Electroacoustic Comparison and Optimization of Low-Power Impulse Sound-Source Needle Series Electrodes

Abstract

The high-power drive of an impulse sound source with drilling makes the system’s life short and difficult to integrate. This report firstly establishes the pulse discharge experimental system and finite element model, and compares and verifies the typical parameters. Second, the study examines how the energy storage capacitor’s charging voltage, discharge electrode gap, and liquid environment conductivity influence the electroacoustic performance of needle series electrodes. Subsequently, the optimal electrode configuration is identified under power constraints, yielding electroacoustic parameters and curves suitable for low-power impulsive sound sources. The findings reveal that the needle–plate electrode outperforms others in pre-breakdown duration, peak impulse wave strength, highest sound pressure level, and electroacoustic conversion efficiency. However, its higher power demand can be mitigated by lowering the charging voltage and narrowing the electrode gap. The charging voltage of the power-limited needle–plate electrode is only 3.5 kV, the impulse wave intensity reaches 1.27 MPa, and the peak system power is effectively controlled within 6.66 kW. A stable 288 dB SPL output is maintained up to 1 kHz, and above 250 dB in the wide bandwidth of 1–100 kHz. Needle–plate electrodes provide broadband excitation and high intensity SPL output despite power limitations.

1. Introduction

As a critical technique in the search and extraction of oil and gas, acoustic logging technology provides key petrophysical parameters for reservoir evaluation by measuring the propagation characteristics of acoustic waves (e.g., velocity, attenuation, frequency response, etc.) in the formation [1,2]. Global oil and gas resource development is gradually expanding to complex reservoirs (e.g., shale oil and gas, dense sandstone, and carbonate rock) and deep sea, and traditional sonic logging technology faces many challenges such as shallow depth of detection, insufficient detection resolution, and difficulty in anisotropy interpretation [3]. With the iterative upgrading of acoustic deep detection technology, it has achieved rapid development in recent years, which not only makes up for the shortcomings of low detection resolution in seismic exploration, but also breaks through the traditional acoustic logging technology in terms of detection depth [4,5]. This technology shows revolutionary application value in the field of three-dimensional geological orientation: through the full-waveform inversion algorithm, it can achieve three-dimensional geological interface imaging around wells, accurately identifying tilted stratigraphic contacts, high-angle fracture systems, geometric parameters of fault surfaces, stratigraphic cusp extinction lines, and tectonic features of salt dome bottom paving. During horizontal well drilling, this approach enables real-time monitoring of reservoir boundaries (upper and lower interfaces) by processing time-domain reflected signals, establishes the geological model of near-bit forward exploration, and obtains the parameters of formation wave impedance in front of the drill bit by its over-detection function, which can provide a real-time decision-making basis for the geosteering system to effectively avoid the geological risk of drilling and optimize the rate of encountering the reservoir [6,7,8,9].

At present, acoustic depth detection applied in mainstream drilling mainly includes drilling monopole acoustic depth-detection technology, drilling dipole acoustic depth-detection technology, and phased-array acoustic depth-detection technology [10,11,12,13]. Monopole longitudinal wave depth-detection technology has a long history of research and development. The radiation frequency of its sound source is usually between 10 kHz and 20 kHz, and the energy attenuation of the sound wave in the process of stratigraphic propagation is significant, which restricts the detection depth. In addition, the acoustic field generated by the monopole source is in a spherical diffusion pattern, which is not directional, and thus the orientation information of the reflector next to the well cannot be obtained [14,15,16]. In order to break through the limitation of the monopole source, researchers introduced a dipole acoustic source for deep detection. The dipole source has a longer acoustic transmission distance and can generate response signals to geological formations tens of meters away. Its low-frequency characteristics are favorable for long-distance target detection, but it is weak in recognizing tiny formations. Furthermore, dipole excitation is prone to produce drill collar noise that interferes with the measurement, and its radiation directivity is dipole symmetric, but there is the problem of 180° azimuthal ambiguity, which limits the application potential [7,17,18]. In order to improve the azimuthal discrimination capability for geological formations, the researchers introduced the dynamic directivity and beam-focusing characteristics of phased arrays into acoustic logging, and developed a phased-array sound source. The source is composed of multiple vibration units, and by regulating the phase and amplitude of each unit, it realizes the directional radiation and reception of acoustic waves, which mainly include two configurations: line array and circular arc array. Among them, the phased line array realizes directional radiation through linearly arranged transducer units, and its directivity is better than that of a single transducer, which can significantly enhance the reflected longitudinal wave signal and improve the detection capability and signal-to-noise ratio. The current phased-array sound-source operating frequency is about 14 kHz, which can realize directional detection and improve azimuthal resolution. The technology is still in the field test stage, and the data processing and interpretation methods need to be improved. In the narrow space downhole, the size of the array is strictly limited; the initial excitation energy is relatively small, resulting in limited energy radiated to the formation outside the well. Thus, the detection range is constrained and the energy coupling efficiency is the core challenge [19,20,21,22].

