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Kinetic separation curves based on process rate considerations

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
There are many graphical representations of separation results involving time as a crucial parameter determining the kinetics of a process. The graphical representations of results of separation are usually in the form of 2D plots relating two parameters which one of them is time. Time can also be utilized as a complex parameter such as a process rate. The plots involving time are called kinetic curves. Theoretically, the number of kinetic curves is infinite. The basic process kinetic curves, relating either yield (or recovery) and time can be modified to obtain numerous local and global efficiency curves. The global efficiency kinetic curves provide characteristic constants which do not change with the time and yield of a process. In this paper the local and global efficiency plots were created using experimental data which followed the so-called first order kinetics. It was shown that the integral 1st order kinetic equation provided the kinetic constant k which was numerically identical with the 1st order specific rate v, while their units were different (k, 1/min; v, %/(%·min). The global efficiency parameters plotted versus the maximum yield provided another type of plot, which can be called the limits kinetic curve. The limits kinetic curves are very useful for characterizing, quantification and classification of separation systems. The limits kinetic curves can be normalized providing one universal curve with a characteristic point, for instance, v50 indicating the specific rate (or kinetic) constant at the maximum recovery equal to 50%. The mathematical equation of the normalized limits kinetic curve was given in the paper.
Słowa kluczowe
Rocznik
Strony
983--995
Opis fizyczny
Bibliogr. 29 poz., rys., tab.
Twórcy
autor
  • Wroclaw University of Science and Technology, Faculty of Geoengineering, Mining and Geology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland
autor
  • Wroclaw University of Science and Technology, Faculty of Geoengineering, Mining and Geology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland
  • Wroclaw University of Science and Technology, Faculty of Geoengineering, Mining and Geology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland
  • NTNU Norwegian University of Science and Technology, Department of Geoscience and Petroleum, Sem Sælands veg 1, N-7491 Trondheim, Norway
Bibliografia
  • ARBITER, N., HARRIS, C.C., 1962. Flotation kinetics. In: Froth flotation: 50th anniversary volume. Fuerstenau D. (Ed.), American Institute of Mining, Metallurgical and Petroleum Engineers, New York.
  • BROZEK, M., MLYNARCZYKOWSKA, A., 2007. Analysis of kinetics models of batch flotation. Physicochem. Probl. Miner. Process., 41, 51-65.
  • BU, X. XIE, G, PENG, Y., GE, L., NI, C, 2017. Kinetics of flotation. Order of process, rate constant distribution and ultimate recovery. Physicochem. Probl. Miner. Process., 53(1), 342−365.
  • CHIPFUNHU, D., ZANINA, M., GRANO, S., 2012. Flotation behaviour of fine particles with respect to contact angle. Chem. Eng. Res. Des., 90, 26–32.
  • DRZYMALA, J., 2006, Atlas of upgrading curves used in separation and mineral science and technology. Physicochem. Probl. Miner. Process., 40, 19-29.
  • DRZYMALA, J., 2007. Mineral Processing. Foundations of theory and practice of minerallurgy. Oficyna Wyd. PWr., Wroclaw.
  • EK, C., 1992. Flotation kinetics. In: Innovations in Flotation Technology (Mavros P., Matis K.A. Eds.). Kluwer Academic Publisher.
  • GHARAI, M., VENUGOPAL, R., 2016. Modeling of flotation process – an overview of different approaches. Miner. Process Extr. Metall. Rev., 37(2), 120-133.
  • HERNAINZ, F., CALERO, M., 2001. Froth flotation: kinetic models based on chemical analogy. Chem. Eng. Process., 40, 269–275.
  • JANICKI, M., BARTKOWICZ, L., ZAKRECKI, B., KOWALCZUK, P.B., 2015. Collectorless coal flotation in the presence of foaming agents. III Polish Mining Congress, Minerallurgy and Utilization of Mineral Resources, Drzymala J., P. B. Kowalczuk (Ed.), 14-16 September, Wroclaw, 52-60 (in Polish), doi: 10.5277/mineralurgia1510.
  • KALINOWSKI, K., KAULA, R., 2013. Verification of flotation kinetics model for triangular distribution of density function of floatabilities of coal particles. Arch. Min. Sci., 58(4) 1279-1287.
