www.elsevier.com/locate/hydromet
Hydrometallurgy 73 (2004) 313–324
Relative importance of diffusion and reaction control during
the bacterial and ferric sulphate leaching of zinc sulphide
Gabriel da Silva*
Department of Chemical Engineering, The University of Newcastle, University Drive, Callaghan, NSW 2308, Australia
BHP Billiton, Newcastle Technology Centre, Vale Street, Shortland, NSW 2308, Australia
Received 28 October 2003; received in revised form 12 December 2003; accepted 16 December 2003
Abstract
A study has been undertaken on the bacterial and ferric sulphate leaching of sphalerite, with the aim of observing the relative
importance of both diffusion and reaction control, across a range of operating conditions. To facilitate this kinetic analysis a
mixed-control rate equation was developed based upon the shrinking particle and shrinking core models, featuring both an
intrinsic rate of zinc extraction and a product layer diffusion coefficient. The ferric sulphate oxidation of a pure sphalerite
sample was first studied, and the process was found to be mainly controlled by surface diffusion, thought to be due to formation
of the elemental sulphur product layer. The mesophilic bacterial oxidation of a high-grade zinc ore was studied at 35 jC, and theprocess was observed to be controlled by both chemical reaction and diffusion. However, during the mesophilic bacterial
oxidation of a low-grade zinc ore at 25 jC, diffusion was found to be rate limiting. It was proposed that this diffusion resistance
arises from an unreacted layer of gangue material.
D 2004 Published by Elsevier B.V.
Keywords: Diffusion; Reaction control; Zinc sulphide
1. Introduction economic interest is sphalerite (ZnS), which is by far
In recent years, great interest has emerged in the use
of biological mineral processing technologies. In par-
ticular, the bioleaching of sulphide minerals has been
frequently studied, due to its widespread applications
in the processing of copper, uranium, refractory gold
and other precious and semi-precious metals, utilising
both heap and tank leaching processes (Rawlings et al.,
2003). Another mineral for which bioleaching is of
0304-386X/$ - see front matter D 2004 Published by Elsevier B.V.
doi:10.1016/j.hydromet.2003.12.004
* Department of Chemical Engineering, The University of
Newcastle, University Drive, Callaghan, NSW 2308, Australia. Tel.:
+61-2-4921-7033; fax: +61-2-4921-6920.
E-mail address: [email protected] (G. da Silva).
the most abundant of the zinc-bearing minerals. Cur-
rently, the majority of sphalerite ores are treated
through flotation, followed by smelting. However,
smelting is becoming increasingly cost intensive due
to tightening environmental restrictions. Also, due to
the need to process complex ores of increasingly low
grades, flotation is becoming more and more difficult.
These difficulties have left producers searching for
more cost effective and environmentally friendly pro-
cessing options.
The hydrometallurgical processing of sphalerite
presents a possible alternative to pyrometallurgical
techniques. Over the last few years, several innovative
leaching processes have been developed for zinc
G. da Silva / Hydrometallurgy 73 (2004) 313–324314
extraction, such as copper catalysed ammonia leach-
ing (Ghosh et al., 2002, 2003), pressure leaching
(Bolorunduro et al., 2003), persulphate leaching (Ba-
bu et al., 2002), simultaneous leaching (Madhuch-
handa et al., 2003; Kai et al., 2000), heap bioleaching
(Harvey et al., 2002) and tank bioleaching (Pani et al.,
2003). Of these, the bioleaching processes perhaps
present some of the most promising technology, due
to their inherent low costs and environmental advan-
tages. Further interest has been generated in the
bioleaching of sphalerite due to its possible environ-
mental implications; bioleaching has been suggested
as a possible means of removing trace amounts of
metals such as zinc and iron from contaminated sedi-
ments and soils (Chartier et al., 2001; Chen and Lin,
2000), and may also be involved in the production of
heavy metal contaminated mine run-off (Baker and
Banfield, 2003).
The bioleaching of zinc sulphide occurs via an
indirect mechanism (Boon et al., 1998; Fowler and
Crundwell, 1998), where mineral oxidation is facili-
tated by the reduction of ferric to ferrous ions (Eq.
(1)). Ferric ions are then bacterially regenerated from
ferrous ions (Eq. (2)), thus maintaining a continual
supply of oxidising agent.
ZnSþ 2Fe3þ ! Zn2þ þ S0 þ 2Fe2þ ð1Þ
2Fe2þ þ 0:5O2 þ 2Hþ!Bacteria 2Fe3þ þ H2O ð2Þ
During the oxidative leaching of sphalerite, a
product layer of elemental sulphur is formed. In the
absence of bacteria, it is well known that this product
layer imparts a diffusion resistance upon the rate of
zinc extraction (Lochmann and Pedlı́k, 1995). How-
ever, during bioleaching, sulphur-oxidising bacterium
of the genus Acidithiobacillus are capable of remov-
ing this layer via Eq. (3), thus reducing the diffusion
resistance (Fowler and Crundwell, 1999).
