Calculation Model of High-Pressure Water Jet Slotting Depth for Coalbed Methane Development in Underground Coal Mine

Transcription

1 applied sciences Article Calculation Model of High-Pressure Water Jet Slotting Depth for Coalbed Methane Development in Underground Coal Mine Jianguo Zhang 1, Yingwei Wang 1, Zhaolong Ge 2,3, *, Songqiang Xiao 2,3, *, Hanyun Zhao 2,3 and Xiaobo Huang 2,3 1 State Key Laboratory of Coking Coal Exploitation and Comprehensive Utilization, Pingdingshan , China; zhangjg_z@126.com (J.Z.); wangyingwei.w@gmail.com (Y.W.) 2 State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing , China; zhaohanyun@cqu.edu.cn (H.Z.); huangxiaobo@cqu.edu.cn (X.H.) 3 School of Resources and Safety Engineering, Chongqing University, Chongqing , China * Correspondence: gezhaolong@cqu.edu.cn (Z.G.); xiaosongqiang@cqu.edu.cn (S.X.); Tel.: (Z.G.) Received: 6 November 2019; Accepted: 29 November 2019; Published: 3 December 2019 Abstract: In underground coal mines, high-pressure water jet slotting is effective at improving coal seams permeability. The slotting depth determines the effect of pressure relief and permeability enhancement in coal seams. However, there is no effective and feasible way of determining the slotting depth; thus, the operational parameters and borehole layout are unknown. This study determined the effects of key parameters, including the nozzle diameter, jet pressure, rotation speed, and slotting time, on the slotting depth. A water jet slotting depth calculation model was established and verified according to the slotting experiments under different operational conditions. The slotting depths were investigated based on the results of field slotting experiments. The results revealed that there exists an optimal nozzle diameter for a higher jet impact velocity. The slotting depth linearly increased with the jet pressure and decreased as a power function with the increase of the jet translation speed. The slotting depth increased with the slotting time, but the growth rate gradually decreased and tended to be stable. As the rotation speed increased, the slotting depth became greater at the initial period and the limit depth was reached faster. Laboratory and field slotting experiments were conducted to verify the model, and the experimental results are approximately in agreement with the theoretical predictions. The results of this study can be useful as guidelines for the hydraulic parameter selection of water jet slotting and for optimizing the layout of coal gas drainage boreholes. Keywords: gas drainage; water jet slotting; slotting depth; coal and gas outburst 1. Introduction Coalbed methane (CBM) is a clean and efficient energy source. The efficient development of CBM could not only increase the clean energy supply but also improve the safety of coal mine production and reduce greenhouse gas emissions. In China, the CBM reserves above 2000 m are estimated at trillion m 3, which is equivalent to the amount of reserved conventional natural gas, ranking in third place globally after Russia and Canada [1]. However, CBM reserves are characterized by their low saturation, low permeability, low reservoir pressure, and relatively high metamorphic grade. In most mining areas, the coal seam permeability is md, which is 3 4 orders of magnitude lower than that in the United States and Australia [2 4]. Moreover, 44% of coal mines in China are high gas and outburst mines and prone to coal and gas outburst accidents during coal extraction [5]. Therefore, Appl. Sci. 2019, 9, 5250; doi: /app

2 Appl. Sci. 2019, 9, x FOR PEER REVIEW 2 of 15 China are high gas and outburst mines and prone to coal and gas outburst accidents during coal extraction Appl. [5]. Sci. Therefore, 2019, 9, 5250 to effectively extract coalbed methane and ensure mining safety, 2 of 15effective measures must be taken to improve the coal seam permeability and control the risk of gas disasters. In coal seams, high-pressure water jet slotting is an effective method of improving the coal seam to effectively extract coalbed methane and ensure mining safety, effective measures must be taken to permeability improve [6 9]. the coal As seam shown permeability in Figure and1, control this technology the risk of gascan disasters. form a disc slot in the coal seam by using a high-pressure In coal seams, water high-pressure jet, which water effectively jet slotting is increases an effective the method area of improving exposed the coal. Additionally, seam the pressure permeability in the [6 9]. coal seam As shown surrounding Figure 1, this the technology slot is fully can form relieved, a disc slot which in theresults coal seam in by the using deformation a of coal and high-pressure the formation water jet, of which cracks. effectively This increases the area the of gas exposed flow coal. channels Additionally, and improves the