Influences on High-Voltage Electro Pulse Boring in Granite

energies

Article Inﬂuences on High-Voltage Electro Pulse Boring in Granite

Changping Li 1,2, Longchen Duan 3,*, Songcheng Tan 3 and Chikhotkin Victor 3

1 School of Mechanical Engineering and Electronic Information, China University of Geosciences, Wuhan 430074, China; [email protected] 2 School of Automation, China University of Geosciences, Wuhan 430074, China 3 School of Engineering, China University of Geosciences, Wuhan 430074, China; [email protected] (S.T.); [email protected] (C.V.) * Correspondence: [email protected]; Tel.: +1-388-608-1092

Received: 1 September 2018; Accepted: 13 September 2018; Published: 17 September 2018

Abstract: As the exploration and drilling of oil, natural gas and geothermal wells are expanding continuously, research into high-efficiency rock drilling technology is imperative. High-voltage electro pulse boring (EPB) has the advantages of high rock breaking efficiency and good wall quality, and is a new and efficient potential method of rock breaking. The design of electrode drill bits and the selection of drilling process parameters are the main obstacles restricting the commercialization of EPB. Accordingly, it is necessary to determine the influences on high-voltage EPB. In this study, based on the equivalent circuit of high-voltage electro pulse breakdown, a mathematical model of high-voltage electro pulse discharge in rock is established. Meanwhile, a numerical simulation model of high-voltage EPB of hard granite is established based on a coaxial cylindrical electrode structure, which is often used for electrode drill bits. The simulation analysis software Comsol Multiphysics (Comsol Multiphysics®5.3a, COMSOL Co., Ltd., Stockholm, Sweden) is used to study the influences of granite composition, electrode spacing and electrode shape on the high-voltage EPB process. In addition, the influences of electrical parameters on high-voltage EPB are calculated according to a model of high-voltage electro pulse discharge in rock. Finally, it is demonstrated that high-voltage EPB is influenced by granite composition, electrical parameters, electrode spacing, and electrode shape, and the relationships between these factors are obtained. This study is of guiding significance for improving rock breaking efficiency, reducing energy loss, designing electrode drill bits and selecting drilling process parameters.

Keywords: high-voltage electro pulse boring; inﬂuence factors; granite composition; electrode; electrical parameters

1. Introduction The exploration and drilling of oil, natural gas and geothermal wells are expanding continuously. Traditional mechanical drilling techniques have the disadvantages of low efficiency and high cost when used for deep and ultra-deep holes and hard rock such as granite. Therefore, research into high-efficiency technology for the drilling of rock is imperative [1,2]. At present, the main methods of non-mechanical rock breakage are by water jet, laser drilling, high-voltage electro pulse discharge, ultrasonic waves, and heat energy [3,4]. EPB [1], a type of high-voltage electro pulse discharge drilling, has high rock-breaking efficiency and produces good wall quality. Hence, it is a new and efficient potential rock breaking technique. High-voltage electric pulse discharge drilling methods can be divided into electrohydraulic rock breaking and electro pulse rock breaking, as shown in Figure1. When discharge plasma is produced in a liquid medium, rock is mainly broken by the mechanical

Energies 2018, 11, 2461; doi:10.3390/en11092461 www.mdpi.com/journal/energies EnergiesEnergies2018 2018, ,11 11,, 2461 x FOR PEER REVIEW 22 ofof 17 17 Energies 2018, 11, x FOR PEER REVIEW 2 of 17 and pressure wave. This effect is called electrohydraulic rock breaking. With a high-pressure short forcesand pressure produced wave. by theThis discharge, effect is called such aselectrohydraulic its shock wave, rock bubble breaking. collapse With and a pressurehigh-pressure wave. short This pulse with a rising time of less than 500 ns [5,6], the breakdown field strength of the rock is less effect is called electrohydraulic rock breaking. With a high-pressure short pulse with a rising time of pulsethan thatwith of a the rising liquid time medium of less used,than such500 ns as [5low,6], conductivity the breakdown water field or oilstrength, as shown of the in rockFigure is 2less. At thanless than that 500of the ns liquid [5,6], the medium breakdown used, ﬁeldsuch strengthas low conductivity of the rock iswater less thanor oil that, as shown of the liquidin Figure medium 2. At this time, the discharge plasma is mainly in the rock. Rock breakage occurs due to the stress caused thisused, time, such the as discharge low conductivity plasma wateris mainly or oil, in asthe shown rock. Rock in Figure breakage2. At thisoccurs time, due the to discharge the stress plasma caused by expansion of the plasma channel. This breaking method is called electro pulse rock breaking. byis mainlyexpansion in the of rock.the plasma Rock breakagechannel. This occurs breaking due to themethod stress is causedcalled electro by expansion pulse rock of the breaking. plasma Andres [7], Fujita et al. [8], and Ito et al. [9] have compared the electrohydraulic and electro pulse Andreschannel. [7], This Fujita breaking et al. method[8], and isIto called et al. electro [9] have pulse compared rock breaking. the electrohydraulic Andres [7], Fujita and etelectro al. [8 ],pulse and rock breaking methods. They found that the electrohydraulic technique breaks rock indirectly, rockIto et breaking al. [9] have methods. compared They the electrohydraulicfound that the andelectrohydraulic electro pulse rocktechnique breaking breaks methods. rock Theyindirectly, found while the electro pulse technique breaks it directly. Given the same amount of power, electro pulse whilethat the the electrohydraulic electro pulse technique technique breaks breaks it directly. rock indirectly, Given the while same the amount electro pulseof power, technique electro breaks pulse rock breaking produces a better breaking effect. Furthermore, electric pulses propagate faster in it directly. Given the same amount of power, electro pulse rock breaking produces a better breaking rockrock breakingthan in water.produces Therefore, a better thebreaking crushing effect. efficiency Furthermore, of electro electric pulse pulses rock propagatebreaking isfaster higher. in rockeffect. than Furthermore, in water. electricTherefore, pulses the propagatecrushing efficiency faster in rock of electro than in pulse water. rock Therefore, breaking the is crushing higher. Electrohydraulic rock breaking occurs mainly via compression failure, while the tensile stress that is Electrohydraulicefﬁciency of electro rock pulse breaking rock breakingoccurs main is higher.ly via compression Electrohydraulic failure, rock while breaking the tensile occurs stress mainly that via is formed in the process of electro pulse rock breaking makes the rock easier to break. Finally, the formedcompression in the failure, process while of electro the tensile pulse stress rock that breaking is formed makes in the the process rock ofeasier electro to pulsebreak. rock Finally, breaking the energy consumption of electro pulse rock breaking is lower than that of electrohydraulic rock energymakes theconsumption rock easier toof break.electro Finally, pulse therock energy breaking consumption is lower of than electro that pulse of electrohydraulic rock breaking is lowerrock breaking. brethanaking. that of electrohydraulic rock breaking. Switch Switch Switch Switch Rock Rock Rock Rock Pulse Power Pulse Power Pulse Supply Power Pulse Supply Power Supply Supply

Electrodes Electrodes Liquid medium Electrodes Liquid medium Electrodes Liquid medium Liquid medium

(a) (b) (a) (b) Figure 1. Two types of high-voltage electro pulse rock breaking: (a) electrohydraulic rock breaking; Figure 1.1. Two typestypes ofof high-voltagehigh-voltage electro pulse rock breaking:breaking: ( a) electrohydraulic rock rock breaking breaking;; (b) electro pulse rock breaking. (b) electro pulse rock breaking.breaking.

