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Journal of Minerals & Materials Characterization & Engineering, Vol. 8, No.7, pp 531-539, 2009
jmmce.org Printed in the USA. All rights reserved
Model for Predictive Analysis of Heat Absorbed by Oxalic Acid Solution
Relative to the Solution Temperature during Leaching of Iron Oxide Ore
C. I. Nwoye*1, C. S. Nwobodo1, C. Nlebedim2, U.C. Nwoye3,
R. A. Umana4 and G. C.Obasi5
1Department of Materials and Metallurgical Engineering, Federal University of
Technology, Owerri, Nigeria.
2Department of Material Science, University of Cadiff, Wales, United Kingdom
3Data Processing, Modelling and Simulation Unit, Weatherford Nig. Ltd. Port-Harcourt
4Department of Mathematics and Computer Science, Federal University of Technology,
5Department of Material Science, Aveiro University, Portugal.
*Corresponding Author: email@example.com
Model for predictive analysis of the quantity of heat absorbed by oxalic acid solution
during leaching of iron oxide ore has been derived. It was observed that the validity of the
model is rooted in the expression (lnQ)/N = √T where both sides of the relationship are
correspondingly almost equal. The model was found to depend on the value of the final
solution temperature measured during the experiment. The respective deviation of the
model-predicted Q values from the corresponding experimental values was found to be
less than 21% which is quite within the acceptable range of deviation limit of experimental
results. The positive values of heat absorbed as obtained from experiment and model
indicate and agree that the leaching process is endothermic in nature.
Keywords: Model, Predictive Analysis, Heat Absorbed, Solution Temperature, Oxalic
Acid, Iron Oxide Ore, Leaching.
The use of different organic and inorganic acids has been evaluated in several studies. Sidhu et
al.  evaluated the dissolution of iron oxides and oxyhydroxides in hydrochloric and perchloric
acids. Lim-Nunez and Gilkes  used synthetic metal-containing goethite and haematite in their
532 C. I. Nwoye, et al. Vol.8, No.7
evaluation while Borghi et al.  studied the effect of EDTA and Fe(II) during the dissolution of
magnetite. The industrial use of sulphuric acid and other inorganic acids to dissolve iron oxide
has not fared too well. Chiarizia and Hotwitz  studied the dissolution of goethite in several
inorganic acids belonging to the families of the carboxylic and diphosphoric acids in the
presence of reducing agents. Ambikadevi and Lalithambika  evaluated the effectiveness of
several organic acids (such as acetic, formic, citric, ascorbic acids etc.) used for dissolving iron
from iron compounds. Oxalic acid was found to be the most promising because of its acid
strength, good comlexing characteristics and high reducing power, compared to other organic
acids. Using oxalic acid, the dissolved iron can be precipitated from the leach solution as ferrous
oxalate, which can be re-processed to form pure haematite by calcinations . Many researchers
have studied the use of oxalic acid to dissolve iron oxide on a laboratory scale [7-13]. Lee et al
 used 0.19-0.48M oxalic acid to dissolve hydrated iron oxide. Iron dissolution was found
 to reach 90% for a 20% slurry within 60mins. using 0.19M oxalic for the finer fraction (<
150μm) containing 0.56% Fe2O3.The coarser fraction (>150μm) containing 1.06% Fe2O3
achieved a lower iron removal, reaching a steady state of only 78% after 1 h of leaching.
Although the pH was not measured or controlled, it was expected that the liquor pH is < pH1 at
the oxalic acid concentration range studied (0.19-0.48). Taxiarchou et al.  found that the
maximum iron dissolution of only 40% is within 3 h at temperatures in the range 90-1000C. At
0.5M oxalate and all temperatures (25, 60 and 800C) the dissolution of iron was faster at a lower
pH in the range pH 1-5 studied. Biological processes for iron dissolution have been evaluated by
several researchers based on the use of several micro organisms that were easily sourced and
isolated. Mandal and Banerjee  recently presented their findings on the study of the use of
Aspergillus niger and their cultural filtrates for dissolving iron present in iron compounds.
