A numerical investigation into key factors controlling hard rock excavation via electropulse stimulation

Daniel Vogler, Stuart D.C. Walsh, Martin O. Saar

a Geothermal Energy and Geofluids, Institute of Geophysics, ETH Zurich, Zurich, Switzerland

b Department of Civil Engineering, Monash University, Melbourne, Australia

c Department of Earth and Environmental Sciences, University of Minnesota, Minneapolis, USA

ABSTRACT Electropulse stimulation provides an energy-efficient means of excavating hard rocks through repeated application of high voltage pulses to the rock surface. As such, it has the potential to confer significant advantages to mining and drilling operations for mineral and energy resources. Nevertheless, before these benefits can be realized, a better understanding of these processes is required to improve their deployment in the field. In this paper, we employ a recently developed model of the grain-scale processes involved in electropulse stimulation to examine excavation of hard rock under realistic operating conditions. To that end, we investigate the maximum applied voltage within ranges of 120—600 kV, to observe the onset of rock fragmentation. We further study the effect of grain size on rock breakage, by comparing fine (granodiorite) and coarse grained (granite) rocks. Lastly, the pore fluid salinity is investigated, since the electric conductivity of the pore fluid is shown to be a governing factor for the electrical conductivity of the modeled system. This study demonstrates that all investigated factors are crucial to the efficiency of rock fragmentation by electropulsing.

Keywords:Electropulse stimulation High voltage breakdown Numerical modeling Drilling Thermo-mechanics

1. Introduction

Drilling through hard rocks is commonly required in geothermal drilling, deep-borehole disposal of nuclear waste, basaltic carbon sequestration and metalliferous mining. However, for hard rocks(granites, basalts and quartzites), conventional drilling methods,which rely on mechanical abrasion, become increasingly ineffective. This can largely be attributed to the increased tool wear and lower penetration rates encountered in hard rocks. This has significant financial repercussions as drilling operations often constitute a major portion of the upfront costs of reservoir operations (Tester et al.,2007).

Here, high voltage electropulse stimulation presents a promising alternative to the excavation and processing of hard rocks by reducing drilling costs (Biela et al., 2008; Bluhm et al., 2000).High voltage pulses have been studied as a means to fragment rock for quite some time (Andres, 1977; Andres et al., 2001; He et al., 2013; Zuo et al., 2014, 2015a), and have also been used for civil engineering demolition and recycling operations(Lisitsyn et al., 1998; Bluhm et al., 2000; Uenishi et al., 2016).Electropulse stimulation works by subjecting the rock surface to high voltage electric pulses of extremely short duration. First, an electric potential is established between a number of electrodes,which are in contact to the rock mass. To prevent breakdown occurring through the drilling mud surrounding the electrodes, a liquid dielectric is used as drilling mud. It is important, however,that the voltage rise time is below a threshold (e.g. 500 ns for water (Bluhm et al., 2000)) to ensure that the breakdown field strength of the solid is lower than that of the liquid. Next, the passage of these high voltage pulses through the rock body coincides with the breakdown of the dielectric properties of the rock and results in localized heating (Andres, 1977; Budenstein,1980; Inoue et al., 1999, 2000). The sudden increase in temperature results in local thermal expansion of the rock,causing rocks to fracture.

Electropulse methods provide an energy efficient means to induce fractures due to the short duration of the voltage pulse (on the order of microseconds),and as the rock is broken under tension(rather than compression, as is typical during mechanical drilling methods). Moreover, the method has the potential to reduce or eliminate time lost to equipment wear and replacement (such as so-called tripping times) as no mechanical contact is necessary to drill (Anders et al., 2017). For these reasons, electropulse stimulation provides an attractive alternative to more conventional approaches in hard rock operations.