Electro pulse Electrohydraulic Electrorock breaking pulse Electrohydraulic rock breaking rock breaking rock breaking

Rising Solid Solid Rising voltage voltage Water Breakdown field strength field Breakdown Water Breakdown field strength field Breakdown

Air 0 0 Air 0 0 500ns Rising time of pulse voltage 500ns Rising time of pulse voltage Figure 2. Relationship between breakdown ﬁeld strength of different media and rising time of Figure 2. Relationship between breakdown field strength of different media and rising time of pulse pulseFigure voltage. 2. Relationship between breakdown field strength of different media and rising time of pulse voltage. voltage. The EPB technique incorporates electro pulse rock breaking. So far, high-voltage electro pulse rock The EPB technique incorporates electro pulse rock breaking. So far, high-voltage electro pulse breakingThe EPB has beentechnique applied incorporates to oil and gaselectro drilling, pulse ore rock crushing, breaking. and So so far, on. high The-voltage energy consumptionelectro pulse rock breaking has been applied to oil and gas drilling, ore crushing, and so on. The energy rockand drillingbreaking efﬁciency has been of EPB applied tools needto oil to and be further gas drilling, improved. ore The crushing former, Sovietand so Union on. developedThe energy a consumption and drilling efficiency of EPB tools need to be further improved. The former Soviet pulseconsumption plasma drillingand drilling rig suitable efficiency for drillingof EPB holestools ofneed 30–50 to mmbe further diameter improved. at a speed The of 15former cm/min Soviet [1]. Union developed a pulse plasma drilling rig suitable for drilling holes of 30–50 mm diameter at a TimoshkinUnion developed et al. [10 a ]pulse designed plasma a plasma drilling channel rig suitable drill bit for that drilling has a holes radially of symmetric30–50 mm electrodediameter andat a speed of 15 cm/min [1]. Timoshkin et al. [10] designed a plasma channel drill bit that has a radially usedspeed it of to 15 achieve cm/min a drilling[1]. Timoshkin speed ofet 16al. cm/min[10] designed in sandstone. a plasma Kusaiynovchannel drill et bit al. [that11] developedhas a radially an symmetric electrode and used it to achieve a drilling speed of 16 cm/min in sandstone. Kusaiynov symmetric electrode and used it to achieve a drilling speed of 16 cm/min in sandstone. Kusaiynov et al. [11] developed an electric pulse drilling unit with a zigzag shape and pointed out that this et al. [11] developed an electric pulse drilling unit with a zigzag shape and pointed out that this

Energies 2018, 11, 2461 3 of 17 electric pulse drilling unit with a zigzag shape and pointed out that this drilling method was most likely to be applied to geothermal energy heat exchange projects. An EPB drilling platform was developed in Norway in 2009, where 381 mm shallow holes were drilled in hard rock. Then, in 2011, EPB was combined with conventional rotary drilling to drill with a breaking volume of 19 cm3 per pulse [1]. In addition, Inoue et al. [12], Bluhm et al. [13], Biela et al. [5], and Vizir et al. [14] have developed high-voltage pulse power supplies. He et al. [15] developed an improved magnetic switch. Ji et al. [16] developed a high-voltage pulse transmission cable. A subsidiary of Badger Explorer was established in 2007 in Norway to develop and operate EPB technology [17]. In 2009, the commercial evaluation and testing of the industrial prototype Demo2000 was carried out. The evaluation report indicates that the technology still needs further research into the basic physical processes of plasma-induced rock fragmentation. The EPB process is defined as random because it is affected by many factors [18]. Boev et al. [19] proposed a mechanism for the formation of a discharge channel in solids, and discussed the influence of electrical parameters on rock breaking efficiency. Wang et al. [20] adopted the boundary element method software Coulomb 3D (Coulomb 3D®, INTEGRATED Engineering Software Inc., Winnipeg, MB, Canada) to analyze the electric field strength of ore under different particle conditions and compositions. Andres et al. [21] used experiments to determine three ways to optimize energy consumption: (1) improve the efficiency of the pulse generator, (2) optimize the geometry of the electrode, and (3) optimize the waveform of the electric pulse. Wielen et al. [22] used a SelFrag high-pressure pulse crusher to carry out pulse discharge experiments on 20 kinds of rocks. The effects of discharge frequency and discharge rate on electro pulse rock breaking were determined. The experimental results show that the discharge voltage and discharge cycle number are the main factors influencing the size of broken rock. The influence of electrode spacing on the discharge effect is complicated. Discharge effect of some kinds of rocks changes with alterations in electrode spacing, while the degree and mode of the change may differ. Kusaiynov et al. [11] concluded that the optimum discharge cycle number and discharge time were determined by drilling in ordinary rock and hard rock. Their experiment revealed that the change of energy released at the beginning of the breakdown, the timing of the pulse voltage supply, and the characteristics of rock influence the rock breaking process. Electrode drill bits and the selection of drilling process parameters are the main obstacles to the commercialization of high-voltage electro pulse rock breaking. To improve the rock breaking efficiency and energy utilization of the electrode drill bit, it is necessary to analyze the influences on high-voltage EPB. In this paper, hard granite is used to study electrical rock breaking. Granite has the characteristics of being hard, compact, and strong, and has low grinding properties. The traditional drilling method has the characteristics of low drilling efficiency and high drill bit wear. The numerical simulation analysis software Comsol (a short name of Comsol Multiphysics) was used to simulate high-voltage EPB in granite immersed in a water medium. The influences of granite composition and the electrical parameters of discharge voltage, number of pulses, discharge frequency, electrode shape and electrode spacing on EPB granite breaking was studied in a multi-phase medium. In the numerical simulation analysis and calculation process, the strength of the electric field and the energy injected into the plasma channel were used to measure the effect of the electrical pulse breaking of granite. The greater the electric field intensity and the higher the energy injected into the plasma channel, the better the EPB granite breaking effect. This paper presents models of (1) the high-voltage EPB of hard granite and (2) high-voltage electro pulse discharge in rock. A theoretical foundation involving the EPB of the electrostatic field is provided. Numerical experiments and calculations are also provided. The rest of the paper is organized as follows. In Section2, high-voltage EPB rock breaking systems and associated drilling processes are introduced. A mathematical model of high-voltage electro pulse discharge in rock, and an EPB numerical simulation model are described. The results and discussion are presented in Section3. The influences of granite composition, electrode spacing, electrode shape and electrical parameters on EPB are introduced in Sections 3.1–3.4 respectively. Finally, conclusions are drawn in Section4. Energies 2018, 11, 2461 4 of 17 Energies 2018, 11, x FOR PEER REVIEW 4 of 17

2. 2.Theory Theory and and Model Model

2.1.2.1. High High-Voltage-Voltage EPB EPB Rock Rock Breaking Breaking Systems Systems EPBEPB systems systems include include a ahigh high-voltage-voltage pulse pulse power supply,supply, aa drilling drilling ﬂuid fluid circulation circulation system, system, and andan an electrode electrode drill drill bit. bit. The The structure structure and and composition composition of an of EPB an systemEPB system and a and drilling a drilling principle principle diagram diagramare shown are shown in Figure in3 Figure. 3.

