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Table 2-2 (Wang et al., 2019) lists the specific surface area used in different studies compared
with the calculated specific surface area based on the average particle size. When comparing
the reaction rates from different studies, the reaction rates should be normalized by the
specific surface area obtained using the same method.
Table 1-2: Specific surface area (SSA) obtained in different studies on pyrite oxidation rate ( after
Wang et al. (2019))
SSA (cm-2·g-1)
Grain size (𝜇m)
Reference
Calculated Measured
McKibben and Barnes (1986) 187.5 (125 – 250) 64 251
Moses and Herman (1991) 41.5 (38 – 45) 289 660
Williamson and Rimstidt (1994) 200 (150 -250) 60 470
Kameia and Ohmotob (2000) 125.5 (74-177) 96 538
Jerz and Rimstidt (2004) 335 (250 – 420) 36 100
Gleisner et al. (2006) 156.5 (63 – 250) 77 1470
Nicholson et al. (1990) 108 (90 – 125) 110 --
León et al. (2004) 108 (90 – 125) 110 --
Tabelin et al. (2017) 605 (500-710) 20 240
Qiu et al. (2016) <74 162 13000
1.3.5 Effect of bacteria
The presence of iron-oxidising and sulphur-oxidising bacteria can accelerate the rate of pyrite
dissolution. Smith (1970) showed that rate of pyrite oxidation with bacteria of the
Ferrobacillus-Thiobacillus group can be more than ten times faster than that without bacteria.
Singer and Stumm (1970) found that the oxidation rate of ferrous ion inoculated with
untreated natural mine water is 106 times larger than that with sterilized natural mine water.
Olson (1991) also showed that the rate of pyrite oxidation with dissolved oxygen increased
by a factor of 34 in the presence of A. ferrooxidans (Gleisner et al., 2006). The catalysis of
bacteria on the oxidation of pyrite has been successfully applied on various bioleaching
operations.
It is widely accepted that bacteria participate in pyrite oxidation through two mechanisms: a
direct mechanism and an indirect mechanism (Evangelou and Zhang, 1995). According to
Evangelou and Zhang (1995), the direct mechanism requires physical contact between
bacteria and the pyrite surface, where the oxygenations of both surface disulphide and
surface ferrous ion are catalysed by bacteria. Consequently, the rate of pyrite dissolution
through Eq.(1-2) is boosted. The indirect mechanism of microbial pyrite oxidation does not
require bacteria attachment on the pyrite surface. Bacteria in solution are able to catalyse the
oxygenation of ferrous ion (Eq.(1-3)), hence increasing the production rate of ferric ion. The
increased ferric ion concentration in solution facilitates pyrite dissolution by the reaction in
Eq.(1-4) which has a much higher reaction rate than pyrite oxidation by DO. |
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Smith (1970) suggested that the indirect mechanism predominates in microbial oxidation of
pyrite. He measured the O uptake rate (mass per hour) with various pyrite masses and a
2
constant solution volume for both abiotic and microbial pyrite oxidation (with constant cell
concentration) and found that, while the chemical oxidation rate increases consistently with
increasing pyrite mass, the O uptake rate with bacteria reaches the maximum rate and levels
2
off at a pyrite to water ratio of 15 g·l-1. The results indicated that, under microbial conditions,
the reaction rate (O uptake rate) is limited by bacteria concentration in solution. Increasing
2
the total available surface area cannot increase the microbial oxidation rate further, which
should not be the case if the direct mechanism of bacteria oxidation is dominant. The study
in Gleisner et al. (2006) also supported the indirect mechanism of microbial pyrite oxidation.
They measured the rate of pyrite oxidation at different DO levels and bacteria concentrations,
and found that the reaction rate can be well predicted by the ferric ion concentration alone
for the pH of 2 – 3, indicating a dominant reaction mechanism with ferric ion as the direct
oxidant. Rodrıǵ uez et al. (2003) concluded that pyrite oxidation is initiated by the direct
mechanism but subsequently, when the cells release to the solution, the indirect mechanism
dominates.
The kinetics of microbial pyrite oxidation have been investigated by Smith (1970), Gleisner et
al. (2006), Olson (1991) and Pesic et al. (1989). Smith (1970) found that for the initial 100
hours of microbial pyrite oxidation, during which bacteria concentration increased from 104
cells·ml-1 (inoculum size) to 106 cells·ml-1, the reaction rate was the same as that of an
identical reaction without bacteria. Between 100 hours and 180 hours, the rate increased
gradually as bacteria concentration increased from 106 cells·ml-1 to about 108 cells·ml-1. The
reaction rate then levelled off after 180 hours while bacteria concentration levelled off at
around 200 hours at a maximum concentration of 2×108 cells·ml-1. The results indicated that
a minimum bacteria concentration is required to generate ferric ions at a sufficient rate such
that a higher reaction rate than abiotic oxidation can be sustained. In Smith (1970), this
minimum bacteria concentration is 106 cells·ml-1. After this minimum concentration, the
reaction rate increases with the bacteria concentration until 108 cells·ml-1 and then it
becomes independent of bacteria concentration. Olson (1991) reached a similar conclusion
that the pyrite oxidation rate becomes independent of bacteria concentration if the initial
bacteria concentration at inoculation is above 106 cells·ml-1 (which will then grow to a higher
population at the time of rate measurement). The bacteria concentration at which the
oxidation rate becomes constant may depend on the pH value due to the corresponding
variations in ferric ion solubility.
Gleisner et al. (2006) measured the pyrite oxidation rate at five different DO levels, each with
two different bacteria concentrations (nine runs in total with a failed run not counted). The
pyrite oxidation rate was found to be positively correlated with bacteria concentration at all
DO levels, although the magnitude of the rate increase with bacteria concentration varies
with the DO level. The oxidation rate increases with the DO level at all bacteria concentrations
(in the investigated range of 0.34 to 27.41 ×106 cells·ml-1). Multiple linear regression analyses
of the logarithm of the rate against DO level and bacteria concentration show that the
reaction rate is of the order of 0.26 with respect to DO level and of the order of 0.739 with |
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respect to bacteria concentration. Compared with abiotic reaction kinetics, which are of the
order of 0.5 with respect to oxygen concentration (Jerz and Rimstidt, 2004; McKibben and
Barnes, 1986; Williamson and Rimstidt, 1994), microbial mediation decreases the order by
about 50% with respect to oxygen concentration. For these reasons, neither the DO level nor
bacteria concentration alone can be used to predict the oxidation rate. However, the
regression analysis of reaction rate against ferric ion concentration (with R2 = 0.951) shows
that the ferric ion concentration is a good predictor for the reaction rate (Gleisner et al., 2006).
Pesic et al. (1989) investigated the kinetics of ferrous ion oxidation by DO with T. ferrooxidans
using the electrochemical method. A reaction rate formula was proposed as Eq. (1-11) under
atmospheric conditions and for Fe2+ < 0.001M, T < 25 ℃ and bacteria concentrations ranging
from 6 to 24 mg dry cells per litter solution.
𝑑𝐹𝑒2+ 58.77
− = 1.62∙1011𝐶 [𝐻+][𝐹𝑒2+]𝑃 𝑒−( 𝑅𝑇 ) 𝑝𝐻 > 2.2
𝑑𝑡 𝑏𝑎𝑐𝑡 𝑂 2
(1-11)
𝑑𝐹𝑒2+ 58.77
− = 1.62∙1011𝐶 [𝐹𝑒2+]𝑃 𝑒−( 𝑅𝑇 ) 𝑝𝐻 < 2.2
{ 𝑑𝑡 𝑏𝑎𝑐𝑡 𝑂 2
The production rate of ferric ion from ferrous ion oxygenation with bacteria can also be
obtained from Eq.(1-11) as each reacted ferrous ion produces a ferric ion. The rate formula
for pyrite dissolution by ferric ion in the presence of dissolved oxygen was derived by
Williamson and Rimstidt (1994) as:
[𝐹𝑒3+]0.93(±0.07)
𝑅 = −10−6.07(±0.07) [𝑚𝑜𝑙𝑚−2𝑠−1] (1-12)
𝐹𝑒𝑆 2 [𝐹𝑒2+]0.4(±0.06)
Despite the similarity in qualitative findings, the rates measured for microbial oxidation in
different studies vary significantly, as can be seen in Table 1-3. Unlike abiotic oxidation, the
deviation in the microbial oxidation rates cannot be explained by the differences in specific
surface areas or pyrite reactivity as discussed in Section 1.3.3 and Section 1.3.4. It may,
however, be explained by the mixed effects of pH, time of measurement and lag of bacteria
activity. For example, the rate measured in Olson (1991) is about ten times faster than the
rate measured in Gleisner et al. (2006) at a comparable oxygen level (DO = 273 𝜇M) and
bacteria concentration (26.6 × 106 cells·ml-1). The difference may be due to the higher
temperature, lower pH and earlier measuring time in Olson (1991). The rate measured in
Smith (1970) under the bacteria concentration of 20 × 106 cells·ml-1 is only slightly lower than
the rate measured in Gleisner et al. (2006) with 16.35 × 106 cells·ml-1 and the difference may
be explained by the higher pH and lower temperature in the experiment in Smith (1970). The
highest reaction rate was obtained in Smith (1970) when measured at the earliest time (nine
days) with the highest bacteria concentration (108 cells·ml-1). |
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Table 1-3: Comparison of measured microbial pyrite oxidation rates from the literature
Measurement DO Cells·ml-1 Rate (mol-
Conditions
Reference time (days) (𝜇M) × 106 FeS ·m-2·s-1)
2
273 16.35 pH 2.2 9.60E-09
273 26.605 Temperature 22℃ 1.71E-08
129 3.745 PS (µm) 156.5 7.78E-09
Gleisner 129 1.63 SSA_c (m2.g-1) 0.0077 4.10E-09
et al. 31 to 75 days 64.8 4.075 SSA_m (m2.g-1) 0.147 4.26E-09
(2006) 64.8 4.095 5.58E-09
13.2 1.58 3.68E-10
<=0.006 0.375 3.68E-11
<=0.006 1.745 3.41E-10
4.5 pH 2 1.43E-07
3.5 Temperature 28℃ 1.27E-07
Olson 4.5 PS (µm) 74.5 2.76E-07
273 25
(1991) 13 SSA_c (m2.g-1) 0.0153 1.63E-07
16.5 SSA_m (m2.g-1) N/A 2.89E-07
15 2.54E-07
Smith 19 273 20 pH 3 1.17E-10
(1970) 9 273 100 Temperature 20℃ 1.28E-07
PSD: particle size
SSA_m: measured specific surface area
Note: the reaction rates listed here are corrected from measured specific surface area (SSA_m) to
calculated specific surface area (SSA_c). The bacteria concentrations in Gleisner et al. (2006) are
averaged values based on the bacteria concentration measured on day 51 and day 64.
Numerical modelling on pyrite oxidation in rock piles
Pyrite oxidation in rock piles or mine tailings often involves processes such as air transport,
heat transfer, microbial activities, water flow and reactive transport. These processes
determine the reaction conditions such as oxygen concentration, temperature, microbial
condition and water content, which affect the pyrite oxidation rate as discussed in Section
1.3, hence also the effluent discharge. However, the pyrite oxidation in turn also affects these
processes therefore it is a coupled system with interdependent components. For example,
oxygen transport is affected by reaction consumption, water content and the possible heat-
induced air flow, while heat transfer is also influenced by the heat generation from pyrite
oxidation; microbial activity in rock piles relies heavily on the temperature and water
environment. In order to quantify the influences of these processes on pyrite oxidation and
the effluent discharge, numerical models have been developed to simulate these processes
for the purpose of prediction of AMD generation. An overview of pyrite oxidation and air
transport in sulfidic rock piles can be found in Ritchie (2003).
Studies have shown that for pyrite oxidation in rock piles or mine tailings, oxygen
concentration is often the rate-limiting factor among all the influencing factors because of the
relatively fast reaction consumption and limited resupply. The oxygen consumption rate
depends on the pyrite oxidation rate based on mass conservation. The representation of the
pyrite oxidation rate (and oxygen consumption rate) in numerical models is generally based |
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on either the apparent reaction kinetics or on the shrinking core model (SCM) (Gerke et al.,
1998). The former approach often uses a fixed rate or first-order kinetics for the modelling of
the pyrite oxidation process in rock piles, and thus ignores the change in the unreacted
particle size and the microscale transport of the gaseous or aqueous reactants during the
reaction, which may significantly affect the reaction rate. The shrinking core model is more
often used in recent modelling work as it adequately describes the oxidative
alternation/dissolution processes for gas-solid or liquid-solid reactions. The theory of the
shrinking core model is described in Levenspiel (1972), which considers mainly two types of
processes during the reaction. One is the diffusion of the gaseous/aqueous reactant from the
bulk phase to the reacting surface through the gas/water film and the oxidized layer. The
other is the chemical reaction at the particle surface of the solid reactant. Depending on the
relative rates of the two processes, the overall apparent reaction rate can be limited purely
by the diffusion processes (when the surface reaction is relatively fast), referred to as
“diffusion control”, or purely by the surface reaction (when the surface reaction rate is
relatively slow), referred to as “surface reaction control”, or simultaneously by both processes
(when their rates are comparable).
Recent advances in numerical models in this area are presented in Lefebvre et al. (2001),
Mayer et al. (2002), Pantelis et al. (2002), Molson et al. (2005) and da Silva et al. (2009). These
models were derived based on, or evolved from, the previous works including Davis and
Ritchie (1986), Pruess (1991), Pantelis (1993), Wunderly et al. (1996), and Gerke et al. (1998).
Davis and Ritchie (1986) developed a mathematical model that couples pyrite oxidation with
oxygen bulk diffusion through the void spaces of the rock piles. Pyrite oxidation in rock
fragments is modelled using the shrinking core model, where it was assumed that the
contained pyrite in the rock particles is immediately reacted in the presence of oxygen and
the reaction progress of the rock fragments is controlled by oxygen diffusion through the
oxidised layer with pyrite being depleted. The reaction rate varies according to the oxygen
concentration solved from the oxygen bulk diffusion. An analytical solution for the one-
dimensional problem was derived. Based on their model, Wunderly et al. (1996) developed a
one-dimensional numerical model for sulphide oxidation in the vadose zone of mine tailings,
named PYROX. In their model, the bulk diffusion coefficient for oxygen varies spatially
depending on moisture content, porosity and temperature. They further coupled the PYROX
model with the existing MINTRAN reactive transport model developed by Walter et al. (1994),
and the resulting model, MINTOX, can simulate sulphide oxidation as well as the geochemical
equilibrium. Similarly, Gerke et al. (1998) coupled a two-dimensional sulphide oxidation
model with MINTRAN to simulate AMD generation in unsaturated overburden mine spoils,
focusing on the effect of system heterogeneity caused by mixing soil materials with different
pre-oxidation levels. Molson et al. (2005) then presented POLYMIN, a 2D reactive mass
transport and sulphide oxidation model, which was derived from the modified MINTRAN
model after Gerke et al. (1998), to simulate acid mine drainage in unsaturated waste rock
piles. They used the solution from the HYDRUS model (Simunek et al., 1999) for the water
flow and hydraulic properties and investigated the effect of internal structure (layers of |
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different particle sizes) on the AMD generation and evolution using multiple scenario
simulations.
A comparable model to POLYMIN is the MIN3P model presented in Mayer et al. (2002). MIN3P
is a general reactive transport model that considers both intro-aqueous reactions and
dissolution-precipitation reactions. The dissolution-precipitation module uses either a purely
surface reaction control approach or a purely diffusion-control approach. The latter was used
for pyrite oxidation in their simulation, which is the same as the shrinking core model used in
POLYMIN. The major difference between the two programs for modelling pyrite oxidation is
that POLYMIN uses the finite element method with triangular elements while the MIN3P
model uses a block-centred finite difference method.
Lefebvre et al. (2001) presented TOUGH AMD to simulate the AMD generation in waste rock
piles. The TOUGH AMD model evolved from a general non-isothermal multiphase flow and
transport simulator, TOUGH2, developed by Pruess (1991). In TOUGH AMD, the pyrite
oxidation rate was given as a volumetric reaction rate as a function of oxygen concentration
and surface kinetic constant. The reaction progress was controlled by a geometric factor
based on the proportion of remaining pyrite. In addition to the oxygen diffusion considered
in the models mentioned above, Lefebvre et al. (2001) also simulated oxygen convection
induced by the thermal gradient inside the waste rock pile. Other TOUGH-series simulation
codes, TOUGHREACT and TOUGH2-CHEM were also used to simulate pyrite oxidation in
variably saturated subsurface flow systems by Xu et al. (2000) where, similarly, the pyrite
oxidation rate was based on first order kinetics with geometric factors controlling the reaction
progress.
Brown et al. (1999) presented the SULFIDOX model (evolved from FIDHELM by Pantelis (1993))
to simulate sulphide oxidation in waste rock piles considering heat transfer, gas flow and
transport of reaction products with water flow. The mathematical formulations are also
described in Pantelis et al. (2002), where the pyrite oxidation was represented by the Monod
model, the bilinear model or a combination of the two. Oxygen transport by both diffusion
and convection were considered in their model and were set as complementary mechanisms
depending on the degree of water saturation. When the water saturation is greater than 0.85,
air velocity is set to zero and the oxygen transport is only via diffusion. A comparable model
to SULFIDOX is the THERMOX model presented in da Silva et al. (2009), where pyrite oxidation,
heat transfer, gas transport by diffusion and convection, and geochemical reactions can be
simulated. In THERMOX, pyrite oxidation is modelled by the shrinking core model assuming
diffusion-control, which is the same as the approach used in Davis and Ritchie (1986) and
Molson et al. (2005).
To summarize, the processes involved in the oxidation of pyrite in rock piles include oxygen
transport by diffusion and/or convection, heat transfer, pyrite oxidation, fluid flow and intro-
aqueous equilibrium. Depending on the focus of the research, these processes are fully or
selectively considered in the numerical models discussed above. A comparison of these
models is summarized in Table 1-4, where the incorporation of the influencing factors for
determining the pyrite oxidation rate are also shown. |
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Table 1-4: Comparison of different numerical models simulating natural oxidation of pyrite
Incorporation of the influencing
factors when determine pyrite
Modelling Oxygen Heat Geochemical Pyrite oxidation
oxidation rate
Models/References dimensions transport transport processes model
O2 Water
T pH Bacteria
conc. content
Davis and Ritchie (1986) 1D Diffusion No No SCM Yes No No No No
PYROX, Wunderly et al. (1996) 1D/2D Diffusion No Yes SCM Yes No No No No
Gerke et al. (1998) 1D/2D Diffusion No Yes SCM Yes No No No No
TOUGH AMD, Lefebvre et al. (2001) 2D Adv + diff Yes Yes Kinetics Yes Yes No No No
Monod and/or
SULFIDOX, Brown et al. (1999) 2D Adv + diff Yes Yes Yes Yes No No Yes
bilinear model(s)
MIN3P, Mayer et al. (2002) 2D Diffusion No Yes SCM Yes No No No No
POLYMIN, Molson et al. (2005) 2D Diffusion No Yes SCM Yes No No No No
THERMOX, da Silva et al. (2009) 2D Adv + diff Yes Yes SCM Yes Yes No No No
Note that some of the models in this table can be used for more general applications than just modelling pyrite oxidation. This table is not intended to
summarize the general capability of the modelling programs, but to summarize the processes/factors incorporated in the models that are specifically for
modelling pyrite oxidation based on the descriptions in these studies. |
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Research objectives
The purpose of this research is to formulate a framework for the evaluation of pyrite oxidation
in refractory gold-bearing stockpiles so that the outputs can be used to estimate gold recovery
from the stockpiles without pre-treatment. The framework developed in this research is
applied to a real case study to demonstrate its application. In refractory gold-bearing rocks,
gold particles are encapsulated in pyrite crystals and pyrite grains are spatially distributed
within rock fragments. The recovery of gold through direct cyanide leaching depends on both
the level and the profile of pyrite oxidation in the rock particles. For example, if the edge of a
pyrite grain is oxidised but the core is not, the gold particles contained at the edge of the
pyrite grain are readily recoverable but those contained in the core are still resistant to direct
cyanide leaching. Therefore, to effectively evaluate the gold recovery by direct cyanide
leaching, the estimation of both the level and the profile of pyrite oxidation in stockpiles
should be incorporated into the evaluation framework.
While the oxidation of pyrite in stockpiles would be subject to the stockpile properties such
as the formation and geometry of the stockpile as well as the distribution of pyrite therein,
understanding the reaction rate of pyrite oxidation under different conditions in the stockpile
is the key to quantifying the oxidation progress, especially when a numerical modelling
approach is used. As can be seen in Section 1.2, the surface kinetics of pyrite oxidation are
complex and can be affected by many factors including oxygen concentration, temperature,
pH value, impurities, microbial activity and degree of water saturation. The prolonged
reaction is subject not only to the surface reaction kinetics, but also to the transport of oxygen
to the reacting site through a possibly developed diffusion barrier (a solution film and/or an
oxidised layer, the development of the diffusion barrier also depends on pH and water
content) during the reaction. Although several rate formulas have been developed for pyrite
oxidation under different conditions, they do not consider some of the important influencing
factors such as the degree of water saturation for prolonged pyrite oxidation. In addition, the
rate formula derived in published research for pyrite oxidation are kinetic rate laws, which do
not capture the geometric change of pyrite grains during the reaction and are thus not
suitable for estimating the oxidation profile of pyrite grains, which is essential for the purpose
of this research. Therefore, the first objective of this research is to derive a reaction rate
formula for pyrite oxidation that incorporates the important influencing factors related to the
stockpile conditions and captures the geometrical variation of pyrite grains during the
reaction.
To understand the reaction conditions for pyrite oxidation in stockpiles, it is essential to
simulate the dynamic and interdependent processes including pyrite oxidation, oxygen
transport, heat transfer and variations of pH values. Spatially variable inputs such as the
degree of water saturation, size distributions of pyrite grains and rock particles should also
be incorporated in the simulation model. The numerical models discussed in Section 1.4
simulate these processes with an emphasis on the aspect of reactive transport for the purpose
of AMD prediction. However, the modelling for pyrite oxidation in these models is, in general,
simplified. As can be seen in Table 1-4, although these models are able to simulate the |
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multiple processes involved, they do not incorporate all of the important influencing factors
when determining the rate of pyrite oxidation. They either use surface reaction kinetics or a
shrinking core model assuming purely diffusional control to describe the rate of pyrite
oxidation, both of which are inadequate to represent the oxidation rate of pyrite grains in
rock particles under different conditions. The second objective of this research, therefore, is
to derive a numerical modelling framework that can simulate pyrite oxidation in stockpiles, in
which related dynamic processes such as oxygen transport and heat transfer are simulated,
the reaction progress and oxidation profile of pyrite grains are modelled and important
influencing factors for pyrite oxidation are incorporated. Finally, the third objective of this
research is to apply the developed numerical method to the evaluation of pyrite oxidation
and the recovery of gold by direct cyanide leaching in one of the stockpiles at the Lihir mine.
The simulation results from the model are compared with the measured oxidation levels of
samples taken from the stockpile for the calibration of the numerical model. Finally, based on
the calibrated model, a more accurate estimation of the oxidation levels and the profiles of
pyrite grains in different areas of the Lihir refractory gold-bearing stockpile are obtained,
together with an evaluation of the potential for gold recovery through direct cyanide leaching.
Thesis outline
Chapter 2 addresses the first objective. In this chapter, a reaction rate model for pyrite
oxidation that incorporates the influences of temperature, oxygen concentration and water
saturation is derived based on reaction rate data available in the literature. This model uses
the framework of the shrinking core model and considers both the surface reaction kinetics
and the diffusion of oxygen through the oxidised layer and/or a thin solution film. The model
also defines the shrinking rate of the unreacted core, from which the reaction progress of a
pyrite grain can be evaluated. This reaction rate model is applicable for prolonged pyrite
oxidation at circum-neutral to alkaline pH under different temperatures and degrees of water
saturation.
In Chapter 3, the developed numerical modelling framework for the simulation of pyrite
oxidation in stockpiles is presented. The model can simulate oxygen transport by both
diffusion and heat-induced air convection, heat transfer and pyrite oxidation. The oxidation
of pyrite within rock particles is modelled considering the coupled diffusion-reaction process
inside rock particles, which, to the author’s knowledge, is the first of its kind for modelling
pyrite oxidation in rock particles in environmental modelling applications. Compared with the
shrinking core model used for the oxidation of pyritic rock fragments in previously published
work mentioned in Section 1.4, the proposed coupled diffusion-reaction process is more
general and does not assume the unrealistic immediate complete reaction of pyrite in the
presence of oxygen. The reaction of pyrite grains contained within rock particles uses the
reaction rate model presented in Chapter 2, together with the rate model for cases without
coating developed on fresh pyrite surface. The choice between these two models during
simulations depends on the pH value, which is estimated from the current oxidation level and
the acid neutralization capacity of the rock at each time step. The developed method is tested
on a simplified synthetic stockpile, with simulation results including the oxygen concentration, |
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temperature, air velocity field, oxidation level as well as the oxidation profile of pyrite grains
in different locations of the stockpile. A comparison among different simulation scenarios is
also conducted in Chapter 3 to investigate the effects of stockpile properties such as the
diffusion coefficient, porosity and geothermal heat on the prolonged pyrite oxidation in the
stockpile.
Chapter 4 presents a case study of modelling the pyrite oxidation in a refractory gold-bearing
stockpile using the numerical method presented in Chapter 3. The modelled stockpile in this
case study is the Kapit Flat stockpile on Lihir island in Papua New Guinea. Characteristics of
the stockpile incorporated in the simulation include geothermal heat, the degree of water
saturation, rock porosity, rock particle size distribution, pyrite grain size distribution, pyrite
reactivity enhanced by arsenic content and the acid neutralisation capacity. The model
settings are calibrated using the measured oxidation level of samples taken from the stockpile
so that an overall more accurate estimation of the stockpile oxidation level can be obtained.
The potential gold recovery by direct cyanide leaching of the Lihir stockpile is also estimated
using the simulated oxidation profile of pyrite grains and the results show some general
agreement with measured values for the samples tested.
Finally, research outcomes and major findings of this research are summarized in Chapter 5.
The limitations of this research are also discussed, which leads to recommendations for
potential follow-up work in future research for the problem addressed.
References
Bailey, LK & Peters, E 1976, 'Decomposition of pyrite in acids by pressure leaching and anodization:
the case for an electrochemical mechanism', Canadian Metallurgical Quarterly, vol. 15, no. 4,
1976/10/01, pp. 333-344.
Blanchard, M, Alfredsson, M, Brodholt, J, Wright, K & Catlow, CRA 2007, 'Arsenic incorporation into
FeS2 pyrite and its influence on dissolution: A DFT study', Geochimica et Cosmochimica Acta, vol. 71,
no. 3, 2/1/, pp. 624-630.
Bonnissel-Gissinger, P, Alnot, M, Ehrhardt, J-J & Behra, P 1998, 'Surface Oxidation of Pyrite as a
Function of pH', Environmental Science & Technology, vol. 32, no. 19, 1998/10/01, pp. 2839-2845.
Brown, P, Luo, X-L, Mooney, J & Pantelis, G 1999, 'The modelling of flow and chemical reactions in
waste piles', in 2nd Internat. Conf. CFD in the Minerals and Process Industries. CSIRO, Melbourne,
Australia, December, pp. 6-8.
