Froth flotation: kinetic models based on chemical analogy

Transcription

1 Chemical Engineering and Processing 40 (2001) Froth flotation: kinetic models based on chemical analogy F. Hernáinz *, M. Calero Departamento de Ingeniería Química, Facultad de Ciencias, Uni ersidad de Granada, Granada, Spain Received 2 March 2000; received in revised form 31 July 2000; accepted 31 July 2000 Abstract This paper studies several kinetic aspects of flotation of celestite and calcite in a mechanical cell with sodium dodecylsulphate as the collector agent, using pure minerals ranging in average particle size between 137 and 74 m, respectively, with a constant ph 3 in the flotation bath in all experiments. The results obtained indicate that both minerals float rapidly and that the flotation rate constant responds to a non-integral order equation. Likewise, a linear relationship exists between flotation rate and particle diameter Elsevier Science B.V. All rights reserved. Keywords: Flotation kinetic; Froth flotation; Flotation rate; Particle 1. Introduction * Corresponding author. Tel.: ; fax: address: hernainz@goliat.ugr.es (F. Hernáinz). In froth flotation, air bubbles are injected into a moving stream of aqueous slurry containing a mixture of particles, so that only hydrophobic ores are collected on the bubble surface and exit the stream. Owing to its simplicity, the process is widely used for separating a great variety of solid particles. However, a number of complex chemical and physical interaction aspects is involved in the flotation process. An extensive work is reported in the literature on the study of this process, which has been studied from different angles. Of these, kinetic approach has been highly instrumental in better understanding leading to reasonably accurate predictions. The quantification of kinetic parameters is of increasing importance in industrial flotation to shed light on the speed of the process. Numerous researchers have studied the kinetic aspects of froth flotation paying special attention to particle size, bubbles and their complex interactions (Trahar and Warren [1]; Jameson [2]; Radoev et al. [3]; Loewenberg and Davis [4]). Arbiter and Harris [5] found that the flotation kinetics is the study of the variation in amount of froth overflow product with flotation time, and the quantitative identification of all rate-controlling variables. With such variables maintained constant, the algebraic relationship between the proportion of mineral floated and flotation time is a flotation rate equation. This contains the constant values of all the rate determining variables implicit in one or more rate constants, which must be evaluated from experimental data. In a recent review of flotation kinetics (Mehrotra and Padmanabhan [6]), the mathematical models describing froth flotation as a rate process are classified into six categories, kinetic models based on chemical analogy, probabilistic and stochastic models, multiphase models, mechanistic models, kinetic models with distributed rate constant and continuous flotation models. This paper aims to determine the flotation rate of celestite and calcite with sodium dodecylsulphate (SDS), using the kinetic models based on chemical analogy. Likewise, this study supplements a previous work (Hernáinz and Calero [7]) in which the flotation rate of both minerals was determined using sodium oleate as collector agent. 2. Experimental 2.1. Mineral species Celestite, SrSO 4, and calcite, CaCO 3, from two different mines were used for this research study /01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S (00)

