International Journal of Nonferrous Metallurgy, 2013, 2, 136-143
http://dx.doi.org/10.4236/ijnm.2013.24020 Published Online October 2013 (http://www.scirp.org/journal/ijnm)
A Statistical Method for Determining the Best Zinc
Pregnant Solution for the Extraction by D2EHPA
Hossein Kamran Haghighi1, Davood Moradkhani2, Mohammad Mehdi Salarirad1
1Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Tehran, Iran
2Faculty of Engineering, University of Zanjan, Zanjan, Iran
Received May 14, 2013; revised July 17, 2013; accepted September 2, 2013
Copyright © 2013 Hossein Kamran Haghighi et al. This is an open access article distributed under the Creative Commons Attribu-
tion License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.
ABSTRACT
The application of D2 EHPA in zinc solvent extraction has extensive background . To utilize more eff ectively, respo nse
surface methodology was used to optimize the concentration condition of zinc pregnant solution (ZPL) extracted by
D2EHPA. In the current research, zinc, iron and manganese extraction along with separation factor of zinc-iron (Sf (Zn-
Fe)) and zinc-manganese (Sf (Zn-Mn)) were considered as the response values. The optimal ZPL conditions extracted
with 30% D2EHPA as the extraction solvent were as follows: Zn 21.96 g/L, Fe 382.57 ppm, Mn 1 g/L, Sf (Zn-Fe) 8.26
and Sf (Zn-Mn) 1529.82. In addition, it was found that the iron and manganese concentration were the most effective
factors affecting the zinc and manganese extraction, respectively.
Keywords: D2EHPA; Response Surface Methodology; Pre gnant Solution; Optimization
1. Introduction
The extraction of zinc sulfate with di-2-ethylhexyl phos-
phoric acid (D2EHPA) is a well-known route in zinc
purification industry. Accordin g to the literatures, extrac-
tion of zinc increases from 10% to ca. 99% with increas-
ing pH from 0.5 to 2.5 and increasing D2EHPA concen-
tration from 5% to 40% (w/w) [1]. It is obvious that en-
hancement of extractant makes distribution coefficient
increase; however, it is noteworthy that the high cost of
the organic extractant limits the usage of D2EHPA to
less than 30% (v/v or w/w) [2]; therefore, the best com-
position of D2EHPA in industrial zinc solvent ex traction
is 30% (v/v) dissolve d i n ker osene.
Mehdi Abad lead and Zinc mine located in Yazd, Iran
with the fixed capacity of 200 M tons of sulf ur and oxide
ore is one of the greatest lead and zinc mines in the world.
The investigations reveal that manganese and iron are the
main and major impurities of Mehdi Abad ore, which
consequently come to leach solution and associate with
zinc ion. Therefore, evaluating the optimized concentra-
tion of impurities for solvent extraction process plays the
significant role in the leaching and pre-concentration
steps. These impurities have undesirable effect on the
process. For instance, Mn2+ ions, oxidized anodically to
4 ions, depolarize the H+ ions discharge and thus
reduce the current efficiency for zinc deposition [3-7].
Furthermore the iron constitutes a severe impurity in zinc
solution and must be removed before electrolysis [8].
Implementing iron (III) solvent extraction into the zinc
roast-leach-electrowin flowsheet as a means of iron re-
jection has been under consideration for at least two
decades [9].
MnO 
Response surface methodology is used to reduce the
number of assays necessary to optimize the process and
to collect results more precise than those obtainable by
traditional full factorial designs [10,11]. Accordingly,
RSM has been increasingly employed to optimize solvent
extraction process. However, there is little information
that shows which concentration of ZPL can be optimally
extracted by D2EHPA. Therefore, the optimization con-
dition of ZPL in detail which is extracted optimally by
30% (v/v) D2EHPA is the aim of this report. In the pre-
sent research, the best concentrations of iron, manganese
and zinc concentration, which are significant factor in
Mehdi Abad ore, were found. Furthermore, the interac-
tions effects between ions and the most effective factors
on extractions were investigated.
2. Experiment
2.1. Reagents
Analytical grade inorganic reagents used in the experi-
C
opyright © 2013 SciRes. IJNM

