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This paper describes the dynamic behavior in a flotation column from the development of a mathematical model of distributed parameters for the collection and the froth zone. For the solution of the mathematical model, the numerical method used was the finite element method. The proposed model includes sub-processes such as particle-bubble collection and detachment and bubble coalescence in the froth zone, among others. For the simulation, each zone of the flotation column is subdivided into volume elements, assuming each volume element is a perfectly mixed tank. The results show that the model adequately describes both the behavior of the collection zone and the froth zone, which are related to each other. During the validation of the mathematical model, satisfactory results were obtained when comparing the experimental data with those obtained through the simulation with low percentages of error (average error less than 5%).

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Piñeres J, Grecco A, Calvo M. Dynamic simulation of a flotation column. inycomp [Internet]. 2023 Sep. 8 [cited 2024 Nov. 22];25(Suplemento):e- 20913117. Available from: https://revistaingenieria.univalle.edu.co/index.php/ingenieria_y_competitividad/article/view/13117

Piñeres, J., Barraza, J. Effect of pH, air velocity and frother concentration on combustible recovery, ash and sulphur rejection using column flotation. Fuel Processing Technology, 2012, (97), 30-37. https://doi.org/10.1016/j.fuproc.2012.01.004 DOI: https://doi.org/10.1016/j.fuproc.2012.01.004

Piñeres , J., Barraza , J., Bellich, S. Effect of diesel oil and mixture of alcohol-glycol ether on Colombian ultrafine coal leaning using a test-rig loop flotation column. Ingeniería e investigación 2022, (42), (e88273).https://doi.org/10.15446/ing.investig.v42n1.88273 DOI: https://doi.org/10.15446/ing.investig.v42n1.88273

Carvalho, T., Durão, F., Fernandes, C. Dynamic characterization of column flotation process: Laboratory case study. Minerals Engineering, 1999, (12), 1339-1346. https://doi.org/10.1016/S0892-6875(99)00121-1 DOI: https://doi.org/10.1016/S0892-6875(99)00121-1

Cruz, E. A comprehensive dynamic model of the column flotation unit operation. Ph.D. Thesis, 1997, Department of mining and minerals engineering, Virginia Polytechnique Institute and State University, Blacksburg, Virginia. A Comprehensive Dynamic Model of the Column Flotation Unit Operation (vt.edu)

Bouchard, J., Desbiens, A., Del Villar, R., Nunez., E. Column flotation simulation and control: An overview. Minerals Engineering, 2009, (22), 519-529.https://doi.org/10.1016/j.mineng.2009.02.004 DOI: https://doi.org/10.1016/j.mineng.2009.02.004

Bouchard, J., Desbiens, A., del Villar, R. Column flotation simulation: A dynamic framework. Minerals Engineering, 2014, (55) 30–41. http://dx.doi.org/10.1016/j.mineng.2013.07.021 DOI: https://doi.org/10.1016/j.mineng.2013.07.021

Yahui, T., Maryam, A., Xiaoli, L., Fei, L., Stevan, D. Three-Phases Dynamic Modelling of Column Flotation Process. IFAC (International Federation of Automatic Control) PapersOnLine; 2018, (51), 99-104. https://doi.org/10.1016/j.ifacol.2018.09.399 DOI: https://doi.org/10.1016/j.ifacol.2018.09.399

Yianatos, J., Vallejos, P., Graub, R., Yañez, A. (2020). New approach for flotation process modelling and simulation, 2020, (156), 106482. https://doi.org/10.1016/j.mineng.2020.106482 DOI: https://doi.org/10.1016/j.mineng.2020.106482

Himmelblau, D., Bischoff, B. Process analysis and simulation. Chapter 4. 1968, John Wiley & Sons, New York.

Walas S, Modeling with differential equations in Chemical Engineering. 1991, Butterworth-Heinemann, Printed in the United State of America.

Dobby G., Finch J. Particle collection in columns, gas rate and bubble size effects. Canadian Metallurgical Quarterly, 1986, (25), 9-13. https://doi.org/10.1179/cmq.1986.25.1.9 DOI: https://doi.org/10.1179/000844386795430559

Dobby, G., Finch, J. Flotation column scale-up and modelling. CIM Bulletin, 1986, (79), 89-96. https://store.cim.org/en/flotation-column-scale-up-and-modelling

Finch, J. & Dobby, G. Column Flotation. 1990, Pergamon Press.

Patwardhan, A., Honaker, R. Development of a carrying-capacity model for column froth flotation. International Journal of Mineral Processing, 2000, (57), 275-293. https://doi.org/10.1016/S0301-7516(99)00081-2 DOI: https://doi.org/10.1016/S0301-7516(99)00081-2

Calvo, M., Grecco, A. Predicción del comportamiento dinámico de una columna de flotación a través de un modelo matemático, 2015, [Undergraduate thesis, Universidad del Atlántico, Barranquilla, Colombia]. http://biblioteca.uniatlantico.edu.co

Yianatos, J., Finch, J., Dobby, G., Manqui X. Bubble size estimation in bubble swarm. Journal of Colloid and Interface Science, 1988, (126), 37 – 44. https://doi.org/10.1016/0021-9797(88)90096-3 DOI: https://doi.org/10.1016/0021-9797(88)90096-3

Thomas, D. Transport characteristics of suspension: VIII. A note on the viscosity of Newtonian suspensions of uniform spherical particles. Journal of colloid and interface science, 1965, (20) 267 277. https://doi.org/10.1016/0095-8522(65)90016-4 DOI: https://doi.org/10.1016/0095-8522(65)90016-4

Received 2023-08-04
Accepted 2023-08-17
Published 2023-09-08