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Journal of Minerals & Materials Characterization & Engineering, Vol. 8, No. 8, pp 621-633, 2009
jmmce.org Printed in the USA. All rights reserved
Model for Predicting the Initial Solution pH at Pre-Assumed Final pH and
Concentration of Dissolved Zinc during Leaching of Galena
in Butanoic Acid Solution
C. I. Nwoye
Department of Materials and Metallurgical Engineering, Federal University of Technology,
Model for predicting the initial solution pH at pre-assumed final pH and concentration of
dissolved zinc, during leaching of galena in butanoic acid solution has been derived. The model;
α = 1.4γ
shows that the initial pH of the leaching is dependent on the values of the pre-assumed final
solution pH and concentration of dissolved zinc. The validity of the model was rooted in the
expression eN(γ/α) = 3√Zn where both sides of the expression were approximately equal to 4. The
respective deviation of the model-predicted initial solution pH value from that of the
corresponding experimental value was less than 2% which is quite within the acceptable
deviation limit of experimental results.
Keywords: Model, Prediction, pH, Butanoic Acid, Galena, Leaching.
It has been discovered  that the lead-zinc deposit of Nigeria especially Ishiagu-Abakiliki area
of telethermal type originated from low temperature hydrothermal solutions associated with
tertiary to recent volcanism. They have been confined to vertical fracture zones in shale’s and
mudstone and to a lesser extent in sand stone. The ore mineral was found  to be galena and
sphalerite accompanied by some chalcopyrite and secondary pyromorphite, anglesite and crussite
and the gangue is chiefly quartz with some siderite and marcarsite. In the Abakiliki zone, the
622 C. I. Nwoye Vol.8, No.8
lead-zinc deposit is due to dense hydrothermally heated connate brine from temperature of 100-
1600C. At this temperature, the brine-rich chlorides from sediments and metals from clay and
feldspar combine with sulphur to form the sulphide . The mineral deposit of Ishiagu-Nigeria
consists of galena (PbS) and sphalerite (ZnS). It is estimated to consist about 75% of the total
deposit with minor pyrite (FeS), chalcopyrite (CuFeS), siderite (FeCO3) and quartz (SiO2). The
chemical and mineralogical composition of the ore are thus: PbS (45.84%), ZnS (30.63%), SiO2
(9.96%), FeS (5.49%), CuFeS (4.38%) and FeCO3 (3.63%) .
A feasibility study  on the extraction of lead from Ishiagu lead-zinc ore has been carried out
with the view to knowing the possibility of extracting lead from Ishiagu galena using different
acid types. The results of the investigation reveal that the weight concentration of lead after
leaching with dilute nitric acid, sulphuric acid and aqueous solution of both acids are 39.5% w/w,
14.16% w/w and 15.18% w/w respectively. These results indicate that nitric acid gave the best
result of recovery (84.2%), with original lead in the ore being 46.9% w/w.
It has been suggested  that flotation of sphalerite could be carried out using some imported
reagents and fuel oil, using a method of recovery called froth flotation. This method was found
to utilize the difference between the physico-chemical surface properties of a mineral. This
conclusion followed a research carried out by Onyemaobi  to evaluate the flotation
performance of Nigeria’s sphalerite from lead-zinc ore with particular reference to the Ishiagu
lead-zinc ore. It has been discovered  that most lead-zinc ores are fine grained and are
concentrated mainly by flotation. The flotation results obtained in this work (Ishiagu ore
inclusive) are that the factors affecting flotation includes (1) Degree of oxidation (2) Abundance
in nature of iron sulphide and nature of a non-sulphide gangue  Galena was found  to float
in slightly alkaline medium (pH9-10) with short-chain xanthates (potassium ethyl xanthates;
isopropyl xanthates). In addition to this, it was discovered that at the critical pH of 10.4 when
ethyl xanthate is used, usage of lime would make it behave like a depressant . Investigation on
the role of pH on flotation of sphalerite from Ishiagu lead-zinc ore has been carried out. The
result of the investigation reveals that if there are no activator ions in the medium, sphalerite
does not float with xanthate and dithiophosphate collector. Activation and flotation of sphalerite
in acid medium (pH4-5) is performed with As, Sb, and Pt ions and in neutral conditions (pH 6.8-
7.3) Ce, Pb, Cu, Cd, Ag, Hg, B and Au ions became effective .
