# Spectral induced polarization monitoring of chalcopyrite ore bioleaching: insights from laboratory column experiments

Véronique Naudet, Alexis Maineult, Philippe Leroy, Nicolas Florsch, Jochen Petersen

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Véronique Naudet, Alexis Maineult, Philippe Leroy, Nicolas Florsch, Jochen Petersen. Spectral induced polarization monitoring of chalcopyrite ore bioleaching: insights from laboratory column experiments. Geophysical Journal International, 2026, 10.1093/gji/ggag075/8494939. hal-05535222

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1 Spectral induced polarization monitoring of chalcopyrite ore bioleaching: insights from

2 laboratory column experiments

3 Véronique Naudet¹,², Alexis Maineult³, Philippe Leroy⁴, Nicolas Florsch⁵, Jochen Petersen⁶

4 1. Univ. Bordeaux, CNRS, Bordeaux INP, I2M, UMR 5295, F-33400, Talence, France

5 2. Arts et Metiers Institute of Technology, CNRS, Bordeaux INP, I2M, UMR 5295, F-33400 Talence, France

7 3. Laboratoire de Géologie, Ecole Normale Supérieure / CNRS UMR 8538, PSL Research University, 75005 Paris, France.

9 4. BRGM, French Geological Survey, 45060 Orléans, France

10 5. UMI 209 UMMISCO, Sorbonne University, Paris, France

11 6. Department of Chemical Engineering, University of Cape Town, South Africa.

12

13 **Corresponding author:** Véronique Naudet [veronique.naudet-maillet@u-bordeaux.fr](mailto:veronique.naudet-maillet@u-bordeaux.fr)

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15 **Abstract**

Bioleaching is a biologically facilitated process that helps to dissolve valuable metals in order to extract them from the mineral gangue. Applied in the field to heap ores, its efficiency mainly depends on solution flow inside the heterogeneous heaps, which is often tortuous and can remain stagnant in the pores and crevices between the particles. Methodologies that can help to monitor the bioleaching processes are therefore needed to improve operational efficiency. In this article, we present for the first time preliminary laboratory-scale investigations on spectral induced polarization (SIP) during the bioleaching of chalcopyrite (CuFeS₂) containing ore material from a mine in Chile. Two column experiments representing different stages of the bioleaching process were monitored under un-saturated and highly acidic environment (pH ~2). Our objective was to explore the feasibility of SIP for detecting changes in electrical properties potentially associated with bioleaching-induced mineral dissolution and alteration. The results show a rapid decrease in SIP phase shift and imaginary conductivity during the early stage of bioleaching, while the real conductivity remains relatively stable. At a more advanced stage of bioleaching, the phase response is weaker and more stable. A relaxation time distribution (RTD)
analysis was applied to further investigate changes in polarization mechanisms. Prior to bioleaching, the RTD exhibits a well-defined peak consistent with polarization controlled by sulfide mineral grains, whereas after one month of bioleaching the RTD broadens and shifts toward larger relaxation times, accompanied by a decrease in chargeability. This combined evolution suggests bioleaching-induced modifications of electrochemically active surfaces, potentially related to mineral dissolution and the formation of passivation layers. Estimated particle sizes derived from the RTD analysis are consistent with scanning electron microscopy observations. Although, the absence of a dedicated abiotic control column prevents us from attributing these changes unambiguously to bioleaching alone, these results highlight the potential of SIP as a non-invasive, real-time and integrative tool to monitor leaching processes and to identify zones that may remain weakly affected by leaching.

**Keywords:** Electrical properties; Numerical modelling; Induced polarization

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# 1. Introduction

The leaching process of low-grade ores in the field, called heap leaching, is an established mineral extraction process (Petersen 2016) of increasing interest due to the rarity of high-grade ores. Large volumes can be processed at low capital and operating cost, only requiring the control of acid application, maintenance of bacteria (either inoculated or naturally occurring) and supply of sufficient oxygen throughout the heap. A related technology, dump leaching, is based on the same principles, but uses run-of-mine (ROM) material, which are unprocessed ore (also called crude ore), usually containing sulfidic minerals. Figure 1.a illustrates a typical heap leaching circuit at the field scale. The ore, usually crushed, is agglomerated with acid and/or irrigation solution prior to being stacked into piles on an impermeable layer fitted with a solution drainage system. The heap, whose height can vary from 6 to 12 m, is aerated through pipes laid out underneath and irrigated from droplines at the top surface with a solution containing sulphuric acid. The leaching of the ore by this solution results in the metal dissolution, which is thus transported with the solution to the bottom and from there recovered through the drainage system into a collection pond. Finally, an appropriate technology (solvent extraction, cementation or adsorption, precipitation, etc.) is used to extract the target metal from the solution and the barren solution can then be returned to the top of the heap for further leaching. Heap leaching is one
of the best available technologies for the economic extraction of disseminated low-grade ores, which could not be proceeded otherwise. It is thus estimated to produce 21% of global copper and 9% of global gold (Marsden & Botz 2017).

<figure><img src="image_2.png" /><figcaption>**Figure 1.** Schematic representation of a heap indicating the major heap-scale transport effects (a) and the physical/chemical and biological interactions in metal sulfide bioleaching at the grain scale (b) (adapted from Petersen & Dixon, 2007 and Petersen 2023). Microorganisms oxidize ferrous to ferric (stage 1), which in turn oxidizes the sulfide phases in the target minerals (stage 2).</figcaption></figure>

Zanbak (2012), in a brief history of the heap-leaching technique in mining, explains that the first written records of heap leaching date back to the 16th century with leaching of saltpetre (Chile). Then, the leaching of pyrite occurred in Germany and Spain followed by the leaching of bauxite in France and St. Petersburg in Russia at the end of the 19th century. The process evolved considerably in the middle of the 20th century with the acid leaching of copper oxide minerals and the cyanide leaching of gold and silver. Continued leaching from dumps of low-grade copper ore lead to the discovery of naturally occurring micro-organisms that enhanced the process. They are commonly acidophilic bacteria or archaea that typically thrive at pH values below 3. The natural strains were cultured and deliberately introduced into leaching processes in both tanks and heaps. Heap bioleaching was first tested in copper sulfide dump leach operations and then introduced as a primary method for metal extraction in Chile in the early 1990's (Brierley 1997), where it is still dominant today. Now, it is a worldwide established geo-biotechnological process for leaching copper sulfides ores and has been explored also for ores of cobalt, nickel, zinc, gold-bearing pyrites, and uranium (Shiers et al. 2016; Vera et al. 2022). In some cases, inoculation is practiced and the microbial environment is enhanced by addition of nutrient
material to the feed solution, but in general microbial growth in bio heaps proceeds naturally with little external intervention (Schnell 1997).

In the present article, we study the bioleaching of a copper sulfide ore containing chalcopyrite (CuFeS₂), which is the most important copper-bearing mineral in the world. To date, low copper extraction is a common problem during chalcopyrite bioleaching, which limits its industrial application. A review of sulfide bioleaching mechanisms can be found in Petersen (2023) and a review of heap bioleaching of chalcopyrite in Pradhan et al. (2008). In the field, heap cycle duration of bioleaching varies with operational practice, mineral grade and composition, but usually is in the order of 8 months to 2 years with a copper extraction usually around 80% for ores containing predominantly chalcopyrite. Active inoculation with bacteria does not appear to be common practice as it is actually not sufficiently economically viable, but occurs usually through the agglomeration process with bacteria contained in the raffinate, or alternatively bacterial populations begin to thrive naturally in the heap after some time. Little, if any, microbiological maintenance is practiced. Figure 1b illustrates the various sub-processes that govern metal sulfide bioleaching, all of which influence the overall process of biologically facilitated metal dissolution to some degree. The reactions of bioleaching are shown in eqs. (1) to (4).

$$CuFeS_2 + 4H^+ + O_2 \rightarrow Cu^{2+} + Fe^{2+} + 2S^0 + 2H_2O \quad (1)$$

$$4Fe^{2+} + O_2 + 4H^+ \xrightarrow{\text{Bacteria}} 4Fe^{3+} + 2H_2O \quad (2)$$

$$CuFeS_2 + 4Fe^{3+} \rightarrow Cu^{2+} + 5Fe^{2+} + 2S^0 \quad (3)$$

$$2S^0 + 3O_2 + 2H_2O \xrightarrow{\text{Bacteria}} 2SO_4^{2-} + 2H^+ \quad (4)$$

The overall reaction shown in eq. (1) typically represents the bioleaching of chalcopyrite, which occurs concurrently through a chemical attack by acid and ferric ion, as expressed by eq. (3). The most important microorganism involved in the biooxidation of minerals are those responsible for production of ferric iron (eq. (2)) and sulfuric acid (eq. (4)), required for bioleaching reactions. The oxidation of ferrous to ferric ion ($Fe^{2+}$ to $Fe^{3+}$) by microorganisms, with concomitant reduction of oxygen (eq. (2)) serves as metabolic energy source for certain types of micro-organisms (e.g. *Acidithiobacillus ferrooxidans* or *Leptospirillum*). The source of oxygen required for his reaction comes from heap aeration, while the acid needs to be supplied through the feed solution, or else through the bio-oxidation
of pyrite or elemental sulfur. For example, the bioleaching of pyrite can be described by the following reaction (Petersen, 2023):

$$108 \quad FeS_2 + 14Fe^{3+} + 8H_2O \rightarrow 15Fe^{2+} + 2SO_4^{2-} + 16H^+ \quad (5)$$

Unlike chalcopyrite, the bioleaching of pyrite follows a different reaction pathway and does not involve the formation of elemental sulfur, but leads directly to acid generation. Ferrous iron ($Fe^{2+}$) and protons produced by pyrite dissolution provide favourable conditions for the bacterial oxidation of $Fe^{2+}$ to $Fe^{3+}$ in the presence of oxygen (eq. (2)). The regenerated ferric iron can then interact with sulfide mineral surfaces, where it is reduced while oxidizing sulfide phases in the target minerals (eq. (3)). The biological oxidation of ferrous to ferric iron can take place in solutions (“non-contact leaching”) or within biofilm at the interface between the microbial cell and the mineral sulfide surface (“contact leaching”), which is filled with extracellular polymeric substances (EPS) or a combination of both (“cooperative leaching”) (Zhao et al. 2019) (Figure 1b). The target sulfide minerals that are not exposed at the solid-liquid interface can be accessible through pores or fissures on the inside of the particle. In this case, the interaction with the bio-oxidation environment is done indirectly through the migration of the ferric/ferrous redox agent diffusing through the pore channel. Mineral surfaces can sometimes be coated or occluded by oxidized sulfur species, precipitated iron phases or intermediate mineral phases, which are highly pH dependant. These surface layers can act as a diffusion barrier to dissolved oxidative species reaching the surface, or can be a barrier to electron transfer by acting as a non-conductor. This phenomenon, referred to a “passivation layer”, can slow down or completely inhibit the rate of the electrochemical leaching mechanism but can be decreased with the particle size of the ore (Po et al. 2022). In the case of chalcopyrite bioleaching, passivation could also be due to the formation of jarosite (Pradhan et al. 2008).

