Journal of Minerals & Materials Characterization & Engineering, Vol. 9, No.4, pp.331-341, 2010
jmmce.org Printed in the USA. All rights reserved
Model for Quantitative Analysis of Phosphorus Removed during Leaching of
Iron Oxide Ore in Oxalic Acid Solution
C. I. Nwoye1*, C. N. Mbah2, C. C. Nwakwuo3 and A. I. Ogbonna1
1Department of Materials and Metallurgical Engineering, Federal University of Technology,
P. M. B 1526, Owerri, Imo State, Nigeria.
2Department of Materials and Metallurgical Engineering. Enugu State University of Science and
Technology, P. M. B 01660, Enugu State, Nigeria.
3Department of Material Science, Oxford University, United Kingdom.
*Corresponding Author: chikeyn@yahoo.com
ABSTRACT
Model for quantitative analysis of the concentration of phosphorus removed (relative to the final
pH of the leaching solution) during leaching of iron oxide ore in oxalic acid solution has been
derived. It was observed that the validity of the model is rooted in the expression lnP = (γ +Nlnγ)
where P is the concentration of phosphorus removed during the leaching process, N is
0.57;dissolution coefficient of phosphorus in oxalic acid solution, and γ is the final pH of the
leaching solution at the time t, when the concentration of phosphorus is evaluated, and both
sides of the expression are correspondingly approximately equal. The model;
P = e( γ + 0.57 lnγ)
depends on the value of the final pH of the leaching solution which varies with leaching time.
The maximum deviation of the model-predicted concentration of removed phosphorus from the
corresponding concentration obtained from the experiment was less than 22%.
The
concentrations of phosphorus removed per unit mass of iron oxide ore added as obtained from
experiment and derived model are 3.8329 and 4.0614 mg/kg/g respectively which are in proximate
agreement.
Keywords: Model, Quantitative Analysis, Phosphorus Removed, Oxalic Acid, Iron Oxide Ore,
Leaching.
332 C. I. Nwoye, C. N. Mbah, C. C. Nwakwuo and A. I. Ogbonna Vol.9, No.4
1. INTRODUCTION
Several works [1-6] have been carried out to remove phosphorus from steel during steel making.
All these works carried out, pointed out low treatment temperature and high oxygen activity as
the only essential and unavoidable process conditions which can enhance the rate of
dephosphorization. High activity of CaO; a product of decomposition of CaCO3 and a slag
forming material is required for enhancement of the dephosphorization process with the
phosphorus forming part of the slag. This process involves pyrometallurgy and is capital
intensive.
It has been reported [7] that the removal of phosphorus from iron can be achieved only by
oxidation during steel making, under a basic slag.
Nwoye [8] derived a model for predicting the time for dissolution of pre-quantified concentration
of phosphorus during leaching of iron oxide ore in oxalic acid solution as:
τ = Log P1/4 (1)
1.8
LogT
Where
T= Leaching temperature ( 0C) in the experiment [9], taken as specified leaching
temperature ( 0C) aiding the expected dissolution of phosphorus .
N= 1.8 (Dissolution coefficient of phosphorus in oxalic acid solution during leaching of iron
oxide ore) determined in the experiment [9].
P = Concentration of dissolved phosphorus (mg/Kg) in the experiment [9], taken as
pre-quantified concentration of phosphorus expected to dissolve after a leaching time t
(mg/Kg) in the model.
τ = Leaching time (sec.) in the experiment [9], taken as time for dissolution of the pre-
quantified concentration of phosphorus (hrs) in the model.
The model was found to depend on a range of specified leaching temperatures (45-700C) for its
validity. It was found [9] that the time for dissolution of any given concentration of phosphorus
decreases with increase in the leaching temperature (up to 700C), at initial pH 5.5 and average
grain size of 150μm.
Nwoye et al. [10] also formulated a model for predicting the concentration of phosphorus
removed during leaching of iron oxide ore in oxalic acid solution. The model is expressed as;
P = 150.5/μ
α
(2)
It was found to predict the removed phosphorus concentration, with utmost dependence on the
final pH of the leaching solution and weight input of the iron oxide ore. The model indicates that
the concentration of phosphorus removed is inversely proportional to the product of the weight
input of the iron oxide ore and the final pH of the leaching solution. Process conditions
considered during the formulation of the model [10] include: leaching temperature of 250C,
initial solution pH 5.5 and average ore grain size; 150μm).
