A study on the performance of second order models and two phase models in iron ore flotation

• Autorzy: Saleh A. M.

Warianty tytułu

PL

Badania modeli drugiego rzędu oraz dwufazowych we flotacji rud żelaza

• Języki publikacji: EN

Abstrakty

EN

In this study, the fit to the experimental data of two second order models and two phase model were compared with first order models. The best fit was observed with the two parameter model with rectangular distribution of floatabilities (model II) and the three parameter fast/slow floating particles model (model I). Also, the three parameter gamma distribution model (model VI) showed good fit to the experimental data. The worst fit was observed with first order two stage kinetic model (model V) which indicates that there is no need to divide the flotation rate into two flotation rates. Model VII which includes six parameters gave acceptable fit to experimental data. This result is in contrast with the results obtained by other investigators which states that increase of parameters in model leads to parameter dilution and increase on model error. Hence, it may be concluded that the number of parameters to obtain an adequate model needs more investigation. The confidence intervals for the three best models (model I, model II and model VI) were estimated at 95% confidence level. Also, model II shows more discrete regions with regard to flotation rate and recovery than model VI. This result indicates the ability of such model to express the changes in flotation reagents and/or flotation conditions over other tested models.

PL

Porównano wierność opisu danych pomiarowych za pomocą kinetycznych modeli drugiego rzędu i modeli dwufazowych. Najlepszy opis odnotowano za pomocą modelu dwuparametrowego z potęgową dystrybucją flotowalności (model II) oraz trójparametrowego modelu dla szybko/wolno flotujących ziarn (model I). Także trójparametrowy model oparty o .-dystrybucję (model VI) dobrze opisywał dane pomiarowe. Najgorsze dopasowanie obserwowano dla modelu pierwszego rzędu dwustopniowego modelu kinetycznego (model V), co wskazuje, że nie ma potrzeby dzielenia szybkości flotacji na dwie części. Model VII, który zawiera sześć parametrów, także daje poprawny opis danych. Wynik ten kontrastuje z wynikami otrzymanymi przez innych badaczy twierdzących, że wzrost liczby parametrów modelu prowadzi do rozmycia oraz wzrostu błędu modelu. Przy 95% poziomie ufności wyznaczono przedziały ufności dla najlepszych modeli I, II oraz VI. Ponadto model II wykazał więcej dyskretnych obszarów w odniesieniu do prędkości flotacji i uzysku, niż model VI. Wskazuje to na lepszą zdolność tych modeli do opisu zmian w procesie flotacji.

Słowa kluczowe

EN

flotation; modeling; second order models; two phase models

PL

flotacja; modelowanie; modele drugiego rzędu; model dwufazowe

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Physicochemical Problems of Mineral Processing
• Rocznik: 2010
• Tom: Vol. 44
• Strony: 215--230
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Saleh A. M.

• Mining & Pet. Dept., Faculty of Engineering, Al-Azhar University, Nasr City, Cairo, Egypt,,

