Underwater plasma breakdown characteristics with respect to highly pressurized drilling applications

Liquid pulsed plasmas have caught the attention of many due to their unique ability for focusing energy. These plasma discharges are capable of releasing stored energy in nanoseconds or quicker resulting in significant power impulses.¹ Several industries have taken interest in the potential these plasma events have to offer. The peak of energy is significant enough to break down surface contaminants or undesirable molecules. The medical field has developed applications capable of safely and quickly sterilizing surfaces, equipment, and even flesh.^2–4 This strategy has also been found to be capable of breaking down pollutants. When an undesired gas is introduced to the plasma it will break down into simpler compounds. If scaled appropriately, this offers the potential to sanitize water sources, clean engine exhausts, or decompose greenhouse gases.^5–7 

Many of the ideas discussed above utilize a fairly low power pulsed plasma. As energy per pulse increases the effects of the discharge change dramatically. When discharged in liquid, the plasma expansion process can create a cavitation bubble and shockwave.^8–11 These effects are potentially destructive and show promise within the oil and gas industry to aid in the drilling process. Several different energy focusing approaches have been attempted, although none have become commonplace yet. Pulsed power laser drilling utilized high energy lasers that vaporize rock downhole. This approach has been shown to be possible although it has limitations regarding the resulting size and depth of hole.¹² Mechanical percussion drilling offers similar energy focusing advantages of pulsed power through swift mechanical impacts that break up the rock.^13,14 This technique demonstrates a clear advantage within the first few impacts but subsequent impacts have diminishing return. Furthermore, dislodging the damaged rock and tool lifetime has proved to be areas of concerns.

The motivation for this research is seeded in the advantage that a hybrid approach may offer the energy focusing methods discussed above which provide distinct advantages in some aspects but they tend to lack in regard to several of the inherent requirements associated with drilling. The potential of a high voltage in-liquid electrode setup at atmospheric conditions has been demonstrated by Lisitsyn et al.¹⁵ and Inoue and Lisitsyn.¹⁶ This high voltage in-liquid electrode setup can be combined with the consistency of traditional drill bits to obtain a more efficient hybrid drilling system. Drilling occurs at pressures between atmospheric pressure to as high as 1350 atm, increasing with the depth of drilling. In order to understand if such an application is feasible at higher pressure, we needed to test and measure several effects occurring in the system. One effect is the changes that occur in the plasma discharge at higher pressures. Other effects are changes in the cutting processes and the rock mechanical properties at higher pressures. It has been shown by Kazi et al.,¹⁷ that at atmospheric conditions, the plasma discharge pulses generated between electrodes result in a maximum of 65% reduction in required specific cutting energy of granite rock. This reduction in cutting force will allow for faster drilling with less wear to the drill bit. A detailed study of the plasma’s effect on the rock substrate at atmospheric pressure has been preformed by Tang et al.¹⁸ They observed micro-cracks in the granite rock substrate propagating as deep as 9.4 mm. Understanding the effect of pressure is necessary to eventually have field application of such a drilling technology. In order to gain a better understanding of plasma discharges at downhole conditions, a number pressurized pulsed plasma experiments were conducted and the results are discussed in this paper.