Buckley, AN & Woods, R 1987, 'The surface oxidation of pyrite', Applied Surface Science, vol. 27, no. 4,
1987/01/01, pp. 437-452.
Chandra, AP & Gerson, AR 2010, 'The mechanisms of pyrite oxidation and leaching: A fundamental
perspective', Surface Science Reports, vol. 65, no. 9, pp. 293-315.
Chiriță, P & Schlegel, ML 2017, 'Pyrite oxidation in air-equilibrated solutions: An electrochemical
study', Chemical Geology, vol. 470, pp. 67-74. |
ADE | ~ 27 ~
Abstract
Natural oxidation of pyrite in refractory gold bearing rock stockpiles may facilitate the
recovery of gold contained in mined low-grade material that was originally sub-economic due
to the cost of pre-treatment to oxidise fresh pyrite. The evaluation of this potential requires
the oxidation level of pyrite under various conditions. This paper proposes a reaction rate
model for prolonged natural oxidation of pyrite under various water saturation conditions
and temperatures and a circum-neutral to alkaline pH. The application is to a natural pre-
treatment process for refractory gold ore to liberate the gold content encapsulated in pyrite
crystals and allow effective cyanidation for gold extraction. The proposed model is based on
the shrinking core model with half-order surface reaction on the pyrite surface. It assumes
that, in unsaturated water conditions and at circum-neutral to alkaline pH, a diffusion barrier
forms on the fresh pyrite surface during the reaction, which prohibits the diffusion of oxygen
to the reacting sites and lowers the reaction rate over time. The diffusion barrier may consist
of a thin solution film, some precipitations of soluble oxidation products and/or insoluble
oxidation products depending on the water saturation and pH. The diffusivity of this diffusion
barrier for oxygen is determined as a function of water saturation and temperature. In this
model, the concept of effective oxygen concentration is also proposed to represent the
change in oxygen concentration at the particle surface due to water; an exponential
relationship is found to be appropriate. Based on the reaction rate data reported in the
literature, the reaction rate constant in the model for the surface reaction is determined as 5
× 10-8 mol0.5· m-0.5·s-1 while the diffusion coefficient is 1.2 × 10-15 m2·s-1 for water saturation of
25% and above and 4.7 × 10-19 m2·s-1 for 0.1% water saturation. This rate model can be used
for predicting and modelling the level of pyrite oxidation in rock piles or mine tailings where
various unsaturated water conditions and circum-neutral to alkaline pH apply. |
ADE | ~ 28 ~
Introduction
Pre-treatment, such as pressure oxidation (POX), bio-oxidation, roasting or ultrafine grinding,
is required for effective cyanidation of refractory gold ore (La Brooy et al., 1994), which
increases the processing cost. Some in situ low-grade refractory gold-bearing material,
although containing potentially economic amounts of gold, is uneconomic to mine and
process due to the relatively high processing cost of current processing technology. In many
gold deposits, this low-grade material must be mined for access purposes but is then stored
either for later disposal or for potential processing after active mining ceases (Ketcham et al.,
1993) . However, over long periods of time (e.g., twenty years), natural oxidation of pyrite
can occur within stockpiles when the pyrite is exposed either to atmospheric water and
oxygen or to aqueous water with dissolved oxygen and the material becomes partially
oxidised. This may reduce or eliminate the need for pre-treatment of the material and render
its processing economically viable. An example is the Lihir orebody on Aniolam Island in the
New Ireland Province of Papua New Guinea where a small, low-grade oxide resource yielded
gold recoveries of 90% or higher in direct cyanide leaching (Ketcham et al., 1993). The extent
of these stockpiles and the discovery of more low-grade refractory gold deposits has
stimulated an interest in studying the potential of natural oxidation as a possible alternative
to hydrometallurgy, which could improve gold recovery and contribute to the profitability of
mining operations. The initial requirement to evaluate this potential is knowledge of the
oxidation level and its distribution over the stockpile. To this end, it is essential to understand
the reaction rate for prolonged pyrite oxidation under different possible reaction conditions
in the stockpiles. The possible reaction conditions that would affect the rate of pyrite
oxidation include various pH environments (acidic, neutral or alkaline), levels of water
saturation, temperature and microbial activity.
The oxidation of pyrite and its reaction rate have been studied extensively in the context of
acid mine drainage (AMD), which is often associated with low pH and intro-aqueous
conditions. It is widely accepted that pyrite oxidation under subaqueous conditions mainly
involves four reactions: (1) pyrite is oxidised by oxygen (Eq. (2-1)), which initiates the
oxidation process; (2) the ferrous ion produced in Eq. (2-1) is oxidised to ferric ion by oxygen
(Eq. (2-2)); (3) the ferric ion oxidises the pyrite (Eq. (2-3)) and (4) ferric ion hydrolyses when
the pH value is above 3 (Eq. (2-4)).
2Fe𝑆 +7𝑂 +2𝐻 𝑂 → 2𝐹𝑒2++4𝑆𝑂 2−+4𝐻+ (2-1)
2 2 2 4
4𝐹𝑒2++𝑂 +4𝐻+ → 4𝐹𝑒3+ +2𝐻 𝑂 (2-2)
2 2
Fe𝑆 +14𝐹𝑒3++8𝐻 𝑂 → 15𝐹𝑒2++2𝑆𝑂 2−+16𝐻+ (2-3)
2 2 4
𝐹𝑒3++3𝐻 𝑂 → 𝐹𝑒(𝑂𝐻) +3𝐻+ (2-4)
2 3 |
ADE | ~ 30 ~
oxygen; they derived the rate law shown in Table 2-1 for the microbial oxidation of ferrous
ion. The microbial oxidation rate of pyrite was measured in Olson (1991) and Gleisner et al.
(2006) and was found to be significantly higher than the abiotic oxidation rate if the pH value
is less than 2. Yu et al. (2001) found a lag phase of about 400 hours before bacteria accelerate
the reaction rate. Williamson et al. (2006) provided a quantitative comparison of iron
transformation rates in these reactions in the context of AMD and concluded that the
oxidation of pyrite (by either oxygen or ferric ion), rather than the oxidation of ferrous ion, is
the rate-determining step in both the initiating stage and the propagation of AMD. Overall,
studies of pyrite oxidation under AMD have shown that pH value and microbial activities are
important influencing factors: for high pH (greater than 4), the aqueous oxidation rate of
pyrite is the rate at which pyrite is oxidised by dissolved oxygen (Eq. (2-1)); when the pH is
less than 4, ferric ion is sufficiently replenished from the bacteria-catalysed oxygenation of
ferrous ion and the aqueous oxidation rate of pyrite is the rate at which pyrite is oxidised by
ferric ion. For AMD, in the unlikely case of abiotic conditions at low pH, the oxidation rate is
limited by the abiotic oxidation of ferrous ion.
In AMD the pH is rarely above 4 and the entire system is mostly under subaqueous conditions
with frequent water flow. In non-AMD environments, pyrite oxidation also occurs under
neutral to alkaline pH and/or unsaturated water conditions. Moses and Herman (1991)
measured the oxidation rate of pyrite with pH 6 and 7 and the reaction rate constant was
determined as 10-3.23 for the proposed rate law that assumes first order kinetics with respect
𝐴
to the ratio of total surface area to reaction solution volume ( in m2·L-1) (see Table 2-1).
𝑉
Nicholson et al. (1988, 1990) and Huminicki and Rimstidt (2009) measured the rate of pyrite
oxidation at neutral to high pH in carbonate-buffered solutions over time and found that the
reaction rate decreased with time due to the Fe oxyhydroxide coating that developed on the
pyrite surface. Nicholson et al. (1990) used the shrinking core model to fit the reaction rate
over time considering the Fe oxyhydroxide coating; the shrinking core model parameters (𝐷
𝑠
and 𝑘′′ in Table 2-1) were determined for each experiment run with different pyrite grain size.
Huminicki and Rimstidt (2009) compared the amount of Fe precipitated onto the grain surface
with the calculated Fe product and inferred that only 3% of Fe released from pyrite oxidation
precipitated on the pyrite surface. They further determined a rate law of prolonged pyrite
oxidation as a function of time considering the diffusion of oxygen through the Fe
oxyhydroxide coating (Table 2-1). For cases where pyrite is oxidised under unsaturated water
conditions, Jerz and Rimstidt (2004) investigated the oxidation rate of dried pyrite in moist air
and observed that at the initial stage (several hours), the reaction rate is significantly higher
than the aqueous oxidation rate but soon decreases to a level below the aqueous oxidation
rate; a rate law was determined as a function of the reaction time and oxygen partial pressure
(Table 2-1). León et al. (2004) measured the pyrite oxidation rate for water saturation of 0.1%,
25%, 70%, 95% and found that the oxidation rate increased from practically no saturation
(0.1%), reached a maximum at 25% saturation and thereafter decreased, which indicates a
non-monotonic influence of water content. Field observations of pyritic mine tailings in
Elberling et al. (2000) also showed that the oxidation rate of pyrite is much faster in well-
drained sites than in wet sites. An experimental study that investigated the release of |
ADE | ~ 31 ~
hazardous trace elements in Tamoto et al. (2015) also found that higher water saturation
lowers the leachabilities of the trace elements released from pyrite oxidation. These studies
show that water condition is another important factor that influences the rate of pyrite
oxidation. However, it has rarely been considered in the rate models for pyrite oxidation.
Predicting the level of pyrite oxidation in rock stockpiles requires the oxidation rate under
various conditions. Water content is often a relevant condition in rock stockpiles as is
temperature since pyrite oxidation is an exothermic reaction. The rate laws published in the
literature for pyrite oxidation cover the following situations: (1) initial oxidation rate in acidic,
neutral and alkaline solutions (subaqueous conditions) with or without microbial activity; (2)
time-dependent oxidation rates at high pH values in carbonate buffered solutions considering
the development of Fe oxyhydroxide coating on a pyrite surface and (3) time-dependent
oxidation rate for atmospheric oxidation of pyrite. However, a reaction rate law that
incorporates the influences of water saturation and temperature for prolonged pyrite
oxidation is not available, although studies have been conducted to investigate the influence
of these two factors. As a result, the oxidation rates used in the modelling of pyrite oxidation
over time in rock stockpiles or waste dumps are based on the rate laws available in the
literature; and the influencing factors, such as water condition and temperature, have been
neglected or simplified in the model simulation. For example, Elberling et al. (1994) used a
uniform reaction rate formula for pyrite oxidation at all depths in a tailing with first-order
kinetics considering only oxygen concentration. A similar approach can also be found in
Ardejani et al. (2014). Wunderly et al. (1996) and Molson et al. (2005) assume that the pyrite
oxidation rate is relatively fast and the volumetric reaction rate is completely controlled by
the diffusion of oxygen through the host rock that contains evenly distributed pyrite; based
on this, a diffusion-controlled shrinking core model is used to describe pyrite oxidation in the
host rock. Lefebvre et al. (2001) and Xu et al. (2000) considered the effect of temperature and
water conditions on the oxidation rate in their models but a simple scaling factor between 0
to 1 is used to give different reaction rates with different temperatures and water saturations.
These assumptions and simplifications may be acceptable for predicting acid mine drainage
and the reactive transport of the reaction species in waste rock piles and tailings but are not
suitable for predicting the pyrite oxidation level, which is the fundamental input for the
evaluation of low-grade refractory gold-bearing material.
The objective of this paper is to fill this research gap by focusing on the rate of prolonged
pyrite oxidation in non-AMD environments for the purpose of modelling and predicting the
pyrite oxidation level in rock stockpiles. Although the starting point of this study is to facilitate
the re-evaluation of low-grade refractory gold-bearing material, the research work on the rate
of pyrite oxidation in this study is generic because pyrite oxidation in non-AMD environments
with circum-neutral to alkaline pH and unsaturated water conditions is also an important
geochemical process that is often associated with the mobility of toxic elements in sulphide
and carbonate rich wastes, excavations in urban constructions or aquifer systems (see Tabelin
et al. (2018) and Karikari-Yeboah et al. (2018)). Furthermore, AMD caused by pyrite oxidation
must be initiated in water with circum-neutral pH before acidity is produced. In this study, we
focus on the quantitative effects of water content and temperature on pyrite oxidation rate |
ADE | ~ 32 ~
over time. We review the reaction rate data measured over time in León et al. (2004), Jerz
and Rimstidt (2004) and Nicholson et al. (1988) within the framework of the shrinking core
model to investigate the quantitative effect of water saturation and temperature. A new
reaction rate model for pyrite oxidation under various water conditions and temperatures is
then derived based on the shrinking core model and the values of the key parameters
obtained from our analyses.
Methods and materials
The derivation of the reaction rate model for pyrite oxidation requires reaction rates
measured over time under different conditions. León et al. (2004) measured the reaction
rates of pyrite oxidation over twelve weeks under different water conditions with neutral to
slightly alkaline pH. Pyrite oxidation rates over time were also reported in Nicholson et al.
(1990) and Jerz and Rimstidt (2004) for partially saturated conditions and in moist air
respectively. In this study, reaction rate data from León et al. (2004) are used to determine
the quantitative effect of water saturation. Data from Nicholson et al. (1990) and Jerz and
Rimstidt (2004) are used for comparison and validation. The effects of temperature are
incorporated on the basis of the measured activation energy as reported in the literature.
In the remaining part of this section, the model derivation process is introduced. Firstly, the
experimental data from the literature used in this study are all converted to the same units
based on the same type of specific surface area for model fitting and data comparison. The
present model is based on the shrinking core model with modification to account for the half-
order surface reaction. The surface reaction rates based on the measured initial oxidation
rates available in the literature are then determined. The effect of water content is then
analysed and incorporated in the proposed model. Finally, in the results section, the oxygen
diffusion coefficient in this model is determined by least squares fitting of the experimental
data using the model.
2.2.1 Data treatment considering the specific surface area
The method for calculating the specific surface area (m2·g-1) in different studies is worth
noting since the surface reaction rate (mol·m-2·s-1) was obtained by dividing the amount of
change in the reactants or products in reaction by the total surface area of pyrite. Jerz and
Rimstidt (2004) used the BET (Brunauer, Emmett and Teller) method to measure the surface
area of the sample, which includes the pore size distribution and is based on the physical
adsorption of gas molecules on solid surfaces. In Nicholson et al. (1988), the specific surface
area was calculated from the particle size, as the product of the number of particles per gram
of sample and the surface area of a single (spherical) particle, which results in the expression:
6
𝐴 = (2-5)
𝑠 𝜌𝑑
where 𝜌 is the pyrite density and 𝑑 is the particle diameter. The measured and calculated
specific surface area in different studies can differ significantly as demonstrated in Table 2-2.
For comparison, the reaction rate data used in the present study are normalised to the surface |
ADE | ~ 35 ~
in different studies with the summarised experimental conditions including pH, pyrite grain
size and oxygen concentration. Based on this information, the values of 𝑘′′ for different
studies were calculated as shown in Table 2-4. Note that all listed reaction rates are converted
to specific reaction rates in mol·m-2·s-1 based on the calculated specific surface area; the
oxygen concentration in Eq. (2-9) is in mol·m-3; the value of the stoichiometric coefficient 𝑏 is
given as 2/7 by Eq. (2-1). The average value of 𝑘′′ for these five studies is 5 × 10-8 mol0.5·m-
0.5·s-1 and this value of 𝑘′′ will be used in this study.
Table 2-4: Initial oxidation rate (IOR) of pyrite oxidation measured in the literature and the
calculated reaction rate constant 𝑘′′
IOR
Ref. Pyrite grain SSA_m O2 Conc. 𝑘′′
pH (mol·m-2·s-
size (µm) (m-2·g-1) (mol·m-3) (mol0.5·m-0.5·s-1)
1)
1 1.9 125-250 0.0251 10-8.76 0.237 1.23E-08
6.7-
2 180-250 N/A 10-8.92 0.258 8.23E-09
8.5
3 6-7 38-45 0.066 10-7.86 0.0268 9.35E-08
2-
4 150-250 0.047 10-8.21 0.258 4.25E-08
10
5 <7 250-420 0.01 10-7.10 8.7 9.42E-08
Average 5.01E-08
1: McKibben and Barnes (1986)
2: Nicholson et al. (1988)
3: Moses and Herman (1991)
4: Williamson and Rimstidt (1994)
5: Jerz and Rimstidt (2004)
2.2.4 The effect of water content
León et al. (2004) showed that the degree of water saturation significantly affects the
oxidation rate and partial water saturation (around 25%) is the most conducive to the reaction.
Welch et al. (1990) also reported a similar trend for the total oxygen consumption by pyrite
for different water contents. This non-monotonic behaviour of pyrite oxidation for different
water content may result from two roles that water plays in the pyrite oxidation reaction. On
one hand, increasing water saturation prohibits oxygen diffusion from the gas phase to the
pyrite surface and also decreases the oxygen concentration due to lower solubility of oxygen
in water than in air. From this perspective, excessive water content can decrease the reaction
rate of pyrite oxidation. On the other hand, insufficient water content leads to the super-
saturation and precipitation of the soluble reaction products. The precipitations could resist
the diffusion of oxygen to the fresh pyrite surface and hence lower the reaction rate. Based
on this discussion, the effect of water content on the oxidation rate of pyrite is summarised
as: an increase in water content would decrease the oxygen concentration 𝐶 while increasing
the diffusivity of the diffusion barrier 𝐷 .
𝑠 |
ADE | ~ 36 ~
For the 𝐷 value of the diffusion barrier, it is reasonable to assume that when there is
𝑠
sufficient water (e.g. above 25% water saturation based on the reaction rate data from León
et al. (2004)) to dissolve all the soluble oxidation products, the diffusion coefficient 𝐷 is a
𝑠
constant. When there is insufficient water to dissolve all soluble oxidation products, the value
of 𝐷 decreases as the water content decreases and reaches the minimum under dry
𝑠
conditions. Based on this assumption, the value of 𝐷 takes the following form considering
𝑠
the effect of the water condition (𝜃 represents the water saturation):
𝑤
𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡𝑤ℎ𝑒𝑛𝜃 ≥ 25%
𝐷 ={ 𝑤
𝑠 𝑓(𝜃 )𝑤ℎ𝑒𝑛0 < 𝜃 < 25% (2-10)
𝑤 𝑤
In this study, for the oxygen concentration affected by water, we use the concept of effective
oxygen concentration to approximate the actual oxygen concentration at the particle surface
affected by the degree of water saturation. The effective oxygen concentration is given by the
oxygen concentration 𝐶 in the gas phase (in air-filled pore space) and a factor 𝐹 the value of
𝑔
which depends on the degree of water saturation 𝜃 :
𝑤
𝐶 (𝜃 ) = 𝐶 ∙𝐹(𝜃 )
𝑒 𝑤 𝑔 𝑤 (2-11)
For the atmospheric pyrite oxidation, the concentration of oxygen is the atmospheric oxygen
concentration; and for pyrite oxidation submerged in solution, the oxygen concentration is
given by oxygen solubility in water. Hence, the following relationships must be included in Eq.
(2-11):
𝐶 (𝜃 = 0) = 𝐶 , ℎ𝑒𝑛𝑐𝑒𝐹(𝜃 = 0) = 1
𝑒 𝑤 𝑔 𝑤
{
𝐶 (𝜃 = 1) = 𝐶 ∙𝐻𝑐𝑐, ℎ𝑒𝑛𝑐𝑒𝐹(𝜃 = 1) = 𝐻𝑐𝑐 (2-12)
𝑒 𝑤 𝑔 𝑤
where 𝐻𝑐𝑐 is the dimensionless Henry’s law solubility, which has a value of 0.03527 for
oxygen at 20 ℃. An exponential relationship is proposed for Eq. (2-12):
𝐹(𝜃 𝑤) = 𝑒log(𝐻𝑐𝑐)∙𝜃 𝑤 (2-13)
and therefore,
𝐶 𝑒(𝜃 𝑤) = 𝐶 𝑔
∙𝑒log(𝐻𝑐𝑐)∙𝜃
𝑤 (2-14)
and the oxygen concentration 𝐶 in Eq. (2-8) should then be replaced with Eq. (2-14).
The values of 𝐷 under different water conditions are then determined by fitting Eq. (2-8) and
𝑠
(2-14) to the experimental data. |
ADE | ~ 37 ~
Results and discussion
Based on the hypothesis in this study, the reaction rate data from León et al. (2004) are fitted
using Eq. (2-8) and (2-14) to determine the value of 𝐷 for two water conditions: 1) when
𝑠
water saturation is greater than or equal to 25% and 2) when water saturation is 0.1%. The
values of the other parameters in Eq. (2-8) are given in Table 2-5.
Table 2-5: The parameters used for fitting the rate model to the rate data in León et al. (2004)
Descriptions Unit Value
Parameters
𝜌 Molar density of pyrite mol·m-3 41674
𝐵
𝐶 O2 concentration in gas phase mol·m-3 8.73
𝑔
𝑏 Stoichiometric coefficient Dimensionless 2/7
𝑅 Radius of pyrite particle µm 108/2
𝑘′′ Reaction rate constant mol0.5·m-0.5 ·s-1 5×10-8
𝐻𝑐𝑐 Henry’s law solubility Dimensionless 0.0353
Fig. 2-1: SCM fitted for reaction rate data in León et al. (2004) with different water saturation: (a)
water saturation of 25%, 70% and 95%; (b) water saturation of 0.1%
Fig. 2-1 compares the fitted curve and the experimental data. For water saturation above 25%
(Fig. 2-1 (a)), the best fitting value of 𝐷 is 1.2 × 10-15 m2·s-1 with an overall R-square value of
𝑠
0.94; the R-square values for reaction rate data under the three different water saturations
are 0.98 (25% water saturation), 0.22 (70% water saturation) and 0.87 (95% water saturation)
respectively. The low R-square value for the case with 70% water saturation is due to the
abnormally low oxidation rate measured on day 3 compared with the trend shown by the
other data sets and predicted by the shrinking core model (excluding this point gives an R-
square value of 0.92). For the case with water saturation of 0.1%, the “best” fit curve for the
experimental data is shown as the dashed line in Fig. 2-1 (b) with the highest R-square value
of 0.86 and a 𝐷 value of 1 ×10-18 m2·s-1. However, the modelled results significantly deviate
𝑠
from all the data points except for the first one. As the data set shows high sensitivity to the
reaction time before day 9, another curve is fitted excluding the first point and is shown as
the solid line in Fig. 2-1 (b). The fitted 𝐷 for this case is 4.7 ×10-19 m2·s-1; the R-square is 0.66
𝑠
for the overall data set and is 0.93 excluding the first data point. Considering the sensitivity
of the reaction rate to reaction time at the start of the reaction, the second fitted curve is
more appropriate to describe the oxidation rate over time than the first one. |
ADE | ~ 38 ~
For cases where the water saturation is between 0.1% and 25%, the value of 𝐷 is unknown
𝑠
due to lack of experimental data and has to be estimated. In addition, the threshold value of
the degree of water saturation, such that all soluble oxidation products are dissolved, needs
further investigation (currently 25% is assumed based on the available rate data). In the
absence of further investigation, it is reasonable to assume that 𝐷 is linearly proportional to
𝑠
the degree of water saturation over the range of 0.1% to 25%, which results in:
𝐷 = 1.2×10−15(𝑓𝑜𝑟𝜃 ≥ 25%)
{ 𝑠 𝑤 (2-15)
𝐷 = −4.35×10−18 +4.82×10−15∙𝜃 (𝑓𝑜𝑟0.1% ≤ 𝜃 < 25%)
𝑠 𝑤 𝑤
The value of 𝑘′′ for the half-order surface reaction as discussed above, is given as:
𝑘′′ = 5×10−8
(2-16)
The proposed reaction rate model for pyrite oxidation in neutral to high pH environments is
now given by Eq. (2-8), (2-14), (2-15) and (2-16). The input variables for pyrite oxidation
prediction are the oxygen concentration in the gas phase 𝐶 , degree of water saturation 𝜃
𝑔 𝑤
and particle size (radius) 𝑅. The other two parameters in Eq. (2-8), the stoichiometric
coefficient 𝑏 and the molar density of pyrite 𝜌 , are constants.
𝐵
2.3.1 Comparison with other studies
To validate the proposed reaction rate model, the model is also fitted to the reaction rate
data from Jerz and Rimstidt (2004) and Nicholson et al. (1990). Note that the experimental
temperatures in Jerz and Rimstidt (2004) and Nicholson et al. (1990) are both 25 °C while the
proposed model is based on 20 °C. Thus, the effect of temperature must be considered in the
validation using these reaction rate data.
The reaction rate dependence on temperature can be generally described by the Arrhenius
equation:
𝐸
− 𝑎
𝑘 = 𝐴𝑒 𝑅̅𝑇
(2-17)
where 𝑘 is the reaction rate constant, 𝐸 is the activation energy of the reaction, 𝑅̅ is the gas
𝑎
constant, 𝑇 is the absolute temperature and 𝐴 is the pre-exponential factor.
The measured activation energy 𝐸 for pyrite oxidation, as published in the literature, varies
𝑎
from 19.1 KJ·mol-1 to 121.1 KJ·mol-1 (Chiriță and Schlegel, 2017; Schoonen et al., 2000). But in
most cases, the measured value is below 90 kJ·mol-1 (e.g. in Chiriță and Schlegel (2017), Smith
(1970) and McKibben and Barnes (1986)). Lasaga (1984) suggested that the diffusion-
controlled reaction would have an activation energy close to 20 kJ·mol-1 which indicates that
the temperature dependence of the oxygen diffusion coefficient 𝐷 can be approximated
𝑠
using the Arrhenius equation with an activation energy of approximately 20 kJ·mol-1. Based
on this information, it is reasonable to assume that the values of 𝐸 for diffusion and surface
𝑎 |
ADE | ~ 39 ~
reaction are 20 kJ·mol-1 and 90 kJ·mol-1 respectively. Hence, the diffusion coefficient and the
surface reaction rate constant in the shrinking core model can be expressed as in Eq. (2-18)
to account for the effect of temperature:
{𝐷
𝑠
=𝐷 𝑠0
∙𝑒−𝐸 𝑅𝑎𝐷
(
𝑇1
−
𝑇1
0)
(2-18)
𝑘′′ =𝑘 0′′ ∙𝑒− 𝑅𝐸𝑎𝑘 ( 𝑇1 − 𝑇1 0)
where 𝐷0 and 𝑘′′ are the values at the reference temperature 𝑇 as given in Eq. (2-15) and
𝑠 0 0
(2-16) at 20°C; 𝐸𝐷 and 𝐸𝑘 are the activation energies for diffusion and surface reaction
𝑎 𝑎
respectively; 𝑇 is the reaction temperature and 𝑅̅ is the gas constant with a value of 8.314.
The reaction rate under different temperatures can then be estimated by incorporating Eq.
(2-18) into the governing equation of Eq. (2-8).
After considering the effect of temperature, a comparison of the modelled results with the
reaction rate data from Nicholson et al. (1990) and Jerz and Rimstidt (2004) is shown in Fig.
2-2 and Fig. 2-4.
Fig. 2-2: Comparison of the modelled results and the experimental data from Nicholson et al. (1990)
for pyrite samples with particle sizes of 215, 108 and 76 microns respectively. The reaction rate data
before 20 days are excluded in the calculation of R-square values considering the “abnormality” of
the reaction rate data at the start of the reaction. |
ADE | ~ 40 ~
Fig. 2-3: Comparison of the reaction data for pyrite oxidation in Nicholson et al. (1990), León et al.
