Optimization of the Graphite Flotation Parameters using a Central Composite Design

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1 Optimization of the Graphite Flotation Parameters using a Central Composite Design O. Oney* and S.Samanli* * Usak University, Department of Mining Engineering, 6400 Usak, Turkey ABSTRACT In this study, the rougher flotation of the low-grade graphite ore was investigated using the response surface methodology based on a central composite design. The collector dosage, frother dosage, depressant dosage and solid-liquid ratio were studied as the independent operating parameters. The results obtained from the experiments were subjected to multiple regression analysis using the Design Expert software package program to optimize the weight and the ash content of the rougher flotation concentrates. Analysis of variance was also used to compare the acceptability of the models for predicting the output variables from the developed models. A rougher graphite concentrate with 33.03% ash content and 1.09% weight was obtained at diesel oil of g/t, methyl isobutyl carbinol of g/t, sodium silicate of g/t and solid ratio of 1.36%. Keywords: Graphite flotation, Central composite design, Response surface methodology, Optimization, Modeling. 1. INTRODUCTION Graphite plays a unique role in different industries due to its physical and chemical characteristics [1, ]. Natural graphite is observed in three commercial varieties: crystalline flake, microcrystalline or amorphous, and crystalline vein or lump [3-6]. Graphite and semi-graphite are principally formed by graphitization and essentially, they are end-member products of the continuous transformation of organic matter from peat through bituminous coals and anthracite to graphite. Graphite and semi-graphite, therefore, represent a high metamorphic grade [7]. Graphite can easily be enriched by flotation because of its high natural hydrophobicity [4, 6, 8]. In froth flotation, graphite ores are often subjected to a suitable hydrocarbon oil treatment to alter their hydrophobicity, enhance recovery and/or improve selectivity [9-1]. The dosages of the collector and the frother have a significant effect on the flotation performance [1, 13]. In graphite flotation, hydrocarbons, e.g., kerosene, fuel oil, paraffin and diesel oil or ionic collectors, e.g., potassium amyl xanthate and dithiophosphate are generally used as collectors. Pine oil and methyl isobutyl carbinol (MIBC) are used as frothers and sodium silicate, quebracho and starch are used to depress gangue minerals. The optimum ph in graphite flotation is between 8 and 9 [4, 8]. Flotation is performed as a continuous operation in a series of cells. Notably often, the grade of concentrate recovered from a single stage of flotation is not sufficiently high and requires re-floating in one or more stages of flotation referred to as cleaner or recleaner stages [14]. To determine the optimal flotation conditions for rough concentrates is highly important to reduce the cleaning stages. Response surface methodology (RSM) is a powerful mathematical technique useful for the modeling and analysis of the problems in which the response influenced by several process parameters and the objective is to optimize the response. In this methodology, the objective is to identify a desirable response in the given domain of input variables. This desirable response can be a maximum or a minimum over a wide range of parameters [15]. Central Composite Designs (CCD) are used extensively in building a second-order response surface model. CCD is one of the most important and efficient experimental designs used in process optimization [15, 16]. The present study aims to model and optimize certain of the operating variables on the weight and ash content of rougher graphite concentrates using multiple regression analysis. A central composite design was used for this purpose. Selected independent variables were diesel oil as the collector, MIBC as frother, sodium silicate 167

2 as depressant and solid-liquid ratio. A second-order polynomial regression equations were later derived to predict the response.. MATERIALS AND EXPERIMENTAL METHODS.1. Materials Samples used in the tests were taken from the Kutahya- Altıntas (Turkey) graphite ore deposit. Graphite samples having 67.87% ash content were ground using a jaw crusher and ball mill to less than 106 µm in size for the flotation tests. After size reduction, the particle size distribution of the samples is given in Fig1. Fig 1: Particle size distribution of graphite sample (d 80 =0.78 µm)... Experimental methods The flotation tests were performed in a modified laboratory Denver type flotation machine with a cell-volume of 1 L. The tests were conducted at natural ph. The impeller speed was 1400 rpm for both conditioning and flotation. The experiments were performed as a rougher flotation. Sodium silicate solution was added to the pulp to depress the gangue minerals. Diesel oil as the collector and MIBC as the frother were added. The pulp was mixed for five minutes each before and after addition of depressant, collector and frother. Followed by mixing period, air was introduced into the cell and the froth products were collected until the froth formation ceased. The products of concentrate and tailing were dewatered, dried and weighed..3 Experimental design A CCD was chosen to design a series of experiments to provide data to determine the relationship between the responses (i.e. weight and ash content of the rougher concentrates) and the four process parameters (Table 1). The independent variables of the experimental study can be listed as follows: diesel oil dosage ( g/t), MIBC dosage ( g/t), depressant dosage ( g/t) and solid-liquid ratio (8%-16 %). The responses were the weight and ash content of the rougher graphite concentrate. Table 1. Values of the independent variables and their coded forms and symbols. Independent Variables Units Symbol Coded variable levels Lowest Low Center High Highest Collector dosage (g/t) x Frother dosage (g/t) x Depressant dosage (g/t) x Solid ratio (%) x Second-order polynomial equation was used to express the investigated responses (Y), namely the weight and ash content of the rougher graphite concentrate as a function of the coded independent variables. The response model was as follows: 168