Even if this technology appears to be very simple and suitable for the treatment of low-grade ore in an economical point of view, the sub-processes taking place within the ore bed and particularly at the microbe-mineral interfaces, are rather complex and their interactions are not yet fully understood, which limit the overall extraction rate using this technique (Vera et al. 2022). This technology is therefore still evolving with many electrochemical studies performed in the laboratory to elucidate mechanisms and kinetics of these sub-processes (Li et al. 2022). Experiments in tanks and columns have shown that it is
generally not the microbial metabolic reactions that limit the kinetics of bioleaching reactions overall, but rather the reaction environment such as humidity, temperature, pH, O₂ and CO₂ availability (Petersen 2023). But one of the main limiting factors is the permeability of the heap at the macro-scale, as the leaching performance is mainly governed by solution flow inside the unsaturated, coarsely granular heaps, and also the air channels between competing for the same space (Robertson et al. 2023). Although care is taken to ensure that the surface of the heap is regularly sprayed with acid, the solution flows along tortuous pathways between the particles but also remains stagnant in the pores inside the particles as well as narrow crevices in between. Since transport of reagents is then limited by slow diffusion in these stagnant spaces, leaching efficiency may be reduced, leading to incomplete extraction. Determining this irregular movement of leachate within these structures is therefore crucial. This can be achieved by physical, chemical and biological analyses of samples taken from the leach solutions. But sampling of ore is rarely undertaken due to the complexity of drilling the heap (i.e. removal of the irrigation line and disturbance of the packing) and the number of samples required to describe the high heterogeneity of the heap. As a result, a good characterization and monitoring of heap bioleaching remain elusive and new innovative methods are required to better describe and monitor the bioleaching processes, at both the laboratory and field scale. Beyond efficiency issues, environmental concerns must also be considered, as improper control of leachate flow can lead to solution leakage and contamination of surrounding ecosystems (Leppänen et al. 2017). Developing reliable monitoring approaches is therefore essential not only for process optimization but also for safer and more sustainable management of mining waste.

Geoelectrical methods seem to be good candidates as they can provide rapidly, non-intrusively and cost-effectively, a spatial and temporal insight into the heap. Electrical resistivity methods have been used to assess information on the internal structure of the heap but also its moisture content, solute concentration and temperature (Moradipour et al. 2015; Rucker et al. 2015; Power et al. 2018). This method was also used in time-lapse during leaching solution injection inside the heap to visualize the movement of the injected leaching solution and to improve the delineation of production zones (Webb et al. 2008; Dimech et al. 2019, 2022; Lizama 2023). Due to the intrinsic polarization and capacitive electrical properties of metallic particles, Induced Polarization (IP), either in the time domain (TDIP) or frequency domain
(known as spectral-IP (SIP)) is a promising method for addressing such challenges. The IP method has long been used for disseminated and massive ore exploration (Pelton et al. 1978; Vanhala & Peltoniemi 1992) and acid mine drainage or mine waste rock characterization (Campbell & Horton 2001; Kemna et al. 2012; Moradipour et al. 2015; Placencia-Gómez et al. 2015; Power et al. 2018; Power & Almpanis 2022). In archaeology, IP is also useful for the localization of buried slag heaps from ancient smelters (Florsch, Llubes, et al. 2011, 2012a; Florsch et al. 2017; Qi et al. 2018). Over the past two decades, thanks to improvements in measurement in the spectral domain and processing techniques, its field of application has been extended to hydrogeological and environmental purposes such as contaminant plumes characterization and remediation (Kemna et al. 2012; Kessouri et al. 2019). Although the IP method has been widely used for ore exploration, its applications on mining leaching processes are relatively scarce. We can cite the works of Placencia-Gómez et al. (2013) who studied the sensitivity of the SIP method to the oxidation mechanisms of sulfide minerals found in mine waste deposits. Or the recent paper of Su et al. (2024), who performed SIP measurements on mine waste rocks with generation and release of acid mine drainage during kinetic column tests. But, as far as we know, no study exists on SIP monitoring of a heap bioleaching process. Moreover, while most of the cited investigations have been performed on laboratory with artificial samples, very few concern real mining rock samples. In this article, we present new and preliminary SIP results obtained at the laboratory scale during a bioleaching of a low-grade chalcopyrite dominant ore material coming from a mine in Chile. The scientific challenge was to determine the feasibility of this method to detect electrical properties changes during the process, in such a heterogeneous, un-saturated and very acidic environment (pH around 2), that can be attributed to metal dissolution. If this is the case, this will open opportunities to apply the SIP method in the field in order to detect and locate zones where the bioleaching process occurred efficiently and where possible areas of unleached mineral particles still remain. We also present in this article one of the first applications of a new relaxation time distribution (RTD) approach.

## 2. Background on Spectral Induced Polarization

### 2.1. Theory

The Spectral Induced Polarization method is based on the concept that the conductivity is frequency-dependent. This complex conductivity value $\sigma^*$ can be expressed as a real and imaginary component

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$\sigma^* = \sigma' + i\sigma''$, where $i^2 = -1$ is the pure imaginary number, $\sigma'$ is the real component (in-phase conductivity) of the complex conductivity, $\sigma''$ is the imaginary component (quadrature conductivity). $\sigma'$ mainly describes the ohmic conduction mechanism through electromigration of the charge carriers in the connected pore space, whereas $\sigma''$ describes the polarization mechanism through the reversible storage of electrical charges (Vinegar & Waxman 1984). It is noted here that the conductivity is linked to Ampere's law through the Maxwell equations. Indeed, taking into account the total current density $J_T$, one can write:

$$J_T = \sigma E + \frac{\partial D}{\partial t} \qquad (6)$$

$$D = \varepsilon_0 E + P = \varepsilon E \qquad (7)$$

with $\sigma$ being the electrical conductivity, $E$ the electrical field, $D$ the dielectric displacement, $P$ the polarization, $\varepsilon_0$ and $\varepsilon$ the vacuum permittivity and medium permittivity respectively. As soon as the polarization can exhibit relaxation and/or response delay, $\varepsilon$ becomes complex, and in the frequency regime we obtain:

$$J_T = \sigma E + i\omega\varepsilon E = (\sigma + i\omega\varepsilon)E \qquad (8)$$

with $\omega$ being the angular frequency and

$$\varepsilon = \varepsilon(\omega) = \varepsilon'(\omega) - i\varepsilon''(\omega) \qquad (9)$$

Leading to

$$J_T = [\sigma + i\omega(\varepsilon' - i\varepsilon'')]E = [(\sigma + \varepsilon''\omega) + i\omega\varepsilon']E \qquad (10)$$

The imaginary part of $\varepsilon$ is included in the real part of the effective conductivity ($\sigma'_{ef} = \sigma + \varepsilon''\omega$). The important fact is that $\varepsilon'$ and $\varepsilon''$ are frequency dependent (as well as $\sigma$). These are not classical dielectric terms in terms of magnitude (as for a solid non conducting substance) because they also include polarization linked with the accumulation of charges in conducting media (water, metals). The relative permittivities encountered in IP can be considerably larger than the permittivity of water (which is 78.4 at IP frequencies for a temperature of 25°C) and are more akin to the very large permittivities encountered by physicists on particular materials (Grosse & Delgado 2010). For example, $10^6$ is a possible value, as for instance in the study by Bechir *et al.* (2022).
Experimentally, the complex conductivity is determined from frequency-dependent measurements of the conductivity magnitude $|\sigma^*|$ and the phase shift $\phi$ (in rad) between a harmonic current applied to the material and the resulting measured harmonic electrical field, such as $\sigma^* = |\sigma^*|e^{i\phi} = \sigma' + i\sigma''$ with:

$$ \sigma' = |\sigma^*|\cos(\phi) \qquad (11) $$

$$ \sigma'' = |\sigma^*|\sin(\phi) \qquad (12) $$

leading to $\phi = \tan^{-1}(\sigma''/\sigma')$. The spectra of the complex conductivity in terms of magnitude, shape and peak of the phase shift, and the frequency of this peak (i.e. associated relaxation time $\tau$) measured over a wide range of frequencies (typically from mHz to kHz) provide insight into the conduction and polarization phenomena in porous media (Pelton et al. 1978). A mineral in contact with water usually expresses a charge at its surface that is compensated by counter-ions in excess in the electrical double layer (EDL) (Bücker et al. 2019). Polarization mechanisms can occur via ion electromigration and back diffusion in the EDL (EDL polarization) and charge build up at the boundary between phases presenting different electrical properties (conductivities or permittivities; Maxwell-Wagner polarization) (e.g., Leroy et al. 2008; Leroy et al. 2025). In presence of conductive or semiconductive materials such as metallic particles (ores including pyrite, chalcopyrite, magnetite), both the real and imaginary conductivity components can be influenced by the metallic particles (Pelton et al. 1978). If the metallic particles are interconnected, forming a continuous electronic conduction path, this influences the real part, but no significant conduction of electronic origin should exist if the metallic particles are disseminated (Slater et al. 2005). Whereas disseminated metallic particles have a strong ability to polarize in a low-frequency electrical field, influencing the imaginary part of the complex conductivity (Gurin et al. 2015). Metallic particle polarization can also be expressed through the chargeability $m$ defining the capability of the medium to reversibly store electrical charges and written as $m = (\sigma_{\infty} - \sigma_0)/\sigma_{\infty}$ where $\sigma_{\infty}$ is the conductivity magnitude at very high or “infinite” frequency and $\sigma_0$ is the conductivity magnitude at zero frequency (direct current -DC condition) (e.g., Tarasov & Titov 2013).

