Generation of Electrohydraulic Shock Waves by Plasma-Ignited

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Generation of Electrohydraulic Shock Waves by Plasma-Ignited Energetic Materials: III. Shock Wave Characteristics With Three Discharge Loads Haibin Zhou, Yongmin Zhang, Hengle Li, Ruoyu Han, Yan Jing, Qiaojue Liu, Jiawei Wu, Youzhi Zhao, and Aici Qiu

Abstract— As an important plasma-assisted technology to generate shock waves (SWs), underwater pulsed discharge has drawn much attention in recent years for its complex physical process. Based on three discharge loads, the water gap (WG) load, the electrical wire (EW) load, and the energetic material (EM) load, the discharge processes are briefly introduced and the characteristics of the associated SWs are analyzed. First, the experimental setups were built and typical structures of the three loads were presented. Second, the inherent characteristics of SWs under the three loads, such as their peak pressure, impulse, and time duration of positive pressure and power spectral density (PSD), were studied and compared. Finally, a cracking effect experiment is carried out to study the SW fracturing characteristics. The results show that SWs generated with the WG load have the lowest peak pressure, impulse, and power density, SWs generated with the EW load have a better energy conversion efficiency and the largest peak pressure, and SWs generated with the EM load have the maximum impulse and power density. Furthermore, SW fracturing characteristics are mainly affected by its inherent characteristics. The peak pressure and impulse determine the shock number of fracturing, and the fracture pattern is significantly affected by the PSD. Index Terms— Cracking effect, plasma ignition, waves (SWs), underwater pulsed discharge (UPD).

U

shock

I. I NTRODUCTION NDERWATER shock waves (SWs) have been well applied in the fields of medicine, military, industry,

Manuscript received May 1, 2015; revised July 22, 2015; accepted September 5, 2015. This work was supported in part by the National Natural Science Foundation of China through the National High Technology Research and Development Program of China under Grant 2013AA064502, in part by the National Basic Research Program of China under Grant 2013CB228004, and in part by the Key Projects in the National Science and Technology Pillar Program during the Twelfth Five-Year Plan Period through the National Key Technology Research and Development Program within the Ministry of Science and Technology, China, under Grant 2012BAK04B02. H. Zhou, Y. Zhang, R. Han, Y. Jing, Q. Liu, J. Wu, and A. Qiu are with the State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University, Xi’an 710049, China (e-mail: [email protected]; [email protected]; [email protected]. edu.cn; [email protected]; [email protected]; [email protected]; [email protected]). H. Li is with the College of Mineral Resource and Geoscience, University of Mining and Technology, Xuzhou 221008, China (e-mail: [email protected]). Y. Zhao is with Xi’an GuanTong Energy Technology Company, Ltd., Xi’an 710068, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPS.2015.2477357

and mining. Especially, they have shown great prospects in the exploitation of unconventional gas. The most widely used technology to stimulate oil and gas reservoirs is hydraulic fracturing [1], [2]. Usually, hydraulic fracturing, based on the interaction between arc plasma and liquid, as a quasi-static process, cannot induce enough fractures in a rather large volume surrounding the borehole, and this will lead to decrease in well production after a period [3]. Furthermore, it has the disadvantages of great energy consumption and stratum contamination due to the use of chemical additions. However, the above problems may be solved by the electrohydraulic SW fracturing reservoir technology. SW is a kind of strong compressive mechanical wave and is characterized by high pressure, high temperature, and high energy density behind the SW front [4]. SW energy can be concentrated on the discontinuity of acoustic impedance caused by macrocracks or microcracks, and then, the existing fractures will be extended and connected. Besides, with the high peak pressure, some new fractures may also be created. With more connected cracks and larger surface area for exchange, the permeability is increased [5], [6] and the reservoir is reconstructed. The reservoir fracturing effects are largely affected by the characteristics of SWs. Furthermore, the inherent characteristics of SWs, such as peak pressure, impulse, and power spectral density (PSD), may be determined by the discharge loads. Therefore, in order to obtain a better application, it is important to study the discharge processes and the characteristics of the associated SWs. As a conventional load of underwater pulsed discharge (UPD), the water gap (WG) has been widely used because of its simple structure, low cost, and convenience for engineering applications. The experimental setup for SW generation with WG electrical discharge has been built, and the fracturing effect experiments for motor specimens have been carried out in [3] and [7]–[10]. The above study has shown that the characteristics of SWs are correlated with the permeability and microstructure of the motor. However, due to the low energy conversion efficiency, SWs are usually not strong enough, so hundreds of shots are needed to achieve a satisfactory fracturing effect. But this will waste time, increase the cost, and, more importantly, greatly shorten the equipment life. The electrical wire (EW), as an increasingly popular