pressurethe flow in the coal seam surrounding the slot is fully relieved, which results in the deformation of coal and conditions, which in turn accelerate the gas desorption and discharge, to result in permeability formation of cracks. This increases the gas flow channels and improves the flow conditions, which in improvement turn accelerate [10,11]. the Therefore, gas desorption it can and be discharge, seen that tothe result slotting permeability depth directly improvement affects [10,11]. the pressure relief range Therefore, and determines it can be seenthe thatgas the slotting drainage depth effect. directly Many affects studies the pressure have relief investigated range and determines water jet slotting. However, themost gas drainage existing effect. studies Many have studies focused have investigated on improving water the jetpermeability slotting. However, mechanism most existing [12 14] and rock-breaking studies capability have focusedof onthe improving water the jet permeability [15], optimizing mechanism and [12 14] improving and rock-breaking the slotting capability system [16,17], of the water jet [15], optimizing and improving the slotting system [16,17], and so on. A few studies and so on. A few studies have investigated the effects of hydraulic parameters and operational have investigated the effects of hydraulic parameters and operational parameters on the slotting depth, parameters but there on the is no slotting applicable depth, theoretical but there modelis for no determining applicable thetheoretical slotting depth model in water for jet determining slotting the slotting depth applications. in water Thisjet leads slotting to theapplications. operational parameters This leads andto borehole the operational layout being parameters unknown when and borehole layout being applying unknown high-pressure when water applying jet slotting high-pressure technology. water jet slotting technology. Figure 1. Figure Technical 1. Technical sketch sketch of coal of coal seam permeability improvement by water by water jet slotting. jet slotting. (a) is the(a) is the process of process high-pressure of high-pressure water water jet jet slotting in in coal coal seams; seams; (b) is(b) the crack is the condition crack condition surrounding surrounding the slots. the slots. This study investigated the effects of hydraulic parameters (nozzle diameter and jet pressure) and operational parameters (rotation speed and slotting time) on the slotting depth. Based on the This rock-cutting study investigated model of athe water effects jet, a model of hydraulic for calculating parameters the water (nozzle jet slotting diameter depthand was established. jet pressure) and operational Water parameters jet slotting experiments (rotation speed were conducted and slotting undertime) different on operational the slotting conditions depth. Based to verifyon the the rockcutting model calculation of model. a water Additionally, jet, a model water for jetcalculating slotting field tests the were water conducted, jet slotting and the depth slotting was depths established. were investigated. The results of this study can be useful as guidelines for selecting the hydraulic Water jet slotting experiments were conducted under different operational conditions to verify the parameters of water jet slotting and optimizing the layout of coal gas drainage boreholes in coal seams. calculation model. Additionally, water jet slotting field tests were conducted, and the slotting depths were investigated. 2. Theory of Rock-Breaking The results of for this a High-Pressure study can be Water useful Jet as guidelines for selecting the hydraulic parameters 2.1. Rock-Breaking of water jet Mechanism slotting of and High-Pressure optimizing Water the Jet layout of coal gas drainage boreholes in coal seams. Many studies have reported that the failure of rock subjected to water jets mainly results from the water-hammer pressure and stagnation pressure [18 20]. At the initial stage, the water-hammer 2. Theory pressure of Rock-Breaking is responsible for for thea majority High-Pressure of rock damage. Water Then, Jet the stagnation pressure further breaks the rock and leads to crack initiation and propagation in the damaged rock. Therefore, it is very 2.1. Rock-Breaking necessary tomechanism analyze the impact of High-Pressure pressure generated Water by Jet high-pressure water jets. Many studies have reported that the failure of rock subjected to water jets mainly results from the water-hammer pressure and stagnation pressure [18 20]. At the initial stage, the water-hammer pressure is responsible for the majority of rock damage. Then, the stagnation pressure further breaks the rock and leads to crack initiation and propagation in the damaged rock. Therefore, it is very necessary to analyze the impact pressure generated by high-pressure water jets.

