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

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.

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Reducing the Magnesium Content from Seawater to Improve Tailing Flocculation: Description by Population Balance Models

Metals ◽

10.3390/met10030329 ◽

2020 ◽

Vol 10 (3) ◽

pp. 329

Author(s):

Gonzalo R. Quezada ◽

Matías Jeldres ◽

Norman Toro ◽

Pedro Robles ◽

Ricardo I. Jeldres

Keyword(s):

Fractal Dimension ◽

Population Balance ◽

Magnesium Content ◽

Reflectance Measurement ◽

Vacuum Filtration ◽

Irregular Structure ◽

Mean Size ◽

The Mean ◽

Magnesium Removal ◽

Suitable Environment

Experimental assays and mathematical models, through population balance models (PBM), were used to characterize the particle aggregation of mining tailings flocculated in seawater. Three systems were considered for preparation of the slurries: i) Seawater at natural pH (pH 7.4), ii) seawater at pH 11, and iii) treated seawater at pH 11. The treated seawater had a reduced magnesium content in order to avoid the formation of solid complexes, which damage the concentration operations. For this, the pH of seawater was raised with lime before being used in the process—generating solid precipitates of magnesium that were removed by vacuum filtration. The mean size of the aggregates were represented by the mean chord length obtained with the Focused beam reflectance measurement (FBRM) technique, and their descriptions, obtained by the PBM, showed an aggregation and a breakage kernel had evolved. The fractal dimension and permeability were included in the model in order to improve the representation of the irregular structure of the aggregates. Then, five parameters were optimized: Three for the aggregation kernel and two for the breakage kernel. The results show that raising the pH from 8 to 11 was severely detrimental to the flocculation performance. Nevertheless, for pH 11, the aggregates slightly exceeded 100 µm, causing undesirable behaviour during the thickening operations. Interestingly, magnesium removal provided a suitable environment to perform the tailings flocculation at alkaline pH, making aggregates with sizes that exceeded 300 µm. Only the fractal dimension changed between pH 8 and treated seawater at pH 11—as reflected in the permeability outcomes. The PBM fitted well with the experimental data, and the parameters showed that the aggregation kernel was dominant at all-polymer dosages. The descriptive capacity of the model might have been utilized as a support in practical decisions regarding the best-operating requirements in the flocculation of copper tailings and water clarification.

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Describing Mining Tailing Flocculation in Seawater by Population Balance Models: Effect of Mixing Intensity

Metals ◽

10.3390/met10020240 ◽

2020 ◽

Vol 10 (2) ◽

pp. 240

Author(s):

Gonzalo R. Quezada ◽

Luís Ayala ◽

Williams H. Leiva ◽

Norman Toro ◽

Pedro G. Toledo ◽

...

Keyword(s):

Fractal Dimension ◽

Aggregate Size ◽

Population Balance ◽

Cost Effective ◽

Time Dependent ◽

Balance Model ◽

Optimal Conditions ◽

Reflectance Measurement ◽

Correct Representation

A population balance model (PBM) is used to describe flocculation of particle tailings in seawater at pH 8 for a range of mixing intensities. The size of the aggregates is represented by the mean chord length, determined by the focused beam reflectance measurement (FBRM) technique. The PBM follows the dynamics of aggregation and breakage processes underlying flocculation and provides a good approximation to the temporal evolution of aggregate size. The structure of the aggregates during flocculation is described by a constant or time-dependent fractal dimension. The results revealed that the compensations between the aggregation and breakage rates lead to a correct representation of the flocculation kinetics of the tailings of particles in seawater and, in addition, that the representation of the flocculation kinetics in optimal conditions is equally good with a constant or variable fractal dimension. The aggregation and breakage functions and their corresponding parameters are sensitive to the choice of the fractal dimension of the aggregates, whether constant or time dependent, however, under optimal conditions, a constant fractal dimension is sufficient. The model is robust and predictive with a few parameters and can be used to find the optimal flocculation conditions at different mixing intensities, and the optimal flocculation time can be used for a cost-effective evaluation of the quality of the flocculant used.

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QMOM-based population balance model involving a fractal dimension for the flocculation of latex particles

Chemical Engineering Science ◽

10.1016/j.ces.2016.07.044 ◽

2016 ◽

Vol 155 ◽

pp. 65-82 ◽

Cited By ~ 7

Author(s):

Mélody Vlieghe ◽

Carole Coufort-Saudejaud ◽

Alain Liné ◽

Christine Frances

Keyword(s):

Fractal Dimension ◽

Population Balance ◽

Balance Model ◽

Population Balance Model ◽

Latex Particles

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Reducing Magnesium within Seawater Used in Mineral Processing to Improve Water Recovery and Rheological Properties When Dewatering Clay-Based Tailings

Polymers ◽

10.3390/polym14020339 ◽

2022 ◽

Vol 14 (2) ◽

pp. 339

Author(s):

Matías Jeldres ◽

Norman Toro ◽

Sandra Gallegos ◽

Pedro Robles ◽

Iván Salazar ◽

...