It has been discovered  that during bioleaching of Ishiagu lead-zinc ore, using mixed cultures
of Acidithiobacillus Ferrooxidans, Acidithiobacillus Thiooxidans and Leptospirillum
Ferrooxidans, higher silica contents of the ore reduce acidity, iron mobility and oxidation. It was
also found  during the leaching of zinc and copper out from their respective sulphide ore that
the concentrations of zinc and copper formed reduced as particle size decreased while silica,
sulphur, iron and lead contents increased. Also leaching rate of copper was found to be lower
than zinc. Results of sedimentation analysis carried out by Nwoye  indicate that the average
grain size of Ishiagu galena concentrate is approximately 100μm. He also found that the
mechanism of bioleaching of Ishiagu galena concentrates was indirect mechanism. This was
sequel to the dominance of Fe3+ ions over H+ during the leaching process. The best operating
conditions for the highest yield of Pb were found to be; leaching temperature of not less than
Vol.8, No.8 Model for Predicting the Initial Solution pH 623
320C, starting pH of leaching solution in the range 1.8 – 2.0, concentration of Fe2+ in the starting
leaching solution: 2g/dm3 (0.007M), grain size of ore to be leached: 0.063μm, mixed culture of
Acidithiobacillus Ferrooxidans (ATF), Acidithiobacillus Thiooxidans (ATT) and a newly
discovered bacteria (CBT). The microorganisms, Acidithiobacillus Ferrooxidans are able to
oxidize ferrous ions and the reduced sulphur compounds  while Acidithiobacillus
Thiooxidans are able to oxide only reduced sulphur compound summarized by the
2Fe2+ + 2H+ + 0.5O2 + bacteria 2 Fe3+ + H2O (1)
S2- S0 S2O32- S4O62- SO32- SO42 (2)
Researchers  discovered that arsenic can be reduced in a complex galena concentrate by
Acidithiobacillus Ferrooxidans. The results of the investigation reveal that arsenopyrite was
totally oxidized. The sum of arsenic remaining in solution and removed by sampling represents
from 22 to 33% in weight (yield) of the original content in the mineral. The rest of the
biooxidized arsenic form amorphous compounds that precipitate galena (PbS) was totally
oxidized too, anglesite (PbSO4) formed is virtually insoluble and remains in the solids. The
influence of seven factors in a batch process was studied. The maximum rate of arsenic
dissolution in the concentrate was found using the following levels of factors; small surface area
of particle exposure; low pulp density, injecting air and adding the leaching medium to the
system. It was also found that ferric chloride and carbon dioxide decreased the arsenic
dissolution rate. Bioleaching kinetic data of arsenic solubilization were used to estimate the
dilution rate for a continuous culture. Calculated dilution rates were relatively small (0.88 -
It has been found  that the leaching rates of single sulphide minerals decreased in the order
pyrite > sphalerite > galena > chalcopyrite, with the rate of pyrite dissolution being of a similar
magnitude to the highest values reported previously . The leaching rates of galena,
chalcopyrite and sphalerite increased by factors of 31, 18 and 1.5, respectively, in the presence of
pyrite, due to its superior catalytic properties. In the galena + pyrite experiment, the
concentration of Fe did not increase appreciably between the first and final sampling times,
whilst the Pb concentration did increase significantly. Hence, galvanically promoted dissolution
of galena + pyrite decreases the pyrite electrode potential and its dissolution rate. Also in the
galena + pyrite experiment, 75% of the total S in solution as measured by ICP –AES was
detectable by HPLC, which detects only anionic species; this could be due to the presence of
colloidal elemental S . Acid leaching of lead sulphide has been investigated . The results
of the investigation indicate that prior to mineral addition, the redox potential of the acid
solutions was 360 ± 10mV (SHE). On addition of the mineral powders, the value changed
rapidly. In most cases, the redox potential then decreased by a few tens to a hundred or more
mV to reach a stable value, except for the single-phase galena + pyrite mixture, for which the
redox potential rose continuously throughout the experiment. The ranges of redox potential at pH