Nwoye  derived a model for evaluating the final pH of the leaching solution during leaching
of iron oxide ore in oxalic acid solution. The model evaluates the pH value as the sum of two
parts, involving the % concentrations of Fe and Fe2O3 dissolved. The model can be expressed as;
= 0.5 K1 + K2
%Fe % Fe2O3 (1)
K1 and K2 = dissolution constants of Fe and Fe2O3 respectively.
= final pH of leaching solution (after time t).
It was also found that the model  could predict the concentration of Fe or Fe2O3 dissolved in
the oxalic acid solution at a particular final solution pH by taking Fe or Fe2O3 as the subject
formular. The prevailing process conditions under which the model works include: leaching time
of 30mins., constant leaching temperature of 30oC, average ore grain size; 150µm and 0.1M
Nwoye  has reported that the heat absorbed by oxalic acid solution during leaching of iron
oxide ore can be predicted using the model he derived which works under the process condition;
initial pH 6.9, average ore grain size; 150µm and leaching temperature; 300C. The model 
can be stated as
Vol.8, No.7 Model for Predictive Analysis of Heat Absorbed 533
Q = KN (2)
Q = Quantity of heat absorbed by oxalic acid solution during the leaching process. (J)
= Final pH of the leaching solution (at time t).
%Fe2O3= Concentration of haematite dissolved in oxalic acid solution during the leaching
KN = 4.57(Haematite dissolution constant in oxalic acid solution) determined in the
Nwoye  carried out further work on the model using the same process conditions and
observed that on re-arranging the model as;
%Fe2O3 = KN (3)
the concentrations of haematite predicted deviated very insignificantly from the corresponding
experimental values. In this case, the value of Q was calculated by considering the specific heat
capacity of oxalic acid. Values of heat absorbed by the oxalic acid solution during the leaching
of iron oxide ore as predicted by the model  agree with the experimental values that the
leaching process is endothermic. This is because all the predicted values of the heat absorbed by
the oxalic acid solution were positive. The model shows that the quantity of heat absorbed by
oxalic acid solution during the leaching process is directly proportional to the final pH of the
solution and inversely proportional to the concentration of haematite dissolved.
The aim of this work is to derive a model for predictive analysis of the heat absorbed by oxalic
acid solution relative to the solution temperature during leaching of Itakpe (Nigeria) iron oxide
ore in oxalic acid solution.
During the leaching process, the iron ore (being in solid phase) was assumed to be stationary.
The leaching occurs as a result of the attack on the ore by hydrogen ions from the oxalic acid
within the liquid phase (in the presence of oxygen).
2.1 Model Formulation
Results of previous research work  carried out were used for this work. Statistical and
computational analysis of these results  presented in Table 1, gave rise to Table 2 which
(lnQ) = √T (approximately) (4)
lnQ = N(√T) (5)
534 C. I. Nwoye, et al. Vol.8, No.7
Q = e(N(√T)) (6)
Introducing the value of N into equation (6)
Q = e(0.987(√T)) (7)
T = Solution temperature during leaching of iron oxide ore in oxalic acid solution. ( 0C)
N = 0.987(Temperature coefficient for oxalic acid solution during leaching of iron oxide ore)
determined in the experiment .
Q = Quantity of heat energy absorbed by the oxalic acid solution during the leaching
Equation (7) is the derived model.
Table 1. Variation of Quantity of Heat Absorbed by Oxalic Acid Solution with Solution
temperature and Weight Input of Iron Oxide Ore .