(2004) and Jerz and Rimstidt (2004)
In Fig. 2-2, the modelled results are a very good fit to the experimental data for different
pyrite particle sizes after around 20 days. However, the modelled results are higher than the
experimental data for the initial oxidation rate. This is due to the fact that the measured initial
oxidation rate in Nicholson et al. (1990) is significantly less than that reported in other studies.
This can be seen in Table 2-4 and Fig. 2-3 where the initial reaction rate constant and the
experimental reaction rate in Nicholson et al. (1990) are compared with those in other studies.
The corresponding R-square values of the fittings in Fig. 2-2 are 0.52, 0.46 and 0.51
respectively if the data for the first 20 days are excluded and are 0.29, -2.36 and -2.24
respectively if those data points are included. The negative values of R-square suggest that
the proposed model is unable to represent the initial ascending trend of the reaction rates
that appears in the modelled data sets. The estimated water saturation for pyrite oxidation
in Nicholson et al. (1990) is around 90%, which is a reasonable estimate given the experiment
description in the original paper. Despite the discrepancy for the initial oxidation rate, the
proposed rate model in this study is validated for prolonged pyrite oxidation with various
pyrite particle sizes. In the original paper Nicholson et al. (1990), the shrinking core model is
also fitted to the oxidation rate over time. The difference between the Nicholson et al. (1990)
fitting and the current model is that the former assumed first-order surface reaction (i.e. Eq.
(2-6) was used) and used oxygen concentration in the atmosphere as the input for oxygen
concentration although the reaction occurred in a partially saturated condition. The fitted
values for 𝑘′′ and 𝐷 in the Nicholson et al. (1990) study are also subject to the grain size of
𝑠
the pyrite sample used in each experiment.
Fig. 2-4 shows a good agreement between the reaction rate predicted by the proposed rate
model and the reaction rate data in Jerz and Rimstidt (2004) for pyrite oxidation in moist air.
The estimated water saturation is 0.11% which is the same as the dry condition case (0.1%
saturation) in León et al. (2004); the diffusion coefficient is fitted as 1.2 ×10-18 m2·s-1 which is
also close to that determined by León et al. (2004) (4.9 ×10-19 m2·s-1). This indicates that the
resistance of the oxygen diffusion barrier in the two cases is at the same level despite the |
ADE | ~ 41 ~
difference in the reaction pH. In León et al. (2004), the pH is around 8.6 before and after the
reaction, providing a favourable environment for the formation of iron oxyhydroxide coating
on the pyrite surface. This iron oxyhydroxide coating, together with other precipitated soluble
reaction products (e.g. ferric (hydroxy) sulphate according to Todd et al. (2003)) due to super-
saturation, prohibits the diffusion of oxygen to the pyrite surface and, as a consequence, the
reaction rate decreases as the coating grows with time. In Jerz and Rimstidt (2004), although
the pH value was not given, the authors implied an acidic pH after the reaction and suggested
that the diffusion barrier for pyrite oxidation in moist air was an acid solution film with
dissolved reaction products (ferrous sulphate). In addition, they observed some iron sulphate
salts on the surface of dried grains, indicating that some soluble reaction products may have
precipitated in the solution film due to super saturation. In their case, the precipitations,
together with the acidic solution film, form the diffusion barrier on the pyrite surface which
has a diffusion coefficient comparable with that determined using data from León et al. (2004)
with an iron hydroxide coating formed in a circum-neutral and high pH environment. It
appears that, under semi-arid conditions, the reaction rate of prolonged pyrite oxidation is
dominantly controlled by the water condition, which leads to the precipitation of oxidation
products regardless of the pH value. Accordingly, the present rate model initially proposed
for circum-neutral to alkaline pH may also be applicable to acidic semi-arid conditions.
Fig. 2-4: Comparison of the modelled results in the present study and the experimental data in Jerz
and Rimstidt (2004); the best fit yields a water saturation of 0.11%
2.3.2 Estimated activation energy
The measured activation energy, 𝐸 , for pyrite oxidation varies from one study to another,
𝑎
but on average, most measurements lie within the range of 50 to 65 KJ·mol-1 for temperatures
from 20°C to 45°C. Smith (1970) measured the rate of aqueous pyrite oxidation under
different temperatures and an 𝐸 of 64 KJ·mol-1 was obtained from the reported oxidation
𝑎
rate. McKibben and Barnes (1986) measured the activation energy for a temperature range |
ADE | ~ 42 ~
of 20°C to 40°C and reported a value of 56.9 KJ·mol-1. Schoonen et al. (2000) measured the
activation energy of pyrite oxidation within a pH range of 2 to 6 by increasing the temperature
in steps from 23°C to 46.3°C during reactions. They found that the activation energies can
vary by as much as 40 KJ·mol-1 with different reaction progress variables and depending on
the pH value. Nevertheless, the activation energy averaged over the pH range is from 50 to
64 KJ·mol-1 depending on the reaction progress variable. In an electrochemical study in Chiriță
and Schlegel (2017), the activation energy for pyrite oxidation was measured for a pH range
of 1 to 5 within a temperature range of 25°C to 40°C; the reported 𝐸 varies from 19.1 to 56.8
𝑎
KJ·mol-1. Nicholson et al. (1988) determined the activation energy for a temperature range of
3°C to 25°C and a value of 88 KJ·mol-1 was obtained which is higher than the 𝐸 reported in
𝑎
the other studies mentioned above. At 60°C, the magnitude of the reaction rate is less than
would be expected for this activation energy which suggests a much smaller activation energy
near a temperature of 60°C. The comparison of activation energy reported in Nicholson et al.
(1988) and the other studies mentioned above implies that the measured activation energy
for pyrite oxidation gradually decreases with increasing temperature.
Nicholson et al. (1988) suggest that the variation in measured activation energy as
temperature increases is due to a change in the relative controlling mechanism from surface
reaction to oxygen diffusion. In other words, temperature affects both the surface reaction
and the diffusion of oxygen through the diffusion barrier and therefore the measured
activation energy will be closer to that of the rate-controlling mechanism (surface reaction or
diffusion). According to this explanation, the activation energy for pyrite oxidation for
different temperature ranges is estimated using the rate model proposed in this study (a
combination of Eq. (2-8), (2-14), (2-15), (2-16) and (2-18)) to investigate the effect of
temperature.
Fig. 2-5: The modelled Arrhenius plot of initial reaction rate for pyrite oxidation
Fig. 2-5 shows the modelled Arrhenius plot for the initial oxidation rate of pyrite, where the
activation energy of the reaction is the negative slope of the curve. The modelled apparent
activation energy below 20 °C is 87.6 KJ·mol-1 and for temperature ranging from 20 to 40 °C,
it drops to 47.0 KJ.mol-1. These values are reasonably consistent with the experimental |
ADE | ~ 43 ~
observations in Nicholson et al. (1990), McKibben and Barnes (1986) and Schoonen et al.
(2000) discussed above. However, the modelled activation energy is sensitive to both reaction
time and the values of 𝐷0 and 𝑘′′. For reactions of long duration, the modelled 𝐸 decreases
𝑠 0 𝑎
rapidly with increasing reaction time and increases with slight decreases in 𝑘′′. This sensitivity
0
to reaction time and the value of both the reaction rate constant and the diffusion coefficient
could be a reason for the discrepancy in the activation energy measured for pyrite oxidation
in the literature.
2.3.3 Application of the proposed model
Given the proposed reaction rate model and the determined values of 𝐷 and 𝑘’’ for pyrite
𝑠
oxidation, it is possible to quantify the effect of other factors on the reaction rate in practical
applications. Fig. 2-6 shows the oxidation rate measured at different times as affected by
different factors. The effect of particle size is shown in Fig. 2-6 (a). The reaction rate per mass
(mol·s-1·g-1) increases with total surface area and hence decreases with increasing particle size
as, in theory, the reaction rate per surface area is independent of particle size and shape. Fig.
2-6 (b) to (d) show the reaction rate per surface area against oxygen partial pressure, degree
of water saturation and temperature, the trend and variations of which are as expected.
Fig. 2-6: The modelled initial oxidation rate (IOR) of pyrite with different: (a) particle sizes; (b) oxygen
partial pressure; (c) water saturation; (d) temperature.
Fig. 2-7 shows the time required to achieve 50% of pyrite oxidation (half-conversion time)
under different conditions predicted using the proposed reaction rate model. It shows that
all four factors – pyrite grain size, oxygen partial pressure, temperature and water saturation
– have significant impact on the reaction rate, especially water saturation. Under the optimal
water condition of 25% saturation and a temperature of 25 °C, the time required to achieve |
ADE | ~ 44 ~
50% oxidation can be less than ten years with a maximum pyrite grain size of 30 µm and
minimum oxygen partial pressure of 5% atm, which is a manageable period of time
considering a typical mine life of a dozen years. A spontaneous rise in temperature due to the
reaction could further shorten the time required to achieve an effective oxidation level for
direct cyanidation.
Fig. 2-7: The half conversion time for pyrite oxidation under different conditions: (a) The effect of
particle size under various oxygen partial pressures at 25°C and 25% water saturation; (b) The effect
of oxygen partial pressure under different temperatures at 25% water saturation and with particle
size of 60 µm; (c) The effect of water saturation under various oxygen partial pressures at 25°C and
with particle size of 60 µm; (d) The effect of temperature under various degrees of water saturation
with particle sizes of 60 µm and 0.2 atm of oxygen partial pressure.
The proposed model is derived from the reaction rate of pure euhedral pyrite crystals at
different grain sizes (see Table 2-4). In rock stockpiles, the pyrite oxidation process is also
subject to the host rock particle size in addition to the factors discussed above. The majority
of the pyrite-bearing rock in refractory gold ore stockpiles is boulder sized while the grain size
of the contained pyrite is normally only in the range of microns to hundreds of microns with
the grade commonly less than 10%. In this situation, pyrite oxidation will initially occur with
pyrite grains on surfaces of the rock particles and gradually extends into the rock as oxygen
and water slowly diffuse into the rock. The proposed model will be used in this framework to
model the oxidation of pyrite grains contained in host rock particles. Research is currently
underway to develop a stockpile pyrite oxidation model taking account of the practical
considerations discussed above (e.g., rock particle sizes, pyrite grade and grain sizes) and the |
ADE | ~ 45 ~
stockpile geometries that affect oxygen and water/moisture concentration within stockpiles,
based on the proposed model.
Note that the types of pyrite in an ore deposit may include framboidal and highly disordered
pyrite which have a much higher reactivity due to their high specific surface area. Pugh et al.
(1984) measured the effect of morphology on the rate of pyrite oxidation and the rates
showed that, depending on the size fraction, oxidation of framboidal pyrite is 1.6 to 3.2 times
faster than that of massive pyrite over 14 days of reaction. The results suggest that, at least
at the initial stage of the reaction, framboidal pyrite is more reactive than massive pyrite. To
model the pyrite oxidation in stockpiles properly, types of pyrite will also have to be
considered. For example, as the proposed model is derived for euhedral pyrite, one simple
approach of dealing with framboidal pyrite, or other types of pyrite with larger surface areas,
is to scale up the reaction rate derived from the generic model or adjust the pyrite grain size
in the present model according to the specific morphology.
2.3.4 Limitations of the proposed model
The proposed reaction rate law using the shrinking core model assumes invariant particle size
during pyrite oxidation, which is not necessarily the case in reality because of the release of
reaction product into the surrounding solution. In particular, at high water-saturation, the
precipitated Fe product may only be a small percentage of the total Fe product (e.g. only 3%
under submerged water condition according to Williamson and Rimstidt (1994)). Therefore,
the precipitation layer on a fresh pyrite surface may, in reality, be much thinner than the
theoretical one implied by the original shrinking core model. In the model proposed here, the
layer between the original particle surface and the fresh pyrite surface is explained as a thin
solution film that is highly saturated with oxidation products together with precipitations.
Nevertheless, in predicting the pyrite oxidation rate, the possible deviation from reality is
compensated by the diffusion coefficient, as it is a fitted value derived directly from
experimental data.
The applicability of the proposed model is limited to certain pH environments. For high water-
saturation conditions, the proposed model is only applicable for neutral or higher pH
environments. For cases where the pH value is less than 4, the oxidation products would all
be dissolved with sufficient water content and no precipitations would be formed. In these
cases, the reaction process would no longer be within the scope of the proposed model and
appropriate rate laws listed in Table 2-1 should be used for the oxidation rate where needed.
At low water saturation, this model may be applied for both acidic and alkaline pH because a
diffusion barrier can be formed by precipitation of the soluble reaction products due to super-
saturation.
Conclusions
Natural oxidation of pyrite has the potential to contribute significantly to recovering gold from
long-term stockpiled, low-grade refractory gold bearing material that otherwise may not be
economically recoverable. Assessing the economic value of the partially oxidised material is |
ADE | ~ 46 ~
of interest to many gold mining companies that have stockpiled a large amount of this low-
grade material. The key information required for this evaluation is the estimated level of
pyrite oxidation in the stockpiles, which in turn requires pyrite oxidation rates under various
conditions within the rock stockpiles, including temperature and water saturation. To this end,
this paper proposes a reaction rate model for predicting pyrite oxidation that incorporates
the influences of temperature, oxygen concentration and water saturation. The rate model is
given as the rate of pyrite destruction and the rate of unreacted core shrinkage:
𝑑𝑁 4𝜋𝑅2𝑏𝐶
(𝑎)− = 𝑒
𝑑𝑡 𝑅 𝑅 1 𝑅2
( −1)+ 𝐶0.5
𝐷 𝑟 𝑘′′𝑟2 𝑒
𝑠 𝑐 𝑐
(𝑏)−𝑑𝑟
𝑐
=
𝑏𝐶/𝜌
𝐵
𝑑𝑡 (𝑅−𝑟)𝑟 𝐶0.5
𝑐 𝑐+
{ 𝑅𝐷 𝑘′′
𝑠
𝐶 =𝐶 ∙𝑒log(𝐻𝑐𝑐 )∙𝜃𝑤
𝑒 𝑔
𝐷
𝑠
=𝐷 𝑠0
∙𝑒−𝐸 𝑅𝑎𝐷
(
𝑇1
−
𝑇1
0)
(2-19)
{ 𝑘′′ =𝑘 0′′ ∙𝑒− 𝑅𝐸𝑎𝑘 ( 𝑇1 − 𝑇1 0)
For 𝑇 = 293.15 K:
0
𝐷0 = 1.2×10−15(𝑓𝑜𝑟𝜃 ≥ 25%)
𝑠 𝑤
𝐷0 = 4.82×10−15∙𝜃 −4.35×10−18(𝑓𝑜𝑟0.1% ≤ 𝜃 < 25%)
𝑠 𝑤 𝑤
𝑘′′ = 5×10−8
0
{𝐻𝑐𝑐 = 0.0353
This model is based on the hypothesis that a diffusion barrier is formed around fresh pyrite
particles in the reaction, which prohibits the diffusion of oxygen to the pyrite surface; it grows
as the reaction proceeds and accounts for the decrease in the reaction rate over time.
Depending on the pH and water conditions, the diffusion barrier may consist of solid oxidation
products/precipitations and a thin solution film with dissolved reaction products. The
corresponding diffusion coefficient is a function of temperature and water saturation. In this
model, the effective oxygen concentration is used to represent the oxygen concentration at
the particle surface as affected by the degree of water saturation. The relationship between
effective oxygen concentration and water saturation is exponential. The parameters
determined in this study for the proposed model, including both the surface reaction rate
constant and the diffusion coefficient, are based on experimental data reported in the
literature. For the diffusion coefficient, the determined value and the relationship with water
saturation provide a reference for other studies where gas diffusion in reaction is important.
The oxidation rate predicted by this model is consistent with the reported data from various
studies. Hence, this model is able to predict the time-dependent reaction rate of prolonged
pyrite oxidation at circum-neutral to alkaline pH under various temperatures and levels of
water saturation. Using this model, and other rate models that consider different reaction |
ADE | ~ 55 ~
Abstract
This study presents a three-dimensional numerical modelling method for predicting the pyrite
oxidation level in refractory gold-bearing stockpiles under various conditions. The physical
and chemical processes incorporated into the model include oxygen transport, heat transfer,
air convection and pyrite oxidation. Different reaction rate models based on the shrinking
core model are used to quantify the oxidation of pyrite grains in rock particles considering the
influence of oxygen concentration, degree of water saturation, temperature and pH
conditions. The oxygen concentration gradient within rock particles is considered for pyrite
oxidation and is solved using the diffusion-reaction equation in the polar-coordinate system.
Particle size distributions for both pyrite grains and rock particles are incorporated in the
modelling of pyrite oxidation and oxygen consumption. Several scenarios with different
parameters were examined and the simulation results show that after ten years, the pyrite
oxidation level over the stockpile is up to 50% depending on the location within the stockpile,
the rock types and stockpile properties such as porosity and water content. The model can
simulate the overall pyrite oxidation level as well as the oxidation profile of the pyrite grains,
i.e., the oxidation depth of pyrite grains of different sizes and at different locations within the
rock particles. These are essential inputs required for the estimation of gold recovery by direct
cyanide leaching for possible reclamation of the partially oxidised stockpile without incurring
expensive pre-treatment of the material. |
ADE | ~ 56 ~
Introduction
The most common gold-bearing minerals in refractory gold ore deposits are sulphides, which
must be pre-treated prior to cyanidation by pressure oxidation (POX), bio-oxidation, roasting
or ultrafine grinding in order to separate the gold particles from the host sulphide minerals.
However, when these sulphides are exposed to air and water for an extensive period of time,
pyrite may be naturally oxidised, which may reduce the need for pre-treatment and hence
reduce the processing cost. This may occur in long-term stockpiles of low-grade gold-bearing
material in many refractory gold mining operations. This low-grade material (below the
prevailing economic cut-off grade) may have been mined to access ore or may have resulted
from limited mining selectivity, and it is commonly stockpiled for potential processing at a
later stage of the mine life. It may also consist of low-grade ore that is stockpiled to give
priority to processing higher-grade ores. Oxidised material can be directly leached to extract
the contained gold without expensive pre-treatment. Hence the natural oxidation of pyrite in
refractory gold-bearing stockpiles may increase the profitability of stockpile reclamation by
enabling gold recovery using direct cyanide leaching. In this context, it is essential to
understand the level of the natural oxidation of pyrite within the stockpile in order to evaluate
the potential for recovering the gold without pre-treatment.
Natural oxidation of pyrite has been studied extensively because of its negative impact on the
environment. When exposed to water and oxygen, pyrite can be oxidised to release sulphate,
iron ions and acid. The resulting effluent is acidic and can dissolve metals and elements that
can be toxic to local flora and fauna if discharged into the local groundwater system; this
process is referred to as acid rock drainage (ARD). Research on the natural oxidation of pyrite,
including both laboratory studies and numerical modelling, has largely focused on ARD, with
the aims of determining the rate-controlling factors and predicting the effluent discharge for
control and remediation. The oxidation reaction in these cases is often associated with low-
pH and intro-aqueous conditions. Pyrite oxidation can also occur in non-acidic conditions and
under different water contents, with different rates of reaction depending on conditions
(Huminicki and Rimstidt, 2009; León et al., 2004; Moses and Herman, 1991; Nicholson et al.,
1988). Prediction of the oxidation level of pyrite in stockpiles requires consideration of the
various reaction conditions that affect the oxidation rate.
Oxygen availability is widely recognised as the most important among all the factors that
affect the pyrite oxidation rate in mine tailings and rock piles. Oxygen, as one of the reactants,
needs to be replenished constantly from the atmosphere into the stockpile to sustain the
reaction. The oxygen can be replenished via diffusion and/or advection. The diffusion rate
depends on the stockpile properties including porosity and water content. The water content
in the stockpile generally inhibits the oxygen transport as oxygen diffuses much slower in
water than in air. Both laboratory studies (León et al., 2004) and field observations (Elberling
et al., 2000) have found that partially saturated conditions are the most favourable for pyrite
oxidation. In addition to diffusion, as pyrite oxidation is exothermic, thermal-induced air
convection may also be an effective source of oxygen resupply. The heat generated from the
reaction raises the temperature of the stockpile, which may induce air movement between |
ADE | ~ 57 ~
the stockpile and the atmosphere. The increased temperature will also directly affect the
oxidation rate, as documented in Chiriță and Schlegel (2017), Schoonen et al. (2000) and
McKibben and Barnes (1986). Other factors, such as particle size distribution, mineral
composition and the shape and size of the stockpile, also affect pyrite oxidation by influencing
the water flow, oxygen transport and the pH environment. As the effects of these factors on
pyrite oxidation are mostly non-linear and interdependent, a coupled numerical modelling
approach is required to predict the pyrite oxidation level in stockpiles.
Many numerical modelling tools have been developed to simulate pyrite oxidation as well as
the related physical and geochemical processes for ore leaching and AMD prediction. Early
modelling work can be found in Cathles and Apps (1975), Jaynes et al. (1984), Davis and
Ritchie (1986), Pantelis (1993), Elberling et al. (1994), Wunderly et al. (1996) and Gerke et al.
(1998). The work reported in these papers has contributed to the development of more
advanced models, including TOUGH AMD (Lefebvre et al., 2001), SULFIDOX (Brown et al.,
1999), MIN3P (Mayer et al., 2002; Pabst et al., 2017), POLYMIN (Molson et al., 2005) and
THERMOX (da Silva et al., 2009).
Cathles and Apps (1975) developed a one-dimensional, non-steady-state model for sulphide
mineral oxidation in the leaching process of a copper waste dump. Their model assumed air
convection to be the dominant transport mechanism for oxygen and considered heat
generation and bacteria catalysis on ferrous ion oxidation. Pyrite oxidation was modelled
using the shrinking core model (Levenspiel, 1999) with a constant surface reaction rate
independent of oxygen concentration. Jaynes et al. (1984) presented a variation of the model
from Cathles and Apps (1975) to study acid mine drainage from a reclaimed coal strip mine.
Their model assumed gaseous diffusion to be the dominant mechanism for oxygen transport.
They also simulated the removal of reaction products with water percolation.
Wunderly et al. (1996) developed a one-dimensional numerical model (PYROX) based on the
work of Davis and Ritchie (1986) to simulate the oxidation of pyrite in the vadose zone of mine
tailings. In the PYROX model, the bulk diffusion coefficient of oxygen is spatially variable
depending on the moisture content, porosity and temperature. They also coupled the PYROX
model with the existing reactive transport model MINTRAN developed by Walter et al. (1994)
to create the MINTOX model for simulating both pyrite oxidation and the subsequent
transport of oxidation products in mine tailing impoundments. A similar approach was taken
by Gerke et al. (1998), in which a 2D pyrite oxidation model was added to the MINTRAN model.
The heterogeneity of hydraulic conductivity and sulphide mineral fractions were incorporated
to provide a better means of simulating the concentration of oxidation products in the
effluent at the local scale. Molson et al. (2005) derived a model (POLYMIN) from the work of
Gerke et al. (1998) for acid mine drainage simulation and studied the effects of the interior
structure of the waste rock pile on the flow path of acid mine drainage. Their model
incorporates oxygen diffusion, kinetic (diffusion-limited) sulphide oxidation, multi-
component advective-dispersive transport and geochemical reactions. The water content in
their model was simulated using HYDRUS-2D (Simunek et al., 1999). |
ADE | ~ 58 ~
Lefebvre et al. (2001) simulated acid mine drainage from waste rock piles using TOUGH AMD
developed by Lefebvre (1995). The model was based on TOUGH2 which was first presented
by Pruess (1991). Their model considered oxygen advection and diffusion, heat transfer,
pyrite oxidation and sulphate transport with water infiltration and liquid flow. Pyrite oxidation
was modelled using kinetic and geometric factors to represent the effects on the volumetric
oxidation rate of temperature, oxygen partial density and the proportion of remaining pyrite.
These factors provide kinetic control for the reaction to avoid the modelling difficulty in
extreme cases such as the total absence of oxygen from the system.
Brown et al. (1999) and Pantelis et al. (2002) provided the SULFIDOX software package, which
evolved from FIDHELM (Pantelis, 1993), to model air and water flow, chemical reactions and
reactive transport in waste rock piles including dissolution and precipitation of minerals. They
used the Monod model, the bilinear model or a combination of the two to describe the
reaction rate of sulphide oxidation Pantelis et al. (2002). Another comprehensive model,
MIN3P, described in Mayer et al. (2002) incorporates a generalized formulation for kinetically
controlled reactions into a multicomponent reactive transport model that can simulate intra-
aqueous reactions, mineral dissolution and precipitation, as well as geochemical equilibrium
processes. For pyrite oxidation, MIN3P uses the shrinking core model and assumes the
reaction is controlled by oxygen diffusion. da Silva et al. (2009) provided a comprehensive
ARD modelling program THERMOX, derived from HYDRUS-2D (Simunek et al., 1999) and
PHREEQC (Parkhurst et al., 1980). This program can simulate oxygen transport by diffusion
and advection, heat transfer, pyrite oxidation and geochemical reactions. In THERMOX, pyrite
oxidation is modelled using the shrinking core model in the same way as used in Wunderly et
al. (1996), Molson et al. (2005) and Mayer et al. (2002), which assumes diffusional control for
the reaction in rock fragments.
To summarise, the processes considered in the modelling programs discussed above include
oxygen transport by diffusion and/or convection, pyrite oxidation, heat transfer and reactive
transports (fluid flow and geochemical reactions). In these models, pyrite oxidation is
modelled by taking a whole rock fragment as the solid reactant and the reaction progress is
represented either by the shrinking core model assuming diffusion of oxygen through the rock
particle controls the reaction or simply by geometric/kinetic factors. The diffusion-controlled
shrinking core modelling approach was used in most of these models (da Silva et al., 2009;
Davis and Ritchie, 1986; Gerke et al., 1998; Mayer et al., 2002; Molson et al., 2005; Wunderly
et al., 1996). This approach assumes that pyrite occurs in a very fine size and is
homogeneously distributed within the rock particles; hence it reacts immediately in the
presence of oxygen. Thus, the oxygen diffusion front inside the rock particle is the reacting
front as well as the boundary that divides the rock particle into two parts: the completely
altered rim and the unreacted core. This assumption simplifies the modelling of the reaction
of pyrite inside rock particles and gives good approximations for the release rate of reaction
products and the overall reaction progress, which is acceptable for ARD prediction. However,
this assumption may not be realistic, especially when the grain size of pyrite inside the rock
particles is significant and, hence, the reaction between pyrite grains and oxygen cannot be
assumed to be immediate, and instead, may be at a rate comparable with oxygen diffusion |
ADE | ~ 59 ~
through the rock particles. In this case, the overall reaction progress is controlled by both the
diffusion of oxygen within the rock particles and the chemical reaction at the pyrite grains.
The purpose of the research presented here differs from that of the ARD prediction models
and is to develop a modelling tool that can effectively predict the distribution of different
pyrite oxidation levels within a stockpile for the estimation of the gold recovery by direct
cyanide leaching from refractory ore. The focus of the model presented in this paper is on the
oxidation of pyrite grains within rock particles. We consider a more general case by using the
diffusion-reaction equation to describe the oxidation of pyrite grains within a rock particle
instead of using the diffusion-controlled shrinking core model. The benefit of using this more
complex model is to allow a wider range of applications considering different material types
with various rock diffusivities and particle size distributions for both rock particles and pyrite
grains. The effects of temperature, water content, oxygen concentration, pH condition and
particle size distributions are also incorporated in the modelling of pyrite oxidation. The
processes that are interdependent with the reaction, including oxygen transport and heat
transfer, are simulated. Other influencing factors such as water content are treated as pre-
defined parameters in this model.
