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Modelling jarosite precipitation in isothermal chalcopyrite bioleaching columns
Hydrometallurgy 98 (2009) 181–191
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Hydrometallurgy j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / h yd r o m e t
Modelling jarosite precipitation in isothermal chalcopyrite bioleaching columns Martin J. Leahy ⁎, M. Philip Schwarz CSIRO Minerals, Clayton, Victoria, 3168, Australia
a r t i c l e
i n f o
Article history: Received 22 January 2009 Received in revised form 23 April 2009 Accepted 24 April 2009 Available online 3 May 2009 Keywords: Model Heap leaching Bioleaching Jarosite Chalcopyrite Numerical model
a b s t r a c t Modelling chalcopyrite leaching involves accounting for the precipitation of jarosite and other iron hydroxide minerals; the difficulty in modelling these processes arises from uncertainty in the precipitation rate, and its dependence on the relevant variables (such as pH, Fe3+ concentration). Furthermore, an added complexity is accounting for the clogging of the macro and micro pore space, and its effects on leaching rate and liquid flow. There has been a lack of modelling of such processes in the literature, and in this work we focus on the inclusion of a basic model of jarosite precipitation with the associated removal of ferric ions from solution. The solubility criterion is formulated from experimental data of the log of ferric concentration versus pH: a linear slope in log Fe versus pH is apparent. This rule forms the basis for the solubility of ferric, and if the rule is met a first order dependence of the overall precipitation rate on the ferric is used. A rate constant for the precipitation rate is needed and a value chosen to provide reasonable model behaviour i.e. a reasonable amount of ferric is removed from solution: comparison with experimental data is needed to ensure appropriate model parameters are chosen. Four cases are considered: a base case, a case without the effects of jarosite precipitation, a higher inlet pH, and a reduced gangue acid consumption case. The base model results show jarosite precipitates after a distance of around 0.8 m below the inlet, at a position where the pH has risen sufficiently from the (lower) inlet value. In the higher inlet pH case, the spatial position where the onset of jarosite precipitation begins is further up in height in the column: the position is higher up because the jarosite criteria is met sooner, due to the pH being higher. Consequently, copper extraction is worse and perhaps non-intuitively, only a small percentage (1%) more overall jarosite precipitates than in the base case. In the reduced gangue acid consumption case, the pH is lower due to reduced acid consumption, and spatial position where the onset of jarosite precipitates begins is lower in the column; overall extraction is far better (89%) and jarosite precipitation is far less (67% less) than the base case. Crown Copyright © 2009 Published by Elsevier B.V. All rights reserved.
1. Introduction Heap bioleaching is a widely practiced leaching process for extracting copper and other metals from large piles of low grade ore, by dripping acid solution through the porous piles and subsequently collecting the metal in the acid solution. The majority of worldwide copper deposits are made up of chalcopyrite — of these, high grade ore can be processed via concentration and smelting. However, the low grade ore is largely unleachable (Watling, 2006) primarily because the passivation of the ore surface by jarosite and iron precipitates prevents ongoing leaching of chalcopyrite (Dixon et al., 2008; Pradhan et al., 2008). Furthermore, jarosite formation causes loss of ferric ions (a chalcopyrite leaching oxidant) from solution, and clogging of pore spaces, preventing solution flow on both a micro and macro-scale (Catalan and Li, 2000). Therefore successful heap leaching technology for low-grade chalcopyrite ores would be highly valued by the copper mining industry worldwide;
⁎ Corresponding author. Tel.: +61 395458360; fax: +61 395458380. E-mail address: [email protected] (M.J. Leahy).
understanding the leaching mechanisms and dynamics within chalcopyrite columns is likely to be central to the success. The literature for geochemical reactive transport modelling is extensive (for example a review in van der Lee and De Windt, 2001) and these often include aspects of jarosite precipitation (Mayer, 1999). However this field focuses on rather long term (tens to thousands of years) geochemical reaction processes and furthermore, has very little emphasis on bioleaching, where bacteria are involved in the catalysis of important oxidants, which is one of the main reactions involved in the shorter time scale of heap bioleaching. In the bioleaching field the literature has very few efforts focused on modelling of jarosite formation. However, one such example is an interesting modelling study by Linklater et al. (2005), which discusses a heap bioleaching operation where pyrite is leaching using oxygen as the main oxidant. Linklater et al. (2005) treat jarosite formation using a standard geochemical model and mineral database. Although chalcopyrite is included in the analysis, the emphasis of the paper is on pyrite oxidation rather than chalcopyrite oxidation. Furthermore, bacterial transport modelling in the form of an attachment and detachment sub model is not considered in that work, which is a standard facet in the literature concerning modelling of heap copper sulfide bioleaching
0304-386X/$ – see front matter. Crown Copyright © 2009 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.hydromet.2009.04.017
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(Leahy et al., 2005; Leahy, 2006; Bennett et al., 2003; Cross et al., 2006; Petersen and Dixon, 2007a,b). Since it is difficult to monitor the process internal to the heap, historically the process has been optimized by trial and error. More recently, comprehensive modelling of the transport of the important variables in the heap has been developed (Leahy et al., 2005; Leahy, 2006; Leahy et al., 2007; Bennett et al., 2003; Cross et al., 2006; Petersen and Dixon, 2007a,b) as a way to improving knowledge of the heap internal behaviour, and in some cases has been used for optimization of operating conditions (Cooper and Dixon, 2006). Typically these models have been developed for leaching of chalcocite — a common secondary copper sulfide (Petersen and Dixon, 2007a). The standard way to validate these models consists of comparing the model prediction to experimental data from an isothermal column, and this has been done for chalcocite ore by several authors. Although this model approach is in principle transferrable to chalcopyrite ore, validation for this case has not been reported in the literature, due to a lack of available data. Modelling chalcopyrite leaching requires accounting for the complication of jarosite and other iron precipitates; the difficulty in modelling these processes arise from:
2. Chemistry modelled
1. calculating the precipitation rate and its functional dependence on the relevant variables (such as pH, Fe3+ concentration), so that appropriate sources and sinks of the relevant species can be accounted for, and; 2. accounting for the clogging of the macro and micro pore space caused by the precipitates, and the subsequent effects on leaching rate and liquid flow.
2Fe
Dixon and Petersen (2003) suggested that jarosite precipitation could be accounted for by using the equilibrium of jarosite with ferric, but did not demonstrate these particular aspects of the model (or parameters) and importantly, they did not demonstrate its effects in the model results in any way. In this paper we attempt to overcome the first of the above limitations by incorporating a sub-model for jarosite precipitation and running the model for a chalcopyrite column bioleaching scenario. We leave the second aspect, clogging of pore spaces, for future work. The model discussed in this paper has been found to compare well with data from large column bioleaching experiments validated previously in chalcocite systems (Leahy et al., 2004; Leahy, 2006; Leahy and Schwarz, submitted for publication). There have been only limited model validation studies for well controlled industrial heap size leaching systems; however the model discussed in this paper has been compared in Leahy (2006) with limited heap scale (nonisothermal) data from Readett et al. (2003). Gebhardt et al. (2007) have also used the data for model validation. The model discussed accounts for the transport and reaction of various important species in heap and column bioleaching, including ferrous and ferric ions, copper ions, hydrogen ions, dissolved and gaseous oxygen, and bacteria (attached and free in solution). The transport of these species is coupled to the following reactions:
The chemistry (and the associated model of the chemistry) can be broken down into several distinct groups: • • • • •
the reaction of chalcopyrite as given in Eq. (1), the reaction of pyrite as given in Eq. (2), iron and sulfur bacterial reactions as given in Eqs. (3) and (4), gangue dissolution by acid in Eq. (5), and jarosite reactions in Eq. (6).
Reactions of the following species are taken into account in the model: Fe2+, Fe3+, H+, Cu2+, free and attached bacteria, dissolved oxygen and gaseous oxygen. Bioleaching of chalcopyrite occurs via the reaction 3þ
2þ
CuFeS2 þ 4Fe →Cu
2þ
þ 5Fe
0
þ 2S
ð1Þ
The dissolution of pyrite is described by: 3þ
FeS2 þ 8H2 O þ 14Fe
2þ
→15Fe
2−
þ
þ 2SO4 þ 16H
ð2Þ
Ferrous ions are re-oxidized to ferric ions in the presence of bacteria by the reaction 2 +
+ 0:5O2 + 2H
+
bacteria 3 → 2Fe
+
ð3Þ
+ H2 O
Sulfur and iron oxidizing acidophilic bacteria such as Acidithiobacillus ferrooxidans are involved when ferrous ions are catalyzed to ferric ions (Eq. (3)), and this increases the overall reaction rate significantly (Watling, 2006). Elemental sulfur produced in Eq. (1) may also be oxidized by Acidithiobacillus ferrooxidans and Sulfobacillus-like bacteria as in Eq. (4): bacteria 0 S + 1:5O2 + H2 O→ H2 SO4
ð4Þ
Gangue minerals are leached by acid, for example for gypsum: þ
CaCO3 þ H →Ca
2þ
−
þ HCO3
ð5Þ
There are many other gangue minerals which are typically present, with the proportion and liberation of each very dependent on ore type. The gangue minerals also react at different rates. Generally, carbonates (e.g. gypsum, siderite) leach much faster than silicates (e.g. quartz, feldspar). Due to these complexities it is often easier to model the acid consumption by gangue (Eq. (5)) — via a bulk term which uses a single rate constant, which is adjusted to achieve the measured pH in the effluent. This is the approach taken in this work. Alternatively individual reactions can be used with a rate constant for each derived from the literature or from specially designed experiments. The latter is a difficult method to apply because although rates are available in the literature, it is hard to know the effective exposure of the minerals which depends in a complex way on liberation and grade. Precipitation of jarosite is typically described by the following reaction (where potassium may be replaced by Na+): þ
3þ
K þ 3Fe
2−
þ
þ 2SO4 þ 6H2 O↔KFe3 ðSO4 Þ2 ðOHÞ6 þ 6H
ð6Þ
• the leaching of copper (and iron) sulfides due to ferric ions, • bacterial consumption of ferrous ions and associated regeneration of ferric ions, • consumption of acid by bacteria, gangue, and acid production by pyrite, and • jarosite precipitation, and the consequent reduction in chalcopyrite leaching rate due to loss of ferric ions.
