application of response surface methodology and central

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Fuel 86 (2007) 769–776

Application of response surface methodology and centralcomposite rotatable design for modeling the influence of some

operating variables of a Multi-Gravity Separator for coal cleaning

N. Aslan *

Mining Engineering Department, Cumhuriyet University, 58140 Sivas, Turkey

Received 9 March 2006; received in revised form 16 October 2006; accepted 31 October 2006Available online 27 November 2006

Abstract

In this study, the application of response surface methodology (RSM) and central composite rotatable design (CCRD) for modelingthe influence of some operating variables on the performance of a Multi-Gravity Separator (MGS) for coal cleaning was discussed. Fouroperating variables of MGS, namely drum speed, tilt angle, wash water and feed solids were changed during the tests based on theCCRD.

In order to produce clean coal with MGS, mathematical model equations were derived by computer simulation programming apply-ing least squares method using MATLAB 7.1. These equations that are second-order response functions representing ash content andcombustible recovery of clean coal were expressed as functions of four operating parameters of MGS. Predicted values were found to bein good agreement with experimental values (R2 values of 0.84 and 0.93 for ash content and combustible recovery of clean coal,respectively).

This study has shown that the CCRD and RSM could efficiently be applied for the modeling of MGS for coal and it is economicalway of obtaining the maximum amount of information in a short period of time and with the fewest number of experiments.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Central composite rotatable design; Response surface methodology; MGS

1. Introduction

The Multi-Gravity Separator (MGS) represents the lat-est development in fine grain mineral concentration. Theparameters that affect the performance of MGS are thedrum speed, tilt angle, shakes amplitude, shakes frequency,wash water and feed solids [1]. The success of concentra-tion with MGS depends on the selection of suitable param-eter levels and minerals. The optimization of theseparameters requires many tests. The total number of exper-iments required can be reduced depending on the experi-mental design technique [2].

doi:10.1016/j.fuel.2006.10.020

* Tel.: +90 346 2191010x1574; fax: +90 346 2191173.E-mail address: naslan@cumhuriyet.edu.tr

Process engineers want to determine the levels of thedesign parameters at which the response reaches its opti-mum. The optimum could be either a maximum or a min-imum of a function of the design parameters. One of themethodologies for obtaining the optimum results isresponse surface methodology (RSM) [3].

It is essential that an experimental design methodologyis very economical for extracting the maximum amountof complex information, a significant experimental timesaving factor and moreover, it saves the material used foranalyses and personal costs [4].

The objective of this study was to establish the func-tional relationships between the some operating parametersof MGS, namely drum speed, tilt angle, wash water andfeed solid and, ash content and combustible recovery ofclean coal for Yenicubuk/Turkey lignite coal. In the

Table 1Relationship between coded and actual values of a variable [12]

Code Actual value of variable

�b xmin

�1 [(xmax + xmin)/2] � [(xmax�xmin)/2a]0 (xmax + xmin)/2+1 [(xmax + xmin)/2] + [(xmax�xmin)/2a]+b xmax

xmax and xmin = maximum and minimum values of x, respectively;a = 2k/4; k = number of variables.

770 N. Aslan / Fuel 86 (2007) 769–776

following sections, the RSM and requirements for CCRDand its applications for modeling the influence of someoperating variables on the performance of a MGS for coalfrom Yenicubuk/Turkey lignite coal are discussed.

2. Response surface methodology (RSM)

RSM is a collection of statistical and mathematicalmethods that are useful for the modeling and analyzingengineering problems. In this technique, the main objectiveis to optimize the response surface that is influenced by var-ious process parameters. RSM also quantifies the relation-ship between the controllable input parameters and theobtained response surfaces [3].

The design procedure for the RSM is as follows [5]:

(i) Designing of a series of experiments for adequate andreliable measurement of the response of interest.

(ii) Developing a mathematical model of the second-order response surface with the best fittings.

(iii) Finding the optimal set of experimental parametersthat produce a maximum or minimum value ofresponse.

(iv) Representing the direct and interactive effects of pro-cess parameters through two and three-dimensional(3D) plots.

If all variables are assumed to be measurable, theresponse surface can be expressed as follows:

y ¼ f ðx1; x2; x3; . . . ; xkÞ ð1Þ

where y is the answer of the system, and xi the variables ofaction called factors.

