was used to solve the population balance equation and reconstruct the bubble size distribution function. The phase distribution at 0°, 90°, and 180° was predicted and the results showed that the superficial velocities of gas and liquid phase were the control parameters. Under higher gas superficial velocity, the buoyant force is dominant and makes the bubbles concentrate on the outer side of the tube wall; while under lower gas superficial velocity, the centrifugal force is dominant and makes the bubbles concentrate on the inner side of the tube wall. These results met well with the experimental results of Usui.

scholarly journals Population Balance Modeling and Opinion Dynamics—A Mutually Beneficial Liaison?

Processes ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 164 ◽  
Author(s):  
Michael Kuhn ◽  
Christoph Kirse ◽  
Heiko Briesen
Keyword(s):  
Opinion Dynamics ◽  
Population Balance ◽  
Initial Distribution ◽  
Balance Model ◽  
Order Moment ◽  
Liquid Droplets ◽  
Population Balance Modeling ◽  
The One ◽  
New Formulation ◽  
Dynamics Problems

In this contribution, we aim to show that opinion dynamics and population balance modeling can benefit from an exchange of problems and methods. To support this claim, the Deffuant-Weisbuch model, a classical approach in opinion dynamics, is formulated as a population balance model. This new formulation is subsequently analyzed in terms of moment equations, and conservation of the first and second order moment is shown. Exemplary results obtained by our formulation are presented and agreement with the original model is found. In addition, the influence of the initial distribution is studied. Subsequently, the Deffuant-Weisbuch model is transferred to engineering and interpreted as mass transfer between liquid droplets which results in a more flexible formulation compared to alternatives from the literature. On the one hand, it is concluded that the transfer of opinion-dynamics problems to the domain of population balance modeling offers some interesting insights as well as stimulating challenges for the population-balance community. On the other hand, it is inferred that population-balance methods can contribute to the solution of problems in opinion dynamics. In a broad outlook, some further possibilities of how the two fields can possibly benefit from a close interaction are outlined.

scholarly journals Improving the Flocculation Performance of Clay-Based Tailings in Seawater: A Population Balance Modelling Approach

Minerals ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 782
Author(s):  
Gonzalo R. Quezada ◽  
Matías Jeldres ◽  
Pedro Robles ◽  
Norman Toro ◽  
David Torres ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Goodness Of Fit ◽  
Aggregate Size ◽  
Population Balance ◽  
Magnesium Content ◽  
Balance Model ◽  
Collision Efficiency ◽  
Reflectance Measurement ◽  
Vacuum Filtration ◽  
The Impact

A population balance model described the flocculation of clay-based mining tailings in treated seawater with reduced magnesium content. For the treatment, 0.06 M of lime was added to the liquor, generating solid magnesium complexes that were subsequently removed by vacuum filtration. Magnesium content varied between 10–1440 ppm when mixing raw seawater with treated seawater. The aggregate size was analysed by the Focused Beam Reflectance Measurement (FBRM) technology. The model follows the dynamics of the aggregation-rupture and it provides a good approximation to the temporal evolution. A decrease in collision efficiency was implemented as an indicator of the polymer depletion, describing the size reduction. Lower magnesium content makes larger aggregates with a higher fractal dimension, but an increase in the concentration of clays reduces both the size of aggregates and the fractal dimension, indicating more open and porous structures, with higher permeability to the passage of fluid. The model efficiently illustrates the experimental data, with R-square (R2) greater than 0.9 and Goodness of Fit (GoF) greater than 95% in most cases, wherein the fitting parameters allowed for analysing the impact of magnesium and clays on the collision efficiency, collision frequency, and fragmentation rate. The model is predictive with few parameters, and it is potentially a powerful tool for water management optimisation.

Modelling the Activated Sludge Flocculation Process Using Population Balance Model (PBM)

2012 ◽  
Vol 610-613 ◽  
pp. 1372-1376 ◽  
Author(s):  
Zhen Liang Li
Keyword(s):  
Activated Sludge ◽  
Population Balance ◽  
Balance Model ◽  
Efficiency Coefficient ◽  
Collision Efficiency ◽  
Mean Size ◽  
Shear Condition ◽  
Best Fit ◽  
Flocculation Process ◽  
Selection Of

This paper describes the application of population balance models to activated sludge flocculation process. It presents the development and selection of appropriate expressions for aggregation and breakage kinetics within the population balance framework to describe the evolution of mean size and steady state distribution of flocs under shear conditions. A size and velocity gradient dependent collision efficiency is introduced into the aggregation expression. In the model, only 2 parameters need to be estimated: collision efficiency coefficient and the breakage frequency coefficient. They are obtained by the “best fit” with the experimental data, and keep unchanged under different shear condition for the same flocs. The modelling results indicate that the population balance models coupled with suitable aggregation and breakage kinetics is appropriate for describing activated sludge flocculation dynamics.

scholarly journals Population Balance Modeling and Opinion Dynamics -- A Mutually Beneficial Liaison?

2018 ◽  
Author(s):  
Michael Kuhn ◽  
Christoph Kirse ◽  
Heiko Briesen
Keyword(s):  
Opinion Dynamics ◽  
Population Balance ◽  
Initial Distribution ◽  
Balance Model ◽  
Order Moment ◽  
Liquid Droplets ◽  
Population Balance Modeling ◽  
The One ◽  
New Formulation ◽  
Dynamics Problems

In this contribution, we aim to show that opinion dynamics and population balance modeling can benefit from an exchange of problems and methods. To support this claim, the Deffuant-Weisbuch model, a classical approach in opinion dynamics, is formulated as a population balance model. This new formulation is subsequently analyzed in terms of moment equations, and conservation of the first and second order moment is shown. Exemplary results obtained by our formulation are presented and agreement with the original model is found. Also the influence of the initial distribution is studied. Additionally, the Deffuant-Weisbuch model is transferred to engineering and interpreted as mass transfer between liquid droplets which results in a more flexible formulation compared to alternatives from the literature. On the one hand, it is concluded that the transfer of opinion-dynamics problems to the domain of population balance modeling offers some interesting insights as well as stimulating challenges for the population-balance community. On the other hand, it is inferred that population-balance methods can contribute to the solution of problems in opinion dynamics. In a broad outlook, some further possibilities of how the two fields can possibly benefit from a close interaction are outlined.

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