The reaction is believed to be non-reversible in chalcopyrite systems, so the back reaction is not considered in this work. Note that we are taking jarosite to mean jarosite or substituted similar minerals such as schwertmannite, ferrihydrite, other stoichiometries of oxyhydroxysulfates.
The paper has the following structure: a description of the chemistry is given followed by the model description, numerical modelling aspects, the main results, and finally the conclusions are given.
3.1. General model
3. Leaching model description
A schematic of the 1D column is shown in Fig. 1. In the model we assume the liquid flow in the column is vertically straight down under
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183
Fig. 1. Schematic heap/column leaching system, and schematic close-up of spherical ore particle leaching under shrinking core kinetics. In the column H is the height, and W represents the width of the column, though the latter is not important in a 1D setting.
gravity; likewise, air flow is also assumed to be uniform and vertically upwards. The only effect of the air flow in this work is to introduce the oxygen which transfers to the liquid phase. The transport equation for oxygen in the gas phase is not shown here, but is represented by a simple advection diffusion equation as described in Leahy et al. (2005). An isothermal model is used in this work, without the effects of variation in temperature, though the model generalizes to include the effects of heat transfer, as discussed in a previous paper by these workers (Leahy et al., 2005). We use a constant superficial liquid velocity which corresponds to that used in the column (around |uL| = 5 L/m2/h): this corresponds to an interstitial liquid velocity given by |vL| = |uL|/εL) where εL is the volume fraction of liquid. The transport equation for the following liquid species concentration Cj(y,t) (kg/m3) at time t (seconds) is given by the advection–diffusion equation for the species in liquid: dissolved oxygen (CL (kg/m3)), free bacteria (Cϕ (bacteria/m3)), ferrous ions (CFe2+ (kg/m3)) and ferric ions (CFe3+ (kg/m3)), hydrogen ions (CH+ (kg/m3)) and copper ions (CCu2+ (kg/m3)) as: 2
eL
ACj A Cj ACj = DL eL + Sj − vL eL At Ay Ay2
ð7Þ
where DL is the diffusion (and dispersion) coefficient for the species in the liquid phase, and Sj (kg/m3/s) is the source/sink term for species j. Note that the velocity vL is taken to be negative (with respect to direction y shown in Fig. 1). More details of the source terms for these species are given below. The attached bacterial population variable Cψ(y,t) is described by an equation similar to Eq. (7) without the advection or diffusion terms i.e. just the transient and source terms, i.e. ρore
ACψ = Sψ At
ð8Þ
where Sψ (kg/m3/s) is the source/sink term for species attached bacteria, with details of the source term given below. The bulk density of the porous medium, is given by ρore =εsρs where εs is the volume fraction of solid and ρs is the intrinsic ore density. The remaining volume fraction, that of air is given by εair =1−(εs + εL). The variable describing the mass of precipitated jarosite (CJarosite(y,t) (kg/m3)), is taken to be proportional to the mass of reacted ferric ion according to the stoichiometry of reaction (6), and is described by the following equation: eL
ACjarosite = Sjarosite At
ð9Þ
3.2. Bacterial reaction rate The growth rate μ (1/s) for both attached and free bacteria is given by μ = μ max f ðT Þ
CL CFe2þ CH + CL + KM;O CFe2þ + KM;Fe CH + + KM;H
ð10Þ
where KM,O (kg/m3) is the half growth rate constant for oxygen, KM,Fe (kg/m3) is the half growth rate constant for ferrous ions, KM,H+ (kg/ m3) is the half growth rate constant for the free acid concentration (CH), μmax is the maximum growth rate coefficient (1/s) and f(T) (−) is the growth function dependent on temperature T (K), which is set to a value 1 in this work (since we consider isothermal conditions at a constant temperature of T = 313.15 K, where it is assumed bacteria are under optimal temperature conditions). The total bacteria concentration ϕT(y,t) (bacteria per unit total volume) is given as the sum of bacteria in liquid, and bacteria attached to particle surfaces, given by /T = eL C/ + ρore Cψ
ð11Þ
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where Cϕ, Cψ are the liquid bacterial concentration (free swimming) and attached bacterial concentration, respectively. 3.3. Free hydrogen ions The source for hydrogen ions (CH+) is based on reactions (from Eqs. (2)–(6)) and is given by: SH+ = −
MH+ μ/T 2R1 MH+ 16R2 MH+ + + MFe Y MCuFeS2 MPy
− μ gangue CH+ +
ð12Þ
6Mjarosite μ jarosite CFe3þ 3MFe
where μgangue (1/s) is the gangue acid consumption rate, MCuFeS2 (g/ mol) denotes the molecular weight of chalcopyrite, MPy (g/mol) is the molecular weight of pyrite, and the ratio of 6 to 3 refers to the stoichiometric ratio with ferric in Eq. (6). The reaction rates R1 and R2 are described in the next section. The jarosite rate constant in the final term in Eq. (12) is described in detail in Section 3.5. Note that term 2 in Eq. (12) corresponds to the acid produced when we combine Eqs. (1) and (4), where we assume the elemental sulfur is consumed quickly (Eq. (4)). We do not account for the elemental sulfur build up in the resultant combination of Eqs. (1) and (4). 3.4. Copper and iron sulfide leaching The rate of leaching of chalcopyrite (i = 1) and iron sulfide (pyrite) (i = 2) are given by Ri = ρore Gi
Aα i At
ð13Þ
lower the pH the more ferric that can be contained in solution. For example, above pH 2 a ferric at a concentration of 0.56 kg/m3 can remain soluble. But at pH 1.5 a ferric at a concentration of 2.9 kg/m3 can remain soluble. Therefore the criterion that jarosite precipitates at pH above 2 is only relevant at ferric concentrations above 0.56 kg/m3, which is typically often achieved in heap leaching scenarios, where ferric may be as high as 3 kg/m3 in practice (Readett et al., 2003). Until now the modelling and description of this process has not been discussed in literature: we use a criterion derived from Fig. 2 to develop a model for when jarosite precipitates. Precipitation rate is modelled by the last term in Eq. (15) which is controlled by a switching function which is either on or off depending if the criterion from Fig. 2 is met. The source for ferrous (Fe2+) and ferric ions (Fe3+) is based on reactions (from Eqs. (1)–(3) and (6)) given by ! 5R1 MFe 15R2 MFe ð14Þ + MCuFeS2 MPy ! ðμ − kdeath Þ/T 4R1 MFe 14R2 MFe − μ jarosite CFe3þ ð15Þ − = + Y MCuFeS2 MPy
SFe2+ = − SFe3+
ðμ − kdeath Þ/T + Y
The “rate constant” in the final term in Eq. (15) is a switching function, which depends on whether the rule (which is a straight line y = mX + C fitted to experimental data in Fig. 2) is met or not, which can be described by μ jarosite = μ jarosite;0
if y N mX + C
μ jarosite = 0 if y V mX + C
ð16Þ ð17Þ
where αi(y,t) (−) is the chalcopyrite or pyrite fraction (mineral species i) leached from the ore (αi = 1 is 100% leached) given by the shrinking core equation, as described in Leahy et al. (2005) and Leahy (2006).
where μjarosite,0 (1/s) is a constant jarosite precipitation rate which prescribes how fast jarosite precipitates, and is unknown but is approximated to give reasonable model behaviour: ideally experimental data would be used for fitting this unknown. The straight line described in Eqs. (16) and (17) has the variables defined as follows:
3.5. Ferrous and ferric ions
y = log10 Fe3+
Anecdotal evidence in the heap leaching community suggests if the pH is higher than 2 then jarosite is likely to precipitate in chalcopyrite bioleaching systems, but there is some degree of confusion surrounding this critical pH value. Data of ferric in solution versus pH (Watling, 2008) is shown in Fig. 2, which indicates a log linear dependence of the ferric in solution to the pH: it shows that the
m = slope of log line; X = pH; C = constant of intersection ðpH = 0Þ
ð18Þ
The constants m and C are chosen so the line described in Eq. (18) approximately overlays the straight line fit to the data, as shown in Fig. 2. The overall jarosite precipitation rate will depend on the number of sites for precipitation, which should be very large given the high surface area of particles. The precipitation rate would be greater than the rate of other processes, and the solution would always be in quasi-equilibrium. The results are likely to be independent of the actual rate, because it is so large. This assumption will be tested in future work. 3.6. Jarosite precipitation Jarosite is assumed to form on particle surfaces and to remain there, so that the jarosite concentration variable is not convected with the liquid. It is also assumed that jarosite cannot be redissolved. The source for the jarosite variable related to formation by reaction (6) is written as follows: Sjarosite =
Fig. 2. Log (Fe3+) versus pH data from Watling (2008) from chalcopyrite leaching systems. The data suggest a log linear dependence, typical of solubility dependence curves. Precipitation is taken to occur above the fitted line.