By applying high-voltage pulses (on the order of kilovolts) across electrodes immersed in liquid, the system produces impulsive waves through rapid discharge-induced liquid–electric interactions [23]. The impulse wave has the characteristics of broadband coverage, high energy output, directional focusing, controllable parameters, and repeatable excitation, which can effectively break through the technical limitations of the traditional sound source, thus showing unique advantages in deep stratum acoustic exploration [24]. A comparison of the impulse sound source with existing industry-standard instruments is shown in

Table 1. Comparison of impulse sound source with existing industry-standard instruments.

Size (mm)	Monopole Instrument	Dipole Instrument	Phased-Array Instrument	Impulse Sound Source
Bandwidth range	10–20 kHz	0.5–5 kHz	Near 14 kHz	0–100 kHz
Azimuthal	Non-directional	180° uncertainty	Directional	Directionality by concentrating energy
Detection distance	Several meters	Several dozen meters	Several dozen meters	Hundred meters
Typical Instruments	CLSS, BAR, CrossWave, Shockwave	Sonic scanner, BAT, MAC series	BAR	Theoretical and experimental research stages

.

However, the system operates under conditions of high voltage, high current, and high power, and suffers from stringent system stability requirements, cyclic life degradation of the pulse capacitors, and the amount of electrode ablation, which is positively correlated with the discharge voltage, capacitance storage capacity, peak current, and gap distance [25]. Additionally, the heavy pulse capacitors and switching components make downhole integration difficult to realize in terms of space [26,27]. Consequently, optimizing this technology for practical applications requires balancing power efficiency with core electroacoustic performance—a critical focus of current research.

Therefore, in this study, an experimental system comprising a set of needle–plate electrodes with in-liquid discharge is constructed to systematically investigate the characteristics of the impulse sound source. The time-domain waveforms of voltage and current and the characteristic curves of impulse wave intensity under typical working conditions are successfully captured through the experiments, and the numerical model’s validity is verified through comparison with finite element simulation outputs. Through the construction of needle–ring, needle–plate, and needle–needle finite element models, the charging voltage mechanism of the energy storage capacitor, the gap of the discharge electrode, and the conductivity of the liquid environment on the electroacoustic parameters are analyzed in depth, and the optimal discharge electrode under low-power conditions is determined through the comparison of electroacoustic parameters. The optimized low-power impulse sound electrode structure and its supporting system are compactly designed to fit the smallest size drill collar, allowing for modular integration of impulse sound-source deep sounding. The quantitative model of electrode electroacoustic characteristics established finally provides the theoretical support and design basis for the engineering application of a miniaturized low-energy impulsive acoustic source.

2. Methods

2.1. Principle

Applying a high-voltage pulse across liquid-submerged electrodes induces dielectric breakdown, creating a conductive plasma channel between them, and the strong electric field established between the electrodes ionizes the liquid molecules, forming a low-impedance conductive path on the order of microseconds [28,29]. The electric energy accumulated in the storage capacitor is instantaneously released through the plasma channel, which triggers intense Joule heating and electromagnetic contraction effects, leading to a rapid expansion of the gas inside the channel. This rapid expansion process forms a high-pressure impulse wave in the surrounding liquid, and this physical mechanism is called the liquid–electric effect, which is an important basic theory for the generation of an impulse wave from an impulse sound source [30,31,32].

The mechanism of impulse wave generation based on the liquid–electric effect can be deconstructed into three characteristic periods [33]. Each period is shown in Figure 1; they are the ionization accumulation period, the flow injection penetration period, and the energy explosion period.

The ionization accumulation period involves the progressive development of conductive flow columns within the inter-electrode gap. By applying a stronger electric field to the discharge gap, field-induced protrusions form on the electrode surfaces, enhancing local field intensity. This, combined with Joule heating, creates a breakdown initiation zone where nearby water molecules undergo thermal vaporization and ionization. Under sustained high-field conditions, these effects collectively establish stable flow injection.

During the flow penetration phase, the conductive column progressively extends toward the opposing electrode. Sustained electric field application drives the expansion and eventual bridging of the flow column between the electrodes, establishing a plasma channel. The duration required for this inter-electrode connection is termed the pre-breakdown time. Studies [34] indicate that breakdown initiates when the inter-electrode average field strength exceeds 8 kV/cm and the boundary boiling temperature surpasses 773.15 K.

Cook, Roberts et al. considered that the plasma channel has the following characteristics: the thickness of the channel boundary layer is much smaller than the radius of the channel, and the temperature and pressure in the plasma channel can be considered to vary uniformly. Therefore, this report refers to Kratel’s proposal to regard the discharged plasma channel similarly to the cylindrical plasma channel model, which is convenient for computational analysis [35,36,37]. The simplified channel model is shown in Figure 2, where a is the plasma channel radius from dielectric breakdown, d is the axial length of the conduction path, and I is the total current through the ionized channel.