The goal is to optimize the response variable (y). It isassumed that the independent variables are continuousand controllable by experiments with negligible errors. Itis required to find a suitable approximation for the truefunctional relationship between independent variablesand the response surface [5].

3. Central composite rotatable design (CCRD)

The experimental design techniques commonly used forprocess analysis and modeling are the full factorial, partialfactorial and central composite rotatable designs. A fullfactorial design requires at least three levels per variableto estimate the coefficients of the quadratic terms in theresponse model. Thus for the four independent variables81 experiments plus replications would have to be con-ducted [6]. A partial factorial design requires fewer experi-ments than the full factorial. However, the former isparticularly useful if certain variables are already knownto show no interaction [7,8].

An effective alternative to the factorial design is the cen-tral composite rotatable design (CCRD), originally devel-oped by Box and Wilson [6] and improved upon by Boxand Hunter [9]. The CCRD gives almost as much informa-

tion as a three-level factorial, requires much fewer teststhan the full factorial and has been shown to be sufficientto describe the majority of steady-state process responses[8,10,11].

The number of tests required for the CCRD includes thestandard 2k factorial with its origin at the center, 2k pointsfixed axially at a distance, say b, from the center to gener-ate the quadratic terms, and replicate tests at the center;where k is the number of variables. The axial points arechosen such that they allow rotatability [9], which ensuresthat the variance of the model prediction is constant atall, points equidistant from the design center. Replicatesof the test at the center are very important as they providean independent estimate of the experimental error. Forfour variables, the recommended number of tests at thecenter is six [9]. Hence the total number of tests requiredfor the four independent variables is 24 + (2 · 4) + 6 = 30[8,9].

Once the desired ranges of values of the variables aredefined, they are coded to lie at ±1 for the factorial points,0 for the center points and ±b for the axial points. Thecodes are calculated as functions of the range of interestof each factor as shown in Table 1.

When the response data are obtained from the testwork, a regression analysis is carried out to determine thecoefficients of the response model (b1,b2, . . . ,bn), their stan-dard errors and significance. In addition to the constant(b0) and error (e) terms, the response model incorporates[8]:

• Linear terms in each of the variables (x1,x2, . . . ,xn).• Squared terms in each of the variables ðx2

1; x22; . . . ; x2

nÞ.• First-order interaction terms for each paired combina-

tion (x1x2,x1x3, . . . ,xn�ixn).

Thus for the four variables under consideration, theresponse model is

y ¼ ðb0 þ eÞ þX4

bixi þX4

biix2i þ

j¼iþ1

bijxixj ð2Þ

The b coefficients, which should be determined in thesecond-order model, are obtained by the least squaresmethod. In general Eq. (2) can be written in matrix form

Y ¼ bX þ e ð3Þ

N. Aslan / Fuel 86 (2007) 769–776 771

where Y is defined to be a matrix of measured values and X

to be a matrix of independent variables. The matrices b ande consist of coefficients and errors, respectively. The solu-tion of Eq. (3) can be obtained by the matrix approach[3,5].

b ¼ ðX 0 � X Þ�1X 0 � Y ð4Þ

where X 0 is the transpose of the matrix X and (X 0 Æ X)�1 isthe inverse of the matrix X 0 Æ X.

The coefficients, i.e. the main effect (bi) and two-factorsinteractions (bij) can be estimated from the experimentalresults by computer simulation programming applyingleast squares method using MATLAB 7.1.

4. Experimental procedure

The central composite rotatable design (CCRD) waschosen to determine the relationship between four operat-ing variables of MGS, namely drum speed, tilt angle, washwater and feed solid and ash content and combustiblerecovery of clean coal.

The coal sample, which is lignite, was taken from theregion of Yenicubuk/Turkey. The sample containing36.1% ash was ground to <500 lm using impact typecrusher and rod mill for MGS tests. The batch MGS testswere conducted at the mineral processing laboratory ofCumhuriyet University/Turkey. For each MGS test,1500 g of the dry coal sample was used. A peristaltic pumpat flow rate of 2 lpm carried out for feeding. Drum speed,tilt angle, wash water and feed solid were changed duringthe tests based on the central composite experimentaldesign, whilst the other operating parameters of MGS werekept constant namely 15 mm of shakes amplitude and4.8 cps of shakes frequency.