Mjarosite μ C 3þ 3MFe jarosite Fe
ð19Þ
where Mjarosite is the molecular weight of jarosite, and the 3 in the denominator refers to the stoichiometric ratio with ferric in Eq. (6).
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185
convergence would be very important in a two-dimensional and three-dimensional fluid flow framework, and remains as future work.
Table 1 Operating conditions of column assumed in the model. Parameter
Value
Total grade of copper G1 Pyrite grade G2 Temperature T (K) Superficial liquid flow velocity (m/s) pH onfluent (solution applied) – Base case, Case 2, and Case 4 – Case 3 Ferrous iron (Fe2+) onfluent (kg/m3) Ferric iron (Fe3+) onfluent (kg/m3) Superficial liquid flow velocity (L/m2/h) Superficial air flow velocity (m3/m2/h) Bacterial pulse (for 1000 s) (cells/m3liquid)
0.7% 0.7% 313.15 2.5 × 10− 2
5. Modelling results and discussion
1.25 (2.757 kg/m3 H2SO4) 1.5 (1.55 kg/m3 H2SO4) 0.1 1 5 2 1 × 1014
The modelling results are shown in Fig. 3(a–e) at various times: we refer to this case as the base case. Jarosite begins to precipitate around 4.2 m height as shown in Fig. 3(e). As mentioned in the modelling section (Section 3) the jarosite precipitated is represented as a scalar variable with units kg/m3. A steady state is achieved for the pH, bacteria ferrous and ferric concentrations. However, the jarosite concentration and copper extraction continue to change steadily over time. In the top 0.8 m (above 4.2 m height) of the column there is no jarosite precipitation — and this is because the pH is too low near the inlet where the pH is 1.25. However at a height of around 4.2 m the jarosite begins to precipitate because the pH rises above about 1.7, while the ferric concentration is high enough for the precipitation to occur. The jarosite precipitation rate declines because ferric is removed from solution by jarosite precipitation: the ferric decline with depth is typical of first order source term and jarosite follows this shape. Precipitation continues to occur further down the column but there is an interplay between the ferric ions available for precipitation and the rising pH due to gangue acid consumption (and bacterial consumption). However, the rule for precipitation in Eqs. (16) and (17) is still met and jarosite still precipitates in the whole column below where it begins at 4.2 m height. The consequence of the ferric ion concentration being severely reduced is that the chalcopyrite leaching Fig. 3(b) is clearly reduced in regions of the column where jarosite is precipitating. This is simply due to the reduction in ferric ions; in addition it is expected that jarosite will further reduce leaching rate by inhibiting intra-particle diffusion at the ore surface. The latter effect needs to be included in future work. Visual evidence of a correspondence between solution channelling and jarosite precipitation has been reported by Catalan and Li (2000) and others. It is likely that the jarosite would cause pore space clogging and prevent even solution flow due to solution channelling: this current work suggests that such an effect is most likely to occur in the upper part of a heap — just below the top (less than 1 m). If the jarosite is indeed most abundant in the upper part of the heap, then this may upset the solution flow for the remainder of the bed below.
5.1. Base case — effect of jarosite precipitation
3.7. Other transport equations We refer the reader to previous publications (Leahy et al., 2005; Leahy, 2006) for further information regarding several other source terms, in particular for oxygen in both gas and liquid phases, copper (Cu2+), bacteria free in solution and bacteria attached to the ore. Note that the bacterial dynamics include growth, attachment and detachment, and attachment and detachment are taken to be occurring for both free and attached bacteria i.e. when bacterial attachment occurs, bacteria are removed from solution, and vice versa: when detachment occurs, bacteria to be added to solution. All conditions and parameters as assumed in the model are summarized in Tables 1 and 2. 4. Numerical solution The source term in Eq. (19) is controlled by the condition in Eqs. (16) and (17) i.e., the term can be zero if the condition is not met, or non-zero (if condition is met), and may be discontinuous so that neighbouring cells can have zero and non-zero formation rates. This can lead to “wobbles” or zig-zag patterns in space and time. To ensure convergence with these discontinuities, we found a small time step (125 s was used) and spatial step (100 cells over 5 m, or spacing of 5 mm was used) is needed compared to the case where jarosite is not included, and that the iteration of the equations at each time step is vital, with up to 20 iterations per time step and an under-relaxation technique needed. The under-relaxation reduces the convergence rate and increases the number of iterations, but the model results remain stable and smooth. This solution technique, with a small time step, small grid spacing and more iterations per time step, means that obtaining the solution takes much longer than would otherwise be needed without jarosite precipitation. This has ramifications for solving these equations coupled to two-dimensional or threedimensional fluid flow. A numerical technique which speeds up
5.2. Case 2 — no jarosite precipitation We now remove the jarosite precipitation term from the model equations to quantify how significant jarosite precipitation is. As shown in Fig. 4, the jarosite precipitation terms have a fairly substantial effect on the overall leaching behaviour. In particular, the
Table 2 Model parameters used for modelling. Parameter
Value
Reference
Interstitial liquid velocity vL (m/s) Temperature T (K) Half growth rate constant KM,O, KM,Fe, KM\H+ (kg/m3) Solid (ore) intrinsic density ρs (kg/m3) Volume fractions εs, εL, εair(−) Maximum bacterial growth rate μmax, kdeath (1/s) Yield Y (bacteria/kg Fe2+) Jarosite precipitation rate μjarosite,0 (1/s) m, C Gangue reaction rate μgangue (1/s) – Base case, Case 2, and Case 3 – Case 4
− 6.944 × 10− 6 313.15 1.6 × 10− 3, 5.58 × 10− 3, 2.055 × 10− 3 2700 0.6, 0.2, 0.2 3.0556 × 10− 5 3.7 × 1013 2 × 10− 6 − 1.4319, 0.8679
Petersen and Dixon (2003) Assumed Leahy et al. (2005), Petersen and Dixon (2003) Leahy et al. (2005) Leahy et al. (2005) Leahy et al. (2005) Leahy et al. (2005) Assumed Fitted line parameters to data Assumed
1.99 × 10− 6 4 × 10− 7
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Fig. 3. Model predicted variables at various times versus height from base (m): (a) pH, (b) total (fraction) copper extracted (−), (c) total bacterial concentration (log plot) (bacteria/ m3), (d) Fe3+ concentration, (e) Fe2+ concentration (log plot) and (f) jarosite precipitated.
ferric ions in solution are much higher over a much larger part of the column (compared with Fig. 3). Consequently, the chalcopyrite leaching remains fairly uniform at all depths and is not significantly reduced as was the case in this region (where jarosite precipitated) in the base case. However, there is some reduction in leaching extent in the lower part of the column and this is due to the pH becoming too high (partly due to gangue consumption, partly due to bacteria consumption) for bacteria to survive, and thus reducing the production of ferric ions. Overall leaching and pregnant leaching solution (PLS) behaviour is shown in Fig. 5 for the case with and without jarosite precipitation: this figure indicates (as also shown in the spatial plots Figs. 3 and 4) the ferric is severely reduced in solution when jarosite precipitation is accounted for in the model, and this is also seen in the overall copper extraction. The overall extraction for these two cases (and other cases considered in this paper) can be seen in Table 3.
base case, despite having only 1% more averaged jarosite precipitated (see Table 3). The difference in these percentages can also be seen by observing the area under the curves in Fig. 6. This result is perhaps non-intuitive, in that it might be expected that reduced leaching would be associated with a proportional increase in jarosite precipitation: this is due to the fact that less ferric is available for precipitation — because more of it is used in chalcopyrite (and pyrite) leaching. This non-intuitive result shows the usefulness of modelling in column and heap bioleaching. The fact that a higher inlet pH leads to worse copper extraction is not surprising, and is consistent with industrial findings, where it is standard practice to keep the inlet pH as low as possible. However, the advantages of this strategy must be balanced against increased loss of acid in leaching gangue minerals, which tends to be proportional to the acid concentration. We address this aspect in the following section.
5.3. Case 3 — inlet pH = 1.5
5.4. Case 4 — reduced acid consumption rate by gangue leaching
Here we discuss the case of a decrease of the acid concentration at the inlet (higher pH = 1.5, from base case of 1.25): the results at one time instant are shown in Fig. 6 together with those of the base case. We see that the position where jarosite begins to precipitate moves upward for higher inlet pH. This is due to the pH criteria for jarosite precipitation being met more easily in the higher inlet pH case. We show the overall copper extraction and PLS variables for the two cases in Fig. 7: it is interesting to note that the case with the inlet pH of 1.5 (i.e. pH of 0.25 higher than base case and roughly double the acid concentration) had 14.8% worse overall copper extraction than the
Here we discuss the case (case 4) where gangue acid consumption is reduced by 20% of base case value — which is represented by Eq. (5) and with a first order rate model in Eq. (15) (last term). Fig. 8 shows the results as spatial plots at various times (Fig. 8), the spatial plots together with the base case at only one time instant (Fig. 9), and the time variation together with the base case (Fig. 10). In Figs. 8 and 9 we see the spatial variation the jarosite precipitation is quite different to the base case. The pH remains much lower (Fig. 9(a)) which is due to the reduced gangue acid consumption rate; consequently jarosite (Fig. 9(e)) does not precipitate until around the mid-height (or 2.5 m
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187
Fig. 4. No jarosite precipitation. Model predicted variables at various times versus height from base (m): (a) pH, (b) total (fraction) copper extracted (−), (c) total bacterial concentration (log plot) (bacteria/m3), (d) Fe3+ concentration, (e) Fe2+ concentration (log plot) and (f) jarosite precipitated.