Mathematical model
3.2.1 Pyrite oxidation
The oxidation of pyrite by oxygen in the stockpile is generally described by the following
stoichiometric equation:
2𝐹𝑒𝑆 2+7𝑂 2+2𝐻 2𝑂 → 2𝐹𝑒2++4𝑆𝑂 42−+4𝐻+ (3-1)
where pyrite is oxidised in the presence of oxygen and water.
In reality, pyrite oxidation may involve multiple reactions including oxygenation of ferrous ion
that generates ferric ion, the oxidation of pyrite by ferric ion and the hydrolysis of ferric ion
(Singer and Stumm, 1970); both oxygen and ferric ion are the oxidants for pyrite oxidation.
The kinetics of this reaction is therefore complex as each individual intermediate step could
be affected differently by reaction conditions. There are numerous published studies on the
kinetics of pyrite oxidation with specific focus on the rate-controlling step of the reaction, e.g.,
see discussions and reviews in Williamson and Rimstidt (1994), Evangelou and Zhang (1995)
and Chandra and Gerson (2010). Experimental studies show that the overall oxidation rate is
affected by factors including the pH condition, oxygen concentration, temperature, water
content and iron-oxidizing bacteria (Wang et al., 2019).
Under the theoretical framework of the shrinking core model, the abiotic oxidation of pure
pyrite can be separated into two different cases depending on whether a diffusion barrier,
such as an oxidised coating or a thin saturated solution film, develops on the fresh pyrite
surface during the reaction. For cases where a diffusion barrier develops, Wang et al. (2019)
proposed a reaction rate model for abiotic oxidation of pyrite grains based on empirical rate |
ADE | ~ 61 ~
Eqs. (3-2) and (3-3) give the reaction rate for pure pyrite grains. The oxidation of pyrite
contained in rock particles will also depend on the diffusion of oxygen inside rock particles
and the process is described by a diffusion-reaction equation. Assuming that rock particles
are perfect spheres, and the reaction status only varies along the radius direction, the
diffusion-reaction equation can be written as:
𝜕𝐶 𝜕2𝐶 2𝜕𝐶
𝜑 𝑟 𝜕𝑡 =𝐷 𝑒( 𝜕𝑟2 + 𝑟 𝜕𝑟)−𝑆 𝑝𝑦 (3-4)
where 𝐶 is the oxygen concentration inside the rock particle varying with the radius location
𝑟 and time 𝑡 and is equivalent to the gaseous oxygen concentration 𝐶 in Eq. (3-2); 𝜑 is the
𝑔 𝑟
porosity of the rock particle; 𝐷 is the oxygen diffusivity in the rock particle and 𝑆 is the rate
𝑒 𝑝𝑦
of oxygen consumption by pyrite grains in a unit volume of the pyrite-bearing rock. The
boundary conditions for Eq. (3-4) is given as Eq. (3-5). At the rock particle surface, the first
type of boundary condition is used and the boundary value for oxygen is given by the oxygen
concentration in the space between rock particles. At the centre of the rock particle, the
boundary condition is set as no diffusive flux, hence, the concentration gradient is zero.
𝐶(𝑟 = 𝑅) =𝐶
0
𝜕𝐶 (3-5)
(𝑟 =0) =0
𝜕𝑟
The value of 𝑆 depends on the local oxygen concentration 𝐶(𝑟,𝑡), pyrite grain size and the
𝑝𝑦
reaction progress of the pyrite grains. In this work, the pyrite grain size distribution (by mass)
is defined as:
𝑅 1𝑅 2…𝑅 𝑖…𝑅
𝑛
𝑃𝑆𝐷 =( )
𝑝𝑦 𝑚 𝑚 …𝑚 …𝑚
1 2 𝑖 𝑛
𝑚 (3-6)
𝑖
𝐹 =
𝑖 4
𝜋𝑅3∙𝜌
3 𝑖 𝑝𝑦
where 𝑅 and 𝑚 represent the 𝑖𝑡ℎ grain size radius and the corresponding relative mass
𝑖 𝑖
proportion. 𝜌 is the pyrite density and 𝐹 represents the number of pyrite grains at the 𝑖𝑡ℎ
𝑝𝑦 𝑖
grain size in a pyrite group with total mass of ∑𝑛 𝑚 and with this grain size distribution.
𝑖=1 𝑖
For each pyrite grain size, the oxygen consumption rate can be calculated by Eq. (3-2) or (3-3).
For a unit volume of pyrite particles, the total oxygen consumption rate is the sum of the rates
for the different sizes. This requires the solution of Eq. (3-2) or (3-3) for each pyrite grain size,
which is computationally costly. For simplification, it is assumed that the depth of oxidation
is the same for pyrite grains of different sizes under the same reaction environment. Hence |
ADE | ~ 63 ~
on its radius location. For example, pyrite grains near the rock surface would have easier
access to oxygen than those in the inner part of the rock particle and hence can be oxidised
more quickly. In other words, the larger the rock particle, the more difficult for the internal
pyrite to be oxidised. The accessibility to oxygen can be determined by the distance between
the location of pyrite and the rock surface and based on this simplification, it can be assumed
that the reaction progress is the same for pyrite with the same distance to the rock particle
surface regardless of the rock particle size. Using this approximation, the solution of the
diffusion-reaction equation (Eq. (3-4)) for a large rock particle can be used for rock particles
of various smaller sizes.
Again, a discrete distribution is used in this work to define the rock particle size distribution
in a stockpile:
𝑅 (1)𝑅 (2)…𝑅 (𝑗)…𝑅 (𝑝)
𝑟𝑜𝑐𝑘 𝑟𝑜𝑐𝑘 𝑟𝑜𝑐𝑘 𝑟𝑜𝑐𝑘
𝑃𝑆𝐷 = ( )
𝑟𝑜𝑐𝑘 𝑚 (1)𝑚 (2)…𝑚 (𝑗)…𝑚 (𝑝)
𝑟𝑜𝑐𝑘 𝑟𝑜𝑐𝑘 𝑟𝑜𝑐𝑘 𝑟𝑜𝑐𝑘
(3-10)
𝑚 (𝑗)
𝑟𝑜𝑐𝑘
𝐹 (𝑗)=
𝑟𝑜𝑐𝑘 4
𝜋𝑅3 (𝑗)∙𝜌
3 𝑟𝑜𝑐𝑘 𝑟𝑜𝑐𝑘
where 𝑅 (𝑗)and 𝑚 (𝑗) represent the jth rock particle size and the corresponding
𝑟𝑜𝑐𝑘 𝑟𝑜𝑐𝑘
relative mass proportion;𝜌 is the rock density and 𝐹 (𝑗) represents the number of rock
rock 𝑟𝑜𝑐𝑘
particles at size 𝑅 (𝑗) among the rock particles of a total mass of ∑𝑝 𝑚 (𝑗) and with
𝑟𝑜𝑐𝑘 𝑗=1 𝑟𝑜𝑐𝑘
this particle size distribution. The largest rock particle of size 𝑅 (𝑝) is discretised into
𝑟𝑜𝑐𝑘
several layers with equal thickness of ∆𝑟; the layer sequence is denoted by 𝑘 and 𝑘 = 1
∆𝑟
represents the outmost layer. The distance to the particle surface for layer 𝑘 is +∆𝑟(𝑘 −
2
1), hence 𝑘 also denotes the distance sequence. All layers in rock particles of different sizes
𝑅 (𝑝)
can be categorized into the distance sequence of 𝑘 ∈ [1, 𝑟𝑜𝑐𝑘 ]. The total amount of pyrite
∆𝑟
𝑃𝑦(𝑘) at layer 𝑘 in a unit volume of stockpile material is given by Eq. (3-11) where 𝑃𝑦% is the
volumetric content of pyrite.
𝑃𝑦%∙∑𝑝
𝑗=1[4
3𝜋∙(𝑟 𝑘3 𝑗(1)−𝑟 𝑘3 𝑗(2))∙𝐹 𝑟𝑜𝑐𝑘(𝑗)]
𝑃𝑦(𝑘) =
4 𝜋∑𝑝 (𝑅3 (𝑗)∙𝐹 (𝑗))
3 𝑗=1 𝑟𝑜𝑐𝑘 𝑟𝑜𝑐𝑘 (3-11)
𝑟 = 𝑚𝑎𝑥{𝑅 (𝑗)−∆𝑟∙(𝑘−1),0}
𝑘,𝑗(1) 𝑟𝑜𝑐𝑘
{𝑟
𝑘,𝑗(2)
= 𝑚𝑎𝑥{𝑅 𝑟𝑜𝑐𝑘(𝑗)−∆𝑟∙𝑘,0}
The oxygen consumption rate of a pyrite group at the distance category 𝑘 can then be
calculated by Eq. (3-7) or Eq. (3-8) with the oxygen concentration 𝐶 (𝑟) solved from Eq. (3-4)
𝑒
for the layer 𝑘. Therefore, for a unit volume of stockpile material, the total oxygen
consumption rate is given by Eq. (3-12) and the reaction progress of the pyrite grains is given
by 𝑟 as defined in Eq. (3-7) or Eq. (3-8) for each layer.
𝑐 |
ADE | ~ 65 ~
3.2.3 Heat transfer
The temperature profile for the stockpile can be described by the heat balance equation.
Holzbecher (1998) presented the heat balance equation based on Fourier’s law as shown in
Eq. (3-16) considering heat source, heat conduction and heat convection through fluid flow
in porous media:
𝜕𝑇
=𝛻∙(−𝛾𝒗𝑇+𝐷 𝛻𝑇)+
𝑞ℎ
with 𝛾
=𝜌∗𝐶∗
ℎ (3-16)
𝜕𝑡 (𝜌𝐶) (𝜌𝐶)
In this work, only air flow is considered for the convective heat transfer. In Eq. (3-16), 𝑇 is the
temperature of the stockpile, 𝒗 is the air velocity field, 𝐷 is the thermal diffusivity, 𝜌 and 𝐶
ℎ
are respectively the density and the specific heat capacity for the stockpile material, and 𝜌∗
and 𝐶∗ are those of the air. 𝑞 is the heat source from pyrite oxidation and is defined as the
ℎ
volumetric rate of heat generation.
The heat generation rate per unit volume of material can be derived from the volumetric
consumption rate of oxygen (Eq. (3-12)) as:
𝑞
ℎ
=𝛿∙𝑏∙𝑅𝑎𝑡𝑒𝑂
𝑣𝑜𝑙 (3-17)
where 𝛿 is the heat produced per mol of pyrite oxidised in the reaction and 𝑏 is the
stoichiometric coefficient. The value of 𝛿 used in this study is 1049 kJ after Wels et al. (2003).
3.2.4 Air velocity
The air velocity field 𝒗 is required for both oxygen transport and heat transfer over the
stockpile. According to Holzbecher (1998), the convective air flow is governed by the following
equations:
Darcy’s law for gas flow in porous media:
𝜅
𝝂 =− (𝛻𝑃−𝜌𝒈)
(3-18)
𝜇
mass conservation of air:
𝜕
(𝜑𝜌) =−𝛻∙(𝜌𝝂) (3-19)
𝜕𝑡
and the ideal gas law: |
ADE | ~ 67 ~
pressure profile. The calculated air velocity is then fed into the transport equations for both
oxygen and heat.
Different iteration approaches were used for the coupling between different processes. As
shown in Fig. 3-1, within each time step, the coupling between temperature and pressure is
first performed using the sequential iterative approach (SIA); the solved temperature and air
velocity are then passed to the oxygen transport and pyrite oxidation processes, which are
coupled using the Newton-Raphson (N-R) method. The calculated heat generation rate is fed
to the temperature equation in the temperature-pressure iteration loop for the next time
step and the above calculations are repeated. A sequential non-iterative approach is adopted
between heat transfer and pyrite oxidation to avoid self-increase of temperature as the two
processes mutually promote each other.
Fig. 3-1: The numerical solution strategy for the coupling among heat transfer, oxygen transport and
pyrite oxidation
For the case study described below, a time step of one day is used for all processes except for
the diffusion-reaction equation of rock particles, where a time step of 1.2 hours is used to
accommodate the small spatial step discretising the rock particles. High Performance
Computing (HPC) clusters were used to run the simulations in this paper and the run time
depends on the number of iterations required and the size of the model. On average, for a
simulation with 14586 nodes and 3650 time-steps, around 900 core-hours are required (each
simulation took around 45 hours using a computer node with 20 cores and 32G memory). |
ADE | ~ 69 ~
Fig. 3-2: Test case model for pyrite oxidation in rock stockpiles
It is assumed that the test case stockpile consists of three different material types, Material
A, Material B and Material C, each of which has different properties for rock particle size
distribution, pyrite grain size distribution, rock diffusion coefficient and porosity, pyrite
content, and acid neutralisation capacity (ANC), as shown in Table 3-1, Table 3-2 and Table
3-3. Values for pyrite content and particle size distributions for rock and pyrite grains are
derived from the measured values for samples taken from a rock stockpile. The porosity
values of the three types of rocks are taken as the measured values of dolomite, sandstone
and mudstone in Peng et al. (2012). Values for the rock diffusion coefficients are assumed
based on the measurements documented in Voutilainen et al. (2018) where the magnitude
of rock diffusivity is around 10-9 m2/s. In Table 3-3, the factor 𝐹_𝐴𝑁𝐶 represents the relative
acid neutralization capacity for different material types, which are used to estimate the pH
value based on Eq. (3-22).
𝑝𝐻 =−𝑙𝑜𝑔 10(2∙𝑂𝑥𝑖𝐿𝑒𝑣𝑒𝑙∙𝑃𝑦%∙𝜌 𝐵/𝜑/1000/𝐹_𝐴𝑁𝐶)
(3-22)
Where 𝑂𝑥𝑖𝐿𝑒𝑣𝑒𝑙 is the overall oxidation level of that block, 𝑃𝑦% is the pyrite content, 𝜌 is
𝐵
pyrite molar density, 𝜑 is the porosity of the bulk material of the block. Other fixed
parameters used in the simulation are given in Table 3-4. |
ADE | ~ 71 ~
In the test case model, each block of the stockpile was randomly assigned a type of rock
material. The model also takes the stockpile construction stage into consideration, i.e., new
material was added to the stockpile at different times. This can take place periodically from
the time when the stockpile was initially constructed to the present date, leading to constant
changes in the size and shape of the stockpile. Consequently, the access to air for both oxygen
replenishment and heat transfer of each block would vary and the total time of exposure to
air of different blocks would also be different depending on the time when the block was
added to the stockpile. The present model updates the geometry of the modelled region
during the simulation according to the variations in the size and shape of the stockpile. Fig. 3-
3 shows the size and shape of the test case stockpile at different stages with block colours
indicating material types.
Fig. 3-3: The size and shape of the stockpile at different stages and its associated distribution of
different types of rock materials
3.3.2 Results of the base case model
The values of stockpile porosity, permeability and degree of water saturation used for the
base case model are given in Table 3-5. All other parameters not specified here use the values
listed in Section 3.3.1. The temperature dependent parameters for pyrite oxidation (i.e., the
reaction rate constant and diffusion coefficient through the diffusion barrier) are as provided
in the governing equations (Eq. (3-2)). |
ADE | ~ 72 ~
Table 3-5: Specific parameters used in the base case simulation
Value Unit
Parameters
Porosity of the stockpile 0.4
Air permeability of the stockpile 10-12 m-2
Water saturation degree of the stockpile 25%
Temperature boundary value at 10 m below 70 °C
Fig. 3-4: Simulated results for the base case model: (a) pyrite oxidation level; (b) oxygen
concentration (mol·m-3); (c) temperature (°C); (d) air velocity (m·s-1)
Fig. 3-4 and Fig. 3-5 shows the simulated results for the base case ten years after the stockpile
construction. The level of pyrite oxidation over the stockpile ranges from 0.12% to 52.41%,
with the highly oxidised blocks mainly on the stockpile surface. The oxygen concentration
profile shows that oxygen concentration is at a significant level only at the surface of the
stockpile which is still far below the atmospheric oxygen concentration (8.28 mol/m3),
whereas for locations beneath the stockpile surface, the oxygen concentration is only 0.2 to
0.4 mol/m3 as a result of relatively fast consumption by pyrite oxidation. The stockpile
temperature has risen due to the heat generated from the reaction over the years. The |
ADE | ~ 74 ~
although all blocks have the same access to oxygen (exposed to the atmosphere), some blocks
are less oxidised than others due to the difference in the types of rock materials. This is further
illustrated in Fig. 3-6 which shows that the oxidation level at the surface (Z = 21m) varies from
less than 0.05 to about 0.35. The oxygen concentration in these blocks also varies and the
variation trend is, in general, opposite to that of the oxidation level. This is mainly because
the oxygen concentration is affected by the oxygen consumption rate in that block, i.e., it will
be maintained at a low value if the consumption rate is high. Fig. 3-6 also shows that as the
depth of the block increases (from the stockpile surface to the bottom), both oxidation level
and oxygen concentration decrease with less variability laterally across the stockpile. This
indicates that as the depth increases, the reaction rate is increasingly limited by the
availability of oxygen and less affected by the reactivity of the materials.
Overall, the oxidation levels for different types of materials are significantly different. Fig. 3-
7 shows the histograms of block oxidation levels for each type of material, which suggests
that the Material B blocks are much less oxidised than the other two types of blocks. The
average oxidation levels for Material A, Material B and Material C blocks are 11.47%, 0.91%
and 6.80% respectively. These differences are caused by the differences in the material
properties, mainly the acid neutralisation capacity which determines the time required to go
into the fast reaction stage in which coating does not develop on pyrite grain surfaces.
Fig. 3-7: Histograms of oxidation level of blocks after ten years for each material types
Fig. 3-8 shows the variations of oxidation level, oxygen concentration and temperature with
time for six selected blocks with their locations marked in Fig. 3-8a. The oxidation levels of
these blocks increase with time at different rates. Oxygen concentration decreases initially
due to consumption by reaction, and then stabilises at a certain level from year two, indicating
an achieved equilibrium between consumption and replenishment. Similarly, the
temperature increases for the first three years due to reaction and then also stabilises in
subsequent years for most blocks, indicating that the heat transfer process over the stockpile
has stabilised. Blocks 1, 2 and 3 are all Material A but with very different oxygen concentration
and temperature over time. Consequently, the oxidation levels of these blocks are
significantly different as shown in Fig. 3-8b. In Fig. 3-8c, although blocks 4, 5 and 6 have very
similar temperatures and accessibility to oxygen, the oxidation rates are very different due to
different types of materials in these blocks. Although the Material C rock type has the highest
diffusion coefficient and the smallest acid neutralisation capacity (see Table 3-3), the block
oxidation level is less than that of the Material A block due to the high pyrite content. |
ADE | ~ 76 ~
In addition to the oxidation level at block scale, the proposed model is also able to estimate
the oxidation profiles of pyrite grains in rock particles, which is an important input required
for the estimation of the gold recovery by direct cyanide leaching from oxidised gold-bearing
material. Gold distribution in pyrite is not homogeneous and can exhibit a certain pattern
termed chemical zoning, resulting from specific rock-fluid interactions and the crystal growth
kinetics during mineralisation (see, for example, Wu et al. (2019)). Pyrite grains may not need
to be completely oxidised to recover the majority of the available gold content depending on
the gold distribution in the pyrite. In some cases, gold may mostly be in the rim or mantle of
the pyrite grains so that a shallow oxidation depth may be sufficient to release most of the
gold content. Therefore, knowing the oxidation profile of pyrite grains is essential for the
estimation of gold recovery without pre-treatment.
As discussed in Section 3.2.1, pyrite grains contained in the rock particles are oxidised to
different degrees, decreasing from the outmost layer to the inner layers of the rock particles.
The shorter the distance to the rock particle surface, the higher the depth of oxidation of the
contained pyrite grains. As an example, the most oxidised block, located at (1m, 51m, 1m),
with an overall oxidation level of 52.41% is used to illustrate the simulated oxidation profile
of pyrite grains within a rock particle. Fig. 3-9 shows the depth of the oxidation of pyrite grains
at different distances to the rock surface after ten years. As can be seen from the Fig. 3-9,
only pyrite grains within a distance of around 25 mm to the surface of the rock particle are
oxidised, with the corresponding depth of oxidation ranging from 6 µm to 404 µm depending
on the distance.
Fig. 3-9: The oxidation depth of the pyrite grains at different distances to the rock particle surface in
the block at x=1m, y=51m, z=1m: left – linear scale; right – lognormal scale.
The oxidation level for pyrite grains of various sizes can be calculated from the depth of
oxidation and the results are shown in Fig. 3-10. As can be seen, the oxidation level for pyrite
grains of different sizes can be very different, ranging from less than 0.08 to about 0.84. For
pyrite grains of the same size, the oxidation level also varies depending on pyrite location
within the rock particle. Fig. 3-11 shows the relative depth of oxidation, i.e., the ratio of the
depth of oxidation to the grain radius. It shows that for pyrite grains smaller than 375 µm,
more than half of the pyrite is almost completely oxidised. As the grain size increases, the
relative depth of oxidation decreases. For pyrite grains larger than 7.95 mm, only a thin layer
of the pyrite rim has been oxidised after ten years. |
ADE | ~ 78 ~
Table 3-6: Scenarios examined for parametric studies
Changes of parameters examined
Cases
0. Base case
1e-10, 5e-10 and 8e-10 m2s-1 for Material A, Material
Smaller rock diffusion
1. B and Material C respectively, which are ten times
coefficient
smaller than those used in the base case.
2. No convection Air velocity is set to zero.
3. Lower porosity Porosity changes from 0.4 to 0.25.
4. Low water saturation Degree of water saturation changes from 25% to 8%.
Degree of water saturation changes from 25% to
5. Higher water saturation
80%.
Boundary temperature value changes from 70°C to
6. No geothermal heat
15°C at the bottom of the extended region.
Fig. 3-12 shows cross-sectional views of the simulated oxidation level, oxygen concentration
and temperature for the scenarios explored. Similar to the base case results, the oxidation
level of the internal part of the stockpile in all cases is less than 20% while only blocks near
the stockpile surface are significantly oxidised, confirming that oxygen is the dominant
limiting factor for the stockpile oxidation in all cases. A comparison of the scenarios reveals
that the oxidation level at the stockpile surface in Cases 1, 3 and 5 is much less than that in
other cases. This can also be seen in Fig. 3-13, where the oxidation level and oxygen
concentration along the central line in the x-direction at different depths of the stockpile are
plotted. The curves fluctuate across the stockpile due to the variations in the location as well
as the types of material. The results of the base case, Case 2 and Case 6 are very close, with
their curves hard to separate in the figure, which indicates that the effects of air convection
and geothermal heat are negligible in the base case.
Among all the cases, Case 1 has the highest oxygen concentration at all depths (Fig. 3-13) due
to slow oxygen consumption resulting from a smaller rock diffusion coefficient. Compared
with the base case, the stockpile in Case 1 is less oxidised at the surface (Z = 21 m) but slightly
more oxidised at Z = 19 m due to a higher oxygen concentration at that depth. This shows
that, when oxygen replenishment is limited, the more reaction that occurs at the stockpile
surface, the less oxygen is available for the reaction internally within the stockpile.
Case 3 uses a decreased stockpile porosity, resulting in smaller oxygen concentration and a
lower oxidation level over the stockpile than the corresponding values of the base case. Case
5 shows similar results by increasing the water content in the stockpile. In both cases, the bulk
transport of oxygen is inhibited, resulting in limited amounts of oxygen available for reaction.
On the contrary, with a lower water content, Case 4 has the highest oxidation level and higher
oxygen concentration than most cases at all depths due to faster oxygen replenishment.
Although published research has shown that the optimal degree of water saturation is around
25% for pyrite oxidation under laboratory conditions (León et al., 2004), this comparison |
ADE | ~ 80 ~
The comparison analyses discussed above confirm that the availability of oxygen is the most
influential rate-limiting factor for pyrite oxidation in stockpiles. The effective transport of
oxygen is dominantly through diffusion and the contribution from convection is negligible
when the permeability of the stockpile is 1 Darcy or smaller and the stockpile is under natural
environmental conditions without any forced air flow. Therefore, properties that affect
oxygen diffusivity over the stockpile would have significant impacts on the pyrite oxidation
level. These properties mainly include the bulk porosity (hence rock particle size) of the
stockpile and water content. Temperature also has some impact on the oxidation level, but
to a much lesser degree compared with the oxygen availability and it has very little impact
unless there is sufficient oxygen available for the reaction.
Fig. 3-13: Oxidation level and oxygen concentration on the vertical section at y=25m and different
depths. Case 1 – smaller diffusion coefficients of rock particles; Case 2 – no convection; Case 3 –
smaller porosity; Case 4 – 8% water saturation degree; Case 5 – 80% water saturation degree; Case 6
– no geothermal heat
3.3.4 Conclusions
This paper presents a numerical modelling framework for estimating the pyrite oxidation level
in refractory gold ore stockpiles. The solution framework couples pyrite oxidation with
phyiscal processes including oxygen transport and geothermal heat transfer, and is capable
of modelling the influences of oxygen concentration, temperature, water content, pH value |
ADE | ~ 85 ~
difficult to solve because it involves both 𝑃 and derivatives of 𝑃2. To solve for pressure in Eq.
(3-C9), the approximation in Eq. (3-C10) is used based on the assumption that the pressure in
the void space fluctuates around an average value of 𝑃 and the fluctuation is small (Warrick,
0
2001).
𝑃 = 𝑃 0+∆𝑃,𝑃 ≈ 𝑃
0 (3-C10)
Eq. (3-C9) can then be manipulated as:
𝜕𝑃 1∂T 𝜅 1 𝛻𝑇 1 𝜅 𝑀𝒈1
2𝑃∙ = 2𝑃∙ ∙P+2𝑃 ∙ ( 𝛻2(𝑃2)− ∙ 𝛻𝑃2)−2𝑃 ∙ 𝛻𝑃2
𝜕𝑡 T ∂t 0 𝜑𝜇 2 𝑇 2 0 𝜑𝜇 𝑅̅ 𝑇
𝜅 𝑀𝒈2𝛻𝑇 (3-C11)
+2𝑃 ∙ 𝑃2
0 𝜑𝜇 𝑅̅ 𝑇2
which then becomes an equation in the variable 𝑃2:
𝜕𝑃2 2∂T 𝜅𝑃 𝜅𝑃 𝛻𝑇 𝜅𝑃 2𝑀𝒈1
= ∙P2+ 0 𝛻2𝑃2− 0 ∙𝛻𝑃2 − 0 𝛻𝑃2
𝜕𝑡 𝑇 ∂t 𝜑𝜇 𝜑𝜇 𝑇 𝜑𝜇 𝑅̅ 𝑇
𝜅𝑃 4𝑀𝒈𝛻𝑇 (3-C12)
+ 0 𝑃2
𝜑𝜇 𝑅̅ 𝑇2
Let 𝑃2 = 𝐵, then Eq. (3-C12) is an equation in 𝐵 which has the form of Eq. (3-C13) with
coefficients independent of the variable 𝐵 and only dependent on the temperature profile.
The coefficients are given in Eq. (3-C14).