Based on the cylindrical approximation in the simplified ionized channel model, the plasma–liquid channel’s time-dependent resistance R_ch is given by:

$$R_{\mathrm{ch}}={\displaystyle \frac{\mathrm{d}}{{\sigma }_{\mathrm{c}}(t)\pi {\mathrm{a}}^2(t)}},$$

(1)

$${\sigma }_{\mathrm{c}}=1.411\times {10}^{-2}{T}^{{\displaystyle \frac{3}{2}}}{\mathrm{e}}^{-{\displaystyle \frac{5000}{T}}},$$

(2)

where σ_c is the plasma channel conductivity and T is the plasma channel temperature.

As a key interfacial parameter, R_ch(t) dynamically connects the plasma channel development with the external circuit behavior during pulsed discharge. The equivalent circuit of the impulse sound-source discharge is shown in Figure 3, where Uc is the charging voltage of the storage capacitor, which characterizes the energy storage level of the storage capacitor; L is the total inductive reactance of the discharge circuit; and R is the equivalent resistance of the system.

During the energy release phase, the plasma channel undergoes rapid radial expansion, producing high-current discharge and intense pressure waves. Upon breakdown, the stored capacitor energy transfers abruptly into the channel as deposition energy. This energy drives a violent hydrodynamic expansion of the ionized column, compressing the surrounding liquid medium and generating powerful impulse waves through its incompressible response.

The initial moment reference is established at the instant of plasma breakdown initiation. The individual physical quantities at the initial moment of the plasma channel are used as initial conditions for the control equations. The initial conditions follow:

$$q_0=C{U}_b,$$

(3)

$$I_0={\displaystyle \frac{U_b}{R+R_0}},$$

(4)

$$n_0={\displaystyle \frac{P_0}{k{T}_0}},$$

(5)

where U_b is the breakdown voltage, R is the equivalent loop resistance, R₀ is the initial resistance of the channel, P₀ is the initial pressure of the channel, and T₀ is the temperature of the channel at the moment of breakdown.

A modified equation of state is used to accurately characterize the plasma:

$$P=nkT-{\displaystyle \frac{{\mu }_0{I}^2}{8{\pi }^2{R_{\mathrm{ch}}}^2}}-{\displaystyle \frac{e^2}{32{\pi }^2{\epsilon }_0}}{\left({\displaystyle \frac{4\pi \mathrm{n}}{3}}\right)}^{{\displaystyle \frac{4}{3}}},$$

(6)

where vacuum permeability μ₀ = 4π × 10⁻⁷ H/m, vacuum dielectric constant ε₀ = 1.6 × 10⁻¹⁹ F/m, unit charge e = 1.6 × 10⁻¹⁹ C, Boltzmann constant k = 1.38 × 10⁻²³ J/K, T is the plasma channel temperature, n is the particle number density, and I is the channel current.

The strength of the impulse wave at a distance D from the midpoint of the discharge electrode gap can be expressed as:

$$P_r={\displaystyle \frac{P\cdot \mathrm{a}}{D}},$$

(7)

where a is the channel radius.

By applying the Fourier transform to Equation (7), the impulse wave intensity is obtained in the frequency domain, denoted as P_rf. This result, when substituted into (8), provides the frequency-dependent sound pressure level of the impulse wave.

$$SPL=20{\log }_{10}\left({\displaystyle \frac{P_{\mathrm{r}f}}{P_{\mathrm{re}f}}}\right),$$

(8)

where P_ref is the accepted reference value for sound pressure (1 × 10⁻⁶ Pa).

During discharge, the energy stored in the capacitor is dissipated as internal, optical, and mechanical energy. Therefore, analyzing the electroacoustic conversion efficiency—a critical metric for assessing the impulse sound source’s performance—is essential. The system’s total energy can be determined using Equation (9):

$$E_0={\displaystyle \frac{C_{\mathrm{b}}{U_0}^2}{2}},$$

(9)

where E₀ is the energy of the storage capacitor in J, C_b is the size of the storage capacitor in µF, and U₀ is the size of the charging voltage in V.

In the process of violent discharge, the electrode gap is pierced to produce an impulse wave, and the acoustic energy expression of the impulse wave can be expressed by Equation (10):

$$E_{\mathrm{yl}}={\displaystyle \frac{4\pi {\mathrm{D}}^2}{\rho \mathrm{c}}}{\displaystyle \underset{0}{\overset{\mathrm{t}}{\int }}{\mathrm{p}}^2(t)}dt,$$

(10)

where ρ is the density of water, c is the speed of sound of the impulse wave in water, and p(t) is the size of the impulse wave.