2 270 F. Hernáinz, M. Calero / Chemical Engineering and Processing 40 (2001) The celestite was taken from the Cerro de Montevives mine, located in Las Gabias, 12 km southwest of the city of Granada (Spain). The mineral, fragmented and selected again by hand to collect only the purest samples, thus guaranteeing a concentration of 97%, as shown by acid leach analysis. The calcite was taken from a deposit near Torredonjimeno (province of Jaen, Spain), with a concentration in CaCO 3, over 99.6% Flotation agents Collector agent Sodium dodecylsulphate supplied by Merck with a 99% purity. The solutions were dissolved in water. The solute was then weighed on a METTLER AJ150 precision balance, and the desired solution obtained by successive dilutions as the agent concentrations used were very small Foaming agent Daksa M-1 pine oil was used with a constant concentration of g/l, sufficient to stabilise the foam Modifying agents HCl and NaOH (Fluka, puriss. p.a.) were used as ph modifiers in the cell, and control was effected by means of a digital ph meter Experimental conditions, apparatus and calculations The mineral, previously ground to the appropriate size, was added to stainless steel tank, fitted with an agitator and a reducer, which provided gyration at 60 rpm. The density of the pulp was then adjusted in the proportion ore:water=80:1250 g, and the collector, ph modifier and foaming agent were added, almost at the same time. This mixture was agitated for a 10-min conditioning period before being subjected to flotation in a mechanical cell for another 5-min period. In the flotation experiments, a DENVER-D12 mechanical cell with a 1.25-l stainless steel tank was used. The speed of impeller was adjusted to 1000 rpm suction caused by the impeller provided the aeration required for the formation of foam. The froths were manually skimmed to the overspill with an aluminium blade and collected by a collector in glass tanks where the mineral was decanted. The temperature in the bath was maintained between 291 and 293 K. The floated mineral was vacuum filtered through a ceramic funnel lined with appropriate filter paper. The sample was dried by a heating stone at 383 K to a constant weight. The percentage of recovery was obtained easily since pure mineral was used. 3. Results and discussion 3.1. Influence of the concentration of SDS Fig. 1. Flotation recovery of celestite vs. concentration of SDS and two different particle sizes. First of all, the influence of SDS concentration on two different average particle sizes of celestite were determined, namely 74 and 137 m, which are the usual limits in flotation operations. Experiments were performed at ph 3, as this ph has proved to be the most appropriate for SDS as a flotation agent on celestite and calcite according to previous papers (Cabrerizo [8]; Navarro [9]; Hernáinz and Navarro [10]), although calcite undergoes a certain degree of solubilisation at this ph, under 0.8% in all cases, as revealed experimentally. The SDS concentration range selected also applies to the collector s use in industrial flotation operations. The recovery percentage of celestite was plotted against SDS concentration in M (mol/l) in Fig. 1. Even at very low concentrations of the agent, the mineral is seen to respond well to flotation at sizes below 74 m. An increase in the collector concentration above M barely alters the celestite recovery percentage, which remains at around 90%. For the mineral size 137 m, however, recovery gradually rises as SDS concentration is increased. At concentrations approaching M, the recovery percentage is very low (10%), at M, the

3 F. Hernáinz, M. Calero / Chemical Engineering and Processing 40 (2001) maintained for calcite and considerably lessened for celestite (a difference of 20%). Both above and below these two concentrations, either the difference in response to flotation for the two concentrations is poor, as in the case of celestite, or the recovery percentages are relatively low, as in the case of calcite. The two concentrations, namely and M, were selected for the kinetic study detailed below Flotation kinetics Fig. 2. Flotation recovery of calcite vs. concentration of SDS and two different particle sizes. percentage rises to 48%, while at M, recovery percentage exceeds 80%. At this latter concentration, the values found for both sizes used are very similar, indicating that this parameter (i.e. size) ceases to be a limiting factor when there is an excessive collector concentration as revealed by Taggart [11], and Pereda and Hernáinz [12]. Fig. 2 shows the results obtained for calcite using the same sizes and SDS concentrations as those used for celestite. For calcite size of 74 m, the recovery percentage of the mineral rises as the SDS concentration is increased up to a value of approximately M. From this point onwards, an increase in agent concentration does not enhance the mineral recovery percentage, which remains constant at around 70%. Low recovery rates, between 15 and 17%, are obtained from calcite flotation for a size of 137 m and throughout the SDS concentration ranges studied. These results suggest that size is clearly one of the factors influencing recovery of this mineral, what coincides with that indicated by Trahar [3]. From a comparative study between celestite and calcite recovery (Figs. 1 and 2), it is seen that certain agent concentrations allow kinetic constants to be determined, given that there is a noticeable separation between both sizes as well as good results in mineral recovery. For example, at M, for both minerals, the difference in separation of the smallest and the largest sizes is of importance (a difference of over 40%) and at M the difference is Flotation kinetics studies the variation of floated mineral mass according to flotation time. If all operational variables are kept constant, the algebraic relationship between the parameters mentioned above is a flotation rate equation. The ways, in which rate equations may be evaluated can be based on assumptions or on facts established about the mechanism of the process, or, more commonly, determined empirically or by analogy with similar rate processes (Arbiter and Harris [5]). By analogy with chemical kinetics, the equation representing flotation kinetics may be expressed thus, dc dt = kc n (1) where C is the concentration of solids, t flotation time, n order of the process, and k is the flotation rate constant. From the kinetics point of view, concentration C in Eq. (1) comes from, C= M (2) V so that, if it is assumed that the volume is not modified during flotation (which is not strictly true as there is always a small loss of liquid when the mineralised froths are collected), the problem becomes considerably simpler, as we may take C as the mineral mass, which remains in the cell as the operation proceeds. Therefore, if we assume that the volume is not altered during operation, the value for the flotation rate constant may be obtained. This constant is complex since it includes operational parameters such as inducement time, aeration, reagent concentration, particle size, prior treatment, design of the flotation cell, etc. Three approaches may be used to calculate this constant, namely, 1. first-order equation (n=1); 2. second-order equation (n=2); 3. non-integral-order equation. The integration for obtaining the constant of flotation rate in the three approaches is described in a previous work (Hernáinz and Calero [7]).