3 Appl. Sci. 2019, 9, of 15 Once a high-pressure water jet impacts the rock, water-hammer pressure forms owing to the liquid jet compression. According to existing studies [21 23], the water-hammer pressure at the central area of a solid, and the duration time, are expressed as follows: P wh = vρ wc w ρ s c s ρ w c w + ρ s c s (1) t wh = Rv 2c 2, (2) w where v and R are the impact velocity and diameter of the water jet, respectively; ρ w and ρ s denote the densities of the water and rock, respectively; c w and c s are the shock velocities of the impact stress wave in the water and sandstone, respectively. The duration of the water hammer pressure is very short, being only a few microseconds. However, the pressure is enormous and causes the main damage to the rock, which results in the formation of a cavity. When steady impact is established, the pressure on the central axis decreases to the much lower Bernoulli stagnation pressure, as follows: Ps = ρ wv 2 2. (3) On one hand, some micro cracks are generated under the impact of enormous water-hammer pressure. On the other hand, natural rock, particularly coal, contains defects and has its own cracks. Therefore, the effect of stagnation pressure on rock failure cannot be ignored Rock-Cutting Model for a High-Pressure Water Jet Cutting rock with a high-pressure water jet is a complicated process, and involves many factors, such as the nozzle diameter, jet pressure, translation speed, standoff distance, cutting times, rock properties, and so on. In recent decades, several classic rock-cutting models have been established and mainly include the Crow cutting model, Rehbinder cutting model, and Hashish cutting model. However, various parameters, such as the rock particle diameter, jet action time, jet dynamic viscosity, rock permeability, and so on, are required in the Rehbinder cutting model [24,25]. Moreover, in the Hashish cutting model, the compressive yield limit, hydrodynamic friction coefficient, and damping coefficient of cutting materials must be calculated or measured in advance [26]. Therefore, the Rehbinder and Hashish models can only be applied to laboratory experiments or theoretical analysis, but cannot be effectively used to analyze the water jet slotting in field applications. In contrast, the Crow model is much simpler to a certain extent, and the required parameters can be obtained more easily. Therefore, it is more suitable for high-pressure water jet slotting field applications. Based on numerous rock-cutting experiments, Crow proposed the general law of hydraulic rock cutting. The cutting depth can be calculated as follows: h = J (p p c) τ 0 d 0 F(v/c e ), (4) where h is the cutting depth; J is the translation time; P and P c are the jet pressure and critical rock-breaking pressure of the water jet, respectively; τ 0 is the shear strength of the rock; d 0 is the nozzle diameter; v is the translation speed; and c e is the theoretical translation speed. As can be seen, the key water jet cutting parameters are considered in the Crow model. However, for water jet slotting in a coal seam, the existing Crow model is not fully applicable, owing to the difference of rock properties and working conditions, and requires further modification.

4 Appl. Appl. Sci. 2019, Sci. 2019, 9, x FOR 9, 5250 PEER REVIEW 4 of 15 4 of 15 operating conditions of water jet slotting, the key parameters mainly include the nozzle diameter, jet pressure, 3. Influence rotation Factor speed, Analysis and slotting for Water time. Jet Slotting Depth To establish a model for calculating the water jet slotting depth, the influence of the key parameters 3.1. Nozzle on the slotting Diameter depth should be investigated. According to the Crow model and the actual operating conditions of water jet slotting, the key parameters mainly include the nozzle diameter, jet pressure, The nozzle diameter determines the flow rate of the water jet and affects the impact energy to a rotation speed, and slotting time. certain extent, as expressed by Equations (5) and (6) [27]. As the nozzle diameter increases, the jet flow 3.1. rate Nozzle and impact Diameterenergy become larger. However, when the nozzle diameter is too large, the jet energy consumption becomes severe, which results in a waste of energy. To improve the impact The nozzle diameter determines the flow rate of the water jet and affects the impact energy to a capacity certain of extent, the water as expressed jet and ensure by Equations the smooth (5) and discharge (6) [27]. Asof the slag nozzle during diameter the water increases, jet slotting the jet flow process, the nozzle rate anddiameter impact energy should become appropriately larger. However, increased. when the nozzle diameter is too large, the jet energy consumption becomes severe, which results in a waste of energy. To improve the impact capacity of 1 2 the water jet and ensure the smooth discharge Q = of πϕslag vd during the water jet slotting process, the nozzle (5) diameter should be appropriately increased. 