Powder Technology 232 (2012) 58–63

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Optimization of combined microwave pretreatment–magnetic separation parametersof ilmenite using response surface methodology

Guo Chen a,b, Jin Chen a,b,1, Jun Li a,b, Shenghui Guo a,b, C. Srinivasakannan c, Jinhui Peng a,b,⁎a Key Laboratory of Unconventional Metallurgy, Ministry of Education, Kunming University of Science and Technology, Kunming 650093, PR Chinab Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming 650093, PR Chinac Chemical Engineering Program, The Petroleum Institute, Abu Dhabi, P.O. Box 253, United Arab Emirates

⁎ Corresponding author at: Key Laboratory of Unconof Education, Kunming University of Science and TPR China. Tel./fax: +86 871 5138997.

E-mail address: realchenguo@yahoo.com.cn (J. Peng1 These authors contributed equally to this work and

authors.

0032-5910/$ – see front matter © 2012 Elsevier B.V. Allhttp://dx.doi.org/10.1016/j.powtec.2012.08.009

a b s t r a c t

a r t i c l e i n f o

Article history:Received 2 June 2011Received in revised form 10 June 2012Accepted 13 August 2012Available online 21 August 2012

Keywords:Microwave pretreatmentIlmeniteMagnetic separationResponse surface methodology

The paper addresses the effect of three major influencing parameters, microwave power, time and mass ofsample on the combined microwave pretreatment and magnetic separation of ilmenite through applicationof process optimization technique response surface methodology. The experimental data obtained werefitted into a quadratic polynomial model using multiple regression analysis and were analyzed by the methodof least squares. It was found that microwave power and time were the most significant factors affecting therecovery ratio while the mass of sample was found to be an insignificant parameter. The optimum processconditions were determined by analyzing response surface plots and by solving the regression model equa-tion. Based on the analysis of variance (ANOVA) and the coefficient of determination (R2=0.9410), themodel was found to be in good agreement with the experimental data. The optimum experiment conditionswere found to be 2400 W of microwave power, 30.11 min of time and 44.80 g of sample mass, resulting in anexperimental recovery ratio of 68.73%, as compared to the model prediction of 69.15%. The crystal structuresof the samples were characterized before and after microwave pretreatment using X-ray diffraction (XRD).

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

Traditional comminution processes consumes a large amount ofenergy to liberate minerals from ores. The high energy consumptionof comminution process is a major economic and environmentalconcern [1–3], which necessitates development of new processingtechnologies with low energy consumption and less pollution to theenvironment [4–7]. The ore pre-treatment is one of the most impor-tant stages of comminution [8,9]. Whittles et al. [10] have reportedthat the microwave power density is an important factor which con-tributes toward decreasing energy consumption and improving recov-ery efficiency. Kingman et al. [11] have reported significant reductionin the iron ore strength in a very short exposure time of high electricfield strength microwave energy on copper carbonatite ore. The useof microwave treatment to enhance the liberation of gold for subse-quent recovery by gravity separation techniques has been reportedby Amankwah et al. [12].

Microwaves are a specific category of radio waves that coverthe frequency range of 300 MHz to approximately 300 GHz [13,14].

ventional Metallurgy, Ministryechnology, Kunming 650093,

).should be regarded as co-first

rights reserved.

Compared to conventional heating methods, the major advantages ofusing microwave heating for industrial processing are rapid heat trans-fer, volumetric and selective heating, compactness of equipment, speedof switching on and off and pollution-free environment [15–17]. Hence,microwave energy is used in industry for various processes such asdrying, calcining, roasting, and smelting [18–22]. Compared with theconventional ore pre-treatment methods, the microwave pretreatmentconsumes much less energy, improves mineral recovery, reduces theprocessing time and is suitable for commercial-scale operation [23–26].

The single-variable optimization methods cannot explain the in-teractions of the parameters of the experimental data, because in-teraction between different factors is easily overlooked, leading to amisinterpretation of the experimental results [27,28]. Recently, manystatistical experimental design methods have been developed for pro-cess optimization. Among them, response surface methodology standsout as a popular method utilized in many fields [29,30]. Response sur-face methodology, includes factorial design and regression analysis,which helps in evaluating the effective factors and selecting the opti-mum experimental conditions [31,32]. Although the optimization ofexperimental conditions using response surface methodology is widelyapplied to mineral process optimization, its specific application to mi-crowave pretreatment process is seldom reported.

The main objective of this study is to investigate the influence ofmicrowave pretreatment on magnetic separation of ilmenite usingresponse surface methodology. Microwave power, time, and mass ofsample are the main three dominant factors selected as independent

Table 1Chemical compositions of Panzhihua ilmenite ore (wt.%).