## 2.2. Laboratory investigations

Over the past two decades, an increasing number of laboratory studies investigating sand-metal bearing mineral mixtures have been performed to understand the dependence of SIP parameters, notably phase shift, imaginary conductivity and chargeability on the different properties of the metallic mineral
inclusions and the pore-filling electrolyte (see Revil et al. 2015 for a comparison of a broad database of experimental data). Regarding polarization of electron conducting minerals, laboratory investigations have shown that SIP measurements are correlated with: (1) metallic particle size, concentration and mineralization affecting the magnitude of the measurements (Gurin et al. 2015; Hupfer et al. 2016; Mellage et al. 2018; Martin & Weller 2023; Emerson et al. 2024); (2) metallic particle distribution and coating (Placencia-Gómez et al. 2013; Gurin et al. 2015; Bücker et al. 2019); (3) pore fluid chemistry affecting the peak of frequency *f* at the maximum phase shift (i.e. the relaxation time τ = 1/(2π*f*); Gurin et al. 2015; Placencia-Gómez & Slater 2016); (4) precipitation-adsorption properties of secondary minerals (Wu et al. 2005; Placencia-Gómez et al. 2013); and (5) redox reactions (Placencia-Gómez et al. 2013, 2015; Hubbard et al. 2014; Emerson et al. 2024). Microbial activity has also been reported to impact SIP measurement during bioremediation (Williams et al. 2005; Flores Orozco et al. 2011; Kessouri et al. 2019). In acidic environments, which is the case in the present article, it is worth mentioning that redox reactions can occur on the surface of the grain. In general, sulfide grains have a long life and are not even affected by natural currents. This is as true of deposits disseminated in granites and shales as it is in marls with or without clay, which are found in abundance in wetlands. In a reducing environment such as peat, on the other hand, anoxia facilitates the formation of sulfides by precipitation from organic matter. In terms of occurrence, stable sulfides are more frequent than situations where sulfides are attacked. In altered granitic terrain, infiltration zones are thus depleted in pyrite (Camerlynck et al., 2014). In the present paper, ongoing redox leaching reactions occur and can therefore modify particle mineralogy, surface area and pore fluid conductivity over time. We should therefore expect an impact on the SIP signals measured during the heap-bioleaching process.

While most of the cited investigations have been performed in laboratory with artificial samples, very few concern real mining rock samples. For instance, Placencia-Gómez et al. (2015) worked on composite samples with mine tailings material containing low and weathered sulfidic minerals and Su et al. (2024) worked on mine waste rocks. In the present study, we worked on real ore coming from a mine in Chile, which has been crushed and agglomerated as performed on the heap in the field.

2.3. Modelling approaches
To understand the physical mechanisms underlying the IP effect, two mechanistic approaches have proven to be fruitful. The first is analytical and is well represented by the series of articles produced by Revil et al. from 2015 to 2018 (e.g., Revil et al. 2015a to Revil et al. 2018). The other approach is numerical with the implementation of finite elements to reproduce ionic mechanisms at the nanoscale. Started by Abdulsamad et al. (2016), this has been extensively explored in the works of Bücker (Bücker 2019; Bücker et al. 2019). A way to quantitatively interpret SIP data is based on fitting phenomenological relaxation models. However, the plethora of existing models (well-illustrated in Dias 2000) is probably no longer relevant, even if models like the Cole-Cole are still of practical interest (Pelton et al. 1978). Indeed, as pointed out in numerous recent publications (Florsch et al. 2012; Florsch et al. 2014), all fit models can be encapsulated in a single linear superposition mechanism, which is the consensus today. In the form for conductivity:

$$S_{\omega}(\omega) = a_{\mathbb{R}} - \int_{0}^{\infty} \frac{g_{\tau}(\tau)}{1+i\omega\tau} d\tau + i\omega C \quad (13)$$

with $a_{\mathbb{R}}$ being the real constant (generally speaking $\sigma_{\infty}$ when using admittance), $g_{\tau}(\tau)$ the Relaxation Time Distribution (RTD), $\tau$ the time constant, and $C$ a constant having the dimension of a capacitance and used to model the high frequency trend of the spectrum. The last term is generally observed above 1 kHz and corresponds to the "normal" electromagnetic response in the presence of a dielectric due to displacement current. Notice that if an IP experiment is realized in pure water, one finds a relative dielectric constant, which is the one of pure water, i.e. close to 80 (at room temperature). The SIP measurements are usually stopped or filtered or corrected at a frequency low enough not to observe this term. For some models, as listed in Florsch et al. (2012, table 1), we have an analytical passage, while for others, numerical integration is required. This was demonstrated at the 2nd workshop for Induced Polarization, Golden, 2011, where we detailed the equivalence of the Cole-Cole and log-normal models, already known from Cole-Cole's original 1941 paper (Florsch et al. 2011). Unfortunately, the transition from spectrum (which is observable) to RTD is an extremely smooth process (Florsch, et al., 2012, figure 2). Inverting spectra to RTD is an ill-posed problem. Florsch, et al. (2012) and Florsch et al. (2014) use smoothing operators in the manner of Tarantola & Valette (1982). More recently, Maineult et al. (2025) cleverly replaced the use of smoothing operators with a priori regular (smooth) solutions
298 using an RTD model based on Bézier curves. In this paper, we use this approach to model our
299 experimental data.

300 **3. Materials and Methods**

301 **3.1. Column preparation**

302 The experiments were conducted from a small tank (Figure 2), previously used for testing bioleaching
303 of ores under various flow conditions (Petersen & Dixon; 2007). The front face of the tank contains
304 multiple holes designed for withdrawing solution and solid samples from within the bed as well as for
305 inserting probes into the rock material. For our experiment, the tank has been subdivided into 6
306 independent compartments, hereafter referred to as columns, allowing different experiments to be
307 conducted simultaneously. Each column measured 10x10 cm in cross-section and 40 cm in height.

<figure><img src="image_3.png" /><figcaption>308
309 **Figure 2.** Photograph of the small tank before subdivision into six individual compartments, two of which were used in our experiment. The front face contains an array of 8 x 13 holes (10 mm in diameter) plugged with rubber septum corks. The central holes were used for the introduction of SIP electrodes.
310
311</figcaption></figure>

312 Two of these columns were used for the experiment presented in this paper. They were packed with an
313 ore containing a low chalcopyrite content (0.5 wt%, Table 1) and a high pyrite content (4 wt%, Table 1)
314 coming from a mine in Chile (Figure 3).

<table><caption>315 **Table 1.** Mineralogical results obtained from a series of heap ores with the Mineral Liberation Analyser
316 (MLA). Only major minerals are reported.</caption><thead><tr><td>Minerals</td><td>wt%</td></tr></thead><tbody><tr><td>Chalcopyrite</td><td>0.5</td></tr><tr><td>Pyrite</td><td>4.0</td></tr><tr><td>Muscovite</td><td>28.6</td></tr></tbody></table>
<table><tr><td>Biotite</td><td>0.5</td></tr><tr><td>Chlorite</td><td>0.7</td></tr><tr><td>Kaolinite</td><td>7.4</td></tr><tr><td>Calcite</td><td>0.0</td></tr></table>

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Bioleaching in this study was primarily focused on chalcopyrite to extract copper, as iron recovery from pyrite dissolution is not economically relevant in this context (Petersen, 2023). Nevertheless, pyrite is the predominant sulfide mineral present in the ore (Table 1) and plays a key role in the bioleaching system. Its oxidation leads to a net production of acidity (eq. (5)), thereby sustaining low pH conditions and promoting further dissolution reactions. Because pyrite dissolution generates more protons than are required for the bacterial regeneration of $Fe^{3+}$ from $Fe^{2+}$, pyrite can effectively sustain and auto-catalyse its own oxidation. The resulting ferric iron and acidic conditions, in turn, enhance the dissolution of chalcopyrite and other copper-bearing sulfides, which can be considered to ‘piggy-back’ on the pyrite-driven redox cycle. Note also that the ore contains significant contents of clays (muscovite, kaolinite, chlorite, and biotite) that adsorb protons from the pore water (Leroy et al., 2025) and hence can increase the pH of the samples, potentially decreasing the efficiency of the bioleaching process. Inductively Coupled Plasma (ICP) analyses of different samples are presented on Table 2 which indicate that the ore contains 0.46% of copper. The analyses also reveal that about 40% of copper reports to chalcopyrite and that <0.3% is the weight fraction of other copper sulfides such as chalcocite, covellite and bornite. So, even if the individual portions of the minerals are low, they still add up in terms of hosting the copper. Usually in bioleaching these minerals dissolve first which chalcopyrite much slower (Petersen & Dixon, 2007).

<table><caption>**Table 2.** Chemical analyses of the low-grade chalcopyrite dominant ore.</caption><thead><tr><td>Element</td><td>%</td></tr></thead><tbody><tr><td>Al</td><td>8.10</td></tr><tr><td>K</td><td>2.54</td></tr><tr><td>Si</td><td>32.48</td></tr><tr><td>Ti</td><td>0.21</td></tr><tr><td>Cu</td><td>0.46</td></tr><tr><td>Fe</td><td>2.48</td></tr><tr><td>S<sup>1</sup></td><td>2.45</td></tr><tr><td>S<sup>2-</sup></td><td>2.33</td></tr><tr><td>SO<sub>4</sub><sup>2-</sup></td><td>0.31</td></tr><tr><td>S<sup>6</sup></td><td>0.09</td></tr></tbody></table>

<table><thead><tr><td>Element</td><td>ppm</td></tr></thead><tbody><tr><td>Ba</td><td>732</td></tr><tr><td>Zr</td><td>15</td></tr><tr><td>Sr</td><td>399</td></tr><tr><td>Zn</td><td>85</td></tr><tr><td>Co</td><td>18</td></tr><tr><td>Mn</td><td>77</td></tr><tr><td>Mg</td><td>2909</td></tr><tr><td>Cr</td><td>13</td></tr><tr><td>V</td><td>52</td></tr><tr><td>Ca</td><td>965</td></tr></tbody></table>

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Figure 3 presents photographs of different grab samples of the low-grade chalcopyrite dominant ore used in our columns before crushing to <20 mm. Chalcopyrite and pyrite grains are clearly identified at the surface of the particle. We also have determined the elemental composition of one of the samples presented in Figure 3 from X-ray fluorescence, XRF analyses (Table 3). Back-scattered images of this sample were realized by scanning electron microscopy (SEM-JSM-IT510-X) equipped with an energy dispersive spectrometer for elemental analysis (Figure 4). From Figs. 3 and 4, mineral particles (i.e. chalcopyrite and pyrite) are visible with a grain size from 10 µm to 1 mm. The elemental composition of the grab sample is quite different from the bulk ore analysis indicating the high variability of mineral composition in this type of ore.