Vol.9, No.4 Model for Quantitative Analysis of Phosphorus Removed 333
Nwoye [11] derived a model for the evaluation of the concentration of dissolved phosphorus
(relative to the final pH of the leaching solution) during leaching of iron oxide ore in oxalic acid
solution. It was observed that the validity of the model is rooted in the relationship lnP = N/α
where both sides of the expression are approximately equal to 4. The model expressed as;
P = e(12.25/α) (3)
depends on the value of the final pH of the leaching solution which varies with leaching time. In
all, the positive or negative deviation of the model-predicted phosphorus concentration from its
corresponding value obtained from the experiment was found to be less than 22%.
Nwoye [12] also derived a model for predicting the concentration of phosphorus removed during
leaching of iron oxide ore in oxalic acid solution. The model is expressed as;
P = [(1.8(T)τ)]4 (4)
was found to be dependent on leaching temperature ranging from 45-700C and specified
leaching time of 0.1381hr (497secs.) recorded during experiment, for its validity. It was found
that the validity of the model is rooted in the expression (P1/4)/N = (T)τ where both sides of the
expression are correspondingly almost equal. The maximum deviation of the model-predicted
values of P from the corresponding experimental values was found to be less than 29% which is
quite within the range of acceptable deviation limit of experimental results.
Model for predictive analysis of the concentration of phosphorus removed (relative to the initial
and final pH of the leaching solution) during leaching of iron oxide ore in sulphuric acid solution
has been derived by Nwoye and Ndlu [13]. It was observed that the validity of the model is
rooted in the mathematical expression; (P/N)1/3 = (eγ/α) where both sides of the relationship are
almost equal. The model;
P = 4.25(eγ/α)3 (5)
shows that the concentration of phosphorus removed is dependent on the values of the initial and
final pH of the leaching solution.
Biological processes for phosphorus removal have also been evaluated based on the use of
several types of fungi, some being oxalic acid producing. Anyakwo and Obot [14] recently
presented their results of a study on the use of Aspergillus niger and their cultural filtrates for
removing phosphorus from Agbaja (Nigeria) iron oxide ore. The results of this work [14] show
that phosphorus removal efficiencies at the end of the 49 days of the leaching process are 81, 63
and 68% for 5, 100 and 250 mesh grain sizes respectively.
An attempt has been made in the past [15] to leach Itakpe iron oxide ore using oxalic acid
solution in order to determine the maximum concentration of phosphorus that is removable.
Results of chemical analysis of the ore indicate that the percentage of phosphorus in the ore is
about 1.18%, which from all indication is quite high and likely to affect adversely the
mechanical properties of the steel involved; hence the need for dephosphorization. It was
reported [15] that phosphorus can be removed from this iron oxide ore through a process
associated with hydrometallurgy. Phosphorus was removed at a temperature of 250C and initial
solution pH 2.5, leading to the dissolution of the phosphorus oxide formed. This involved using
334 C. I. Nwoye, C. N. Mbah, C. C. Nwakwuo and A. I. Ogbonna Vol.9, No.4
acid leaching process to remove phosphorus from the iron oxide ore in readiness for steel making
process.
The aim of this work is to derive a model for quantitative analysis of the concentration of
phosphorus removed relative to the final pH of the solution during leaching of Itakpe (Nigerian)
iron oxide ore using oxalic acid solution. This derivation is embarked on in furtherance of the
previous work [15].
2. MODEL
The solid phase (ore) is assumed to be stationary, contains the un-leached iron remaining in the
ore. Hydrogen ions from the oxalic acid attack the ore within the liquid phase in the presence of
oxygen.
2.1 Model Formulation
Experimental data obtained from research work [15] carried out at SynchroWell Research
Laboratory, Enugu were used for this work. Results of the experiment as presented in report [15]
and used for the model formulation are as shown in Table 1.
Computational analysis of the experimental data [15] shown in Table 1, resulted to Table 2
which indicate that;
lnP = (γ +Nlnγ) (approximately) (6)
P = e(γ +Nlnγ) (7)
Introducing the value of N into equation (7)
P = e( γ + 0.57 lnγ) (8)
Where
P = Concentration of phosphorus removed during leaching of iron oxide ore using oxalic
acid (mg/Kg)
N= 0.57; (Dissolution coefficient of phosphorus in oxalic acid solution) determined in the
experiment. [15]
γ = Final pH of the leaching solution at the time t, when the concentration of phosphorus is
evaluated.
Equation (8) is the derived model.
Vol.9, No.4 Model for Quantitative Analysis of Phosphorus Removed 335
Table1: Variation of Concentration of Phosphorus Removed with final pH of Leaching
Solution [15].