ΣFe TiO2 SiO2 CaO MgO Al2O3 Others

30.67 15.71 20.38 6.48 7.12 3.33 16.28

59G. Chen et al. / Powder Technology 232 (2012) 58–63

variables while recovery ratio of ilmenite is selected as a dependentvariable. The optimum process conditions that result in highestilmenite recovery are identified using the Design Expert softwarepackage.

2. Experimental

2.1. Materials

The ilmenite utilized in the present study was obtained fromPanzhihua City, Sichuan Province, China. The chemical compositionsof ilmenite were shown in Table 1. The mineralogical analysis ofthe ilmenite was performed using X-ray diffraction. Fig. 1 shows theXRD pattern of the ilmenite. It was observed that magnetite (Fe3O4)and ilmenite (FeTiO3) were the main crystalline compounds in theore; in addition, a minor amount of SiO2, CaO, TiO2, MgO and Al2O3

was also present.

2.2. Characterization

The raw and microwave pretreated ilmenite was characterized byX-ray diffractometer (D/Max 2200, Rigaku, Japan) at a scanning rateof 0.25°/min with 2θ ranging from 5° to 100° using CuKα radiation(λ=1.5418 Å) and a Ni filter. The voltage and anode current operatedwere 35 kV and 20 mA, respectively.

2.3. Instrumentation

The microwave pretreatment experiments were carried out in alab-made microwave muffle furnace (Fig. 2). Typical industrial micro-wave muffle furnace consists of a magnetron to produce the micro-waves, a waveguide to transport the microwaves, a resonance cavityto manipulate microwaves for a specific purpose, and a control systemto regulate the temperature and microwave power. The power supplyof the microwave muffle furnace was two magnetrons at 2.45 GHzfrequency and 1.5 kW power, which was cooled by water circulation.The inner dimensions of the multi-mode microwave resonance cavitywere 260 mm in height, 420 mm in length and 260 mm in width. Thetemperature was measured using a Type K thermocouple with a thinlayer of aluminum shielding, placed at the closest proximity to the

Fig. 2. Schematic diagramandpicture ofmicrowave reactor ofmulti-modewith continuouscontrollable power. 1—Oven door; 2—Observation door; 3—Microwavemulti-mode cavity;4—Time; 5—Power controller; 6—Fireproof materials; 7—Raw materials; 8—Ventilationhole; 9—Temperature.

0 20 40 60 80 100

0

500

1000

1500

554

4

3

3 1

2

12

2

11

1-Ilmenite2-Fe3O4

3-Magnesium alumosilicate4-Rutile TiO2

5-Aluminum silicate

2

1

2

Inte

nsity

/CP

S

2-Theta/deg

Fig. 1. The X-ray diffraction pattern of the ilmenite.

sample. The thermocouple provides feedback information to the controlpanel that controls the power to the magnetron, controlling the tem-perature of the sample during the microwave pretreatment process inorder to prevent the sample from overheating.

2.4. Procedure

Ilmenite (16.36–83.64 g) was weighed and placed in the micro-wave muffle furnace which was irradiated for varying exposure times(6.48–48.52 min) at different power levels (522.75–2877.25 W). Afterirradiation the sample was naturally cooled in the furnace to the room

Table 3Experimental design matrix and results.

Run Variables Recoveryratio (%)

Microwave power (W) Time (min) Mass of sample (g)

1 1000.00 15.00 30.00 58.002 2400.00 15.00 30.00 66.003 1000.00 40.00 30.00 60.004 2400.00 40.00 30.00 66.005 1000.00 15.00 70.00 57.006 2400.00 15.00 70.00 62.007 1000.00 40.00 70.00 60.008 2400.00 40.00 70.00 65.009 522.75 27.50 50.00 61.0010 2877.25 27.50 50.00 72.0011 1700.00 6.48 50.00 60.0012 1700.00 48.52 50.00 64.0013 1700.00 27.50 16.36 62.0014 1700.00 27.50 83.64 61.0015 1700.00 27.50 50.00 66.0016 1700.00 27.50 50.00 65.0017 1700.00 27.50 50.00 66.0018 1700.00 27.50 50.00 68.0019 1700.00 27.50 50.00 65.0020 1700.00 27.50 50.00 65.00

Table 4Analysis of the variance (ANOVA) for response surface quadratic model for recoveryratio.