𝜕𝐵
=𝛼∙𝛻2𝐵+𝜷∙𝛻𝐵+𝜃∙𝐵
(3-C13)
𝜕𝑡
𝜅𝑃
0
α =
𝜑𝜇
𝜅𝑃 1𝜕𝑇
0
𝛽 =− ∙
𝑥 𝜑𝜇 𝑇𝜕𝑥
𝜅𝑃 1𝜕𝑇
0
𝛽
𝑦
=−
𝜑𝜇
∙ 𝑇𝜕𝑦
(3-C14)
𝜅𝑃 1 𝜕𝑇 2𝑀𝒈
0
𝛽 =− ∙( + )
{ 𝑧 𝜑𝜇 𝑇 𝜕𝑧 𝑅̅
2∂T 𝜅𝑃 4𝑀𝒈 1 𝜕𝑇
0
𝜃 = +
𝑇 ∂t 𝜑𝜇 𝑅̅ 𝑇2𝜕𝑧 |
ADE | ~ 88 ~
part of the stockpile (or the modelled region) but are directly in contact with the stockpile
boundaries. The purpose of using this approach is to generate solutions for all nodes within
the stockpile or the modelled region, including the boundary nodes. For example, for oxygen
concentration at the top stockpile surface, the boundary value is assigned to the virtual
boundary that can be regarded as air blocks covering the stockpile surface. Consequently, the
oxygen concentration in the stockpile surface blocks can be solved by considering oxygen
transport and consumption.
Acknowledgement
This research was financially supported by Newcrest Mining Limited.
References
Aachib, M, Aubertin, M & Mbonimpa, M 2002, 'Laboratory measurements and predictive equations
for gas diffusion coefficient of unsaturated soils', in 55th Canadian Geotechnical Conference and 3rd
joint IAH-CNC and CGS Groundwater Specialty Conference.(Niagara Falls, Ontario), pp. 163-172.
Al-Shemmeri, T 2012, Engineering fluid mechanics, Bookboon.
Brown, P, Luo, X-L, Mooney, J & Pantelis, G 1999, 'The modelling of flow and chemical reactions in
waste piles', in 2nd Internat. Conf. CFD in the Minerals and Process Industries. CSIRO, Melbourne,
Australia, December, pp. 6-8.
Cathles, L & Apps, J 1975, 'A model of the dump leaching process that incorporates oxygen balance,
heat balance, and air convection', Metallurgical Transactions B, vol. 6, no. 4, pp. 617-624.
Chandra, AP & Gerson, AR 2010, 'The mechanisms of pyrite oxidation and leaching: A fundamental
perspective', Surface Science Reports, vol. 65, no. 9, pp. 293-315.
Chiriță, P & Schlegel, ML 2017, 'Pyrite oxidation in air-equilibrated solutions: An electrochemical
study', Chemical Geology, vol. 470, pp. 67-74.
Cussler, EL 2009, Diffusion: mass transfer in fluid systems, Cambridge university press.
da Silva, JC, do Amaral Vargas, E & Sracek, O 2009, 'Modeling Multiphase Reactive Transport in a Waste
Rock Pile with Convective Oxygen Supply', Vadose Zone Journal, vol. 8, no. 4, pp. 1038-1050.
Davis, GB & Ritchie, AIM 1986, 'A model of oxidation in pyritic mine wastes: part 1 equations and
approximate solution', Applied Mathematical Modelling, vol. 10, no. 5, pp. 314-322.
Elberling, B, Nicholson, RV & Scharer, JM 1994, 'A combined kinetic and diffusion model for pyrite
oxidation in tailings: a change in controls with time', Journal of Hydrology, vol. 157, no. 1–4, pp. 47-
60.
Elberling, B, Schippers, A & Sand, W 2000, 'Bacterial and chemical oxidation of pyritic mine tailings at
low temperatures', Journal of Contaminant Hydrology, vol. 41, no. 3–4, pp. 225-238.
Evangelou, VP & Zhang, YL 1995, 'A review: Pyrite oxidation mechanisms and acid mine drainage
prevention', Critical Reviews in Environmental Science and Technology, vol. 25, no. 2, 1995/05/01, pp.
141-199. |
ADE | ~ 93 ~
Abstract
This paper presents a case study of the modelling of the natural oxidation of pyrite in a
refractory gold ore stockpile at a mine on the island of Aniolam in Papua New Guinea to
predict the gold recovery through direct cyanide leaching. The stockpile comprises low-grade
material that was mined twenty years ago to access the orebody. The value of this low-grade
resource could be increased if the processing cost could be reduced. The natural oxidation of
the gold-bearing pyrite in the stockpile may reduce the processing cost by reducing or
eliminating the need for pre-treatment of the material and enable gold recovery via direct
cyanide leaching. Depending on the oxidation level and the gold recovery that could be
achieved by direct cyanide leaching, reclamation of the stockpile may be more profitable if
the pyrite oxidation stage could be fully or partially bypassed. In this paper, we describe the
modelling of the pyrite oxidation level in the stockpile using the numerical model reported in
our previous work. The characteristics of the stockpile used in the model are the stockpile
geometry, the geothermal heat underneath the stockpile, and the properties of the different
types of material, including the acid neutralization capacity, rock particle size distribution and
pyrite grain size distribution. Limited onsite test results were used to calibrate the model and
the final oxidation level over the stockpile was estimated using the calibrated model. Based
on the simulation results, it was found that the accessibility to oxygen is the limiting factor for
the level of pyrite oxidation when diffusion is the dominant mechanism for oxygen transport
within the stockpile. However, experimental tests on samples showed that sufficient oxygen
resupply should have been available in the stockpile and therefore there may be air
movement mechanisms other than diffusion and thermal-induced air convection onsite. This
study also demonstrates that the numerical model can be used to estimate the gold recovery
via direct cyanide leaching from the simulated oxidation profile together with the gold
distribution in pyrite grains and gold fractions in pyrite of different sizes. |
ADE | ~ 94 ~
Introduction
Material containing low-grade commodity metals comprise an important part of the metal
resource and recovering metals from these materials to maximise the profit of mining
operations has been a significant industry focus for some time. For refractory gold ores that
have ultra-fine gold particles encapsulated within the gold-bearing minerals (sulphides), the
processing cost is relatively high because of the expensive pre-treatment (such as pressure
oxidation (POX), bio-oxidation, roasting or ultrafine grinding) required to liberate the gold
particles from sulphide ores for the effective extraction of gold through cyanidation. However,
for sulphide refractory ores that have been exposed to oxygen and moisture over a long
period of time, the processing cost may be reduced if the metal-bearing sulphides are
naturally oxidised. The oxidised material can be directly leached without pre-treatment, thus
providing a basis for cheaper recovery of the contained metal. An example application of this
approach is the Lihir gold orebody on Aniolam Island in the New Ireland Province of Papua
New Guinea, where a 90% or higher gold recovery was achieved by direct cyanide leaching of
a small, low-grade oxide resource that was present as a capping over the orebody (Ketcham
et al., 1993). This example shows that natural oxidation of the gold-bearing sulphides can
facilitate gold extraction at a lower cost by reducing the need for the pre-treatment that is
normally required for fresh unoxidized refractory ore. In many refractory gold mining
operations, significant amounts of low-grade material may be stockpiled for extensive periods
of time for two reasons. First, low-grade ore may be stockpiled to give priority to processing
higher grade ores. Second, material that contains low-grade ore may be mined for access to
the orebody and be stockpiled for potential processing at a later stage if the metal price
increases sufficiently or cheaper processing methods become available. The increasing need
for processing low-grade resources, and the fact that exposed sulphides are naturally reactive,
has stimulated industry interest in assessing the natural oxidation of sulphides in refractory
materials to exploit the potential for more profitable recovery. An important aspect of
evaluating this potential is to estimate the extent to which sulphides (mainly pyrite) can be
oxidised in natural conditions.
Natural pyrite oxidation has been widely studied as it is a significant contributor to Acid Mine
Drainage (AMD). Many laboratory studies have been conducted to investigate pyrite
oxidation (León et al., 2004; McKibben and Barnes, 1986; Nicholson et al., 1988; Williamson
and Rimstidt, 1994) and numerical models have been developed to predict AMD for the
purposes of control and remediation (da Silva et al., 2009; Davis and Ritchie, 1986; Elberling
et al., 1994; Lefebvre et al., 2001; Mayer et al., 2002; Molson et al., 2005; Pabst et al., 2017;
Walter et al., 1994; Wunderly et al., 1996). These models have demonstrated that numerical
modelling can be an effective means of simulating the physical and chemical processes
involved in pyrite oxidation in rockpiles. In our previous work (Wang et al., 2019), these
studies have been reviewed and a reaction rate model has been developed for the oxidation
of pyrite grains, which is then used in a coupled numerical modelling framework developed
for the prediction of pyrite oxidation levels in stockpiles under various conditions. Unlike the
models developed in the context of AMD, where reactive transport is the focus, the numerical
model developed in Wang et al. (2021) focuses on incorporating various influencing factors |
ADE | ~ 95 ~
(abiotic) affecting the pyrite oxidation rate in order to predict the oxidation level of pyrite
under different conditions.
The purpose of this paper is to present a case study in which the pyrite oxidation level in a
low-grade refractory gold-bearing stockpile is estimated using the model developed in Wang
et al. (2021). The modelled stockpile is the Kapit Flat stockpile at the Lihir Gold Mine on
Aniolam Island in Papua New Guinea. The stockpile characteristics considered in the model
include the changing geometry of the stockpile during the construction stage, the geothermal
heat source under the stockpile and the types of materials within the stockpile. Properties of
different types of materials such as pyrite content, rock and pyrite particle size distributions,
porosity and diffusivity of intact rocks and the relative acid neutralization capacity are
incorporated in the modelling of the volumetric oxygen consumption and the progress of
pyrite grain oxidation. Bulk stockpile properties, such as water content and porosity, are
estimated from the onsite conditions and previous laboratory test results. The modelled
pyrite oxidation level was compared with that measured on samples taken from the stockpile
and the differences were used to calibrate the oxygen concentration within the stockpile,
which was found to be the most decisive factor for pyrite oxidation. The calibrated model was
then used to estimate the level of pyrite oxidation at the block scale and the oxidation profile
of pyrite grains for the entire stockpile. This result was used to estimate the potential gold
recovery by direct cyanide leaching and to provide input for reclamation scheduling.
Materials and method
Most input parameters related to the site characteristics required by the model were sourced
from existing reports of laboratory tests of materials from the deposit. Some parameters were
assumed when relevant information was not available.
4.2.1 Numerical modelling method
The model presented in Wang et al. (2021) is used in this case study for modelling the pyrite
oxidation. The physical and chemical processes considered include pyrite oxidation in rock
particles, heat transfer, heat-induced air convection and oxygen transport through diffusion
and air convection.
Pyrite oxidation in a rock particle
Because of the oxygen concentration gradient within a rock particle, the oxidation of pyrite
grains may differ depending on the depths of the grains from the rock particle surface. This is
a diffusion-reaction process that can be described by the diffusion-reaction equation using
the polar coordinate system given in Eq. (4-1), where 𝐶 is the oxygen concentration inside the
rock particle as a function of the radial coordinate 𝑟 and time 𝑡; 𝜑 and 𝐷 are the porosity
𝑟 𝑒
and oxygen diffusion coefficient of the rock particle respectively; and 𝑆 is the sink term
𝑝𝑦
representing the oxygen consumption by pyrite grains inside the rock particle. The term 𝑆
𝑝𝑦
depends on both the oxygen concentration 𝐶, which is solved by Eq. (4-1), and the reaction
progress of the pyrite grains at that radial location. |
ADE | ~ 96 ~
𝜕𝐶 𝜕2𝐶 2𝜕𝐶
𝜑 = 𝐷 ( + )−𝑆
𝑟 𝜕𝑡 𝑒 𝜕𝑟2 𝑟 𝜕𝑟 𝑝𝑦 (4-1)
For a single pyrite grain, the reaction can be described by different reaction rate models under
different reaction conditions. For reactions under circum-neutral to alkaline conditions
and/or low-water-content conditions, diffusion barriers, such as the oxidised layer (an iron
hydroxide coat) or a thin saturated solution film, can develop on the surface of the pyrite
grain, which subsequently inhibits the diffusion of oxygen to the fresh pyrite layer (Wang et
al., 2019) . For this case, the reaction rate model derived by Wang et al. (2019) is used to
model the reaction progress controlled by both diffusion and reaction for the pyrite grain. For
reactions under acidic and intro-aqueous conditions, the reaction products are dissolved and
diluted in the pore-water and thus neither a solid coating nor a concentrated/saturated
solution film is formed on the pyrite surface. Hence the reaction rate is controlled only by the
surface reaction and the corresponding reaction rate model should be used for this case.
The sizes of pyrite grains in a rock particle are important influencing factors for the overall
oxidation rate. For the same pyrite content, the smaller the grain sizes, the higher the overall
reaction rate of the pyritic rock particle due to larger pyrite surface area. To consider the
effect of pyrite grain size distribution, Wang et al. (2021) proposed a rate formula for a group
of pyrite grains of different sizes. Assuming the pyrite grain size distribution shown in Eq. (4-2),
defined by 𝑛 size categories, the oxygen consumption rate of the pyrite group with a total
mass of ∑𝑛 𝑚 can be approximated by Eqs. (3-7) and (3-8) respectively for reactions with
𝑖=1 𝑖
and without a diffusion barrier formed during the reaction (Wang et al., 2021).
𝑅 𝑅 …𝑅 …𝑅
1 2 𝑖 𝑛
𝑃𝑆𝐷 = ( )
𝑝𝑦 𝑚 𝑚 …𝑚 …𝑚
1 2 𝑖 𝑛
𝑚 (4-2)
𝑖
𝐹 =
𝑖 4
𝜋𝑅3 ∙𝜌
3 𝑖 𝑝𝑦
𝑛
4𝜋𝑅2∙𝐶 (𝑟)
𝑖 𝑒
𝑅𝑎𝑡𝑒𝑂 = ∑[ ∙𝐹(𝑖)]
𝑔𝑝 𝑅 𝑅 1 𝑅2
𝑖=1 𝐷𝑖 (
𝑟
(𝑖 𝑖)−1)+
𝑘′′𝑟
(𝑖𝑖 )2𝐶 𝑒(𝑟)0.5
𝑠 𝑐 𝑐
𝑑𝑟 𝑏𝐶 (𝑟)/𝜌 (4-3)
−
𝑐
=
𝑒 𝐵
𝑑𝑡 (𝑅 −𝑟 )𝑟 𝐶 (𝑟)0.5
𝑛 𝑐 𝑐 + 𝑒
𝑅 𝐷 𝑘′′
𝑛 𝑠
{ 𝑟 (𝑖) = 𝑚𝑎𝑥{0,𝑅 −(𝑅 −𝑟 )}
𝑐 𝑖 𝑛 𝑐 |
ADE | ~ 97 ~
𝑛
4𝜋𝑅2∙𝐶 (𝑟)
𝑖 𝑒
𝑅𝑎𝑡𝑒𝑂 = ∑[ ∙𝐹(𝑖)]
𝑔𝑝 1 𝑅2
𝑖=1 ∙ 𝑖 ∙𝐶 (𝑟)0.5
𝑘′′ 𝑟 (𝑖)2 𝑒
𝑐
𝑑𝑟 𝑏∙𝐶 (𝑟)/𝜌 (4-4)
𝑐 𝑒 𝐵
− =
𝑑𝑡 𝐶 (𝑟)0.5
𝑒
𝑘′′
{ 𝑟 (𝑖) = 𝑚𝑎𝑥{0,𝑅 −(𝑅 −𝑟 )}
𝑐 𝑖 𝑛 𝑐
In Eqs. (4-2), (3-7) and (3-8), 𝑅 and 𝑚 are the radius and the mass proportion of the ith grain
𝑖 𝑖
size respectively. 𝐹 is the number of pyrite grains of size 𝑅 in a pyrite group with a total mass
𝑖 𝑖
of ∑𝑛 𝑚 . 𝑅𝑎𝑡𝑒𝑂 is the oxygen consumption rate of the pyrite group at the radial location
𝑖=1 𝑖 𝑔𝑝
𝑟 inside a rock particle. 𝐶 (𝑟) is the effective oxygen concentration depending on the degree
𝑒
of water saturation.𝑟 is the simulated unreacted core radius of pyrite of grain size 𝑅 and
𝑐 𝑛
𝑟 (𝑖) is the unreacted core radius of the pyrite grain size 𝑅 which is estimated from 𝑟 . 𝜌 is
𝑐 𝑖 𝑐 𝐵
the molar density of pyrite and 𝑏 is the stoichiometric coefficient given as the mole ratio of
reacted pyrite to consumed oxygen. 𝐷 is the diffusion coefficient of oxygen through the
𝑠
diffusion barrier developed during the reaction and 𝑘′′ is the surface reaction rate constant
of pyrite. According to Wang et al. (2019), the values of 𝐷 and 𝑘′′ depend on the degree of
𝑠
water saturation, 𝑆 , and the temperature, 𝑇. The effective oxygen concentration 𝐶 also
𝑤 𝑒
depends on the degree of water saturation, 𝑆 . Their values are given as Eq. (4-5) in Wang et
𝑤
al. (2019), where 𝐷0 and 𝑘′′ are the values of 𝐷 and 𝑘′′ at the reference temperature 𝑇 , 𝐸𝐷
𝑠 0 𝑠 0 𝑎
and 𝐸𝑘 are the activation energies for diffusion and surface reaction respectively, 𝑇 is the
𝑎
reaction temperature in Kelvin, 𝑅̅ is the gas constant, 𝐻𝑐𝑐 is the Henry’s law solubility and 𝐶
𝑔
is the oxygen concentration in gas phase which is solved using Eq. (4-1).
𝐶 = 𝐶
∙𝑒log(𝐻𝑐𝑐)∙𝑆
𝑤
𝑒 𝑔
𝐷
𝑠
= 𝐷
𝑠0∙𝑒− 𝑅𝐸 ̅𝑎𝐷
(
𝑇1
−
𝑇1
0)
{ 𝑘′′ = 𝑘 0′′
∙𝑒− 𝑅𝐸 ̅𝑎𝑘
(
𝑇1
−
𝑇1
0)
For 𝑇 = 293.15 K: (4-5)
0
𝐷0 = 1.2×10−15(𝑓𝑜𝑟𝑆 ≥ 25%)
𝑠 𝑤
𝐷0 = 4.82×10−15∙𝜃 −4.35×10−18(𝑓𝑜𝑟0.1% ≤ 𝑆 < 25%)
𝑠 𝑤 𝑤
𝑘′′ = 5×10−8
0
{𝐻𝑐𝑐 = 0.0353
The oxygen consumption rate at different radial locations in the rock particle (𝑆 ) is given in
𝑝𝑦
Eq. (3-9) where 𝑃𝑦% is the volumetric pyrite content. The reaction progress is known from
the unreacted core radius 𝑟 (𝑖) for pyrite grains of different sizes and at different radial
𝑐
locations in the rock particle, as discussed above. |
ADE | ~ 98 ~
𝑃𝑦%
𝑆 = 𝑅𝑎𝑡𝑒𝑂 ∙
𝑝𝑦 𝑔𝑝 4 (4-6)
𝜋∑𝑛 (𝑅3 ∙𝐹)
3 𝑖=1 𝑖 𝑖
Overall pyrite oxidation within a unit volume of the stockpiled materials
Rocks in a stockpile can range from very fine particles to very blocky fragments and the
progress of pyrite oxidation will differ across the size range. The rock particle size distribution
can be defined generally using a non-parametric form as shown in Eq. (4-7) with 𝑚 categories
of sizes, where 𝑅 (𝑗) is the average radius of rock particles in category 𝑗 and 𝑚 (𝑗) is
𝑟𝑜𝑐𝑘 𝑟𝑜𝑐𝑘
the mass proportion of rock particles in that size category. 𝐹 (𝑗) is the number of particles
𝑟𝑜𝑐𝑘
for the category among rocks of a total mass of
∑𝑝
𝑚 (𝑗). This distribution can be
𝑗=1 𝑟𝑜𝑐𝑘
quantified by measuring rock sizes in the stockpile directly or indirectly using
photogrammetry or laser scanning. For a unit volume of the stockpiled materials with
different rock particle sizes, the overall volumetric oxygen consumption rate 𝑅𝑎𝑡𝑒𝑂 is given
𝑣𝑜
in Eq. (3-11) (Wang et al., 2021).
𝑅 (1)𝑅 (2)…𝑅 (𝑗)…𝑅 (𝑝)
𝑟𝑜𝑐𝑘 𝑟𝑜𝑐𝑘 𝑟𝑜𝑐𝑘 𝑟𝑜𝑐𝑘
𝑃𝑆𝐷 = ( )
𝑟𝑜𝑐𝑘 𝑚 (1)𝑚 (2)…𝑚 (𝑗)…𝑚 (𝑝)
𝑟𝑜𝑐𝑘 𝑟𝑜𝑐𝑘 𝑟𝑜𝑐𝑘 𝑟𝑜𝑐𝑘
(4-7)
𝑚 (𝑗)
𝑟𝑜𝑐𝑘
𝐹 (𝑗) =
𝑟𝑜𝑐𝑘 4
𝜋𝑅3 (𝑗)∙𝜌
3 𝑟𝑜𝑐𝑘 𝑟𝑜𝑐𝑘
𝑝 𝑃𝑦(𝑘)
𝑅𝑎𝑡𝑒𝑂 = ∑ (𝑅𝑎𝑡𝑒𝑂 (𝑘)∗ )
𝑣𝑜 𝑔𝑝 4
𝑗=1 𝜋∑𝑛 (𝑅3 ∙𝐹)
3 𝑖=1 𝑖 𝑖
4
𝑃𝑦%∙∑𝑝 𝑗=1[ 3𝜋∙(𝑟 𝑘3
𝑗(1)
−𝑟 𝑘3 𝑗(2))∙𝐹 𝑟𝑜𝑐𝑘(𝑗)]
(4-8)
𝑃𝑦(𝑘) =
4
𝜋∑𝑝 (𝑅3 (𝑗)∙𝐹 (𝑗))
3 𝑗=1 𝑟𝑜𝑐𝑘 𝑟𝑜𝑐𝑘
𝑟 = max{𝑅 (𝑗)−∆𝑟∙(𝑘−1),0}
𝑘,𝑗(1) 𝑟𝑜𝑐𝑘
{𝑟
𝑘,𝑗(2)
= max{𝑅 𝑟𝑜𝑐𝑘(𝑗)−∆𝑟∙𝑘,0}
Eq. (3-11) is derived on the assumption that the oxidation of pyrite in rock particles depends
on the distance of the pyrite grains to the nearest void space between rock particles as this
distance determines the accessibility to oxygen. Based on this assumption, within a unit
volume of the stockpiled material, the oxidation of pyrite grains in different rock particles is
the same if their distance to the void space (i.e., to the surface of the rock particles) is the
same. In Eq. (3-11), 𝑘 denotes the sequence of discrete layers in the largest rock particle with
𝑘 = 1 representing the outermost layer and thus it represents the distance to the void space
(particle surface). Using this representation, pyrite oxidation at different radial locations
inside rock particles of different sizes can be estimated using the same layer sequence𝑘. The |
ADE | ~ 99 ~
oxidation rate of a pyrite group in layer 𝑘is 𝑅𝑎𝑡𝑒𝑂 (𝑘), which is given by Eq. (3-7) or (3-8),
𝑔𝑝
and the pyrite volume fraction for layer 𝑘 in all rock particles is calculated as 𝑃𝑦(𝑘) from the
rock particle size distribution. In Eq. (3-11), 𝑟 and 𝑟 are the outer and inner radius
𝑘𝑗(1) 𝑘𝑗(2)
respectively of layer 𝑘 in a rock particle of size 𝑅 (𝑗) and ∆𝑟 is the uniform layer thickness.
𝑟𝑜𝑐𝑘
Based on these equations, the pyrite oxidation in the unit volume at a location within a
stockpile can be calculated by simulating the diffusion-reaction process of only the largest
rock particle using Eq. (4-1).
Oxygen transport in the stockpile
The transport of oxygen in the stockpile is given by Eq. (3-13), where 𝑈 is the oxygen
concentration in the void space within the stockpile, 𝜑 is the stockpile porosity, 𝐷 is the
𝑏
oxygen diffusion coefficient in the stockpile, 𝝂 is the air velocity field and 𝑞 is the source
𝑂
2
term from the reaction and has a non-positive value.
𝜕
𝜕𝑡(𝜑𝑈) = 𝛻(𝐷 𝑏 ∙𝛻𝑈)−𝛻 ∙(𝝂∙𝑈)+𝑞 𝑂
2
(4-9)
The diffusion coefficient is calculated from the temperature value and the water content
using Eq. (3-15) derived in Wang et al. (2021).
1
𝐷 = (1.1005×10−5 ∙𝑇1.726𝜃3.3 +10−7 ×(0.0058𝑇2 −2.146𝑇
𝑏 𝜃 𝑠2 𝑎 (4-10)
+163.35)𝜃3.3)
𝑤
The source term 𝑞 is the volumetric oxygen consumption rate and is given in Eq. (4-11):
𝑂
2
𝑞 = −𝑅𝑎𝑡𝑒𝑂
𝑂 𝑣𝑜 (4-11)
2
The heat-induced air velocity can be calculated from the temperature and pressure profile
within the stockpile. The partial differential equation for the pressure profile, as given in Eq.
(4-12), was derived in Wang et al. (2021) based on mass conservation, the ideal gas law and
Darcy’s law for air flow in porous media. The air velocity is then given by Darcy’s Law as Eq.
(4-13). In these two equations, 𝐵 is the square of the pressure 𝑃, 𝑃 is a reference pressure
0
known from the ambient environment, 𝜅 is the air permeability of the stockpile, 𝜇 is the air
viscosity, 𝑀 is the molar mass of air, 𝑅̅ is the gas constant, 𝒈 is the gravitational acceleration
and 𝑇 is the absolute temperature obtained by solving the heat transfer equation. |
ADE | ~ 100 ~
𝜕𝐵
= 𝛼 ∙𝛻2𝐵+𝜷∙𝛻𝐵+𝜃 ∙𝐵
𝜕𝑡
𝜅𝑃
0
α =
𝜑𝜇
𝜅𝑃 1𝜕𝑇
0
𝛽 =− ∙
𝑥 𝜑𝜇 𝑇𝜕𝑥
𝜅𝑃 0 1𝜕𝑇 (4-12)
𝛽 =− ∙
𝑦 𝜑𝜇 𝑇𝜕𝑦
𝜅𝑃 1 𝜕𝑇 2𝑀𝒈
0
𝛽 =− ∙( + )
{ 𝑧 𝜑𝜇 𝑇 𝜕𝑧 𝑅̅
2∂T 𝜅𝑃 4𝑀𝒈 1 𝜕𝑇
0
𝜃 = +
𝑇 ∂t 𝜑𝜇 𝑅̅ 𝑇2 𝜕𝑧
𝑃 = 𝐵1/2
𝜅
𝝂 = − (𝛻𝑃−𝜌𝒈)
(4-13)
𝜇
Temperature profile in the stockpile
The temperature profile is given by Eq. (3-16), where 𝑇 is the temperature of the stockpile, 𝒗
is the velocity field of air, 𝐷 is the thermal diffusivity of the stockpile, 𝜌 and 𝐶 are
ℎ
respectively the density and the specific heat capacity of the stockpile material and 𝜌∗ and 𝐶∗
are those of the air. The source term 𝑞 is the heat flux generated from pyrite oxidation.