The ratio of the acoustic energy of the impulse wave to the total energy of the impulse sound-source system is then the electroacoustic conversion efficiency, and thus the expression for the electroacoustic conversion efficiency is given in (11):

$$\eta ={\displaystyle \frac{{\mathrm{E}}_{\mathrm{yl}}}{{\mathrm{E}}_0}}\times 100\%,$$

(11)

2.2. Experiment and Verification

Figure 4 illustrates the experimental setup for the electrode discharge in the impulse sound-source system, which consists of three primary components: the impulse energy storage capacitor charging system, the electrode discharge system, and the electroacoustic parameter measurement system.

The pulse energy storage capacitor charging system consists of a voltage regulator, voltage booster, current-limiting resistor, silicon rectifier stack, and pulse capacitor. The charging process for the utility 220 V operates through the T1 regulator and T2 booster, and through the silicon pile D rectifier to charge the pulse energy storage capacitor C1; the charging system work is complete after the capacitor reaches the working voltage. The electrode discharge system includes a voltage divider resistor, a voltage display, a high-voltage discharge switch TVS, two electrodes, a water tank, an equivalent inductive component L1, and a resistive component R2. Through the voltage divider (attenuation ratio 2500:1), the capacitor’s potential difference is visualized on the display, constituting the charging voltage circuit check and monitor. By controlling the trigger switch to make the TVS conductive, when the capacitor’s stored high voltage is suddenly discharged through the liquid-immersed electrode, a gap breakdown occurs; at this time, the electrical energy stored in the pulse energy storage capacitor C is instantly released in the electrode gap, resulting in the formation of a complex impulse wave discharge process in the liquid. The measurement system employs a Tektronix P6015A (Beaverton, OR, USA) high-voltage probe for electrode gap potential measurement, a Pearson 1330 (Pearson Electronics, Palo Alto, California, USA) current probe for discharge current monitoring, and a PCB W138A01 (PCB Piezotronics, Buffalo, NY, USA) pressure sensor positioned 0.17 m from the gap center to quantify impulse wave intensity. The PCB pressure sensor was calibrated at 22 degrees Celsius, 46% humidity, and an input range of 200–1000 PSI (in steps of 200 PSI), and the calibrated pressure sensor possessed a better linear relationship, which increased the accuracy of the measured data. All signals are captured and stored using a digital oscilloscope. According to the schematic diagram of the impulse acoustic discharge experimental system shown in Figure 4, the impulse sound-source electrode discharge experimental system was constructed, as shown in Figure 5.

Table 2. Electrode structure size.

Structure		Size (mm)
Anodic (Needle electrode)	Cone top radius	1
	Cone bottom radius	5
	Cone height	10
	Column height	12
Cathode (Plate electrode)	Radius	5
	Thickness	2

presents the electrode’s geometric specifications.

Table 3. External circuit and liquid environment parameters.

External Circuit Parameters		Liquid Environmental Parameters
Charging voltage (kV)	12.8	Conductivity (S/m)	0.07
Energy storage capacitor (µF)	15	Initial temperature (K)	293.15
Equivalent resistance (Ω)	0.22	Hydrostatic pressure (Pa)	101,325
Equivalent inductance (µH)	8.18	Relative dielectric constant of water	81

summarizes the external circuit characteristics and liquid medium parameters.

The discharge process is controlled by trigger control box, and the high-voltage electrical energy stored in the capacitor is instantaneously loaded on the needle–plate electrode pair. When dielectric breakdown occurs in the electrode gap, a high-intensity impulse wave is released in the liquid–electrode gap. The voltage signal output from the pressure sensor is recorded by an oscilloscope, and combined with the voltage–pressure mapping relationship defined by Equation (12), the impulse wave pressure parameters can be directly deduced, which in turn can be quantitatively calculated to characterize its intensity properties.

$$P={\displaystyle \frac{{\mathrm{U}}_{\mathrm{e}}}{S}}(P\mathrm{a}),$$

(12)

where Ue represents the oscilloscope-measured voltage RMS value, S denotes the pressure sensor’s sensitivity (calibrated at 0.73 mV/kPa), and P is the impulse wave pressure intensity.

After analyzing the experimental data, the dynamic characteristics of the needle–plate electrode discharge system showed obvious phase characteristics (shown in Figure 6), the black line represents the voltage value, the blue line represents the current value. During the discharge process, stage 1 (ionization accumulation and flow-through periods) shows a pre-breakdown delay of 595.6 µs. When the system enters stage 2 (energy explosion period), the critical breakdown voltage of 11.21 kV is measured when the electrode breaks down, accompanied by a violent energy release phenomenon. It was observed that the voltage and current showed typical second-order decay oscillation characteristics after breakdown; the current waveform reached a peak value of 11.43 kA in the initial discharge phase, and the voltage waveform was synchronized to produce a high-frequency oscillatory response. Furthermore, measurements from the PCB underwater sensor showed that the peak impulse wave intensity could reach 7.67 MPa. The experimental data completely recorded the dynamic characteristics of the whole process from pre-breakdown and discharge development to impulse wave formation.