Pressurized pulsed plasma experiments have been conducted by Jones and Kunhardt,¹⁹ Gamaleev et al.,²⁰ and others. These papers offer insights into specific aspects such as breakdown time-lag or duration but thus-far no publication has been found that investigates the effects of pressurized plasmas at the same energy level and depth investigated here. In this paper, we performed a number of experiments at pressures ranging from 1 to 350 atm in a custom deigned pressure vessel. A resistance capacitance (RC) circuit with an air gapped spark switch was used to create nanosecond voltage pulses. Voltage, current, and imaging data were collected under many different conditions. These data offer insight into potential design criteria for hybrid hard rock drilling such as electrical requirements, electrode gap, and voltage minimums. It was found that the required breakdown voltage and the breakdown time-lag increased at higher pressures. Two different types of discharge modes between the pressurized electrodes were observed, a complete plasma breakdown and an incomplete plasma breakdown. The difference between the two modes is the formation of a plasma arc channel. The channel formation occurs only in a complete plasma breakdown scenario. In an incomplete discharge, no plasma channel is formed. These two modes can be co-related to the required breakdown voltage minimums and the associated breakdown time-lag. A smaller electrode gap (0.25 mm) between the pressurized electrodes confirmed that the required breakdown voltage minimums decrease compared to a larger electrode gap (0.75 mm). The results are discussed in detail in Sec. III A. A nanosecond gated intensified charge-coupled device (ICCD) camera and a high speed camera were used to conduct shadowgraph imaging of plasma generated shockwaves and cavitation bubbles. The cavitation bubble radius and growth time was found to decrease as the pressure was increased. However, the plasma generated shockwave speed remained within expected speed of sound in water with increased pressure. These experiments have helped to round out our knowledge of the plasma behavior, plasma effects, cavitation bubble behavior, and system feasibility at different pressures. These data will help to efficiently shape hybrid drilling designs in the future.

In order to perform experiments, a pressure vessel capable of withstanding pressures up to 400 atmospheres was constructed, as shown in Fig. 1. The vessel is comprised of highly rated fittings and contains a high voltage feedthrough, two sight glasses, and a safety relief valve along with a rupture disk. The vessel proved capable of withstanding input voltages up to 28 kV at a pressure of 375 atm. The sight glasses were made of quartz and offer a clear view (aperture diameter of 19 mm) of the electrodes allowing for imaging of the pressurized plasma events. In order to reach the desired pressures, the interior volume of the vessel is limited. As a result, a number of components were created using additive manufacturing (SLA 3D printing) to tweak electrode orientation and position within the vessel.

A resistor capacitor circuit, as shown in Fig. 2, was used in conjunction with an air-spark switch in order to power the pressurized electrodes. The micrometer stage mounted air-spark switch allows us to control the circuit breakdown voltage and also allows for nanosecond pulsing capabilities. The circuit was powered using a negative polarity DC power supply (Spellman SL100-30) which is isolated from the discharge using a 20 M$Ω$ resistor in series with a 100 nF capacitor bank.

In addition to the vessel, a number of diagnostic equipment were used to measure voltage and current characteristics. The voltage traces were measured using the North Star PVM-4 high voltage probe, which was placed before the pressurized electrodes and after the air-spark switch. The current entering the vessel was measured with the Pearson Electronics (model 5046) current monitor. The current signal entering the oscilloscope was attenuated using a BNC attenuator (HAT-20+, 20dB, 50$Ω$⁠). A Tektronix DPO 3054 (500 MHz, 2.5 GS/s) oscilloscope recorded the data and provided event triggers for the imaging equipment. The cavitation bubble and the generated shockwaves at different pressures were observed using a dual-lens type shadowgraph setup, as shown in Fig. 2. The illumination source was a solid state class IIIb 300 mW laser emitting light at 532 nm wavelength. The overall laser intensity was controlled using neutral density and bandpass (532 nm $±$ 10 nm) filters. These filters were placed right after the test section in order to prevent image over saturation due to the bright plasma generated light. High frame rate videos of the cavitation event were taken using a monochrome Photron SA-5 CMOS camera, and the shockwaves were observed using a nanosecond gated ICCD camera (Stanford Computer Optics 4-picos ICCD camera). The ICCD and the high speed cameras were triggered with the help of the oscilloscope. The oscilloscope was triggered using the current probe. The signal delay along the current probe BNC cable was calculated to be 69 ns. Typical Photron SA-5 camera record settings were 300 000 fps, $256×64$ pixels and a 1/2 713 000 s shutter speed. The ICCD images were captured at an exposure of 40 ns at $1024×1036$ pixels, and multi-exposure mode was also used.