H. K. HAGHIGHI ET AL. 137
ments have been illustrated in Table 1. The synthetic
solutions were prepared with the chemicals at the target
concentrations and are presented in Table 2. The extrac-
tant, D2EHPA, was provided from BDH in England. It
was dissolved in the industrial kerosene from Tehran
Refinery Company, Iran as the diluent. The metal ion
concentrations in the solutions were analyzed by Perkin-
Elmer AA300 model atomic absorption spectro-photo-
meter.
2.2. Procedure of Extraction
The extraction experiments were carried out in mechani-
call agitated and thermostatic beakers. In each experi-
ment, 50 mL of the solution containing various zinc, iron
and manganese concentrations (see Table 3) and 50 mL
of the extractant were agitated by a magnetic stirrer at a
constant rate. The pH of the solution was adjusted to 2.5
by sulfuric acid and hydrogen hydroxide. After agitating
the beakers for 10 min at equilibrium state, the organic
phase was separated from the aqueous phase in a separa-
tor funnel. After separation, the concentrations of ions in
the aqueous phase were analyzed by Perkin-Elmer
AA300 model atomic absorption spectrophotometer.
Concentration of metal ions calculation in the organic
Table 1. Inorganic reagents used in the experiments.
Solution/Application Component Supplier Prepared Concentration
Aq. Feed MgSO4·H2O Fisher See Table 2
Aq. Feed FeSO4·7H2O Merck See Table 2
Aq. Feed ZnSO4·H2O Merck See Table 2
Aq. Feed H2O2 Mojallali 3 cc per liter
pH adjusting H2SO4 Mojallali 98%
pH adjusting NaOH Mojallali 36 %
Table 2. The coded values and corresponding actual values of the optimization parameters.
Factor Name Units Type Low Actual High Actual
A Zn g/L Numeric 15 60
B Fe ppm Numeric 10 1000
C Mn g/L Numeric 1 5
Table 3. The coded, experimental and predicted values for RSM design using D2EHPA as solvent.
Factor 1 Factor 2 Factor 3 Resp. 1 Resp. 2 Resp. 3 Resp. 4 Resp. 5
Run A: Zn g/L B: Fe ppm C: Mn g/L %E Zn %E Fe %E Mn Sf (Zn-Fe) Sf (Zn-Mn)
1 38.8 150.25 2.20225 100 100 31.88784 0.258231 82874.33
2 13.1625 10.83 0.9145 100 100 78.13013 1.215394 3684.115
3 15.36 754.3 1.055 99.86784 100 64.52133 0.001002 415.5133
4 15 10 5 99.8432 98.6 61.98 9.041147 390.6007
5 23.765 155.4 0.959 99.91601 99.10553 38.18561 10.73688 1925.76
6 13.11 11.17 4.354 87.12433 99.99991 99.45361 6.06E-06 0.037175
7 40.65 45 2.946 92.61993 99.99978 66.05567 2.79E-05 6.449126
8 15.81 494.3 3.276 93.52309 99.98988 99.42643 0.001461 0.083297
9 44.65 561.9 0.6347 63.91937 99.61559 9.878683 0.006836 16.1617
10 44.65 561.9 0.6347 63.91937 99.61559 9.878683 0.006836 16.1617
11 24.07 750.1 4.921 81.79477 99.94267 17.57773 0.002577 21.06741
12 28.1 7.29 1.9926 87.16014 99.98601 75.27351 0.00095 2.229862
13 32.82 764.2 2.565 80.34735 99.91364 10.72125 0.003534 34.04499
14 15.02 733.8 0.921 99.9674 99.91823 55.23344 2.509152 2485.134
15 56.2 14.58 0.9963 93.58007 99.993 50.54702 0.00102 14.261
16 28.175 394.1 2.537 83.9929 99.92641 8.671659 0.003864 55.26286
17 13.1625 10.83 0.9145 100 100 100 ignored ignored