ℎ
𝜕𝑇 𝑞 𝜌∗𝐶∗
= ∇∙(−𝛾𝒗𝑇+𝐷 ∇𝑇)+ ℎ with 𝛾 =
ℎ (4-14)
𝜕𝑡 (𝜌𝐶) (𝜌𝐶)
The volumetric heat generation rate 𝑞 is calculated by Eq. (4-15) where 𝛿 is the heat
ℎ
produced per mole of pyrite oxidised and 𝑏 is as defined in Eq. (3-8).
𝑞 = 𝛿 ∙𝑏∙𝑅𝑎𝑡𝑒𝑂
ℎ 𝑣𝑜𝑙 (4-15)
Integrated modelling framework
The relationships described above are the governing equations for modelling the pyrite
oxidation in stockpiles. In this study, a finite difference scheme, the Douglas-Gunn method, is
used to solve the partial differential equations (Eqs. (3-13), (4-12) and (3-16)) based on the
3D stockpile geometry. Instead of following the numerical solution strategy described in
Wang et al. (2021), a sequential non-iterative approach is used in this work to reduce the
computational cost. The spatial grid sizes for the x, y and z directions used in the simulation
are 10 m, 10 m and 12 m, respectively, resulting in a total of 21,452 blocks/node points that
have to be calculated for the final stockpile geometry. As the rate of oxygen consumption by |
ADE | ~ 101 ~
pyrite is relatively high compared with that of the oxygen bulk transport and heat transfer
over the stockpile, different time steps are used in the simulation for pyrite oxidation and
other processes. In general, for modelling the pyrite oxidation in rock particles, the time step
is adjusted dynamically depending on the reaction rate during the simulation and for other
processes a time step of one day is used. The typical run time using a 32-core, 64GB-memory
cluster with parallel programming is around 80 hours for a 20-year simulation timeframe.
4.2.2 Site characteristics and model inputs
The gold-bearing refractory stockpile in this study is the Kapit Flat stockpile at the open-cut
gold mine on Aniolam (also known as Lihir) Island in Papua New Guinea, owned and
operated by Newcrest Mining Limited since August 2010. Stockpiled material at Lihir is
classified as a Measured Mineral Resource with a total of approximately 83Mt at 1.9 g/t gold
as at December 2019 (Newcrest 2019 Resources and Reserves, 2020). The Kapit Flat
stockpile, which is modelled in this study, is the largest of several stockpiles. Gold in the Lihir
orebody is mainly present as solid solution gold within pyrite and is thus classified as
refractory and resistant to recovery by standard cyanidation and carbon adsorption
processes. Oxidation of the sulphide minerals is therefore required to release the gold
particles before effective gold extraction by cyanidation, which uses the pressured oxidation
(POX) as the pre-treatment method at Lihir Mine. The average sulphur grade of the
stockpiled material is around 6% and the main sulphide mineral is pyrite. More details about
the Lihir deposit can be found in the recent technical report released by Newcrest (e.g.
Gleeson et al. (2020)).
Fig. 4-1: The shape and spatial distributions of materials of the stockpile at years 1, 2, 5 and 12 |
ADE | ~ 102 ~
The Kapit Flat stockpile is located near the open pit and has a maximum footprint of about 25
hectares and a height of up to 60 m. The stockpile commenced in 1998 and since then new
material has been mined and dumped from time to time until 2010 (Gardner, 2018a). The size
and shape of the stockpile changed over the twelve-year period and different areas of the
stockpile had different exposure histories to the atmosphere, which is believed to have
affected the oxidation at different locations within the stockpile.
By way of example, Fig. 4-1 shows the shape of the stockpile at years 1, 2, 5 and 12
respectively. The materials making up the stockpile are categorised as three types: porphyry,
epithermal and argillic, using an “alteration domain” classification based on geology,
mineralization and metallurgy. The spatial distributions of the three types of materials are
shown in Fig. 4-1 using different colours.
The input variables for pyrite oxidation modelling of the Kapit Flat stockpile include the
degree of water saturation, bulk porosity of the stockpile, boundary temperature conditions
including the geothermal heat, rock particle size distribution, pyrite grain size distribution, the
acid buffering ability of the materials and the porosity and diffusivity of intact rocks. Many of
these properties depend on the type of material. Although the values of these parameters
were not measured specifically for this study, some previous laboratory test results were
available to provide reference values for this study.
Laboratory test results for samples from run of mine blast waste were used to estimate the
relevant properties of the stockpiled materials. The tests suggested that the bulk porosity of
the samples is around 30% to 40% with a maximum particle size of 37.5 mm, and the intrinsic
permeability ranges from 8×10-16 to 4×10-10 m2. Thus, in the case study, the value of 40% is
used for the stockpile porosity and 10-12 m2 for the permeability for air flow. The test results
also suggested that the samples have a thermal conductivity between 1 and 1.4 W/m/°C
under saturated conditions and 0.1 and 0.8 W/m/°C under dry conditions with a moisture
content (by volume) between 4% and 9%, hence the value of 1 W/m/°C is used for the
stockpile in this model. For the water content, it is believed that the stockpile has remained
partially saturated as the climate on the island is very humid with abundant rainfall and
efficient water runoff drainage has been maintained to avoid ponding. The simulation
therefore uses a water saturation of 25% as the average condition for the simulation period.
A previous laboratory study was conducted to investigate the potential for acid rock drainage
(ARD) from any long-term stockpiling of low-grade sulphide ore and the column test results
can be found in Doyle et al. (2003). Four column tests lasting from 56 to 224 days were
conducted and it was observed that the dissolution of pyrite was accompanied by the
dissolution of the acid buffering minerals such as calcite and orthoclase together with the
precipitation of jarosite and iron oxide. The measured and theoretical acid consumption
based on the column leaching results and the assumed reaction stoichiometry indicate that
all columns except column four were acid consuming. These tests indicate that the stockpiled
material, which is known to contain acid buffering minerals, is likely to undergo pyrite
oxidation in a non-acidic environment for a long initial period, after which the net acid
generation may become positive if the buffering minerals are consumed while pyrite remains. |
ADE | ~ 103 ~
The length of this initial period depends on the amount of contained pyrite and the acid
buffering minerals, which vary for different types of materials. This variation with types of
materials can be seen from the pH values measured before and after the cyanide leaching
tests conducted on samples of different types of materials. The final pH values after the
cyanide leaching were around 3, 5 and 7 for the sample materials of argillic, epithermal and
porphyry respectively (Gardner, 2018b), indicating that, on average, the acid buffering
capacity increases in the order of argillic > epithermal > porphyry. An assumed factor
representing the relative acid neutralization capacity (𝐹_𝐴𝑁𝐶) is used for the estimation of
the pH value in the simulations conducted in this work. The formula used to estimate the pH
value is given in Eq. (4-16), where the generated acid is calculated from the oxidation level
𝑂𝑥𝑖𝐿𝑒𝑣𝑒𝑙, pyrite content 𝑃𝑦% and the neutralization factor𝐹_𝐴𝑁𝐶; 𝜌 is the pyrite molar
𝐵
density and 𝜑 is the stockpile porosity. The values of 𝐹_𝐴𝑁𝐶 are set to 1, 2 and 4 for argillic,
epithermal and porphyry materials respectively to account for their relative acid
neutralisation capacity. The pH value calculated by Eq. (4-16) for each time step determines
which reaction rate model (with or without coating) should be used for pyrite oxidation in
each block.
𝑝𝐻 =−log (2∙𝑂𝑥𝑖𝐿𝑒𝑣𝑒𝑙∙𝑃𝑦%∙𝜌 /𝜑/1000/𝐹_𝐴𝑁𝐶)
10 𝐵 (4-16)
The distributions of rock particle size and pyrite grain size were measured for the three types
of materials and the results are shown in Fig. 4-2 and Fig. 4-3. As can be seen from Fig. 4-2,
the rock particle size distributions differ slightly among the three types of materials, with the
porphyry materials being the blockiest. The pyrite grain size decreases in the order of argillic >
porphyry > epithermal materials.
Fig. 4-2: Rock particle size distribution (by mass) for epithermal, porphyry and argillic materials |
ADE | ~ 104 ~
Fig. 4-3: Pyrite grain size distribution for the three types of materials; left: relative mass
distributions, right: the grain sizes of P10, P20, P50, P80 and P90 for the three types of materials
The porosity and diffusivity inside the rock particles are believed to vary for the three types
of materials. As measured data are not available, these values are estimated from those
measured for other types of rocks as published in the literature. Fig. 4-4 shows sample photos
of the epithermal, porphyry and argillic materials. The porosity of these materials is estimated
to be 0.09, 0.15 and 0.3 respectively from the measured values for dolomite, sandstone and
mudstone in Peng et al. (2012) where similar rock structures were observed. The gas diffusion
coefficients in the rocks used in the simulations are 10-10, 5×10-10 and 8×10-10 m2/s
respectively.
Fig. 4-4: Sample photos for epithermal, porphyry and argillic materials
Studies have shown that impurities, such as arsenic within the pyrite crystal structure, can
increase the reactivity of pyrite (Lehner and Savage, 2008; Lehner et al., 2007). Arsenic is the
most common impurity identified in Lihir pyrites and evidence has shown that pyrite with
higher arsenic content appears to oxidise more readily than that with lower content. The
average arsenic contents in the three different types of materials are different, with
epithermal pyrite being the highest (1320 ppm) followed by porphyry pyrite (830 ppm) and
argillic pyrite (600 ppm). To account for the difference in pyrite reactivity of different types of |
ADE | ~ 105 ~
materials, adjustment factors of 2, 1.25 and 1 were applied to modify the oxidation rate in
our simulations for the epithermal, porphyry and argillic pyrite respectively.
The Kapit Flat stockpile is situated over a main heat source of an active geothermal area and
the temperature below the surface is higher than that of the atmosphere. In 2017, several
holes were drilled and the temperatures logged in them were up to 70°C at a depth of around
80 m. A constant temperature boundary condition of 70°C in the case study model is thus set
at, and beyond, a depth of 84 m. In other words, for the simulation of temperature, the
modelled region includes the stockpiled material and the ground directly beneath it to a depth
of 84 m with a constant bottom boundary temperature set at 70°C.
To summarise, the value of all parameters related to the stockpile materials are given in Table
3-1, Table 3-2 and Table 4-3. All other parameters used in the simulations are listed in Table
4-4.
Table 4-1: Rock particle size distribution (by mass) for different types of materials
+25 -25 +6.3 -6.3 +0.25 -0.25
Rock particle size (mm) bin
Average size used for simulation (diameter) 50 15.65 3.275 0.25
Epithermal 22.36 30.18 24.83 22.64
Mass dist. (%) Porphyry 32.94 28.22 19.92 18.92
Argillic 31.4 30.73 19.78 18.09
Table 4-2: Pyrite grain size distribution for different types of materials
-600 -212 -106 -53 -20 -10 -5
Pyrite grain size (µm) bin
+212 +106 +53 +20 +10 +5 +1
Average size used for
406 159 79.5 36.5 15 7.5 3
simulation
Epithermal 3.7 6.2 16.4 25.3 24.8 15.7 8
Mass dist.
Porphyry 17.9 10.7 19.2 21.2 16.6 9.7 4.7
(%)
Argillic 32.6 15 18.1 15 10.4 6.4 2.5
Table 4-3: Parameters used in the simulations for different types of materials
Epithermal Porphyry Argillic
Parameters
Porosity 0.09 0.15 0.3
Diffusion coefficient (m2s-1) 10-11 5×10-11 8×10-11
Pyrite content 5% 3% 10%
ANC factor 2 4 1
Pyrite reactivity factor 2 1.25 1 |
ADE | ~ 106 ~
Table 4-4: Other parameters used in modelling the pyrite oxidation of the Kapit Flat stockpile
Value Unit
Parameters
Porosity of the stockpile 0.4
Air permeability of the stockpile 10-12 m-2
Degree of water saturation of the stockpile 25%
Temperature boundary value at depth of 84 m 70 °C
Stoichiometric coefficient of pyrite reaction 2/7 Pyrite to oxygen
Pyrite molar density 𝜌 4.17×104 mol·m-3
𝐵
Gravitational acceleration 𝑔 -9.8 m·s-2
Reference air density 𝜌 1.165 kg·m-3
Gas constant 𝑅̅ 8.314 Pa·m3·mol-1·K-1
Henry’s law constant 𝐻𝑐𝑐 3.2×10-2 @ 25 °C
Specific heat capacity of air 𝐶 1006.1 J·K-1·kg-1
𝑔
Volumetric heat capacity of rock media 1.98×106 J·K-1·m-3
Heat generated per mole of pyrite reacted 1.409×106 J·mol-1
Heat diffusivity of the stockpile material 1.4×10-6 m2·s-1
Initial O concentration 𝐶 in air 8.28 mol·m-3
2
Initial and reference pressure 𝑃 1 atm
0
Initial and atmosphere temperature 𝑇 25 °C
0
4.2.3 Sample test results
Fig. 4-5: The pyrite oxidation level and gold recovery by direct cyanide leaching for samples taken
from the Kapit Flat stockpile
In 2017, sonic drill holes were drilled in the Kapit Flat stockpile and 55 samples were taken.
These samples were then analysed in the laboratory, where the sulphur content in sulphate
and sulphide forms were measured as well as the gold recovery by direct cyanide leaching. |
ADE | ~ 108 ~
Fig. 4-7: Simulated air velocity field over the Kapit Flat stockpile at the 20th year
As can be seen in Fig. 4-6a, the simulated oxidation level over the Kapit Flat stockpile varies
from less than 0.1 to as high as 0.7. It is much higher at the boundaries including both the
bottom and the surface, while the oxidation level is mostly less than 0.2 within the stockpile
away from boundaries. This can also be seen in Fig. 4-8 where the histograms of the oxidation
level for blocks at the surface-boundary, bottom-boundary and non-boundary locations are
plotted. The significant differences among the three categories are apparently caused by the
differences in oxygen concentrations, which can be seen in Fig. 4-6b. Constant values of 1
mol·m-3 and 3 mol·m-3 of oxygen concentrations were used as the first-type boundary
conditions for the blocks at the bottom and the surface of the stockpile respectively. These
conditions provide enough oxygen for pyrite oxidation at the boundary locations, resulting in
high oxidation levels. Inside the stockpile, while the simulated oxygen concentration varies
across the stockpile, it is rarely above 0.15 mol·m-3 at non-boundary locations as a result of |
ADE | ~ 109 ~
fast consumption of oxygen relative to the resupply rate. Consequently, among the blocks at
the non-boundary locations, the oxidation level ranges from almost no oxidation to 20%, with
a few blocks reaching higher levels of up to 40%. The major cause of this small variation is not
due to material properties such as reactivity or pyrite content. Instead, it is a result of the
varying sizes and shapes of the stockpile during the 12 years of intermittent stockpiling. As
oxygen is always limited at locations other than the boundaries, the time of exposure to the
atmosphere during the stockpile construction is the key influencing factor for the oxidation
level for non-boundary blocks. Overall, for a stockpile of this size, the accessibility to oxygen
is the most dominant decisive factor that determines the level of pyrite oxidation.
Fig. 4-8: The distribution of oxidation levels for blocks at different locations
Fig. 4-6c shows the temperature profile which mainly follows the topography of the stockpile,
gradually increasing from the surface to the deeper locations. As heat has been generated
from pyrite oxidation, at some locations in the stockpile the temperature can be higher than
the geothermal-boundary temperature (set at 70°C). The temperature has reached a
maximum of 89°C at a depth of 60 m. Fig. 4-7 shows the heat-induced air velocity field over
the stockpile. As can be seen, air can be recharged into the stockpile. However, the magnitude
of the air velocity is only up to 8 mm/day, which is insignificant for oxygen resupply compared
with diffusion as discussed in Wang et al. (2021). In this case, although the increased
temperature can enhance the oxidation rate in general, it is a less important factor compared
with the accessibility to oxygen.
Fig. 4-9 shows a comparison between the simulated oxidation levels and those obtained from
the sample tests. The samples were taken at different depths of the sonic drill holes drilled in
2017 and were then tested in the laboratory for sulphide and sulphate content. The oxidation
level is calculated as the ratio of sulphate sulphur to total sulphur. The comparison shows that
the current model underestimates the oxidation level by nearly 20% at most sample locations.
It also significantly overestimates the oxidation level at some locations near the bottom and
surface boundaries. As discussed above, oxygen concentration is the most decisive factor
among all the influencing variables. The mismatch between the simulated results and the test
results indicates that the simulated oxygen concentrations and the boundary values may
deviate from the actual values. The boundary values set at the bottom or surface boundaries
for oxygen concentration seem to be too high although considering oxygen consumption,
they were set to be much smaller than the atmospheric concentration (8 mol·m-3). At non-
boundary locations, the simulated oxygen concentrations appear to be too small to yield
oxidation levels comparable to the tested samples. This further indicates that, in addition to |
ADE | ~ 110 ~
the modelled diffusion and heat-induced convection, there must be other sources and/or
mechanisms for oxygen resupply inside the stockpile, such as natural air flow, barometric
pressure fluctuation and rainwater infiltration. In this case in particular, rainwater infiltration
has possibly played a significant role for oxygen resupply. Although the low solubility of
oxygen in water limits the amount of dissolved oxygen entering the stockpile in each rainfall
event, the abundant rainfall on Lihir Island guarantees the frequency of rainwater infiltration
events, which, over a long term, may have provided significant amounts of oxygen. In addition,
frequent rainwater infiltration may cause internal flow channels inside the stockpile which
may facilitate air exchange and oxygen resupply. However, these mechanisms for additional
oxygen resupply were not included in the current version of the model due to a lack of data
records and limited model capacity. A quick and simple way to consider the enhanced oxygen
resupply by these mechanisms is to set a low background oxygen concentration inside the
stockpile. Considering all these issues, another simulation was run with a set background
value of 0.5 mol·m-3 imposed for oxygen concentration and with boundary values changed to
0.5 and 2 mol·m-3 respectively for the bottom and surface of the stockpile.
Fig. 4-9: Comparison of the simulated oxidation level and the measured ratio of Sulphate-S/Total-S
at the sample locations |
ADE | ~ 111 ~
The re-simulated oxidation levels at sample locations are also plotted in Fig. 4-9 and show
that, after adjusting the oxygen concentration, the simulation results are, on average, closer
to the test results. Two further observations can be made. Firstly, the model input does not,
and cannot, completely represent all the in-situ conditions. Secondly, the ratio of the sample
sulphate-S to the total-S does not necessarily represent the true oxidation level as some
sulphate content may have been present prior to the material being mined. From the
mineralogical analysis of fresh material, it is known that there are sulphates present within the
in-situ deposit, predominantly anhydrite within porphyry material, but they can also be present in
small amounts in both epithermal and argillic materials. Given these two considerations, the re-
simulated result can be accepted as a reasonable estimation of the stockpile oxidation. In the
following discussions, the simulation results refer to those from the model with oxygen
concentration adjustments.
Fig. 4-10: Simulated oxidation levels for the Kapit Flat stockpile with adjusted oxygen concentrations
Fig. 4-10 shows the updated cross-sections of the oxidation level after adjusting the oxygen
concentration. The average oxidation level of the stockpile is 25.4% and the highest value is
64%. Fig. 4-11 shows the histograms of the oxidation level for blocks of different types of
materials. The average oxidation level for epithermal blocks is the highest of the three (29%)
followed by porphyry blocks (22%) and argillic blocks (21%). This order appears to be
consistent with the pyrite reactivities of the three materials listed in Table 4-3. Overall, for
this case study, the oxidation level of a block is affected mostly by the accessibility to oxygen
followed by the material properties. |
ADE | ~ 113 ~
grain size becomes smaller, more pyrite grains are oxidised at a higher level (Fig. 4-12b). About
half of the pyrite grains of size 3 µm are almost completely oxidised and most of the remaining
pyrite grains are less than 5% oxidised, with the remainder having oxidation levels between
these two extremes. Similarly, other small grain sizes (7 and 15 µm) are either almost
completely oxidised or have little or no oxidation and only a very small fraction have oxidation
levels between the two extremes.
The oxidation profiles of pyrite grains vary across the stockpile. The profiles vary with the
block oxidation level as well as the material type because properties such as rock porosity,
rock particle size distribution and pyrite grain size distribution differ for different types of
material. As a result, each block has a unique oxidation profile. With this information over the
stockpile together with the distribution of gold in pyrite grains, it is possible to evaluate the
readily recoverable gold by direct cyanide leaching.
Mineralogical analysis of the Lihir orebody found that a significant proportion of pyrite grains
contain less than 1 ppm of gold. This type of pyrite is classified as “no value” pyrite. The
average proportion of “no value” pyrite differs for different types of materials, which on
average is 24% for porphyry pyrite, 32% for epithermal pyrite and 60% for argillic pyrite.
Analyses of samples from the Lihir orebody using LA-ICP-MS (Laser Ablation Inductively
Coupled Plasma Mass Spectrometry) also showed different patterns of gold distribution in
pyrite grains for different materials. One is an aggregation pattern where gold particles occur
in several patches distributed either at the edge, or in the core, of the pyrite grain. Another is
a uniform pattern where gold particles are evenly distributed within pyrite grains. The third
and fourth types are those where gold particles are mainly distributed in the rims at or near
the edge of pyrite grains surrounding barren or variable grade cores. The fifth type is bladed
where high-grade gold content occurs on only one side of a pyrite grain. These gold
distributions in pyrite grains indicate that a complete oxidation of pyrite may not be necessary
for full recovery of the contained refractory gold. In other words, a high gold recovery may be
achieved with only partial oxidation of pyrite. This can be seen in the sample test results for
gold recovery via direct cyanide leaching shown in Fig. 4-5, which indicates that, in general,
gold extraction via direct cyanidation increases as the pyrite oxidation level increases and the
gold extraction percentage is always higher than the pyrite oxidation level.
Fig. 4-13: Modelled gold distribution (by mass) in pyrite grains |
ADE | ~ 114 ~
Considering a mixture of all five gold distribution patterns mentioned above with slightly
more rim patterns (the third and fourth types) than the others, an average gold distribution
in pyrite grains can be estimated and the result is shown in Fig. 4-13. This indicates that, for a
pyrite grain of any size, the gold content is most abundant in the first three outer layers of
the discretised 40 layers and it decreases towards the inner part of the pyrite grain.
With the estimated gold distribution in pyrite grains, the cyanide-available gold recovery can
then be estimated from the simulated oxidation profile for each block. Here it is assumed that
the proportions of the gold content (mass fraction) contained in pyrites of different sizes are
0.05, 0.05, 0.1, 0.2, 0.2, 0.2, 0.2 respectively (in order of decreasing pyrite grain size). The
estimated cyanide-available gold recovery for blocks at the same oxidation level as the
samples is shown in Fig. 4-14 together with the measured cyanide gold recoveries for the
samples tested. Fig. 4-15 shows the statistics of the estimated cyanide-available gold recovery
for all blocks in the stockpile together with the sample test results for comparison. These
comparisons show that the mean of the estimated gold recovery via direct cyanide leaching
is very close to the mean of the measured cyanide gold recovery at comparable oxidation
levels. However, the measured cyanide gold recovery for samples at similar oxidation levels
has a much wider range of variability than that of the estimated values, especially for
oxidation levels less than 30%. This indicates that the gold distribution in pyrite grains may
vary much more significantly than that used in the model. When gold is more abundant at the
edges of pyrite grains, a higher gold recovery can be achieved via direct cyanide leaching at a
relatively low oxidation level. When gold is more abundant in the inner part of the pyrite
grains, a lower cyanide-available gold recovery can be expected. In Fig. 4-15, the estimated
cyanide gold recovery for oxidation levels from 50% to 70% continues to increase but there is
a lack of test data for comparison. In addition, since the highest oxidation level from the
simulation result is 71%, there are no estimated values for gold recovery at higher oxidation
levels.
Fig. 4-14: Comparison of the cyanide-available gold recovery measured from test samples and that
estimated from the model for blocks at oxidation levels comparable to the samples |
ADE | ~ 115 ~
Fig. 4-15: The mean value and the range of variability in cyanide-available gold recovery for all blocks
in the stockpile for different ranges of oxidation levels compared with those from the sample test
results
Overall, the relationship between gold recovery via direct cyanide leaching and the pyrite
oxidation level can be estimated from the oxidation profile, the gold fraction in pyrites of
different grain sizes and the gold distribution patterns in the pyrite grains. While the oxidation
profile can be simulated from the pyrite oxidation model presented in this paper, a reliable
understanding of the other two variables can only be achieved through extensive laboratory
analyses of samples, which are both expensive and time-consuming. An alternative approach
is to use assumed values initially and derive acceptable estimates by calibrating the model for
estimating gold recovery via direct cyanide leaching using the measured gold recovery values
obtained from test samples, as has been done in this paper.
Conclusions
This paper presents a case study on modelling the natural oxidation of pyrite in a refractory
gold ore stockpile at the Lihir mine in Papua New Guinea for the purpose of estimating the
potential gold recovery via direct cyanide leaching without pre-treatment. The pyrite
oxidation model simulates natural processes including the oxidation of pyrite in rock particles,
heat transfer, heat-induced air convection and oxygen transport over the refractory gold ore
stockpile. The site characteristics incorporated in the Kapit Flat stockpile model include
geothermal heat, the degree of water saturation and the properties of three types of material:
rock porosity, rock particle size distribution, pyrite grain size distribution, pyrite reactivity
enhanced by arsenic content and the acid neutralisation capacity. The simulation results show
that for a large stockpile of this size, the key factor that mostly affects the oxidation level is
the accessibility to oxygen. Hence, the time that the material is exposed to the atmosphere
during the construction of the stockpile is an important input to the model. A comparison of
the simulation and test results shows that the oxidation level in the stockpile is
underestimated by assuming diffusion and/or heat-induced air convection as the dominant
mechanism(s) for oxygen transport in the model. This suggests that there are other
mechanisms, such as air convection induced by wind, fluctuations in barometric pressure and
rainwater infiltration, that play important roles in oxygen resupply in the stockpile. To
accommodate this additional oxygen resupply, a background oxygen concentration is added |
ADE | ~ 120 ~
Conclusions
This work addresses the research problem of evaluating pyrite oxidation in refractory gold-
bearing stockpiles for the purpose of estimating the potential gold recovery without pre-
treatment. To solve this problem, two models were developed in this work to describe pyrite
oxidation at the small grain scale and at the bulk stockpile scale respectively. A real refractory
gold ore stockpile was used as a case study.
The small scale model, a reaction rate model, describes the reaction rate of prolonged
oxidation of pure pyrite grains for cases where diffusion barriers such as an oxidised layer
and/or a thin solution film develops on fresh pyrite surfaces, a situation corresponding to
pyrite oxidation in unsaturated water conditions and/or a circum-neutral to alkaline pH
environment. This model considers both the surface reaction kinetics and the micro-scale
transport of oxygen, and incorporates the effects of oxygen concentration, temperature and
degree of water saturation on the oxidation rate of pyrite grains. The model parameters,
including the diffusion coefficient, the surface reaction rate constant and the activation
energy, were determined from the reaction rate data published in the literature.