4 272 F. Hernáinz, M. Calero / Chemical Engineering and Processing 40 (2001) Fig. 3. Flotation recovery of celestite vs. flotation time, with Celestite Fig. 3 shows the recovery percentage plotted against flotation time at ph 3 and M of SDS for the following average particle sizes, 137, 115, 96.5, 81 and 74 m. The flotation rate is very fast for all sizes studied, with the greatest part of the mineral having floated within 3 min. These experiments also reveal that a decrease in size increases mineral recovery as pointed out by Trahar [13] when using other minerals. An increase in flotation rate is also seen to occur as size decreases, although for 81 and 74 m, results are very similar as indeed occurs for 115 and 96.5 m. Fig. 4 shows the results obtained using an SDS Fig. 4. Flotation recovery of celestite vs. flotation time, with 2.22 concentration of M. The recovery percentage is seen to increase considerably, reaching maximum recovery within 3 min. It may also be seen that particle size becomes less important than in the previous case where SDS concentration was M (Fig. 3). The results for four of the five sizes used are very similar in order to the recovery percentage. The values obtained for the three assumptions under consideration are shown in Table 1. The correlation coefficient, r 2, obtained for k l indicates that the operation may not be assimilated in order 1 at either of the two SDS concentrations used. For order 2, the correlation coefficients give acceptable values in some cases, mainly with the smaller sizes used. Table 1 Celestite SDS (M) Average particle size ( m) n=1 n=2 n-non-integral k R k q (min 1 1 (min 1 ) r 2 k 2 (g 1 min 1 ) r 2 ) r

5 F. Hernáinz, M. Calero / Chemical Engineering and Processing 40 (2001) Fig. 5. Flotation recovery of calcite vs. flotation time, with 1.33 However, it is in the non-integer order that the correlation coefficient gives the best results, and, therefore, k q may be taken as representative of the process. The values for k q lessen with a decrease in the mineral size, for the two SDS concentrations used, which mainly agrees with results found for other minerals by other researchers (Trahar [13]; Laplante et al. [14,15]). However, those found by Hernáinz and Calero [7] for the same mineral with sodium oleate are different, since k q is similar for all the particle sizes Calcite Recovery percentages for calcite are shown in Figs. 5 and 6, plotted against flotation time at ph 3 for the five average particle sizes of mineral selected using and M of SDS, respectively. Table 2 Calcite Fig. 6. Flotation recovery of calcite vs. flotation time, with 2.22 It may be seen that relatively high recovery rates are achieved for size of 74 m. It is also clear that as size increases, in all cases, recovery percentage decreases. Table 2 shows the results obtained again checking the adjustment by first-, second- and non-integral-order equations. In this case, the correlation coefficients indicate that the representative kinetics of the process also correspond to a non-integral order Flotation rate and particle diameter The flotation rate of fines particles is low relative to that of other sizes, primarily as a result of the decreased probability of collision between particles and air bubbles as the particle size is reduced (Trahar [13]; Ready SDS (M) Average particle Size ( m) n=1 n=2 n-non-integral k r 2 R k q (min 1 1 (min 1 ) r 2 k ) r 2 2 (g 1 min 1 )