<table><caption>**Table 3.** Chemical element composition from XRF realized one of the samples presented on Figure 3</caption><thead><tr><td>Element</td><td>%</td></tr></thead><tbody><tr><td>Al</td><td>3.26</td></tr><tr><td>K</td><td>1.05</td></tr><tr><td>Si</td><td>20.96</td></tr><tr><td>Ti</td><td>0.33</td></tr><tr><td>Cu</td><td>1.62</td></tr><tr><td>Fe</td><td>5.62</td></tr><tr><td>S</td><td>5.83</td></tr><tr><td>Ba</td><td>0.05</td></tr><tr><td>Zr</td><td>0.01</td></tr><tr><td>Sr</td><td>0.05</td></tr><tr><td>Zn</td><td>0.01</td></tr><tr><td>Co</td><td>&lt;LOD</td></tr><tr><td>Mn</td><td>0.03</td></tr><tr><td>Mg</td><td>1.44</td></tr><tr><td>Cr</td><td>0.01</td></tr><tr><td>V</td><td>0.02</td></tr><tr><td>Ca</td><td>0.92</td></tr></tbody></table>
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Photographs of the low-grade chalcopyrite dominant ore used in our columns before crushing it to 20 mm. Chalcopyrite and pyrite grains (Cpy & Py).</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 4.** SEM back-scatter image of the sample presented on Figure 3. Ccp = chalcopyrite; Bt = biotite; Qz = quartz; Ap = apatite; Mnz = monazite; All = allanite. The ore sample was polished and carbon-coated for the imaging.</figcaption></figure>

Prior to charging into the columns, the ore was agglomerated with a mixture of water (70 g/kg of dry ore) and sulfuric acid (8 g/kg of dry ore), resulting in a final moisture content of 7.5%, which corresponds to operating conditions at the mine site. The particle size distribution of the ore agglomerated inside the columns ranges from 20 mm down to sub-micron, usually with about 20% of size < 500 micron (Figure 5).

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<figure><img src="image_6.png" /><figcaption>**Figure 5.** Particle size distribution of the low-grade chalcopyrite dominant ore agglomerated inside the columns</figcaption></figure>

The columns were aerated from the bottom and the ore bed rests on a perforated stage to allow a flow of gas from underneath the bed out towards the top enabling a continuous aeration with a rate around 420 mL/min (corresponding to 0.5 m³/m²/hr). Leaching conditions inside the columns (Col. 1 and Col. 2) were created by percolation of an acidic fluid and a nutritive solution composed of distilled water with acid and ferrous/ferric sulfate in amounts corresponding to conditions at the mine site (1 g/L of ferrous iron as sulphate, 1 g/L of ferric iron as sulphate and 10 g/L of sulfuric acid). This solution was added dropwise from the top of the columns at approximately 5 L/m²/hr, so that it can percolate through the ore within the column and be recovered from the bottom of the system (Figure 6a). The experiments were therefore carried out under unsaturated aerobic conditions, at room temperature (22°C) and very acidic conditions with a pH between 1.8 and 2.2 and a solution oxidation-redox potential (ORP) around 700 mV (i.e. Eh=920 mV). Bioleaching conditions was then created by inoculation of a mesophilic bacterial culture derived from a blend of pure cultures of *Leptospirillum ferrooxidans* and *Acidithiobacillus ferrooxidans*, which are iron- and sulfur- oxidizing bacteria. This culture was continuously maintained on a –40 mesh fines fraction of the original ore sample in standard culture medium, kept in an incubator shaking at 150 revolutions per minute at 30°C, with weekly transfers.

Column 1 (Col. 1) had been continuously supplied with a nutritive solution without acid for 28 days prior to the first SIP measurement. At time $t=0$ h, the acidic fluid and the bacterial consortium was
introduced, marking the start of bioleaching. In column 2 (Col. 2), the same bacterial consortium had been inoculated but 28 days earlier, and the acidic nutritive solution had been flowing continuously since then. Therefore, Col. 1 represents the very beginning of the bioleaching process, whereas Col. 2 reflects a more advanced stage of the process. Figure 6a illustrates the two columns used to test SIP monitoring of the bioleaching process.

<figure><img src="image_7.png" /><figcaption>**Figure 6.** Experimental set-up with column 1 just at the beginning of the bioleaching process and column 2 where the bioleaching is ongoing for 28 days (a), and photograph of the clay inserted between the electrode and the ore to improve electrical contact (b).</figcaption></figure>

To geochemically monitor the bioleaching process, the effluent should have been periodically collected and analysed in terms of pH, sulfate concentration, wetting fluid conductivity, bacteria counting, and dissolved concentration of selected metals. In addition, SEM images of samples collected at different heights and times (before and after the bioleaching process) would have been highly valuable for obtaining information on the dissolution of chalcopyrite and pyrite, as well as for observing bacterial colonization on the surfaces of ore grains. Unfortunately, due to logistical constraints this was not possible in these preliminary experiments. As we did not measure the fluid conductivity of the nutritive solution that flows inside the columns, we calculated it from the geochemical software PhreeqC
considering the above geochemical conditions. We obtained a fluid conductivity of 3.1 S/m. If this oxygenated solution equilibrates with the ore in the column (without constraint on the redox potential), then its fluid conductivity rises to 3.7 S/m.

## 3.2. SIP measurements

SIP measurements were performed with a SIP-FUCHS-II system (Radic Research, Berlin, Germany) from 0.1 to 12 000 Hz. For these preliminary experiments we only used four nonpolarizing Cu/CuSO₄ electrodes that were inserted into the centre of each column through pierced rubber septum corks at 5 cm intervals. We also used clay between electrodes and the ore to improve electrical contact as the agglomerated grains ore are very heterogeneous (Figure 6b). We performed a 4-day SIP monitoring with a Wenner electrode configuration. Laboratory SIP measurements are usually affected by additional mechanisms at high frequencies (above the hundreds of hertz), like those associated with the impedance of the potential electrodes and the parasitic inductive and capacitive coupling between cables of the SIP instrument, which is often assumed to contribute to measurement errors (Huisman et al. 2016). In the case of our experiment, the question of coupling was tested by implementing the programs from Ingeman Nielsen & Baumgartner (2006) and we confirmed that we had no EM coupling problems. For detailed information regarding this implementation, see Ghorbani et al. (2009). The SIP-FUCHS-II operates on a frequency-by-frequency basis. For a given frequency, the signal is divided into several segments. The complex magnitude (real and imaginary parts) is calculated for each segment using a discrete Fourier transform (DFT). The standard deviation of these complex values is then estimated using simple statistics across the segments, and this standard deviation is taken as representative of the measurement error. The uncertainties in magnitude and phase are obtained through error propagation when transforming from real and imaginary components to magnitude and phase. The largest error observed with the SIP-FUCHS-II system during the experiment, for all measurements acquired below 1 kHz, was 0.01 Ohm·m for the magnitude and 1 mrad for the phase. For data measured above 1 kHz, these errors increased to 0.08 Ohm·m and 6 mrad, respectively. Therefore, measurements obtained at frequencies greater than 1 kHz are not discussed in this paper. Based on the magnitude and phase shift of the impedance recorded by the instrument and considering the geometric factor of the electrode configuration, the measured impedance was transformed into resistivity amplitude (|ρ| = 1/|σ|) and
phase shift (φ), and in terms of the real and imaginary conductivity spectra (σ' and σ'', respectively). When the polarization is associated with electron conductors and in the absence of a strong influence of the redox-active species, φ can be a valuable parameter to plot as it is directly proportional to chargeability (m), and is therefore, strongly controlled by the volume concentration of electron conductors and only weakly dependent on the fluid chemistry (Wong 1979; Gurin et al. 2013). In contrast, the imaginary conductivity σ'' is strongly impacted by the conductivity of the background material and then the pore fluid chemistry (Slater et al. 2005; Gurin et al. 2015).

## 4. Results

Figure 7 and Figure 8 show the raw SIP spectra up to 1 kHz in terms of resistivity magnitude (a), minus measured phase shift (b), real part of conductivity (c) and imaginary part of conductivity (d) for Col. 1 and Col. 2 respectively. On Figure 7, the black circles (time t=0h) characterize the electrical state of the ore just before bioleaching started, i.e. acid percolation and bacteria inoculation. Its real conductivity is around 80 mS/m at 0.1 Hz with a slight increase with frequency around 85 mS/m at 750 Hz. The SIP measurements performed one day after the bioleaching started show a slight decrease of the real electrical conductivity from around 80 mS/m to around 65 mS/m at low frequency (Figure 7a). These variations are not really significant and cannot be discussed here as we cannot compare it with the effluent fluid conductivity that has changed due to the injected nutritive flow with bacteria. But these values can be compared with the electrical conductivity estimated from the second Archie's law:

$$ \sigma_b = \sigma_w S_w^n \theta^m \quad (14) $$

with σ_b being the bulk electrical conductivity, σ_w the water (wetting fluid) electrical conductivity, S_w the water saturation, n the saturation exponent, θ the porosity, and m the cementation exponent (Archie 1942). Taking σ_w = 3.7 S/m (estimated from PhreeqC), S_w = 0.5, and θ = 0.3, n = 2, and m = 2 (standard realistic values regarding heap-leaching experiments from Robertson et al. 2023), we obtained an estimation of the bulk electrical conductivity of 83 mS/m. This estimated value is in the same range of the in-phase conductivity measured in the columns (Figure 7a). What is important to notice in this column 1 is the phase shift of 20 mrad at 5 Hz measured just before the bioleaching started (Figure 7b, curve at time 0 h). Such phase amplitude and frequency range have also been observed on laboratory experiments performed on a sulfide-sand mixture. We can cite the works of Martin et al. (2022) who
measured a phase shift of 25 mrad around 2 Hz on unsaturated pyrite-sand mixture samples containing 453 2.75 vol.% of pyrite or the works of Placencia-Gómez et al. (2013) who measured a phase shift around 454 100 mrad at 89 Hz on pyrite-sand mixture during aqueous oxidation conditions. In our experiments, 455 quite one day after the inoculation of bacteria, the phase peak almost disappears and remains fairly flat 456 around 5 mrad at 5 Hz throughout the experiment (Figure 7b). 457

<figure><img src="image_8.png" /><figcaption>**Figure 7.** Raw SIP spectra measured on column 1 at three different times during the experiment: 0 hour just before bioleaching, i.e. acid percolation and bacteria inoculation to the nutritive flow that had been active during 28 days, 22 hours and 95 hours after starting bioleaching. (a) Resistivity amplitude, (b) minus phase shift, (c) real part of conductivity and (d) imaginary part of conductivity.</figcaption></figure>

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SIP results for Col. 2, where the bioleaching process had been ongoing for 28 days, are presented in Figure 8. The in-phase conductivity is higher than in Col. 1 with values between 90 and 105 mS/m at low frequency. The three measurements show a weak increase in conductivity with frequency, with similar shapes. The phase spectra (and imaginary part of conductivity) indicate a very slight peak of around 7 mrad at around 5 Hz throughout the experiment, similar to the last two measurements in Col. 1 (Figure 7).

