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Journal of Minerals & Materials Characterization & Engineering, Vol. 8, No.3, pp 181-188, 2009
jmmce.org Printed in the USA. All rights reserved
Model for Evaluation of the Concentration of Dissolved Phosphorus during
Leaching of Iron Oxide Ore in Oxalic Acid Solution
C. I. Nwoye
Department of Materials and Metallurgical Engineering,
Federal University of Technology, Owerri, Imo State, Nigeria
Model for 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 has been derived. 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 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%, which is quite within the
acceptable deviation limit of experimental results hence establishing the validity and precision of
Keywords: Model, Evaluation, Phosphorus dissolution, Oxalic Acid, Iron Oxide Ore, Leaching.
The presence of Fe
was found to significantly enhance the leaching of iron extraction from
silica sand at a temperature even as low as 25
[1, 2]. Ferrous oxalate, however, is oxidized
quickly by air during the dissolution and in general an induction period of a few hours was
observed unless a strong acidic environment (<pH 1) or an inert atmosphere is maintained.
Maintaining the high level of ferrous oxalate in the leach liquor using an inert gas was found to
enhance the reaction kinetics . It is believed that during this process, removal of phosphorus
from the iron compound and subsequent dissolution of the phosphorus oxide formed were
182 C.I. Nwoye Vol.8, No.3
It has been reported  that the optimum pH for dissolving iron oxide is pH 2.5 – 3.0. The
solution pH governs the distribution of various oxalate ions in the leach system. Below pH 1.5,
oxalic acid exists mainly as H
, whereas HC
is the most predominant species at pH 2.5 –
Final pH of leaching solution has been found to depend on the leaching time, initial pH for the
leaching solution and the leaching temperature [5,6].
Models for computational analysis of the concentration of dissolved haematite and heat absorbed
by oxalic acid solution during leaching of iron oxide ore have been derived . These models
= K (γ/µ) (1)
Q = K
= Concentration of dissolved haematite in oxalic acid solution.
γ = Final pH of the leaching solution at time t at which %Fe
µ = Weight of iron oxide added into the oxalic acid leaching solution (g)
K = Constant of proportionality associated with haematite dissolution
= Constant of proportionality associated with heat absorption
Q = Quantity of heat absorbed by oxalic acid solution during the leaching process (J)
Nwoye  found that optimization of the weight input of iron oxide ore could be achieved using
the model; (%Fe
= K (γ/µ) ) by comparing the concentrations of dissolved haematite at
different weights input of the iron oxide ore, with the view to identifying the optimum weight
input of iron oxide ore that gives the maximum dissolution of Fe
. The model also indicates
that the concentration of haematite dissolved during the leaching process is directly proportional
to the final pH of the leaching solution and inversely proportional to the weight input of the iron
It was also found  that values of Q obtained from both the experiment and model (Q = K
agree to the fact that leaching of iron oxide ore using oxalic acid solution is an endothermic
process, hence the absorbed positive heat energy by the leaching solution. The quantity of heat
energy absorbed by the oxalic acid solution during the leaching process (as calculated from the
model; Q = K
µ) was found to be directly proportional to the weight input of the iron oxide ore.
These results were obtained at initial pH 6.9, average grain size of 150µm and leaching
temperature of 30
C. The constants of proportionality K and K
associated with the respective
derived models were evaluated to be 0.0683 and 66.88 respectively.
Several works [8-13] 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
Vol.8, No.3 Model for Evaluation of the Concentration of Dissolved Phosphorus 183
dephosphorization. High activity of CaO; a product of decomposition of CaCO
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
It has been reported  that the removal of phosphorus from iron can be achieved only by
oxidation during steel making, under a basic slag.
Nwoye  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 P
T= Leaching temperature (
C) in the experiment , taken as specified leaching
C) 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 .
P = Concentration of dissolved phosphorus (mg/Kg) in the experiment , taken as
pre-quantified concentration of phosphorus expected to dissolve after a leaching time t
in the model.
τ = Leaching time (sec.) in the experiment , 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 (45-70
C) for its
validity. It was found  that the time for dissolution of any given concentration of phosphorus
decreases with increase in the leaching temperature (up to 70
C), at initial pH 5.5 and average
grain size of 150µm.