A three-dimensional finite element model of the needle–plate electrode system was constructed based on the experimental parameters, and the coupled electromagnetic–thermal multiphysics field was used to realize the transient joint solution of the current field and heat transfer field [38,39]. The numerical model implements high-resolution mesh splitting for the core area of the discharge (the tip of the needle and adjacent areas), and a gradually coarsening mesh was used in the non-sensitive areas to control the computational scale within a reasonable range.

Discharges only follow fundamental laws in fluid heat transfer and current field coupling; only heat transfer through conduction and electrical Joule heating are considered, with water momentum excluded from the analysis.

Electric field equations:

$$\nabla \cdot J=Q_{J\cdot V},$$

(13)

$$J=(\sigma +{\epsilon }_0{\epsilon }_r{\displaystyle \frac{\partial }{\partial t}})E,$$

(14)

$$E=-\nabla V,$$

(15)

Thermodynamic equations:

$$\rho C_P{\displaystyle \frac{\partial T}{\partial t}}+\nabla \cdot q=Q_{\mathrm{rh}},$$

(16)

$$q=-k\nabla T,$$

(17)

$$Q_{\mathrm{rh}}={\displaystyle \frac{1}{2}}R\mathrm{e}(J\cdot E^{*}),$$

(18)

with the following variables: current density J, charge density Q_j·v, conductivity σ, vacuum dielectric constant ε_r, electric field strength E, potential V, density ρ, constant pressure heat capacity C_P, temperature T, heat flux q, thermal conductivity k, and electrical loss Q_rh.

The transient characteristics of the impulsive acoustic source needle–plate electrode breakdown obtained from the numerical simulations are shown in Figure 7: (a) temperature field distribution during the breakdown phase and (b) spatial gradient of the potential field at the corresponding moment. At 575.44 µs, the temperature is 781 k and the voltage is 11.1 kV; the field strength averaged over the gap is calculated to be 15.86 kV/cm, and according to the judgment condition of the electrode breakdown, the needle–plate electrode breaks down, so the pre-breakdown time is 575.44 µs.

Through the finite element simulation, the initial values obtained were substituted into Equations (6) and (7) for calculation, and the simulation parameters obtained were compared with the experimental parameters, as shown in

Table 4. Comparison of simulated and measured results.

Parameters	Breakdown Voltage/kV	Pre-Breakdown Time/μs	Peak Current/kA	Peak Impulse Wave Intensity/Mpa
Experiment	11.21	595.6	11.43	7.67
Simulation	11.1	575.44	11.86	7.89
Relative error	0.98%	3.38%	3.76%	2.87%

. Errors between numerical simulations and experimental measurements can be caused by errors in the position of the PCB pressure sensor installation or by deviations in the ambient temperature from the calibration ambient temperature, but are within the allowable range. From the data comparison, results demonstrate that the finite element model’s accuracy is confirmed by cross-validation with the experimental data, which provides the necessary numerical simulation basis for carrying out comparative studies with different needle electrode configurations.

3. Results

In drilling-based deep detection using impulse sound sources, the electrode configuration critically influences key output parameters including wave intensity, system power, and operational bandwidth. This component serves dual functions: facilitating breakdown discharge and acting as the primary transducer that converts stored electrical energy from capacitors into acoustic impulses.

Needle series electrodes are characterized by a simple structure, easy realization, high speed of the plasma synthesis jet, easy generation of the discharge current column, and formation of a plasma channel with high concentration. Thus, the study focuses on needle series electrodes (needle–ring, needle–plate, and needle–needle configurations). Using the control variable method, we investigate how variations in the capacitor’s charging voltage, the gap of the discharge electrode, and the conductivity of the liquid environment affect the pre-breakdown time, maximum impulse wave intensity, maximum system power, maximum sound pressure level, and electroacoustic conversion efficiency of the three electrodes. Finally, the three electrodes are comprehensively compared and analyzed in terms of electroacoustic properties, and we determine the electrode structure most suitable for low-power excitation conditions.

3.1. Models

Before implementing the finite element modeling, the geometric characteristic parameters of the three electrode structures need to be pre-determined. The dimensional parameters of the electrode configurations for the anode and cathode of the three electrodes are shown in detail in

Table 5. Dimensional parameters of electrode configurations.