Fig. 5. Time plots (days) for Case 2 (no jarosite precipitation) and base case. (a) overall (fraction) copper extracted, (b) average jarosite precipitated, (c) ferric concentration in PLS, and (d) pH in PLS.
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Table 3 Comparison (%) of overall results (at end of simulation after 116 days) for each case, as compared with base case.
Base Case Case 2 – no jarosite precipitation included Case 3 – inlet pH (increased by 0.25 pH units) Case 4 – gangue rate constant (20% reduction of base case value)
% Change in overall extraction (+ indicates increased extraction, – indicates decreased)
% Change in overall jarosite precipitated (+ indicates increased precipitation, – indicates reduced precipitation)
0 +80.3%
0 0
− 14.8%
+1%
+89%
−67%
height), as compared to the base case where jarosite precipitates around 4.2 m height. The maximum jarosite precipitation (less than 40 kg/m3) is less than in the base case, where the maximum value is as high as 110 kg/m3. The average jarosite precipitation for reduced rate case (Fig. 10(b)) is 67% of the base case value, as shown in Table 3. The corresponding increase in chalcopyrite leached is 89%. Case 4 (gangue rate reduction) was found to have the most significant effect on jarosite and overall copper extraction. We note for the reduced rate case in Fig. 9 (dashed line) that the copper extraction looks very similar to the shape of case 2 (no jarosite
precipitation), but the shape is not due to the pH being too high, rather it is due to jarosite precipitation removing ferric ions from solution.
6. Conclusions This paper discusses the column bioleaching model for chalcopyrite, incorporating the effects of jarosite precipitation. The underlying model has been validated previously in chalcocite systems. We model jarosite precipitation using a simple rule based model for when jarosite is precipitating, which has not previously been attempted in the literature. The conclusions we draw from this work are: • The model predicts jarosite precipitation in the top region of the column, where the pH becomes high enough (far enough away from inlet), and where the ferric is high enough to allow this. • The overall effect of jarosite precipitation was quantified by comparing the results with the case where jarosite precipitation was not included in the model: in this case we found an increase in overall copper extraction of 80%, as compared with the base case. • A higher inlet pH caused the height at which jarosite precipitation begins to be higher up in the column, and as expected, copper extraction reduced, declining by 14.8% as compared with the base case. Unexpectedly, this resulted in only 1% more jarosite being precipitated (average over whole column), which was due to the fact that the position where jarosite begins to precipitate moves higher in the column, but has less ferric available for precipitation (since more of it is used in chalcopyrite (and pyrite) leaching).
Fig. 6. Base case and inlet pH = 1.5 case (Case 3). Model predicted variables at one time instant (at 116 days) versus height from base (m): (a) pH, (b) total (fraction) copper extracted (−), (c) total bacterial concentration (log plot) (bacteria/m3), (d) Fe3+ concentration, (e) Fe2+ concentration (log plot) and (f) jarosite precipitated.
M.J. Leahy, M.P. Schwarz / Hydrometallurgy 98 (2009) 181–191
189
Fig. 7. Time plots (days) for Case 3 (inlet pH=1.5 case) and base case. (a) overall (fraction) copper extracted, (b) average jarosite precipitated, (c) ferric concentration in PLS, and (d) pH in PLS.
Fig. 8. Base case and reduced gangue rate (case 4). Model predicted variables at various times versus height from base (m): (a) pH, (b) total (fraction) copper extracted (−), (c) total bacterial concentration (log plot) (bacteria/m3), (d) Fe3+ concentration, (e) Fe2+ concentration (log plot) and (f) jarosite precipitated.
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Fig. 9. Base case and reduced gangue rate (case 4). Model predicted variables at one time instant (at 116 days) versus height from base (m): (a) pH, (b) total (fraction) copper extracted (−), (c) total bacterial concentration (log plot) (bacteria/m3), (d) Fe3+ concentration, (e) Fe2+ concentration (log plot) and (f) jarosite precipitated.
Fig. 10. Time plots (days) for Case 4 (reduced gangue rate) and base case. (a) overall (fraction) copper extracted, (b) average jarosite precipitated, (c) ferric concentration in PLS, and (d) pH in PLS.
M.J. Leahy, M.P. Schwarz / Hydrometallurgy 98 (2009) 181–191
• Reducing the gangue acid consumption rate constant had the strongest effect on the jarosite precipitation (which decreased by 67% as compared with the base case) and associated copper extraction (increased by 89%). The reduced rate constant caused the pH to remain much lower throughout the column, and jarosite precipitation began at the mid-height of the column, compared to the top 0.8 m in the base case. In future work, the modelling needs to be closely compared with experimental column data. One of the benefits would be improving rate constant determination for the precipitation rate. The experiment would need to be able to elucidate the connection between jarosite precipitation and inhibited particle scale leaching, due to particle surface coverage by jarosite. This may involve doing very small particle scale experiments which can investigate fine detail behaviour. In future work, clogging of the macroscopic pore space and permeability reduction need to be coupled with the liquid flow model used: close connection with experimental evidence is necessary. Coupling of the modelling of liquid flow with jarosite precipitation and associated reduction in permeability is also a future aspect that needs to be addressed. There have been only limited model validation studies for industrial heap size leaching systems in which the leaching and measurements are well controlled, and future work should address this. Nomenclature Concentration (kg/m3) of the following species: j = L (dissolved oxygen), j = Fe2+ (ferrous ions), j = Fe3+ (ferric ions) j = ϕ (free bacteria), j = H+ (free acid ion concentration), j = Cu2+ (copper ion concentration) y Distance from the bottom of the heap/column (m) t Time (s) Superficial Liquid Flow Velocity (m/s) uL Interstitial Liquid Flow Velocity (m/s) vL Source term for species j (kg/m3/s) Sj Grade (−) of copper sulfide (i = 1) and pyrite (i = 2) Gi KM,O, KM,Fe, KM\H+ The half growth rate constant for the oxygen in liquid concentration, ferrous ion concentration and free acid concentration (kg/m3) and f(T) (−) is the growth temperature dependence function, Density of solid (s) (kg/m3) ρs εs ,εL,εair Volume fraction (−) of solid liquid and air, respectively. μmax, kdeath μmax is the maximum growth rate coefficient (1/s), and death rate coefficient (1/s), respectively. Yield (Y) Yield coefficient (bacteria/kg Fe2+) μjarosite,0 Jarosite precipitation rate (1/s) m, C Log linear fitted line function parameters, slope m (−), and constant of intersection C (log10(kg/m3)) Gangue rate constant (1/s) μgangue f(T) Bacterial function of temperature (−) Cj
Acknowledgements The authors gratefully acknowledge Helen Watling for many helpful discussions.