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Fig. 1.

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Schematic of SW generation and measurement system.

discharge load, is becoming a research focus [7], [11]–[15] because of its complex physical processes. When an EW with a certain length and diameter is placed between the two electrodes of the WG load, an EW load is created. Various wires with different materials and sizes have been adopted and SWs of several hundreds of gigapascals are generated and measured [15]–[20]. The EW load has the advantages of better discharge stability [21] and higher energy conversion efficiency than the WG load [11]. However, limited by the total energy stored in the capacitor, the SW is still not strong enough to fracture objects within several shots. In order to increase SW energy, the energetic material (EM) load ignited by an EW is proposed in this paper. The EM load consists of an EW and tightly wrapped and agglutinated chemical EMs (aluminum powder, ammonium nitrate, etc.). With the extra energy introduced by the chemical materials, SW energy is enhanced greatly. In this paper, the SW inherent characteristics are analyzed based on an anechoic tank. Then three kinds of SWs are separately applied on coal cube specimens to examine their fracturing patterns. Finally, the correlations between the inherent characteristics and the fracturing characteristics of SWs are obtained. This paper may serve as a guide to the practical application of SW fracturing. II. E XPERIMENTAL M ETHODS Two experimental arrangements were designed and built to investigate the characteristics of SWs. A. Shock Wave Generation and Measurement System A schematic of the SW generation and measurement system is shown in Fig. 1. The coaxial pulsed capacitor C of ∼8 μF is charged to ∼24 kV with a constant current power supply in about 10 s, and then discharges to the load at a water depth of 3 m through a triggered switch S. SWs are generated along with the volume expansion of the load, then propagate in tap water, and are finally measured by the pressure sensor placed at a distance of 3 m from the load center and recorded by a DPO4104B oscilloscope. The SW- measuring probe is a PCB138A11-type pressure sensor with a resonant frequency

Fig. 2.

Schematic of an SW fracturing effect research platform.

of ≥1 MHz and a rise time of ≤1.5 μs, which is produced by PCB Piezotronics, Inc. The anechoic tank (the length, width, and depth are 25, 8, and 7 m, respectively) is wrapped by the conical sound absorption material to eliminate reflected waves. In the anechoic tank, interference-free SW pressure waveforms in a quasi-free field can be obtained easily, and a characteristic study of SWs is accomplished. The measurement of SWs is hard, especially in practical application. The PCB138A11 pressure probe has a maximum resonant frequency of 1 MHz, and another study has proved its nonlinear response problem [22]. However, in our study, in the 25 m × 8 m × 7 m anechoic tank, no other probe is more applicable. In [22] and [23], the probe is placed at a distance of just less than 20 cm from the explosion wire, and the pressure front is too steep to measure with the PCB138 series probe. Along with the traveling of the SW, the high-frequency energy is attenuated and absorbed. Besides, in this study, to measure the SW waveforms accurately is not our main task, and we just study the SW characteristics generated by three different loads. The PCB138A11 is sufficient to give enough information. B. Research Platform of Fracturing Effects for Shock Waves The experiments of SW fracturing effects are achieved in a cylindrical water tank (diameter 990 mm and height 1200 mm), as shown in Fig. 2. The water tank is fixed on a rubber cushion to reduce shock and vibration. The device is driven by a pulsed voltage source and the whole circuit system has circuit parameters (capacitance, loop inductance, period, and loop intrinsic resistance) similar to those of the SW generation and measurement system in Section II-A. The pulsed voltage and current are monitored by a self-made