The pressurized load electrodes used were 1.6 mm diameter lanthanated tungsten weld electrodes, which is shown in Fig. 2. The electrodes were bent at an angle and held in place with a 3D printed electrode holder such that the resulting electrode gap was approximately 1 mm. Experimental tests were conducted in tap water with an electrical conductivity of 780 $μ$S cm$−1$ and were consistent in all our tests. To perform the experiments, the pressure within the vessel was set, and the air-spark gap was calibrated to set a breakdown voltage in the circuit. The capacitor was then charged by supplying DC voltage and once the air spark gap switch breaksdown the load electrodes discharge to release energy underwater.

Once the capacitor has reached a voltage that is substantial enough to cause the air-spark switch to breakdown one of two events will occur, a complete plasma discharge or an incomplete plasma discharge. The preferred event is a complete plasma discharge where a plasma channel forms between the pressurized electrodes resulting in the formation of a cavitation bubble and an intense shockwave. This event is depicted in Fig. 3 where time = 0 is the moment the pressurized electrodes breakdown. The moment that the air-spark switch triggers has been defined as V1, and the moment the pressurized electrode breakdown is defined as V2. There are two key parameters that can be evaluated from these scope traces: lag time and voltage drop. The time between V1 and V2 will be referred to as the lag time. The difference in voltage between V1 and V2 will be referred to as the voltage drop.

In the event, the voltage within the system is too low and by the time it reaches the pressurized electrodes an incomplete plasma breakdown occurs. This is where the required voltage to create a fully formed plasma channel is greater than the voltage provided, and no plasma channel is formed. The resulting voltage and current data are shown in Fig. 4. A clear spike in voltage occurs at V1 and the subsequent voltage drop begins. However, instead of a second peak and an associated discharge between the pressurized electrodes, the voltage bleeds off to zero through electrolysis and Joule heating effects.

In order to minimize the number of incomplete discharges, the input voltage set by the air-spark switch must be set sufficiently high. Figure 5 illustrates the required voltage range at each pressure for a specific pressurized electrode gap. The red region is where incomplete discharges will occur, the green region shows where successful discharges are guaranteed, and the yellow portion shows the transition area between the two. The values shown in Fig. 5 are for a spark gap of approximately 0.75 mm. If lower breakdown voltages are required, a smaller electrode gap can be utilized in order to allow for lower voltages. Figure 6 shows the same graph but utilizing a 0.25 mm pressurized electrode gap. A notable decrease of roughly 5–10 kV can be seen at all pressures. These graphs offer information on reasonable input voltage design criteria for a hybrid drilling system.

In the event of a successful discharge, the V2 breakdown voltage will be a key factor to the amplitude of the emitted shockwave. The higher the breakdown voltage, the more energy is stored in the capacitor and can be transferred to the liquid. Electrolysis and heating effects will bleed away potential energy in the lag time before V2 occurs. For this reason, minimizing the lag time will help to maximize the voltage within the V2 breakdown. Figure 7 illustrates the associated cost with operating at higher pressures. A clear trend of increasing slope with pressure can be seen indicating that more voltage will be lost at higher pressures. Furthermore, at ultrahigh pressures (350 atm), a distinct shift in the lag time can also be seen. This increase will further diminish the potential of the energy release at V2. It should also be noted that the breakdown lag time is in the order of microseconds.

In order to quantify the impact of the shockwave, the energy of system was calculated by integrating the product of voltage and current curves with respect to event time, $∫0tVIdt$⁠. Figure 8 shows typical energy traces as the event occurs. A clear discontinuity is seen where the V2 discharge occurs. The energy that accumulates after the discontinuity is energy that has the potential to aid in the drilling process. Energy that accumulates before then is energy lost to inefficiencies. The inefficiencies in this prebreakdown process include Joule heating and streamer propagation through the water between the electrodes, resistive losses also occur during plasma formation. This highlights the importance of minimizing the voltage loss and lag time before V2, especially at higher pressures.