The System of High-Voltage Pulse Power Supply

Transmission cable Spark Rectifier switch Lifting Inductor eye Industrial Storage on the frequency capacitor of high circuit voltage Resistance on the circuit

Pump-controlled device Liquid-solid separator of drilling fluid Crushed Drilling Fluid rock Circulation System

Liquid medium of low conductivity

Electrode Drill Bit

High voltage Insulating Low voltage electrode block electrode

Figure 3. Figure 3. StructureStructure and and drilling drilling principle principle diagram diagram of ofan an EPB EPB system system.. The high-voltage pulse power supply system consists of an energy storage capacitor, spark switch, The high-voltage pulse power supply system consists of an energy storage capacitor, spark and rectifier, which uses a capacitor pulse generator to provide a high-voltage direct current pulse switch, and rectifier, which uses a capacitor pulse generator to provide a high-voltage direct current with a voltage rise time of less than 500 ns. Firstly, alternating current is obtained and boosted. pulse with a voltage rise time of less than 500 ns. Firstly, alternating current is obtained and boosted. At this moment, high-voltage direct current is obtained after the alternating current is rectified by At this moment, high-voltage direct current is obtained after the alternating current is rectified by a a high-voltage silicon stack rectifier. When the spark switch is disconnected, the storage capacitor high-voltage silicon stack rectifier. When the spark switch is disconnected, the storage capacitor stores the energy of the power supply; when the spark switch is closed, the energy is injected into stores the energy of the power supply; when the spark switch is closed, the energy is injected into the high- and low-voltage electrodes of the electrode drill bit through a transmission cable within a the high- and low-voltage electrodes of the electrode drill bit through a transmission cable within a short time to achieve the discharge breaking of rock. The drilling fluid circulation system is composed short time to achieve the discharge breaking of rock. The drilling fluid circulation system is of a liquid medium of low conductivity, a pump-controlled drilling fluid device, and a liquid-solid composed of a liquid medium of low conductivity, a pump-controlled drilling fluid device, and a separator. The low conductivity liquid medium not only acts as an insulating medium but also liquid-solid separator. The low conductivity liquid medium not only acts as an insulating medium returns the debris created. The liquid medium can be low-conductivity water or oil. After the spark but also returns the debris created. The liquid medium can be low-conductivity water or oil. After is closed, the breakdown voltage of the rock under the high-voltage short pulse discharge is less the spark is closed, the breakdown voltage of the rock under the high-voltage short pulse discharge than the breakdown voltage of the low-conductivity water or oil medium. Therefore, the rock can be is less than the breakdown voltage of the low-conductivity water or oil medium. Therefore, the rock broken first and EPB can be realized when the discharge continues. Usually, a water medium with can be broken first and EPB can be realized when the discharge continues. Usually, a water medium a relatively low breakdown voltage is selected in place of an oil medium with a high breakdown with a relatively low breakdown voltage is selected in place of an oil medium with a high voltage, so as to avoid generating oil pollution. The lower the conductivity of the water medium, the breakdown voltage, so as to avoid generating oil pollution. The lower the conductivity of the water better the electrical pulse rock breaking effect. Nevertheless, water that acts as an insulating medium medium, the better the electrical pulse rock breaking effect. Nevertheless, water that acts as an has higher requirements for electrode spacing, insulation, and discharge parameters [23]. Electrode insulating medium has higher requirements for electrode spacing, insulation, and discharge parameters [23]. Electrode drill bits include a high-voltage electrode, low-voltage electrode, and

Energies 2018, 11, x FOR PEER REVIEW 5 of 17 Energies 2018, 11, 2461 5 of 17 insulating block. The high- and low-voltage electrodes of an electrode drill bit can be arranged as a coaxial cylindrical electrode structure, and a structure of multiple groups of high- and low-pressure drillelectrodes. bits include The electrode a high-voltage drill bit electrode, directly affects low-voltage the energy electrode, consumed and insulating by rock breaking block. The and high- the anddrilling low-voltage efficiency. electrodes of an electrode drill bit can be arranged as a coaxial cylindrical electrode structure,The drilling and a structure process ofused multiple by EPB groups systems of high- is as and follows: low-pressure (1) the electrodes.breakdown The field electrode strength drill of bitwater directly is greater affects than the energythat of consumed rock under by a rock specific breaking voltage and discharge. the drilling Therefore, efficiency. the rock is first struckThe by drilling an electric process shock. used At by this EPB time, systems a small is as follows:discharge (1) precursor the breakdown is formed field strengthinside the of waterrock. isMoreover, greater than the thatdegrees of rock of voltage under adecrease specific voltagein the electrode discharge. and Therefore, current thedecrease rock isin first the struckloop are by ansmall. electric (2) When shock. the At thispilot time, develops a small a dischargeplasma channel precursor [23], is formedthe plasma inside channel the rock. bridge Moreover, produced the degreesconnects of the voltage high- decreaseand low- involtage the electrode electrodes. and Then, current the decrease main discharge in the loop channel are small. is formed. (2) When For the pilottime developsbeing, the a voltage plasma on channel the high [23],-voltage the plasma electrod channele drops bridge rapidly, produced and the connects current the in high- the loop and low-voltageincreases rapidly. electrodes. (3) The Then, energy the mainin the discharge storage capacitor channel is is formed. released For to thethe time plasma being, channel, the voltage and the on theplasma high-voltage channel electrodeis heated drops and rapidly,expands, and which the current works in on the the loop surrounding increases rapidly. rock mass. (3) The When energy the in thestress storage exceeds capacitor the stress is released strength to of the the plasma rock, channel,the rock andis broken. the plasma Finally, channel broken is heated rock is and returned expands, to whichthe ground works by on the the circulating surrounding water rock medium. mass. When the stress exceeds the stress strength of the rock, the rock is broken. Finally, broken rock is returned to the ground by the circulating water medium. 2.2. Mathematical Model of High-Voltage Electro Pulse Discharge in Rock 2.2. Mathematical Model of High-Voltage Electro Pulse Discharge in Rock An equivalent circuit of high-voltage electro pulse breakdown is shown in Figure 4. Capacitive pulseAn generators equivalent are circuit mostly of high-voltageused in electro electro discharge pulse technologies breakdown is. Other shown types in Figure of energy4. Capacitive sources pulsecan resul generatorst in similar are mostly equivalent used incircuits. electro A discharge capacitor, technologies. C, is used Otherto store types energy of energy from sourcesthe power can resultsupply in. The similar spark equivalent switches circuits. can be Am capacitor,echanical C,switches is used, tohigh store-voltage energy solid from-state the powerswitches supply. or Marx The sparktrigger switches switches can. W beater mechanical of low conductivity switches, high-voltage acts as an solid-stateinsulating switchesmedium orbetween Marx trigger the electrodes switches.. WaterThe circuit of low resistance conductivity Rz includes acts as an resistors insulating on capacito mediumrs, between connecting the electrodes. wires and Thespark circuit switches. resistance The Rinductivez includes inductance resistors on L capacitors,includes the connecting inductance wires of the and capacitors, spark switches. connecting The inductive wires and inductance discharge L includeschannels. the When inductance the spark of theswitch capacitors, is closed, connecting the capacitor wires pulse and dischargegenerator channels.produces Whena high the-pressure spark switchpulse to is impact closed, the capacitorrock and pulseproduce generator a plasma produces channel. a high-pressure The energy from pulse the to impactstorage thecapacitor rock and is producerepeatedly a plasma injected channel. into the The plasma energy channel from the. The storage energy capacitor results isin repeatedly increases in injected the channel into the pressure plasma channel.and radial The size energy, and results generation in increases of mechanical in the channel stress pressure waves andthat radialcause size,the androck generation to undergo of mechanicalintermittent stress breakdown. waves that cause the rock to undergo intermittent breakdown.

Figure 4.4. EquivalentEquivalent circuit circuit of of high high-voltage-voltage electro electro pulse pulse breakdown: breakdown: 1–water 1–water medium, medium, 2-rock, 2-rock, C–

Cstorage–storage capacitor, capacitor, S– S–sparkspark switches, switches, RRz–zcircuit–circuit resistance, resistance, LL––inductiveinductive inductance, Rtdtd––resistanceresistance of plasma channel.channel.