However, the fundamental physical processes involved during electropulse stimulation remain poorly understood, hindering commercial deployment of this drilling technology. In this paper,we employ a recently developed model of the grain-scale processes involved in electropulse stimulation to examine excavation of hard rock under realistic operating conditions. In particular, we investigate the effect of the maximum applied voltage on rock breakage.We also consider the effect of grain size by considering rock analogues of granite (coarse grained) and granodiorite (fine grained)rocks.Finally,we study the impact of the brine’s salt concentration in the rock on electric field and consequently on rock fragmentation. We thereby highlight important material characteristics that dominate the efficiency of rock fragmentation by electropulse drilling.

2. Model description

The simulations considered in this paper use a recently developed model that couples the electrical breakdown and conductive path of the pulse, with subsequent resistive heating and induced damage to the rock. All model components are described in detail in Walsh and Vogler (2020), and a summary of different stages involved in the simulation are provided below.

Simulations of the system behavior are conducted in MOOSE, a multiphysics finite element solver developed by Idaho National Laboratory(Gaston et al.,2009).MOOSE is an open source platform and is therefore a suitable framework to implement the individual processes investigated in this study.

The system consists of a 2 cm thick solid body, composed of various minerals, which are designed based on statistical parameters of real rock types, as shown in Fig. 1. Two electrodes are positioned on opposing sides of the solid body, between which an electric potential is established. This ultimately leads to electric breakdown, an electric current through the rock mass and consequently heating of the material and thermo-mechanical strains.With electrodes on opposing sides of the rock, the presented configuration further separates processes occurring in the dielectric (i.e. drilling mud) between the two electrodes, with similar configurations employed in other studies on electropulse fragmentation(Andres et al.,2001;Bluhm et al.,2000;Shi et al.,2014;Zuo et al., 2014, 2015b).

Fig.1. System geometry and boundary conditions. An electric potential is established across a laterally confined rock slab.The rock slab consists of a heterogeneous mineral composition and has a thickness of 2 cm.

The model simulates three different material phenomena to reproduce the effect of the electrical stimulation on the rock. The first is the passage of the voltage pulse through the rock,the second is the resistive heating that occurs subsequently, while the third represents the mechanical response,induced by the thermal shock load. While these physical processes are coupled, the initial transmission of the pulse and subsequent damage to the can rock act on distinct timescales, which enables the electrical and mechanical effects of the pulses to be considered independently.

2.1. Electric current

Similar to other models examining the material effects of high voltage discharges,we represent the electrical discharge as a quasistatic process(Ogasawara et al.,2010;Abdelal and Murphy,2014;Li et al.,2018).We simulate the passage of the electric pulse through the rock using Ohm’s law:

whereJiis the electric current;Λijis the conductivity;andEjis the electric field,which is related to the electric potential φ byEj= φ，j.

The electric current causes resistive heating of the rock(Eq.(2)),which increases the temperature according to Eq. (3):

where Δθ is the increase in temperature,qDis the increase in energy in the system,cpis the specific heat capacity of the solid phase,and ρ is the density of the solid phase.

2.2. Electrical conductivity

In hard rocks, such as granite and granodiorite, conductivity is largely governed by the fluids in the rock matrix, as individual mineral compositions are several orders of magnitude less conductive than the in situ fluid (i.e. pore fluid).

We employ two rules to capture this behavior. The first is a mixture model that represents the amount of current flowing through each phase in the matrix. In the model, the relative conductivity is represented with Glover’s two phase extension to Archie’s law (Glover et al., 2000; Glover, 2010). The underlying assumption of Glover’s mixture model is that each phase represents a separate conducting pathway:

where Λmis the matrix/two phase conductivity; Λsand Λfare the effective solid and fluid electrical conductivities, respectively;φfis the fluid volume fraction;mis the Archie’s exponent;andp=We adopt a value of 1.5 for Archie’s exponent (m), based on measurements (Pape et al.,1985).