4 ρπμdv Q = 1 w 4 πϕvd2 (5) ω = (6) 8 ω = ρ wπµd 2, v 3, (6) where Q and ω are the jet flow rate and impact 8kinetic energy, respectively; μ is the flow rate coefficient; where Qv and is the ω are water the jet flow velocity; rate and d is impact the nozzle kineticdiameter; energy, respectively; and ρw is µ the is the water flowdensity. rate coefficient; vhuang is the water conducted jet velocity; a computational, d is the nozzle diameter; numeric, andfluid ρ w is dynamics the water density. simulation to investigate the influence Huang of nozzle conducted diameter a computational, on jet flow numeric, characteristics, fluid dynamics such simulation as the axial to investigate velocity, theand influence the axial dynamic of nozzle pressure diameter and onits jetattenuation flow characteristics, coefficient such[28]. as theas axial shown velocity, in Figure and the 2, axial the dynamic axial velocities pressure and and its attenuation coefficient [28]. As shown in Figure 2, the axial velocities and dynamic pressures dynamic pressures of the water jet were obtained with different nozzle diameters. As the nozzle of the water jet were obtained with different nozzle diameters. As the nozzle diameter increased, diameter increased, the attenuation coefficient of the jet axial dynamic pressure first decreased and the attenuation coefficient of the jet axial dynamic pressure first decreased and then increased. When the then increased. When the nozzle diameter was 3 mm, the attenuation coefficient was the minimum nozzle diameter was 3 mm, the attenuation coefficient was the minimum because the increase of the because nozzle the diameter increase affected of the nozzle the attenuation diameter coefficient affected of the the attenuation axial dynamic coefficient pressure, of although the axial the dynamic jet pressure, energyalthough increased. the Moreover, jet energy theincreased. influence ofmoreover, the nozzle diameter the influence on theof slotting the nozzle depthdiameter was not too on the slotting large. depth The jet was pressure not too andlarge. flow rate The of jet common pressure high-pressure and flow rate pumps of common satisfy thehigh-pressure requirement forpumps a satisfy 3 mm the nozzle. requirement Therefore, to a 3 investigate mm nozzle. the Therefore, effect of other to parameters investigate onthe theeffect slotting of depth, other parameters the nozzle on the slotting diameterdepth, was sethe as anozzle constant diameter of 3 mm. was set as a constant of 3 mm. 2 3 Figure Figure 2. (a) 2. Axial (a) Axial velocity velocity and and (b) (b) axial dynamic pressure of of a a water water jet jet with with different different nozzle nozzle diameters diameters [28]. [28] Jet Pressure 3.2. Jet Pressure The relationship between the jet pressure and the jet velocity is expressed by Equation (7). As can be The seen, relationship the jet pressure between determines the jet the pressure jet velocity and and the jet impact velocity energy, is expressed and thus affects by Equation the slotting (7). As can be seen, the jet pressure determines the jet velocity and impact energy, and thus affects the slotting depth. To obtain the effect of jet pressure on the slotting depth, water jet cutting experiments were conducted with different jet pressures.

5 Appl. Sci. 2019, 9, x FOR PEER REVIEW 5 of 15 Appl. Sci. 2019, 9, of 15 2P v = ϕ, (7) depth. To obtain the effect of jet pressure on the ρ slotting w depth, water jet cutting experiments were conducted with different jet pressures. where P is the jet velocity and φ is the nozzle velocity 2P coefficient. The cutting experiment was conducted on v = an ϕ independently, (7) ρ w designed and developed water jet test system in the Laboratory of High-pressure Water Jets at Chongqing University, China. The where P is the jet velocity and ϕ is the nozzle velocity coefficient. system mainly consisted of a high-pressure pump, pressure and flow control system, and water jet The cutting experiment was conducted on an independently designed and developed water jet test platform, as shown in Figure 3. The high-pressure pump, manufactured by Nanjing Luhe Coal test system in the Laboratory of High-pressure Water Jets at Chongqing University, China. The system Mine Machinery Co., Ltd., had a rated pressure of 56 MPa and rated flow rate of 200 L/min. The mainly consisted of a high-pressure pump, pressure and flow control system, and water jet test pressure-flow platform, ascontrol shown system in Figureconsisted 3. The high-pressure of a pressure pump, sensor manufactured of 0 70 MPa by Nanjing with a Luhe precision Coal Mine of ±0.1% and an Machinery ultrasonic Co., flowmeter Ltd., had a rated of pressure m/s of ± 56 1%. MPa Additionally, and rated flowit rate was of convenient 200 L/min. The to adjust pressure-flow the system pressure control and system monitor consisted and record of a pressure the pressure sensor of and 0 70flow MPaat with different a precision times. of The ±0.1% water and an jet ultrasonic test platform was flowmeter comprised of of a translation m/s ± 1%. console Additionally, and rock it wasbearing convenient system. to adjust The the translation system pressure console and had a translational monitor and speed record of the pressure m/s, and flow the at rock different bearing times. system, The water with jet an test