According to the Kirchhoff equations,equations, thethe followingfollowing equationsequations cancan bebe obtained.obtained. di di ++ + = L L+ (R (+ RzR R) tdi( )()t it) + U Uc( ()t t) = 00 (1) dt dt z td c where ii isis thethe currentcurrent inin thethe loop,loop, UUcc is instantaneousinstantaneous voltage of capacitor,capacitor, and the energyenergy storagestorage capacitance C exists as: dU (t) C c = i(t) (2) dt

Energies 2018, 11, 2461 6 of 17

By calculating the integral of the two sides of Equation (2), the direction of the charge voltage U0 on the initial capacitor is opposite to the discharge voltage. Therefore, it can be concluded that:

t 1 Z U = i(t)dt − U (3) c C 0 0

The plasma channel adopts a Weizel-Rompe model of impedance [24,25], which can be expressed in the form of a current integral.

Z t −1/2 2 Rtd(t) = Ktdltd( i (t)dt) (4) 0 where Ktd is the resistance coefﬁcient, and ltd is the length of the plasma channel. Equation (5) can be obtained by substituting Equations (3) and (4) into Equation (1), then differentiating the two sides of the equation. It can be concluded that:

" − # − d2i(t) R K l Z t 1/2 di(t) K l Z t 3/2 1 + z + td td ( i2(t)dt) − td td ( i2(t)dt) i3(t) + i(t) = 0 (5) dt2 L L 0 dt 2L 0 LC set:   x1 = i(t)  di x2 = dt (6)  R t 2 x3 = 0 i (t)dt The second-order differential equation can be simpliﬁed into a system of ﬁrst-order differential equations. From the system of Equation (6), it can be concluded that:  dx1 = x  dt 2 dx2 Ktdltd −1.5 3 Rz Ktdltd −1.5 1 dt = 2L x3 x1 − ( L + L x3 ) − LC x1 (7)  dx3 2 dt = x1

The initial conditions of the equations are as follows:  x (0) = 0  1 U0 x2(0) = L (8)   x3(0) = 0

The discharge voltage Utd of the plasma channel can be expressed as:

Utd(t) = i(t)Rtd (9)

The power Ptd injected into the plasma channel can be expressed as:

2 Ptd(t) = i (t)Rtd (10)

The power injected into the plasma channel is discretized and integrated. The energy injected into the plasma channel Wtd can be expressed as:

Z t 2 Wtd(t) = i (t)Rtddt (11) 0

The system of Equation (7) is a rigid system, which can be solved numerically by the numerical method of differential equations with variable order. The discharge circuit parameters refer to a high-voltage direct current power supply (China Teslaman High-Voltage Power Supply Co., Ltd., Energies 2018, 11, 2461 7 of 17

Dalian, China), which has a maximum output voltage of 50 kV. The capacity of the capacitor is 8 uF, and the maximum output energy is 10 kJ [26]. The effects of discharge voltage, discharge waveform, and discharge frequency on EPB were studied by changing the voltage and capacitance. In the process of simulation, the values of the charge voltage U0 are 50 kV, 80 kV, and 100 kV, respectively. The values of capacitance C are 8 uF, 18 uF, and 28 uF, respectively. The electrical circuit resistance Rz is 1 Ω and 1/2 the inductance L is 5 uH. The resistance coefﬁcient Ktd is 611 V·S /m [24]. It is assumed that the length of the plasma channel is equal to the spacing between the electrodes, which is 33 mm.

2.3. EPB Numerical Simulation Model In the process of rock breaking and drilling, there are rock solids, pore gases in rock, insulating liquid among electrodes, and plasma. At the same time, an electric field, temperature field, flow field and stress field exist in the process of discharge. In other words, EPB is carried out in a coupled environment of multi-phase media and multi-physical fields. Accordingly, the physical field simulation software Comsol can be used, which is based on the finite element method. The real physical phenomena are simulated by solving a partial differential equation or partial differential equation group. Moreover, the software can realize the real-time interaction between the design model Solidworks (Solidworks®2016, Dassault Systèmes SolidWorks Corp., Concord, MA, USA) and the simulation model in Comsol through the LiveLink™ for Solidworks (a plug-in of Comsol) interface. Rock is well insulated in the process of EPB. According to the discharge relaxation theory [27], the discharge relaxation time of the rock τ is far more than external discharge time T. The electrostatic interface of the AC/DC module in Comsol is used to simulate drilling in the electro pulse rock breaking process. The main equation involved in the simulation analysis of the spatial electric field distribution is a Poisson equation of the electrostatic field. Its differential form can be expressed by Equation (12):

− ∇(ε0εr∇V − P) = ρ (12) where ε0 is vacuum permittivity, εr is relative permittivity, P is polarization intensity vector, and ρ is the electric ﬁeld density in space.

2.3.1. Building the Simulation Model In the EPB simulation process, granite rock is simulated and analyzed. Granite samples were taken from high-abrasiveness strata in the Harizha mining area of the ore-forming band in Kunlun, China. When mechanical drilling is used in this mining area, strata with high abrasiveness are often encountered, which reduces drilling efﬁciency and shortens the drill bit lifespan markedly. One type of testEnergies samples 2018, 11 and, x FOR mineral PEER REVIEW slices of granite from the Harizha mining area are shown in Figures5 and8 of 617.

Figure 5.5. Rock sample from Harizha.

Figure 6. Mineral slice from Harizha.

According to the analysis of a mineral slice of granite, the compositions of granite from this mining area are potassium feldspar 38%, plagioclase 25%, quartz 25%, biotite 8%, sphene 1%, limestone 1%, zircon 1%, and magnetite 1%. Thus, the granite in this area is mainly composed of potassium feldspar, plagioclase, quartz, and biotite. To study the effect of rock composition on EPB, the compositions of the granite models used in the simulation were: 25% potassium feldspar, 25% plagioclase, 25% quartz, 25% biotite; 25% potassium feldspar, 25% quartz, 25% magnetite, 25% plagioclase; 50% biotite, 25% potassium feldspar, 25% quartz; 50% potassium feldspar and 50% quartz. The electrode layout used in the simulation model adopted a coaxial cylindrical electrode structure. To study the influences of electrode spacing and shape on EPB, the diameter of the low voltage electrode and the angle between the conical surface of the high-voltage electrode and the granite plane were selected as global parameters, and the distance between the high- and low-voltage electrodes was half the diameter of the low-voltage electrode. Real-time changes to electrode spacing and electrode shape in the Solidworks model and Comsol simulation model were realized through the LiveLink™ for Solidworks interface. To avoid the influence of electrode shape on electrode spacing, the high-voltage electrode was designed as an inverted trapezoid. When the electrode shape changed, only the angle between the conical surface of the high-voltage electrode and the rock surface changed. Simultaneously, the spacing between the electrodes was kept unchanged. The EPB simulation model is shown in Figure 7. Granite was composed of four module domains in the simulation model, which were defined by changing the material parameters of different domains.

Energies 2018, 11, x FOR PEER REVIEW 8 of 17

Energies 2018, 11, 2461 8 of 17 Figure 5. Rock sample from Harizha.

Figure 6.6. Mineral slice from Harizha.