The pore fluid content within the rock matrix, governed by the microporosity, however, is not distributed equally in the rock matrix.We adopt estimates from Montgomery and Brace(1975),who quantified microporosity for the minerals encountered in the hard rocks investigated in their work(i.e.quartz,plagioclase,K-feldspar and biotite, see Table 2). Most notably, the microporosity of plagioclase is two times larger than that of the other minerals.This,in turn, results in a larger effective electrical conductivity within plagioclase minerals, which can facilitate inhomogeneous distributions of electric current. The resulting electrical conductivity of the fluid phase and its dependency on temperature can be estimated with empirical relations for NaCl solutions (Arps,1953;Ucok et al., 1980; Fleury and Deschamps, 2008; Sinmyo and Keppler, 2017). A more detailed description can be found in Walsh and Vogler (2020).

Transmission of the pulse heats the fluid and rock phases.During discharge,we assume heating is localized to the individual phases, according to the following equations:

whereqfandqsare the energies deposited by resistive heating in the fluid and solid phases, respectively;are the heat capacities of the fluid and solid phases,respectively;ρfis the density of the fluid and ρsis the density of the solid.When simulating the thermal expansion stage,the increase in temperature is calculated from the heat of the two phases:

Heating of the rock mass and resulting conductivity changes can further increase conductivity and favor a breakdown of its dielectric properties (O’dwyer,1958; Kao, 2004). This coupled behavior between electric current and dependence of electrical conductivity on temperature is modeled as thermal breakdown (Kao,1984, 2004).Thermal breakdown can lead to a channeling behavior of the electric current, depending on a range of factors such as microporosity, pore fluid salinity, rock matrix composition and others(Ogasawara et al., 2010; Wang, 2017).

2.3. Thermo-mechanical response

Within the rock mass,heat transfer occurs via thermal diffusion with the thermal conductivity,κ:

Heating of the rock mass induces a mechanical response in form of a linear thermal strain with reference temperature θref, thermal expansion coefficient α, and Kronecker delta tensor δij:

The corresponding thermal stresses σthermalare computed from the linear thermal strainand the stiffness tensorCijklas

The thermal stresses can then be considered by the mechanical failure criteria to determine regions of material fragmentation.

2.4. Failure criteria

This study employs a previously developed failure criterion(Diederichs et al.,2004;Diederichs,2007;Rojat et al.,2008),which was created to capture spalling damage on rock surfaces, for example in tunnels,and which is thus suitable for capturing failure due to stress states near excavation surfaces. The damage model has been thoroughly tested against experiment data from Lac du Bonnet granite, obtained from the Underground Research Laboratory in Manitoba, Canada by Diederichs (Diederichs et al., 2004).Building on that work,Rojat et al.(2008)used the failure criterionto study excavation surface damage in tunneling operations in the Swiss Alps, where spalling on the surfaces occurred in massive granite,granodiorite and gneiss formations.

Table 1Mineral composition and grain size distributions for granite and granodiorite,obtained from Lac du Bonnet granitic rocks (Eberhardt et al.,1999).

The employed failure criterion uses the well-known Hoek-Brown criterion,which predicts failure in rock specimen,subjected to confinement (Hoek and Brown,1980,1997):

While the Hoek-Brown criterion is used for intact rock laboratory specimens without defects, Diederichs et al. (2004) and Diederichs (2007) expanded the Hoek-Brown criterion by introducing additional failure envelopes that correspond to the lower thresholds of rock strength in massively or moderately jointed rock masses that are situated near excavation surfaces and therefore not confined. Specifically, failure between the Hoek-Brown failure envelope (rock strength of intact rock specimen) and spalling failure envelope (lower strength threshold of jointed rock masses) is assumed to be brittle in nature and consists of crack propagation near excavation surfaces. The lack of confinement on excavation surfaces can yield locally high tensile stresses, which then exceed the tensile strength of the rock σt. This tensile failure can cause crack dilation that further reduces the strength of the rock mass.A failure envelope below the Hoek-Brown envelope is further supported by the stress—strain history of in situ rock mass,which can result in pre-existing damage that a laboratory specimen is not exposed to.Whether a rock strength below the Hoek-Brown failure envelope is encountered or not,however, depends on a multitude of factors, such as material heterogeneities, excavation surface effects,pre-existing damage,strain localization due to grain size and material heterogeneities, local tensile stresses (Rauenzahn and Tester, 1989), or damage nucleation sites in form of minor minerals (Tang and Kaiser, 1998; Rauenzahn and Tester, 1989;Diederichs et al., 2004) or micropores (Walsh and Lomov, 2013).It should be emphasized that failure by spalling indicates a region that has the potential to fail if it is adjacent to a free surface.