S0 þ 1:5O2 þ H2O!Bacteria
SO2�4 þ 2Hþ ð3Þ
During bioleaching, the rate of zinc extraction is
often still controlled by product layer diffusion, in
spite of the bacterial oxidation of elemental sulphur.
For example, if the rate of elemental sulphur bioox-
idation is inadequate, then this product layer may
build up to a stage where diffusion through it becomes
rate limiting. For the bioleaching of low-grade ore at
larger particle sizes (such as during heap leaching
processes), an inert layer of gangue material is often
left behind after reaction, which may be capable of
limiting the rate of zinc extraction through molecular
diffusion. A further source of product layer diffusion
may arise during the bioleaching of binary zinc/lead
sulphide material, where galena (PbS) is oxidised to
insoluble lead sulphate in galvanic preference to the
oxidation of sphalerite (da Silva et al., 2003). Diffu-
sion through the deposited lead sulphate product layer
is then thought to hinder the rate of zinc extraction.
The effects of lead sulphate are especially significant,
as sphalerite and galena are very commonly associat-
ed, and are thus often processed simultaneously (Liao
and Deng, 2004). Furthermore, diffusion limitation
may also arise from material which precipitates from
solution onto the mineral particle surfaces.
This study explores the relative importance of
reaction- and diffusion-related phenomena occurring
during the bacterial and ferric sulphate oxidation of
zinc sulphide. In order to perform the required kinetic
analysis, a rate equation featuring both a diffusion and
reaction term is derived. This rate equation is then
applied to a variety of experimental data. Experiments
have been performed on a range of mineral samples,
including pure mineral sphalerite, and high- and low-
grade sphalerite ores.
2. Theory
The following adapted form of the shrinking par-
ticle model (Yagi and Kunni, 1955) is well known to
describe the chemically controlled ferric leaching of
sphalerite, as well as other sulphide minerals.
t ¼ 2qZnSR
rZnS1� rc
R
h ið4Þ
where t is the reaction time (s), qZnS is the molar
density of sphalerite within the ore (mol m� 3), rZnS is
the intrinsic rate of zinc extraction (mol m� 2 s� 1), R
is the initial radius of the particle (m), and rc is the
radius of the reacting particle core (m). Application of
this model requires that a conversion be made from
fractional mineral extraction (X) to rc/R. For this, Eq.
(5) is applied, which assumes that the reacting par-
G. da Silva / Hydrometallurgy 73 (2004) 313–324 315
ticles are mono-sized spheres. This assumption is the
same that is applied when a plot of [1� (1�X)1/3] vs.
t is made to test for surface reaction control.
rc
R¼ ð1� X Þ1=3 ð5Þ
During ferric leaching, the intrinsic rate of min-
eral oxidation is known, from both theory and
experiment, to vary in the half order of ferric ion
concentration for the oxidation of sphalerite (Crund-
well, 1987; Jin et al., 1984; Warren et al., 1985), as
well as other metal sulphides (Fowler et al., 2001;
Fuerstenau et al., 1987; Hirato et al., 1986). This
relationship may be represented by Eq. (6), where
kZnS is the rate constant of zinc extraction (mol0.5
m� 0.5 s� 1). Here, the ferric ion concentration is
expressed in mol m� 3.
rZnS ¼ kZnS½Fe3þ�0:5 ð6Þ
Although kZnS in the above equation is an intrinsic
property, it is expected to vary depending on the
nature of the particular mineral sample tested. For
example, it has been shown that iron impurities within
the sphalerite crystal matrix dramatically affect the
rate of zinc dissolution during oxidative leaching
(Crundwell, 1988; Palencia and Dutrizac, 1991). Also,
the presence of other mineral species such as pyrite,
galena, manganese dioxide and chalcopyrite will
affect the magnitude of kZnS through galvanic inter-
action (Attia and El-Zeky, 1990; da Silva et al., 2003;
Kai et al., 2000; Madhuchhanda et al., 2003; Mehta
and Murr, 1982).