The large scale model, a multi-component numerical modelling framework, can simulate the
oxidation of pyrite in stockpiles together with related processes including oxygen transport
and heat transfer that are interdependent with pyrite oxidation. This model incorporates the
developed reaction rate model (in combination with the other reaction rate model for intro-
aqueous, low pH conditions) as one of its components to simulate pyrite oxidation under
different stockpile conditions. The simulation outputs from the multi-component model
include oxygen concentration, temperature, oxidation level and the oxidation profile of pyrite
grains over the stockpile, which are used subsequently to estimate the potential gold recovery
through direct cyanide leaching. A synthetic stockpile was used to demonstrate the
application of the proposed numerical modelling method and a comparison among different
simulation scenarios was conducted to investigate the effects of stockpile properties such as
porosity, diffusion coefficient and geothermal heat on the simulated oxidation level. It was
found that the availability of oxygen is the most important limiting factor for pyrite oxidation
and hence the properties that affect oxygen transport, such as porosity and diffusion
coefficient, significantly influence the pyrite oxidation level.
Finally, the developed numerical modelling framework was applied to a real case study - the
Kapit Flat stockpile on Lihir Island in Papua New Guinea. The oxidation level and oxidation
profile of the pyrite grains over the Kapit Flat stockpile were simulated using the actual
stockpile characteristics. It was found that for rocks at different locations in the stockpile, the
histories of the exposure of the rocks to the atmosphere dominantly determine the oxidation
level based on the influencing factors considered. The numerical model was calibrated with
the measured oxidation level for samples taken from the stockpile. The comparison between
the model outputs and the measurements revealed that there was oxygen resupply in
addition to the modelled diffusion and heat-induced convection, which was most likely the
result of frequent rainwater infiltration. A background oxygen level was added to the
numerical model based on the calibration results to account for the effects of this additional |
ADE | ~ 121 ~
oxygen resupply. The simulated oxidation level based on the calibrated model is in general
agreement with the measured results for the Kapit Flat stockpile. For the case study, an
example was also given to illustrate the estimation of potential gold recovery through direct
cyanide leaching from the estimated oxidation profile of pyrite grains at different locations in
the stockpile.
Limitations
The model developed in this work describes the pyrite oxidation process in stockpiles/rock
piles. There are three main limitations on the proposed approach. The first is related to
confining the influencing factors for pyrite oxidation to an abiotic environment in this model.
Although microbial activities are believed not to have significant effects on the long-term
oxidation rate when oxygen is limited, omitting microbial activities restricts the use of the
model to simulating pyrite oxidation with bacteria catalysis when sufficient oxygen is supplied.
The second limitation is that, because of the simplification used to simulate the pH variations,
the simulation of fluid flow and intro-aqueous equilibriums are not currently incorporated in
the model. This may have some impact on the pyrite oxidation simulation results as the pH
value determines whether a model, with or without the coating, should be used. In addition,
the lack of capability for fluid flow simulation also limits the incorporation of the possible
mechanism for oxygen resupply through rainwater infiltration, which might be an important
process for the prediction of the level of pyrite oxidation, as shown in the Kapit Flat stockpile
case study. Although the effect of this process can be included by using a simplified approach,
as demonstrated, by adding a calibrated background oxygen level, the missing capability still
limits the applicability of the model to cases where the rainwater infiltration is highly
heterogeneous.
For the simulation of the pyrite oxidation in the Kapit Flat stockpile, although this work
endeavours to incorporate as many of the stockpile characteristics as possible, not all relevant
information was available for this research. Consequently, some input parameters were
estimated instead of measured, and assumptions for these estimations were made. This leads
to uncertainties in the modelling outcomes.
Future work
This work provides a numerical modelling framework for the evaluation of pyrite oxidation in
refractory gold-bearing stockpiles. The model incorporates the effects of oxygen
concentration, temperature, degree of water saturation and pH values on the oxidation rate
of pyrite grains. Rock properties including porosity, diffusion coefficient and rock particle size
distributions are considered. Other stockpile properties including geothermal heat, bulk
porosity, diffusion coefficient, degree of water saturation and material stockpiling sequence
are also incorporated into the model. This model can be further improved by incorporating
the influence of microbial activity to include the ability to simulate bacteria-catalysed pyrite
oxidation with sufficient oxygen supply. The simulation of pH variations can also be improved
and oxygen resupply through rainwater infiltration can be incorporated by adding model
components to enable the simulation of fluid flow and intro-aqueous equilibriums. This |
ADE | Abstract
Metallic plates are one of the major components of liquid containment structures
and are widely used in petrochemical and civil engineering. In many cases, the
metallic plates have one side exposed to liquid and are subjected to different types
of loads with varying amplitudes. Corrosion damage and material degradations are
the two major concerns. Damage detection of the submerged plate structures plays
an important role in maintaining the structural integrity and safety of high-valued
infrastructures (e.g. liquid storage tanks and pipes). Guided wave testing is one of
the most promising damage detection approaches. Although guided wave based
techniques have been extensively studied on different structures in gaseous
environments, the design and implementation for the structures immersed in liquid
have not been well investigated.
This research aims at enhancing the understanding of guided wave
propagation and interaction with damage in submerged structures. The focus of this
research is on metallic plates that have one side in contact with liquid and the other
side exposed to air. The specific objectives of this thesis include the investigation
on the propagation characteristics of guided waves in metallic plates with one side
exposed to liquid, the development of numerical models to investigate the scattering
characteristics of guided waves at corrosion pit damage, the analyses of the
influence of the surrounding liquid medium on the linear and nonlinear guided
waves features, and the evaluation of the sensitivity of linear and nonlinear guided
waves features to different types of damage in the one-side immersed metallic plate.
The main body of the thesis consists of four journal articles (Chapters 2-5).
Chapter 2 discusses the propagation characteristics and sensitivity to damage of
linear guided waves in a metallic plate loaded with water on one side. The targeted
damage is local thickness thinning (e.g. corrosion pits) with a size of around a few
millimeters. Chapter 3 further investigates and compares the guided wavefields
between a plate surrounded by air and the same plate with one side partly exposed
to water. The influence of the surrounding liquid medium on the guided wave
propagation is demonstrated experimentally and numerically. Chapters 4 and 5
study two different nonlinear guided wave features, which are second harmonic
i |
ADE | Declaration
I, Xianwen Hu, hereby declare that this work contains no material which has been
accepted for the award of any other degree or diploma in my name, in any university
or other tertiary institution and, to the best of my knowledge and belief, contains no
material previously published or written by another person, except where due
reference has been made in the text. In addition, I certify that no part of this work
will, in the future, be used in a submission in my name, for any other degree or
diploma in any university or other tertiary institution without the prior approval of
the University of Adelaide and where applicable, any partner institution responsible
for the joint-award of this degree.
I acknowledge that the copyright of published works contained within this thesis
resides with the copyright holder(s) of those works. I also give permission for the
digital version of my thesis to be made available on the web, via the University’s
digital research repository, the Library Search, and also through web search engines,
unless permission has been granted by the University to restrict access for a period
of time.
I acknowledge the support I have received for my research through the provision of
Adelaide Graduate Research Scholarship by The University of Adelaide.
Signature: _ Date: _0_7_/0_3_/_2_0_2_2________
iii |
ADE | Acknowledgment
First of all, my sincere thanks go to my principal supervisor, Professor Ching-Tai
(Alex) Ng, for his invaluable supervision and continuous support during my Ph.D.
study. His rich knowledge and enthusiasm encouraged me to explore new research
areas in the field of structural health monitoring. I would like to thank my co-
supervisor, Professor Andrei Kotousov, for his treasured mentorships and
contributions. I would also like to thank Professor Francis Rose for his technical
advice.
I would like to extend my thanks to my fellow colleagues, Dr. Carman Yeung, Mr.
Juan Allen, Dr. James Hughes, Mr. James Vidler, Dr. Munawwar Mohabuth, Ms.
Tingyuan Yin, Mr. Ahmed Aseem, Mr. Jinhang Wu, Mr. Min Gao, Mr. Chang Jiang,
Mr. Yuqiao Cao, Mr. Hankai Zhu, and Mr. Zijie Zeng. Thank them for spending
cherished time with me in the laboratory and office. Their assistance and
encouragement have been a strong source of inspiration to me. Also, thanks to my
beloved technicians Mr. Brenton Howie, Mr. Jon Ayoub, Mr. Gary Bowman, and
Mr. Ian Ogier. Their plentiful experience and treasured support played an important
role in shaping my experimental methods. Without their technical assistance, this
work would hardly be completed.
I would like to acknowledge the University of Adelaide for the financial support
through the provision of Adelaide Graduate Research Scholarship. Due to the
COVID-19 pandemic, my life and work have been severely affected since 2020.
Thanks to the Adelaide Graduate Centre for extending the length of my candidature
and scholarship, and providing me with financial support to complete this project.
Thanks to the Faculty of Engineering, Computer, and Mathematical Science and
the School of Civil, Environmental, and Mining Engineering for the additional
financial subsidies to support me in presenting my research at international
conferences.
Last but not least, I would like to thank my family. Special thanks to my father who
told me that studying can change a person’s life. Special thanks to my mother who
inspired me to be patient and grateful. Their love is beyond words. I am proud of
myself for undertaking the Ph.D. program. It is a tough yet rewarding journey.
iv |
ADE | List of publications
This thesis by publications consists of a collection of published and accepted (for
publication) journal articles in accordance with the requirements outlined in “the
academic program rules” and “specifications for thesis” of The University of
Adelaide. A complete list of the articles included in this thesis is presented here.
(1). X. Hu, C.T. Ng, A. Kotousov (2021), Scattering characteristics of quasi-
Scholte waves at blind holes in metallic plates with one side exposed to
water, NDT & E International, 117, 102379.
(2). X. Hu, C.T. Ng, A. Kotousov (2022), Numerical and experimental
investigations on mode conversion of guided waves in partially immersed
plates, Measurement, 190, 110750.
(3). X. Hu, C.T. Ng, A. Kotousov (2022), Early damage detection of metallic
plates with one side exposed to water using the second harmonic generation
of ultrasonic guided waves, Thin-Walled Structures, 176, 109284.
(4). X. Hu, C.T. Ng, A. Kotousov (2022), Structural health monitoring of
partially immersed plates using nonlinear guided wave mixing,
Construction and Building Materials (in-print).
The following book chapters and refereed conference papers are also derived from
the research by the candidate within the candidature:
Book chapters:
(5). X. Hu, C.T. Ng, A. Kotousov (2021), Chapter 4: Damage detection of
partially immersed plates using guided waves. In Recent Advances in
Structural Health Monitoring Research in Australia: Nova Science
Publishers Inc (In-print).
Conference papers:
(6). X. Hu, C.T. Ng, A. Kotousov (2021), Experimental investigations on
second harmonics generated by leaky guided waves in immersed plates,
v |
ADE | Chapter 1
Chapter 1. Research overview
1.1 Background
Metallic plates are the main components in liquid containment structures, such as
liquid storage tanks and pipelines. They are widely used in petrochemical and civil
engineering. When the devices are in service as shown in Figure 1.1, the metallic
plates have one side exposed to liquid and are subjected to different types of loads
with varying amplitudes. Over time, the structural materials are degrading, and
corrosion can grow extensively in localized regions on the submerged sides of these
structures. Failure to control the structural defects leads to leakage, catastrophic
structural failures, and huge costs of downtime, fatalities, and environmental
damage. For instance, it is estimated that the global cost of corrosion contributes to
3.4% of the global gross domestic product (GDP), which is around US$ 2.5 trillion
per year [1]. Up to 30% of these costs can be saved through proper damage control
practices including periodic inspections and repair.
Figure 1.1 Example of tanks and pipes filled with liquid
1 |
ADE | Chapter 1
In the past few decades, many non-destructive testing (NDT) methods have
been proposed to minimize the impacts of in-service failure of high-valued
infrastructures. These NDT techniques include visual inspection by divers and
robots [2], hydro test [3], ultrasonic testing [4], acoustic emission [5, 6], magnetic
flux leakage test [7] and eddy current test [8]. These NDT approaches are not
,
economic and inconvenient because they require periodic shutdown of the facilities
to implement inspection. Recent research has put forward the concept of structural
health monitoring (SHM), which is to permanently install lightweight and durable
sensors on the structure and continuously evaluate the structural integrity. SHM has
the potential to reduce costs by scheduling the maintenance only as needed [9]. Both
the NDT and SHM communities have conducted extensive research to detect
defects at an earlier stage and track the damage evolution. Earlier detection of
damage allows more time to plan actions that would ultimately enhance safety.
Figure 1.2 Comparison of inspection area between (a) conventional ultrasonic
testing using bulk waves and (b) guided wave testing
Guided wave testing is one of the most promising SHM approaches, which
can achieve much larger inspection ranges than the conventional NDT approaches,
by using a small number of sensors permanently attached to the structures. Guided
waves are defined as elastic waves propagating along a boundary or between
parallel boundaries of a structure. Figure 1.2 compares the inspections of a plate
2 |
ADE | Chapter 1
structure using conventional ultrasonic testing and guided wave testing,
respectively. Conventional ultrasonic testing inspects the structure using bulk
waves (e.g. longitudinal wave and shear wave). The inspection area is the local
region below the transducer. The transducer must be moved along the surface to
collect data. In contrast, guided waves cover the total thickness of the structures
over a fairly long distance. The inspected area using guided waves is much larger,
compared to the conventional ultrasonic testing.
Previous studies have demonstrated that guided waves have high sensitivity
to various structural defects and can inspect inaccessible locations [10]. The
majority of the work on the applications of guided waves has been conducted on
the structures in gaseous environments. In the literature, there were limited studies
that employed guided waves to detect damage in structures immersed in liquid. The
interaction between guided waves and defects in submerged structures has not been
fully understood. To provide support for the further development of the structural
health monitoring techniques for submerged structures, this thesis investigates the
feasibility of using both the linear and nonlinear guided waves to detect and
characterize damage in plate structures with one side exposed to liquid. The
following section provides a brief review of research progress in the field of damage
detection using linear and nonlinear guided waves.
1.2 Literature review
1.2.1. Linear guided wave testing
Linear guided waves are sensitive to defects with a size comparable to the
wavelength of the selected guided wave modes. Generally, they are around a few
millimeters. Typical examples of these defects include small corrosion pits, dents,
cuts, and notches. The interaction between guided waves and these defects can
generate scattered waves at the same frequency components as the incident waves.
The scattered waves can alter the transmitted guided wave signals, such as wave
amplitude changes, arrival time delays, phase shifts, and mode conversions.
There are various types of guided wave modes depending on the structural
boundaries. For example, Rayleigh waves propagate on the surface of a semi-
3 |
ADE | Chapter 1
infinite solid [11, 12]. Edge waves travel along the structural edges [13, 14]. Lamb
waves refer to guided waves in thin-walled structures such as plates and pipes [15,
16]. In this study, we focus on the thin-walled plate structure with one side
immersed in liquid. Guided waves in the immersed plate structures have leaky
Lamb modes and the quasi-Scholte mode. Leaky Lamb waves are composed of
multiple leaky symmetric and antisymmetric wave modes. They also are called
leaky guided waves because the wave energy can transmit into the surrounding
liquid medium through the solid-liquid interface.
The application of leaky guided waves for submerged thin-walled structures
is limited to several guided wave modes at their corresponding low attenuation
frequency region because most of the leaky guided waves decay quickly due to high
attenuation. The fundamental leaky symmetric Lamb wave mode (leaky S ) is one
0
of the most popular wave modes and has been employed to estimate circular holes,
notches, and corrosion in metal plates immersed in water [17-21]. When the
excitation frequency is below the cut-off frequency of the higher-order wave modes,
leaky S wave has very low attenuation and is well separated from the other wave
0
modes due to the fastest propagation speed. The structural defects can be evaluated
by leaky S wave with relatively simple signal processing techniques. However, it
0
is not sensitive to small and shallow defects on the structural surfaces. To overcome
this limitation, researchers also investigated the first-order leaky symmetric Lamb
wave mode (leaky S ) [20, 22] and the first-order leaky anti-symmetric Lamb wave
1
mode (leaky A ) [19] to evaluate different defects in immersed plate structures.
1
Generally, the higher-order guided wave modes (leaky S and leaky A ) have high
1 1
sensitivity to the shallow defects at the plate surface. However, the experimentally
measured signals are much more complicated due to the presence of multiple wave
modes.
The quasi-Scholte wave was also studied to detect notch damage in
immersed metal plates [23]. The quasi-Scholte wave can be generated at low
excitation frequencies and has very low attenuation. It should be noted that the
quasi-Scholte wave has a much lower phase velocity compared to leaky S wave at
0
a given frequency. A lower phase velocity indicates a shorter wavelength and higher
sensitivity to small and shallow defects at the structural surface [24]. This is due to
4 |
ADE | Chapter 1
the fact that the size of the defects should be larger than half the wave wavelength
of the passing guided waves to ensure the scattered waves by the defects can be
measurable [25].
1.2.2. Nonlinear guided wave testing
Generally speaking, it is better to identify defects sooner than later. Earlier detection
of damage allows more time to plan maintenance action and substantially improves
safety. In the early damage stage, all material has the inherent material nonlinearity
that is attributed to microstructural defects such as micro cracks, persistent slip
bands, and dislocation [9, 26, 27]. As the loads increase, these microstructural
defects accumulate and evolve into macro cracks. The evolution from
microstructural defects to macro cracks takes up a major part of the total service
life [9]. After that, the macro cracks grow quickly to critical points, leading to
catastrophic failure.
The microstructural defects are too small to be detected by linear guided
wave testing as mentioned above. However, they can distort the passing guided
waves and generate new wave components at frequencies other than the incident
waves. The new wave components are called the nonlinear guided wave features
and have been shown to change significantly during the early damage stage in air-
coupled structures [11, 28-36]. This phenomenon enables researchers to identify
smaller defects and track material degradation in the early stage. However,
nonlinear guided waves have not yet been well studied for damage detection for
structures immersed in liquid. The influence of the liquid coupling on the generation
of the nonlinear guided waves is unknown.
1.3 Research aims and objectives
This research aims at enhancing the understanding of guided wave propagation and
interaction with damage in submerged structures. The focus of the current research
is on metallic plates that have one side in contact with liquid and the other side
exposed to air. The intended application includes damage detection for liquid
5 |
ADE | Chapter 1
containment structures such as water towers, storage tanks, and ship hulls. The
project comprises the following objectives:
Objective 1: To investigate the propagation characteristics of leaky guided
waves in a metallic plate with one side exposed to liquid
An analytical analysis is conducted to derive the dispersion curves and mode shapes
of the leaky guided waves in a metal plate with one side exposed to liquid.
According to the theoretical results, the low attenuation frequency range of the
fundamental leaky guided wave modes (leaky S , leaky A , and quasi-Scholte
0 0
waves) are identified. After that, the propagation characteristics of the selected
wave modes are investigated through experimental measurements. Finally, the
influence of the surrounding liquid is demonstrated by comparing the signals
experimentally measured from a metal plate with and without liquid.
Objective 2: To develop a 3D FE model to investigate the scattering
characteristics of leaky guided waves at corrosion pit damage
A 3D FE model is developed to simulate the interaction between leaky guided
waves and corrosion pits. The numerical simulation can provide a visualization of
the guided wave fields and help interpret the experimental data. The scattering
characteristics of leaky guided waves are analyzed by means of scattering directive
pattern (SDP), which provides the scattering amplitudes in all directions around the
damage.
Objective 3: To analyze the effect of the surrounding liquid medium on the
linear and nonlinear guided wave features
The influence of the surrounding liquid on the linear and nonlinear guided wave
features is demonstrated by comparing the signals experimentally measured from a
metal plate with and without liquid. Nonlinear interactions between guided waves
and the microstructures in materials are investigated. The focus has been on the
generation of second harmonics and combination harmonics.
6 |
ADE | Chapter 1
Objective 4: To evaluate the sensitivity of linear and nonlinear leaky guided
waves to various damage in the metallic plate with one side exposed to liquid
Fatigue is one of the major concerns for submerged structures that are subjected to
cyclic loading with varying amplitudes. In the fatigue stage, the microstructural
defects in the material continue to grow and accumulate, which can be evaluated by
the nonlinear guided wave features. Corrosion damage is another important issue
for metallic structures operating in humid environments. Corrosion pits with a few
millimeters can be evaluated by linear guided wave features. Numerical and
experimental studies are conducted to evaluate the sensitivity of both linear and
nonlinear guided waves to different types of damage in the immersed plate.
1.4 Structure of the thesis
This thesis consists of four journal articles in regard to applying guided waves for
damage detection of submerged structures. Chapter 1 provides a brief background
on the research and introduces the significance of safety inspection for submerged
structures. This is followed by an overview of guided wave techniques for damage
detection, which can be further categorized into linear guided wave testing and
nonlinear guided wave testing. Then, the aims and objectives of the research are
presented and a brief outline of the thesis is formulated.
Chapter 2 (Paper 1) discusses the propagation characteristics and sensitivity
to damage of linear guided wave features on a metallic plate loaded with water on
one side. The targeted damage is local thickness thining (e.g. corrosion pits) with a
size of around a few millimeters, which is the major concern for metallic structures.
To simulate corrosion pits, blind holes are mechanically drilled on a steel plate with
one side exposed to water. The interaction of guided waves with the blind holes is
investigated.
Chapter 3 (Paper 2) further investigates the behaviors of guided waves in a
metallic plate with one side partly exposed to water. The influence of the
surrounding liquid medium on the guided wave propagation is demonstrated
7 |
ADE | Chapter 1
experimentally and numerically by comparing the guided wavefields between the
plate surrounded by air and the plate with one side partly exposed to water. The
findings of this chapter indicate that the defects (e.g. corrosion pits) on partially
immersed plates (e.g. tanks or pipes partially filled with liquids) can be evaluated
by sending guided waves on the dry section of the plates and measuring the guided
wave signals on the immersed section.
Chapter 4 (Paper 3) explores the nonlinear guided wave testing using tone
burst signals with a single central excitation frequency. In the literature, the linear
guided wave testing can only identify defects with a size comparable to the
wavelength of the passing guided waves, which are around a few millimeters. The
nonlinear guided wave features have better sensitivity to microstructural defects
that precede the damage in the macroscale and allow earlier damage detection. This
chapter investigates the feasibility of the second harmonic generation by guided
waves in metallic plates with one side exposed to water. Three criteria are proposed
for the selection of guided wave modes and excitation frequencies, which ensures
the measurable and cumulative generation of the second harmonics due to the
material nonlinearity. Both experiments and numerical simulations are conducted
and the results demonstrated that the second harmonics by leaky S waves are
0
sensitive to the early-stage damage in plates with one side immersed in water.
Chapter 5 (Paper 4) numerically and experimentally investigates the
nonlinear guided waves mixing two different frequencies in an aluminum plate
loaded with water on one side. Leaky S waves are excited at two different
0
frequencies on the wall of a metal tank filled with water. The nonlinear interaction
between leaky S waves with two different frequencies can produce cumulative
0
combination harmonics at the sum frequency. Compared to the second harmonics
studied in Paper 3, the combination harmonics are less affected by the higher
harmonics produced by the instrumentations. In addition, mixing guided waves
with different frequencies provides more flexibility for the selection of guided wave
modes and excitation frequencies. In addition, the combination harmonics show a
better sensitivity to the early stage of fatigue damage than the second harmonics.
Chapter 6 summarizes the contributions and significance of the research
carried out in this thesis and provides recommendations for future studies.
8 |
ADE | Chapter 2
Chapter 2. Scattering characteristics of quasi-Scholte waves at
blind holes in metallic plates with one side exposed to water
Abstract
Corrosion is one of the major issues in metallic structures, especially those
operating in humid environments and submerged in water. It is important to detect
corrosion at its early stage to prevent further deterioration and catastrophic failures
of the structures. Guided wave-based damage detection technique is one of the
promising techniques for detecting and characterizing damage in structures. In
water-immersed plate structures, most of the guided wave modes have strong
attenuation due to energy leakage into the surrounding liquid. However, there is an
interface wave mode known as quasi-Scholte waves, which can propagate with low
attenuation. Therefore, this mode is promising for structural health monitoring
(SHM) applications. This paper presents an analysis of the capability of quasi-
Scholte waves in detecting internal corrosion-like defects in water-immersed
structures. A three-dimensional (3D) finite element (FE) model is developed to
simulate quasi-Scholte wave propagation and wave scattering phenomena on a steel
plate with one side exposed to water. The accuracy of the model is validated through
experimental measurements. There is good agreement between the FE simulations
and experimental measurements. The experimentally verified 3D FE model is then
employed in a series of parametric studies to analyze the scattering characteristics
of quasi-Scholte waves at circular blind holes with different diameters and depths,
which are the simplest representation of progressive corrosion. The findings of this
study can enhance the understanding of quasi-Scholte waves scattering at corrosion
damage of structures submerged in water and help improve the performance of in-
situ damage detection techniques.
Keywords: Quasi-Scholte waves; guided waves; scattering; submerged structure;
corrosion; metallic plate
12 |
ADE | Chapter 2
2.2. Introduction
Structures that have one side exposed to water are commonly encountered, such as
water tanks, pipelines, and ship hulls. These structures often incorporate plate-like
components, which are prone to corrosion as a result of electrochemical reactions
in the presence of water. Corrosion can occur in a localized region and deteriorate
the strength of the structures. It is important to detect and control corrosion so that
catastrophic failures and leakage can be avoided.
Among various structural health monitoring (SHM) techniques [1-3],
guided wave-based techniques have attracted increasing interest due to the ability
to inspect large areas compared to the conventional non-destructive evaluation
(NDE) techniques, high sensitivity to different types and small damage, and the
ability to inspect inaccessible locations. A review of guided wave-based SHM
techniques can be found in [4]. However, the majority of the studies on guided
waves have focused on the structures with traction free boundary conditions [5-8].
Meanwhile, there are limited studies on using guided waves for safety inspections
on structures submerged in water, especially the quasi-Scholte waves.
2.2.1. Damage detection of submerged structures using guided waves
Energy of guided waves in structures immersed in water can leak into the
surrounding medium so that most of the guided wave modes have high attenuation
characteristics, which significantly reduces the inspection area. As a result, the
practical applications are limited to specific guided wave modes and the excitation
frequencies need to be at their corresponding low attenuation frequency bands [9].
Several studies demonstrated the feasibility of using guided waves for damage
inspection in submerged structures. Na and Kundu [10] investigated the capability
of the flexural cylindrical guided wave modes in detecting defects in underwater
pipes. They found that the amplitudes of the transmitted signals would be decreased
after they passed through various types of damage in pipes. This phenomenon could
be used to evaluate the extent and distinguish the type of damage. Chen et al. [11]
employed the fundamental antisymmetric leaky lamb wave mode (leaky A waves)
0
to evaluate corrosion damage in a submerged metallic plate. The amplitudes and
14 |
ADE | Chapter 2
the speed of leaky A waves were found to be significantly affected by the
0
surrounding fluid medium. Pistone et al. [12] used a pulsed laser to generate guided
waves in a water-immersed aluminum plate and collected the wave signal by an
array of immersed transducers. They concluded that the fundamental symmetric
leaky lamb wave mode (leaky S waves), which had the fastest wave speed and the
0
least decay, could be used to detect cracks and holes in the plate. Sharma and
Mukherjee [13] used a pair of immersed ultrasonic transducers to generate and
measure guided waves in a steel plate, both sides of which were fully immersed in
water. Leaky S waves, the first order symmetric leaky lamb wave mode (leaky S
0 1
waves), and the first order anti-symmetric leaky lamb wave mode (leaky A waves)
1
were excited at their corresponding low attenuation frequency bands. Each of these
wave modes demonstrated a different sensitivity to notch-like defects and the
decrease in amplitudes of the transmitted signal could be related to the severity of
the damage. Takiy et al. [9] implemented experiment studies to verify the existence
of guided wave modes at their theoretically predicted low attenuation frequency
bands. It was confirmed that the higher order guided wave modes at their
corresponding low attenuation frequency bands were also suitable to be used for
damage detection in submerged structures.