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
j
ij i
iji
YA AXAX
A
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
X
XX
X
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
X
XX
X
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

H. K. HAGHIGHI ET AL. 139
Table 4. Analysis of variance (ANOVA) of developed models for zinc extraction.
Source comment Sum of Squares df Mean Square F-Value p-value Prob > F
Model 1841.69 6 306.95 11.04 0.0029 significant
A-Zn 79.98 1 79.98 2.88 0.1336
B-Fe 151.85 1 151.85 5.46 0.052
C-Mn 40.43 1 40.43 1.45 0.2669
AB 38.9 1 38.9 1.4 0.2754
AC 83.32 1 83.32 3 0.127
BC 27.87 1 27.87 1 0.35
Rl
L
203
esidua194.54 7 27.79
ack of Fit 194.54 6 32.42
Pure Error 0 1 0
Cor Total 36.213
Table 5. Analysis of variance (ANOVA) of developed models for manganese extraction.
Source Sum of Squares df Mean Square F-Value p-value Prob > F
Model 14489.83 9 1609.981 50.42903 0.0009 significant
A-Zn 127.3896 1 127.3896 3.990193 0.1164
B-Fe 357.9424 1 357.9424 11.21174 0.0286 significant
Rl
L
14653
C-Mn 1330.366 1 1330.366 41.67074 0.0030 significant
AB 2234.237 1 2234.237 69.98246 0.0011 significant
AC 1478.275 1 1478.275 46.30365 0.0024 significant
BC 1176.359 1 1176.359 36.84678 0.0037 significant
A^2 2206.262 1 2206.262 69.1062 0.0011 significant
B^2 1087.321 1 1087.321 34.05789 0.0043 significant
C^2 2547.387 1 2547.387 79.79115 0.0009 significant
esidua127.7027 4 31.92568
ack of Fit 127.7027 3 42.56757
Pure Error 0 1 0
Cor Total 17.13
Table 6. Analysis of variance (ANOVA) of developed models for separation factor of zinc and manganese.
Source Sum of Squares df Mean Square F-Value p-value Prob > F
Model 1.12E + 07 3 3.75E + 06 5.6 0.0162 significant
A-Zn 6.28E + 06 1 6.28E + 06 9.39 0.012 significant
B-Fe 7.73E + 05 1 7.73E + 05 1.15 0.3078
C-Mn 7.40E + 06 1 7.40E + 06 11.06 0.0077 significant
Residual
1.79 07
6.69E + 06 10 6.69E + 05
Lack of Fit 6.69E + 06 9 7.44E + 05
Pure Error 0 1 0
Cor Total E +13
relationship between the variables and responses. Three manganese as Equations (3) to (5). These plots are shown
dimensional (3D) plots for the aforementioned responses
were molded based on the model equations for zinc and
manganese extraction and separation factor of zinc-
in Figures 4 to 6. In these figures, two variables versus
responses at the center level of third variable have con-
structed the plots.