60 G. Chen et al. / Powder Technology 232 (2012) 58–63

temperature. After microwave pretreatment, the treated samples wereground for 60 s by using a laboratory crusher (XMQ 240×90, conicalball mill, China). Subsequently, magnetic separation trials were carriedout to determine the liberation. Magnetic separations were realized onthe electromagnetic separator (XCGS-73, Magnetic tube, China) with amagnetic field intensity of 3.0KOe, which is specified to the wet modeof separation. At the end of the experimental, the recovery ratio wascalculated based on the following equation:

Recovery ratio %ð Þ ¼ mm0

� 100 ð1Þ

where m and m0 were the metal weight separated using magneticseparator (g) and the total metal weight of sample (g), respectively.

2.5. Experimental design

Microwave power (χ1), time (χ2), and mass of sample (χ3) werechosen as independent variables, while recovery ratio (Y) was theresponse (dependent variable). The range and the levels of the inde-pendent variables investigated in this study are given in Table 2. Onthe basis of preliminary experiments the levels of independent vari-ables were chosen to be 1000 to 2400 W, 15 to 40 min and 30 to70 g, respectively.

The design matrix was generated using the design expert software(version 7.1.5, STAT-EASE Inc., Minneapolis, USA), which depicts theexperimental conditions and the resultant output variable (recoveryratio) as shown in Table 3. As seen from Table 3, the complete designconsisted of 20 experimental points (8 factorial points, 6 axial pointsand 6 center points), covering all combinations of the independentvariables along with the repeat experimental runs.

For the purpose of statistical calculations, the chosen independentvariables were coded according to Eq. (2) [33,34]:

Xi ¼χi−χ0ð ÞΔχ

ð2Þ

where Xi is a coded value of the variable, χi is the actual value of var-iable, χ0 is the actual value of the Xi at the center point level, and Δχis the step change of variable.

The quadratic equation for predicting the optimal conditions canbe expressed according to Eq. (3) [35,36]:

Y ¼ β0 þXk

i¼1

βiχi þXk

i¼1

βiiχ2i þ

Xn−1

i¼1

Xn

j¼iþ1

βijχiχj ð3Þ

where β0 is a constant coefficient, βi is the linear coefficient, βii isthe quadratic coefficients and βij is the interaction coefficients, k isthe number of factors studied and optimized in the experiment, χi,χj are the coded values of independent variables, and the terms χiχj

and χi2 represent the interaction and quadratic terms, respectively.

The software ‘Design Expert’ was used for the central compositedesign, experimental data analysis, quadratic model buildings, poly-nomial equations evaluation, and three dimensional response surfaceand contour plotting.

Table 2Coded value of the independent variables and experimental ranges.

Independent variables Coded parameters

−1.682 −1 0 1 1.682

Microwave power (W) 522.75 1000.00 1700.00 2400.00 2877.25Time (min) 6.48 15.00 27.50 40.00 48.52Mass of sample (g) 16.36 30.00 50.00 70.00 83.64

3. Results and discussion

The objective of the present work is to assess the effect of operatingvariables such as microwave power, time and sample mass on recoveryratio of ilmenite using central composite design of the response surfacemethodology and to identify the optimal experimental conditions tomaximize the recovery ratio of ilmenite [37]. Table 3 also provides theresults of the experiments in terms of percentage recovery of ilmenite,which was found to vary from 57.00 to 72.00%.

3.1. Statistical analysis

The ANOVA results of the quadratic model for recovery ratio aresummarized in Table 4. According to Joglekar and May [38], the corre-lation coefficient of a good fit of a model should be at a minimumof 0.80, while an high R2 value illustrates better agreement betweenthe calculated and observed results within the range of experiments[33,39]. The correlation coefficient (R2=0.9410) clearly indicatesthe proximity of the model equation with the experimental data.The adjusted determination coefficient (R2=0.8879) is also highadvocating the significance of the model [6,17]. The closer the valueof adjusted R2 to 1, the better is the correlation between the experi-mental and predicted values [40]. The lack-of-fit F-value of 1.18implies that it is not significant relative to the pure error. There is a42.90% chance that a large lack-of-fit F-value could occur due to noise.The coefficient of variation (CV) indicates the degree of precision withwhich the experiments were conducted and is a good index of the reli-ability of the experiment [17,29]. A lower CV means a higher reliability

Source of variation Degrees offreedom

Sum ofsquares

Meansquare

F-value p-value

Linear 11 93.66 8.51 6.23 0.02802FI 8 89.16 11.14 8.15 0.0167Quadratic 5 8.09 1.62 1.18 0.4290Cubic 1 6.55 6.55 4.79 0.0802Residual error 10 14.92 1.49Lack-of-Fit 5 8.09 1.62 1.18 0.4290Pure error 5 6.83 1.37Total 19 252.95

R2=0.9410; adj. R2=0.8879; CV=1.93%; Adequate precision=15.754 (>4.0).