Fig. 2. Rock material microstructure for coarse- and fine-grained compositions.Compositions are based on granite (top) and granodiorite (bottom) data of mineral phase percentages and average grain sizes,listed in Table 1 and Eberhardt et al.(1999).

Table 2Mechanical and thermal material properties of K-feldspar,plagioclase,quartz and biotite,adopted for this paper(Montgomery and Brace,1975;Bass,1995;Findikakis,2004;Huotari,2004; Mavko et al., 2009; Clauser and Huenges,2013).

The resulting failure modes can be summarized as follows: (1)Tensile failure;(2)Spalling failureis tensile);(3)Spalling failureis compressive); (4) Hoek-Brown failureis tensile); and (5)Hoek-Brown failureis compressive).Further information on the different failure modes can also be found in associated works(Diederichs et al.,2004;Rojat et al.,2008;Vogler et al.,2020;Walsh and Vogler,2020).The values for the failure models in this study are assumed to be 1 fors,0.5 fora,122 MPa for σc,25 MPa form,10 MPa for σt,and 8 for the spalling limit(σ1/σ3)(Jaeger et al.,2009;Rojat et al., 2008; Rauenzahn and Tester, 1989; Kazerani, 2013; Vogler et al., 2017). It should be noted that a spalling limit of 8 denotes the lower bound of this ratio, as used in previous studies (Rojat et al., 2008).

2.5. Material composition

Thermo-mechanical damage relies on contrasts in material properties, such as electrical conductivities of fluid or solid phase Λfand Λs,thermal expansion coefficient α or porosity of individual grain types. The material composition, such as grain sizes and volumetric percentages of grains, may therefore influence the material response to electro-pulsing (Tang and Kaiser, 1998).Herein, we study the impact of material composition by investigating a range of materials,i.e.a fine-grained and a coarse-grained material. Specifically, we investigate the known material compositions of granite and granodiorite (Eberhardt et al., 1999), since granitic rocks have been extensively investigated as hard rocks commonly encountered in drilling operations (Rinaldi, 1984;Rauenzahn and Tester,1989,1991; Walsh et al., 2014; Kant et al.,2017a, 2017b; H?ser et al., 2018; Rossi et al., 2020). The resulting volumetric percentages of the mineral phases and their average grain sizes are shown in Table 1. To reduce the complexity of the analysis,we use the granite composition as a baseline case for most of our simulations; however, we explicitly compare granite and granodiorite material compositions for given cases.

Fig. 3. Zoom into a region of 3 cm width and 2 cm height in the granite and granodiorite system domains (from Figs.1 and 2).

The mineral phase data presented in Table 1 can be used to generate a representative material composition with four minerals:K-feldspar, plagioclase, quartz and biotite. This is achieved with a Voronoi tessellation with separate phases for the four different mineral types, with each Voronoi cell representing a single grain.After an initial Voronoi grid is built,the cell volumes are iteratively relaxed until the desired grain size and mineral volumes are obtained (Walsh and Lomov, 2013; Walsh, 2013; Singh et al., 2015),examples of which are shown in Fig. 2.

Isotropic thermo-mechanical properties of the rocks are then assigned to different mineral cells(see Table 2),which are available from literature data (Bass,1995; Findikakis, 2004; Huotari, 2004;Mavko et al., 2009; Clauser and Huenges, 2013).