While exploring methods of maximizing the energy that occurs within the primary discharge, a different discharge mode was discovered. It was found that if an excess of voltage is provided then the lag time reduces from the order of microseconds to nanoseconds. This is referred to as overvoltaging the system. Figure 9 shows the voltage and current traces of such an event. The calculated energy trace of this event is shown as an inset plot in Fig. 9, compared to Fig. 8 no distinct slope change is observed. It was found that providing at least 7 kV above the minimum breakdown voltage can reduce the lag time up to 50$×$ its original value. This reduction helps to ensure that all of the charged energy within the system makes it to the V2 discharge.

Figures 10(a)–10(g) show a series of shadowgraph images of cavitation bubbles generated by the plasma discharge at seven different pressures. These were taken by a high speed camera with a 532 nm laser backlight at a 300 000 fps record rate and a shutter speed of 369 ns. It is to be noted that the $t=0$ $μ$s marked frames at different pressures represent the unperturbed system, a system condition that would occur if no voltage was applied to the circuit. The standalone annotated image on the left in Fig. 10 also represents an unperturbed system indicating the ground and high voltage electrodes. At atmospheric pressure, from Fig. 10(a), it can be seen that the diameter of the bubble starts growing until it reaches a maximum diameter at around 80 $μ$s and then collapses to a minimum at around 253 $μ$s, this cycle of oscillations continues to decay as time passes. The whole process, from start of the cavitation bubble to its disappearance, takes about 700 $μ$s. The maximum radius during the process was approximately 3.72 mm. It should also be noted that after the first oscillation of the bubble its shape becomes aspherical and it eventually disappears due to condensation or simply dissolves away. In Figs. 10(b)–10(g), nearly identical 25 kV (31.25 J capacitor energy) plasma discharges were performed at pressures of (b) 34, (c) 68, (d) 136, (e) 210, (f) 272, and (g) 340 atm, and a cavitation bubble pattern similar to a plasma discharge in 1 atm can be observed at these pressures. However, it must be noted that the maximum bubble radius decreases with increasing pressure. This is evident from Fig. 11, where bubble radius change vs time at different pressures is plotted. These data were obtained from the high speed videos of the cavitation bubble shadowgraphs. In Fig. 12, $rmax$ and $tgrowth$ have been plotted as a function of pressure, where $rmax$ is the maximum radius the cavitation bubble reaches and $tgrowth$ is the time it takes to reach $rmax$⁠. It can be noted that as the pressure increases, $tgrowth$ decreases, indicating that the rate of bubble decay increases with increasing pressure.

In atmospheric conditions, the plasma initiation mechanism, usually known as the prebreakdown process, starts with streamer propagation in water between the electrodes after which the plasma channel forms.¹¹ However, there is not sufficient evidence in the literature that describes the prebreakdown process at higher pressures and whether it mimics an atmospheric pressure discharge. In this paper, such short timescales have not been investigated due to limitations of the imaging equipment. From Fig. 10, it can be seen that a conductive plasma channel is formed between the two electrodes in a similar fashion across all pressures. The plasma channel at 340 atm [shown in Fig. 10(g) at 3.3 $μ$s], for instance, evolves into a “spherical” shape [shown in Fig. 10(g) at 6.6 $μ$s]. This channel is a region of high temperature (substantiated by the partial melting observed on the high voltage tungsten electrode tip) and high pressure,¹¹ which initiates the cavitation bubble expansion. Bubble dynamics are mostly influenced by bubble internal pressure (vapor and gas pressure), liquid hydro-static pressure, surface tension, and bubble inertia. The cavitation bubble expansion can be explained due to the sudden increase in temperature and pressure locally at the electrode tips caused by plasma generation.²¹ The bubble continues to grow as long as the internal pressure is more than the surface tension and the hydro-static pressure. Temperature and pressure inside the bubble decrease as its volume expands. The bubble growth decelerates once its internal pressure becomes less than the surface tension and hydro-static pressure. After growth deceleration, the inertial effects take over to cause bubble implosion, this cycle continues in a decaying fashion.