Electrode Configuration		Size (mm)
Needle electrode	Vertebral apical radius	1
	Radius of the base of the vertebrae	5
	Vertebral body height	10
	Needle point-ball radius	1
	Needle column radius	5
	Needle column height	12
Ring electrode	Large radius	8.5
	Small radius	1.5
Plate electrode	Radius	10
	Height	3

. Among them, the needle–needle electrode pair adopts a bipolar symmetric design, and its anode and cathode adopt the needle electrode configuration; the needle–ring electrode system consists of a needle anode and a ring cathode, and the needle–plate electrode system is configured as a composite structure of a needle anode and a plate cathode.

The finite element models of the three electrode structures constructed according to Table 5 are shown in Figure 8.

3.2. Different Charging Voltages

As the dominant factor governing acoustic output, the storage capacitor’s voltage directly determines the performance of needle-configuration electrodes; it is of great engineering value to carry out a systematic study on the electroacoustic response characteristics under different charging voltage conditions. Therefore, the charging voltage is reduced in 1 kV steps starting from 12 kV, systematically analyzing the electroacoustic performance of each needle series configuration across varying charging voltages. The parameter settings of the external circuit and liquid environment for the finite element model of the three needle series electrodes are shown in Table 3.

Based on the calculation, the electroacoustic characteristics of the needle series electrodes at different charging voltages are shown in Figure 9. Figure 9a–e show the influence laws of charging voltage on the pre-breakdown time, maximum impulse wave intensity, maximum system power, maximum sound pressure level, and electrode electroacoustic conversion efficiency for the needle series electrodes.

According to the analysis of the finite element calculation data shown in Figure 9, the needle series electrode structures show the following characteristic differences in different charging voltage discharges: (1) Pre-breakdown characteristics (Figure 9a)—the pre-breakdown times of the three electrodes are negatively correlated with the charging voltages, among which the needle–plate electrode exhibits the lowest breakdown threshold (7 kV) and the shortest pre-breakdown delay, which is about 40–60% shorter than that of the other electrodes under the same voltage conditions. (2) Impulse wave intensity (Figure 9b)—with an increase in charging voltage, the maximum impulse wave intensity of the three electrodes show a linear growth trend. The peak intensity of the needle–plate electrode reaches 12.14 MPa at 12 kV, which is 10.67% and 24.58% higher than that of the needle–ring and needle–needle electrode structures. (3) System power characteristics (Figure 9c)—the maximum power of each electrode system increases with the increase in charging voltage, and the power output of the needle–plate structure reaches 135.1 kW at 12 kV, but the calculated data show that the slope of its power-charging voltage curve is steeper, indicating that an appropriate reduction in the charging voltage can lead to a decrease in the power level. (4) Acoustic properties (Figure 9d,e)—the sound pressure level and electroacoustic conversion efficiency of each electrode structure show a positive correlation with the charging voltage, and the needle–plate electrode achieves a peak sound pressure level of 304.3 dB and an electroacoustic conversion efficiency of 3.45% at 12 kV, while the needle–plate electrode’s sound pressure level and electroacoustic conversion efficiency are better than those of the needle–ring and needle–needle electrodes at the same charging voltage.

The comprehensive simulation results show that the needle–plate electrode has a significant advantage in terms of discharge performance parameters, but its higher power consumption may produce loss on the tip of the needle–plate electrode. By reasonably reducing the charging voltage, a reasonable control of the system power can be realized while maintaining good discharge characteristics. This performance-balancing strategy provides an important reference for the design of an impulse sound-source system.

3.3. Different Electrode Gaps

Gap changes in the structure of the needle series electrodes cause changes in the radius, length, and resistance of the isoion channels between the anode and cathode, which inevitably have an effect on the electroacoustic parameters excited by the needle series electrodes. Therefore, the electroacoustic characteristics of the needle series electrode structure with the electrode gap starting from 1 mm and increasing to 6 mm in steps of 1 mm were investigated under the same charging voltage and the same liquid conductivity. The finite element models for all three needle-type electrode configurations share identical external circuit parameters and liquid environment conditions, as specified in Table 3. The simulated electroacoustic performance of the needle-type electrodes across the varying gap distances, shown Figure 10. Subplots (a)–(e) reveal the corresponding parameter influence patterns of electrode gap on the pre-breakdown time, maximum impulse wave intensity, maximum system power, maximum sound pressure level, and electrode electroacoustic conversion efficiency of the needle series electrodes.

Comprehensive simulation results in Figure 10a–e show that the needle–plate electrode structure exhibits multidimensional performance advantages under the same electrode gap conditions. Specifically, comparative analysis reveals the needle–plate electrode’s advantages: its breakdown initiation time is reduced relative to other configurations (Figure 10a) while simultaneously generating both the strongest acoustic pulses (Figure 10b) and highest power delivery (Figure 10c), and it can be attained by increasing the electrode gap to achieve the neutralization. In terms of acoustic characteristics, the needle–plate electrode structure has a better peak sound pressure level and electroacoustic conversion efficiency than the other two electrodes at the same electrode gap (Figure 10d,e).