2.5 recorded for each single mineral sample are plotted onto the potential pH diagram for the S –
H2O system. Although the pH of the leach solution was kept constant, the generation or
consumption of protons could be determined by monitoring the volume of acid needed to
maintain a pH of 2.5. Dissolution of oxidation products formed during grinding of galena
624 C. I. Nwoye Vol.8, No.8
produced dissolved Pb(II) and sulphur concentrations significantly higher than in the case of
sphalerite leaching. However, concentrations of both species decreased over the first hour of the
experiment, probably due to restricted solubility of PbCl2 and PbSO4, the latter phase having a
particularly low solubility product Ksp (PbSO4) = 10-7.86. The equations of the reactions
involved are as follows.
(1-y)(PbS + 4Cl- PbCl2-4 + S + 2e-) (3)
y (PbS + 4Cl- + 4H2O PbCl2-4 + SO2-4 + 8H+ +8e-) (4)
Though the dissolved metal to sulphur ratios were not as high as in the case of sphalerite
leaching, they increased from 1.3 (y = 0.7) after 19mins to 2.5 (y = 0.4) after 182min. Based on
the XPS data, no significant changes in S speciation occur at the surfaces of these minerals as a
result of atmospheric oxidation and acid leaching. Elemental S has been reported  at the
surfaces of both air oxidized and acid-leached galena but no evidence for the presence of
elemental S was obtained here possibly due to the sulphur desorption in UHV chamber of the
instrument, which had no low – temperature range .
Lead sulphide is rapidly attacked by ferric ion over a wide range of conditions. Soluble lead
chlorocomplexes as well as ferric and ferrous chlorocomplexes are formed. It is to be expected
after all, that the various metal chlorocomplexes would play an important role in the leaching
reaction mechanism. In addition, it is clear from the result of previous workers that the effect of
Fe3+, Cl- and H+ are coupled, and that the reaction kinetics and the mechanism of ferric chloride
leaching of PbS have not been clearly established . Rapid parabolic kinetics were observed in
this study under all conditions and it was shown that the parabolic rate constant was directly
proportional to the area of galena being leached. In the presence of ferric ion, the rate was
insensitive to HCl concentrations < 3.0M, but increased rapidly at higher acidities because of
direct acid attack of the sulphide. In the absence of ferric ion, the rate increased steadily with
increasing HCl concentrations, and linear kinetics was observed. The galena leaching rate
increased as (FeCl3) for FeCl3 concentrations in the range 0.01-0.1M, but decreased slightly with
increasing FeCl3 concentrations in the range 0.1M to 2.0M FeCl3. The rate was virtually
independent of the concentration of the FeCl2 reaction product. The presence of significant
amount of the PbCl2 reaction product, however, caused the galena leaching rate to decrease
rapidly. A minimum leaching rate was realized in saturated PbCl2 solutions . Studies  on
the ferric chloride brine leaching of galena concentrate have been carried out. The results of the
investigation reveal several advantages of ferric chloride over the reagents as a leaching media
which includes that it exhibits substantially faster dissolution rates for most sulphides, it is
regenerated easily by chlorination of ferrous chloride leaching by-products, and it has greater
potential for the treatment of complex sulfides . Further studies  on the ferric chloride
brine leaching of galena concentrate have been carried with the view to investigating the
thermodynamics and kinetics of the process. Seon–Hyo etal  discovered that under the
leaching condition of their work, the distribution of the various metal chloro complexes is
relatively insensitive to the extent of PbS dissolution . Investigations  on the Cl2-O2
leaching of galena flotation concentrate have been done with the view to evaluating the kinetics
of the process. The results of this investigation indicate that the rate of gas transfer can be
Vol.8, No.8 Model for Predicting the Initial Solution pH 625
enhanced by increasing the partial pressure of the gas and by using vigorous agitation to increase
the surface area of the liquid-gas interface.