According toto the the analysis analysis of of a minerala mineral slice slice of granite, of granite, the compositions the compositions of granite of granite from this from mining this areamining are potassiumarea are potassium feldspar 38%,feldspar plagioclase 38%, plagioclase 25%, quartz 25%, 25%, quartz biotite 8%,25%, sphene biotite 1%, 8%, limestone sphene 1%, zirconlimestone 1%, 1%, and zircon magnetite 1%, 1%. and Thus, magnetite the granite 1%. Thus, in this the area granite is mainly in this composed area is ofmainly potassium composed feldspar, of plagioclase,potassium feldspar, quartz, andplagioclase, biotite. Toquartz, study and the biotite. effect of To rock study composition the effect of on rock EPB, composition the compositions on EPB, of the granitecompositions models of used the ingranite the simulation models used were: in 25% the potassiumsimulation feldspar, were: 25% 25% potassium plagioclase, feldspar, 25% quartz, 25% 25%plagioclase, biotite; 25%25% potassiumquartz, 25% feldspar, biotite; 25% 25% quartz, potassium 25% magnetite,feldspar, 25% 25% quartz plagioclase;, 25% 50%magnetite, biotite, 25% potassiumplagioclase feldspar,; 50% biotite, 25%quartz; 25% potassium 50% potassium feldspar, feldspar 25% andquartz; 50% 50% quartz. potassium feldspar and 50% quartz.The electrode layout used in the simulation model adopted a coaxial cylindrical electrode structure. To studyThe theelectrode influences layout of electrode used in spacing the simulation and shape model on EPB, adopted the diameter a coaxial of the lowcylindrical voltage electrode andstructure. the angle To study between the theinfluences conical surfaceof electrode of the spacing high-voltage and shape electrode on EPB, and the the diameter graniteplane of the were low selectedvoltage electrode as global parameters,and the angle and between the distance the conical between surface the high- of andthe high low-voltage-voltage electrodes electrode wasand halfthe thegranite diameter plane of thewere low-voltage selected as electrode. global Real-timeparameters, changes and tothe electrode distance spacing between and electrodethe high- shape and inlow the-voltage Solidworks electrodes model was and half Comsol the diameter simulation of modelthe low were-voltage realized electrode. through Real the-time LiveLink changes™ for to Solidworkselectrode spacing interface. and To electrode avoid the shape influence in the of Solidworks electrode shape model on and electrode Comsol spacing, simulation the high-voltagemodel were electroderealized through was designed the LiveLink™ as an inverted for Soli trapezoid.dworks interface. When the To electrode avoid the shape influence changed, of electrode only the shape angle betweenon electrode the conical spacing, surface the high of the-voltage high-voltage electrode electrode was designed and the rock as an surface inverted changed. trapezoid. Simultaneously, When the theelectrode spacing shape between changed, the electrodesonly the angle was keptbetween unchanged. the conical The surface EPB simulation of the high model-voltage is shownelectrode in Figureand the7. Graniterock surface was composed changed. of fourSimultaneously, module domains the inspacing the simulation between model, the electrodes which were was defined kept byunchanged.Energies changing 2018, 11 The the, x FOR materialEPB PEER simulation REVIEW parameters model of differentis shown domains.in Figure 7. Granite was composed of four module9 of 17 domains in the simulation model, which were defined by changing the material parameters of different domains.

FigureFigure 7.7. EPBEPB simulationsimulation model.model.

2.3.2. Definition and Solution of the Simulation Model According to the Poisson equation of the electrostatic field, the main parameter affecting the electric field density and distribution in the rock is the electrical permittivity of the rock. The material properties used in the simulation model are shown in Table 1.

Table 1. Properties of the materials used in the simulation model.

Material Electrical Permittivity Material Electrical Permittivity Water 80 [28] Potassium feldspar 6.2 Plagioclase 6.91 Quartz 6.53 Biotite 9.28 Magnetite 65

When the influences of granite composition, electrode spacing, and electrode shape on EPB are simulated and analyzed, the load voltage is 50 kV. To simulate the effect of electrode spacing and electrode shape on EPB, the diameter of the low voltage electrode and the angle between the conical surface of the high-voltage electrode and granite plane are parameterized and scanned. The list of parameter values is set separately in Comsol: range (66 mm, −3 mm, 33 mm) and range (46°, 2°, 82°). The first indicates that the initial spacing between the high- and low-voltage electrodes is 33 mm, the step length is −1.5 mm, and the limit spacing is 16.5 mm. The spacing between the high- and low-voltage electrodes changes continuously. The second range indicates that the initial angle between the electrode cone and the horizontal plane of the granite is 46°. The step length is 2° and the limit angle is 82°. The shape of the high-voltage electrode changes continuously. The default grid and solver were used to simulate and analyze the EPB model. In the simulation of the effect of granite composition on EPB, the arrow size and the arrow and surface colors reflect the electric field intensity. In the simulation of the influence of electrode spacing and electrode shape change on EPB, the electric field intensity and distribution on the granite surface and the interior variation can be obtained as the electrode spacing and shape are varied by a fixed step size.

3. Results and Discussion

3.1. Influence of Granite Composition on EPB The results of the simulation of the influence of granite composition on EPB are shown in Figure 8. In the process of simulating the effect of granite composition on EPB, the electrical parameters, electrode spacing, and electrode shape remain constant. It can be seen from Figure 8a that different granite compositions affect the field strength. This conclusion is consistent with that of Wang et al. [20]. The electrical permittivity of plagioclase and biotite is larger than that of

Energies 2018, 11, 2461 9 of 17

2.3.2. Definition and Solution of the Simulation Model According to the Poisson equation of the electrostatic field, the main parameter affecting the electric field density and distribution in the rock is the electrical permittivity of the rock. The material properties used in the simulation model are shown in Table1.

Table 1. Properties of the materials used in the simulation model.

Material Electrical Permittivity Material Electrical Permittivity Water 80 [28] Potassium feldspar 6.2 Plagioclase 6.91 Quartz 6.53 Biotite 9.28 Magnetite 65

When the influences of granite composition, electrode spacing, and electrode shape on EPB are simulated and analyzed, the load voltage is 50 kV. To simulate the effect of electrode spacing and electrode shape on EPB, the diameter of the low voltage electrode and the angle between the conical surface of the high-voltage electrode and granite plane are parameterized and scanned. The list of parameter values is set separately in Comsol: range (66 mm, −3 mm, 33 mm) and range (46◦, 2◦, 82◦). The first indicates that the initial spacing between the high- and low-voltage electrodes is 33 mm, the step length is −1.5 mm, and the limit spacing is 16.5 mm. The spacing between the high- and low-voltage electrodes changes continuously. The second range indicates that the initial angle between the electrode cone and the horizontal plane of the granite is 46◦. The step length is 2◦ and the limit angle is 82◦. The shape of the high-voltage electrode changes continuously. The default grid and solver were used to simulate and analyze the EPB model. In the simulation of the effect of granite composition on EPB, the arrow size and the arrow and surface colors reflect the electric field intensity. In the simulation of the influence of electrode spacing and electrode shape change on EPB, the electric field intensity and distribution on the granite surface and the interior variation can be obtained as the electrode spacing and shape are varied by a fixed step size.