The experimental setup used for this study is presentedin Fig. 1. The setup consisted of a feed slurry tank with astirrer, a peristaltic pump for supplying feed to the MGSat consistent rates, a laboratory/pilot scale MGS unit andsample containers for collecting the clean coal and tailings.To obtain the required feed solids, measured quantities ofsolids and water were mixed in the slurry tank. The MGSvariables were adjusted at the required levels as per the cen-tral composite experimental design. The feed slurry was

Fig. 1. MGS experimental setup.

pumped into the MGS drum at the required flow rate usingthe peristaltic pump while the MGS was in operation. Sam-ples from the clean coal and tailing streams were collectedat steady-state conditions. The samples were filtered, driedand analyzed for ash content and combustible recovery.The combustible recovery was calculated using Eq. (5).

Combustible recovery; ð%Þ ¼ M cð1� AcÞM fð1� AfÞ

� 100 ð5Þ

where Ac is ash content of clean coal, Af is ash content offeed, Mc is mass of clean coal and Mf is mass of feed.

5. Results and discussion

A four-factor and five-coded level CCRD was used todetermine the responses (ash content and combustiblerecovery of clean coal). The four variables of MGS weredrum speed, tilt angle, wash water and feed solids. Thenumber of tests at the center points was six, making thetotal number of tests required for the four independentvariables (drum speed, tilt angle, wash water and feed sol-ids): 24 + (2 · 4) + 6 = 30 [8].

The drum speed (v), tilt angle (a), wash water (w) andfeed solid (s) were independent variables studied to predicty responses (ash content and combustible recovery of cleancoal). The four independent variables and their levels forthe CCRD used in this study are shown in Table 2.

Using the relationships in Table 2, coded and actual lev-els of the variables for each of the experiments in the designmatrix were calculated as given in Table 3.

Considering the effects of main factors and also theinteractions between two-factor, Eq. (2) takes the form:

y ¼ b0 þ b1x1 þ b2x2 þ b3x3 þ b4x4 þ b11x21 þ b22x2

þ b33x23 þ b44x2

4 þ b12x1x2 þ b13x1x3 þ b14x1x4

þ b23x2x3 þ b24x2xx þ b34x3x4 ð6Þ

The coefficients, i.e. the main effect (bi) and two-factorinteractions (bij) were estimated from the experimental dataobtained by computer simulation programming applyingleast squares method using MATLAB 7.1.

From the experimental design in Table 3, experimentalresults obtained listed in Table 4 and Eq. (4), the second-order response functions representing ash content (y1)and combustible recovery (y2) of clean coal can beexpressed as a function of four operating parameters ofthe MGS, namely drum speed (v), tilt angle (a), wash water(w) and solid (s). The relationship between responses (ashcontent and combustible recovery of clean coal) and oper-ating parameters were obtained for coded unit as follows:

For ash content of clean coal model equation:

y1 ¼ 22:62� 1:46x1 � 1:04x2 þ 0:45x3 þ 0:10x4

þ 1:08x21 � 0:25x2

2 � 0:23x23 þ 0:12x2

4 þ 1:52x1x2

þ 0:65x1x3 þ 0:14x1x4 � 0:51x2x3 þ 0:22x2x4

� 0:17x3x4 ð7Þ

Table 2Four independent variables of MGS and their levels for CCRD

Variable Symbol Coded variable level

Lowest Low Center High Highest

�b �1 0 +1 +b

Drum speed (v), rpm x1 175 200 225 250 275Tilt angle (a), � x2 1 3 5 7 9Wash water (w), lpm x3 1 3 5 7 9Solid (s), % x4 10 20 30 40 50

Table 3Coded and actual levels of four variables of MGS

Run Coded level of variables Actual level of variables

x1 x2 x3 x4 v (rpm) a (�) w (lpm) s (%)

1 �1 �1 �1 �1 200 3 3 202 �1 �1 �1 +1 200 3 3 403 �1 �1 +1 �1 200 3 7 204 �1 �1 +1 +1 200 3 7 405 �1 +1 �1 �1 200 7 3 206 �1 +1 �1 +1 200 7 3 407 �1 +1 +1 �1 200 7 7 208 �1 +1 +1 +1 200 7 7 409 +1 �1 �1 �1 250 3 3 20