Systematic simulation calculations show that the needle electrode and plate electrode structures act synergistically to provide the best electroacoustic parameters compared to the needle–ring and needle–needle electrode structures. Furthermore, under different electrode gaps, the smaller the electrode gap, the more favorable for the needle–plate electrode excitation. Compared with the 6 mm and 1 mm electrode gaps, the pre-breakdown time is shortened by 387.8 µs, the maximum impulse wave intensity is increased by 1.51 MPa, the maximum sound pressure level is improved by 1.3 dB, and the electroacoustic conversion efficiency is increased by 0.984%. Therefore, a smaller electrode gap is favorable for needle–plate electrode excitation.

3.4. Different Liquid Conductivities

The electrode structure of the impulse sound source works in a liquid discharge environment, and the liquid conductivity directly affects the current density and the formation of the discharge channel, which plays a key role in the excitation of the impulse sound source. Therefore, the electroacoustic characteristics of the needle series electrodes with liquid conductivity ranging from 0.03 S/m to 0.13 S/m in steps of 0.02 S/m were investigated when both the applied voltage and inter-electrode distance were held constant. All three needle electrode configurations share identical external circuit parameters and liquid medium properties in the finite element model, as defined in Table 3.

After calculation, the results obtained for the electroacoustic characteristics of the needle series electrodes at different liquid conductivities are shown in Figure 11. Figure 11a–e present the effects of liquid conductivity on five key performance metrics of needle-type electrodes: pre-breakdown duration, peak impulse wave intensity, maximum system power, highest sound pressure level, and electroacoustic conversion efficiency.

The combined numerical simulation data in Figure 11a–e show that the needle–plate electrode configuration exhibits systematic advantages over the other two needle electrodes in a liquid medium environment with constant conductivity. Specifically, the pre-breakdown time, the maximum impulse wave intensity, the maximum sound pressure level, and the electroacoustic conversion efficiency of the needle–plate electrode structure are all larger than those of the remaining two electrodes, showing significant advantages. Under the same liquid conductivity, the system power of the needle–plate electrode structure is also the largest, and changing the liquid conductivity has little effect on the system power. Compared with 0.13 S/m and 0.03 S/m liquid conductivity, the pre-breakdown time of the needle–plate electrode was shortened by 1111.25 µs, the maximum impulse wave intensity was increased by 2.61 MPa, the maximum sound pressure level was improved by 1.8 dB, and the electroacoustic conversion efficiency was improved by 0.91%. Therefore, the needle–plate electrode should be made to work in an environment with a larger liquid conductivity.

Based on the above findings, the needle–plate electrode configuration has significant advantages in terms of key metrics such as pre-breakdown time, peak impulse wave intensity, sound pressure level polarity, and electroacoustic conversion efficiency. However, it should be noted that the system operating power of this electrode configuration is at a high level. The research data indicate that the system energy consumption can be effectively reduced by three optimization strategies: first, appropriately tuning down the charging voltage parameters; second, shortening the electrode spacing design; and third, regulating the conductive properties of the liquid medium. This multidimensional parameter synergistic adjustment can realize the optimization of the overall energy efficiency of the system while maintaining the excellent performance index of the electrodes.

4. Discussion

4.1. Optimization

As the preferred electrode configuration, the needle–plate electrode needs to be optimized to match the low-power requirements for acoustic deep-detection technology with drilling. Experimental data show that lowering the charging voltage, narrowing the electrode spacing, and improving the conductivity of the liquid medium can synergistically realize the system power consumption regulation. Based on this, in this study, for the working condition boundary of 1 mm electrode spacing and 0.13 S/m liquid conductivity, a critical charging voltage prediction model of the needle–plate electrode is established by numerical simulation to quantify the minimum system energy consumption for this configuration. The calculation results shown in

Table 6. Minimum charging voltage determination for needle–plate electrodes.

Charging Voltage of Storage Capacitor/kV	Temperature at the Moment of Breakdown/K	Voltage at the Moment of Breakdown/kV	Gap Mean Field Strength/kV/cm	Electrode Breakdown?
7	780	6.34	63.4	Yes
6	782	5.19	51.9	Yes
5	778	4.01	40.01	Yes
4	774	2.65	26.5	Yes
3.5	775	1.81	18.1	Yes
3	Not breakdown!

reveal that the needle–plate electrode system power can reach the theoretical minimum level when the charging voltage is reduced to the breakdown criticality.

From Table 6, it is apparent from the data that the minimum charging voltage at which the needle–plate electrode can breakdown is 3.5 kV. Therefore, the impulse wave characteristics are calculated for a charging voltage of 3.5 kV, an electrode gap of 1 mm, and a liquid conductivity of 0.13 S/m. The results of the numerical simulations are shown in

Table 7. Quantitative electroacoustic characteristics of needle–plate electrodes under low-power conditions.

