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

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.

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

Mathematical Problems in Engineering ◽

10.1155/2019/5243860 ◽

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.

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Solving the inverse problem for aggregation in activated sludge flocculation using a population balance framework

Water Science & Technology ◽

10.2166/wst.2007.589 ◽

2007 ◽

Vol 56 (6) ◽

pp. 95-103 ◽

Cited By ~ 5

Author(s):

I. Nopens ◽

N. Nere ◽

P.A. Vanrolleghem ◽

D. Ramkrishna

Keyword(s):

Experimental Data ◽

Inverse Problem ◽

Particle Size ◽

Activated Sludge ◽

Predictive Power ◽

Population Balance ◽

Model Structure ◽

Forward Simulation ◽

Floc Size

Many systems contain populations of individuals. Often, they are regarded as a lumped phase, which might, for some applications, lead to inadequate model predictive power. An alternative framework, Population Balance Models, has been used here to describe such a system, activated sludge flocculation in which particle size is the property one wants to model. An important problem to solve in population balance modelling is to determine the model structure that adequately describes experimentally obtained data on for instance, the time evolution of the floc size distribution. In this contribution, an alternative method based on solving the inverse problem is used to recover the model structure from the data. In this respect, the presence of similarity in the data simplifies the problem significantly. Similarity was found and the inverse problem could be solved. A forward simulation then confirmed the quality of the model structure to describe the experimental data.

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

MRS Proceedings ◽

10.1557/proc-752-aa14.5 ◽

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.

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Numerical Modelling of Dispersed Water in Oil Flows Using Eulerian-Eulerian Approach and Population Balance Model

Processes ◽

10.3390/pr9081345 ◽

2021 ◽

Vol 9 (8) ◽

pp. 1345

Author(s):

Hassan Pouraria ◽

Ki-Heum Park ◽

Yutaek Seo

Keyword(s):

Experimental Data ◽

Volume Fraction ◽

Population Balance ◽

Numerical Results ◽

Turbulent Dispersion ◽

Balance Model ◽

Population Balance Model ◽

Water Volume ◽

Horizontal Pipe ◽

Eulerian Approach

Formation of a dispersed oil—water flow pattern is a common occurrence in flow lines and pipelines. The capability of predicting the size of droplets, as well as the distribution of dispersed phase volume fraction is of utmost importance for proper design of such systems. The present study aims at modelling dispersed water in oil flows in a horizontal pipe by employing a multi-fluid Eulerian approach along with the population balance model. To this end, momentum and continuity equations are solved for oil and water phases, and the coupling between the phases is achieved by considering the drag, lift, turbulent dispersion, and virtual mass forces. Turbulent effects are modelled by employing the standard k-ε model. Furthermore, a population balance model, based on the method of class, along with the breakup and coalescence kernels is adopted for modelling the droplet size distribution. The obtained numerical results are compared to the experimental data in literature for either the in situ Sauter mean diameter or water volume fraction. A comparison among the obtained numerical results and the published experimental data shows a reasonable agreement.

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A Population Balance Model for Shear-Induced Polymer-Bridging Flocculation of Total Tailings

Minerals ◽

10.3390/min12010040 ◽

2021 ◽

Vol 12 (1) ◽

pp. 40

Author(s):

Zhuen Ruan ◽

Aixiang Wu ◽

Raimund Bürger ◽

Fernando Betancourt ◽

Rafael Ordoñez ◽

...

Keyword(s):

Population Balance ◽

Particle Collision ◽

Balance Model ◽

Population Balance Model ◽

Frequency Model ◽

Floc Size ◽

Bridging Flocculation ◽

Polymer Bridging ◽

The Difference ◽

Fitting Parameters

Shear-induced polymer-bridging flocculation is widely used in the solid–liquid separation process in cemented paste backfill, beneficial to water recycling and tailings management in metal mines. A flocculation kinetics model based on Population Balance Model (PBM) is proposed to model the polymer-bridging flocculation process of total tailings. The PBM leads to a system of ordinary differential equations describing the evolution of the size distribution, and incorporates an aggregation kernel and a breakage kernel. In the aggregation kernel, a collision frequency model describes the particle collision under the combined effects of Brownian motions, shear flow, and differential sedimentation. A semi-empirical collision efficiency model with three fitting parameters is applied. In the breakage kernel, a new breakage rate coefficient model with another three fitting parameters is introduced. Values of the six fitting parameters are determined by minimizing the difference between experimental data obtained from FBRM and modeling result through particle swarm global optimization. All of the six fitting parameters vary with flocculation conditions. The six fitting parameters are regressed with the flocculation factors with six regression models obtained. The validation modeling demonstrates that the proposed PBM quantifies well the dynamic evolution of the floc size during flocculation under the given experimental setup. The investigation will provide significant new insights into the flocculation kinetics of total tailings and lay a foundation for studying the performance of the feedwell of a gravity thickener.

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