3 Y = βo + i=1 b i x i + i=1 b ii x i + i=1 j=i+1 b ij x i x j...(1) A total of 30 flotation tests were conducted according to the central composite design with coded values. The ash content and the weight of the rougher graphite concentrates values are given in Table. Table. Central composite design of the coded and actual independent variables (X 1, X, X 3 and X 4 ) and the experimental results. Test Number Coded level of variables x 1 x x 3 x 4 Actual independent variables Collector dosage Frother dosage Depressant dosage Solid ratio Observed depended variables Weight Ash Content (g/t) (g/t) (g/t) (%) (%) (%)

4 3. RESULTS AND DISCUSSIONS Design Expert (trial version) software package program was used for the regression and graphical analyses of the data obtained. The results of the regression analysis are given in Table 3. Table 3. Model summary statistics for the rougher graphite concentrate. Rougher concentrate Unit Std. Deviation R Squared Adjusted R- Squared Predicted R-Squared Weight (%) Ash Content (%) The R-squared values of the second-order regression equation for the weight and the ash content of the rough concentrate were calculated as and , respectively, i.e., the four independent explanatory variables for the right side of this equation present 98.96% of the change in weight and 96.53% of the change in ash content. These R-squared values indicate that variability of responses was explained well by the model. The significance of the independent variables and their interactions were tested by means of the analysis of variance (ANOVA). The statistics for the quadratic equations of the weight of rougher graphite concentrate are given in Table 4. Table 4. ANOVA for the quadratic equations of the weight of the rougher graphite concentrate. Source Sum of Squares df Mean Square F Value Prob > F Model < Collector dosage (x 1 ) < Frother dosage (x ) < Depressant dosage (x 3 ) < Solid ratio (x 4 ) < x 1 x x 1 x x 1 x x x x x 4 3.3E E x 3 x < x x x x Residual Lack of Fit Pure Error Cor. Total The probability (p-value) of the regression model is less than , i.e., there is a significant multiple regression relationship between the independent variables and the response variable. It is desirable to obtain large F values in ANOVA. There is a possibility value (P) corresponding to the F statistic. The P value that corresponds to the F statistic is used to decide whether a significant amount of variance is explained. The Model F-value of implies that the model is significant. The lack of fit which measures the fitness of the model resulted in no significance. The Lack of Fit F-value of 0.87 implies the lack of fit is not significant relative to the pure error. The coefficients of the regression equation for weight are also shown in Table 170

5 4.When error probability (α) is taken as 0.05, the results can be trusted with 95% confidence, i.e., this is an important model and the at least one of the model coefficients is important. Values greater than indicate the model terms are not significant. In this case, collector dosage (X 1 ), frother dosage (X ), depressant dosage (X 3 ), solid ratio (X 4 ), X 1 X, X 1 X 4, X 3 X 4, and X are significant for the weight of the rougher graphite concentrate. The statistics for the quadratic equations of the ash content of the rougher graphite concentrate are given in Table 5. Table 5. ANOVA for the quadratic equations of the ash content of the rougher graphite concentrate. Source Sum of Squares df Mean Square F Value Prob > F Model < Collector dosage (x 1 ) < Frother dosage (x ) < Depressant dosage (x 3 ) Solid ratio (x 4 ) < x 1 x x 1 x x 1 x x x x x x 3 x x < x x x Residual Lack of Fit Pure Error Cor. Total The Model F-value of 7.84 implies that the model is significant. Collector dosage (X 1 ), frother dosage (X ), solid ratio (X 4 ), X 1 X 3, X 1 X 4, X X 3, X 1, X, X 3 and X 4 are important model terms for the ash content of the rougher graphite concentrate. Second-order polynomial equations with coded values for the weight and the ash content of the rougher graphite concentrate were obtained as follows: Weight of the rougher graphite concentrate (%) = X X X X X 1 X X 1 X X 3 X X...() Ash content of the rougher graphite concentrate (%) = X X +.47 X X 1 X X 1 X X X X X X X 4...(3) To gain a better understanding of the effects of the independent variables and their interactions on the dependent variables, three-dimensional (3D) response surface plots are presented in Fig and Fig 3. Fig..a shows the effect of the frother dosage and the collector dosage on the weight of the rougher graphite concentrate. The weight was its lowest level at the minimum collector dosage (400 g/t) and frother dosage (100 g/t). As both dosages increased, the weight of the rougher graphite concentrate also increased. At maximum collector dosage (1000 g/t) and depressant dosage (500 g/t), the weight was slightly reduced (Fig.b). The lowest weight of rougher concentrate was obtained the lowest solid ratio (8%) and collector dosage (400 g/t). When the solid ratio increased, the weight was also increased (Fig.c). concentrate was reduced (Fig.f). 171