<figure><img src="image_9.png" /><figcaption>Figure 8. Raw SIP spectra measured on column 2 where the bioleaching process had been ongoing for 28 days with a nutritive flow and bacteria. (a) Resistivity amplitude, (b) minus phase shift. (c), real part of conductivity and (d) imaginary part of conductivity.</figcaption></figure>

# 5. Discussion
From column experiments on chalcocite (Petersen & Dixon 2003) and chalcopyrite (Velásquez-Yévenes et al. 2022), it has been shown that about 30% of the copper is rapidly extracted during the first week, mainly corresponding to the rinsing of the acid soluble copper fraction dissolved during acid agglomeration. After this first rapid stage, these authors observed that the copper extraction rate decreases to a more or less constant rate, reaching 50-60% after two months, before declining. This behaviour has been attributed to the slower leaching of sulfide mineral grains embedded within ore particles, where diffusion of reagents and reaction products through narrow pores and cracks becomes limiting, or to occlusion or passivation layers that covered chalcopyrite surfaces inhibiting the electrochemical leaching mechanism (Zhao et al. 2019). In ore with high pyrite content, such as in our experiment (4 wt%), pyrite oxidation plays a key role by sustaining the Fe³⁺/Fe²⁺ redox cycle (eq. (5)), thereby enhancing the bacterial dissolution of chalcopyrite (Zhao et al. 2015). Our SIP experiments are consistent with these observations. In Col. 1, the phase shift rapidly decreased from 20 mrad to 5 mrad within one day after inoculation, reflecting the onset of intense bioleaching reactions during the early stage of the experiment. This rapid evolution is likely controlled by the coupled oxidation of chalcopyrite and pyrite, whereby chalcopyrite dissolution is driven by acid attack (eq. (1)) and ferric iron (eq. (3)), while pyrite oxidation continuously regenerates Fe³⁺ through bacterial activity (eq. (5)). We interpret this decrease as the combined effects of sulfide mineral alteration, including chalcopyrite dissolution, pyrite oxidation, and the evolution of redox-active species as Fe³⁺ and Fe²⁺ in the pore fluid. These species are known to influence SIP responses by modifying electrochemical double-layer properties at mineral-fluid interfaces and by altering polarization mechanisms within mixtures of porous media and metallic particles (Wong 1979; Slater et al. 2005; Hubbard et al. 2014). Our results are also consistent with Placencia-Gómez et al. (2013) and Placencia-Gómez & Slater (2014, 2016) who shown that the capacitive and polarization properties of sulfide disseminated metallic particles decreased due to oxidation promoted by atmospheric O₂ or due to oxidoreduction reactions promoted by Fe³⁺ ions. Given the limited resources and time available for these experiments, it was not possible to perform SIP monitoring over periods shorter than a few hours. Consequently, the very early dynamics of the initial leaching phase could not be resolved in greater detail, and short-lived transient electrochemical effects may have been missed.
In Col. 2, after one month of bioleaching, SIP monitoring revealed a weak phase shift that remained nearly constant throughout the experiment (Figure 8). This observation suggests either a reduced number of polarizable particles due to the bioleaching process, or the formation of more passive surface layers compared to the initial state of Col. 1 prior to bioleaching. This interpretation is consistent with the fact that, after one month and under such pH conditions, chalcopyrite had fully dissolved, while pyrite was predominantly attacked, expected to be strongly oxidized, and very likely fragmented into small particles, which then became involved in highly complex dissolution processes (Komaka et al. 2016; Jiang et al. 2020). Comparison of the two columns reveals that the spectrum of Col. 2 is flatter and its polarization is a little bit shifted towards lower frequencies relative to Col. 1 (Figure 7b and Figure 8b). This shift of the polarization peak toward lower frequencies and the flattening of the spectra have been observed in experiments on metallic particles subjected to redox reactions, including dissolution processes, and are supported by both experimental results (e.g., Placencia-Gómez & Slater, 2016) and mechanistic modeling. In particular, mechanistic models developed by Bücker et al. (2018, 2019) demonstrate that charge transfer and volume-diffusion relaxation at the mineral-fluid interface associated with redox reactions can lead to such low-frequency shifts and changes in polarization magnitude. In addition, the real part of the conductivity of Col. 2 is higher than that of Col. 1. According to Placencia-Gómez et al. (2013), such variations are indicative of oxidation-dissolution process, and an associated increase in dissolved ions in the pore fluid, including oxidizing products such as Fe²⁺ and Fe³⁺. An important aspect of the bioleaching is the bio-colonisation at the surface of minerals with the formation of biofilms and extracellular polymeric substances (EPS). These microbial structures are known to have an impact on geophysical properties and particularly on IP signals as they modify and alter the electrical double layer at the surface of the minerals (Atekwana & Slater 2009; Kessouri et al. 2019). Within these biofilms, sulfur intermediates can accumulate and iron precipitation can occur, leading to passivation layers that can slow down or even inhibit electrochemical leaching mechanisms (Zhao et al. 2019) and therefore modify SIP signal (Placencia-Gómez et al. 2013; Gurin et al. 2019). To go further with these results, we used eq. 13 to model our data. Taking the real constant $a_{gR} = \sigma_{\infty}$ and $g_{\tau}(\tau) = -(\sigma_0 - \sigma_{\infty})G(\tau)$ with $\sigma_0$ the limit of the conductivity magnitude at null frequency, $\sigma_{\infty}$ the
limit of the conductivity magnitude at “infinite” frequency, and $G(\tau)$ the normalized relaxation time distribution, eq. 13 of the complex electrical conductivity $\sigma(\omega)$ can be modified as:

$$ \sigma(\omega) = \sigma_{\infty} + (\sigma_0 - \sigma_{\infty}) \int \frac{G(\tau)}{1+i\omega\tau} d\tau + i\omega C - i\omega K \quad (15) $$

with the terms $+i\omega C$ and $-i\omega K$ taking into account the high frequency behaviour of the spectrum with a dielectric and an additional term linked to possible experimental coupling effect between cables respectively. Note that the minus in the last term results from the fact that the phase is increasing at high frequency. We applied the algorithm developed by Maineult et al. (2025) to search by optimization the parameters $\sigma_0$, $\sigma_{\infty}$, $G$ and $(C - K)$. The relaxation time distribution RTD $G(\tau)$ is being defined by a Bézier curve. Note here that in order to better constrain our modelling, we use all the spectra from $f_{min} = 0.091553$ Hz to $f_{max} = 12 000$ Hz with 9 control points, on the interval $[\tau_{min} = 1/(2\pi f_{max})$, $\tau_{max} = 1/(2\pi f_{min})]$. The cost function for the adjustment between measurements and predictions is given by:

$$ R = \frac{\sum_{i=1}^{N} (|\sigma_{mes}^{i}| - |\sigma_{pred}^{i}|)^2}{\sum_{i=1}^{N} (|\sigma_{mes}^{i}| - (|\sigma_{mes}^{i}|))^2} + \frac{\sum_{i=1}^{N} (\varphi_{mes}^{i} - \varphi_{pred}^{i})^2}{\sum_{i=1}^{N} (\varphi_{mes}^{i} - (\varphi_{mes}^{i}))^2} \quad (16) $$

where $\langle|\sigma_{mes}^{i}|\rangle$ and $\langle\varphi_{mes}\rangle$ are the mean values of the conductivity amplitude and the phase respectively and $N$ is the number of frequencies. Figure 9 presents the results of the modelling for SIP measurements performed at time $t=0h$ in Col. 1 (before bioleaching) and in Col. 2 (after one month of bioleaching). For both columns, the measurements and the predictions are in very good agreement (Table 4).

<table><caption>**Table 4.** Optimized parameters and cost-function values.</caption><thead><tr><th>Material</th><th>σ<sub>0</sub> (mS m<sup>-1</sup>)</th><th>σ<sub>∞</sub> (mS m<sup>-1</sup>)</th><th>C-K (μF m<sup>-1</sup>)</th><th>R</th></tr></thead><tbody><tr><td>Unleached (column 1)</td><td>80.83</td><td>92.87</td><td>-0.0207</td><td>3.1 10<sup>-4</sup></td></tr><tr><td>Leached (column 2)</td><td>91.18</td><td>100.86</td><td>-0.0328</td><td>1.7 10<sup>-3</sup></td></tr></tbody></table>

After removing the term $i\omega(C - K)$ taking into account the high frequency behaviour of the spectrum, the ‘corrected’ phase spectra reveal two clear peaks for measurements performed before the bioleaching (Col. 1), and after one month of bioleaching (Col. 2) (Figure 10).
<figure><img src="image_10.png" /><figcaption>**Figure 9.** Complex conductivity spectra in the whole frequency range for measurements performed before the bioleaching (Col. 1), and after one month of bioleaching (Col. 2). Dots are measurements and circles predictions of eq. (15). The grey area greater than 1 kHz represents the range of frequencies in which we consider the phase errors due to the additional polarization mechanisms more significant.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Figure 10.** Corrected complex conductivity spectra in the whole frequency range after removing the $i\omega(C - K)$ term for measurements performed before the bioleaching (Col. 1), and after one month of bioleaching (Col. 2). The grey area greater than 1 kHz represents the range of frequencies in which we consider the phase errors due to the additional polarization mechanisms more significant.</figcaption></figure>

The RTD $G(\tau)$ obtained from the corrected complex conductivity spectra are presented on Figure 11. Prior to bioleaching (Col. 1), the RTD exhibits a well-defined peak with dominant relaxation times between 0.01 and 0.1 s. In a porous media free of redox-active ionic species, RTD parameters are known to be closely related to the volumetric content and the effective size of polarizable mineral particles. The total chargeability primarily reflects the volume fraction of electrochemically active particles, while the

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characteristic relaxation time corresponds to an effective electrochemical length scale often associated with particle size (Florsch et al. 2012b; Revil et al. 2015b). Using the conductivities data from Table 4, the total chargeability $m = (\sigma_{\infty} - \sigma_0)/\sigma_{\infty}$ was calculated. This yields $m \approx 0.13$ for Column 1 prior to bioleaching and $m \approx 0.096$ for Column 2 after one month of bioleaching. Based on the relationship proposed by Revil et al. (2015b, Figure 5), these values correspond to an estimated metallic particle volume fraction of approximately 3% for Col. 1 and 2% for Col. 2. The estimated volume fraction before bioleaching is consistent with the mineralogical characterization of the ore (Table 1), which indicates a combined pyrite and chalcopyrite content of about 4.4 wt%. The decrease in chargeability observed after one month of bioleaching indicates a reduction in the number or polarization particles, rather than a substantial change in total metallic content.