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Fig. 3. Structures of three loads. Schematic of (a) WG load, (b) EW load, and (c) EM load. (d) Hardware of (a). (e) Hardware of (b). (f) Hardware of (c).

capacitive voltage divider (3950 V/V, 100 kV, 75 MHz) and a Pearson current monitor (0.01 V/A, 50 kA, 4 MHz). The specimen is a coal cube (length 30 cm) collected from a coal mine in Shaanxi Province, China, and is placed at a distance of 250 mm from the wave source and a water depth of 500 mm. C. WG Load, EW Load, and EM Load Configurations The schematics of WG load, EW load, and EM load are shown in Fig. 3(a)–(c), and Fig. 3(d)–(f) gives the hardware structures machined in a factory according to the above designs. The WG load consists of a needle electrode and a plane electrode. The gap between two electrodes is about 8 mm and can be easily adjusted according to requirements. The radius of curvature of the needle electrode is 5 mm and the diameter of the plane electrode is 20 mm. The SW generation mechanism under the WG load can be summarized into the expansion of discharge channel initiated by high-voltage breakdown [7]. A Mo-wire (length 60 mm and diameter 0.18 mm) connecting two plane electrodes is chosen for the EW load in this experiment. Along with the electrical energy injection, the metal wire will be converted into liquid state, metal vapors, and finally plasma [24]. The fast liquid–gas phase transition will lead to a dramatic volume expansion and the associated strong SW is emitted. The EM load consists of the same Mo-wire and tightly wrapped and agglutinated chemical EM with a mass of ∼10 g and an energy density of ∼3.0 kJ/g. When a high voltage is applied on the EM load, the middle Mo-wire will be heated and the discharge process is just similar to that of the EW load. The state of high temperature and pressure induced by EW explosion will ignite the chemical materials, and then, a chemical reaction process starts. The joint contributions of EW explosion and chemical explosion will help to generate a stronger SW, especially the energy and impulse of SWs are greatly increased. Above all,

Fig. 4. Typical waveforms of the discharge current and the resistive voltage. (a) Waveforms for WG load. (b) Waveforms for EW load (Mo-wire, = 180 μm with a −24.2-kV voltage). (c) Waveforms for EW load (Mo-wire, = 200 μm with a −24.2-kV voltage).

the generations of SWs with the above three loads are based on completely different principles, so it is reasonable that the three kinds of SWs have quite different characteristics. D. Discharge Characteristics Under Three Loads Typical wave forms of the discharge current and the resistive voltage drop (which is obtained by removing the inductive voltage, and the calculation method is shown in [24]) on WG load, EW load, and EM load are shown in Fig. 4. The current pulse has an amplitude of ∼16 kA and a period of ∼15.4 μs under the WG load. Fig. 4(a) shows that at the onset of the discharge, the voltage is ∼22.5 kV (corresponding stored energy is ∼2.03 kJ), and before breakdown, the voltage



