Mathematical models of the column flotation process a review

Tuteja, Ravinder; Spottiswood, D.J.; Misra, V. N.

doi:10.1016/0892-6875(94)90038-8

Cited by 25 publications

(4 citation statements)

References 5 publications

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“…As soon as the surface load of the bubbles reaches the saturation value, the balance of mass transfer at the gas-liquid interface indicates that the interfacial exchange is zero. Thus, the interfacial mass balance indicates that the particle attachment is balanced by detachments: (9) where C * bS = k a /k d C 0 C mb (mass per unit surface) defines the surface load of the bubbles at saturation. The superficial concentration of the bubbles at saturation is marked ( * ) because, when reached in a bubble column, it also corresponds to the concentration at the gas outlet (x = L).…”

Section: A Kinetic Model Applied To a Flotation Columnmentioning

confidence: 99%

“…Many models have been developed in order to determine the factors involved in the modeling of the constant of flotation kinetics and excellent reviews have been produced, establishing the state-of-the-art in this domain [9,10]. These studies show that there is a variety of kinetic models used for flotation; but when confronted with the experiments, the disparity in their results may indicate that the mechanisms involved in flotation phenomena are too complex to be described by relatively simple formulations.…”

Section: Kinetic Models For Flotationmentioning

confidence: 99%

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Gas‐Liquid Mass Transfer Approach applied to the Modeling of Flotation in a Bubble Column

Chahed

M'Rabet

2008

Chem Eng & Technol

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A kinetic model developed to describe flotation in a bubble column is presented. This model, developed on the basis of the theory of mass transfer in gas-liquid flows, makes explicit in its formulation the effect of the superficial saturation of bubbles on the kinetics of flotation. The model is applied to the simulation of flotation column experiments for which the classical first-order models, commonly used in flotation modeling, are insufficient to represent the flotation kinetics. The results of the simulations obtained under different hypotheses of simplification and compared to experimental data show that the model succeeds in representing the flotation kinetics in these cases.

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Section: A Kinetic Model Applied To a Flotation Columnmentioning

confidence: 99%

Section: Kinetic Models For Flotationmentioning

confidence: 99%

Gas‐Liquid Mass Transfer Approach applied to the Modeling of Flotation in a Bubble Column

Chahed

M'Rabet

2008

Chem Eng & Technol

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“…It has been extensively studied since the middle of last century. Various types of models concerning both the dynamics of flotation process and the sub-processes of flotation have been proposed, e.g., flotation rate model [5], mass balance model [6], attachment time model [7], etc. A static simulation of characteristic parameters (suspended minerals, mineralized froth) based on the mass balance equation was proposed to predict the concentrate grade and flotation recovery rate [8].…”

Section: Introductionmentioning

confidence: 99%

Moving Horizon Estimation of Sulfur Concentrate Grade Based on Kinetic Models Under Multiple Working Conditions

Sun

Zhou

et al. 2020

IEEE Access

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This paper proposed a moving horizon approach to predict sulfur concentrate grade in a sulfur flotation process. In this approach, the grade prediction problem is formulated as a moving horizon estimation problem. To build the nominal model for the estimation, the kinetic of sulfur flotation process are firstly studied. The unknown variable in the kinetic model, i.e., the flux of overflow, is obtained using machine vision technology. Moreover, to account for the multi-modal characteristic of sulfur flotation process, the kinetic model parameters are identified for different working conditions. To eliminate the effect of , a robust parameter identification approach is adopted. Finally, the kinetic model is embedded in the moving horizon estimation framework, which reconstructs the concentrate grade using from online measured process variables. Experimental results demonstrate the feasibility and efficient of the proposed method.INDEX TERMS moving horizon estimation, kinetic modeling, parameter identification, mineral processing

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“…These models try to connect the hydrodynamic process conditions (interfacial area of bubbles, bubble size distribution, and particle size distribution) to mineral recovery and provide an improvement to the theoretical understanding of column flotation. [13][14][15][16][17][18] Some of these models can be classified as micro-scale models, [19,20] implying that they were developed to estimate design parameters for a column flotation system, such as particle velocity [21] and gas dispersion, [22,23] and not for use in process control.…”

mentioning

confidence: 99%

Modelling and boundary optimal control design of hybrid column flotation

2021

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A three-phase continuous hybrid flotation column that seeks to obtain the benefits of both mechanical cells and flotation columns is modelled as the interconnection of a CSTR representing the well-mixed zone and two plugflow reactors (PFR) representing pulp and froth zones. The plant model accounts for the micro-scale processes such as bubble-particle collision and attachment and the appearance and breakage of bubbles. This complex distributed parameter system (DPS) is described by sets of nonlinear coupled conservation counter-current hyperbolic partial differential equations (PDEs) and one set of ordinary differential equations (ODEs). The dynamic conservation law-based model for the continuous hybrid flotation column including wellstirred, pulp (bubbly), and froth zones, is utilized in an optimal model-based controller design. This linear quadratic regulator (LQR)-based controller accounts for optimality, stability, and performance. The controller design utilizes a linear model obtained by linearization at operating steady states of interest. A full-state optimal feedback control law is designed and controller performance has been demonstrated through a numerical simulation of physically meaningful and relevant plant operating conditions. The LQR-based optimal controller outperforms proportional-integral (PI)-based control by more than an order of magnitude in terms of a return to steady state after a perturbation in the initial condition.

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Mathematical models of the column flotation process a review

Cited by 25 publications

References 5 publications

Gas‐Liquid Mass Transfer Approach applied to the Modeling of Flotation in a Bubble Column

Gas‐Liquid Mass Transfer Approach applied to the Modeling of Flotation in a Bubble Column

Moving Horizon Estimation of Sulfur Concentrate Grade Based on Kinetic Models Under Multiple Working Conditions

Modelling and boundary optimal control design of hybrid column flotation

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