2.2.2. Quasi-Scholte waves in immersed structures
In addition to the symmetric and anti-symmetric guided wave modes, there is an
interface wave mode known as quasi-Scholte waves existing at the water-plate
interface. This interface wave mode has low attenuation but it is rarely used for
evaluating damage in structures since it has been reported that a large proportion of
energy is propagating into the fluid at high frequencies [14]. However, it is found
that most of the wave energy of the quasi-Scholte mode at low excitation
frequencies is conserved in the structures during the propagation. Tian and Yu [15,
16] experimentally investigated guided wave propagation on a steel plate loaded
with water on a single side. They used a scanning laser Doppler vibrometer to
measure the wave signals along a line and plotted the data in the frequency-
wavenumber spectrum. It was demonstrated that leaky A waves were indiscernible
0
at low frequencies due to high attenuation while quasi-Scholte waves appeared
15 |
ADE | Chapter 2
clearly. Recently, Hayashi and Fujishima [17] studied the feasibility of using quasi-
Scholte waves for damage detection in a thin aluminum plate that had one side
immersed in water. The scattered waves due to a through-thickness notch could be
observed at the low-frequency range. It should be noted that this study only
measured the reflected signals. The scattering characteristics were not investigated.
The practical application of the guided waves relies on a distributed
transducer network, by which the guided wave signal is sequentially emitted by one
of the transducers, and the rest of the transducers are used to measure the impinging
waves. The majority of guided wave-based damage detection techniques employ
the waves scattered at the damage and received by the transducers at different
directions to detect and identify the damage [5, 18-20]. Therefore, understanding
the scattering characteristics at different directions plays an important role in the
development of the guided wave-based damage detection techniques. In the
literature, different studies investigated the scattering characteristics of guided
waves at different types of defects. However, the majority of the studies focused on
traction free conditions, and the scattering characteristics of guided waves in plates
loaded with water have not been well investigated. In particular, there are very
limited studies investigating the scattering characteristics of the interface wave
mode, quasi-Scholte waves, in plates loaded with water.
This paper presents comprehensive numerical and experimental analyses of
the scattering characteristics of quasi-Scholte waves at corrosion-like defects in
structures exposed to water, such as water tanks and pipelines. The numerical
method using a three-dimensional (3D) finite element (FE) model is employed to
investigate the guided wave propagation and scattering phenomena on a one-side
water-immersed steel plate with a circular blind hole that represents a corrosion
spot or wall thinning, which is exposed to water. The scattering characteristics are
investigated in terms of scattering directivity patterns (SDPs), which display the
energy distribution of the scattered waves around the damage. The findings of this
study provide a guide on the selection of appropriated excitation frequencies and
sensor locations to evaluate corrosion damage, which can advance the guided wave-
based damage detection techniques for submerged structures.
16 |
ADE | Chapter 2
This paper first presents the theoretical prediction of guided waves traveling
along a steel plate that has one side submerged in water in Section 2.3. Sections 2.4
and 2.5 describe the 3D FE simulation and experimental verification, respectively.
The accuracy of the simulation results is validated through experimental
measurements. Then, a series of numerical studies are carried out using the
experimentally verified 3D FE model to investigate the characteristics of the
scattered quasi-Scholte waves at blind holes with different dimensions in Section
2.6. Finally, discussions and conclusions are provided and drawn in Sections 2.7
and 2.8, respectively.
2.3. Guided waves in one-side water-immersed plates
Guided waves in plate-like structures are comprised of multiple symmetric and anti-
symmetric wave modes, which are represented by symbols S and A , respectively,
i i
with the subscript (i = 0, 1,…) representing the order of the wave modes. The
majority of the studies consider the plates that are placed open to the air. The
boundary conditions for the top and bottom sides of the plates are traction-free as
shown in Figure 2.1(a). The characteristic equation of the guided waves can be
described as [21]
tanqh 4k2qp
(2.1)
tanph k2 q22
for symmetric modes S , and
i
tanqh k2 q22
(2.2)
tanph 4k2qp
for anti-symmetric modes A , where hd 2; q2 w2 c2 k2; p2 w2 c2k2;
i T L
d , w, and k represent the plate thickness, circular frequency, and wavenumber,
respectively; c and c are the longitudinal wave speed and the transverse wave
L T
speed of the plate, respectively. It can be seen from Eqs (2.1) and (2.2) that the
characteristics of guided wave modes depend on the product of the plate thickness
and the frequency. The solutions can be presented as guided wave dispersion curves
17 |
ADE | Chapter 2
that describe the relationship between the frequency-thickness product and the
characteristics of the guided wave modes.
Figure 2.1. Boundary conditions (a) free plate; and (b) one-side water-immersed
plate
When one side of the plate is immersed in water, as shown in Figure 2.1(b),
the interface between the water and the plate is no longer traction free and the
guided wave propagation changes [22]. The wave energy can leak into the water
through out-of-plane motions of the particles at the water-plate interface. However,
the displacements of the water and the plate are discontinuous in the shear direction
because water cannot sustain shear loads [23, 24]. The governing equations of
guided waves in the one-side water-immersed plate can be expressed as [25, 26]
det Gw,k,c ,c ,c ,d,, 0 (2.3)
w T L w
where c and represent the bulk wave speed and density of water, respectively.
w w
G represents the characteristic matrix for the coupled fluid and solid waveguide.
By solving Eq (2.3), one can obtain the dispersion curves of guided waves for the
one-side water-immersed steel plate.
The calculation can be done by the commercial software DISPERSE, which
employs the global matrix method to calculate dispersion curves in a multi-layer
waveguide [27]. In this method, the bulk wave characteristics of each layer are first
determined from the corresponding material properties. Then, the stresses and
18 |
ADE | Chapter 2
displacements in each layer can be expressed in terms of the partial waves, which
are assembled into one large global matrix with the boundary conditions. The global
matrix can be solved for its modal response to find valid combinations of a certain
frequency, wavenumber, and attenuation. The process repeats until all dispersion
curves are traced.
Figure 2.2 shows the phase velocity and attenuation dispersion curves of a
steel plate that has its bottom surface immersed in water. There are three wave
modes within the frequency-thickness band up to 1 MHz-mm: quasi-Scholte waves,
leaky A waves, and leaky S waves. Unlike leaky A waves and leaky S waves,
0 0 0 0
quasi-Scholte waves are one of the interface wave modes that have the most energy
concentrated at the water-plate interface instead of radiating into the liquid [28]. In
general, the phase velocity of quasi-Scholte waves, at a given excitation frequency,
is much smaller than leaky S waves and leaky A waves as shown in Figure 2.2(a).
0 0
Smaller phase velocity means a shorter wavelength, which means higher sensitivity
to small defects [11]. In addition, the attenuation of quasi-Scholte waves is almost
zero for the entire frequency-thickness range (Figure 2.2(b)). Therefore, quasi-
Scholte waves theoretically have the potential for long-range inspection and are
expected to have a high sensitivity to damage.
Figure 2.2. (a) Phase velocity and (b) attenuation dispersion curves of 1 mm thick
steel plate with one side immersed in water
19 |
ADE | Chapter 2
Figures 2.3(a)-2.3(c) present the mode shapes of quasi-Scholte waves at 100
kHz-mm, 300 kHz-mm, and 500 kHz-mm as denoted by the three red dots in Figure
2.2(a). It should be noted that the mode shape diagram only demonstrates the
maximum amplitudes of the in-plane displacements and the out-of-plane
displacements. A 1mm thick steel plate is located in the upper region while the
bottom region represents the half-space water area. It can be seen that the
displacements in the plate comprise the main part of the total displacements at the
frequency-thickness range lower than 300 kHz-mm. This range is known as the
dispersive region, in which the phase velocity of quasi-Scholte waves changes
significantly with the product of the frequency and plate thickness as shown in
Figure 2.2(a). The range of frequency-thickness over 300 kHz-mm is the non-
dispersive region. In this region, the phase velocity of the quasi-Scholte wave is
almost constant. However, the deformation of the modeshape in the plate is
negligible compared to the deformation of the modeshape in the water as shown in
Figure 2.3(c). Due to this observation, the quasi-Scholte wave in the non-dispersive
region cannot be detected from the dry plate surface since most of the wave energy
concentrates at the waterside of the submerged plate. Therefore, the rest of the study
focuses on the frequency-thickness product values lower than 300 kHz-mm.
Figure 2.3. Theoretical mode shapes of quasi-Scholte waves at (a) 100 kHz-mm, (b)
300 kHz-mm, and (c) 500 kHz-mm. (red line denotes in-plane displacements; blue
line denotes out-of-plane displacements)
20 |
ADE | Chapter 2
2.4. Wave propagation and interaction simulation
3D FE simulation was used to simulate guided wave propagation on a steel plate
loaded with water on a single side. The commercial FE software, ABAQUS, was
used to generate the geometry and mesh the FE model. This study aims to
investigate the interaction of quasi-Scholte waves with blind holes, which is a local
phenomenon. Therefore, only a rectangular section of the plate was modeled with
absorbing regions attached to its edges to reduce unwanted waves reflected from
the boundaries and improve the computational efficiency. Figure 2.4 shows the
configuration of the 3D FE model. The dimension of the steel plate was 270 mm ×
320 mm × 2 mm (W LH ) with 40 mm wide absorbing regions applied to its
edges. The bottom surface was in contact with a 100 mm thick water layer. Table
2.1 summarizes the material properties of the steel plate and the water for the 3D
FE model. The plate and absorbing regions were discretized by 3D eight-node
reduced integration solid elements (C3D8R). The water layer was modeled using
3D eight-node reduced integration acoustic elements (AC3D8R). The interface
between the water and the steel plate was defined by surface-based tie constraint in
ABAQUS/Explicit, which tied the acoustic pressure on the fluid surface with the
displacements on the solid surface [29]. This allowed the wave energy in the plate
to transmit into the water through the out-of-plane displacements.
Table 2.1 Material properties of the steel and water used in the 3D FE model
Density Young’s Bulk modulus
Poisson’s
modulus
(kg/m3) (GPa) ratio (GPa)
Plate 7800 200 0.3 --
Water 1000 -- -- 2.2
The guided waves were excited on the top water-free surface through
applying the out-of-plane nodal displacements by a 5 mm diameter circular
transducer [30, 31]. The excitation signal was a five-cycle Hann window-modulated
sinusoidal tone bust [32]. In order to compare the FE simulations with experiment
results, the excitation frequency in this study was selected as 100 kHz, at which the
21 |
ADE | Chapter 2
The absorbing regions located at the four edges of the plate were divided
into 40 layers of which the mass-proportional damping coefficients (C ) gradually
M
increased from the innermost layer to the outmost layer. The absorbing layers can
avoid the wave reflections from the boundaries, and hence, it allows using a small
FE model to analyze the wave propagation and the scattering phenomena in a large
structure. The mass-proportional damping coefficient of each absorbing layer was
defined as [35, 36]
C C X(x3) (2.4)
M Mmax
where x represents the distance between the current layer and the interface
between the absorbing regions and the steel plate;
X x3
denotes a function of x,
whose value varies from 0 when x 0 to 1 at the outmost layer of the absorbing
region xx ; C is the mass-proportional damping coefficient of the outmost
max Mmax
layer in the absorbing region and was set as 3106, which was obtained by trial
and error [37].
The dynamic simulations were accomplished by the explicit module of
ABAQUS, which used the central-difference integration. For wave propagation
problems, it is recommended that the time step increment should be less than the
ratio of the minimum element size to the speed of the dilatational wave. In this study,
the increment time step was automatically determined by ABAQUS in all
simulations [38].
Figures 2.5(a) and 2.5(b) present the snapshots of the simulated out-of-plane
displacements in the 2 mm thick one-side water-immersed steel plate before and
after the guided wave interaction with a circular blind hole, respectively. The
excitation frequency was 100 kHz and the corresponding frequency-thickness
product was 200 kHz-mm, which was in the dispersion region of quasi-Scholte
waves. The diameter and depth of the blind hole were 10 mm and 1.5 mm,
respectively. Guided waves were excited and propagated omnidirectionally and
gradually diminished when they reached the absorbing layers as shown in Figure
2.5(b). There were no obvious boundary reflections observed from the plate edges.
After the interaction of the incident waves with the circular blind hole, part of wave
23 |
ADE | Chapter 2
energy transmitted through and there were some waves reflected from the blind
hole. Figures 2.5(c) and 2.5(d) show the contour snapshot of the corresponding
acoustic pressure in the water. It can be seen that there was only one wave packet
observed in the plate. This wave packet had a flexure mode shape and most of the
wave energy was confined to the water-plate interface rather than radiating into
water. Due to these features, it was identified that this wave packet was related to
the quasi-Scholte mode. The simulation results demonstrated that the out-of-plane
excitation on the surface of the one-sided water-loaded plate dominantly generates
the quasi-Scholte waves that are able to detect damage at the water-plate interface
by wave scattering.
Figure 2.5. Snapshots of the simulated out-of-plane displacements in a 2 mm thick
one-side water-immersed steel plate at different time instances; (a) before the
incident wave reaches the circular blind hole; (b) after interaction of the incident
wave with the circular blind hole; (c) and (d) the corresponding contour snapshots
of the acoustic pressure.
2.5. Experimental validation
To study the wave propagation in a plate with one side exposed to water, a test
metal tank was designed with the front wall being the test plate as shown in Figure
24 |
ADE | Chapter 2
2.6(a). The test plate was a 2 mm thick steel plate and the material properties are
given in Table 2.1. During the test, the metal tank was filled with water so that the
internal surface of the test plate was in contact with water while the external surface
of the test plate was exposed to the air. To validate the accuracy of the 3D FE model
to simulate guided wave scattering phenomena, a blind hole was drilled at the
internal surface of the test plate to model a corrosion pit (see, Figure 2.6(b)). A
Cartesian coordinate system was defined with the origin being located at the left
bottom of the test plate (see, Figure 2.6(a)). A circular piezoceramic transducer (5
mm diameter, 2 mm thickness) was mounted to the outer side (water-free surface)
of the test plate at x = 200 mm and y = 200 mm, and it was used as the actuator to
excite guided wave bursts. The excitation signal was generated by a function
generator (AFG 3021B) and the voltage was increased by an amplifier (Krohn-Hite
7500). The out-of-plane displacements at various scanning points were measured
by the non-contact laser scanning Doppler vibrometer (Polytec PSV-400-M2-20).
The excitation signal was a five-cycle Hann window-modulated sinusoidal tone
burst. The experimentally measured data were collected with a sampling rate of
10.26 MHz. The measured signals were filtered by applying a band-pass filter and
averaging procedure applied to 1000 recordings. The overall experiment setup is
shown in Figure 2.6(c).
25 |
ADE | Chapter 2
magnitudes of leaky A waves are too small to be observed due to its high
0
attenuation characteristics as shown in Figure 2.2(b). To further investigate the
accuracy of the 3D FE model, the phase velocity dispersion curves were calculated
with the same strategy for the experimental measurements and FE simulations.
The excitation frequency was swept from 70 kHz to 150 kHz in steps of 10
kHz. In this frequency range, the measured signals had a good signal-to-noise ratio
in the experiment. At each excitation frequency, the out-of-plane displacements
were collected at eleven points along the horizontal direction with a spatial step of
2 mm, which was less than half of the wavelength of the quasi-Scholte wave mode.
The measured time domain signals were then transformed into the frequency
domain by fast Fourier transform (FFT). After that, the phase of each measured
signal was calculated and the phase velocity between two measurements was
calculated by
2f
C (1)
p x
where and x are the phase difference and distance between the two
measurement points, respectively. C and f are the phase velocity and the central
p
frequency of the excitation, respectively. The phase velocity at each excitation
frequency was determined by taking the average of the calculated phase velocities
at the measurement points. Figure 2.7(b) presents the phase velocity dispersion
curves of quasi-Scholte waves calculated by DISPERSE, FE simulations, and
experimental measurements. The maximum deviation is less than 2%. There is good
agreement between the theoretically calculated, numerically simulated, and
experimentally measured phase velocity dispersion curves.
The measured signals were also converted into the time-frequency spectrum
by short-time Fourier transform (STFT) to determine the traveling time of quasi-
Scholte waves. The group velocity was calculated by
x
C f (2)
g c t
27 |
ADE | Chapter 2
where t is the difference of the time of arrival between the two measurement
points, which were away from each other by x. For the excitation frequency of
100 kHz, the group velocities obtained from the FE simulations and the
experimental measurements are 2143 m/s and 2131 m/s, respectively. They are very
close to the theoretical value of 2143 m/s calculated by DISPERSE. Therefore, it
can be concluded that the FE model can accurately simulate the wave on the steel
plate loaded with water on a single side.
Figure 2.7. (a) Typical FE simulated and experimentally measured signal at 100
kHz (black solid lines: simulation results; red dash lines: experimental results); (b)
Phase velocity dispersion curves from the theoretical calculation (solid black line),
FE simulations (black circles), and experimental measurements (red triangles).
2.5.2. Guided wave scattering at a blind hole
The accuracy of wave scattering simulation using the 3D FE model was
investigated through experimental measurements. A circular blind hole was drilled
at the internal surface of the plate as shown in Figure 2.6(b). The depth and the
diameter of the blind hole were measured to be 1.3 mm and 12 mm, respectively.
A polar coordinate system was defined with the origin being the center of the blind
hole as shown in Figure 2.6(a). Incident waves were excited by a piezoceramic
transducer located at r = 80 mm and θ = 180o. A scanning laser Doppler vibrometer
was employed to scan a circular path covered by 36 points at r = 50 mm, from 0o to
360o with the increment step of 10o. The 3D FE model of the damaged plate with
the same dimensions has a blind hole at the water-plate interface. The same strategy
28 |
ADE | Chapter 2
was employed to obtain the simulated out-of-plane displacements at the same 36
locations at the top surface (water-free surface).
Figure 2.8(a) shows a typical signal obtained from the FE simulations and
experimental measurements. The measurement point was located at r = 50 mm and
θ = 170o. The incident wave was the selected interface wave mode, the quasi-
Scholte wave, and a small magnitude of the scattered wave, which was generated
by the interaction of the quasi-Scholte wave with the blind hole. There is a small
phase shift in the scattered waves, which could be the result of a small misalignment
of the blind hole between the 3D FE model and the experiment. However, the
simulated scattering amplitudes relative to the incident wave were consistent with
the experimental measurements. Figure 2.8(b) shows the maximum absolute
amplitudes of the simulated and the experimentally measured signals, where the
amplitudes were normalized by the peak amplitudes of the signal at r =50 mm and
θ =180o. In general, the 3D FE model well predicted the experimental results. It
should be noted that although this study focuses on a particular excitation frequency,
the 3D FE model can simulate wave propagation for other excitation frequencies as
long as the size of elements is small enough to meet the minimum number of the
FE nodes per wavelength requirement.
Figure 2.8. (a) FE simulated and experimentally measured signal at r =50 mm, θ
=170o of the one-side water-immersed steel plate with a blind hole; (b) Polar
directivity patterns of the normalized maximum absolute amplitudes of quasi-
Scholte waves measured on the circular path.
29 |
ADE | Chapter 2
2.6. Scattering of quasi-Scholte waves due to circular blind holes at
the water-plate interface
The experimentally validated 3D FE model was employed in a series of parametric
studies to analyze the scattering characteristics of quasi-Scholte waves at circular
blind holes at the water-plate interface. The simulations were carried out for the
model with and without the blind hole so that the scattered waves could be extracted
by subtracting the signals of the intact model from those measured from the model
with the blind hole. The center of the blind hole was set as the origin of the polar
coordinate system. Guided waves were generated on the water-free side by a 5 mm
diameter circular transducer, of which the center was located at r = 80 mm and θ =
180o. The normal displacements were obtained at 36 nodal points which were
located at r = 50 mm and 0o < θ < 360o with a 10o step increment. Then, the SDPs
were determined by plotting the maximum magnitudes of the scattered waves in all
directions around the blind hole. The amplitudes of the SDPs were normalized by
the maximum absolute amplitudes of the wave signal at r =50 mm and θ =180o.
Figures 2.9(a)-2.9(c) show the SDPs of the 100 kHz incident quasi-Scholte waves
at the 2 mm, 6 mm, and 10 mm diameter circular blind holes with the depth of 0.5
mm located at the water-plate interface. The results indicate that the SDPs are
dependent on the size of the circular blind hole. For the 2 mm diameter circular
blind hole, the amplitudes of the reflected waves are comparable to the forward
scattering amplitudes. However, the forward scattered waves increase significantly
for the blind hole with larger diameters. The following sections investigate the
effect of the diameter and the depth of the blind hole on the SDPs.
30 |
ADE | Chapter 2
Figure 2.9. SDPs for the one-side water-loaded plate with (a) 2 mm, (b) 6 mm, and
(c) 10 mm diameter circular blind hole with 0.5 mm depth.
2.6.1. Influence of the diameter of the circular blind hole
The SDPs of quasi-Scholte waves have been shown to change significantly with the
size of the blind hole. This section explores the effect of the diameter of the blind
hole on the scattering phenomenon in terms of the blind hole diameter to
wavelength ratio (RDW). For a circular blind hole with a depth of 0.5 mm, the
forward scattering amplitudes are given in Figure 2.10(a) at θ = 0o, 20o, 40o, 60o,
80o, 280o, 300o, 320o, and 340o. For θ = 0o, 20o, and 340o, the amplitudes increase
with RDW and have relatively larger amplitudes than those in other directions. The
scattering amplitudes at θ = 40o and 320o rise until the RDW reaches 1.2 then reduce
with RDW. The magnitudes of the scattered waves at θ = 60o, 80o, 280o, and 300o
are small and exhibit slight fluctuation with RDW.
Figure 2.10(b) presents the backward scattering amplitudes at θ = 100o, 120o,
140o, 160o, 180o, 200o, 220o, 240o, and 260o. It can be seen that the overall behavior
of the scattering magnitudes in the backward direction is much more complicated
than that in the forward direction. For θ = 180o, 200o, 160o, 220o, 140o, 240o, and
120o, the amplitudes fluctuate following a sinusoidal pattern but the overall trend is
a slow increase. The minima of the scattering amplitudes at θ = 220o and 140o and
θ = 240o and 120o are obtained with RDW of around 1.2, which are slightly behind
the minima of scattered waves at θ = 180o, 200o, and 160o. Additionally, the
amplitudes at θ = 260o and 100o are considerably small and show moderate variation
with RDW. In general, the amplitudes of the backward scattered waves are smaller
than those in the forward directions. Besides, the scattering amplitudes are almost
31 |
ADE | Chapter 2
negligible in the directions perpendicular to the incident waves. Therefore, a sensor
located at these directions is unlikely to detect any differences between damaged
and undamaged plates.
Figure 2.10. Normalized amplitudes for (a) the forward scattered waves and (b) the
backward scattered waves at a circular blind hole in the one-side water-loaded steel
plate as a function of RDW.
2.6.2. Influence of the depth of the circular blind hole
The above section demonstrates that the scattering characteristics are dependent on
RDW. This section shows that the SDPs of quasi-Scholte waves also relate to the
depth of the circular blind hole. Figures 2.11(a) and 2.11(b) show the SDPs of the
100 kHz incident quasi-Scholte waves at the 6 mm diameter circular blind hole
with the depth being 1.0 mm and 1.5 mm located at the water-plate interface. Both
the forward and backward scattering amplitudes increase with the depth of the blind
hole. For shallow blind holes (Figures 2.9(b) and 2.11(a)), the forward scattering
amplitudes are much larger than the magnitudes of the backward scattered waves.
However, the backward and forward scattering amplitudes are comparable in the
case of deeper damage (Figure 2.11(b)). In addition, the scattering amplitudes at the
directions perpendicular to the incident wave are weak for shallow damage (Figures
2.9(b) and 2.11(a)) but they become comparable to those in other directions for the
deeper blind hole (Figure 2.11(b)). Therefore, it can be seen that both the diameter
and depth of the blind hole have a significant influence on the SDPs.
32 |
ADE | Chapter 2
Figure 2.11. SDPs for the one-side water-loaded plate with a 6 mm diameter circular
blind hole with a depth of (a) 1.0 mm and (b) 1.5 mm
2.7. Advantages of quasi-Scholte waves for damage detection
In the foregoing studies, it has been demonstrated that it is feasible to utilize guided
waves for detecting damages in submerged structural components. One of the
biggest challenges in terms of practical applications is that guided waves have
multimodal features. For example, within the frequency-thickness range up to 1
MHz-mm, there are only quasi-Scholte waves, leaky A waves, and leaky S waves
0 0
existing simultaneously on the one-side water-loaded steel plate. Other higher-order
wave modes will appear if the excitation frequency is higher [9]. When the
measured signals contain multiple guided wave modes, it is very difficult to extract
the damage-related wave signals that convey the information about the damage.
Therefore, the use of guided waves at low excitation frequencies for damage
detection is much more preferable since the measured signal has limited guided
wave modes, which does not require sophisticated signal processing techniques.
Among these aforementioned three wave modes at the low-frequency band,
leaky A waves and leaky S waves continuously radiate energy into the
0 0
surrounding medium. Leaky A waves have mostly out-of-plane displacements and
0
decay rapidly due to the significant energy leakage into water. While leaky S waves
0
have a small attenuation because it is dominated by the in-plane motions. But leaky
S waves are relatively insensitive to shallow surface corrosion since most of it is
0
33 |
ADE | Chapter 2
wave energy is confined to the mid-plane region of the plate [13, 40]. Unlike the
leaky A mode and the leaky S modes, the quasi-Scholte mode is an interface wave
0 0
mode whose energy is confined to the water-plate interface instead and does not
significantly radiate into the water. This behavior enables the quasi-Scholte wave
mode to travel over long distances with very low attenuation. In addition, the quasi-
Scholte wave mode has a much smaller wavelength than leaky A waves and leaky
0
S waves, which means that quasi-Scholte waves are more sensitive to small-scale
0
damage at the same excitation frequency. Sections 2.4 and 2.5 have numerically
and experimentally demonstrated that at low frequencies, quasi-Scholte waves
dominate over other wave modes when a circular piezoceramic transducer is
installed on the water-free surface of the one-side water-immersed plate to excite
guided waves. This phenomenon indicates that damage in the submerged structures
can be potentially detected and evaluated based on a single wave mode. This
significantly simplifies the practical implementations. In recognition of the above
observations, it can be finally concluded that the quasi-Scholte wave mode is
promising for damage detection in submerged structures. However, it should be
noted that only the quasi-Scholte waves at the low frequency-thickness range (in
the dispersive region) could be applicable for detecting damage in the submerged
structures. Because at higher frequencies where the quasi-Scholte mode is non-
dispersive, the signal of quasi-Scholte waves cannot be detected from the plate
surface since the displacements in the plate are negligible compared to the
displacements in the water (see Figure 2.3).
2.8. Conclusion
This paper has presented a study on guided wave propagation in a steel plate with
one side immersed in water for SHM application on water-filled tanks and pipes, in
particular, the focus has been directed on the interface wave mode, quasi-Scholte
waves, and its scattering characteristics at circular blind holes. This interface wave
mode at low frequencies has low attenuation and most of the excitation energy is
conserved in the structures during the propagation. A 3D FE model has been
developed to simulate the guided wave propagation in a steel plate exposed to water
on one side. It has been confirmed that the signal measured from the water-free
34 |
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