2.6. Pore fluid

Microporosity distribution in the grains, which is known to be non-uniform (Montgomery and Brace, 1975), is another driving factor of heterogeneity in electropulse drilling. These pores are assumed to be filled with fluid of a given salinity. With increasing salinity,the pore fluid contribution to the electrical conductivity of the mixed material Λmrises,since increasing salinity increases the electrical conductivity of the mixed material Λf(see Eq.(4)).A fluid salinity of 3%, roughly representative of sea water, serves as the base case in this study,while a wider range of salinities between 3%and 20%is investigated in Section 3.3(Batzle and Wang,1992;Jones et al., 1998; Shimojuku et al., 2014; Sakuma and Ichiki, 2016).Higher salinities are also possible and are increasingly common at greater depths(Walsh et al., 2017).

Fig. 4. Damage (rock fragmentation) in coarse-grained granite sample for maximum applied voltages between 120 kV and 600 kV.

Fig.5. Physical processes occurring during electrical conduction of current through the fluid and mineral phases:(a)Electric field ?φ;(b)Temperature of the fluid phase Tfluid;(c)Electrical conductivity of the fluid phase Λf; and (d) Electrical conductivity of the material mix Λm. Shown are time steps of 1.2 μs and 2 μs.

3. Simulation results

In the following sections, we outline the effect of changing different features of both the applied electric discharge and the rock properties on the simulated electropulse tests. We consider the effect of maximum voltage and pulse duration as well as grain size and pore fluid composition.A pore fluid concentration of 3%,a coarse grained rock matrix of granitic rock and an applied voltage of 600 kV serve as our base case.To investigate system sensitivity,the respective properties are varied,while the others are applied from the base case. Electropulses are applied for 2 μs, and rock fragmentation efficiency is reported in that time period. It should be noted, that 2 μs duration represents an unusually long pulse, with commonly reported values ranging around 1 μs(Inoue et al.,1999).However, different setups for the creation of a sufficiently large electric potential vary significantly in their pulse frequency, pulse length and intermittent time, thus leading to difficulties when defining and comparing configurations with multiple pulses. We therefore use a slightly longer pulse of 2 μs as representative of the processes occurring during initial electropulsing, as rock destruction and crack formation have been experimentally observed during the first pulse (Inoue et al.,1999). To ease visualization of the system domain, simulation results are illustrated in a zoomed-in region of the entire system domain (Figs.1 and 2), which shows a 3 cm wide region of the rock domain between the two electrodes(Fig. 3).

3.1. Voltage and pulse duration

The importance of maximum voltage on rock fragmentation(i.e.damage) during electropulse tests is well known from previous studies(Andres,1989;Inoue et al.,1999,2000).This study therefore quantifies the effect of maximum voltage, by performing simulations with a single pulse,where the voltage varies between 120 kV and 600 kV. Our objective is to observe the onset of rock fragmentation as well as the increase in efficiency,potentially obtained when the voltage is increased.

Fig. 6. Rock damage in granite(coarse-grained) and granodiorite(fine-grained) for 0.4 μs,1.2 μs and 2 μs (from left to right). Regions around the two electrodes (top and bottom electrodes) are shown in greater detail above and below. D indicates the failure mode discussed in Section 2.4.

Fig.7. Electrical conductivity of the fluid(top row),temperature of the fluid(middle row)and temperature of the mixed material(bottom row)for the coarse-grained granite(left column) and fine-grained granodiorite (right row).

As shown in Fig.4,significant rock fragmentation does not occur before 1 μs, with the most pronounced influence of the voltage difference between 1 μs and 2 μs. Here, damage is observed for pulses between 240 kV and 360 kV,which is in line with the values reported in previous literature(Lisitsyn et al.,1998;Inoue et al.,1999;Andres et al., 2001). Fragmentation rises exponentially with pulse duration, and the effect is magnified with increasing voltage, suggesting that moderate increases in maximum applied voltage can yield substantial increases in fragmentation. This increase in pulse and energy efficiency for rock fragmentation with voltages above 200 kV was also observed experimentally(Inoue et al.,1999,2000).