While the shrinking particle model is capable of
describing the rate of sphalerite oxidation when
surface reaction is rate controlling, it is often found
that the rate controlling mechanism is one of product
layer diffusion. To describe such situations, we may
use the shrinking core model with diffusion control
(Yagi and Kunni, 1955), where D is the diffusion
coefficient of the reactant (ferric ions) through the
product layer (m2 s� 1).
t ¼ qZnSR2
12D½Fe3þ�1� 3
rc
R
� �2
þ2rc
R
� �3� �
ð7Þ
So as to determine the relative importance of
reaction and diffusion, it is desirable to incorporate
both of the above models into a single relationship
describing leaching under conditions of mixed reac-
tion and diffusion control (mixed control). This is
easily performed, as both Eqs. (4) and (7) represent
resistances, and as such, are additive. This property
has been used to derive Eq. (8), the overall rate
equation for the ferric leaching of sphalerite.
t ¼ qZnSRR
12D½Fe3þ�1� 3
rc
R
� �2
þ2rc
R
� �3� ��
þ 2
rZnS1� rc
R
� �h i�ð8Þ
In many cases, the above models cannot be directly
applied to leaching data, as they do not take into
account the possible presence of a lag period. This is
especially important during bioleaching, where lag
periods are often encountered during the initial stages
of bacterial growth and adaptation. During a lag
period, the above model fails due to the violation of
one of the boundary conditions used in its formula-
tion. In the derivation, it is assumed (for both the
shrinking core and shrinking particle models) that at
zero time, the radius of the reacting particle core is
equal to the initial particle radius; i.e., at t = 0, rc =R.
Essentially, this fixes the model to an initial extraction
of zero. However, if at the initial time the leaching
kinetics do not follow the tested model, this boundary
condition does not apply. To account for this short-
coming, the model has been derived with a new
boundary condition that does not fix the model to
any specific point (Eq. (9)). Instead, the user may
specify at which point to begin modelling the extrac-
tion kinetics. We have specified that at t = tlag,
rc =Rlag. Here, tlag and Rlag are taken from the first
experimental data point proceeding the lag period,
though any known point after the lag period may in
fact be used.
t � tlag¼qZnSR
R12D½Fe3þ�
("1� 3
�rc
R
�2
þ 2�
rc
R
�3
#�"1� 3
�Rlag
R
�2
þ 2�
Rlag
R
�3
#)
þ 2rZnS
("1�
�rc
R
�#�"1�
�Rlag
R
�#)8>>>><>>>>:
9>>>>=>>>>;
ð9ÞEquation (9) provides a model capable of describ-
ing leaching under conditions of mixed control, in
which a lag period is observed. This model would also
Table 1
Chemical composition of zinc samples
Sphalerite
mineral sample
High-grade
ore
Low-grade
ore
Zn (wt.%) 66.7 14.7 0.58
Pb (wt.%) 0.01 1.46 0.33
Fe (wt.%) 0.27 16.0 4.99
S (wt.%) 33.0 21.5 1.13
SO4 (wt.%) 1.70 0.00 0.05
qZnS (mol m� 3) 41,000 8900 350
G. da Silva / Hydrometallurgy 73 (2004) 313–324316
be applicable in the opposite situation, where an initial
period of rapid extraction is encountered, for example,
due to the rapid acid leaching of oxidised surface
material (see Crundwell, 1987).
Often, during leaching testwork, we wish only to
observe the relative importance of diffusion and
reaction. As such, it may be more useful to write
Eq. (9) in terms of an observed rate constant (kV) anddiffusion coefficient (D V), as in the following.
t � tlag ¼1
DV
(1� 3
rc
R
� �2
þ2rc
R
� �3� �
� 1� 3Rlag
R
� �2
þ2Rlag
R
� �3" #)
þ 1
k V1� rc
R
� �h i� 1� Rlag
R
� �� �)ð10Þ
(
Here, the ratio of k V to DV will reveal the relative
contribution of diffusion and reaction effects. That is,
a kV/DV ratio greater than one would indicate that
diffusion control dominates, while a ratio of less than
one would indicate that reaction control dominates.
3. Materials and methods
3.1. Mineral samples
Three mineral samples were utilised in the present
study. These included a pure sphalerite specimen and
two whole-ore samples of high and low zinc grades,
obtained from different ore deposits. The chemical
analysis of the significant components within each
sample is given in Table 1. Also included in the table
is the molar density of sphalerite within each sample,
calculated using the density of pure crystalline sphal-
erite, and by taking into account the mass fraction of
the sample present as sphalerite.
The crystalline mineral sample consisted of essen-
tially pure sphalerite, and was obtained from BK
Minerals, Australia. The sphalerite was low in iron,
and was associated with a negligible amount of
galena. The vast majority of sulphur within the sample
was associated with the zinc, apart from a small
amount of sulphate sulphur, presumably present due
to minor surface oxidation. For the leaching experi-
ments, the mineral sample was crushed and ground,
and sieved into size fractions of � 45, � 75 + 45,
� 125 + 75 and � 212 + 125 Am.