Where M = Mass of iron oxide ore used for the leaching process (g)
Table 2: Variation of lnP with (γ +Nlnγ)
3. BOUNDARY AND INITIAL CONDITION
Consider iron ore in cylindrical flask 30cm high containing leaching solution of oxalic acid. The
leaching solution is stationary i.e (non-flowing). The flask is assumed to be initially free of
attached bacteria. Initially, atmospheric levels of oxygen are assumed. Varying weights (2-16g)
of iron oxide ore were used as outlined in Table 1. The initial pH of leaching solution; 1.2 and
leaching time of 3hrs was used for all samples. A constant leaching temperature of 25oC was
used. Ore grain size; 150µm, volume of leaching solution; 0.1 litre and oxalic acid concentration;
0.1mol/litre were used. These and other process conditions are as stated in the experimental
technique [15].
M (g) γ P (mg/Kg)
2
4
6
8
10
12
14
16
3.12
3.19
3.20
3.29
3.41
3.63
3.74
3.84
42.84
59.60
45.60
54.20
54.80
75.86
88.23
96.50
M (g) lnP (γ +Nlnγ)
2
4
6
8
10
12
14
16
3.7575
4.0877
3.8199
3.9927
4.0037
4.3289
4.4799
4.5695
3.7686
3.8512
3.8630
3.9688
4.1092
4.3649
4.4919
4.6069
336 C. I. Nwoye, C. N. Mbah, C. C. Nwakwuo and A. I. Ogbonna Vol.9, No.4
The boundary conditions are: atmospheric levels of oxygen (since the cylinder was open at the
top) at the top and bottom of the ore particles in the liquid and gas phases respectively. At the
bottom of the particles, a zero gradient for the liquid scalar are assumed and also for the gas
phase at the top of the particles. The leaching solution is stationary. The sides of the particles are
taken to be symmetries.
4. MODEL VALIDATION
The formulated model was validated by direct analysis and comparison of model-predicted P
values and those obtained from experiment [15] for equality or near equality. Analysis and
comparison between these P values reveal deviation of model-predicted P values from those of
the experiment. This is believed to be due to the fact that the surface properties of the ore and the
physiochemical interactions between the ore and leaching solution which were found to play
vital roles during the leaching process [15] were not considered during the model formulation.
This necessitated the introduction of correction factor, to bring the model-predicted P values to
those of the experimental values.
Deviation (Dv) (%) of model-predicted P values from the experimental P values is given by
Dv = Dp – DE x 100 (9)
DE
Where
Dp = Predicted P values by the model
DE = Experimental P values
Correction factor (Cf) is the negative of the deviation i.e
Cf = -Dv (10)
Therefore
Cf = -100 Dp – DE (11)
DE
Introduction of the corresponding values of Cf from equation (11) into the model gives exactly
the corresponding experimental P values [15].
5. RESULTS AND DISCUSSION
The derived model is equation (8). A comparison of the values of P from the experiment and
those from the model shows a maximum deviation less than 22% which is quite within the
acceptable deviation limit of experimental results. The validity of the model is believed to be
rooted in equation (6) where both sides of the equation are correspondingly approximately equal.
Table 2 also agrees with equation (6) following the values of lnP and (γ + Nlnγ) obtained
following statistical and computational analysis carried out on Table 1.
Phosphorus removed per unit mass of iron oxide ore added during the leaching process was
determined following comparison of the concentration of phosphorus removed per unit mass of
Vol.9, No.4 Model for Quantitative Analysis of Phosphorus Removed 337
iron oxide ore (added) obtained by calculations involving experimental results as well as derived
model.
5.1 Determination of the Concentration of Phosphorus Removed per Unit Mass of Iron
Oxide Ore Added
Concentration of phosphorus removed during leaching in oxalic acid solution per unit mass Pm
(mg/kg/g) is calculated from the equation;
Pm = P/m (12)
Therefore, a plot of concentration of phosphorus removed against mass of iron oxide ore added (as in
Fig.1) gives a slope, S at points (96.5, 16) and (42.84, 2) following their substitution into the mathematical
expression;
S = ΔP/Δm (13)
Eqn. (13) is detailed as
S = P
2
- P
1
/ m
2
- m
1
(14)
Where
ΔP = Change in the concentrations of phosphorus removed P
2
, P
1
at mass values m
2
, m
1
. Considering the
points (96.5, 16) and (42.84, 2) for (P
2
, m
2
) and (P
1
, m
1
) respectively, and substituting them into
eqn. (14), gives the slope as 3.8329 mg/kg/g which is the concentration of phosphorus removed per
unit mass added during the actual experimental leaching process
.
R
2
= 0.80 1
0
20
40
60
80
10 0
12 0
0510152 0
Mass of iron o xide o re added (g)
Fig.1-Effect of mass of iron oxide ore (added) on the concentration of phosphorus removed as
obtained from experiment [15].