Alluding back to Fig. 12, the relationship between the radius and pressure can be explained with the help of a generalized Rayleigh–Plesset model presented by Brennen.²² The generalized dynamic force balance is depicted in Eq. (1), where $R$ is the bubble radius, $νL$ is the kinematic viscosity of the liquid, $S$ is the surface tension of the liquid, $ρL$ is the density of the liquid, $Pb$ is the bubble internal pressure, and $P∞$ is the ambient fluid pressure. The bubble pressure shown in Eq. (2), which includes both the gas pressure and vapor pressure, can be described using the ideal gas law, where $m$ represents the mass of gas and vapor, $Ru$ is the universal gas constant, $T$ is the ambient temperature, and $Vb$ is the bubble volume expressed as $43πR3$⁠,

In a state of equilibrium, the first square bracketed term in Eq. (1) becomes zero and can be simplified further down as shown in Eq. (3). Replacing $Pb$ with Eq. (2), we find that $P∞$ is equal to the sum of a $1R3$ term and a $1R$ term. Comparing the two terms, it is evident that the $1R$ term is a lot smaller than the $1R3$ term and can, therefore, be neglected, which leads us to Eq. (4). In this equation, the new term $A=mRuT43π$ is defined to be a constant, where it is assumed that mass $m$ remains the same at every pressure because the plasma discharge has identical energy input at all pressures, and the ambient temperature $T$ and $Ru$ are also constants. Finally, Eq. (5) can be derived from Eq. (4), where the proportionality of $R$ as a function of ambient pressure is represented,

The relationship seen in Eq. (5) is plotted in Fig. 12 as an inset plot on the top right against the actual experimental $rmax$ data. It can be seen that the experimental data closely follows this relationship as expected. However, there is one outlier at 1 atm where $rmax$ is lower than the predicted radius. Looking back at Fig. 11, once the bubble radius nears it maximum size at 1 atm, its expansion is possibly decelerated or impeded by the electrodes and the electrode holder (electrode housing shown in Fig. 2), hence causing this outlier.

Figures 13(a)–13(f) show a series of shadowgraphs of shockwaves at different pressures captured with the ICCD at an exposure per frame of 40 ns. Initially, shadowgraph imaging of the 25 kV pulsed plasma event with an ICCD kept saturating the captured image such that the laser backlight was not visible. This problem was solved using a combination of a neutral density filter and bandpass filter (⁠$532±10$ nm), which reduced frame saturation to acceptable levels and allowed the laser backlight to be visible. A multi-exposure mode on the ICCD was used to capture shockwave propagation through water. A multi-exposure mode allows us to open and close the ICCD shutter multiple times by setting a customized delay between successive exposures. This mode superimposes all successive exposures onto one image, thereby allowing to capture the fast moving shockwave. From Figs. 13(a)–13(f), it can be noted that the plasma induced shockwave occurs at all different pressures. The time stamps for the different wavefronts at each pressure are depicted to show the time difference between the successive exposures with the plasma initiation being the reference time event (⁠$t=0$ s). Table I summarizes the calculated shockwave speed and compares it with speed of sound in water (as shown in column three) derived with a bi-linear interpolation from the literature²³ at 16 $°$C and matches it within a 4$%$ range. The shockwave speeds at higher pressure are higher because the local temperature in the discharge region (around electrode vicinity) may be slightly higher than 16 $°$C, causing the sound speed to be slightly higher. The local water temperature being higher could be substantiated by melted electrode tips observed after multiple experiments. Joule heating may also have an effect in raising local water temperature for the duration of the experiment. There could be a possibility that the shockwave is initially supersonic and then decays to sonic speeds as the distance increases. In Fig. 13, the first shocks captured by the ICCD are 2 $μ$s after the discharge initiation. It is likely that if a higher speed shock was present it was during the 0–2 $μ$s phase. Considering the experimental and local temperature uncertainty, it is hard to conclude if the shock is supersonic.