The zinc within the high-grade ore sample existed
as sphalerite, with the lead present as galena. The
sphalerite contained significant iron dispersed within
the mineral matrix, with the remaining iron present
largely as the sulphide minerals pyrite and pyrrhotite.
No sulphur was detected as being in the sulphate
form. The gangue material contained silicate minerals
such as quartz and garnet.
For the low-grade ore sample, zinc was again
present as a high iron sphalerite, while the lead existed
mainly as galena. Some sulphate sulphur was detected
in the sample, believed to be due to partial oxidation
of galena to lead sulphate. Iron was present mainly as
the sulphide mineral pyrrhotite, along with oxide
minerals such as magnetite. Little pyrite was present.
According to the sulphur content of the ore, around
30% of the iron existed as sulphide material. Minerals
were hosted within gangue of mostly quartz and
feldspar.
3.2. Bacterial culture
Bioleaching experiments were inoculated using a
mixed culture of mesophilic bacteria, which was
harvested from a mine site. This culture was found
to contain three dominant bacteria, resembling the
species Acidithiobacillus thiooxidans, Acidithiobacil-
lus ferrooxidans and Leptospirillum ferrooxidans. All
bioleaching experiments were conducted in Modified
Kelly’s Medium (MKM), containing 0.4 g L� 1 am-
monium sulphate, 0.4 g L� 1 magnesium sulphate and
0.04 g L� 1 potassium orthophosphate, adjusted to pH
2 with sulphuric acid. Bacteria were introduced into
the bioleaching experiments from a continually main-
tained inoculum reactor, which was stirred and aerat-
G. da Silva / Hydrometallurgy 73 (2004) 313–324 317
ed, and kept at 35 jC. The inoculum reactor was
periodically fed on a sulphide mineral concentrate,
and the bacteria were routinely examined under an
optical microscope. For the flask leaching experi-
ments at 25 jC, a flask of inoculum was first removed
from the 35 jC inoculum reactor to adapt it to the new
temperature. The flask was placed in an incubator at
25 jC for several days, and the bacteria were exam-
ined microscopically before being used to inoculate
the bioleaching experiments.
3.3. Ferric sulphate leaching
Ferric leach tests were conducted according to the
methodology of da Silva et al. (2003). Here, the
leaching medium was a 0.09 mol L� 1 solution of
Fe2(SO4)3 (i.e., 0.18 mol L� 1 Fe(aq)3 +), acidified with
0.51 mol L� 1 H2SO4. Experiments were conducted at
0.5% weight per volume solids content, with 0.25 g of
sample being added to 50 mL of reaction solution in a
250-mL flask. During reaction, samples were re-
moved and analysed for zinc concentration using
inductively coupled plasma (ICP) mass spectrometry.
Flasks were agitated periodically and kept at 21 jC.
3.4. Bioleaching
Reactor bioleaching tests again followed the meth-
odology of da Silva et al. (2003). Leaching was
conducted in 1-L bioreactors, maintained at 35 jC,stirred at 500 rpm and aerated at 150 mL min� 1.
Experimental composition was 90% MKM medium
and 10% bacterial inoculum. Solids were added at
10% weight per volume. Aliquots of solution were
periodically removed and assayed for zinc and iron
concentration using ICP. The volume of solution
removed from the reactor was replaced by MKM
and the removed metal content was factored into the
metal extraction levels. Water lost through evapora-
tion was regularly replaced, in order to maintain a
constant reactor volume. Solution pH and Eh were
monitored periodically, and sulphuric acid was added
as required in order maintain the reaction solution at
around pH 2. The concentration of ferrous ions was
also monitored, via titration with potassium dichro-
mate, which allowed for the calculation of ferric iron
concentration as the difference between the total iron
and the ferrous iron concentrations. At the conclusion
of the experiments, the reactor contents were filtered
and washed, and the solution assayed for metal con-
centrations. The residue was dried and weighed, and
then analysed for chemical composition. Extraction
levels were adjusted relative to the metal content of
the final residue.
Bioleaching tests were also conducted in agitated
flasks, as well as bioreactors. Flask bioleaching
experiments do not involve the intensive mechani-
cal stirring of the reactor leaching experiments, and
provide a better description of the abrasive effects
that the ore witnesses during heap leaching. The
leaching kinetics, however, are not expected to
model those actually observed during heap leach-
ing, due to the other complex phenomena which
occur within the heap. The flask tests consisted of
90 mL MKM and 10 mL inoculum, in a 250-mL
flask. To this, 5 g of solids was added to initiate
the tests. Flasks were placed in an incubator, which
maintained temperature at 25 jC and provided
continual agitation. The flask solution was sampled
periodically, as per the bioreactor experiments.