Keyword(s):

Yield Stress ◽

Aggregate Size ◽

Complete Removal ◽

Mineral Processing ◽

Water Recovery ◽

Concentrated Suspensions ◽

Reflectance Measurement ◽

Pre Treatment ◽

A Minor ◽

The Impact

In areas where access to water for mineral processing is limited, the direct use of seawater in processing has been considered as an alternative to the expense of its desalination. However, efficient flotation of copper sulfides from non-valuable phases is best achieved at a pH > 10.5, and raising the pH of seawater leads to magnesium precipitates that adversely affect subsequent tailings dewatering. Seawater pre-treatment with lime can precipitate the majority of magnesium present, with these solids then being removed by filtration. To understand how such treatment may aid tailings dewatering, treated seawater (TSw) was mixed with raw seawater (Rsw) at different ratios, analyzing the impact on the flocculated settling rate, aggregate size as measured by focused beam reflectance measurement (FBRM), and vane yield stress for two synthetic clay-based tailings. A higher proportion of Tsw (10 mg/L Mg2+) led to larger aggregates and higher settling rates at a fixed dosage, with FBRM suggesting that higher calcium concentrations in Tsw may also favor fines coagulation. The yield stress of concentrated suspensions formed after flocculation decreased with higher proportions of Tsw, a consequence of lower flocculant demand and the reduced presence of precipitates; while the latter is a minor phase by mass, their high impact on rheology reflects a small particle size. Reducing magnesium concentrations in seawater in advance of use in processing offers advantages in the water return from thickening and subsequent underflow transport. However, this may not require complete removal, with blending Tsw and Rsw an option to obtain acceptable industrial performance.

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

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.236-238.1250 ◽

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.

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

International Journal of Chemical Engineering ◽

10.1155/2016/8743105 ◽

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

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.610-613.1372 ◽

2012 ◽

Vol 610-613 ◽

pp. 1372-1376 ◽

Cited By ~ 2

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.

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Copper Tailing Flocculation in Seawater: Relating the Yield Stress with Fractal Aggregates at Varied Mixing Conditions

Metals ◽

10.3390/met9121295 ◽

2019 ◽

Vol 9 (12) ◽

pp. 1295 ◽

Cited By ~ 5

Author(s):

Matías Jeldres ◽

Eder C. Piceros ◽

Norman Toro ◽

David Torres ◽

Pedro Robles ◽

...

Keyword(s):

Fractal Dimension ◽

Rheological Properties ◽

Yield Stress ◽

Structural Changes ◽

Structural Characteristics ◽

Mixing Time ◽

Aggregate Size ◽

Mixing Rate ◽

Reflectance Measurement ◽

Mixing Intensity

The implications of physical conditions of the feedwell on the rheological properties of synthetic copper tailings, flocculated in seawater, were analysed. The mixing intensity of flocculation was related to the structural characteristics of the aggregates, and the outcomes were linked to the yield stress of the pulp sediments. Tailings settling assays were conducted by using a 30 mm turbine type stirrer with an in-situ aggregate size characterisation. The structural characteristics of the aggregates were determined by using the focused beam reflectance measurement (FBRM). After a mixing time between the pulp and the flocculant, the sample was allowed to settle for 2.5 h, where the variation of the sediment height was minimal. The sediment was gently removed and subjected to rheological characterisation. The yield stress was measured on an Anton Paar MCR 102 rheometer (ANAMIN Group, Santiago, Chile), with a vane-in-cup configuration. The mixing intensity was related to the characteristics of the aggregates, and the outcomes were linked to the yield stress of the flocculated pulp sediments. More aggressive hydrodynamics deteriorated the structure of the aggregates, promoting the reduction of both its size and the fractal dimension. This brought direct consequences on the rheological properties of the sediments: at higher mixing level, the yield stress was lower. The explanation lies in the structural changes of the aggregates, where at a fixed mixing rate, the yield stress presented a seemingly exponential increase over the fractal dimension. Additionally, correlations were found between the rheological properties with settling rate and aggregate size.

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Comparison of One Dimensional and Two Dimensional Population Balance Model for Optimization of a Crystallization Process

10.22541/au.161879969.99113470/v1 ◽

2021 ◽

Author(s):

Tamar Rosenbaum ◽

Victoria Mbachu ◽

Niall Mitchell ◽

John Gamble ◽

Patricia Cho ◽

...

Keyword(s):

Aspect Ratio ◽

Crystallization Process ◽

Population Balance ◽

Seed Morphology ◽

Balance Model ◽

Population Balance Model ◽

Two Dimensional ◽

Population Balance Modeling ◽

One Dimensional ◽

The Impact

In this work, the advantage of two-dimensional population balance modeling (2D PBM) for a needle-shaped API is highlighted by comparing the one-dimensional population balance model (1D PBM) developed for an antisolvent crystallization with the 2D PBM. The API utilized for this work had extremely slow desupersaturation, and was not able to achieve solubility concentration despite a ~50 h seed bed age. While the 1D PBM is useful in optimizing the crystallization process to enhance desupersaturation, it is unable to match the particle size quantiles well. 2D PBM was necessary to probe the impact of crystallization process parameters on particle aspect ratio (AR). Simulations utilizing the 2D PBM indicated that regardless of antisolvent addition rate or seed morphology, the final material would still be high aspect ratio. This knowledge saved the investment of much time and efforts in trying to minimize particle AR with changes in crystallization processing parameters alone.

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