191
References Bennett, C.R., Cross, M., Croft, T.N., Uhrie, J.L., Green, C.R., Gebhardt, J.E., 2003. A comprehensive copper stockpile leach model: background and model formulation. Hydrometallurgy 2003. Leaching and Solution Purification, vol. 1. TMS, pp. 315–328. Catalan, L., Li, M., 2000. Decommissioning of copper heap-leach residues by rinsing with water and alkaline solutions — a pilot scale study. Environmental Engineering Science 17 (4), 191–202. Cooper, G., Dixon, S., 2006. Modeling chalcocite leaching. SME Annual Meeting March 27–March 29, 2006, St. Louis, MO, vol. 4. Cross, M., Bennett, C.R., Croft, T.N., McBride, D., Gebhardt, J.E., 2006. Computational Modeling of reactive multi-phase flows in porous media: applications to metals extraction and environmental recovery processes. Minerals Engineering 19, 1098–1108. Dixon, D., Petersen, J., 2003. Comprehensive modelling study of chalcocite column and heap bioleaching. In: Riveros, P.A., Dixon, D.G., Dreisinger, D.B., Menacho, J. (Eds.), Hydrometallurgy of Copper, Proceedings of Copper 2003, vol. 6. CIM-MetSoc, Montreal, pp. 493–516. Dixon, D.G., Mayne, D.D., Baxter, K.G., 2008. Galvanox™) — A novel galvanically-assisted atmospheric leaching technology for copper concentrates conference information: John Dutrizac International Symposium on Copper Hydrometallurgy, 2007 Toronto, Canada. Canadian Metallurgical Quarterly 47 (3), 327–336. Gebhardt, J.E., Hernandez, A., Cross, M., Bennett, C.R., McBride, D., 2007. Analysis of heap leaching processes with modelling and simulation tools. In: Houlachi, G.E., Edwards, J.D., Robinson, T.G. (Eds.), Copper-Cobre 2007. CIM, Montreal, Canada, pp. 231–243. Leahy, M.J., 2006. Temperature and air flow effects in the modelling of bacteria in heap bioleaching of chalcocite, PhD thesis, The University of Melbourne Australia. Leahy, M.J. and Schwarz, M.P., submitted for publication. Experimental modelling validation for isothermal columns. To be submitted to Hydrometallurgy. Leahy, M., Davidson, M., Schwarz, M., 2004. A column bioleaching model for chalcocite: an investigation of oxygen limitation and bacterial inoculation on leaching. BACMIN Proceedings. AusIMM, Bendigo, Australia, pp. 41–47. Leahy, M.J., Davidson, M.R., Schwarz, M.P., 2005. A model for heap bioleaching of chalcocite with heat balance: bacterial temperature dependence. Minerals Engineering 18, 1239–1252. Leahy, M.J., Davidson, M.R., Schwarz, M.P., 2007. A model for heap bioleaching of chalcocite with heat balance: mesophiles and moderate thermophiles. Hydrometallurgy 85, 24–41. Linklater, C.M., Sinclair, D.J., Brown, P.L., 2005. Coupled chemistry and transport modelling of sulphidic waste rock dumps at the Aitik mine site, Sweden. Applied Geochemistry 20 (2), 275–293. Mayer, K.U., 1999. A numerical model for multicomponent reactive transport in variably saturated porous media, PhD thesis, Waterloo, Canada. Petersen, J., Dixon, D., 2003. The dynamics of chalcocite heap bioleaching. In: Young, C., Alfantazi, A., Anderson, C., Dreisinger, D., Harris, B., James, A. (Eds.), Hydrometallurgy 2003 — Fifth International Conference in Honour of Professor Ian Ritchie, Leaching and Solution Purification, vol. 1. TMS, Warrendale, PA, pp. 351–364. Petersen, J., Dixon, D., 2007a. Principles, mechanisms and dynamics of chalcocite heap bioleaching. In: Donati, E., Sand, W. (Eds.), Microbial Processing of Metal Sulfides. Springer Verlag, Berlin. Petersen, J., Dixon, D., 2007b. Modeling and optimization of heap bioleach processes. In: Donati, E., Sand, W. (Eds.), Microbial Processing of Metal Sulfides. Springer Verlag, Berlin. Pradhan, N., Nathsarma, K.C., Srinivasa Rao, K., Sukla, L.B., Mishra, B.K., 2008. Heap bioleaching of chalcopyrite: a review. Minerals Engineering 21, 355–365. Readett, D., Sylwestrzak, L., Franzmann, P., Plumb, J., Robertson, W., Gibson, J., Watling, H., 2003. The life cycle of a chalcocite heap bioleach system. In: Young, C., Alfantazi, A., Anderson, C., Dreisinger, D., Harris, B., James, A. (Eds.), Hydrometallurgy 2003 — Fifth International Conference in honour of Professor Ian Ritchie Volume 1: Leaching and Solution Purification. Vancouver, Canada, August 24–27 2003. TMS, Warrendale, Pennsylvania, USA, pp. 365–374. van der Lee, J., De Windt, 2001. Present state and future directions of modelling of geochemistry in hydrogeological systems. Journal of Contaminant Hydrology 47, 265–282. Watling, H.R., 2006. The bioleaching of sulphide minerals with emphasis on copper sulphides — a review. Hydrometallurgy 84, 81–108. Watling, H.R., 2008, Personal communication.
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Hydrometallurgy j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / h yd r o m e t
Modelling jarosite precipitation in isothermal chalcopyrite bioleaching columns Martin J. Leahy ⁎, M. Philip Schwarz CSIRO Minerals, Clayton, Victoria, 3168, Australia
a r t i c l e
i n f o
Article history: Received 22 January 2009 Received in revised form 23 April 2009 Accepted 24 April 2009 Available online 3 May 2009 Keywords: Model Heap leaching Bioleaching Jarosite Chalcopyrite Numerical model
a b s t r a c t Modelling chalcopyrite leaching involves accounting for the precipitation of jarosite and other iron hydroxide minerals; the difficulty in modelling these processes arises from uncertainty in the precipitation rate, and its dependence on the relevant variables (such as pH, Fe3+ concentration). Furthermore, an added complexity is accounting for the clogging of the macro and micro pore space, and its effects on leaching rate and liquid flow. There has been a lack of modelling of such processes in the literature, and in this work we focus on the inclusion of a basic model of jarosite precipitation with the associated removal of ferric ions from solution. The solubility criterion is formulated from experimental data of the log of ferric concentration versus pH: a linear slope in log Fe versus pH is apparent. This rule forms the basis for the solubility of ferric, and if the rule is met a first order dependence of the overall precipitation rate on the ferric is used. A rate constant for the precipitation rate is needed and a value chosen to provide reasonable model behaviour i.e. a reasonable amount of ferric is removed from solution: comparison with experimental data is needed to ensure appropriate model parameters are chosen. Four cases are considered: a base case, a case without the effects of jarosite precipitation, a higher inlet pH, and a reduced gangue acid consumption case. The base model results show jarosite precipitates after a distance of around 0.8 m below the inlet, at a position where the pH has risen sufficiently from the (lower) inlet value. In the higher inlet pH case, the spatial position where the onset of jarosite precipitation begins is further up in height in the column: the position is higher up because the jarosite criteria is met sooner, due to the pH being higher. Consequently, copper extraction is worse and perhaps non-intuitively, only a small percentage (1%) more overall jarosite precipitates than in the base case. In the reduced gangue acid consumption case, the pH is lower due to reduced acid consumption, and spatial position where the onset of jarosite precipitates begins is lower in the column; overall extraction is far better (89%) and jarosite precipitation is far less (67% less) than the base case. Crown Copyright © 2009 Published by Elsevier B.V. All rights reserved.
1. Introduction Heap bioleaching is a widely practiced leaching process for extracting copper and other metals from large piles of low grade ore, by dripping acid solution through the porous piles and subsequently collecting the metal in the acid solution. The majority of worldwide copper deposits are made up of chalcopyrite — of these, high grade ore can be processed via concentration and smelting. However, the low grade ore is largely unleachable (Watling, 2006) primarily because the passivation of the ore surface by jarosite and iron precipitates prevents ongoing leaching of chalcopyrite (Dixon et al., 2008; Pradhan et al., 2008). Furthermore, jarosite formation causes loss of ferric ions (a chalcopyrite leaching oxidant) from solution, and clogging of pore spaces, preventing solution flow on both a micro and macro-scale (Catalan and Li, 2000). Therefore successful heap leaching technology for low-grade chalcopyrite ores would be highly valued by the copper mining industry worldwide;
⁎ Corresponding author. Tel.: +61 395458360; fax: +61 395458380. E-mail address: [email protected] (M.J. Leahy).
understanding the leaching mechanisms and dynamics within chalcopyrite columns is likely to be central to the success. The literature for geochemical reactive transport modelling is extensive (for example a review in van der Lee and De Windt, 2001) and these often include aspects of jarosite precipitation (Mayer, 1999). However this field focuses on rather long term (tens to thousands of years) geochemical reaction processes and furthermore, has very little emphasis on bioleaching, where bacteria are involved in the catalysis of important oxidants, which is one of the main reactions involved in the shorter time scale of heap bioleaching. In the bioleaching field the literature has very few efforts focused on modelling of jarosite formation. However, one such example is an interesting modelling study by Linklater et al. (2005), which discusses a heap bioleaching operation where pyrite is leaching using oxygen as the main oxidant. Linklater et al. (2005) treat jarosite formation using a standard geochemical model and mineral database. Although chalcopyrite is included in the analysis, the emphasis of the paper is on pyrite oxidation rather than chalcopyrite oxidation. Furthermore, bacterial transport modelling in the form of an attachment and detachment sub model is not considered in that work, which is a standard facet in the literature concerning modelling of heap copper sulfide bioleaching
0304-386X/$ – see front matter. Crown Copyright © 2009 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.hydromet.2009.04.017
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(Leahy et al., 2005; Leahy, 2006; Bennett et al., 2003; Cross et al., 2006; Petersen and Dixon, 2007a,b). Since it is difficult to monitor the process internal to the heap, historically the process has been optimized by trial and error. More recently, comprehensive modelling of the transport of the important variables in the heap has been developed (Leahy et al., 2005; Leahy, 2006; Leahy et al., 2007; Bennett et al., 2003; Cross et al., 2006; Petersen and Dixon, 2007a,b) as a way to improving knowledge of the heap internal behaviour, and in some cases has been used for optimization of operating conditions (Cooper and Dixon, 2006). Typically these models have been developed for leaching of chalcocite — a common secondary copper sulfide (Petersen and Dixon, 2007a). The standard way to validate these models consists of comparing the model prediction to experimental data from an isothermal column, and this has been done for chalcocite ore by several authors. Although this model approach is in principle transferrable to chalcopyrite ore, validation for this case has not been reported in the literature, due to a lack of available data. Modelling chalcopyrite leaching requires accounting for the complication of jarosite and other iron precipitates; the difficulty in modelling these processes arise from:
2. Chemistry modelled
1. calculating the precipitation rate and its functional dependence on the relevant variables (such as pH, Fe3+ concentration), so that appropriate sources and sinks of the relevant species can be accounted for, and; 2. accounting for the clogging of the macro and micro pore space caused by the precipitates, and the subsequent effects on leaching rate and liquid flow.