6 (a) (b) (c) (d) (e) (f) Fig : 3D response surface plots of weight of rougher graphite concentrates. 17

7 (a) (b) (c) (d) (e) (f) Fig 3: 3D response surface predicting the ash content of the rougher flotation concentrates. The effect of the collector dosage and the frother dosage water on the ash content of the rougher graphite concentrate is illustrated in Fig.3a. The ash content was lowest at low collector dosage (400 g/t) and low frother dosage (100 g/t). The ash content reached its maximum value at the highest levels of both reagent dosages. The depressant dosage reduced the ash content of the rougher graphite concentrate slightly. (Fig 3.b). The solid ratio and the collector dosage had a significant effect on the ash content of the rougher graphite concentrate (Fig 3.c). With increasing solid ratio and collector dosage, the ash content of the rougher 173

8 concentrate increased rapidly. When solid ratio increased, the ash content of the rougher concentrate increased and reached its maximum level at a solid ratio of 16% (Fig 3.e and Fig 3.f). Fig.4 shows the correlation between the experimental and the predicted data for the weight and the ash content of the rougher graphite concentrates. Fig. 4 indicates that the predicted data calculated from the models are in good agreement with the experimental data in the range of operating parameters. Fig 4: Predicted and actual values of weight (a) and ash content (b) for rougher graphite concentrates. Design Expert software was used for the solution of the quadratic regression models. It is possible to find the levels of parameters that maximize the weight and minimize the ash content of the rougher graphite concentrate. On this basis, a rougher graphite concentrate with values of 33.03% of ash content and 1.09% of weight was calculated at diesel oil (X 1 ) of g/t, methyl isobutyl carbinol (X ) of g/t, sodium silicate (X 3 ) of g/t and solid ratio (X 4 ) of 1.36%. 4. CONCLUSIONS In this study, rougher flotation tests were performed on graphite samples to obtain concentrates with the maximum weight and the minimum ash content. CCD was used to model and optimize the effect of four essential process parameters on the weight and the ash content of the rougher graphite concentrates. The R- squared values of second-order regression equation for the weight and the ash content of the rougher concentrate were calculated as and , respectively. These R-squared values indicate that there are strong correlations between the independent and dependent variables. The predicted values obtained using the model equations agreed well with the observed values. As a result, a rougher graphite concentrate was obtained with 33.03% ash content and 1.09% weight. Under optimal conditions, the experimental values were in agreement with the predicted values. Optimization using the response surface method may help to improve the production of the rougher graphite concentrates. REFERENCES 1. Ravıchandran, V., Eswaraiah C., Manısankar, P. 01. Beneficiation of low grade graphite ore deposits of Tamilnadu (India), Ultra Chemistry Vol. 8(), Acharya, B.C., Rao, D.S., Prakash, S., Reddy, P.S.R., Bıswal, S.K Technıcal note processıng of low grade graphıte ores of Orıssa, Indıa, Minerals Engineering, 9, Graffin, G.D.,1983. Graphite, Industrial minerals and Rocks (Nonmetallics other than Fuels); Lefond, S. J., volume, fifth edition, Society of Mining Engineers of The American Institute of Mining, Metallurgical and Petroleum Engineers, Inc., New York, Kaya, O., Canbazoğlu, M A study on the floatability of graphite ore from Yozgat Akdağ madeni (Turkey), The Journal of Ore Dressing, 9, 17, Li, H., Feng,Q., Yang,S., Ou, L., Lu,Y The entrainment behaviour of sericite in microcrystalline graphite flotation, International Journal of Mineral Processing 17, Crossley, P Graphite high-tech supply sharpens up. Ind. Miner.,

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