Relative importance of diffusion and reaction control during the bacterial and ferric sulphate...

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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


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-


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


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.


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.


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.


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.


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


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.

References

Attia, Y.A., El-Zeky, M.A., 1990. Effect of galvanic interaction

of sulfides on extraction of precious metals from refractory

complex sulfides by bioleaching. Int. J. Miner. Process. 30,

99–111.

Babu, M.N., Sahu, K.K., Pandey, B.D., 2002. Zinc recovery from

sphalerite concentrate by direct oxidative leaching with ammo-

nium, sodium and potassium persulphates. Hydrometallurgy 64,

119–129.

Baker, B.J., Banfield, J.F., 2003. Microbial communities in acid

mine drainage. FEMS Microbiol. Ecol. 44, 139–152.

Bobeck, G.E., Su, H., 1985. The kinetics of dissolution of sphalerite

in ferric chloride solution. Metall. Trans. B 16B, 413–424.

Bolorunduro, S.A., Dreisinger, D.B., Van Weert, G., 2003. Zinc and

silver recoveries from zinc– lead– iron complex sulphides by

pressure oxidation. Miner. Eng. 16, 375–389.

Boon, M., Snijder, M., Hansford, G.S., Heijnen, J.J., 1998. The

oxidation kinetics of zinc sulphide with Thiobacillus ferrooxi-

dans. Hydrometallurgy 48, 171–186.

Chartier, M., Mercier, G., Blais, J.F., 2001. Partitioning of trace

metals before and after biological removal of metals from sedi-

ments. Water Res. 35, 1435–1444.

Chen, S., Lin, J., 2000. Influence of solid content on bioleaching of

heavy metals from contaminated sediment by Thiobacillus spp.

J. Chem. Technol. Biotechnol. 75, 649–656.

Crundwell, F.K., 1987. Kinetics and mechanism of the oxidative

dissolution of a zinc sulphide concentrate in ferric sulphate

solutions. Hydrometallurgy 19, 227–242.

Crundwell, F.K., 1988. Effect of iron impurity in zinc sulfide con-

centrates on the rate of dissolution. AIChE J. 34, 1128–1134.

da Silva, G., Lastra, M.R., Budden, J.R., 2003. Electrochemical

passivation of sphalerite during bacterial oxidation in the pres-

ence of galena. Miner. Eng. 16, 199–203.

Fowler, T.A., Crundwell, F.K., 1998. Leaching of zinc sulfide by

Thiobacillus ferrooxidans: experiments with a controlled redox

potential indicate no direct bacterial mechanism. Appl. Environ.

Microbiol. 64, 3570–3575.

Fowler, T.A., Crundwell, F.K., 1999. Leaching of zinc sulfide by

Thiobacillus ferrooxidans: bacterial oxidation of the sulfur prod-

uct layer increases the rate of zinc sulfide dissolution at high

concentrations of ferrous ions. Appl. Environ. Microbiol. 65,

5285–5292.

Fowler, T.A., Holmes, P.R., Crundwell, F.K., 2001. On the kinetics

and mechanism of the dissolution of pyrite in the presence of

Thiobacillus ferrooxidans. Hydrometallurgy 59, 257–270.

Fuerstenau, M.C., Nebo, C.O., Elango, B.V., Han, K.N., 1987. The

kinetics of leaching galena with ferric nitrate. Metall. Trans. B

18B, 25–30.

Ghosh, M.K., Das, R.P., Biswas, A.K., 2002. Oxidative ammonia

leaching of sphalerite: Part I. Noncatalytic kinetics. Int. J. Miner.

Process. 66, 241–254.

Ghosh, M.K., Das, R.P., Biswas, A.K., 2003. Oxidative ammonia

leaching of sphalerite: Part II. Cu(II)-catalyzed kinetics. Int. J.

Miner. Process. 70, 221–234.

Harvey, T.J., Van Der Merwe, W., Afewu, K., 2002. The application

of the GeoBiotics GEOCOATR biooxidation technology for the

treatment of sphalerite at Kumba Resources’ Rosh Pinah mine.

Miner. Eng. 15, 823–829.

Hirato, T., Kinoshita, M., Awakura, Y., Majima, H., 1986. The

leaching of chalcopyrite with ferric chloride. Metall. Trans. B

17B, 19–28.

Jin, Z., Warren, G.W., Henein, H., 1984. Reaction kinetics of the

ferric chloride leaching of sphalerite—an experimental study.

Metall. Trans. B 15B, 5–12.

Kai, T., Suenaga, Y., Migita, A., Takahashi, T., 2000. Kinetic model

for simultaneous leaching of zinc sulfide and manganese diox-

ide in the presence of iron-oxidizing bacteria. Chem. Eng. Sci.

55, 3429–3436.

Liao, M.X., Deng, T.L., 2003. Zinc and lead extraction from com-

plex raw sulfides by sequential bioleaching and acidic brine

leach. Miner. Eng. 17, 17–22.

Lizama, H.M., Fairweather, M.J., Dai, Z., Allegretto, T.D., 2003.

How does bioleaching start? Hydrometallurgy 69, 109–116.


Lochmann, J., Pedlı́k, M., 1995. Kinetic anomalies of dissolution of

sphalerite in ferric sulfate solution. Hydrometallurgy 37, 89–96.

Madhuchhanda, M., Devi, N.B., Rath, P.C., Rao, K.S., Para-

mguru, R.K., 2003. Leaching of manganese nodule in hydro-

chloric acid in presence of sphalerite. Can. Metall. Q. 42,

49–60.

Mehta, A.P., Murr, L.E., 1982. Kinetic study of sulfide leaching by

galvanic interaction between chalcopyrite, pyrite, and sphalerite

in the presence of T. ferrooxidans (30 jC) and a thermophilic

microorganism (55 jC). Biotechnol. Bioeng. 24, 919–940.Palencia, I., Dutrizac, J.E., 1991. Effect of the iron content of

sphalerite on its rate of dissolution in ferric sulphate and ferric

chloride. Hydrometallurgy 26, 211–232.

Pani, C.K., Swain, S., Kar, R.N., Chaudhury, G.R., Sukla, L.B.,

Misra, V.N., 2003. Bio-dissolution of zinc sulfide concentrate

in 160 l 4-stage continuous bioreactor. Miner. Eng. 16,

1019–1021.

Rawlings, D.E., Dew, D., du Plessis, C., 2003. Biomineralization of

metal-containing ores and concentrates. Trends Biotechnol. 21,

38–44.

Warren, G.W., Henein, H., Jin, Z., 1985. Reaction mechanism for

the ferric chloride leaching of sphalerite. Metall. Trans. B 16B,

715–724.

Yagi, S., Kunni, D., 1955. Studies on combustion of carbon par-

ticles in flames and fluidized beds. 5th Symposium (Internation-

al) on Combustion. Reinhold, New York, pp. 231–244.

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