drops to ∼16 kV (corresponding stored energy is ∼1.02 kJ), which means that approximately half of the total energy is lost due to leakage. Energy leakage is a key cause of the low energy conversion efficiency for WG load discharge. Besides, multichannel discharge is also a disadvantage in forming the SWs, because the deposited energy is dispersed and discharge channel expansion is impaired. For the EW load and the EM load, the typical discharge current and voltage waveforms are shown in Fig. 4(b) and (c), respectively. The amplitude and rise time of pulsed current for the EW load are ∼27 kA and ∼1.05 μs, respectively. The EM load’s amplitude and the rise time of the pulsed current are ∼27 kA and ∼2 μs, respectively. III. I NHERENT C HARACTERISTICS OF T HREE K INDS OF S HOCK WAVES A. Parameters to Describe Shock Wave Characteristics The ideal SW pressure P has the step-form front and the exponentially decaying form tail, as given by (1), where ε(t − t0 ) is the step function, Pm is the peak pressure, and τ is the time constant. In [3], [7], and [8], a kind of pressure waveform is approximated by (2). But the actual waveform is quite different from the ideal one, and it is difficult to obtain an accurate time constant. Therefore, time duration of positive pressure (TDPP) is taken in this paper to describe the pressure wave. Impulse J [25], [26], calculated by (3) [27], represents the momentum transferred to objects and is an important parameter to characterize the damage effects of the SW. The power density Pd can be calculated with the periodogram method and (4), where P f is the pressure in frequency domain, ρc is the acoustic impedance (density times the sound speed) [28], and ρ0 c0 is the acoustic impedance in the condition of static pressure. For a pressure of less than 100 MPa, the approximation ρc ≈ ρ0 c0 is acceptable, and the calculation of Pd can be simplified. According to the above analysis, Pm , TDPP, J , and PSD are chosen to describe the SW characteristics P(t) = ε(t − t0 )Pm e− −αt

(t−t0 ) τ

−bt

P(t) = Pm (e −e ) TDPP J (TDPP) = P(t)dt Pd =

0 P 2f

ρc

∼ =

P 2f ρ0 c0

.

Fig. 5.

Pressure profiles of SW-WGD, SW-EWE, and SW-EME.

(1) (2) (3) (4)

B. Characteristic Analysis of Shock Waves With the energy of about 2.3 kJ stored in the capacitor, UPD experiments are repeated with more than 20 shots under each load. Fig. 5 shows the typical pressure profiles of SWs induced by WG discharge (SW-WGD), SWs induced by EW explosion (SW-EWE), and SWs induced by EM explosion (SW-EME) ignited by a Mo-wire, and all these time profile waveforms are measured by the pressure gauge PCB138A05. For the three waveforms, a compressive SW, a low-amplitude oscillation, and a bubble wave are observed. The compressive SW has the largest peak pressure

Fig. 6. Waveforms of the compressive SWs and impulses of SW-WGD, SW-EWE, and SW-EME.

and the low-amplitude oscillations have the longest time duration. More importantly, the three bubble waves [29] have different amplitudes, wave shapes, and time of arrival, which may indicate the difference in SW generation mechanisms. Waveforms of the compressive SWs and the impulses calculated according to (3) are shown in Fig. 6. It shows


Fig. 7.

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PSDs of SW-WGD, SW-EWE, and SW-EME.

Fig. 9.

Fig. 8. Power distribution in different frequency bands for SW-WGD, SW-EWE, and SW-EME.

that SW-WGD has a minimum peak pressure of ∼0.301 MPa, while SW-EWE has a maximum peak pressure of ∼0.714 MPa. The TDPPs of SW-WGD, SW-EWE, and SW-EME are about 50, 24, and 1687 μs, respectively. Thus, the impulses of SW-WGD, SW-EWE, and SW-EME are 6.135, 8.576, and 70.70 kPa·ms, respectively. The periodogram method is a simple way to calculate the power density distribution. First, discrete Fourier transform is required to get the amplitude distribution along with the frequency and then calculate the square of the amplitude. Based on the periodogram method and (4), the PSDs of the three pressure waveforms in Fig. 5 are obtained and shown in Fig. 7. And according to the PSD features, the frequency band is divided into three ranges, the low-frequency band (LFB) as 0–500 Hz, the middle-frequency band (MFB) as 500 ∼ 5 kHz, and the high-frequency band (HFB) as 5–500 kHz. Then we integrate the power density versus the frequency in three frequency bands separately, and the total power in each frequency band is obtained and shown in Fig. 8. Some preliminary conclusions can be obtained as follows by analyzing Figs. 7 and 8. 1) In LFB and MFB, SW-EME has a significantly larger power than SW-WGD and SW-EWE. In HFB, the power of SW-EWE and SW-EME are greater than that of SW-WGD. 2) The total power of SW-EME in full band is significantly larger than that of both SW-EWE and SW-WGD, and