3. Results and Discussion

3.1. Influence of Granite Composition on EPB The results of the simulation of the influence of granite composition on EPB are shown in Figure8. In the process of simulating the effect of granite composition on EPB, the electrical parameters, electrode spacing, and electrode shape remain constant. It can be seen from Figure8a that different granite compositions affect the field strength. This conclusion is consistent with that of Wang et al. [20]. The electrical permittivity of plagioclase and biotite is larger than that of potassium feldspar and quartz. The field strength of plagioclase and biotite is larger than that of potassium feldspar and quartz. The maximum electric field strength of granite with this kind of composition is 13.3 kV/mm. It can be seen from Figure8b that the model of granite with this kind of composition contains 25% magnetite with an electrical permittivity of 65. In the process of EPB, the maximum electric field strength of this kind of composition is 20.7 kV/mm. It can be seen from Figure8c that the granite simulation model of this kind of composition contains 50% biotite. The electric field intensity of biotite is greater than that of potassium feldspar and quartz. The maximum electric field strength of the granite is greater than that shown in Figure8a. It can be seen from Figure8d that the electric field strength of the granite simulation model of this kind is the smallest, and the electric field strength of each component is uniformly distributed. This phenomenon is due to the similar electrical permittivities of potassium feldspar and quartz. It also can be concluded from Figure8 that the electric field intensity is higher near the boundaries of the different components and the high-voltage electrode. Energies 2018, 11, x FOR PEER REVIEW 10 of 17 potassium feldspar and quartz. The field strength of plagioclase and biotite is larger than that of potassium feldspar and quartz. The maximum electric field strength of granite with this kind of composition is 13.3 kV/mm. It can be seen from Figure 8b that the model of granite with this kind of composition contains 25% magnetite with an electrical permittivity of 65. In the process of EPB, the maximum electric field strength of this kind of composition is 20.7 kV/mm. It can be seen from Figure 8c that the granite simulation model of this kind of composition contains 50% biotite. The electric field intensity of biotite is greater than that of potassium feldspar and quartz. The maximum electric field strength of the granite is greater than that shown in Figure 8a. It can be seen from Figure 8d that the electric field strength of the granite simulation model of this kind is the smallest, and the electric field strength of each component is uniformly distributed. This phenomenon is due to the similar electrical permittivities of potassium feldspar and quartz. It also can be concluded fromEnergies Figure2018, 11 ,8 2461 that the electric field intensity is higher near the boundaries of the different10 of 17 components and the high-voltage electrode.

FigureFigure 8 8.. SimulationSimulation results results of of the the influence influence of of granite granite composition composition on on EPB EPB:: (a (a) )1 1–potassium–potassium feldspar, feldspar, 22–quartz,–quartz, 3 3–plagioclase,–plagioclase, 4– 4–biotite,biotite, (b ()b 1)– 1–potassiumpotassium feldspar, feldspar, 2–quartz, 2–quartz, 3–plagioclase, 3–plagioclase, 5–magnetite, 5–magnetite, (c) 1(–c)potassium 1–potassium feldspar, feldspar, 2–quartz, 2–quartz, 4–biotite, 4–biotite, (d) (1d–)potassium 1–potassium feldspar, feldspar, 2–quartz. 2–quartz. 3.2. Influence of Electrode Spacing on EPB 3.2. Influence of Electrode Spacing on EPB When the influence of electrode spacing on EPB is simulated, the granite composition, electrode When the influence of electrode spacing on EPB is simulated, the granite composition, shape and electrical parameters remain constant. The electric field intensity and distribution for 12 electrode shape and electrical parameters remain constant. The electric field intensity and spacings of high- and low-voltage electrodes were simulated and analyzed. The high- and low-voltage distribution for 12 spacings of high- and low-voltage electrodes were simulated and analyzed. The electrode spacing ranged from 33 mm to 16.5 mm with a step size of −1.5 mm. Curves of the maximum high- and low-voltage electrode spacing ranged from 33 mm to 16.5 mm with a step size of −1.5 mm. electric field intensity on the granite surface are shown in Figure9a according to changes in electrode Curves of the maximum electric field intensity on the granite surface are shown in Figure 9a spacing. It can be seen from Figure9a that the maximum electric field intensity on the surface of the according to changes in electrode spacing. It can be seen from Figure 9a that the maximum electric granite increases as the electrode spacing decreases. The granite is composed of potassium feldspar, field intensity on the surface of the granite increases as the electrode spacing decreases. The granite plagioclase, quartz, and biotite. The maximum electric field intensity on the granite surface was is composed of potassium feldspar, plagioclase, quartz, and biotite. The maximum electric field 22.69 kV/mm at 16.5 mm. The influence of electrode spacing on the composition of granite was further intensity on the granite surface was 22.69 kV/mm at 16.5 mm. The influence of electrode spacing on determined on the basis of the study by Wielen et al. [22]. The curve of the average electric field the composition of granite was further determined on the basis of the study by Wielen et al. [22]. intensity on the granite surface is shown in Figure9b with various electrode spacings. It shows that The curve of the average electric field intensity on the granite surface is shown in Figure 9b with the average electric field intensity on the granite surface decreases with decreases in electrode spacing.

Energies 2018, 11, x FOR PEER REVIEW 11 of 17 Energies 2018, 11, x FOR PEER REVIEW 11 of 17 various electrode spacings. It shows that the average electric field intensity on the granite surface Energiesvarious2018 electrode, 11, 2461 spacings. It shows that the average electric field intensity on the granite surface11 of 17 decreases with decreases in electrode spacing. decreases with decreases in electrode spacing.

(a) (b) (a) (b) Figure 9. Relationships between electrode spacing and (a) maximum and (b) average electric field FigureFigure 9.9. RelationshipsRelationships between between electrode electrode spacing spacing and and (a) (maximuma) maximum and and(b) average (b) average electric electric field intensity. fieldintensity. intensity. In the simulation of the electric field distribution in granite during EPB, several 2-mm-interval InIn thethe simulationsimulation ofof thethe electricelectric fieldfield distributiondistribution inin granitegranite duringduring EPB,EPB, severalseveral 2-mm-interval2-mm-interval cross-sections were built within the granite model, starting at 2 mm from the surface. The results of cross-sectionscross-sections were were built built within within the the granite granite model, model, starting starting at 2at mm 2 mm from from the the surface. surface. The The results results of the of the simulation of the influence of electrode spacing on the electric field distribution are shown in simulationthe simulation of the of influence the influence of electrode of electrode spacing spacing on the electricon the fieldelectric distribution field distribution are shown are in shown Figure 10in Figure 10 for the granite interior during EPB. It can be seen from the diagram that the maximum forFigure the granite10 for the interior granite during interior EPB. during It can beEPB. seen It can from be the seen diagram from the that diagram the maximum that the electric maximum field electric field intensity in the granite interior increases with decreases in electrode spacing. The intensityelectric field in the intensity granite interiorin the granite increases interior with decreases increases in with electrode decreases spacing. in electrode The distribution spacing. of The the distribution of the electric field is more concentrated and is deeper. This means that the granite electricdistribution field isof morethe electric concentrated field is and more is deeper. concentrated This means and is that deeper. the granite This breakagemeans that depth the duringgranite breakage depth during primary discharge is deeper, but the range of electric field intensity is primarybreakage discharge depth during is deeper, primary but the discharge range of electricis deeper, field but intensity the range is narrower. of electric At the field same intensity time, the is narrower. At the same time, the electric field distribution inside the granite shows that its intensity electricnarrower. field At distribution the same time, inside the the electric granite field shows distribution that its intensity inside the was granite greatest shows in the that vicinity its intensity of the was greatest in the vicinity of the high-voltage electrode. The greater the radial distance from the high-voltagewas greatest electrode.in the vicinity The greater of the thehigh radial-voltage distance electrode. from theThe high-voltage greater the electrode,radial distance the smaller from thethe high-voltage electrode, the smaller the intensity of the electric field. intensityhigh-voltage of the electrode, electric field. the smaller the intensity of the electric field.

