H. K. HAGHIGHI ET AL.

138

phase was carried out according to the concentrations of

ions in the aqueous phase.

2.3. Experimental Design of RSM

To determine the optimal combination of extraction

variables for the extraction ions, response surface method

(RSM) was used. Table 2 shows the coded parameters

and their levels, and Table 3 illustrates the coded, ex-

perimental and predicted values. As seen in Table 3,

three factors (i.e. concentrations of three ions) as the in-

putted data were used to model the extraction . The valu es

for the extraction percent of zinc, iron, manganese (%E

Zn, %E Fe and %E Mn), separation factor of zinc-iron

(Sf (Zn-Fe)) and zinc-manganese (Sf (Zn-Mn)) in each

trial were average of duplicates. Based on the experi-

mental data, regression analysis was done and fitted into

the quadratic model as shown in Equation (1).

2

011

1

11

kk

ii iii

ii

kk

ij i

iji

YA AXAX

iXX e

(1)

where Y represents the response, Xi and Xj are variables, k

is the number of independent variables (factors), A0 is

assigned as the constant coefficient, Aii and Aij are inter-

action coefficients of linear, quadratic and the second-

order terms, respectively, and ei stands for th e error. De-

sign-Expert 7.0.1.0 (Trial version, Stat-Ease Inc., Min-

neanopolis, MN, USA) was used for the experimental

design and regression analysis of the experimental data.

The Student’s t-test and Fischer’s F-test were used to

check the statistical significance of the regression co-

efficient, and determine the second-order model equation,

respectively. The lack of fit, the coefficient of determina-

tion (R2) and the F-test value obtained from the analysis

of variance (ANOVA) were applied to evaluate the ade-

quacy of the model.

3. Result and Discussion

If all the aforementioned variables are assumed to be

measurable, the response surface will be expressed as

Equation (2):

123

,,,,X

i

YfXXX (2)

where Y is candidate of responses and the Xi varia b les ar e

called factors. To model using RSM, a total of 18

experimental runs are required. The results inserted to

Design Expert software were used to fit a model to these

results. The equations of models in terms of coded fac-

tors are obtained as Equations (3) to (5) for %E Zn, %E

Mn, Sf (Zn-Fe) and Sf (Zn- Mn), respectively:

For %E Zn:

12

1213 23

%EZn 81.4312.0911.656.14

8.97 12.833.66

3

XX

XXXX

X

3

(3)

The equation of model for iron extraction is not

significant because p-value of model is less than 0.05.

This is due to high extraction percent of iron (III) in any

pH ranges, which reaches above 99%.

For %E Mn:

12

12 13 23

22

13

2

2

%EMn19.3127.0922.7858.09

74.38 78.88 29.75

94.9060.53 43.60

XX

XXXX

XXX

X

(4)

Selective extraction of A ion from B ion can be ex-

pressed by

AB

SfA-B =DD,

where

Aorganic aqueous

D=AB

and

Borganic aqueous

D=BA . The equation of model for

SfZn-Fe is not presented in this study because it is

not significant due to p-value less than 0.05. Neverthe-

less,

Sf Zn-Mn has been modeled using RSM as

Equati onn (5).

1

23

Sf Zn-Mn560.691419.98

387.08 1014.53

X

XX

(5)

The result of analysis of variance (ANOVA) is illus-

trated in Table 4-6.

The results of this table reveal that the prediction

models of the zinc and manganese extraction percent and

separation factor of zinc-manganese are significant since

the p-value is less than 0.05.

The result of Table 4 indicated that the effect of ions

concentration and their in teractions on the zinc ex traction

are not significant. As observed in this table, iron con-

centration has the highest effect on zinc extraction. The

reason for this effect is probably because of selective

extraction of iron (III) ions (i.e., among other species) by

D2EHPA. Table 5 illustrates th e results of Mn ex traction.

The effect of all factors (variables) and their interactions

except zinc concentration are significant on Mn extrac-

tion. As Table 5, manganese concentration has the high-

est effect on manganese extraction. In addition, Table 6

displays that the results of

Sf Zn-Mn

, the zinc and

manganese concentration are only significant factors.

The high value of correlation coefficient (R2) indicates

that the model has been fitted very well. If this is a re-

sponse surface design which is intended to be used for

modeling the design space, then the R-squared values

should be rather high (perhaps above 0.60) (Design Ex-

pert 7 Help). R2 was found to be 0.904 for %E Zn, 0.991

for %E Mn and 0.627 for

SfZn-Mn , as shown in

Figures 1 to 3, which are acceptable statistically.

3.1. 3D Response Surface Plots

The 3D response surface plots simulated by Design-Ex-

pert software are graphical representations in order to

understand the interaction effects of variables and the

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