4. Results and discussion
4.1. Ferric sulphate oxidation
Tests were first performed on the initial leaching
kinetics of pure sphalerite in ferric sulphate media.
These experiments were conducted in an attempt to
observe the intrinsic kinetics of the oxidation reaction,
and to study the effect of the elemental sulphur
product layer, under conditions in which it is not
removed through bacterial action. The ferric oxidation
of sphalerite was studied using four distinct particle
size fractions (� 45, � 75 + 45, � 125 + 75 and
� 212 + 125 Am) of the pure sphalerite mineral sam-
ple. Zinc extraction results are presented in Fig. 1, and
it can be seen that the extraction rate increased with
decreasing particle size, indicating a surface con-
trolled extraction process (i.e., either surface reaction
or molecular diffusion).
Zinc extraction data from the four experiments
were fitted to the mixed-control rate equation (Eq.
(8)) through a least-squares iteration of the parameters
rZnS and D. Initially, a solution to the model was
attempted using only one rZnS value and one D value
Fig. 1. Ferric sulphate leaching of mineral sphalerite at varying
particle sizes. Tests were conducted in flasks at 21 jC with
[Fe3 +] = 0.18 mol L� 1 and [H2SO4] = 0.51 mol L� 1 at 0.5% weight
per volume solids. The lines represent model predictions obtained
by fitting Eq. (8) to the experimental data using the kinetic
parameters of Table 2.
Table 2
Kinetic parameters for the ferric sulphate leaching of mineral
sphalerite, rZnS = 5.0 10� 5 mol m� 2 s� 1 and k ZnS = 3.7 10� 6
mol0.5 m� 0.5 s� 1 for all fractions
Size fraction (Am) D (m2 s� 1) k V/DV
� 45 3.7 10� 15 69
� 75 + 45 3.5 10� 15 97
� 125 + 75 5.9 10� 15 97
�212+125 1.2 10� 14 82
G. da Silva / Hydrometallurgy 73 (2004) 313–324318
for all four particle sizes. However, this approach
failed to yield an accurate description of the experi-
mental data, and instead the data was modelled using
a single rZnS value and four D values (one for each
particle size). The model predictions obtained using
this approach are included along with the experimen-
tal results in Fig. 1. The model parameters used for
each of the four size fractions are given in Table 2, as
well as the ratios of kVto DV. It was found that all four
sets of data were well described with a single rZnSvalue of 5.0 10� 5 mol m� 2 s� 1, corresponding to
an intrinsic rate constant of 3.2 10� 6 mol0.5 m� 0.5
s� 1. The ratio of k Vto D, for each experiment is in all
cases greater than 1, indicating that diffusion control
is dominant. This diffusion resistance is believed to be
due to the layer of elemental sulphur which is known
to form on the surface of sphalerite particles under-
going leaching in ferric media (Fowler and Crundwell,
1999; Jin et al., 1984).
Ideally, a single diffusion coefficient would be
expected to fit all four sets of leaching data. However,
the present results seemingly indicate that the rate of
diffusion of ferric ions through the product layer
increases with increasing particle size. It is believed
that this phenomenon is a result of the increased
surface area per particle of the larger size fractions.
This increased surface area results in a less coherent
product layer, which may begin to crack and break up.
These cracks allow for increased rates of mass trans-
fer, thus increasing its diffusion coefficient. Also as a
result of this product layer attrition, the actual layer of
elemental sulphur is of lesser thickness than that
predicted by the shrinking core model, and provides
less overall resistance to diffusion. Seeing as the
model does not account for these phenomena, it
predicts observed diffusion coefficients of greater
magnitude than the actual values. As such, the intrin-
sic diffusivity of ferric ions through elemental sulphur
is thought to be the value obtained for the smaller
sized particles, i.e., 3.6 10� 15 m2 s� 1. This value
may be compared to that obtained by Bobeck and Su
(1985) during ferric chloride leaching experiments at
87 jC. They calculated a diffusion coefficient of
1.3 10� 12 m2 s� 1, approximately three orders of
magnitude greater than that calculated here. However,
it is believed that this discrepancy arises from the
much greater temperature of the latter experiment and
from the effect of chloro-complex formation on the
composition of the occlusive product layer.
4.2. Bacterial oxidation (high-grade sphalerite ore)
A bacterial oxidation experiment was conducted in
a reactor test using the high-grade ore sample, to
provide data by which to test the developed rate
equation under bioleaching conditions. Fig. 2 shows
the rate of both zinc and iron extraction obtained from
this experiment. It can be seen that there was a
significant initial lag period, and only minor zinc
and iron extraction had occurred in the first 20 days
of reaction. Lag periods such as this are often ob-
served during bioleaching experiments (Lizama et al.,
2003), and represent a period of bacterial adaptation.