Nwoye  derived a model for predicting the leaching rate of lead during bioleaching of galena
using different strains of bacteria such as ATF, ATT and the newly discovered bacteria (CBT
and CTT). The model;
Ø = e- (ϒ + lnϒ) (5)
referred to as pH-model, calculates the leaching rate when the pH of the leaching solution is
known at any instant during the leaching process.
Where γ = pH of the leaching solution at any instant during the leaching process.
Ø = Leaching rate of lead from galena (g/dm3hr-1)
On multiplying both sides of the model by leaching time t, the model then calculates the
concentration of Pb leached out as
Ө = e-(ϒ + lnϒ)t.
Nwoye  also derived a model (known as ΔG – model) for predicting the leaching rate of lead
relative to the bacterial leaching index and the free energy change associated with the
bioleaching process involved. The model;
Ø = 10(ΔG/C) (6)
calculates the leaching rate when the values of the free energy change ΔG, associated with the
leaching reaction as well as bacterial leaching index C, are known. This model indicates that the
value of the leaching rate and concentration of leached Pb depends largely on the nature and
leaching ability of bacteria or bacteria consortium used. It was observed that the greater the value
of C, the higher the bacterial leaching ability and tendency. It was also found that the bacterial
leaching index of bacillus spp is within the range 2-2.2 while mixed cultures of bacillus spp gave
greater value (close to 3) of C than the case of single bacillus spp . Based on the fore going,
given the values of the leaching rate and the associated free energy change, the specie of the
bacteria used can be identified by calculating the value of C, just by re-arranging the model as C
= ΔG/log Ø. It was observed that pseudomonas spp. of bacteria have a value of C, less than 1.
This value was found to be associated with very poor yield of Pb and leaching rate. Furthermore,
on multiplying both sides of the model by the leaching time t, the model then calculates the
concentration of leached Pb as
Ө = (10(ΔG/C) ) t.
Nwoye  further derived a more comprehensive and precision-enhanced model by jointly
associating the pH-model and ΔG-model. The resultant model;
ΔG = Log e-(ϒ+Inϒ) C (7)
not only calculates both the leaching rate and concentration of leached Pb (though indirectly),
but also calculates directly the free energy change associated with the leaching process as well as
the bacterial leaching index, as the case may be providing that two of the process parameters are
known. The pH of the leaching solution during the leaching process can also be calculated using
626 C. I. Nwoye Vol.8, No.8
It has been found [10,21] that the final pH of the leaching solution depend on the leaching time,
initial pH for the leaching solution and the leaching temperature.
The aim of this work is to derive a model for predicting the initial solution pH at pre-assumed
final pH and concentration of dissolved zinc during butanoic acid leaching of Ishiagu (Nigeria)
galena. The proposed work resulted from the need to be informed about the range of initial
solution pH at which a feasible butanoic acid leaching of galena should commence having pre-
assumed the final pH and concentration of dissolved zinc expected at the end of the leaching
process. It is expected that the model would guide extractive metallurgists in achieving
maximum yield through the application of the optimum initial pH of the leaching solution. This
derivation is in furtherance of the previous work .
During the leaching process, the ore was assumed to be stationary in the reaction vessel and
contains the un-leached lead and zinc as part of reaction remnants. The ore was attacked by
hydrogen ions from butanoic acid within the liquid phase, and in the presence of oxygen.
2.1 Model Formulation
Results from experimental work  carried out at SynchroWell Research Laboratory, Enugu
were used for the model derivation. These results are as presented in Table 1.