Nwoye et al.  also formulated a model for predicting the concentration of phosphorus
removed during leaching of iron oxide ore in oxalic acid solution. 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  include: leaching temperature of 25
C, initial solution pH 5.5 and
average ore grain size; 150µm).
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  recently
presented their results of a study on the use of Aspergillus niger and their cultural filtrates for
184 C.I. Nwoye Vol.8, No.3
removing phosphorus from Agbaja (Nigeria) iron oxide ore. The results of this work  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  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  that phosphorus can be removed from iron oxide ore through a process associated
with hydrometallurgy. Phosphorus was removed at a temperature of 25
C and initial solution pH
2.5, leading to the dissolution of the phosphorus oxide formed. This involved using 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 evaluation of the concentration of phosphorus
removed relative to the final pH (only) 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 .
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
2.1 Model Formulation
Experimental data obtained from research work  carried out at SynchroWell Research
Laboratory, Enugu were used for this work.
Results of the experiment as presented in report
 and used for the model formulation are as
shown in Table 1.
Computational analysis of the experimental data  shown in Table 1, resulted to Table 2
which indicate that;
lnP = N/α (approximately) (4)
P = e
Introducing the value of N into equation (5)
P = e
P = Concentration of phosphorus removed during the leaching process (mg/Kg)
Vol.8, No.3 Model for Evaluation of the Concentration of Dissolved Phosphorus 185
N= 12.25; (pH coefficient for phosphorus dissolution in oxalic acid solution.)
determined in the experiment .
α = Final pH of the leaching solution at the time t when the concentration of dissolved
phosphorus is evaluated.
Equation (6) is the derived model.
Table1. Variation of final pH of leaching solution with concentration of phosphorus removed
M (g) (α) P (mg/Kg)
Where M = Mass of iron oxide ore used for the leaching process (g).
Table 2. Variation of lnP with N/α.
M (g) lnP N/α
3. BOUNDARY AND INITIAL CONDITION
Consider iron oxide 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
(2-10g) of iron oxide ore were used as outlined in Table 1. The initial pH of leaching solution;
2.5 and leaching time of 3 hrs were used for all samples. A constant leaching temperature of
186 C.I. Nwoye Vol.8, No.3
C was used. Ore grain sizes at 150µm (average) and oxalic acid concentration at 0.1mol/litre
were used. These and other process conditions are as stated in the experimental technique .
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 comparism of P values from model
data and those from the experimental data for equality or near equality.
Analysis and comparism between these data reveal deviations 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  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 experiment (See Table 3).
Deviation (Dv) (%) of model- predicted P values from experimental P values is given by
Dv = Dp – DE x 100 (7)
Where Dp = Model-predicted P values
DE = Experimental P values
Correction factor (Cf) is the negative of the deviation i.e
Cf = -Dv (8)
Cf = -100 Dp – DE (9)
Introduction of the corresponding values of Cf from equation (9) into the model gives exactly the
corresponding experimental P values .
5. RESULTS AND DISCUSSION
The derived model is equation (6). A comparison of the values of P from the experimental data
and those from the model show very insignificant positive and negative deviations, hence
depicting the reliability and validity of the model. This is shown in Table 3. The positive and
negative deviation of the model-predicted P values from those of the experiment is less than 22%
which is quite within the acceptable deviation limit of experimental results. The validity of the
Vol.8, No.3 Model for Evaluation of the Concentration of Dissolved Phosphorus 187
model is believed to be rooted on equation (4) where both sides of the equation are
approximately equal to 4. Table 2 also agrees with equation (4) following the values of lnP and
N/α evaluated from Table1.
Table 3. Comparison between concentrations of phosphorus removed as predicted by model and
as obtained from experiment .
(mg/Kg) Dv (%) Cf (%)
= P values from experiment 
= P values predicted by model.
The model was used to evaluate the concentration of phosphorus removed (relative to the
solution pH) during leaching of Itakpe iron oxide ore. The validity of the model is believed to be
rooted on the relationship lnP = N/α where both sides of the expression are approximately equal
Further works should incorporate more process parameters into the model with the aim of
reducing the deviation of the model-predicted P values from those of the experiment.
The author thanks Dr. Ekeme Udoh, 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.
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