H. K. HAGHIGHI ET AL. 140
Figure 1. Relationship between predicted and actual (ob-
served) values for zinc extraction.
Figure 2. Relationship between predicted and actual (ob-
served) values for manganese extraction
nganese and iron
concentration on zinc extractn at 40˚C and pH of 2.5. It
ex
Figure 4(a) shows the effect of ma
io
presses that increasing iron concentration in the aque-
ous feed decreases zinc extraction and enhancement of
manganese concentration increases zinc ions extraction.
Figure 4(b) demonstrates that at high levels of zinc and
manganese concentrations, the zinc extraction decreases.
Furthermore, in Figure 4(c), enhancement of zinc and
iron ions in the aqueous phase reduces zinc extraction. It
is noteworthy that high concentration of ions in aqueous
phase diminishes the capability of D2EHPA, which is
related to specific capacity of extractant; moreover, Fig-
Figure 3. Relationship between predicted and actual (ob-
served) values for separation factor of zinc and manganese.
Figure 5(a) shows considerable effect of iron concen-
ganese concentration
on
ave ZPL with the lowest
est zinc extraction, the
ptimum
co
ures 4(b) and (c) ju stify this note.
tration and invariable effect of man
the manganese extraction. Figure 5(b) illustrates that
enhancement of manganese ions in the aqueous phase
increases its extraction. In addition, this figure shows that
zinc ions have approximately invariable effect on man-
ganese extraction. In Figure 5(c), the effect of zinc and
iron concentrations on manganese extraction is relative.
As seen in this figure, the lowest manganese extraction
has occurred at the middle levels of zinc and iron con-
centrations. Finally, all plots of Figure 6 shows that
higher amount of ions in the aqueous phase decreases
separation factor of zinc-manganese.
3.2. Optimization by RSM
The aim of optimization is to h
impurities. Therefore, the high
lowest iron and manganese extraction and the highest
values of separation factors were considered for opti-
mizing by RSM. This optimization was carried out by
DX7 software and the results of the process optimization
with respect to the aforementioned aim were obtained as
illustrated in Tab le 7 . As seen in this table, the zinc, iron
and manganese extraction percent at pH of 2 and tem-
perature of 40˚C reached 93.72%, 99.20% and 11.18%,
respectively. At this condition, it was found that Zn
21.22 g/L, Fe 376.08 ppm and Mn 1.00 g/L are extracted
by 30% (v/v) D2EHPA dissolved in kerosene.
This result reveals that to extract more effectively by
30% D2EHPA, the best ZPL should be as the o
ndition of ions concentration. The desirability of this

H. K. HAGHIGHI ET AL. 141
Figure 4. 3D response surface plots showing effect of two variables (factors) on zinc extraction at the center level of other
variable. (a) Mn and Fe concentration (g/L and ppm, respectively). (b) Zn and Mn concentration (g/L). (c) Zn and Fe con-
centration (g/L and ppm, respectively).
Figure 5. 3D response surface plots showing effect of two variables (factors) on manganese extraction at the center level of
other variable. (a) Mn and Fe concentration (g/L and ppm, respectively). (b) Zn and Mn concentration (g/L). (c) Zn and Fe
concentration (g/L and ppm, respe c t ively).

H. K. HAGHIGHI ET AL. 142
Figure 6. 3D response surface plots showing effect of two variables (factors) on separation factor of zinc-manganese at the
center level of other variable. (a) Mn and Fe concentration (g/L and ppm, respectively). (b) Zn and Fe concentration (g/L and
ppm, respectively) (c) Zn and Mn concentration (g/L).
Name Goal Zn (g/L) Fe (ppm)Mn (g/L) %E Zn %E Fe %E Mn Sf (Zn-Fe) Sf (Zn-Mn)
Table 7. Results of process optimization and optimum levels of variable.
Zn is in range
Fe is in range
E Zn
Sf (Zn-Fe)
Sf (Zn)
21.22 376.08 1 93.72 99.20 11.18 8.10 1582.39
Mn is in range
maximize
E Fe mi nimize
E Mn minimize
maximize
-Mnmaximize
opditied 0.67, which is statistically
Figure ws the desirability of the opti-
um condition. As seen in this figure, at the optimum
condition of iron con centration factor and the lowest lev-
els of zinc and manganese concentration, the desirability
of the model is high.
timum conon achiev
7 shoacceptable.
m

H. K. HAGHIGHI ET AL. 143
Figure 7. Response surface plot showing effect of ions concentration on desirability of optimum condition.
4. Conclusions
1) At the optimum condition, the zinc, iron and man-
ganese ex
0˚C reachebest aqueous feed for extractio
traction percent at pH of 2 and temperature of
d 93.72%, 99.20% and 11.18%, respectively. 4As a result, the
30% n by
2) As ANOVA tables indicate, iron extraction and


SfZn-Fe are not significant responses to model.
3) Iron and manganese concentration had the highest
ef
c from an Industrial Zinc Leach Residue by Solvent
Extraction Using D2EHPA,” Minerals Engineering, Vol.
22, No. 2, 2009,
http://dx.doi.o 8.05.002
fect on the zinc and manganese extraction, respec-
tively.
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