**1. Introduction**

Improving the rate of penetration (ROP) is the focus of research in petroleum industries, because ROP is inversely proportional to drilling cost in unconventional reservoirs, which is typically 30% to 40% of the total well costs. Drilling at grea<sup>t</sup> depth is challenging, due to the hostile environment and the enhanced mechanical properties of the rock, making conventional rotary drilling methods inadequate. Over the past few decades, researchers and engineers have proposed some unconventional drilling techniques based on a different rock damage mechanism rather than using the drill bit's mechanical force to cut the rock. Laser drilling applies a continuous high-power laser beam to remove the rock; researchers in the Gas Technology Institute have determined its technical feasibility and

investigated the e ffects of specific laser energy on various rock types [1–3]. Electrical plasma drilling uses high thermal loads at thousands of degrees Celsius to spall, melt, and vaporize rock, where the thermal conductivity of the rock is a critical factor in breaking the rock [4,5]. However, lasers and plasma can generate high temperatures in downhole, disabling sensors near the drill bit that measure drilling parameters and formation characteristics, which are essential for directional drilling and risk analysis [6,7].

High voltage spark discharge (HVSD) can generate strong pulse pressure waves in water, known as the electrohydraulic e ffect (EHD) [8]. It has been adopted in a wide range of applications, such as underwater sound source, extracorporeal shock wave lithotripsy, well cleaning [9–11], and alternative hydraulic fracturing [12–16]. We have recently proposed a new drilling technology that couples the pressure waves of HVSD with the drill bit's mechanical force, which can potentially crush hard rock and increase the ROP without generating high temperatures like other new drilling techniques [17]. We conducted a series of laboratory experiments using pressure waves to destroy shale, sandstone, and concrete, and investigated the e ffects of discharge voltage, discharge energy, and the number of discharges on rock damage [18].

We have conceptually designed a new drilling system inspired by conventional rotary drilling (Figure 1). In this system, the drill string is connected to a custom drill bit with several HVSD reactors integrated into the bit's nozzle, and the power required to generate the electrohydraulic e ffect comes from either surface power supply or a downhole electric generator [19,20]. During drilling operations, the HVSD reactors create pressure waves amplified by ellipsoidal reflectors that act upon the rock. The rock is crushed to a depth of only a few millimeters, but this dramatically reduces the mechanical properties of the surface material, making it easier to be crushed by the drill bit, and increasing the ROP in hard rock and abrasive formations.

Numerous previous experiments employing HVSD to crush rocks used tap water with very low conductivity as the reaction medium, ignoring the e ffect of conductivity on pressure waves. However, in drilling practice, drilling fluids are complex compositional mixtures with a wide range of conductivities. Conductivity can influence the characteristics of high-voltage spark discharges, such as breakdown voltage, energy loss, and breakdown delay time, but previous studies have been inconsistent on the e ffect of conductivity on pressure wave intensity [21,22]. Moreover, few studies have been done on the e ffect of conductivity on HVSD fragmentation and the potential mechanism of rock breaking.

This research aims to investigate the e ffect of electrical conductivity on the discharge characteristics of high voltage spark discharge, the magnitude of pressure waves and rock damage, and to analyze the fragmentation mechanism from stress wave propagation. Then, we performed breaking experiments on cement mortar, an analogue for natural rock, with a single pulse energy of 1444 J in water with various conductivities. Utilizing mortar rather than natural rock is because the controllability and consistency of the mortar properties facilitate quantitative analysis of the relationship between conductivity and sample breaking. We reconstructed the model of the mortar sample before and after damage using X-ray computed tomography to analyze the damage mechanism, measured the surface damage by the size distribution and cumulative area of the pores, applied through transmission technique to detect microcracks inside the sample, and quantified the internal damage by the acoustic amplitude attenuation coe fficient.

The results indicate that an increase in conductivity led to a nonlinear decrease in breakdown voltage, breakdown delay time, and an increase in energy loss. Both surface and internal damage of the samples exhibited a typical two-stage pattern, with pores and two types of tensile cracks being the predominant forms of damage. Stress waves induced by pressure waves propagating inside the sample play a crucial role, and tensile waves formed by reflection at the edge of the sample are among the leading causes of sample damage. The study o ffers some critical insights into the e ffect of electrical conductivity on sample damage, which will provide significant guidance for drilling tools design, and facilitate the implementation of the drilling technology based on HVSD.