R
2
= 0.9136
0
20
40
60
80
10 0
12 0
33.54
Fina l pH of le a c hing s o lu t io n
Fig.2-Effect of final pH on the concentration of phosphorus removed as obtained from
experiment [15],
338 C. I. Nwoye, C. N. Mbah, C. C. Nwakwuo and A. I. Ogbonna Vol.9, No.4
Also similar plot (as in Fig. 2) using model-predicted results gives a slope. Considering points
(100.18, 16) and (43.32, 2) for (P
2
, m
2
) and (P
1
, m
1
) respectively and substituting them into eqn.
(14) gives the value of slope, S as 4.0614 mg/kg/g. This is the model-predicted concentration of
phosphorus removed per unit mass of iron oxide ore used for the leaching process. A comparison of
these two values of removed phosphorus concentrations per unit mass of iron oxide ore used shows
proximate agreement. This indicates a very high degree of validity for the model.
An ideal comparison of the concentration of phosphorus removed per unit mass of iron oxide ore used as
obtained from experiment and as predicted by the model for the purpose of testing the validity of the
model is achieved by considering the R2 values. The values of the correlation coefficient, R calculated
from the equation;
R = R2
(15)
using the r-squared values (coefficient of determination) from Figs.1-4 show a very close
correlation;(0.8950),(0.9558) for Figs. 1 & 2 and (0.9108),(0.9673) for Figs. 3 & 4 between
values of the concentration of phosphorus removed obtained from experiment and derived model
respectively. This also shows that the model-predicted concentrations of phosphorus removed are
very much in proximate agreement with the corresponding concentration of phosphorus removed
obtained from experiment [15]. Fig.4 shows that final pH contributed more significantly to the
validity of the model compared with the mass of iron oxide ore added (Fig.3). This is shown in
their respective R2 values.
R
2
= 0.8296
0
20
40
60
80
10 0
12 0
0510 15 20
Mass of iron oxide ore added (g)
Fig.3-Effect of mass of iron oxide ore (added) on the concentration of phosphorus removed as
predicted by derived model
R2 = 0.9356
0
20
40
60
80
10 0
12 0
33.54
Fina l pH of le a c hing s olut ion
Fig.4-Effect of final pH on the concentration of phosphorus removed as predicted by derived
model
Vol.9, No.4 Model for Quantitative Analysis of Phosphorus Removed 339
Comparison of Figs. 5 and 6 show that both values of the concentration of phosphorus removed
obtained from the experiment [15] (line ExD) and the derived model (line MoD) in relation to
both the mass of iron oxide ore (added) and final solution pH are generally quite close hence
depicting proximate agreement and validity of the model.
0
20
40
60
80
10 0
12 0
05101520
Mass of iron oxide ore added (g)
MoD
ExD
Fig.5-Comparison of the concentrations of phosphorus removed in relation to mass of iron oxide
ore (added) as obtained from experiment [15] and derived model
0
20
40
60
80
10 0
12 0
33.54
Fina l pH of le a c hing s olution
MoD
ExD
Fig.6-Comparison of the concentrations of phosphorus removed in relation to final pH as
obtained from experiment [15] and derived model
5.2 Effect of Mass of Iron Oxide Ore (added) on the Deviation (from Experimental Values)
of Model-Predicted Concentration of Phosphorus Removed
It was found that the validity of the model is rooted in the expression P = e( γ + 0.57 lnγ) where both
sides of the expression are correspondingly approximately equal. Table 2 also agrees with
equation (6) following the values of P and e( γ + 0.57 lnγ) evaluated from Table 1 as a result of the
corresponding computational analysis. The maximum deviation of the model-predicted
concentration of phosphorus removed from the corresponding experimental value is 22% which
is quite within the acceptable deviation range of experimental results, hence depicting the
usefulness of the model.
340 C. I. Nwoye, C. N. Mbah, C. C. Nwakwuo and A. I. Ogbonna Vol.9, No.4
Table 3 indicates that the highest and least deviations; -21.06% and 1.12% corresponds to the
model-predicted concentrations of removed phosphorus: 47.05 and 43.32 mg/kg respectively.
Table 3 also shows that these percent deviations also correspond to the mass of iron oxide ore
used: 4 and 2g as well as final leaching solution pH 3.19 and 3.12 respectively.