The relaxation time $\tau$ is known to be inversely proportional to the effective diffusion coefficient of the charge carriers, $D$ (in m$^2$ s$^{-1}$), and proportional to the square of an effective metallic particle radius, $a$ (in m) (Florsch et al. 2012b; Revil et al. 2015b), according to:

$$ \tau \propto \frac{a^2}{D} \qquad (17) $$

Before the onset of bioleaching (Col. 1), the relaxation time associated with the maximum of the RTD peak is $\tau \approx 0.037$ s (Figure 11). Using reported values of $D$ ranging from $2.9 \times 10^{-5}$ to $4.0 \times 10^{-6}$ m$^2$ s$^{-1}$ (Revil et al. 2015b, Figs. 2 and 3), this corresponds to an effective particle diameter between approximately 0.4 to 1 mm. These values are consistent with the size of pyrite and chalcopyrite grains observed in the ore samples (Figure 3).

After one month of bioleaching (Col. 2), the shift of the RTD toward larger $\tau$ values (around 0.042 s) could, within the adopted model, be interpreted as an increase in the effective size of the polarizable particles, although the distribution becomes broader and flatter. However, this interpretation must be treated with caution. The concurrent decrease in chargeability indicates that bioleaching reduces the number or efficiency of polarization particles. The observed increase in $\tau$ is therefore more plausibly attributed to changes in effective electrochemical length scales caused by mineral dissolution, surface roughening, fragmentation, and/or the formation of passivation layers on sulfide grains. These processes modify the electrochemically active surface and polarization pathways without implying an actual
increase in physical grain size. Taken together, the combined evolution of chargeability and relaxation times suggests that SIP is sensitive to bioleaching-induced alterations of sulfide mineral surfaces and their electrochemical properties, rather than to purely geometrical changes in particle size.

<figure><img src="image_12.png" /><figcaption>**Figure 11.** Relaxation time distributions G(τ) obtained with the corrected complex conductivity spectra for measurements performed before the bioleaching (Col. 1), and after one month of bioleaching (Col. 2).</figcaption></figure>

## Conclusion

We have presented the first laboratory results of spectral induced polarization (SIP) monitoring during sulfidic mineral bioleaching of a low-grade chalcopyrite dominant ore material from a mine in Chile. The bioleaching process consists in extracting copper present at low grade in the ore by injecting an acid

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and nutritive solution and supplying sufficient oxygen to both enhance the microorganism activity and induce the dissolution of the sulfidic mineral. Sulfidic minerals are known to be highly polarizable and with SIP measurements they are characterized by a high phase shift (or a high imaginary component) of the complex conductivity. Our preliminary experiments consisted of SIP measurements performed over 5 days on two columns (Col. 1 and Col. 2) packed with heterogeneous agglomerated chalcopyrite ore and in un-saturated and highly acidic environment (pH ~2). In Col. 1 SIP monitoring began immediately before the onset of bioleaching process was initiated by adding acid in the percolating fluid and inoculating a mesophilic bacterial culture (*Leptospirillum ferrooxidans* and *Acidithiobacillus ferrooxidans*). In contrast, monitoring in Col 2, started one month after the initiation of bioleaching. Results show a drastic decrease of the phase shift in Col. 1 during the early stage of bioleaching (from 20 mrad to 5 mrad at 5 Hz), while Col. 2 displayed a weaker and more stable phase shift (~7 mrad again at 5 Hz).

Beyond the evolution of the phase magnitude, the relaxation time distribution analysis highlights significant changes in polarization mechanisms during bioleaching. Prior to bioleaching, a well-defined relaxation peak is observed, consistent with polarization controlled by sulfide mineral grains. After one month of bioleaching, the relaxation time distribution becomes broader and shifts toward larger τ values, while the chargeability decreases. This combined evolution suggests a reduction in the number or effectiveness of electrochemically polarization particles, together with changes in effective electrochemical length scales. These observations are consistent with bioleaching-induced surface alteration processes, such as mineral dissolution, surface roughening, fragmentation, and/or the formation of passivation layers on sulfide grains, rather than with a simple increase in physical grain size. Although the absence of a dedicated abiotic reference column and the lack of effluent chemistry or mineralogical characterization prevent us from drawing firm conclusions about the direct role of bioleaching on the SIP response, our results highlight the potential of SIP as a complementary tool to monitor biogeochemical transformations during sulfide ore leaching. At the heap scale, leaching efficiency is known to be strongly controlled by solution flow inside the heap, which is often restricted to preferential flow channels implying that a large portion of the bed, although moist, will see no flowing solution. It is therefore postulated that diffusion of reagents and reaction products through such stagnant
zones and into the flowing solution is the key rate-limiting factor in heap leaching. Taken together, this work suggests that geo-electrical methods, and particularly the SIP method, can be very promising and attractive to delineate areas that have been unaffected by the leaching process. Future column experiments including true abiotic column, replicate and detailed monitoring of effluent biogeochemistry (bacterial activity, pH, fluid conductivity, water composition, redox potential), combined with MEB analyses will be required to better constrain the biogeochemical processes underlying the SIP measurements. Coupling such datasets with theoretical electrochemical models should help to better understand the different subprocesses involved in low-grade sulfide ore bioleaching and improve its efficiency.

## Acknowledgements

This work was supported by the French National program EC2CO (Ecosphère Continentale et Côtière). All the experiments were conducted in the laboratories of the Centre for Bioprocess Engineering Research at the University of Cape Town, South Africa. We hereby acknowledge the help from the UMR 6112 LPG "Laboratoire de planétologie et Géosciences" including colleagues Nicolas Stephant and Laurent Lenta for the SEM analyses and the preparation of the polished section. Laurent André from BRGM is also thanked for his help in the PhreeqC program. Philippe Leroy also acknowledges the IMAGE project funded by the French national research agency (ANR) (grant ANR-21-CE04-0013) for supporting his work. We thank the two reviewers Matthias Bücker and Edmundo Placencia-Gómez and the Editor Line Meldgaard Madsen for their useful and constructive comments.

## Data availability statement

The data underlying this article will be shared on reasonable request to the corresponding author

## References

Abdel Aal, G.Z., Atekwana, E.A. & Revil, A., 2014. Geophysical signatures of disseminated iron minerals: A proxy for understanding subsurface biophysicochemical processes. *Journal of Geophysical Research: Biogeosciences*, **119**, 1831–1849. doi:10.1002/2014JG002659

Abdulsamad, F., Florsch, N., Schmutz, M. & Camerlynck, C., 2016. Assessing the high frequency behavior of non-polarizable electrodes for spectral induced polarization measurements.

*Journal of Applied Geophysics*, **135**, 449–455. doi:10.1016/j.jappgeo.2016.01.001
661 Archie, G.E., 1942. The Electrical Resistivity Log as an Aid in Determining some reservoir characteristics. *Transactions of the AIME*, **146**, 54–62. doi:10.2118/942054-G

663 Atekwana, E.A. & Slater, L.D., 2009. Biogeophysics: A new frontier in Earth science research. *Reviews of Geophysics*, **47**, 2009RG000285. doi:10.1029/2009RG000285

665 Atekwana, E.A., Werkema, D.D. & Atekwana, E.A., 2006. Biogeophysics: the effects of microbial processes on geophysical properties of the shallow subsurface. *Applied Hydrogeophysics* **71**, 161–193, eds. Vereecken, H., Binley, A., Cassiani, G., Revil, A. & Titov, K., Springer Netherlands. doi:10.1007/978-1-4020-4912-5_6

669 Bechir, M.B., Almeshal, A. & Dhaou, M.H., 2022. Interpretation of the giant dielectric constant in the single crystal of the CH3NH3PbBr3 perovskite. *Materials Research Bulletin*, **149**, 111723. doi:10.1016/j.materresbull.2021.111723

672 Binley, A. & Slater, L.D., 2020. Resistivity and induced polarization: Theory and applications to the near-surface earth. Cambridge University Press.

674 Brierley, J.A., 1997. Heap leaching of gold-bearing deposits: Theory and operational description. in *Biomining: Theory, Microbes and Industrial Processes*, 103–115, ed. Rawlings, D.E., Springer. doi:10.1007/978-3-662-06111-4_5

677 Bücker, M., Flores Orozco, A. & Kemna, A., 2018. Electrochemical polarization around metallic particles — Part 1: The role of diffuse-layer and volume-diffusion relaxation. GEOPHYSICS, **83**, E203–E217. doi:10.1190/geo2017-0401.1

680 Bücker, M., Undorf, S., Flores Orozco, A. & Kemna, A., 2019. Electrochemical polarization around metallic particles — Part 2: The role of diffuse surface charge. GEOPHYSICS, **84**, E57–E73. doi:10.1190/geo2018-0150.1

683 Bücker, M., Flores Orozco, A., Undorf, S. & Kemna, A., 2019. On the role of Stern- and diffuse-layer polarization mechanisms in porous media. *JGR Solid Earth*, **124**, 5656–5677. doi:10.1029/2019JB017679

686 Bücker, M.B., 2019. *Pore-scale modelling of induced-polarization mechanisms in geologic materials*, Thesis, Universitäts- und Landesbibliothek Bonn. Retrieved from https://bonndoc.ulb.uni-bonn.de/xmlui/handle/20.500.11811/7886
689 Camerlynck C., L. Longuevergne and C., Rocques, 2014. TDIP imaging of watershed over crystalline basement. Proceedings of the 3rd International Workshop on Induced Polarization, 6 – 9 April
690
691 2014, Ile d'Oléron, France, PP. 90-91.