Computational analysis of these experimental results  shown in Table 1, resulted to Table 2
which indicate that;
e[N(γ/α)] = 3√Zn (approximately) (8)
e[N(γ/α)] = (Zn)1/3 (9)
Taking the natural Log of both sides of equation (9)
N(γ/α) = ln[(Zn)1/3] (10)
(γ/α) = ln[(Zn)1/3] (11)
(α/γ) = N (12)
Introducing the value of N into equation (12) reduces it to;
α = 1.4γ (13)
Vol.8, No.8 Model for Predicting the Initial Solution pH 627
N = 1.4 (Dissolution coefficient of zinc in butanoic acid) determined in the experiment .
α = Initial pH of the butanoic acid leaching solution just before the leaching process started.
γ = Final pH of the butanoic acid leaching solution at time t.
Zn = Concentration of dissolved Zn during the leaching process (mg/kg)
Equation (13) is the derived model.
Table 1. Variation of the initial and final pH of the butanoic acid leaching solution with the
concentration of dissolved Zinc .
(γ) (α) Zn (mg/kg)
Table 2. Variation of eN(γ/α) with 3√Zn.
(γ/α) N(γ/α) eN(γ/α) 3√Zn
628 C. I. Nwoye Vol.8, No.8
3. BOUNDARY AND INITIAL CONDITION
Iron oxide ore was placed in cylindrical flask 30cm high containing leaching solution of
hydrogen peroxide. The leaching solution is non flowing (stationary). Before the start of the
leaching process, the flask was assumed to be initially free of attached bacteria and other micro
organism. Initially, the effect of oxygen on the process was assumed to be atmospheric. In all
cases, weight of iron oxide ore used was 5g. The initial pH range of leaching solutions used;
3.80-4.83 and leaching time of 2 hrs (120 minutes) were used for all samples. A constant
leaching temperature of 25oC was used. Hydrogen peroxide concentration at 0.27mol/litre and
average ore grain size;150µm were also used. Details of the experimental technique are as
presented in the report .
The leaching process boundary conditions include: atmospheric levels of oxygen (considering
that the cylinder was open at the top) at both the top and bottom of the ore particles in the gas
and liquid phases respectively. A zero gradient was assumed for the liquid scalar at the bottom of
the particles and for the gas phase at the top of the particles. The sides of the particles were
assumed to be symmetries.
4. MODEL VALIDATION
The formulated model was validated by calculating the deviation of the model-predicted initial
pH from the corresponding experimental pH values.
The deviation recorded 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. It
is expected that introduction of correction factor to the predicted initial pH, gives exactly the
experimental initial pH values.
Deviation (Dn) (%) of model-predicted initial pH values from those of the experiment is given
Dn = PI – EI x 100 (14)
Where PI = Predicted initial pH values
EI = Experimental initial pH values
Since correction factor (Cr) is the negative of the deviation,
Cr = - Dn (15)
Substituting equation (14) into equation (15) for Dn,
Cr = -100 PI - EI
Vol.8, No.8 Model for Predicting the Initial Solution pH 629
It was observed that addition of the corresponding values of Cr from equation (16) to the model-
predicted initial pH gave exactly the corresponding experimental initial pH values .
5. RESULTS AND DISCUSSION
The derived model is equation (13). An ideal comparison of the initial pH 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 (coefficient of determination). The values of the correlation coefficient, R
calculated from the equation;
R = √R2
using the r-squared values (coefficient of determination) from Figs.1 and 2 show a better
correlation (0.9565) with model-predicted initial solution pH than that obtained from experiment
(0.9300). This suggests that the model predicts more accurate, reliable and ideal initial solution
pH than the actual experiment despite its deviations from the experimental values.
