Bioleaching kinetics
Lecture #5
Bioleaching kinetics
Lecture #5
Biooxidation versus chemical
oxidation
• The rate of bacterial oxidation is
higher than that of chemical
oxidation under the same
conditions.
Model of leaching kinetic
• The leaching of mineral particles by a
reagent in solution can be
represented by the reaction:
aA
(s)
+ bB
(aq)
aqueous and solid
products
A – the solid undergoing leaching
B – the reagent in solution
„a” and „b” are stoichiometric coefficients
Subprocesses in
biooxidation
• Growth bacteria
• Ferrous to ferric oxidation Fe
2+
Fe
3+
• Disolved oxygen consumption O
2
H
2
O
• Disolved carbon dioxide consumption
CO
2
The rtes of oxygen and carbon dioxide
utilization are measured by gas
analyzers.
Subprocess
• The bacterial oxidation of ferrous (Fe
2+
) to
ferric (Fe
3+
) ions.
• The kinetic of bacterial growth was
described by Monod equation:
max
-maximum of specific growth rate [1/h]
• K
S
– Monod’s constant [mol/L]
• c
S
- substrate concentration [mol/L]
S
S
c
K
c
S
max
Kinetic equations
• The rate of oxygen utilization is correlated
to ferric to ferrous ratio:
• The rate of ferrous iron utilization:
2
3
max
2
2
2
1
Fe
Fe
K
q
q
O
O
O
2
3
max
2
2
2
1
Fe
Fe
K
q
q
Fe
Fe
Fe
Kinetic parameters for Fe
2+
oxidation
Acidithibacillus
ferrooxidans
Leptospirillum
ferrooxidans
Units
q
O2
max
2.2
1.7
molO
2
/
molC/h
q
Fe2+
max
8.8
6.8
molFe
2+
/
molC/h
K
O2
0.05
0.0005
K
Fe2+
0.05
0.0005
Logistic model
• The logistic equation is written for the
rate of conversion of sulfide mineral [X].
where: k
m
rate constant.
• The fraction bioleached with time is
given by integrating logistic equation.
max
1
X
X
X
k
dt
dX
m
t
k
t
k
m
m
e
X
X
e
X
t
X
1
1
max
0
0
Kinetic of (bio-) leaching
process
• The kinetic of leaching reaction are
described by:
The shrinking core modeel
The shrinking particle model
Shrinking particle and core
models
Kinetic of bioleaching
• The rate of the heterogeneous
reaction is controlled by:
1. film diffusion
2. chemical reaction
3. product layer diffusion
x
x
t
k
x
t
k
x
t
k
1
2
1
3
1
1
1
3
2
3
3
1
2
1
Shrinking core model
1-(2/3)α-(1-α)
2/3
=kt
α-is the fraction of leached
k-is the rate constant (1/day)
t –is time (day)
Shrinking particle and core
models
[1-(1-X)
1/3]
versus time
[1+2(1-X)-3(1-X)
2/3
] versus
time
where X is fractional conversion
Bacteria oxidation
• According to the model proposed by Michaelis-
Mentan the dissolution rate is given by following
equation:
where: V is the extraction rate of metal
V
max
is the maximum metal extraction rate
K
s
is the Michaelis’ constant
S is the pulp density
K
s
constant gives an idea aobout the efficiency of
bacteria to the mineral surface.
S
K
S
V
V
s
max
Plot of Michaelis-Menten for the copper
and zinc dissolution
Plot of 1/V versus
1/S for Cu and Zn
The higher rate K
S
for Cu then K
S
for
Zn indicates a
preference of
bacteria for copper.
Indirect mechanism of bioleaching of
galena
PbS
(s)
+ 2Fe
3+
(aq)
Pb
2+
(aq)
+S
0
(s)
+ 2 Fe
2+
(aq)
Pb
2+
(aq)
+ SO
4
2-
(aq)
PbSO
4(s)
Galena bioelaching
Effect of particle size on the bioleaching of
galena
Microphotograph (magnification of 50x0 of a
partially oxidized galena particle
a) unreacted galena
b) lead sulfate/elemental sulfur product layer