10 +1 �1 �1 +1 250 3 3 4011 +1 �1 +1 �1 250 3 7 2012 +1 �1 +1 +1 250 3 7 4013 +1 +1 �1 �1 250 7 3 2014 +1 +1 �1 +1 250 7 3 4015 +1 +1 +1 �1 250 7 7 2016 +1 +1 +1 +1 250 7 7 4017 �b 0 0 0 175 5 5 3018 +b 0 0 0 275 5 5 3019 0 �b 0 0 225 1 5 3020 0 +b 0 0 225 9 5 3021 0 0 �b 0 225 5 1 3022 0 0 +b 0 225 5 9 3023 0 0 0 �b 225 5 5 1024 0 0 0 +b 225 5 5 5025 0 0 0 0 225 5 5 3026 0 0 0 0 225 5 5 3027 0 0 0 0 225 5 5 3028 0 0 0 0 225 5 5 3029 0 0 0 0 225 5 5 3030 0 0 0 0 225 5 5 30

772 N. Aslan / Fuel 86 (2007) 769–776

For combustible recovery of clean coal model equation:

y2 ¼ 76:41� 3:07x1 þ 2:48x2 þ 1:52x3 þ 0:23x4 þ 2:49x21

þ 0:09x22 þ 0:40x2

3 þ 0:83x24 þ 3:57x1x2 þ 1:99x1x3

� 0:50x1x4 � 0:55x2x3 þ 0:50x2x4 � 0:67x3x4 ð8Þ

The response factors at any regime in the interval of ourexperiment design can be calculated from Eqs. (7) and (8).

Experimental results and the predicted values obtainedusing model equations (Eqs. (7) and (8)) are given in Table4 and Figs. 2 and 3. As can be seen, the predicted valuesmatch the experimental values reasonably well, with R2

of 0.84 for ash content and R2 of 0.93 for combustiblerecovery of clean coal.

5.1. Effect of variables of MGS on ash content

The three-dimensional (3D) response surface plots dem-onstrate the effect of different variables of MGS on ashcontent of the clean coal and they are depicted inFig. 4(a–f). The figures show the 3D response surface plotsrelationship between two variables of MGS and ash con-tent of the clean coal at center level of other two variables.Fig. 4a shows the effect of drum speed and tilt angle on ashcontent of clean coal at center level of wash water and

Table 4Observed and predicted values of ash content and combustible recovery

Run Variables Ash content, % Combustible recovery, %

v (rpm) a (�) w (lpm) s (%) Observed Predicted Observed Predicted

1 200 3 3 20 25.90 25.06 83.05 83.402 200 3 3 40 25.30 24.87 85.72 85.203 200 3 7 20 27.75 26.02 85.61 84.904 200 3 7 40 26.83 25.16 87.30 84.025 200 7 3 20 23.89 24.69 79.04 81.326 200 7 3 40 23.92 25.36 82.90 85.127 200 7 7 20 24.11 23.61 80.10 80.628 200 7 7 40 23.54 23.61 80.77 81.749 250 3 3 20 18.57 17.53 68.30 67.14

10 250 3 3 40 17.89 17.91 67.35 66.9411 250 3 7 20 23.07 21.10 78.71 76.6012 250 3 7 40 22.49 20.81 76.18 73.7213 250 7 3 20 22.03 23.22 75.93 79.3414 250 7 3 40 23.70 24.46 80.60 81.1415 250 7 7 20 25.29 24.75 86.25 86.6016 250 7 7 40 24.97 25.32 85.97 85.7217 175 5 5 30 29.48 29.87 93.04 92.5118 275 5 5 30 23.70 24.05 78.80 80.2319 225 1 5 30 21.05 19.56 72.63 71.8120 225 9 5 30 24.61 23.70 81.23 81.7321 225 5 1 30 19.13 20.78 70.95 74.9722 225 5 9 30 23.78 22.60 81.79 81.0523 225 5 5 10 23.80 22.90 79.40 79.2724 225 5 5 50 22.03 23.28 79.28 80.1925 225 5 5 30 22.62 22.62 76.41 76.4126 225 5 5 30 22.62 22.62 76.41 76.4127 225 5 5 30 22.62 22.62 76.41 76.4128 225 5 5 30 22.62 22.62 76.41 76.4129 225 5 5 30 22.62 22.62 76.41 76.4130 225 5 5 30 22.62 22.62 76.41 76.41

R2 = 0.84

15 20 25 30 35Ash content, (%)

Observed

Fig. 2. Relation between experimental and predicted ash content of cleancoal using Eq. (7).