2Fe
Dixon and Petersen (2003) suggested that jarosite precipitation could be accounted for by using the equilibrium of jarosite with ferric, but did not demonstrate these particular aspects of the model (or parameters) and importantly, they did not demonstrate its effects in the model results in any way. In this paper we attempt to overcome the first of the above limitations by incorporating a sub-model for jarosite precipitation and running the model for a chalcopyrite column bioleaching scenario. We leave the second aspect, clogging of pore spaces, for future work. The model discussed in this paper has been found to compare well with data from large column bioleaching experiments validated previously in chalcocite systems (Leahy et al., 2004; Leahy, 2006; Leahy and Schwarz, submitted for publication). There have been only limited model validation studies for well controlled industrial heap size leaching systems; however the model discussed in this paper has been compared in Leahy (2006) with limited heap scale (nonisothermal) data from Readett et al. (2003). Gebhardt et al. (2007) have also used the data for model validation. The model discussed accounts for the transport and reaction of various important species in heap and column bioleaching, including ferrous and ferric ions, copper ions, hydrogen ions, dissolved and gaseous oxygen, and bacteria (attached and free in solution). The transport of these species is coupled to the following reactions:
The chemistry (and the associated model of the chemistry) can be broken down into several distinct groups: • • • • •
the reaction of chalcopyrite as given in Eq. (1), the reaction of pyrite as given in Eq. (2), iron and sulfur bacterial reactions as given in Eqs. (3) and (4), gangue dissolution by acid in Eq. (5), and jarosite reactions in Eq. (6).
Reactions of the following species are taken into account in the model: Fe2+, Fe3+, H+, Cu2+, free and attached bacteria, dissolved oxygen and gaseous oxygen. Bioleaching of chalcopyrite occurs via the reaction 3þ
2þ
CuFeS2 þ 4Fe →Cu
2þ
þ 5Fe
0
þ 2S
ð1Þ
The dissolution of pyrite is described by: 3þ
FeS2 þ 8H2 O þ 14Fe
2þ
→15Fe
2−
þ
þ 2SO4 þ 16H
ð2Þ
Ferrous ions are re-oxidized to ferric ions in the presence of bacteria by the reaction 2 +
+ 0:5O2 + 2H
+
bacteria 3 → 2Fe
+
ð3Þ
+ H2 O
Sulfur and iron oxidizing acidophilic bacteria such as Acidithiobacillus ferrooxidans are involved when ferrous ions are catalyzed to ferric ions (Eq. (3)), and this increases the overall reaction rate significantly (Watling, 2006). Elemental sulfur produced in Eq. (1) may also be oxidized by Acidithiobacillus ferrooxidans and Sulfobacillus-like bacteria as in Eq. (4): bacteria 0 S + 1:5O2 + H2 O→ H2 SO4
ð4Þ
Gangue minerals are leached by acid, for example for gypsum: þ
CaCO3 þ H →Ca
2þ
−
þ HCO3
ð5Þ
There are many other gangue minerals which are typically present, with the proportion and liberation of each very dependent on ore type. The gangue minerals also react at different rates. Generally, carbonates (e.g. gypsum, siderite) leach much faster than silicates (e.g. quartz, feldspar). Due to these complexities it is often easier to model the acid consumption by gangue (Eq. (5)) — via a bulk term which uses a single rate constant, which is adjusted to achieve the measured pH in the effluent. This is the approach taken in this work. Alternatively individual reactions can be used with a rate constant for each derived from the literature or from specially designed experiments. The latter is a difficult method to apply because although rates are available in the literature, it is hard to know the effective exposure of the minerals which depends in a complex way on liberation and grade. Precipitation of jarosite is typically described by the following reaction (where potassium may be replaced by Na+): þ
3þ
K þ 3Fe
2−
þ
þ 2SO4 þ 6H2 O↔KFe3 ðSO4 Þ2 ðOHÞ6 þ 6H
ð6Þ
• the leaching of copper (and iron) sulfides due to ferric ions, • bacterial consumption of ferrous ions and associated regeneration of ferric ions, • consumption of acid by bacteria, gangue, and acid production by pyrite, and • jarosite precipitation, and the consequent reduction in chalcopyrite leaching rate due to loss of ferric ions.
The reaction is believed to be non-reversible in chalcopyrite systems, so the back reaction is not considered in this work. Note that we are taking jarosite to mean jarosite or substituted similar minerals such as schwertmannite, ferrihydrite, other stoichiometries of oxyhydroxysulfates.
The paper has the following structure: a description of the chemistry is given followed by the model description, numerical modelling aspects, the main results, and finally the conclusions are given.
3.1. General model
3. Leaching model description
A schematic of the 1D column is shown in Fig. 1. In the model we assume the liquid flow in the column is vertically straight down under
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183
Fig. 1. Schematic heap/column leaching system, and schematic close-up of spherical ore particle leaching under shrinking core kinetics. In the column H is the height, and W represents the width of the column, though the latter is not important in a 1D setting.
gravity; likewise, air flow is also assumed to be uniform and vertically upwards. The only effect of the air flow in this work is to introduce the oxygen which transfers to the liquid phase. The transport equation for oxygen in the gas phase is not shown here, but is represented by a simple advection diffusion equation as described in Leahy et al. (2005). An isothermal model is used in this work, without the effects of variation in temperature, though the model generalizes to include the effects of heat transfer, as discussed in a previous paper by these workers (Leahy et al., 2005). We use a constant superficial liquid velocity which corresponds to that used in the column (around |uL| = 5 L/m2/h): this corresponds to an interstitial liquid velocity given by |vL| = |uL|/εL) where εL is the volume fraction of liquid. The transport equation for the following liquid species concentration Cj(y,t) (kg/m3) at time t (seconds) is given by the advection–diffusion equation for the species in liquid: dissolved oxygen (CL (kg/m3)), free bacteria (Cϕ (bacteria/m3)), ferrous ions (CFe2+ (kg/m3)) and ferric ions (CFe3+ (kg/m3)), hydrogen ions (CH+ (kg/m3)) and copper ions (CCu2+ (kg/m3)) as: 2
eL
ACj A Cj ACj = DL eL + Sj − vL eL At Ay Ay2
ð7Þ
where DL is the diffusion (and dispersion) coefficient for the species in the liquid phase, and Sj (kg/m3/s) is the source/sink term for species j. Note that the velocity vL is taken to be negative (with respect to direction y shown in Fig. 1). More details of the source terms for these species are given below. The attached bacterial population variable Cψ(y,t) is described by an equation similar to Eq. (7) without the advection or diffusion terms i.e. just the transient and source terms, i.e. ρore
ACψ = Sψ At
ð8Þ
where Sψ (kg/m3/s) is the source/sink term for species attached bacteria, with details of the source term given below. The bulk density of the porous medium, is given by ρore =εsρs where εs is the volume fraction of solid and ρs is the intrinsic ore density. The remaining volume fraction, that of air is given by εair =1−(εs + εL). The variable describing the mass of precipitated jarosite (CJarosite(y,t) (kg/m3)), is taken to be proportional to the mass of reacted ferric ion according to the stoichiometry of reaction (6), and is described by the following equation: eL
ACjarosite = Sjarosite At
ð9Þ
3.2. Bacterial reaction rate The growth rate μ (1/s) for both attached and free bacteria is given by μ = μ max f ðT Þ
CL CFe2þ CH + CL + KM;O CFe2þ + KM;Fe CH + + KM;H
ð10Þ
where KM,O (kg/m3) is the half growth rate constant for oxygen, KM,Fe (kg/m3) is the half growth rate constant for ferrous ions, KM,H+ (kg/ m3) is the half growth rate constant for the free acid concentration (CH), μmax is the maximum growth rate coefficient (1/s) and f(T) (−) is the growth function dependent on temperature T (K), which is set to a value 1 in this work (since we consider isothermal conditions at a constant temperature of T = 313.15 K, where it is assumed bacteria are under optimal temperature conditions). The total bacteria concentration ϕT(y,t) (bacteria per unit total volume) is given as the sum of bacteria in liquid, and bacteria attached to particle surfaces, given by /T = eL C/ + ρore Cψ
ð11Þ
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where Cϕ, Cψ are the liquid bacterial concentration (free swimming) and attached bacterial concentration, respectively. 3.3. Free hydrogen ions The source for hydrogen ions (CH+) is based on reactions (from Eqs. (2)–(6)) and is given by: SH+ = −
MH+ μ/T 2R1 MH+ 16R2 MH+ + + MFe Y MCuFeS2 MPy
− μ gangue CH+ +
ð12Þ
6Mjarosite μ jarosite CFe3þ 3MFe
where μgangue (1/s) is the gangue acid consumption rate, MCuFeS2 (g/ mol) denotes the molecular weight of chalcopyrite, MPy (g/mol) is the molecular weight of pyrite, and the ratio of 6 to 3 refers to the stoichiometric ratio with ferric in Eq. (6). The reaction rates R1 and R2 are described in the next section. The jarosite rate constant in the final term in Eq. (12) is described in detail in Section 3.5. Note that term 2 in Eq. (12) corresponds to the acid produced when we combine Eqs. (1) and (4), where we assume the elemental sulfur is consumed quickly (Eq. (4)). We do not account for the elemental sulfur build up in the resultant combination of Eqs. (1) and (4). 3.4. Copper and iron sulfide leaching The rate of leaching of chalcopyrite (i = 1) and iron sulfide (pyrite) (i = 2) are given by Ri = ρore Gi
Aα i At
ð13Þ
lower the pH the more ferric that can be contained in solution. For example, above pH 2 a ferric at a concentration of 0.56 kg/m3 can remain soluble. But at pH 1.5 a ferric at a concentration of 2.9 kg/m3 can remain soluble. Therefore the criterion that jarosite precipitates at pH above 2 is only relevant at ferric concentrations above 0.56 kg/m3, which is typically often achieved in heap leaching scenarios, where ferric may be as high as 3 kg/m3 in practice (Readett et al., 2003). Until now the modelling and description of this process has not been discussed in literature: we use a criterion derived from Fig. 2 to develop a model for when jarosite precipitates. Precipitation rate is modelled by the last term in Eq. (15) which is controlled by a switching function which is either on or off depending if the criterion from Fig. 2 is met. The source for ferrous (Fe2+) and ferric ions (Fe3+) is based on reactions (from Eqs. (1)–(3) and (6)) given by ! 5R1 MFe 15R2 MFe ð14Þ + MCuFeS2 MPy ! ðμ − kdeath Þ/T 4R1 MFe 14R2 MFe − μ jarosite CFe3þ ð15Þ − = + Y MCuFeS2 MPy
SFe2+ = − SFe3+
ðμ − kdeath Þ/T + Y
The “rate constant” in the final term in Eq. (15) is a switching function, which depends on whether the rule (which is a straight line y = mX + C fitted to experimental data in Fig. 2) is met or not, which can be described by μ jarosite = μ jarosite;0
if y N mX + C
μ jarosite = 0 if y V mX + C
ð16Þ ð17Þ
where αi(y,t) (−) is the chalcopyrite or pyrite fraction (mineral species i) leached from the ore (αi = 1 is 100% leached) given by the shrinking core equation, as described in Leahy et al. (2005) and Leahy (2006).