  • KELSALL, D.F., 1961. Application of probability in the assessment of flotation systems. Trans. Inst. Min. Metall., 70, 191-204.
  • KLIMPEL, R.R., 1980. Selection of chemical reagents for flotation. In: Mular A., Bhappu R. (Eds.)., Mineral Processing Plant Design, 2nd Ed. SME, Littleton, CO., pp 907-934.
  • KOWALCZUK, B.P, ZAWALA, J., 2016. A relation between time of the three –phase contact formation and flotation kinetics of naturally hydrophobic solids. Colloids and Surfaces A., Phys. Eng. Aspects, 506, 371-377.
  • KOWALCZUK P.B., ZAWALA J., KOSIOR D., DRZYMALA J., MALYSA K., 2016. Three-phase contact formation and flotation of highly hydrophobic polytetrafluoroethylene in the presence of increased dose of frothers. Ind. Eng. Chem. Res. 55(3), 839–843.
  • KOWALCZUK, P. B., MROCZKO, D., DRZYMALA, J., 2015. Influence of frother type and dose on collectorless flotation of copper-bearing shale in a flotation column. Physicochem. Probl. Miner. Process., 51(2), 547−558.
  • KUDLATY, T., 2016. Maximum size of floating particles of copper-bearing shale in the presence of frothers. BSc thesis (P.B. Kowalczuk-supervisor), Wroclaw University of Science and Technology, Wroclaw, Poland (in Polish).
  • LAZIC, P., CALIC, N., 2000. Boltzmann's model of flotation kinetics. Proc. XXI IMPC (Rome), vol. B, 87-93.
  • LI, Y., ZHAO, W., GUI, X., ZHANG, X., 2013. Flotation kinetics and separation selectivity of coal size fractions. Physicochem. Probl. Miner. Process., 49(2), 387−395
  • LOVEDAY, B.K., 1966. Analysis of froth flotation kinetics. Trans. Am. Soc. Min. Metal. Eng., C219-C225.
  • LYNCH, A.J., JOHNSON, N.W., MANLAPIG, E.V., THORNE C.G., 1981. Mineral and coal flotation circuits. Elsevier Scientific Publishing Co., Amsterdam.
  • MERTA, P., DRZYMALA, J., 2016. Influence of sodium chloride and sodium acetate on flotation of anthracite coal as a model substance rich in kerogen. In Kupferschiefer II, Kowalczuk P. B., Drzymala J. (Eds.), WGGG, Wroclaw, 195-200 (in Polish), doi: 10.5277/lupek1632.
  • POLAT, M., CHANDER, S., 2000. First-order flotation kinetics models and methods for estimation of true distribution of flotation rate constants. Int. J. Miner. Process., 58, 145-166.
  • SOMASUNDARAN, P., LIN, I.J., 1973. Method for evaluating flotation kinetics parameters. Transactions of SME, 254, 181-184
  • STUMM, W., MORGAN, J.J., 1970. Aquatic chemistry, an introduction emphasizing chemical equilibria in natural waters. Wiley, New York.
  • SZAJOWSKA, J., WEJMAN, K., KOWALCZUK, P. B., 2014. Froth flotation of shale and quartz the in Hallimonda tube. In Kupferschiefer, Kowalczuk P. B., Drzymala J. (Eds.), WGGG, Wroclaw, 91-97 (in Polish), doi: 10.5277/lupek1417.
  • WILLS, B., NAPIER MUNN, T., 2006. Wills' mineral processing technology. An introduction to the practical aspects of ore treatment and mineral recovery. 7th ed., Butterworth-Heinemann, London.
  • YIANATOS, J., BERGH, L., VINNETT, L., CONTRERAS, F., DIAZ, F., 2010. Flotation rate distribution in the collection zone of industrial cells. Miner. Eng., 23, 1030-1035.
  • ZHANG, H., LIU, J., CAO, Y., WANG, Y., 2013. Effects of particle size on lignite reverse flotation kinetics in the presence of sodium chloride. Powder Technol., 246, 658–663.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-4b0c9f9f-57aa-4e50-b048-81d6edbcc975
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