692 Campbell, D.L. & Horton, R.J., 2001. Spectral induced polarization studies of mine waste piles in Colorado and New Mexico. in *14th EEGS Symposium on the Application of Geophysics to Engineering and Environmental Problems*, European Association of Geoscientists & Engineers, p. cp-192-00008. doi:10.4133/1.2922850

696 Dias, C.A., 2000. Developments in a model to describe low-frequency electrical polarization of rocks.
697 *GEOPHYSICS*, **65**, 437–451. doi:10.1190/1.1444738

698 Dimech, A., Cheng, L., Chouteau, M., Chambers, J., Uhlemann, S., Wilkinson, P., Meldrum, P., et al., 2022. A Review on applications of time-lapse electrical resistivity tomography over the last 30 years: Perspectives for Mining Waste Monitoring. *Surv Geophys*, **43**, 1699–1759.
700
701 doi:10.1007/s10712-022-09731-2

702 Dimech, A., Chouteau, M., Aubertin, M., Bussière, B., Martin, V. & Plante, B., 2019. Three-dimensional time-lapse geoelectrical monitoring of water infiltration in an experimental mine waste rock pile. *Vadose Zone Journal*, **18**, 1–19. doi:10.2136/vzj2018.05.0098

705 Donati, E.R. & Sand, W. (Eds.), 2007. *Microbial processing of metal sulfides*, Springer.

706 Emerson, H.P., Szecsody, J.E., Halter, C., Robinson, J.L., Thomle, J.N., Bowden, M.E., Qafoku, O., et al., 2024. Spectral induced polarization of corrosion of sulfur modified Iron in sediments. *Journal of Contaminant Hydrology*, **267**, 104439. doi:10.1016/j.jconhyd.2024.104439

709 Flores Orozco, A., Williams, K.H., Long, P.E., Hubbard, S.S. & Kemna, A., 2011. Using complex resistivity imaging to infer biogeochemical processes associated with bioremediation of an uranium-contaminated aquifer. *J. Geophys. Res.*, **116**, G03001. doi:10.1029/2010JG001591

712 Florsch, N., Camerlynck, C. & Revil, A., 2012. Direct estimation of the distribution of relaxation times from induced-polarization spectra using a Fourier transform analysis. *Near Surface Geophysics*, **10**, 517–531. doi:10.3997/1873-0604.2012004
715 Florsch, N., Camerlynck, C. & Stockwell, J., 2011. The spectral response relative to a log-normal time constant distribution. *Golden Workshop on Induced Polarization* *Denver, Colorado, 2011*,
716
717 Colorado School of Mine. Retrieved from https://hal.science/hal-04855835

718 Florsch, N., Feras, A., Bonnenfant, J. & Camerlynck, C., 2017. La polarisation provoquée, outil géophysique de spatialisation des amas de scories pour l'estimation des productions sidérurgiques. *archeosciences*, 23-33. doi:10.4000/archeosciences.4958

721 Florsch, N., Llubes, M. & Téreygeol, F., 2012. Induced polarization 3D tomography of an archaeological direct reduction slag heap. *Near Surface Geophysics*, **10**, 567-574.
doi:10.3997/1873-0604.2012042

724 Florsch, N., Llubes, M., Téreygeol, F., Ghorbani, A. & Roblet, P., 2011. Quantification of slag heap volumes and masses through the use of induced polarization: application to the Castel-Minier site. *Journal of Archaeological Science*, **38**, 438-451. doi:10.1016/j.jas.2010.09.027

727 Florsch, N., Revil, A. & Camerlynck, C., 2014. Inversion of generalized relaxation time distributions with optimized damping parameter. *Journal of Applied Geophysics*, **109**, 119-132.
doi:10.1016/j.jappgeo.2014.07.013
729 Florsch, N., Camerlynck, C. & Revil, A., 2012b. Direct estimation of the distribution of relaxation times from induced-polarization spectra using a Fourier transform analysis. *Near Surface Geophysics*, **10**, 517-531. doi:10.3997/1873-0604.2012004

733 Ghorbani, A., Camerlynck, C. & Florsch, N., 2009. CR1Div: A Matlab program to invert 1D spectral induced polarization data for the Cole-Cole model including electromagnetic effects.
*Computers & Geosciences*, **35**, 255-266. doi:10.1016/j.cageo.2008.06.001

736 Grosse, C. & Delgado, A.V., 2010. Dielectric dispersion in aqueous colloidal systems. *Current Opinion in Colloid & Interface Science*, **15**, 145-159. doi:10.1016/j.cocis.2009.11.004

738 Gurin, G., Tarasov, A., Ilyin, Y. & Titov, K., 2013. Time domain spectral induced polarization of disseminated electronic conductors: Laboratory data analysis through the Debye decomposition approach. *Journal of Applied Geophysics*, **98**, 44-53.
doi:10.1016/j.jappgeo.2013.07.008
742 Gurin, G., Titov, K. & Ilyin, Y., 2019. Induced polarization of rocks containing metallic particles: evidence of passivation effect. *Geophysical Research Letters*, **46**, 670–677.
doi:10.1029/2018GL080107

745 Gurin, G., Titov, K., Ilyin, Y. & Tarasov, A., 2015. Induced polarization of disseminated electronically conductive minerals: a semi-empirical model. *Geophysical Journal International*, **200**, 1555–1565. doi:10.1093/gji/ggu490

748 Horton, G.W. & Frangos, W., 2005. Electrical properties of leach ore, cripple creek mining district, Colorado | Symposium on the Application of Geophysics to Engineering and Environmental Problems 2005. *Symposium on the Application of Geophysics to Engineering and Environmental Problems*, 1388. doi:10.4133/1.2923472

752 Hubbard, C.G., West, L.J., Rodriguez-Blanco, J.D. & Shaw, S., 2014. Laboratory study of spectral induced polarization responses of magnetite — Fe2+ redox reactions in porous media. *Geophysics*, **79**, D21–D30. doi:10.1190/geo2013-0079.1

755 Huisman, J.A., Zimmermann, E., Esser, O., Haegel, F.-H., Treichel, A. & Vereecken, H., 2016. Evaluation of a novel correction procedure to remove electrode impedance effects from broadband SIP measurements. *Journal of Applied Geophysics* New trends in Induced Polarization, **135**, 466–473. doi:10.1016/j.jappgeo.2015.11.008

759 Hupfer, S., Martin, T., Weller, A., Günther, T., Kuhn, K., Djotsa Nguimeya Ngninjio, V. & Noell, U., 2016. Polarization effects of unconsolidated sulphide-sand-mixtures. *Journal of Applied Geophysics*, **135**, 456–465. doi:10.1016/j.jappgeo.2015.12.003

762 Ingeman-Nielsen, T. & Baumgartner, F., 2006. CR1Dmod: A Matlab program to model 1D complex resistivity effects in electrical and electromagnetic surveys. *Computers & Geosciences*, **32**, 1411–1419. doi:10.1016/j.cageo.2006.01.001

765 Jiang, L., Zhou, H. & Peng, X., 2007. Bio-oxidation of pyrite, chalcopyrite and pyrrhotite by *Acidithiobacillus ferrooxidans*. *Chinese Science Bulletin*, **52**, 2702–2714. doi:10.1007/s11434-007-0352-4
768 Kemna, A., Binley, A., Cassiani, G., Niederleithinger, E., Revil, A., Slater, L., Williams, K.H., et al., 2012. An overview of the spectral induced polarization method for near-surface applications. *Near Surface Geophysics*, **10**, 453–468. doi:10.3997/1873-0604.2012027

771 Kessouri, P., Furman, A., Huisman, J.A., Martin, T., Mellage, A., Ntarlagiannis, D., Bücker, M., et al., 2019. Induced polarization applied to biogeophysics: recent advances and future prospects. *Near Surface Geophysics*, **17**, 595–621. doi:10.1002/nsg.12072

774 Kocaman, A. T., Cemek, M., & Edwards, K. J. 2016. Kinetics of pyrite, pyrrhotite, and chalcopyrite dissolution by *Acidithiobacillus ferrooxidans*. Canadian journal of microbiology, **62**(8), 629–642. doi:10.1139/cjm-2016-0085

777 Leppänen, J.J., Weckström, J. & Korhola, A., 2017. Multiple mining impacts induce widespread changes in ecosystem dynamics in a boreal lake. Sci Rep, **7**, 10581. doi:10.1038/s41598-017-11421-8

780 Leroy, P., Revil, A., Kemna, A., Cosenza, P. & Ghorbani, A., 2008. Complex conductivity of water-saturated packs of glass beads. *Journal of Colloid and Interface Science*, **321**, 103–117. doi:10.1016/j.jcis.2007.12.031

783 Leroy, P., Maineult, A., Mendieta, A. & Jougnot, D., 2025. A mechanistic model for the complex conductivity of clay materials. I. Theory. *Geophysical Journal International*, ggae411. doi:10.1093/gji/ggae411

786 Li, J., Yang, H., Tong, L. & Sand, W., 2022. Some Aspects of Industrial Heap Bioleaching Technology: From Basics to Practice. *Mineral Processing and Extractive Metallurgy Review*, **43**, 510–528, Taylor & Francis. doi:10.1080/08827508.2021.1893720

789 Lizama, H.M., 2023. In-situ leaching of copper from spent heaps. *Hydrometallurgy*, **215**, 105997. doi:10.1016/j.hydromet.2022.105997

791 Maineult, A., Camerlynck, C. & Florsch, N., 2025. Short note: on the determination of the relaxation time distributions using Bézier curves. *Geophysical Journal International*, **244**, ggaf421. doi:10.1093/gji/ggaf421
794 Marsden, J.O. & Botz, M.M., 2017. Heap leach modeling -- A review of approaches to metal

795 production forecasting. *Minerals & Metallurgical Processing*, **34**, 53–64, Society for Mining,

796 Metallurgy, & Exploration, Inc. doi:10.19150/mmp.7505

797 Martin, T. & Weller, A., 2023. Superposition of induced polarization signals measured on pyrite–sand

798 mixtures. *Geophysical Journal International*, **234**, 699–711. doi:10.1093/gji/ggad091

799 Martin, T., Weller, A. & Behling, L., 2022. Desaturation effects of pyrite–sand mixtures on induced

800 polarization signals. *Geophysical Journal International*, **228**, 275–290.

801 doi:10.1093/gji/ggab333

802 Mellage, A., Holmes, A.B., Linley, S., Vallée, L., Rezanezhad, F., Thomson, N., Gu, F., et al., 2018.

803 Sensing coated iron-oxide nanoparticles with spectral induced polarization (SIP): Experiments

804 in natural sand packed flow-through columns. *Environ. Sci. Technol.*, **52**, 14256–14265.

