Lagrangian reconciliation of expeditious analyzes on microflotation of hematite and dolomite by carboxylates




Fuerstenau cell; Cottonseed oil; Quick analysis; Lagrange multipliers.


Microflotation campaign of a synthetic binary mixture of hematite and dolomite was carried out in order to evaluate the potential of saponified cottonseed oil as a collector. Hematite content was determined by expeditious methods, namely image analysis, pycnometry, and carbonate thermolysis by calcination. An algebraic reconciliation algorithm of redundant data (via Lagrange multipliers) was developed to treat the raw data from the different analytical techniques, aiming to increase the accuracy of the results, with the additional piece of information arising from product weighing, by introducing a dummy variable. At the stage of the study reported here, the physicochemical conditions for the selective flotation of hematite were not optimized; however, the results showed potential (both under acid and alkaline conditions) for the selective anionic flotation of the hematite/dolomite system. Prospective tests evaluating the analytical techniques employed showed pycnometry and calcination tended to be more reliable methods. Although the imaging method has shown promise, it still lacks some improvement in procedure for greater accuracy. The minimization of closure errors in mass balancing by using the mentioned optimization algorithm under constraints showed to be very relevant for the adequate evaluation of the separation process, using very small samples, as in the case of microflotation.

Author Biographies

Bruna de Oliveira Gomes, Universidade Federal de Ouro Preto

Technician in Industrial Chemistry (2011) from the Federal Center for Technological Education of Minas Gerais, graduated in Mining Engineering (2020) and master's degree in Mineral Engineering (2022) from the Federal University of Ouro Preto. She has experience in physical-chemical methods of ore concentration and has been conducting research on the use of natural inputs for the iron ore flotation process.

Fernanda Bento Sales, Universidade Federal de Ouro Preto

She is currently a student of the Mining Engineering course at the Federal University of Ouro Preto. She was a scientific initiation fellow in the project “Crambe oil in the flotation of oxidized minerals” and is currently a technological initiation fellow in the research “Ultrasound in flotation”.

Felipe de Orquiza Milhomem, Universidade Federal do Mato Grosso

He has a degree in Mining Engineering and Environment from the Federal University of Pará (2010) and master's degree (2013) and doctorate (2020) in Mineral Engineering from the Graduate Program in Mineral Engineering at the Federal University of Ouro Preto (2013). He served as a professor at the Federal Institute of Minas Gerais, Ouro Preto campus, where he taught the subjects Mineral Research, Mineral Technology and Environment (2012 to 2014) and the Federal Institute of Goiás — Goiânia Campus, teaching the subjects of Mining I, Mining II, Applied Informatics and Applied Informatics II. He is currently a professor in the Mining Engineering course at the Federal University of Mato Grosso.



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How to Cite

GOMES, B. de O. .; SALES, F. B. .; LUZ, J. A. M. da; MILHOMEM, F. de O. . Lagrangian reconciliation of expeditious analyzes on microflotation of hematite and dolomite by carboxylates. Research, Society and Development, [S. l.], v. 12, n. 1, p. e29912139831, 2023. DOI: 10.33448/rsd-v12i1.39831. Disponível em: Acesso em: 3 feb. 2023.