6 274 F. Hernáinz, M. Calero / Chemical Engineering and Processing 40 (2001) and Ratcliff [16]). However, the form of the relationship between flotation rate and particle size is not yet clear. The most recent theoretical analyses suggest that, k d m (3) where k is a suitable measure of the flotation rate, d the particle diameter, and m is the number between 1.5 and 2. Fig. 7 shows the rate constant, k q, plotted against average particle size for the celestite and calcite at and M of SDS. In this figure, the k q with r 2 lower of 0.93 has not been represented. The results shown in Fig. 7 support a roughly linear relationship between flotation rate and particle diameter. In this sense, Table 3 shows the results obtained checking the adjustment. The correlation coefficient, r 2, obtained indicates that a linear relationship exists between flotation rate and particle diameter. Likewise, the values of m are between 1.1 and 1.35, what is lightly inferior to that found for other minerals by other researchers (Jameson [2]; Trahar [13]). 4. Conclusions 1. The flotation rate is very fast for both minerals and for all sizes studied, with the greater part of the mineral having floated within 3 min. 2. The results obtained on flotation of celestite and calcite indicate that the representative kinetics of the process correspond to a non-integral order although the correlation coefficient gives the best results (r in the most cases), and, therefore, k q may be taken as representative of the process. The value for k q lessens with a decrease in the mineral size, for the two SDS concentrations used. The values of k q are between and min 1 for celestite, and and min 1 for calcite. 3. Likewise, the correlation coefficient, r 2, obtained of the k q plotted against average particle size indicates that a linear relationship exists between flotation rate and particle diameter (r for celestite and r for calcite). Appendix A. Nomenclature C mass of mineral remaining in the machine (g) d diameter of particle ( m) k flotation rate constant k first-order flotation rate constant (min 1 1 ) k 2 second-order flotation rate constant (g 1 min 1 ) k q non-integral order flotation rate constant (min 1 ) n order of the process R recovery of mineral at infinite time t flotation time (min) References Fig. 7. Variation in flotation rate constant with particle size of celestite and calcite. Table 3 SDS (M) m r 2 Celestite Calcite [1] W.J. Trahar, L.J. Warren, The floatability of very fine particles a review, Int. J. Miner. Sci. 3 (1976) [2] G.L. Jameson, Physical factors affecting recovery rates in flotation, Miner. Sci. Eng. 9 (1977) [3] B.P. Radoev, L.B. Alexandrova, S.D. Tchaljovska, On the kinetics of froth flotation, Int. J. Miner. Process. 28 (1989) [4] M. Loewenberg, R.H. Davis, Flotation rate of fine spherical particles and droplets, Chem. Eng. Sci. 49 (1994) [5] N. Arbiter, C.C. Harris, in: D.W. Fuerstenau (Ed.), Froth Flotation, AIME, Ann Arbor, MI, 1962, p. 215 Fiftieth anniversary volume. [6] S.P. Mehrotra, N.P.H. Padmanabhan, Flotation kinetics a review, Trans. Indian Inst. Met. 43 (1990) [7] F. Hernáinz, M. Calero, Flotation rate of celestite and calcite, Chem. Eng. Sci. 51 (1996) [8] M. Cabrerizo, Propiedades Electrocinéticas y de Adsorción de Tensioactivos Iónicos sobre Celestina y su Aplicación a la Flitación, Ph.D. thesis, University of Granada, Spain, 1986.

7 F. Hernáinz, M. Calero / Chemical Engineering and Processing 40 (2001) [9] P. Navarro, Aplicación del Lauril Sulfato Sódico en la Flotación de Minerales, Ph.D. thesis, University of Granada, Spain, [10] F. Hernáinz, P. Navarro, Lauril sulfato sódico como colector en la flotación de minerales (I). Influencia de algunas variables de operación, Afinidad 458 (1995) [11] A.F. Taggart, Elementos de Preparación de Minerales, Interciencia, Madrid, 1 a ed., 1996, pp [12] J. Pereda, F. Hernáinz, Aplicaciones del módulo de separación a la flotación de minerales, Afinidad 365 (1980) [13] W.J. Trahar, A rational interpretation of the role of particle size in flotation, Int. J. Miner. Process. 8 (1981) [14] A.R. Laplante, J.M. Toguri, H.W. Smith, The effect of air flow rate on the kinetics of flotation. Part. I: the transfer of material from the slurry to the froth, Int. J. Miner. Process. 11 (1983) [15] A.R. Laplante, J.M. Toguri, H.W. Smith, The effect of air flow rate on the kinetics of flotation. Part. II: the transfer of material from the froth over the cell lip, Int. J. Miner. Process. 11 (1983) [16] D. Ready, G.A. Ratcliff, Removal of fines particles from water by dispersed air flotation: effects to bubble size and particle size on flotation efficiency, Can. J. Chem. Eng. 51 (1973)