A preliminary demonstration of granite rock cracking at a drilling relevant pressure of 340 atm was performed as a proof of concept. The rock substrate comparison before and after plasma treatment is shown in Fig. 14. The electrode gap was set to 1 mm with tap water (780 $μ$S cm$−1$⁠) as the dielectric medium. The electrodes were in direct contact with the rock surface. The air-spark gap breakdown voltage was set to 25 kV (31.25 J per pulse) and a total of 30 pulses. Granite was chosen as it has a hardness rating of 7 on the Mohs hardness scale and diamond has a hardness rating of 10. The granite rock was loaded into the vessel and pressurized gradually to 340 atm over a period of few minutes. Since this confining pressure of 340 atm is only about 17% of granite’s compressive strength (typical compressive strength is around 200 MPa), it is to be noted that gradual cyclic pressurization and de-pressurization of the rock substrate will not cause any fractures in it. Figure 15 shows a series of shadowgraphs of the plasma discharge event on top of a rock substrate at 272 atm. The electrodes were touching the rock surface, and five pulses of a 25 kV plasma discharge were performed on the same spot. It is to be noted that the $t=0$ $μ$s marked frame represents the unperturbed system, a system condition that would occur if no voltage was applied to the circuit and no plasma discharge occurred. Optical microscopy of the rock surface was performed before and after the plasma treatment and was shown in Fig. 16. When plasma is discharged on a rock surface (as seen in Fig. 15), one of two phenomena may occur, an electrocrushing process or an electrohydraulic process. In an electrocrushing process, the plasma discharge occurs through the rock substrate and rock “crushing” occurs due to the plasma expansion process.²⁴ In an electrohydraulic process, the plasma discharge occurs in water and the rock breakage occurs due to the induced shockwave and the cavitation bubble. Looking at Fig. 15, the plasma channel is visible very near the surface along with a cavitation bubble, which points to this being an electrohydraulic process.

The pressurized experiments discussed here highlight items that show promise in aiding the development of a hybrid drilling system. Breakdown characteristics are not significantly affected by pressure indicating applicability of technique to various deep water and subterranean conditions. The breakdown process, spark, resulting bubble, and resulting shockwave were investigated over a large pressure range of 1–350 atm. The required breakdown voltage increases slightly with the pressure. The cavitation bubble radius and growth time decreases with increasing pressure but no other significant pressure related effects were found. This required increase to breakdown voltage can be mitigated by reducing the distance between electrodes. It was found that minimizing time delay between the air-spark switch and the pressurized discharge is critical to minimize lost voltage within the system. In order to reduce this delay, an input voltage well above the required breakdown voltage can be utilized. Tests seem to indicate at least 7 kV above the breakdown voltage is sufficient to minimize the lag time and lost energy.

It has been confirmed that the plasma discharge creates shockwaves and cavitation bubbles up to 340 atm. We found that the speed of these shockwaves fall in line with the expected speed in sound in water at corresponding pressures. This is important as it is believed that these two effects are the primary cause of inducing cracks within the rock structure. The damaging potential of plasma discharges has shown sufficient to damage granite at a pressure of 340 atm. The findings within this paper suggest that a hybrid plasma drilling system holds potential and is feasible within the pressures present downhole.

This research offers a secure foundation for downhole hybrid drilling technology. Future work will need to be conducted in order to establish complete feasibility. This work includes investigating the plasma event at shorter timescales, higher and lower power, and within different fluids. Furthermore, the effect of the plasma upon the rock will need to be further investigated. The pulse frequency, power input, and downhole systems will need to be considered.

The authors would like to gratefully acknowledge funding from the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy (DOE/EERE—1809670). We also appreciate the help from members of the Plasma Engineering and Non-equilibrium Processing Laboratory at Texas A&M University.

The data that support the findings of this study are available from the corresponding author upon reasonable request.