FigureFigure 10.10. ResultsResults of of the the simulation simulation of the of influence the influence of electrode of electrode spacing onspacing the electric on the field electric distribution field Figure 10. Results of the simulation of the influence of electrode spacing on the electric field distributionin the granite in interior.the granite interior. distribution in the granite interior. 3.3. Influence of Electrode Shape on EPB 3.3. Influence of Electrode Shape on EPB 3.3. Influence of Electrode Shape on EPB The influence on EPB of an electrode with a cone-horizontal surface angle of 46◦, step length of The influence on EPB of an electrode with a cone-horizontal surface angle of 46°, step length of 2◦, andThe maximum influence taper on EPB of 82 of◦ anwas electrode analyzed. with The a granitecone-horizontal composition, surface electrode angle spacingof 46°, step and electricallength of 2°, and maximum taper of 82° was analyzed. The granite composition, electrode spacing and parameters2°, and maximum remained taper constant. of 82° Curves was analyzed. of the maximum The granite and average composition, electric electrode field intensities spacing on and the electrical parameters remained constant. Curves of the maximum and average electric field graniteelectrical surface parameters with various remained electrode constant. shapes Curves are shown of the in Figure maximum 11. It isand shown average that theelectric maximum field electric field intensity on the granite surface increases with increases of the angle. The granite was

Energies 2018, 11, x FOR PEER REVIEW 12 of 17 Energies 2018, 11, 2461 12 of 17 intensities on the granite surface with various electrode shapes are shown in Figure 11. It is shown that the maximum electric field intensity on the granite surface increases with increases of the angle. composedThe granite of was potassium composed feldspar, of potassium plagioclase, feldspar, quartz, plagioclase, and biotite. quartz, With an and angle biotite. of 82 With◦, the an maximum angle of electric82°, the ﬁeldmaximum intensity electric on the field granite intensity surface on is the 22.09 granite kV/mm. surface However, is 22.09 the kV/mm. average However, electric ﬁeld the intensityaverage electric of the surfacefield intensity decreases of the with surface increases decrease of angle.s with increases of angle.

Figure 11.11. Simulation of maximum and average electric field ﬁeld intensities according to electrode shape.shape.

Kusaiynov etet al.al [. 11[1]1 designed] designed an an electrode electrode drill drill with with a zigzag a zigzag shape shape that can that increase can increase the electric the fieldelectric strength field strength without changingwithout changing the input. the The input. distribution The distribution of the electric of fieldthe inelectric granite field during in granite EPB is shownduring inEPB Figure is shown 12. It in can Figure be seen 12. thatIt can the be maximum seen that electricthe maximum field intensity electric infield granite intensity increases in granite with increases ofwith angle, increases but the extentof angle, of thebut increase the extent is low. of Atthe the increase same time, is low. the electrodeAt the same shape time, has little the effectelectrode on the shape internal has little electric effect field on depth.the internal electric field depth.

Figure 12. Simulation results of the influence of electrode shape on the electric field distribution Figure 12. Simulation results of the influence of electrode shape on the electric field distribution within granite. within granite. 3.4. Influence of Electrical Parameters on EPB 3.4. Influence of Electrical Parameters on EPB The effects of discharge voltage, discharge waveform and discharge frequency on electric pulse The effects of discharge voltage, discharge waveform and discharge frequency on electric pulse drillingThe were effects simulated of discharge and voltage, analyzed. discharge The discharge waveform waveform and discharge is related frequency to the parameters on electric ofpulse the drilling were simulated and analyzed. The discharge waveform is related to the parameters of the electricdrilling circuitwere simulated such as its and capacitance. analyzed. Finally,The discharge the energy waveform injected is into related the graniteto the parameters was measured of the to electric circuit such as its capacitance. Finally, the energy injected into the granite was measured to evaluate the effect of EPB in granite. With charging voltages of U1 = 50 kV, U2 = 80 kV, and U3 = 100 kV, evaluate the effect of EPB in granite. With charging voltages of U1 = 50 kV, U2 = 80 kV, and U3 = 100 theevaluate equivalent the effect discharge of EPB voltage in granite. waveform, With charging discharge voltages current waveform,of U1 = 50 kV, power U2 waveform= 80 kV, and and U energy3 = 100

EnergiesEnergies2018 2018,,11 11,, 2461 x FOR PEER REVIEW 13 ofof 1717

kV, the equivalent discharge voltage waveform, discharge current waveform, power waveform and waveformenergy waveform injected intoinjected the plasmainto the channel plasma were channel determined were determined (Figure 13). (Figure This waveform 13). This veriﬁes waveform the changesverifies inthe voltage, changes current, in voltage, and energy current, in theand three energy stages in ofthe granite three fragmentationstages of granite during fragmentation EPB. In the secondduring stage,EPB. In the the voltage second on thestage, high-voltage the voltage electrode on the high decreases-voltage rapidly, electrode and the decreases current inrapidly, the circuit and increasesthe current rapidly. in the In circuit this stage, increases the power rapidly. and energyIn this ofstage, the plasma the power channel and increase energy theof fastest.the plasma The energychannel injected increase into the the fastest. plasma The channel energy is convertedinjected into into shockwavethe plasma energychannel and is channelconverted heating into energy.shockwave This energy stage is and the plasmachannel channel heating expansion energy. This stage stage and isis thethe mainplasma stage channel in which expansion the energy stage in theand capacitor is the main is converted stage in which into shockwave the energy energyin the capacitor [25]. is converted into shockwave energy [25].

100 60 Current i1 90 Urch1 Urch2 50 Current i2 80 Urch3 Current i3 70 40

60 30 50 20 40 Current(kA)

30 10 Discharge voltage(kV) Discharge 20 0 10

0 -10 0 5 10 15 20 25 30 0 20 40 60 80 100 Time(us) Time(us) (a) (b) 700 10 Wch1 Pch1 9 600 Wch2 Pch2 8 Wch3 Pch3 500 7

6 400 5 300 4

200 3 The energy injected into injected energy The the plasma channel(kJ) channel(kJ) plasma the 2 plasma channel(MW) channel(MW) plasma The power injected into the the into injected power The 100 1

0 0 0 10 20 30 40 50 60 70 80 90 100 0 20 40 60 80 100 Time(us) Time(us) (c) (d)

FigureFigure 13.13. ((aa)) VoltageVoltage waveformwaveform ofof equivalentequivalent circuit,circuit, ((bb)) currentcurrent waveform,waveform, ((cc)) powerpower waveformwaveform ofof injectioninjection into plasma channel, channel, (d (d) )energy energy waveform. waveform. L L= 5 = uH, 5 uH, C = C 8 = uF, 8 uF, U (kV): U (kV): U1 U= 150,= U 50,2 = U 80,2 = U 80,3 = U100.3 = 100.

TheThe maximummaximum energy energy storage storage capacity, capacity the, maximumthe maximum power power and energyand energy injected injected into the into granite the plasmagranite channelplasma channel and the and energy the energy conversion conversion rate in rate Table in2 Tablecan be 2 obtainedcan be obtained and extrapolated and extrapolate fromd Figurefrom Figure 13. It can13. beIt can concluded be concluded that the that power the andpower energy and injectedenergy injected into the graniteinto the plasma granite channel plasma increasechannel withincrease increases with inincreases the charging in the voltage charging of the voltage high-voltage of the electrichigh-voltage pulse powerelectric supply pulse system.power Thus,supply the system. granite Thus, is easier the togranite break is during easier drilling.to break However,during drilling. the energy However, conversion the energy efﬁciency conversion of the plasmaefficiency channel of the injectedplasma intochannel the graniteinjected decreases. into the granite The primary decreases. discharge The primary time of discharge the waveform time isof withinthe waveform 30 us, and is within the ratio 30 ofus, primary and the discharge ratio of primary time to dischargedischarge cycletime timeto discharge is small. cycle The energytime is injectedsmall. The into theenergy plasma injected channel into increases the plasma with increaseschannel inincreases the discharge with frequencyincreases perin unitthe discharge time, and thefrequency granite isper easier unit totime, break. and The the total granite energy is easier injected to break. into the The plasma total channelenergy injected increases into with the increases plasma inchannel discharge increases cycle number,with increases and the in granitedischarge is more cycle easily number broken., and the granite is more easily broken.