Fig.5 illustrates the occurring processes in the rock domain.The electric fieldcauses a current through the system domain(Fig. 5a). As current passes through the rock domain, energy dissipation in fluid and mineral phases causes a heating of the respective phases.This is illustrated in Fig.5b,where local heating,dependent on the current through individual mineral phases, can be observed. This heating further increases the electrical conductivity of the fluid phase Λf(Fig.5c).As the electrical conductivity of the fluid phase dominates overall conductivity Λm,this increase of Λfalso causes an increase in Λm(Fig.5d).This increase of Λmcauses a reduction ofas increasing electrical conductivity decreases electrical resistance. With increasing applied voltage, the electric field will increase,resulting in a stronger current through the rock mass and thereby increasing energy dissipation and heating. As increased heating with increased voltage causes larger thermal strains, material damage also increases with applied voltage(Fig. 4).

Noteworthy here is the behavior of Plagioclase minerals (see also Fig. 3, left). While Plagioclase has a higher porosity, a higher proportion of the material is available for electrical conduction of current via the fluid phase. This results in the higher electrical conductivity of the mixed phase Λm(Fig. 5d) in the longer Plagioclase band starting near the center between the two electrodes.As this can result in less resistance in the Plagioclase minerals, less energy is dissipated, which explains a smaller increase in temperature of the pore fluidTfluidin the Plagioclase band (Fig. 5b).Although this results in a comparatively smaller increase in electrical conductivity of the pore fluid Λfin this Plagioclase band(Fig.5c),the electrical conductivity of the mixed phase Λmremains higher in this band due to the larger porosity of Plagioclase minerals.

However, estimation of an optimum applied voltage remains difficult. During drilling operation, the electrode distance and configuration (if more than two electrodes are employed) determines drilling operation efficiency. While a wider-spaced electrode configuration yields a larger borehole diameter, energy consumption to achieve electrical breakdown between two electrodes also increases with spacing(Vazhov et al.,2010).Additional complications of high voltages arise with an increasing expenditure for insulation (Bluhm et al., 2000).

3.2. Grain size

This section investigates the effect of grain size on the extent and nature of damage from the electropulse, by studying the response of two distinct rock types. Specifically, we compare the results of simulated tests, conducted on granite (coarser grained)and granodiorite(finer-grained).

Table 1 provides the data on the mineral composition and grainsize distributions for Lac du Bonnet granite and granodiorite. As shown in Table 1,there is little difference in the mineral makeup of the two rocks, i.e. the granodiorite has a lower proportion of K-feldspar than the granite, which is compensated by increased amounts of plagioclase and biotite.More significant is the change in grain size,which varies between 0.9 mm and 3.7 mm in the coarsegrained granite samples, compared to a range of 0.6—1 mm in the granodiorite samples.

Grain size plays an important role in the induced damage, as shown in Fig.6.Smaller grains are more likely to be damaged by the pulse,due to local differences in electrical conductivity,heating and thermal expansion. This is evidenced by the results from the granodiorite simulation, which show increased damage at grain boundaries. It should also be noted, that this effect is likely enhanced in real rocks, which are more likely to contain microcracks and entrapped fluids at grain boundaries (Moore and Lockner,1995).

Fig. 8. Induced rock damage in granite (coarse-grained) and granodiorite (finegrained).

Fig. 7 illustrates the impact of smaller grains, as found in granodiorite, with high electric conductivities being distributed across more channels. Coarser-grained rock exhibits a higher probability of containing individual mineral clusters (see the Plagioclase band in Figs.3 and 7),which can act as higher resistors.This behavior is mirrored by the respective temperature distributions in the fluid and the material mix, which naturally leads to more widely distributed temperature gradients across grain boundaries,where large differences in the electrical conductivities can be observed. These temperature gradients can then lead to thermal strains and rock fragmentation. Induced rock damage fragmentation is summarized in Fig.8,where the damaged areas of granite and granodiorite are compared. While initial damage near the rock surface yields similar behavior,greater heating over longer pulse duration and the resulting increased depth of penetration of the damage regions into the solid domain result in increasingly rapid fragmentation for the granodiorite. Higher contrasts of electrical conductivities among grains are therefore shown to significantly impact the efficiency of electropulse shocks for rock fragmentation.