Where µ = Mass of iron oxide ore used for the leaching process (g)
Q (J) T(0C) μ (g)
Vol.8, No.7 Model for Predictive Analysis of Heat Absorbed 535
Table 2. Variation of lnQ with √T
3. BOUNDARY AND INITIAL CONDITION
In a cylindrical flask of height; 30cm, iron oxide ore was placed prior to the addition of oxalic
acid which was used as the leaching solution. Initially, the flask was assumed to be free of
bacteria and other micro organisms. It was assumed that atmospheric oxygen affected the process
initially. Weights input of iron oxide ore considered for the work ranged from 6-42g. Other
process conditions used include: initial pH of leaching solution; 6.5, leaching time; 30 minutes,
leaching temperature of 25oC, average ore grain size; 150µm, and oxalic acid concentration at
The boundary conditions considered for the model formulation were: assumption of a zero
gradient for the liquid scalar and also gas phase at the top of the particles. It was also assumed
that atmospheric oxygen interacted with the non flowing leaching solution and also with the top
and bottom part of the ore particles (which were in the gas and liquid phases respectively). The
sides of the particles were assumed to be symmetrical. These process conditions are presented in
details in the report .
4. MODEL VALIDATION
The validity of model was established by calculating the deviation of the model-predicted Q
values from values obtained from the experimental work  carried out.
It was believed that deviations of model-predicted Q values from the corresponding experimental
values resulted from non-consideration (during model formulation) of the surface properties of
the ore and the physiochemical interactions between the ore and leaching solution which were
536 C. I. Nwoye, et al. Vol.8, No.7
found to have played vital roles during the leaching process . Based on the foregoing, it is
expected that a correction factor be added to the model-predicted values to make up for those
factor neglected during the model formulation.
The deviation (Dv) (%) of model-predicted Q values from the corresponding experimental Q
values is expressed as;
Dv = Qp – Qe x 100 (8)
Where Qp = Predicted Q values from model
Qe = Experimental Q values
On the other hand, correction factor (Ct) is expressed as the negative of the deviation. Therefore
Ct = -Dv (9)
Substituting equation (8) into equation (9)
Ct = -100 Qp – Qe (10)
Addition of Ct values obtained from equation (10) to the model-predicted values of Q gives
exactly Q values as obtained from the experiment .
5. RESULTS AND DISCUSSION
The derived model is equation (7). A comparison of the values of Q from the experiment and
those from the model shows very minimum positive and negative deviation hence depicting the
reliability and validity of the model. This is shown in Table 3. The respective positive and
negative deviations of the model-predicted Q values from the corresponding experimental Q
values is less than 21%, which is quite within the acceptable range of deviation limit of
experimental results. Table 2 was found to agree with equation (1) following the values of lnQ/N
and √T evaluated from Table 1.
The validity of the model is believed to be rooted on equation (1) where both sides of the
equation are corresponding almost equal. The positive values of heat absorbed as obtained from
experiment and model indicate and agree that the leaching process is endothermic in nature.
Vol.8, No.7 Model for Predictive Analysis of Heat Absorbed 537
Table 3. Comparison between heat absorbed by oxalic acid solution as predicted by model and as
obtained from experiment .
Where Qexp = Q values from experiment 
QM = Q values predicted by model
The model predicts the quantity of heat absorbed by oxalic acid solution relative to the solution
temperature during leaching of Itakpe iron oxide ore. The validity of the model is believed to be
rooted on equation (1) where both sides of the equation are correspondingly almost equal. The
deviation of the model-predicted Q values from the corresponding experimental Q values is less
than 21% which is quite within the acceptable range of deviation limit of experimental results.
The positive values of heat absorbed as obtained from experiment and model indicate and agree
that the leaching process is endothermic in nature.
It is expected that more process parameters should be incorporated into the model in further
works with the aim of reducing the deviations of the model-predicted Q values from those of the
The authors thank 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.
Qexp QM Dv (%) Ct (%)
538 C. I. Nwoye, et al. Vol.8, No.7
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Vol.8, No.7 Model for Predictive Analysis of Heat Absorbed 539