Bibliografia

• 1. ARBITER, N AND HARRIS, C.C., 1962 "Flotation Kinetics” – in Froth flotation: 50th Anniversary volume, New York, American Institute of Mining, Metallurgical and petroleum Engineers, PP. 215-246.
• 2. ARBITER, N., 1951, "Flotation rates and flotation efficiency" Trans. AIME, Vol. 190, , PP. 791-796.
• 3. ALEXANDER, D.J., RUNGE, K.C., FRANZIDIS, J.P. AND MANLAPIG, E.V., 2000, "The application of multi-component floatability to full scale flotation circuists" Proceedings of the Aus IMM, 7th Mill operators conference, Kalgoorlie, PP. 167-178.
• 4. APLING, A.C. AND ERSAYIN, S., 1986, “Reproducibility of semi-batch flotation testwork with the leeds open-Top cell and of derived kinetic parameters “Trans Instn. Min., Metall. (sec. C: Mineral Processing Extr. Metall.), 95, June , pp. C83-C88.
• 5. GULSOY, O.Y., 2005, "A simple model for the calculation of entrainment flotation" Korean Journal of chemical Engineering, Vol. 22, number 4, July , PP. 628-634.
• 6. HEINDEL, T.J. , 1997, "The fundamentals of flotation deinking "TAPPI pulping conference, San Francisco, California, Oct. , PP. 19-23.
• 7. HEINDEL, T.J., BLOOM, F., 2006, "Dispersed air flotation theory" Encyclopedia of surface and colloid science, subject-Material science, Somasundaran, P. and Hubbard, A (eds). published in Aug 15, 2006.
• 8. HARRIS, M.C., 1997, "A practical framework for flotation circuit modeling and simulation" presented at the SAIchE,, the 8th national meeting of the South African Institute of chemical Engineers, Cape Town, April 16-18.
• 9. HUBER-PANU, I., ENE- DANALACHE E., COJOCARIU, D.,G, 1976, “Mathematical models of batch and continuous flotation” flotation- A.M. Gaudin Memorial Volume, M.C. Fuerstenau, (ed) AIME, New York, NY, Vol. 2 chapter 5, PP. 675-724.
• 10. JOWETT, A., GHOSH, S.K., 1965, "Flotation Kinetics: Investigations leading to process optimization” 7th int. mineral processing congr., New York., PP. 175-184.
• 11. KELSALL, D.F. , 1961, "Application of probability in assessment of flotation systems" Trans. IMM, Vol. 70, PP. 191-204.
• 12. KLIMPEL, R.R., 1980, " Selection of chemical reagents for flotation " Mineral processing plant design, 2nd edition, Mular, A.L. and Bhappu, R.B.(eds), chapter 45, AIME, New York, NY, PP. 907-934.
• 13. KLIMPEL, R.R., 1984, "The effect of chemical reagents on the flotation recovery of minerals" chemical Engineering, Vol. 91. No. 18, sept. 1984.
• 14. KLIMPEL, R.R., AUSTIN, L.G., 1984, “The back calculation of specific rates of breakage from continuous mill data” Powder Technology, Vol. 38, pp. 77-91.
• 15. MEHROTRA, S.P. AND KAPUR, P.C., 1974, "The effects of aeration rate, particle size and density on the flotation rate distributions "Powder Tech., Vol. 9, PP. 213-219.
• 16. MIKA, T.S., FUERSTENAU, D.W., 1969, "A microscopic model of the flotation process "8th int. mineral processing congr. Leningrad, 1968, Paper S4.
• 17. MATHE, Z.T., HARRIS, M.C., O'CONNER, C.T., 2000, "A review of methods to model the froth phase in non-steady state flotation systems" Minerals Engineering, Vol. 13, No. 2, PP. 127-140.
• 18. MEYER, W.E. AND KLIMPEL, R.R., 1984, "Rate limitations in froth flotation" Trans AIME, Vol. 274, PP. 1852-1858
• 19. SALEH, A.M.,2009, “Assessment of first order batch flotation models in coal flotation” Journal of Al-Azhar University Engineering sector (JAUES) Vol. 4, No. 12, July 2009, PP. 467-476.
• 20. WOODBURN, E.T., KROPHOLLER, H.W., GREENE, J.C.A., 1976, "The utilization and limitations of mathematical modeling in the prediction of flotation networks "in Flotation: A.M. Gaudin Memorial volume, 2, AIME, Fuerstenau M.C. (ed), PP.638-674.
• 21. WOODBURN, E.T., 1970, "Mathematical modeling of flotation processes" Minerals Sci. Engng. 2(1), PP. 3-17.
• 22. YIANATOS, J.B., 2007, "Fluid flow and kinetic modeling of flotation related processes in columns and mechanically agitated cells- Review" Chemical Engineering Research and design, Vol. 85, Issue Al2, Dec. 2007, PP. 1591-1603.