Phenomena-based models can be used in a predictive manner, but statistical modelling methods can also yield interesting findings and can serve as a tool for analysing the effects of different variables on the overall phenomenon. In addition, the generation of theoretical models can sometimes be limited due to the unideality of the studied system. Statistical modelling, in this case multiple-linear regression (MLR), was used to describe the effects of temperature and acid concentration on the dissolution of magnetite, Fe3O4 with oxalic acid. Whereas a linear model with an interaction term was sufficient in describing the dissolution of synthetic Fe3O4, a more complex full quadratic model had to be used to describe the dissolution of industrial Fe3O4 in the same conditions. 1. Introduction Both phenomena based thermodynamic and kinetic models could be utilised in the study of iron oxide dissolution. Sometimes the acquisition of data can, however, be very laborious and complex characteristics of the dissolution phenomenon may be difficult to account for through theory. Experimental modelling methods can provide an additional tool for understanding the behaviour of the system, for example the effects of different variables and the interaction of those variables to account for dissolution. Whereas kinetic studies of dissolution are common amongst metallurgist and soil scientists, equilibrium studies determining solubility are less published. Solubility, however, has key significance in any dissolution system because the difference between the equilibrium concentration and the concentration of the solute in the liquid phase determine the driving force for dissolution. Empirical modelling could also be found useful in describing solubility, as widely accepted theoretical models, for example, the Debye-Hückel law, do not apply in concentrated solutions. Statistical modelling methods have been utilised to describe the kinetics of dissolution of iron from kaolin by chemical leaching and bioleaching [1]. In addition, nonlinear regression modelling has been employed in estimating the effects of different parameters, namely, sulphuric acid concentration, sucrose concentration, and temperature, on the acidic dissolution of manganiferous ores [2]. The dissolution of other components besides iron has also been described using statistical methods. The use of statistical methods in research of pharmaceuticals has been summarised elsewhere [3]. In particular principal component analysis (PCA) has been popular in analysing the dissolution profiles of different
References
[1]
V. Arslan and O. Bayat, “Removal of Fe from kaolin by chemical leaching and bioleaching,” Clays & Clay Minerals, vol. 57, no. 6, pp. 787–794, 2009.
[2]
F. Beolchini, M. Petrangeli Papini, L. Toro, M. Trifoni, and F. Vegliò, “Acid leaching of manganiferous ores by sucrose: kinetic modelling and related statistical analysis,” Minerals Engineering, vol. 14, no. 2, pp. 175–184, 2001.
[3]
T. O'Hara, A. Dunne, J. Butler, and J. Devane, “A review of methods used to compare dissolution profile data,” Pharmaceutical Science and Technology Today, vol. 1, no. 5, pp. 214–223, 1998.
[4]
E. Adams, R. De Maesschalck, B. De Spiegeleer, Y. Vander Heyden, J. Smeyers-Verbeke, and D. L. Massart, “Evaluation of dissolution profiles using principal component analysis,” International Journal of Pharmaceutics, vol. 212, no. 1, pp. 41–53, 2001.
[5]
R. M. Maggio, P. M. Castellano, and T. S. Kaufman, “PCA-CR analysis of dissolution profiles. A chemometric approach to probe the polymorphic form of the active pharmaceutical ingredient in a drug product,” International Journal of Pharmaceutics, vol. 378, no. 1-2, pp. 187–193, 2009.
[6]
R. Salmimies, M. Louhi-Kultanen, B. Ekberg, A. H？kkinen, J. Kallas, and M. Huhtanen, “Fouling of filter media: solubility of oxalate solutions,” in Proceedings of the 10th World Filtration Congress, pp. 14–18, Leipzig, Germany, April 2008.
[7]
B. Herath, C. Albano, A. Anttila, and B. Flykt, “Empirical modelling of a dewatering process using multivariate data analysis,” Filtration and Separation, vol. 29, no. 1, pp. 44–57, 1992.
[8]
M. Huhtanen, A. H？kkinen, B. Ekberg, and J. Kallas, “Experimental study of the influence of process variables on the performance of a horizontal belt filter,” Filtration, vol. 11, no. 2, pp. 120–125, 2011.
[9]
J. S. Thella and R. Venugopal, “Modeling of iron ore pelletization using factorial design of experiments and polynomial surface regression methodology,” Powder Technology, vol. 211, no. 1, pp. 54–59, 2011.
[10]
P. S. Sidhu, R. J. Gilkes, R. M. Cornell, A. M. Posner, and J. P. Quirk, “Dissolution of iron oxides and oxyhydroxides in hydrochloric and perchloric acids,” Clays & Clay Minerals, vol. 29, no. 4, pp. 269–276, 1981.
[11]
V. I. E. Bruyére and M. A. Blesa, “Acidic and reductive dissolution of magnetite in aqueous sulfuric acid. Site-binding model and experimental results,” Journal of Electroanalytical Chemistry, vol. 182, no. 1, pp. 141–156, 1985.
[12]
M. A. Blesa, H. A. Marinovich, E. C. Baumgartner, and A. J. G. Maroto, “Mechanism of dissolution of magnetite by oxalic acid-ferrous ion solutions,” Inorganic Chemistry, vol. 26, no. 22, pp. 3713–3717, 1987.
[13]
F. H. Sweeton and C. F. Baes, “The solubility of magnetite and hydrolysis of ferrous ion in aqueous solutions at elevated temperatures,” The Journal of Chemical Thermodynamics, vol. 2, no. 4, pp. 479–500, 1970.
[14]
D. Panias, M. Taxiarchou, I. Paspaliaris, and A. Kontopoulos, “Mechanisms of dissolution of iron oxides in aqueous oxalic acid solutions,” Hydrometallurgy, vol. 42, no. 2, pp. 257–265, 1996.
[15]
M. Taxiarchou, D. Panias, I. Douni, I. Paspaliaris, and A. Kontopoulos, “Dissolution of hematite in acidic oxalate solutions,” Hydrometallurgy, vol. 44, no. 3, pp. 287–299, 1997.
[16]
S. O. Lee, T. Tran, Y. Y. Park, S. J. Kim, and M. J. Kim, “Study on the kinetics of iron oxide leaching by oxalic acid,” International Journal of Mineral Processing, vol. 80, no. 2–4, pp. 144–152, 2006.
[17]
G. E. P. Box, W. G. Hunter, and J. S. Hunter, Statistics for Experiments, John Wiley & Sons, Hoboken, NJ, USA, 1987.
[18]
D. Montgomery, Design and Analysis of Experiments, John Wiley & Sons, Toronto, Canada, 1997.
[19]
G. Tatterson, Scaleup and Design of Industrial Mixing Processes, McGraw-Hill, New York, NY, USA, 1994.
[20]
R. Salmimies, M. Mannila, J. Kallas, and A. H？kkinen, “Acidic dissolution of magnetite: experimental study on the effects of acid concentration and temperature,” Clays & Clay Minerals, vol. 59, no. 2, pp. 136–146, 2011.