805 doi:10.1021/acs.est.8b03686

806 Moradipour, M., Hojat, A., Ranjbar, H., Nasab, S.K., Roodposhti, H.R. & Daneshpajouh, S., 2015.

807 Application of geophysical methods to determine subsurface acid saturated zones of heap No.

808 3 at Sarcheshmeh copper mine, Iran. doi:10.1109/IWAGPR.2015.7292630

809 Pelton, W.H., Ward, S.H., Hallof, P.G., Sill, W.R. & Nelson, P.H., 1978. Mineral discrimination and

810 removal of inductive coupling with multifrequency IP. *Geophysics*, **43**, 588–609.

811 doi:10.1190/1.1440839

812 Petersen, J. & Dixon, D.G., 2003. The dynamics of chalcocite heap bioleaching. Hydrometallurgy,

813 Proceedings of the 5th International Symposium Honoring Professor Ian M. Ritchie. C.

814 Young, A. Alfantazi, C. Anderson, A. James, D. Dreisinger, and B. Harris, editors. 1, 351–

815 364.

816 Petersen, J. and Dixon, D.G., 2007. Principles, mechanisms and dynamics of chalcocite heap

817 bioleaching. In: Donati, E.R., Sand, W. (eds) Microbial Processing of Metal Sulfides.

818 Springer, Dordrecht. https://doi.org/10.1007/1-4020-5589-7_10

819 Petersen, J., 2016. Heap leaching as a key technology for recovery of values from low-grade ores – A

820 brief overview. *Hydrometallurgy*, **165**, 206–212. doi:10.1016/j.hydromet.2015.09.001
821 Petersen, J., 2023. From understanding the rate limitations of bioleaching mechanisms to improved

822 bioleach process design. *Hydrometallurgy*, **221**, 106148. doi:10.1016/j.hydromet.2023.106148

823 Placencia-Gómez, E., Parviainen, A., Slater, L. & Leveinen, J., 2015. Spectral induced polarization

824 (SIP) response of mine tailings. *Journal of Contaminant Hydrology*, **173**, 8–24.

825 doi:10.1016/j.jconhyd.2014.12.002

826 Placencia-Gómez, E., Slater, L., Ntarlagiannis, D. & Binley, A., 2013. Laboratory SIP signatures

827 associated with oxidation of disseminated metal sulfides. *Journal of Contaminant Hydrology*,

828 **148**, 25–38. doi:10.1016/j.jconhyd.2013.02.007

829 Placencia-Gómez, E. & Slater, L.D., 2016. On the pore water chemistry effect on spectral induced

830 polarization measurements in the presence of pyrite. *Journal of Applied Geophysics*, **135**,

831 474–485. doi:10.1016/j.jappgeo.2015.11.001

832 Po, A., Hubau, A., Joulian, C., Dakkoune, A., Julcour-Lebigue, C., Bourgeois, F., Touzé, S., et al.,

833 2022. Bioleaching of chalcopyrite: the effect of particle size on passivation, bacterial growth

834 and activity, Presented at the 24th International Biohydrometallurgy Symposium (IBS).

835 Retrieved from https://hal.science/hal-04752743

836 Power, C. & Almpanis, A., 2022. Improved imaging efficiency of large mine waste rock piles with

837 integrated electrical and electromagnetic geophysical techniques. *Journal of Applied*

838 *Geophysics*, **206**, 104824. doi:10.1016/j.jappgeo.2022.104824

839 Power, C., Tsourlos, P., Ramasamy, M., Nivorlis, A. & Mkandawire, M., 2018. Combined DC

840 resistivity and induced polarization (DC-IP) for mapping the internal composition of a mine

841 waste rock pile in Nova Scotia, Canada. *Journal of Applied Geophysics*, **150**, 40–51.

842 doi:10.1016/j.jappgeo.2018.01.009

843 Pradhan, N., Nathsarma, K.C., Srinivasa Rao, K., Sukla, L.B. & Mishra, B.K., 2008. Heap bioleaching

844 of chalcopyrite: A review. *Minerals Engineering*, **21**, 355–365.

845 doi:10.1016/j.mineng.2007.10.018

846 Qi, Y., Soueid Ahmed, A., Revil, A., Ghorbani, A., Abdulsamad, F., Florsch, N. & Bonnenfant, J.,

847 2018. Induced polarization response of porous media with metallic particles — Part 7:
848 Detection and quantification of buried slag heaps. *GEOPHYSICS*, **83**, E277–E291.

849 doi:10.1190/geo2017-0760.1

850 Revil, A., Abdel Aal, G.Z., Atekwana, E.A., Mao, D. & Florsch, N., 2015. Induced polarization response of porous media with metallic particles — Part 2: Comparison with a broad database
851
852 of experimental data. *GEOPHYSICS*, **80**, D539–D552. doi:10.1190/geo2014-0578.1

853 Revil, A., Coperey, A., Mao, D., Abdulsamad, F., Ghorbani, A., Rossi, M. & Gasquet, D., 2018. Induced polarization response of porous media with metallic particles — Part 8: Influence of temperature and salinity. *GEOPHYSICS*, **83**, E435–E456. doi:10.1190/geo2018-0089.1

856 Revil, A., Florsch, N. & Mao, D., 2015. Induced polarization response of porous media with metallic particles — Part 1: A theory for disseminated semiconductors. *GEOPHYSICS*, **80**, D525–D538. doi:10.1190/geo2014-0577.1

859 Revil, A., Vaudelet, P., Su, Z. & Chen, R., 2022. Induced Polarization as a Tool to Assess Mineral Deposits: A Review. *Minerals*, **12**, 571. doi:10.3390/min12050571

861 Robertson, S.W., Basson, P., Staden, P.J. van & Petersen, J., 2023. Properties governing flow of solution and air through crushed ore for heap leaching: Part II unsaturated dual-phase flow. *Hydrometallurgy*, **215**, 105990. doi:10.1016/j.hydromet.2022.105990

864 Rucker, D.F., Milczarek, M.A., Baldyga, C.A. & Cubbage, B., 2015. Investigating leaching alternatives for heterogeneous heap leach pads. *Proceedings of Heap Leach Solutions*, 14-16, Reno, USA.

867 Schnell, H.A., 1997. Bioleaching of copper. in *Biomining: Theory, Microbes and Industrial Processes*, pp. 21–43, ed. Rawlings, D.E., Springer. doi:10.1007/978-3-662-06111-4_2

869 Shiers, D.W., Collinson, D.M. & Watling, H.R., 2016. Life in heaps: a review of microbial responses to variable acidity in sulfide mineral bioleaching heaps for metal extraction. *Research in Microbiology* Special issue on Biohydrometallurgy: recent advances in microbiology and molecular biology, **167**, 576–586. doi:10.1016/j.resmic.2016.05.007

873 Slater, L.D., Choi, J. & Wu, Y., 2005. Electrical properties of iron-sand columns: Implications for induced polarization investigation and performance monitoring of iron-wall barriers. *GEOPHYSICS*, **70**, G87–G94. doi:10.1190/1.1990218
876 Su, D., Almpanis, A. & Power, C., 2024. Complex electrical measurements of waste rock during acid mine drainage generation and release: Kinetic column tests. *Journal of Environmental Management*, **351**, 119996. doi:10.1016/j.jenvman.2023.119996

879 Tarantola, A. & Valette, B., 1982. Generalized nonlinear inverse problems solved using the least squares criterion. *Reviews of Geophysics*, **20**, 219–232. doi:10.1029/RG020i002p00219

881 Tarasov, A. & Titov, K., 2013. On the use of the Cole–Cole equations in spectral induced polarization. *Geophysical Journal International*, **195**, 352–356. doi:10.1093/gji/ggt251

883 Vanhala, H. & Peltoniemi, M., 1992. Spectral IP studies of Finnish ore prospects. *GEOPHYSICS*, **57**, 1545–1555. doi:10.1190/1.1443222

885 Velásquez-Yévenes, L., Malverde, S. & Quezada, V., 2022. A sustainable bioleaching of a low-grade chalcopyrite ore. *Minerals*, **12**, 487. doi:10.3390/min12040487

887 Vera, M., Schippers, A., Hedrich, S. & Sand, W., 2022. Progress in bioleaching: fundamentals and mechanisms of microbial metal sulfide oxidation – part A. *Appl Microbiol Biotechnol*, **106**, 6933–6952. doi:10.1007/s00253-022-12168-7

890 Vinegar, H.J. & Waxman, M.H., 1984. Induced polarization of shaly sands. *GEOPHYSICS*, **49**, 1267–1287, Society of Exploration Geophysicists. doi:10.1190/1.1441755

892 Webb, G., Tyler, S. w., Collord, J., Van Zyl, D., Halihan, T., Turrentine, J. & Fenstemaker, T., 2008.

893 Field-scale analysis of flow mechanisms in highly heterogeneous mining media. *Vadose Zone Journal*, **7**, 899–908. doi:10.2136/vzj2007.0130

895 Williams, K.H., Ntarlagiannis, D., Slater, L.D., Dohnalkova, A., Hubbard, S.S. & Banfield, J.F., 2005.

896 Geophysical imaging of stimulated microbial biomineralization. *Environ. Sci. Technol.*, **39**, 7592–7600. doi:10.1021/es0504035

898 Wong, J., 1979. An electrochemical model of the induced-polarization phenomenon in disseminated sulfide ores. *GEOPHYSICS*, **44**, 1245–1265. doi:10.1190/1.1441005

900 Wu, Y., Slater, L.D. & Korte, N., 2005. Effect of precipitation on low frequency electrical properties of zerovalent iron columns. *Environ. Sci. Technol.*, **39**, 9197–9204, American Chemical Society. doi:10.1021/es051052x
903 Zanbak, C., 2012. Heap leaching technique in mining within the context of best available techniques

904 (BAT) - *Introductory Statement by Euromines*. doi:10.13140/RG.2.2.36374.86081

905 Zhao, H., Wang, J., Gan, X., Zheng, X., Tao, L., Hu, M., Li, Y., *et al.*, 2015. Effects of pyrite and

906 bornite on bioleaching of two different types of chalcopyrite in the presence of Leptospirillum

907 ferriphilum. *Bioresource Technology*, **194**, 28–35. doi:10.1016/j.biortech.2015.07.003

908 Zhao, H., Zhang, Y., Zhang, X., Qian, L., Sun, M., Yang, Y., Zhang, Y., *et al.*, 2019. The dissolution

909 and passivation mechanism of chalcopyrite in bioleaching: An overview. *Minerals*

910 *Engineering*, **136**, 140–154. doi:10.1016/j.mineng.2019.03.014

911

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