Fig. 1- Effect of initial solution pH on the
conce ntra tion of z i nc dissolved during buta noi c
a cid l eachi ng of ga lena (as obta i ned from the
Initia l pH
Zn (m g/kg)
Fig. 2- Effect of initial solution pH on the
conce ntra tion of z i nc dissol ve d during buta noi c
a ci d l e achng of ga l ena (a s predicte d by de ri ve d
3.5 44.5 5
Initia l pH
Concentration of Zn
630 C. I. Nwoye Vol.8, No.8
Comparison between Figs.3 and 4 also show that the final solution pH from experiment has a
better correlation (0.9954) with the initial pH predicted by the model than that obtained from the
relationship between experimental values of the final and initial solution pH (0.9926).
Fig. 3- Effect of initial solution pH (from mode l) on
th e fi n al p H (as o b tai n ed fro m the ex p erim ent [22 ])
Initia l pH
Fi nal pH
Fig. 4- Effe ct of ini tial solution pH on the final pH
(both a s obta i ned from the expe ri m ent )
= 0. 9926
Initia l pH
However, Fig. 5 shows very close alignment of the curves from model-predicted values of the
initial pH (MoD) and that from the corresponding experimental values (ExD). The degree of
alignment of these curves is indicative of the proximate agreement between both experimental
and model-predicted initial solution pH. The validity of the model is believed to be rooted on
equation (8) where both sides of the equation are approximately equal to 4. Table 2 also agrees
with equation (8) following the values of eN(γ/α) and 3√Zn evaluated following statistical and
computational analysis carried out on the experimental results in Table1.
Based on the foregoing, the model is believed to be very valid as a predictive tool. Furthermore,
Fig.6 shows insignificant positive and negative deviations of the mode-predicted initial pH from
the corresponding experimental values. It was also shown in Fig.6 that the positive and negative
deviations of the model-predicted initial pH values from those of the experiment were less than
2% which is quite within the acceptable deviation limit of experimental results. The positive and
Vol.8, No.8 Model for Predicting the Initial Solution pH 631
negative deviations (of the model-predicted initial pH) from the actual experimental values show
undulating relationship (as in Fig.6) with the model-predicted initial pH.
Fig. 5- Comparison betwe e n the initia l solution
pH as obtained from the experiment  and as
pre di cte d by model
60 6570 7580 85
Conce ntra tion of Zn (mg/ kg)
Fig. 6- Va riation of model-predicte d initia l solution
pH with its associated deviation from experimental
Initia l pH
Devi ati o n (%)
The least and highest magnitude of deviation of the model-predicted initial solution pH (from the
corresponding experimental values) are -0.22% and 1.71% which correspond to initial solution
pH 4.54 and 4.75 respectively. Correction factor for the model-predicted initial solution pH
(shown in Fig.7) similarly shows an undulating relationship with model-predicted initial pH.
However, the orientation of this curve is opposite that of the deviation values of model-predicted
initial pH (Fig.6). This is because correction factor is the negative of the deviation as shown in
eqns. (15) and (16). 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.
Based on the foregoing, Fig.7 indicates that a correction factor of -0.22 and 1.71% make up for
the least and highest deviation of 0.22 and -1.71% resulting from application of initial solution
pH 4.54 and 4.75 respectively. It is pertinent to state that the actual deviations are just the
632 C. I. Nwoye Vol.8, No.8
modulus of the values. The role of the sign attached to the values is just to show when the
deviation is surplus or deficit.
Fig. 7- Va ri ati on of model-pre di cte d i ni tial pH w i th
its associated correction factor
Initia l pH
Cor rection factor
The model predicts the initial solution pH at pre-assumed final solution pH and concentration of
dissolved zinc during leaching of Ishiagu (Nigeria) galena in butanoic acid solution. This
prediction could be done during the leaching process providing the expectant final pH of the
solution and concentration of dissolved zinc are known. The validity of the model is believed to
be rooted in the expression eN(γ/α) = 3√Zn where both sides of the expression are approximately
equal to 4. The respective deviation of the model-predicted initial solution pH value from that of
the corresponding experimental value is less than 2% which is quite within the acceptable
deviation limit of experimental results.
The author thanks Dr. Ekeme Udoh and Pearl Bassey, modelling experts 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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