However, after this period the rate of zinc extraction
increased, and reaction proceeded to completion. Iron
extraction, however, did not proceed past about 30%.
Fig. 2. Extraction kinetics of a high grade sphalerite ore undergoing
bacterial oxidation in the presence of a mixed culture of mesophilic
bacteria at 35 jC.
G. da Silva / Hydrometallurgy 73 (2004) 313–324 319
In order to successfully apply the developed rate
equation, the leaching reaction should be proceeding
under constant conditions. During reaction, the solu-
tion pH was monitored, and adjusted back to around
pH 2.0 when required. The solution Eh (vs. a standard
hydrogen electrode [SHE]) was also recorded, as a
measure of the oxidation potential of the reaction
solution. The recorded pH and Eh of the solution
are presented in Fig. 3. During the reaction lag period,
the pH can be seen to fluctuate between about 2 and 3,
with frequent acid addition being required. This
fluctuation in pH could be expected to cause reduced
bacterial activity, thus lengthening the duration of the
lag period. During this initial period, acid dissolution
Fig. 3. Solution pH and Eh (SHE) during bacterial oxidation of a
high-grade sphalerite ore in the presence of a mixed culture of
mesophilic bacteria at 35 jC.
of the iron oxide minerals is occurring, as can be seen
in Fig. 2. However, once sufficient iron levels were
achieved in solution, the solution acidity remained
relatively steady at around pH 2. Subsequently, little
additional iron extraction was observed. From Fig. 3,
the solution Eh can be seen to initially decline during
the bacterial adaptation period, due to a lack of
bacterial ferric generation. However, following this
lag period, the Eh increased to around 650 mV vs.
SHE. Significantly, during the period of zinc extrac-
tion following the lag period (between around 20 and
40 days), both the pH and Eh of the reaction solution
remained relatively constant, thus allowing us to
apply the developed kinetic model.
During reaction, the ferrous iron levels in solution
were monitored. When combined with the known
total iron concentration, this permitted calculation of
the ferric iron levels. Both the ferrous and ferric
concentrations during the bioleaching experiment are
shown in Fig. 4. Initially, the concentration of ferric
ions in solution was negligible, indicating that mini-
mal bacterial oxidation was occurring, as was already
thought to be the case. At around 20 days, significant
ferric generation occurred, and solution ferric concen-
tration remained at an average value of about 1600 mg
L� 1 for the next 10 days, during the period in which
the majority of zinc extraction occurred. Once most of
the sphalerite had been leached, the ferric iron con-
centration rose further, as it was no longer being
reduced to ferrous iron by sphalerite.
Fig. 4. Solution ferric and ferrous iron concentrations during
bacterial oxidation of a high-grade sphalerite ore in the presence of a
mixed culture of mesophilic bacteria at 35 jC.
G. da Silva / Hydrometallurgy 73 (2004) 313–324320
The above results for pH, Eh and ferric iron con-
centration demonstrate that reaction conditions during
the bioleaching experiment were essentially constant,
once the initial lag period was overcome. In modelling
this experiment, it was decided only to test for the
relative importance of diffusion and reaction control,
due to the fact that the particle sizing of the ore sample
was not accurately enough known. Due to the presence
of a significant lag period, Eq. (10) was used to model
the data, with tlag = 17 days. To fit the model to the data,
the parameters kVand D were varied, so as to obtain the
best least-squares description of the experimental
results. The model prediction is shown in Fig. 5, along
with the experimental data being modelled. The lag
periodmodel can be seen to effectively describe the rate
of zinc extraction across the entire period of reaction.
From application of the kinetic model to the
experimental data of Fig. 5, a kV/DV ratio of 0.99 is
obtained, indicating that chemical reaction and mo-
lecular diffusion are of relatively similar importance.
This value is not, however, directly comparable to that
obtained earlier for ferric sulphate leaching, due to the
lower concentration of ferric ions in the bioleaching
experiment (0.03 vs. 0.18 mol L� 1). When comparing
these ratios, due to the half order ferric dependence of
kVand the first-order ferric dependence of DV, we are
required to multiply each k V/DVratio by the ferric ion
concentration to the half power. This transformation
results in an adjusted k V/DV ratio for the bioleaching
experiment that is almost 200-fold less than that for
Fig. 5. Bacterial oxidation of a high grade sphalerite ore in the
presence of a mixed culture of mesophilic bacteria at 35 jC.Comparison between experimental data (open squares) and model
prediction (solid line) was obtained by fitting Eq. (10).
the ferric leaching experiments. As such, it can be
concluded that diffusion is less significant during this
bioleaching experiment than it was during the ferric
sulphate leaching experiments.