R2 = 0.93

60 65 70 75 80 85 90 95 100

Combustible recovery (%) Observed

Fig. 3. Relation between experimental and predicted combustible recov-ery using Eq. (8).

N. Aslan / Fuel 86 (2007) 769–776 773

solid. Noting that drum speed and tilt angle has a minoreffect on ash content of clean coal. However, it is worthnoting that a lower ash content of clean coal is obtainedat the center level of drum speed. Fig. 4b shows the effectof drum speed and wash water on ash content of clean coalat center level of tilt angle and solid. As can be seen inFig. 4b, ash content depends more on the drum speedrather than on wash water. It is also worth noting that

lower ash content is obtained at the center level of drumspeed. Fig. 4c shows the effect of drum speed and solidon ash content of clean coal at center level of tilt angleand wash water. The general form of three-dimensionalrelationship is similar to the previous figure. Fig. 4d showsthe effect of tilt angle and wash water on ash content atcenter level of drum speed and solid. A minimum ash

Drum speed (v), rpmTilt angle (a),º

Drum speed (v), rpmWash water (w), lpm

Drum speed (v), rpmSolid (s), %

Tilt angle (a), ºWash water (w), lpm

Tilt angle (a), ºSolid (s), %

Wash water (w), lpmSolid (s), %

Fig. 4. Response surface plots showing the effect of two variables on ash content of clean coal. Other two variables are held at center level. (a) Drum speedand tilt angle; (b) drum speed and wash water; (c) drum speed and solid; (d) tilt angle and wash water; (e) tilt angle and solid; (f) wash water and solid.

774 N. Aslan / Fuel 86 (2007) 769–776

content is obtained with minimum level wash water at themaximum tilt angle level. Fig. 4e shows the effect of tiltangle and solid on ash content of clean coal at center levelof drum speed and wash water. The general form of three-dimensional relationship is similar to the previous figure.Ash content depends more on the tilt angle rather thanon solid. It is worth noting that lower ash content isobtained at the maximum wash water level. Fig. 4f showsthe effect of wash water and solid on ash content of cleancoal at center level of drum speed and tilt angle. Notingthat wash water has a significant effect on ash content ofclean coal whilst solid has a trivial effect.

5.2. Effect of variables of MGS on combustible recovery

Fig. 5(a–f) show the 3D response surface plots relation-ship between two variables of MGS and combustiblerecovery of clean coal at center level of other two variables.Fig. 5a shows the effect of drum speed and tilt angle oncombustible recovery of clean coal at center level of washwater and solid. As can be seen, maximum combustiblerecovery is obtained with minimum level drum speed butmaximum tilt angle level. It can be also seen that the centerlevel of drum speed is not a good condition for gettinghigher combustible recovery. Fig. 5b shows the effect of

Drum speed (v), rpmTilt angle (a),º

Drum speed (v), rpmWash water (w), lpm

Drum speed (v), rpmSolid (s), %

Tilt angle (a), ºWash water (w), lpm

Tilt angle (a), ºSolid (s), %

Wash water (w), lpmSolid (s), %

Fig. 5. Response surface plots showing the effect of two variables on combustible recovery of clean coal. Other two variables are held at center level. (a)Drum speed and tilt angle; (b) drum speed and wash water; (c) drum speed and solid; (d) tilt angle and wash water; (e) tilt angle and solid; (f) wash waterand solid.

N. Aslan / Fuel 86 (2007) 769–776 775

drum speed and wash water on combustible recovery ofclean coal at center level of tilt angle and solid. The generalform of three-dimensional relationship is similar to the pre-vious figure, however the effect of drum speed is more pow-erful than previous. Fig. 5c shows the effect of drum speedand solid on combustible recovery of clean coal at centerlevel of tilt angle and wash water. As can be seen fromFig. 5c, combustible recovery depends more on the drumspeed rather than on solid. Fig. 5d shows the effect of tiltangle and wash water on combustible recovery of cleancoal at center level of drum speed and solid. Both variables

have same effect on combustible recovery of clean coal.As the tilt angle is increased, combustible recovery isincreased, just as wash water. Fig. 5e shows the effect of tiltangle and solid on combustible recovery of clean coal atcenter level of drum speed and wash water. Noting that,as the tilt angle is increased, combustible recovery isincreased steadily, noting also that center level of solid isnot good for getting a higher combustible recovery. Fig. 5fshows the effect of wash water and solid on combustiblerecovery of clean coal at center level of drum speed and tiltangle. Noting that the general form of three-dimensional

776 N. Aslan / Fuel 86 (2007) 769–776

relationship is similar to the previous figure. Namely, as thewash water is increased, combustible recovery is increasedprogressively, noting also that center level of solid is notgood condition to be obtained a higher combustible recov-ery but the extreme levels of solid are good for combustiblerecovery.