Energies 2018, 11, 2461 14 of 17 Energies 2018, 11, x FOR PEER REVIEW 14 of 17

TableTable 2.2.Maximum Maximum energy energy storage storage capacity, capacity, the the injected injected maximum maximum power power and energy,and energy and the, and energy the conversionenergy conversion rate with rate charging with charging voltages voltages of U1 = 50of U kV,1 = U 502 =kV, 80 U kV,2 = U803 =kV, 100 U kV.3 = 100 kV.

ChargingCharging MaximumMaximum Energy Energy InjectedInjected Injected Maximum EEnergynergy Injected VoltagesVoltages StorageStorage Capacity Capacity MaximumMaximum Power Power Power ConversionConversion Rate Rate Maximum Power 50 kV 10 kJ 241.5 MW 3.2 kJ 32% 80 50kV kV 25.6 kJ 10 kJ462.5 241.5 MW MW 5.53.2 kJ kJ 21%32% 10080 kV kV 40 kJ 25.6 kJ621.1 462.5 MW MW 7.15.5 kJ kJ 18%21% 100 kV 40 kJ 621.1 MW 7.1 kJ 18%

When the capacitor values of equivalent circuit are C1 = 8 uF, C2 = 16 uF, and C3 = 64 uF, the equivalentWhen discharge the capacitor voltage values waveform, of equivalent discharge circuit current are Cwaveform,1 = 8 uF, Cpower2 = 16 waveform uF, and Cand3 = energy 64 uF, thewaveform equivalent injected discharge into the voltage plasma waveform, channel dischargeare as shown current in Figure waveform, 14. It power can be waveform seen that andthe energycapacitance waveform value injectedhas a great into influence the plasma on channelthe output are asvoltage shown and in Figurecurrent 14 waveform.. It can be The seen pulse that thewidth capacitance of the discharge value has voltage a great and inﬂuence current onincreases the output with voltage increases and in current capacitance. waveform. The power The pulse and widthenergy of injected the discharge into the voltage plasma and channel current increase increases simultaneously with increases in a in single capacitance. discharge. The However, power and as energythe capacitance injected into value the plasmaincreases channel, the charge increase and simultaneously discharge time in a increase, single discharge. and the However, discharge as rate the capacitancedecreases. value increases, the charge and discharge time increase, and the discharge rate decreases.

50 35 Current i1 45 Urch1 Urch2 30 Current i2 40 Urch3 25 Current i3 35 20 30

25 15

Current(kA) 10 15

Discharge voltage(kV) Discharge 5 10

5 0

0 -5 0 10 20 30 40 50 60 70 80 90 100 0 50 100 150 200 250 300 Time(us) Time(us) (a) (b) 300 14 Pch1 Wch1 Wch2 Pch2 12 250 Wch3 Pch3 10 200

8 150 6

100 4 plasma channel(kJ) channel(kJ) plasma The energy injected into the the into injected energy The plasma channel(MW) channel(MW) plasma The power injected into the into injected power The 50 2

0 0 0 20 40 60 80 100 120 140 160 180 200 0 50 100 150 200 250 300 Time(us) Time(us) (c) (d)

Figure 14.14. (a) Voltage waveformwaveform of equivalent circuit, ( b) current waveform, ( (cc)) power power waveform waveform of of injectioninjection into plasma plasma channel, channel, (d (d) )energy energy waveform, waveform, U U = 50 = 50kV, kV, L = L 5 = uH, 5 uH, C (uF): C (uF): C1 = C8,1 C=2 8,= 16, C2 C=3 16,= C643. = 64. 4. Conclusions 4. Conclusions Hard granite was used to investigate EPB in this paper, allowing a mathematical model of Hard granite was used to investigate EPB in this paper, allowing a mathematical model of high-voltage electro pulse discharge in rock to be established. A numerical simulation model of high-voltage electro pulse discharge in rock to be established. A numerical simulation model of EPB EPB was established simultaneously. The inﬂuences of continuously varied granite composition, was established simultaneously. The influences of continuously varied granite composition, discharge parameters, electrode shape and electrode spacing on EPB were simulated and analyzed. discharge parameters, electrode shape and electrode spacing on EPB were simulated and analyzed. The relationships between various factors and EPB in granite were obtained from the simulations. The following conclusions can be drawn:

Energies 2018, 11, 2461 15 of 17

The relationships between various factors and EPB in granite were obtained from the simulations. The following conclusions can be drawn: (1) The distribution of electric field intensity is not uniform with different rock compositions. The more types of rock composition, the greater the difference in the electrical properties of each component, and the greater the electric field intensity during EPB. The electric field intensity is greater closer to the boundaries of different rock components and to the electrode. Thus, in hard rock drilling, the drilling effect of EPB is good at more rock compositions and different electrical properties. (2) The ability and depth to break granite are weakened, but the radial breaking range of granite is increased with increased electrode spacing. When the electrode spacing is reduced by half, the maximum electric field intensity on the granite surface is increased by 1.7 times, in theory. Under the premises of ensuring breakage range and insulation, a small electrode spacing should be selected to improve rock breaking efficiency and breaking depth. (3) The ability of EPB to break granite is enhanced with an increase in the angle between the conical surface of the high-voltage electrode and the granite plane, but this has little effect on drilling range and depth. A zigzag-shaped electrode can be used to increase the electric field strength in granite [11], achieve the objective of improving crushing efficiency. (4) As the voltage increases, the granite breaking ability of EPB becomes stronger, but the energy conversion efficiency decreases. With increases in capacitance, the granite breaking ability of EPB becomes stronger, but the charging and discharging rate and discharging frequency are lower. The primary discharge time of the waveform is very short, and the duty ratio of pulse power supply is small. Energy consumption of efficient EPB can be reduced by increasing frequency of pulse power supply or the number of discharges. This study of the influences on high-voltage EPB of granite is of significance for improving rock breaking efficiency, reducing energy losses, designing electrode drill bits and selecting drilling process parameters. The mathematical model and EPB numerical simulation model used in this study is helpful in analyzing the influence of various factors on EPB under various conditions, including extreme ones. The results of this paper allow better optimization of the electric pulse bit and drilling parameters according to the required drilling rate, hole diameter and other practical specifications. It will inform further theoretical and experimental study of EPB and rock fracture mechanics.

5. Patents Changping Li; Xianfeng Tan; Longchen Duan; et al. An Electrode drill bit owned multi electrode pair and experimental device of electrical breaking. CHN.Patent 201820098015.X, 22 January 2018. Longchen Duan; Changping Li; Xianfeng Tan; et al. An electric pulse drill bit of rock breaking and its experimental device. CHN.Patent 201820085807.3, 18 January 2018.

Author Contributions: Conceptualization, L.D. and C.V.; Data curation, C.L. and S.T.; Formal analysis, C.L. and S.T.; Methodology, C.L.; Project administration, L.D.; Software, C.L.; Writing–original draft, C.L. Acknowledgments: This work was supported by the National Natural Science Foundation of China (41672364; 41602373) and the Innovation Fund of Petro-China (2016D-5007-0307). Conﬂicts of Interest: The authors declare no conﬂict of interest. Energies 2018, 11, 2461 16 of 17

Nomenclature

L Inductive inductance, H i Current in the loop, A Rz Circuit resistance, Ω Rtd Resistance of plasma channel, Ω Uc Instantaneous voltage of capacitor, V C Energy storage capacitance, F U0 Charge voltage, V 1/2 Ktd Resistance coefﬁcient, V·S /m ltd Length of the plasma channel, m Ptd Power injected into the plasma channel, W Wtd Energy injected into the plasma channel, J τ Discharge relaxation time of the rock, s T External discharge time, s ε0 Vacuum permittivity, F/m εr Relative permittivity P Polarization intensity vector, C/m2 ρ Electric ﬁeld density in space, C/m3

References

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