where μjarosite,0 (1/s) is a constant jarosite precipitation rate which prescribes how fast jarosite precipitates, and is unknown but is approximated to give reasonable model behaviour: ideally experimental data would be used for fitting this unknown. The straight line described in Eqs. (16) and (17) has the variables defined as follows:
3.5. Ferrous and ferric ions
y = log10 Fe3+
Anecdotal evidence in the heap leaching community suggests if the pH is higher than 2 then jarosite is likely to precipitate in chalcopyrite bioleaching systems, but there is some degree of confusion surrounding this critical pH value. Data of ferric in solution versus pH (Watling, 2008) is shown in Fig. 2, which indicates a log linear dependence of the ferric in solution to the pH: it shows that the
m = slope of log line; X = pH; C = constant of intersection ðpH = 0Þ
ð18Þ
The constants m and C are chosen so the line described in Eq. (18) approximately overlays the straight line fit to the data, as shown in Fig. 2. The overall jarosite precipitation rate will depend on the number of sites for precipitation, which should be very large given the high surface area of particles. The precipitation rate would be greater than the rate of other processes, and the solution would always be in quasi-equilibrium. The results are likely to be independent of the actual rate, because it is so large. This assumption will be tested in future work. 3.6. Jarosite precipitation Jarosite is assumed to form on particle surfaces and to remain there, so that the jarosite concentration variable is not convected with the liquid. It is also assumed that jarosite cannot be redissolved. The source for the jarosite variable related to formation by reaction (6) is written as follows: Sjarosite =
Fig. 2. Log (Fe3+) versus pH data from Watling (2008) from chalcopyrite leaching systems. The data suggest a log linear dependence, typical of solubility dependence curves. Precipitation is taken to occur above the fitted line.
Mjarosite μ C 3þ 3MFe jarosite Fe
ð19Þ
where Mjarosite is the molecular weight of jarosite, and the 3 in the denominator refers to the stoichiometric ratio with ferric in Eq. (6).
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convergence would be very important in a two-dimensional and three-dimensional fluid flow framework, and remains as future work.
Table 1 Operating conditions of column assumed in the model. Parameter
Value
Total grade of copper G1 Pyrite grade G2 Temperature T (K) Superficial liquid flow velocity (m/s) pH onfluent (solution applied) – Base case, Case 2, and Case 4 – Case 3 Ferrous iron (Fe2+) onfluent (kg/m3) Ferric iron (Fe3+) onfluent (kg/m3) Superficial liquid flow velocity (L/m2/h) Superficial air flow velocity (m3/m2/h) Bacterial pulse (for 1000 s) (cells/m3liquid)
0.7% 0.7% 313.15 2.5 × 10− 2
5. Modelling results and discussion
1.25 (2.757 kg/m3 H2SO4) 1.5 (1.55 kg/m3 H2SO4) 0.1 1 5 2 1 × 1014
The modelling results are shown in Fig. 3(a–e) at various times: we refer to this case as the base case. Jarosite begins to precipitate around 4.2 m height as shown in Fig. 3(e). As mentioned in the modelling section (Section 3) the jarosite precipitated is represented as a scalar variable with units kg/m3. A steady state is achieved for the pH, bacteria ferrous and ferric concentrations. However, the jarosite concentration and copper extraction continue to change steadily over time. In the top 0.8 m (above 4.2 m height) of the column there is no jarosite precipitation — and this is because the pH is too low near the inlet where the pH is 1.25. However at a height of around 4.2 m the jarosite begins to precipitate because the pH rises above about 1.7, while the ferric concentration is high enough for the precipitation to occur. The jarosite precipitation rate declines because ferric is removed from solution by jarosite precipitation: the ferric decline with depth is typical of first order source term and jarosite follows this shape. Precipitation continues to occur further down the column but there is an interplay between the ferric ions available for precipitation and the rising pH due to gangue acid consumption (and bacterial consumption). However, the rule for precipitation in Eqs. (16) and (17) is still met and jarosite still precipitates in the whole column below where it begins at 4.2 m height. The consequence of the ferric ion concentration being severely reduced is that the chalcopyrite leaching Fig. 3(b) is clearly reduced in regions of the column where jarosite is precipitating. This is simply due to the reduction in ferric ions; in addition it is expected that jarosite will further reduce leaching rate by inhibiting intra-particle diffusion at the ore surface. The latter effect needs to be included in future work. Visual evidence of a correspondence between solution channelling and jarosite precipitation has been reported by Catalan and Li (2000) and others. It is likely that the jarosite would cause pore space clogging and prevent even solution flow due to solution channelling: this current work suggests that such an effect is most likely to occur in the upper part of a heap — just below the top (less than 1 m). If the jarosite is indeed most abundant in the upper part of the heap, then this may upset the solution flow for the remainder of the bed below.
5.1. Base case — effect of jarosite precipitation
3.7. Other transport equations We refer the reader to previous publications (Leahy et al., 2005; Leahy, 2006) for further information regarding several other source terms, in particular for oxygen in both gas and liquid phases, copper (Cu2+), bacteria free in solution and bacteria attached to the ore. Note that the bacterial dynamics include growth, attachment and detachment, and attachment and detachment are taken to be occurring for both free and attached bacteria i.e. when bacterial attachment occurs, bacteria are removed from solution, and vice versa: when detachment occurs, bacteria to be added to solution. All conditions and parameters as assumed in the model are summarized in Tables 1 and 2. 4. Numerical solution The source term in Eq. (19) is controlled by the condition in Eqs. (16) and (17) i.e., the term can be zero if the condition is not met, or non-zero (if condition is met), and may be discontinuous so that neighbouring cells can have zero and non-zero formation rates. This can lead to “wobbles” or zig-zag patterns in space and time. To ensure convergence with these discontinuities, we found a small time step (125 s was used) and spatial step (100 cells over 5 m, or spacing of 5 mm was used) is needed compared to the case where jarosite is not included, and that the iteration of the equations at each time step is vital, with up to 20 iterations per time step and an under-relaxation technique needed. The under-relaxation reduces the convergence rate and increases the number of iterations, but the model results remain stable and smooth. This solution technique, with a small time step, small grid spacing and more iterations per time step, means that obtaining the solution takes much longer than would otherwise be needed without jarosite precipitation. This has ramifications for solving these equations coupled to two-dimensional or threedimensional fluid flow. A numerical technique which speeds up
5.2. Case 2 — no jarosite precipitation We now remove the jarosite precipitation term from the model equations to quantify how significant jarosite precipitation is. As shown in Fig. 4, the jarosite precipitation terms have a fairly substantial effect on the overall leaching behaviour. In particular, the
Table 2 Model parameters used for modelling. Parameter
Value
Reference
Interstitial liquid velocity vL (m/s) Temperature T (K) Half growth rate constant KM,O, KM,Fe, KM\H+ (kg/m3) Solid (ore) intrinsic density ρs (kg/m3) Volume fractions εs, εL, εair(−) Maximum bacterial growth rate μmax, kdeath (1/s) Yield Y (bacteria/kg Fe2+) Jarosite precipitation rate μjarosite,0 (1/s) m, C Gangue reaction rate μgangue (1/s) – Base case, Case 2, and Case 3 – Case 4
− 6.944 × 10− 6 313.15 1.6 × 10− 3, 5.58 × 10− 3, 2.055 × 10− 3 2700 0.6, 0.2, 0.2 3.0556 × 10− 5 3.7 × 1013 2 × 10− 6 − 1.4319, 0.8679
Petersen and Dixon (2003) Assumed Leahy et al. (2005), Petersen and Dixon (2003) Leahy et al. (2005) Leahy et al. (2005) Leahy et al. (2005) Leahy et al. (2005) Assumed Fitted line parameters to data Assumed
1.99 × 10− 6 4 × 10− 7
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Fig. 3. Model predicted variables at various times versus height from base (m): (a) pH, (b) total (fraction) copper extracted (−), (c) total bacterial concentration (log plot) (bacteria/ m3), (d) Fe3+ concentration, (e) Fe2+ concentration (log plot) and (f) jarosite precipitated.
ferric ions in solution are much higher over a much larger part of the column (compared with Fig. 3). Consequently, the chalcopyrite leaching remains fairly uniform at all depths and is not significantly reduced as was the case in this region (where jarosite precipitated) in the base case. However, there is some reduction in leaching extent in the lower part of the column and this is due to the pH becoming too high (partly due to gangue consumption, partly due to bacteria consumption) for bacteria to survive, and thus reducing the production of ferric ions. Overall leaching and pregnant leaching solution (PLS) behaviour is shown in Fig. 5 for the case with and without jarosite precipitation: this figure indicates (as also shown in the spatial plots Figs. 3 and 4) the ferric is severely reduced in solution when jarosite precipitation is accounted for in the model, and this is also seen in the overall copper extraction. The overall extraction for these two cases (and other cases considered in this paper) can be seen in Table 3.
base case, despite having only 1% more averaged jarosite precipitated (see Table 3). The difference in these percentages can also be seen by observing the area under the curves in Fig. 6. This result is perhaps non-intuitive, in that it might be expected that reduced leaching would be associated with a proportional increase in jarosite precipitation: this is due to the fact that less ferric is available for precipitation — because more of it is used in chalcopyrite (and pyrite) leaching. This non-intuitive result shows the usefulness of modelling in column and heap bioleaching. The fact that a higher inlet pH leads to worse copper extraction is not surprising, and is consistent with industrial findings, where it is standard practice to keep the inlet pH as low as possible. However, the advantages of this strategy must be balanced against increased loss of acid in leaching gangue minerals, which tends to be proportional to the acid concentration. We address this aspect in the following section.