Table 5Regression coefficients of predicated second-order polynomial model for the responsevariable.

Source Regression analysis

Coefficient Standarderror ofcoefficient

Degrees offreedom

Sum ofsquares

Meansquares

F-value p-value

Model 65.88 0.50 9 238.03 26.45 17.73 b0.001χ1 3.11 0.33 1 132.26 132.26 88.65 b0.001χ2 1.08 0.33 1 15.88 15.88 10.64 0.0085χ3 −0.56 0.33 1 4.32 4.32 2.90 0.1196χ1χ2 −0.066 0.32 1 0.064 0.064 0.043 0.8406χ1χ3 −1.66 0.32 1 39.59 39.59 26.53 0.0004χ2χ3 −1.83 0.32 1 48.48 48.48 32.50 0.0002χ12 −0.25 0.43 1 0.50 0.50 0.34 0.5755

χ22 −0.50 0.43 1 2.00 2.00 1.34 0.2738

χ32 0.50 0.43 1 2.00 2.00 1.34 0.2738

Fig. 4. Normal probability versus internally studentized residuals.

61G. Chen et al. / Powder Technology 232 (2012) 58–63

of the experiment. The lower value of CV (1.93%) demonstrates thatthe performed experiments were highly reliable. Adequate precisionmeasures of the signal-to-noise ratio greater than 4 are generally desir-able [6,17,29]. The signal to noise ratio of 15.754, clearly indicates thesuitability of the model to navigate the design space [29,34].

Multiple regression coefficients obtained by employing a least squaretechnique for second-order polynomialmodel are summarized in Table 5.The quadraticmodel F-value of 17.73 implies that themodel is significantfor recovery ratio. The values of Prob>F>0.0500 indicate that themodelterms are significant [17,33]. Table 5 presents the linear termsχ1, χ2,and the interaction terms χ1χ3 and χ2χ3 to be significant model termsbased on the values of “Prob>F” less than 0.050.

The quadratic model equation developed relating to the depen-dent and independent variables is presented in Eq. (4)

Y ¼ 65:88þ 3:11χ1 þ 1:08χ2−0:56χ3−0:07χ1χ2−1:66χ1χ3

−1:83χ2χ3−0:25χ21−0:50χ2

2 þ 0:50χ23

ð4Þ

where χ1, χ2 and χ3 corresponds to independent variables of micro-wave power (W), time (min) and mass of sample (g), respectively.

Fig. 3 shows the proximity of the model prediction with the exper-imental data validating the goodness of the fit. In addition the stan-dardized residuals were found to be small, which authenticate the

Fig. 3. Predicted values versus experimental values of recovery ratio.

appropriateness of the model. The normal probability plot of the stan-dardized residuals shown in Fig. 4 demonstrates that there were noabnormalities.

3.2. Process analysis

Figs. 5 through 7 show the response surface curves of the indepen-dent variables on the dependent variable. The response surface curvesare easy and convenient way to understand the interaction effects be-tween two independent variables and to locate the optimum levels.

Fig. 5 shows the effect of microwave power and time on the recov-ery ratio at a fixed mass of sample of 50 g. An increase in microwavepower as well as time shows an increase in recovery ratio; howeverthe rate of increase is higher at lower levels as compared to higherlevels of microwave power and time. An increase in the microwavepower possibly increases inter granular fracture, which usually occursin the weak and brittle grain boundary under microwave irradiation.An increase in the recovery ratio with time was well understood, as

Fig. 5. Response surface plot for the interactive effect of microwave power and time:fixed mass of sample at optimum point of 50 g.

Fig. 6. Response surface plot for the interactive effect of microwave power and mass ofsample: fixed time at optimum point of 27.5 min.

0 20 40 60 800

500

1000

1500

2000

2500

3000

11

2

1

22

1

1

1-Fe3O4

2-Ilmenite

21

Inte

nsity

/CP

S2-Theta/deg

Fig. 8. The X-ray diffraction patterns of the magnetic separation concentrates.

Table 6Validation of the model.

Microwave power(W)

Time(min)

Mass of sample(g)

Recovery ratio

Predicted Experimental

2400 30.11 44.80 69.15 68.73

62 G. Chen et al. / Powder Technology 232 (2012) 58–63

the number of intergranular fracture increases with increase in themicrowave exposure time. However the increase in recovery ratio,with both the microwave power as well as the time seems to reachan asymptote indicating the optimum conditions.