6. Summary and conclusions

The application of response surface methodology (RSM)and central composite rotatable design (CCRD) for model-ing the influence of some operating variables on the perfor-mance of the Multi-Gravity Separator (MGS) treating coalhas been discussed.

The central composite rotatable design (CCRD) wasused to design an experimental program to provide datato model the effects of drum speed, tilt angle, wash waterand feed solids on the performance of Multi-Gravity Sepa-rator treating coal from Yenicubuk/Turkey lignite coalcontaining approximately 36.1% ash. The ranges of valuesof variables of MGS used in the design were; drum speed:175–275 rpm, tilt angle: 1–9�, wash water: 1–9 lpm and feedsolids: 10–50%. A total of 30 tests including center pointswere conducted. The mathematical model equations werederived for both ash content and combustible recovery byusing sets of experimental data and a mathematical soft-ware package (MATLAB 7.1).

The predicted values match the experimental values rea-sonably well, with R2 of 0.84 for ash content and R2 of 0.93for combustible recovery of clean coal.

In order to gain a better understanding of the effect ofthe variables of MGS on ash content and combustiblerecovery of clean coal, the predicted models were presentedthree-dimensional (3D) response surface graphs.

This study demonstrates that the central compositerotatable design (CCRD) and response surface methodol-

ogy (RSM) can be successfully used for modeling the someoperating parameters of Multi-Gravity Separator for Yen-icubuk/Turkey coal and that it is economical way ofobtaining the maximum amount of information in a shortperiod of time and with the fewest number of experiments.

References

[1] Aslan N, Canbazoglu M. Processing of thickener underflow fromcelestite concentrator by Multi-Gravity Separator. In: Kemal M,Arslan V, Akar A, editors. Changing scopes in mineral process-ing. A.A Balkema; 1996. p. 103–6.

[2] Ozbayoglu G, Atalay MU. Beneficiation of bastnaesite by a multi-gravity separator. J Alloy Compd 2000;303–304:520–3.

[3] Kwak JS. Application of Taguchi and response surface methodolo-gies for geometric error in surface grinding process. Int J Mach ToolManuf 2005;45:327–34.

[4] Kincl M, Turk S, Vrecer F. Application of experimental designmethodology in development and optimization of drug releasemethod. Int J Pharm 2005;291:39–49.

[5] Gunaraj V, Murugan N. Application of response surface methodol-ogies for predicting weld base quality in submerged arc welding ofpipes. J Mater Process Technol 1999;88:266–75.

[6] Box GEP, Wilson KB. On the experimental attainment of optimumconditions. J R Stat Soc, Ser B Stat Meth 1951;13:1–45.

[7] Box GEP, Hunter WG. The 2k�p fractional factorial designs part Iand II. J Technometrics 1961;3:311–458.

[8] Obeng DP, Morrell S, Napier TJN. Application of central compositerotatable design to modeling the effect of some operating variables onthe performance of the three-product cyclone. Int J Miner Process2005;769:181–92.

[9] Box GEP, Hunter JS. Multi-factor experimental design for exploringresponse surfaces. Ann Math Stat 1957;28:195–241.

[10] Cilliers JJ, Austin RC, Tucker JP. An evaluation of formal exper-imental design procedures for hydrocyclone modelling. In: SvarovskyL, Thew MT, editors. Proc fourth Int Conf Hydrocyclones. South-ampton: Kluwer Academic Publishers; 1992. p. 31–49.

[11] Crozier RD. Flotation theory, reagents and ore testing. NewYork: Pergamon Press; 1992.

[12] Napier-Munn TJ. The central composite rotatable design, JKMRC.The University of Queensland Brisbane, Australia, 2000. p. 1–9.

application of response surface methodology and central

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