5.3. Case 3 — inlet pH = 1.5
5.4. Case 4 — reduced acid consumption rate by gangue leaching
Here we discuss the case of a decrease of the acid concentration at the inlet (higher pH = 1.5, from base case of 1.25): the results at one time instant are shown in Fig. 6 together with those of the base case. We see that the position where jarosite begins to precipitate moves upward for higher inlet pH. This is due to the pH criteria for jarosite precipitation being met more easily in the higher inlet pH case. We show the overall copper extraction and PLS variables for the two cases in Fig. 7: it is interesting to note that the case with the inlet pH of 1.5 (i.e. pH of 0.25 higher than base case and roughly double the acid concentration) had 14.8% worse overall copper extraction than the
Here we discuss the case (case 4) where gangue acid consumption is reduced by 20% of base case value — which is represented by Eq. (5) and with a first order rate model in Eq. (15) (last term). Fig. 8 shows the results as spatial plots at various times (Fig. 8), the spatial plots together with the base case at only one time instant (Fig. 9), and the time variation together with the base case (Fig. 10). In Figs. 8 and 9 we see the spatial variation the jarosite precipitation is quite different to the base case. The pH remains much lower (Fig. 9(a)) which is due to the reduced gangue acid consumption rate; consequently jarosite (Fig. 9(e)) does not precipitate until around the mid-height (or 2.5 m
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Fig. 4. No jarosite precipitation. Model predicted variables at various times versus height from base (m): (a) pH, (b) total (fraction) copper extracted (−), (c) total bacterial concentration (log plot) (bacteria/m3), (d) Fe3+ concentration, (e) Fe2+ concentration (log plot) and (f) jarosite precipitated.
Fig. 5. Time plots (days) for Case 2 (no jarosite precipitation) and base case. (a) overall (fraction) copper extracted, (b) average jarosite precipitated, (c) ferric concentration in PLS, and (d) pH in PLS.
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Table 3 Comparison (%) of overall results (at end of simulation after 116 days) for each case, as compared with base case.
Base Case Case 2 – no jarosite precipitation included Case 3 – inlet pH (increased by 0.25 pH units) Case 4 – gangue rate constant (20% reduction of base case value)
% Change in overall extraction (+ indicates increased extraction, – indicates decreased)
% Change in overall jarosite precipitated (+ indicates increased precipitation, – indicates reduced precipitation)
0 +80.3%
0 0
− 14.8%
+1%
+89%
−67%
height), as compared to the base case where jarosite precipitates around 4.2 m height. The maximum jarosite precipitation (less than 40 kg/m3) is less than in the base case, where the maximum value is as high as 110 kg/m3. The average jarosite precipitation for reduced rate case (Fig. 10(b)) is 67% of the base case value, as shown in Table 3. The corresponding increase in chalcopyrite leached is 89%. Case 4 (gangue rate reduction) was found to have the most significant effect on jarosite and overall copper extraction. We note for the reduced rate case in Fig. 9 (dashed line) that the copper extraction looks very similar to the shape of case 2 (no jarosite
precipitation), but the shape is not due to the pH being too high, rather it is due to jarosite precipitation removing ferric ions from solution.
6. Conclusions This paper discusses the column bioleaching model for chalcopyrite, incorporating the effects of jarosite precipitation. The underlying model has been validated previously in chalcocite systems. We model jarosite precipitation using a simple rule based model for when jarosite is precipitating, which has not previously been attempted in the literature. The conclusions we draw from this work are: • The model predicts jarosite precipitation in the top region of the column, where the pH becomes high enough (far enough away from inlet), and where the ferric is high enough to allow this. • The overall effect of jarosite precipitation was quantified by comparing the results with the case where jarosite precipitation was not included in the model: in this case we found an increase in overall copper extraction of 80%, as compared with the base case. • A higher inlet pH caused the height at which jarosite precipitation begins to be higher up in the column, and as expected, copper extraction reduced, declining by 14.8% as compared with the base case. Unexpectedly, this resulted in only 1% more jarosite being precipitated (average over whole column), which was due to the fact that the position where jarosite begins to precipitate moves higher in the column, but has less ferric available for precipitation (since more of it is used in chalcopyrite (and pyrite) leaching).
Fig. 6. Base case and inlet pH = 1.5 case (Case 3). Model predicted variables at one time instant (at 116 days) versus height from base (m): (a) pH, (b) total (fraction) copper extracted (−), (c) total bacterial concentration (log plot) (bacteria/m3), (d) Fe3+ concentration, (e) Fe2+ concentration (log plot) and (f) jarosite precipitated.
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Fig. 7. Time plots (days) for Case 3 (inlet pH=1.5 case) and base case. (a) overall (fraction) copper extracted, (b) average jarosite precipitated, (c) ferric concentration in PLS, and (d) pH in PLS.
Fig. 8. Base case and reduced gangue rate (case 4). Model predicted variables at various times versus height from base (m): (a) pH, (b) total (fraction) copper extracted (−), (c) total bacterial concentration (log plot) (bacteria/m3), (d) Fe3+ concentration, (e) Fe2+ concentration (log plot) and (f) jarosite precipitated.
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Fig. 9. Base case and reduced gangue rate (case 4). Model predicted variables at one time instant (at 116 days) versus height from base (m): (a) pH, (b) total (fraction) copper extracted (−), (c) total bacterial concentration (log plot) (bacteria/m3), (d) Fe3+ concentration, (e) Fe2+ concentration (log plot) and (f) jarosite precipitated.
Fig. 10. Time plots (days) for Case 4 (reduced gangue rate) and base case. (a) overall (fraction) copper extracted, (b) average jarosite precipitated, (c) ferric concentration in PLS, and (d) pH in PLS.
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• Reducing the gangue acid consumption rate constant had the strongest effect on the jarosite precipitation (which decreased by 67% as compared with the base case) and associated copper extraction (increased by 89%). The reduced rate constant caused the pH to remain much lower throughout the column, and jarosite precipitation began at the mid-height of the column, compared to the top 0.8 m in the base case. In future work, the modelling needs to be closely compared with experimental column data. One of the benefits would be improving rate constant determination for the precipitation rate. The experiment would need to be able to elucidate the connection between jarosite precipitation and inhibited particle scale leaching, due to particle surface coverage by jarosite. This may involve doing very small particle scale experiments which can investigate fine detail behaviour. In future work, clogging of the macroscopic pore space and permeability reduction need to be coupled with the liquid flow model used: close connection with experimental evidence is necessary. Coupling of the modelling of liquid flow with jarosite precipitation and associated reduction in permeability is also a future aspect that needs to be addressed. There have been only limited model validation studies for industrial heap size leaching systems in which the leaching and measurements are well controlled, and future work should address this. Nomenclature Concentration (kg/m3) of the following species: j = L (dissolved oxygen), j = Fe2+ (ferrous ions), j = Fe3+ (ferric ions) j = ϕ (free bacteria), j = H+ (free acid ion concentration), j = Cu2+ (copper ion concentration) y Distance from the bottom of the heap/column (m) t Time (s) Superficial Liquid Flow Velocity (m/s) uL Interstitial Liquid Flow Velocity (m/s) vL Source term for species j (kg/m3/s) Sj Grade (−) of copper sulfide (i = 1) and pyrite (i = 2) Gi KM,O, KM,Fe, KM\H+ The half growth rate constant for the oxygen in liquid concentration, ferrous ion concentration and free acid concentration (kg/m3) and f(T) (−) is the growth temperature dependence function, Density of solid (s) (kg/m3) ρs εs ,εL,εair Volume fraction (−) of solid liquid and air, respectively. μmax, kdeath μmax is the maximum growth rate coefficient (1/s), and death rate coefficient (1/s), respectively. Yield (Y) Yield coefficient (bacteria/kg Fe2+) μjarosite,0 Jarosite precipitation rate (1/s) m, C Log linear fitted line function parameters, slope m (−), and constant of intersection C (log10(kg/m3)) Gangue rate constant (1/s) μgangue f(T) Bacterial function of temperature (−) Cj
Acknowledgements The authors gratefully acknowledge Helen Watling for many helpful discussions.
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