Fracturing photos of SW-WGD, SW-EWE, and SW-EME.

it can be explained by the extra energy introduced by the EM. 3) The power density of SW-EWE is greater than that of SW-WGD in almost every frequency region. Considering the same initial stored energy, we can draw the conclusion that the energy conversion efficiency of SW-EWE is greater than that of SW-WGD. 4) For SW-EME, the energy distributed in LFB plays a dominant role, while for SW-EWE, the energy distributed in HFB is more prominent. As for SW-WGD, energy distribution is balanced in all frequency bands. IV. F RACTURING C HARACTERISTICS OF T HREE K INDS OF S HOCK WAVES In order to study the SW fracturing effect and to verify the conclusions given in Section III-B, an experiment with the experimental configuration shown in Fig. 2 is carried out. Three kinds of SWs are separately applied on coal cube specimens, and the fractures are detected with visual and statistical methods. A. Visual Analysis of Fracture Induced by Three Kinds of Shock Waves The SW repetition frequencies are ∼0.1 Hz for SW-WGD, ∼0.02 Hz for SW-EWE, and 0.01 Hz for SW-EME because of some operating time loss. The photos of coal cube specimens before, in, and after shocking are shown in Fig. 9. For SW-WGD, as many as 200 shots are taken; for SW-EWE, 50 shots are necessary; and for SW-EME, eight shots are enough. It clearly shows that with a certain amount of shots, tiny but dense fractures and large but sparse fractures are initiated or extended in all the three coal specimens.



Fig. 11. Average fracture number per centimeter of specimens with SW-WGD, SW-EWE, and SW-EME.

Fig. 10.

SEM images of typical micrograms of microfractures.

By analyzing the fracturing patterns in Fig. 9 and the corresponding PSD in Fig. 8, some conclusions can be drawn. 1) For SW-WGD, more than 200 shots are needed to generate effective visible fractures because of its lower power density and impulse. 2) For SW-EWE, reticular and multiple fractures appear after ∼50 shots. A possible explanation is that more energy is distributed in the high-frequency region. 3) As for SW-EME, dominant energy in the low-frequency region will break the coal cube into small dices within only eight shots. Suppose that more energy is distributed in the high-frequency region, multiple fractures may also appear. Microfractures are usually invisible to human eyes and some typical micrograms of microfractures as seen through a Quanta 250 scanning electron microscope (SEM) are shown in Fig. 10. Their structures and shapes are various and may be affected by the characteristics of SW and material, which need further research. B. Statistical Study of Fractures Induced by Shock Waves With the statistical method, fracture characteristics are analyzed. First, we draw lines L 1 –L 5 randomly but evenly distributed on the photos in Fig. 9 and zoom in the photo to proper size until every fracture is identifiable. Then, the number of fractures intersected with L 1 –L 5 is counted. Finally, we divide the total number of fractures by the total length of L 1 –L 5 and the average fracture number per centimeter is obtained. The average fracture numbers per centimeter of specimens with SW-WGD, SW-EWE, and SW-EME are shown in Fig. 11. The fracture numbers per centimeter of three specimens have a similar increase of about 100%, while the shock number of SW-EME is the least, and it indicates that SW-EME has the most effective fracturing effect.

Fig. 12. Average fracture width of specimens with SW-WGD, SW-EWE, and SW-EME.