The reduction in the significance of diffusion in
this bioleaching experiment, when compared to the
ferric leaching experiments, indicates that the elemen-
tal sulphur product layer formed by the ferric oxida-
tion reaction is being in some part removed, believed
to be due to bacterial oxidation. However, a signifi-
cant diffusion contribution still exists, which may be
due to a number of reasons. Firstly, incomplete
bacterial oxidation of the elemental sulphur product
layer could have been occurring, with the residual
layer of elemental sulphur still providing some resis-
tance to diffusion. However, this is not thought to be
the case, due to the good levels of bacterial activity
demonstrated by the high ferric concentration and Eh
of the reaction solution. Another source of diffusion
resistance may arise from the unreacted gangue which
remains after leaching. According to the chemical
analysis presented in Table 1, at least 40% of the
ore sample was present as gangue material of some
form. Other possible sources of product layer diffu-
sion include a deposited layer of lead sulphate arising
from oxidised galena, or from a precipitated layer of
jarosites. However, it is not possible from the avail-
able data to determine the exact nature of the product
layer that was responsible for the diffusion resistance
that was observed during this bioleaching experiment.
4.3. Bacterial oxidation (low-grade sphalerite ore)
Often, bioleaching is utilised for the processing of
low-grade ores, for which conventional treatment
would otherwise prove uneconomical. In such cases,
heap-leaching technology is often utilised, where
larger sized ore particles are leached in a non-abrasive
environment. Under these conditions, leaching can
leave behind a layer of unreacted gangue material,
which can contribute to diffusion resistance. So as to
study this phenomena, two repeat experiments were
conducted on a coarse (ca. 0.5 mm) sample of low-
grade zinc ore. This experiment was conducted as a
flask leach, in order to minimise the mechanical
attrition of the product layer, and to better simulate
the heap-leaching conditions. For comparative purpo-
ses, a similar experiment was conducted in a bioreac-
Fig. 7. Solution pH during two identical flask bacterial oxidation of
a low-grade sphalerite ore in the presence of a mixed culture of
mesophilic bacteria at 25 jC. Open and closed squares represent
repeat experiments.
G. da Silva / Hydrometallurgy 73 (2004) 313–324 321
tor at 35 jC. Zinc extraction data for all three experi-
ments are given in Fig. 6, and it can be seen that the
three experiments returned very similar kinetics.
However, a slight lag period was observed during
the reactor leach experiment, possibly due to the
higher solids loading. Following this lag, however,
the reactor experiment was faster, and ultimately
achieved complete extraction in a similar time period
to the flask leach experiments. Due to the lag period,
less kinetic data is available for the reactor test, thus
making the flask results more suitable to modelling.
Also, the flask leach experiments are more represen-
tative of heap leaching conditions due to the less
severe mixing conditions. As such, from this point
onwards we will only concern ourselves with the
results from the flask leach experiments.
As with the previous bioleaching experiment per-
formed on a high-grade zinc ore, in order to apply the
developed kinetic model we must first be sure that
solution conditions remain constant over the course of
the reaction. Fig. 7 shows the change in solution pH
during the two flask experiments, while the change in
Eh is shown in Fig. 8. Fig. 9 shows the ferric and
ferrous ion concentrations for both experiments. Dur-
ing both of the flask leaching experiments, the total
iron extraction remained relatively constant at around
40%. Average ferric iron concentrations during the
first 12 days of leaching were 11.5 and 10.8 mol m� 3
for the first and second experiments, respectively. The
Fig. 6. Zinc extraction kinetics of a low-grade sphalerite ore
undergoing bacterial oxidation in the presence of a mixed culture of
mesophilic bacteria. Open and closed squares represent repeat flask
leach experiments at 25 jC with 5% pulp density, open triangles
represent reactor leach experiment at 35 jC with 10% pulp density.
higher ferric concentration in the first experiment in
comparison to the other flask leach explains the
slightly higher rate of zinc extraction.
In fitting the mixed-control rate equation to the data
of Fig. 6, it was found that only diffusion was signif-
icant, without a reaction term being required. It is
believed that this diffusion controlled regime is due
to the presence of an unreacted gangue layer, as the
presence of bacteria should prevent the build-up of
elemental sulphur, as seen in the previous experiment.
Also, the low sulphide mineral content of the ore
means that even if negligible oxidation of elemental
Fig. 8. Solution Eh during the flask bacterial oxidation of a low
grade sphalerite ore in the presence of a mixed culture of mesophilic
bacteria at 25 jC. Open and closed squares represent repeat
experiments.