Parameters	Pre-Breakdown Time/µs	Impulse Wave Intensity/MPa	System Power/kW
Value	831.76	1.27	6.66

.

The numerical simulation data in Table 7 show that the needle–plate electrode system with a low-power configuration exhibits excellent discharge characteristics: its pre-breakdown time delay reaches 831.76 µs, the impulse wave intensity reaches 1.27 MPa, and the peak power of the system is effectively controlled within 6.66 kW.

The frequency response curve for the sound pressure level of the needle–plate electrode under low-power conditions is shown in Figure 12. From the sound pressure-level frequency response curve, it can be seen that the needle–plate electrode exhibits the following characteristics under low-power conditions. (1) Low-frequency stability: In the frequency band below 1 kHz, the sound pressure level of the electrode system is stably maintained at ≥288 dB, and this low-frequency strong acoustic field characteristic can effectively improve the signal penetration in deep geological exploration. (2) Wide bandwidth adaptability: Although the 1–100 kHz range shows non-linear attenuation characteristics, the sound pressure level is always above the 250 dB threshold, which meets the demand of shallow high-resolution detection. This dual-mode characteristic of strong low-frequency penetration and high-frequency accuracy preservation verifies the core advantages of the needle–plate electrode configuration under power constraints, i.e., wide-band excitation capability and high-intensity sound pressure level output.

4.2. Prospects

Although the broadband response characteristics of low-power needle–plate electrodes have been demonstrated to have potential for engineering applications, the research paradigm is still doubly limited. Firstly, the existing results focus on laboratory-scale simulations and simplified model experiments, and secondly, practical working condition elements such as electrode material aging and downhole multiphase flow interference have not yet been incorporated into the research system. To promote the industrialization of this technology in drilling acoustic depth sounding, the following core challenges urgently need to be overcome:

• Optimized design of electrode configurations: This study focuses only on three typical structures in the needle series, while stick electrodes, coaxial electrodes, and spiral electrodes may be further optimized for impulse wave spectral characteristics through parameter tuning.
• Downhole systems need to withstand the ”three high” of composite working conditions and extreme environment adaptability verification: Downhole operation systems need to withstand the ”three-high” composite working conditions, that is, facing a high temperature of not less than 150 °C, a high pressure of not less than 100 MPa, and a vibration acceleration of not less than 8 g in the harsh working conditions; thus, it is necessary to build an accelerated-aging experimental platform to evaluate the pulse energy storage capacitor’s discharge frequency, aging speed of the electrode materials, and dynamic sealing of the insulation structure for its entire lifecycle reliability.
• Miniaturization and integration: The narrow space on the inner wall of the drill collar puts higher demands on the size requirements and positional arrangement of the various components of the impulse sound source.
• Adaptivity: For varying detection requirements, such as different detection targets, different detection distances, and different excitation conditions, the low-power impulse sound source can be controlled with real-time feedback to adaptively adjust the charging voltage and electrode gap.
• Decoupling under strong noise interference signals: Downhole signals face the challenge of decoupling signals from complex working conditions, high overlap between noise and useful signals from drill bit–rock interactions, multimodal vibration harmonics of the drilling column, and the challenge of separating the useful signals under strong direct wave interference, which is a complex challenge for future engineering realizations.
• Integration with MWD or LWD: Integration greatly promotes the development of geosteering technology, drilling engineering, and reservoir evaluation, and makes “drilling and testing integration” and “real-time reservoir description” possible, which is the key technical direction to improve the success rate and economic efficiency of exploration and development.

The breakthrough of these technical restrictions will promote the acoustic deep-detection technology with drilling from the laboratory to industrialized application, and its research results can not only improve the resolution and detection depth of acoustic logging in oil and gas exploration, but also provide a new type of technological means for the development of deep resources, offshore oil and gas exploration, and other fields.

5. Conclusions

Previous impulsive acoustic source systems have been constrained in their practical application due to lifetime problems resulting from high-power operation. To break through this restriction, this study systematically investigated the electroacoustic characteristics of needle series electrodes under power-constrained conditions, and the core findings are as follows:

(1)

Reducing the power of an impulsive source system can be synergized by a variety of parameter adjustments. One of the effective ways to accomplish this is to reduce the voltage at which the impulse capacitor is charged. It is worth noting, however, that the reduction in power can lead to a degradation of the acoustic properties of the electrodes.

(2)

The needle–plate electrode has the best overall performance among the needle family electrodes, with short pre-breakdown time, high maximum impulse wave intensity, high maximum sound pressure level, and high electroacoustic conversion efficiency under the same conditions. In particular, its optimized low-power version requires only 6.66 kW to maintain a high level of SPL output in the 1 kHz frequency range. This feature significantly enhances its application value in the exploration and development of deep oil and gas reservoirs with drilling.