Fig. 6 shows the effect of microwave power and mass of sample onthe recovery ratio at the time of 27.5 min. As can be seen, the recov-ery ratio increases with increase in microwave power and mass ofsample, however the effect of mass of sample is not as significant asthe microwave power. It is also evident from the low p value of thisparameter through the ANOVA analysis indicating the insignificanceof the mass sample on the recovery ratio. Fig. 7 shows the effect oftime and mass of sample on the recovery ratio at the microwavepower of 1700 W. The effect of time is found to be significant whilethe effect of mass of sample is found to be insignificant on the recov-ery ratio.

3.3. Process optimization

The optimized conditions were calculated by using ‘Design Expert’software package and were identified to be 2400 W microwave power,

Fig. 7. Response surface plot for the interactive effect of time and mass of sample: fixedmicrowave power at optimum point of 1700 W.

30.11 min time, and 44.80 gmass of sample, with an estimated recoveryratio of 69.15%. Experiments were repeated at the optimized conditionsto check its validity of the model and results were summarized inTable 6. A yield of 68.73% clearly indicates that the optimized conditionsgenerated using the Design Expert software was sufficiently accurate.

The magnetically separated samples under the optimum experi-mental conditions were characterized by XRD, and the results wereshown in Fig. 8. It can be found from Fig. 8 that the diffraction peaksof magnetite (Fe3O4) and ilmenite (FeTiO3) gradually broadened andtheir intensities increased under microwave pretreatment followed bymagnetic separation processes [41]. All the X-ray diffraction peaks ofmagnetite (Fe3O4) and ilmenite (FeTiO3) matched well with those ofthe standard XRD pattern.

The chemical compositions of ilmenite concentrate and gangue atoptimum conditions were shown in Tables 7 and 8, respectively. Thedemonstration of microwave irradiation techniques can be appliedeffectively and efficiently to the treatment processing of ilmenite.The comparison of recovery rate of ilmenite between conventionaland microwave conditions is shown in Fig. 9. It can be seen thatthe recovery rate of ilmenite increases with increasing microwavepower. And the recovery rates of microwave treated ilmenite werehigher than that of the conventional treated sample.

Table 7Chemical compositions of ilmenite concentrate under optimized conditions (wt.%).

TiO2 ΣFe SiO2 CaO MgO Al2O3

45.35 14.23 15.38 8.48 8.12 4.33

Table 8Chemical compositions of gangue under optimized conditions (wt.%).

ΣFe TiO2 SiO2 CaO MgO Al2O3

51.87 11.89 17.56 5.78 6.34 4.23

40

50

60

70

3.02.52.01.50 1.0

Rec

over

y ra

te o

f mag

netit

e/%

Microwave power/kW

Fig. 9. The recovery rate of ilmenite at conventional and microwave conditions.

63G. Chen et al. / Powder Technology 232 (2012) 58–63

4. Conclusion

The response surface methodology was applied to assess the effectof microwave power, time and mass of sample on recovery ratio ofilmenite and to identify the optimized experimental conditions inorder to maximize the recovery ratio. The optimum conditions wereidentified to be a microwave power of 2400 W, time of 30.11 minand mass of sample of 44.80 g resulting in a maximum recoveryratio of 68.73%. The statistical analysis identified only the microwavepower and time to be significant parameters while the mass of sam-ple was found to be insignificant. The results show that response sur-face methodology is one of the suitable methods to optimize the bestoperating conditions in a multi-factor operating environment for thepurpose of obtaining maximum recovery ratio of ilmenite. It can beconcluded that microwave pretreatment can turn out to be a poten-tial pre-treatment to enhance magnetic separation of ilmenite andimprove recovery ratio of magnetite (Fe3O4) and ilmenite (FeTiO3).

Nomenclaturem the metal weight of magnetic separation concentrates (g)

defined by Eq. (1)m0 the total metal weight of sample (g) defined by Eq. (1)χ1 Microwave power (kW)χ2 time (min)χ3 mass of sample (g)Y recovery ratio (%)k the number of factors

Greek symbolsXi the coded value of the variable defined by Eq. (2)χ0 the actual value of the Xi defined by Eq. (2)Δχ the step change of variable defined by Eq. (2)β0 the constant coefficient defined by Eq. (3)βi the linear coefficient defined by Eq. (3)βii the quadratic coefficients defined by Eq. (3)βij the interaction coefficients defined by Eq. (3)

Acknowledgments

Financial supports from the National Natural Science Foundationof China (No: 51090385), and the National Basic Research Programof China (No: 2007CB613606) were sincerely acknowledged.

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