Fig. 10. Bacterial flask oxidation of a low grade sphalerite ore in the
presence of a mixed culture of mesophilic bacteria at 25 jC.Comparison between repeat experiments (open and closed squares)
and model predictions (solid and dashed lines) obtained by fitting
Eq. (8) using diffusion coefficients of 3.8 10� 13 and 3.2 10� 13
m2 s� 1 for experiments 1 and 2, respectively.
G. da Silva / Hydrometallurgy 73 (2004) 313–324322
sulphur was occurring, the thickness of the layer would
not be significant enough to impart significant diffu-
sion resistance. Figure 10 shows the comparison
between the results of the flask leach experiments
and their respective model predictions. The diffusion
coefficients obtained from the model for experiments 1
and 2, respectively, were 3.8 10� 13 and 3.2 10� 13
m2 s� 1, yielding an average value of approximately
3.5 10� 13 m2 s� 1, which is two orders of magnitude
greater than that found during the ferric sulphate
leaching experiments for the diffusion of ferric ions
through elemental sulphur. This result indicates that
the product layer of gangue material provides less
resistance to mass transfer than the elemental sulphur
layer, and is of a greater porosity. While no reaction
contribution was found for the above data, it should be
noted that no noticeable discrepancy arises if a kZnSvalue similar to that found during the ferric leaching
experiments (ca. 10� 6 mol0.5 m� 0.5 s� 1) is substituted
into the rate equation.
Upon termination of both flask leach experiments
after 33 days of reaction, the sample residues were
filtered, washed, and then dried. From 5 g of initial
sample, experiment 1 yielded 4.70 g of residue at
0.04% zinc grade, while experiment 2 yielded 4.59 g
of residue at 0.03% zinc grade. Once the known mass
of dissolved zinc and iron is factored in, the total mass
unaccounted for in experiments 1 and 2 is 0.19 and
Fig. 9. Solution ferric and ferrous iron concentrations during the
flask bacterial oxidation of a low grade sphalerite ore in the
presence of a mixed culture of mesophilic bacteria at 25 jC. Openand closed squares denote ferric concentrations for the repeat
experiments, open and closed triangles denote ferrous concen-
trations for the repeat experiments.
0.28 g, respectively. This equates to an average
gangue dissolution of less than 5%, indicating that
the vast majority of the gangue material that was
initially introduced into the experiments remained at
their conclusion. This finding indicates that the
gangue material remained largely unreacted, and
was therefore capable of imparting a diffusion limita-
tion upon the rate of zinc extraction.
5. Conclusions
A number of kinetic models, describing the rate of
leaching under conditions of reaction, diffusion and
mixed control have been developed. The possible
advent of lag periods during the initial stages of
leaching is also accounted for in the models. The
developed models were applied to experimental
results obtained for the leaching of sphalerite, under
a range of different conditions. From the modelling
results, several important conclusions can be drawn
concerning the relative significance of reaction and
diffusion control during the bacterial and ferric sul-
phate leaching of zinc sulphide. These are as follows:
(1) The ferric sulphate oxidation of sphalerite is
controlled by both chemical reaction and product
layer diffusion, with diffusion being the dominant
G. da Silva / Hydrometallurgy 73 (2004) 313–324 323
process. Product layer diffusion is thought to arise
due to formation of a layer of elemental sulphur.
The diffusivity of ferric ions through this product
layer was estimated as 3.6 10� 15 m2 s� 1 at 21
jC, while the intrinsic rate of zinc extraction was
5.0 10� 5 mol m� 2 s� 1 with an intrinsic rate
constant of 3.2 10� 6 mol0.5 m� 0.5 s� 1. The
elemental sulphur product layer is also believed to
be susceptible to mechanical attrition, particularly
during the leaching of larger particle size material.
(2) During bacterial oxidation of high-grade sphaler-
ite ore at 35 jC in batch bioreactors, the kinetics
of zinc dissolution were controlled equally by
both chemical reaction and molecular diffusion.
This reduction in the importance of mass transfer
was attributed to continual removal of the ele-
mental sulphur product layer through bacterial
action. Some degree of diffusion control was still
witnessed, though it was not possible to deter-
mine whether this was due to incomplete removal
of the elemental sulphur product layer, or from
some other surface material such as gangue, lead
sulphate or jarosite precipitates.
(3) For the bacterial oxidation of low-grade sphalerite
ore at 21 jC in batch flask experiments, the
kinetics of zinc extraction was wholly controlled
by mass transfer. It is believed that this mass
transfer limitation arises from a residual layer of
inert gangue material. The diffusivity of ferric
ions through the product layer was estimated as
being 3.5 10� 13 m2 s� 1.
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