3.3. Pore fluid salinity

Fig.9. Rock damage in granite(coarse grained)for brine salt concentrations of 3 wt%,10 wt% and 20 wt%.

Fig.10. Effect of pore-fluid salt concentration on the electrical conductivity of the material mix (top) and temperature of the fluid (bottom).

As previously mentioned, the pore fluid salinity plays an important role in determining the electrical conductivity of the rock matrix. Salinities of geothermal brines vary over several orders of magnitude.Moreover,experimental studies suggest that even rocks with low brine salinity may experience higher-than-expected porefluid electrical conductivities, due to surface effects (Brace,1971).Due to the wide degree of variability and uncertainty around the effects of pore-fluid salinity in granitic rocks, we conduct in this section a series of simulations, examining the sensitivity of the material response to the brine’s salt concentration.

We consider the effect of three different pore-fluid compositions:3 wt%,10 wt%and 20 wt%NaCl,representing a range of porefluid salinities, from sea water to highly saline brine. All concentrations are evaluated for coarse-grained granitic rock and electric voltage of 600 kV is applied.

As shown in Figs. 9 and 10, variations in the pore-fluid salt concentration have a particularly strong influence on the strength of the electropulse, propagating through the rock matrix. Higher salt concentrations within each pore result in greater electrical conductivities of the pore fluid and, therefore, overall electrical conductivity. Higher electrical conductivity yields a larger stimulated volume, increased heat dissipation and, lastly, increased thermal strains. It should be noted that a sub-linear increase in fragmentation is observed with increasing salinity, as pore fluid content drives the electrical conductivity of the material mix,which nonetheless still depends on the electrical conductivity of the solid as well. As shown above, material heterogeneity, in the form of microporosity, governs the electrical conductivity of the mixed material (Fig.10).

4. Conclusions

This study investigates rock fragmentation for the purpose of drilling through intact rock mass by electropulse drilling. A numerical model is employed to investigate the influences of maximum applied electrical voltage, electropulse duration, material composition and the salinity of the brine’s salt concentration in the rock pore space.

For a single pulse, our simulations suggest that rock fragmentation is initiated when the applied electric voltage reaches a few hundred kV, which is consistent with previous experimental investigations in other studies. Once this threshold is reached, fragmentation efficiency increases rapidly with applied voltage.

The results of the simulations demonstrate a strong dependency of fragmentation efficiency on the grain size of the solid rock subjected to the electric pulse.In particular,for the smaller grains,material failure is commonly located at grain boundaries. This concentration of damage is induced by sharper contrasts in thermal expansion at these locations, and highlights the importance of small-scale heterogeneity to this process. Heterogeneities in the material properties induce concentrations in the electric field,which in turn result in localized heating. These discrepancies are more evident in smaller grained rock leading to more localized heating and subsequent material failure due to thermal strains.

As electropulse stimulation relies on sufficiently high electrical conductivity in the rock mass, an increase in fragmentation efficiency with increasing pore-fluid salinity is to be expected. An increase in salinity causes a significant increase of electrical conductivity of the pore fluid and,thus,the material,which results in more rapid heating and, consequently, fragmentation. It should be highlighted, that this result is caused by the high pore-fluid electrical conductivities, which govern the overall conductivity of the material. These effects may also occur in real samples with small pores due to surface effects that increase pore conductivity.

The presented results highlight the importance of material property contrasts for successful material fragmentation with electropulse excavation, with mineral porosity, thermal expansion coefficient and thermal conductivity being especially noteworthy.

Declaration of Competing Interest

The authors wish to confirm that there are no known conflicts of interests associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.

Acknowledgments

This project was supported by Innosuisse - Swiss Innovation Agency-under grant number 28305.1 PFIW-IW.We appreciate the support from SwissGeoPower. MOS further thanks the Werner Siemens Foundation (Werner Siemens-Stiftung — WSS) for their endowment of the Geothermal Energy and Geofluids(GEG.ethz.ch)group at ETH Zurich (ETHZ), Switzerland.