5.3 Effect of Mass of Iron Oxide Ore (Added) on the Correction Factor to the Model-
Predicted Concentration of Phosphorus Removed
Table 3 shows that the highest and least correction factors (21.06 and -1.12%) which are same in
also corresponds the model-predicted concentrations of removed phosphorus: 47.05 and 43.32
mg/kg respectively, the mass of iron oxide ore used: 4 and 2g as well as final leaching solution
pH 3.19 and 3.12 respectively. Table 3 also shows that the values of the correction factor are
opposite that of the deviation. This is attributed to the fact that correction factor is the negative of
the deviation as shown in eqns. (10) and (11). It is believed that the correction factor takes care
of the effects of the surface properties of the ore and the physiochemical interaction between the
ore and the leaching solution which (affected experimental results) were not considered during
the model formulation.
Table 3: Comparison between concentrations of phosphorus removed as predicted by the
model and as obtained from the experiment.
Where Pexp = Experimental P values
PM = Model-predicted P values
6. CONCLUSION
The model is useful for the quantitative analysis of the concentration of phosphorus removed
during leaching of Itakpe iron oxide ore in oxalic acid solution. It was observed that the validity
of the model is rooted in the expression lnP = (γ +Nlnγ) where both sides of the expression are
correspondingly approximately equal. The model is dependent on the value of the final pH of the
leaching solution which varies with leaching time.
Further works should incorporate more process parameters into the model with the aim of
reducing the deviations of the model- predicted P values from those of the experimental.
Dv (%) Cf (%)
+1.12
-21.06
+4.41
-2.36
-7.12
+3.66
+12.54
+3.81
-1.12
+21.06
-4.41
+2.36
+7.12
-3.66
-12.54
-3.81
Vol.9, No.4 Model for Quantitative Analysis of Phosphorus Removed 341
ACKNOWLEDGEMENT
The author thanks Dr. Andrew Ukoh, a modelling expert at Linkwell Modelling Centre Calabar
for his technical inputs. The management of SynchroWell Nig. Ltd. Enugu is also appreciated for
permitting and providing the experimental data used in this work.
REFERENCES
[1] Turkdogan, E.T., Pearson, J. (1953) J. Iron and Steel Inst., 221, pp. 393-401.
[2] Decker, A., Sevrin, R., Scimar, R. (1962) Open Hearth Proceedings, 45, pp. 421- 456.
[3] Duke, D. A., Ramstad, H. F., Meyer, H. W. (1962) Open Hearth Proceedings, vol 45, pp.81-
98.
[4] Kootz,T., Neuhaus, H. (1961) Stahl u. Eisen, 81, pp. 1810-1815.
[5] Kootz, K., Behrens,K., Maas, H., Baumgarten,. P. (1965) Stahl u. Eisen, 85, pp 857-865.
[6] Edneral, F. P. (1979) Electrometallurgy of Steel and Ferro-alloys, MIR Publisher,5th edition
Moscow. pp 30-239.
[7] Zea,Y. K. (1945) J. Iron and Steel Inst., 151, pp. 459-504.
[8] Nwoye, C. I. (2008) Model for predicting the Time of Dissolution of Pre-quantified
Concentration of Phosphorus during Leaching of Iron Oxide Ore in Oxalic Acid. Inter. J.
Nat. Appl. Sc., 4(3):168-174.
[9] Nwoye, C. I. (2006) SynchroWell Research Work Report, DFM Unit, No 2561178, 66-83.
[10] Nwoye, C. I., Agu, P. C., Mark, U., Ikele, U. S., Mbuka, I. E., and Anyakwo, C. N. (2008)
Model for Predicting Phosphorus Removal in Relation to Weight of Iron Oxide Ore and pH
during Leaching with Oxalic Acid. Inter. J. Nat. Appl. Sc., 4(3): 292-298.
[11] Nwoye, C. I. (2009) Model for Evaluation of the Concentration of Dissolved Phosphorus
during Leaching of Iron Oxide Ore in Oxalic Acid Solution. JMMCE,8(3):181-188
[12] Nwoye, C. I. (2009) Model for Predicting the Concentration of Phosphorus Removed during
Leaching of Iron Oxide Ore in Oxalic Acid Solution. J. Eng. & Appl. Sc. (in press)
[13] Nwoye, C. I. and Ndlu, S. (2009) Model for Predictive Analysis of the Concentration of
Phosphorus Removed during Leaching of Iron Oxide Ore in Sulphuric Acid Solution
JMMCE, 8(4):261-270.
[14] Anyakwo, C. N., and Obot, O.W. (2008) Phosphorus Removal from Nigeria`s Agbaja Iron
Ore by Aspergillus niger, IREJEST 5(1), 54-58.
[15] Nwoye, C. I. (2003) SynchroWell Research Work Report, DFM Unit, No 2031196, 26-60.