The average fracture width is also an important parameter to describe the fracture characteristics. Similar with the method to obtain the average fracture number per centimeter, several lines are drawn on photos in Fig. 9, then zoom in the photo until every pixel is clear and visible. Second, the pixel number of the fracture is counted. Finally, dividing the total pixel number by the number of fractures, the average fracture width is obtained. The average fracture widths of specimens with SW-WGD, SW-EWE, and SW-EME are shown in Fig. 12. The average fracture widths of all the three specimens increase significantly. The average fracture width with SW-EME has the minimum initial value before shock and the maximum relative and absolute growth after shock, which proves that SW-EME has the best fracturing efficiency. And this may be explained by its higher power density in LFB and the maximum impulse. V. C ONCLUSION In this paper, we studied and compared the SWs generated with the WG load, the EW load, and the EM load. Plasmas are indispensable in these process. An interference-free SW measurement system in an anechoic tank was built to study the inherent and fracturing characteristics of the three kinds of SWs. The peak pressure, impulse, TDPP, and PSD were proved to be the key parameters to characterize the


compressive SWs. And SWs with different inherent characteristics had different fracturing patterns. With the same electrical energy stored in the capacitor, the SWs generated with the WG load have the lowest peak pressure and impulse, and more than 200 shots are needed to generate effective visible fractures in the coal cube. The SWs generated with the EW load have a better energy conversion efficiency and obvious fractures appear after 50 shots. The SW-EME has the maximum impulse and power density because of the extra chemical energy, and the coal cube specimen is torn into small dices within only eight shots. It can be concluded that the SW peak pressure and impulse determine the shot number of fracturing. The average fracture width with SW-EWE is the smallest, which may be determined by the much more energy distribution in the higher frequency region. While the average fracture width with SW-EME has the minimum initial value before shock and the maximum relative and absolute growths after shock, which proves that SW-EME has the best fracturing efficiency. And this may be explained by its higher power density in the lower frequency region and the maximum impulse. It can be concluded that SWs with more energy distributed in higher frequency region will generate tiny but dense fractures, while SWs with more energy distributed in the lower frequency region will generate large but sparse fractures. It is proved that the fracture pattern is significantly affected by impulse and PSD. This paper gives a correlation between the inherent characteristics and fracturing characteristics of SWs and will guide the practical application in the SW fracturing reservoir technology and many other fields. R EFERENCES [1] J. Zhang and X. Bian, “Numerical simulation of hydraulic fracturing coalbed methane reservoir with independent fracture grid,” Fuel, vol. 143, pp. 543–546, Mar. 2015. [2] T. Guo, S. Zhang, Z. Qu, T. Zhou, Y. Xiao, and J. Gao, “Experimental study of hydraulic fracturing for shale by stimulated reservoir volume,” Fuel, vol. 128, pp. 373–380, Jul. 2014. [3] W. Chen, “Experimental study on an alternative oil stimulation technique for tight gas reservoirs based on dynamic shock waves generated by pulsed arc electrohydraulic discharges,” J. Petroleum Sci. Eng., vols. 88–89, pp. 67–74, Jun. 2012. [4] W. Tang, Shock Wave Physics. Beijing, China: Science Press, 2011. [5] J. Cao and D. D. L. Chung, “Defect dynamics and damage of concrete under repeated compression, studied by electrical resistance measurement,” Cement Concrete Res., vol. 31, no. 11, pp. 1639–1642, 2001. [6] J. Cao and D. D. L. Chung, “Minor damage of cement mortar during cyclic compression, monitored by electrical resistivity measurement,” Cement Concrete Res., vol. 31, no. 10, pp. 1519–1521, Oct. 2001. [7] G. Touya, T. Reess, L. Pécastaing, A. Gibert, and P. Domens, “Development of subsonic electrical discharges in water and measurements of the associated pressure waves,” J. Phys. D, Appl. Phys., vol. 39, no. 24, pp. 5236–5244, 2006. [8] O. Maurel, “Electrohydraulic shock wave generation as a means to increase intrinsic permeability of mortar,” Cement Concrete Res., vol. 40, no. 12, pp. 1631–1638, Dec. 2010.

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