ultimate platformbearing was comprised weight of 5 t, could of a translation move up, console down, and forward, rock bearing and system. backward. The translation Moreover, console the nozzle had a translational diameter and speed standoff distance were m/s, 3 and and the165 rockmm, bearing respectively. system, with The an ultimate translation bearing speed weight was of set 5 t, to could a constant move up, of down, 0.12 m/s. forward, and backward. Moreover, the nozzle diameter and standoff distance were 3 and 165 mm, Although it was very difficult to obtain coal blocks with large sizes, the coal block easily split when respectively. The translation speed was set to a constant of 0.12 m/s. Although it was very difficult to impacted by the water jet, owing to the typical anisotropy and abundant joints and fissures in the obtain coal blocks with large sizes, the coal block easily split when impacted by the water jet, owing to coal. This made it difficult to quantitatively evaluate the jet cutting efficiency. Besides, shaped coal of the typical anisotropy and abundant joints and fissures in the coal. This made it difficult to quantitatively certain evaluate proportions the jet cutting has similar efficiency. physical Besides, and mechanical shaped coalproperties, of certain proportions such as the has compressive similar physical strength, tensile andstrength, mechanical and properties, Poisson s such ratio, asof the raw compressive coal. It can strength, well reflect tensile the strength, internal and relationship Poisson s ratio, between water ofjet rawparameters coal. It can and well rock-breaking reflect the internal efficiency relationship of coal between in the water experiment jet parameters [29,30]. andtherefore, rock-breaking shaped coals efficiency of size 200 of coal 200 in the 200 experiment mm were used [29,30]. as Therefore, the cutting shaped targets coals because of sizethey 200 were 200 adequately 200 mm were similar to coal; used the asf the coefficient cutting targets was because they were adequately similar to coal; the f coefficient was Figure3. 3. System used in cutting experiment. The The cutting cutting experiment experiment results resultsare are presented in Figure And And the the relationship relationship between between the jet the jet pressure and the cutting depth can be obtained as shown in Figure 5. When the jet pressure was low, pressure and the cutting depth can be obtained as shown in Figure 5. When the jet pressure was low, the cutting depth was shallow and approximately equal to zero because the jet pressure was lower the cutting depth was shallow and approximately equal to zero because the jet pressure was lower than the critical rock-breaking pressure of the water jet. As the jet pressure increased, the cutting than the critical rock-breaking pressure of the water jet. As the jet pressure increased, the cutting depth gradually increased, and the sample was completely cut through at a jet pressure of 22 MPa. depth gradually increased, and the sample was completely cut through at a jet pressure of 22 MPa. As can be seen from the fitting curve, the cutting depth linearly increased with the jet pressure. Therefore, the relationship between the jet pressure and the cutting depth can be expressed as follows: h ( ) P = k1 P Pc, (8)

6 Appl. Sci. 2019, 9, of 15 As can be seen from the fitting curve, the cutting depth linearly increased with the jet pressure. Therefore, the relationship between the jet pressure and the cutting depth can be expressed as follows: Appl. Sci. 2019, 9, x FOR PEER REVIEW 6 of 15 Appl. Sci. 2019, 9, x FOR PEER REVIEW h P = k 1 (P P c ), (8) 6 of 15 where hp is the cutting depth under different jet pressures; k1 is the proportionality coefficient; and P where and where Pc hp are is the h P isjet cutting the pressure cutting depth depth and under critical different rock-breaking jet pressures; pressure, kk1 1 is is respectively. the proportionality The critical coefficient; rock-breaking and and P P and pressure Pc and are Pcould c the arejet the show pressure jet the effect and and critical of the rock-breaking coal strength on pressure, slotting respectively. depth to a The certain The critical critical extent. rock-breaking pressure pressure could could show show the the effect effect of ofthe thecoal strength on slotting depth depth to to a certain a certain extent. extent. Figure 4. Comparison of cutting depth subjected to high-pressure water jet with different jet Figure pressures. Figure Comparison of cutting depth depth subjected subjected to high-pressure to high-pressure water jet with water different jet with jet pressures. different jet pressures. Figure5. 5. The effect of jet pressure on on cutting depth. Figure 5. The effect of jet pressure on cutting depth Rotation Speed and Slotting Time 3.3. Rotation Speed and Slotting Time 3.3. Rotation TheSpeed waterand jet slotting Slotting in Time a coal seam is different from conventional moving water jet cutting. First, The water the nozzles jet slotting are fixed in to a coal the drill seam bit is with different their axes from perpendicular conventional to the moving drill bit water axis. jet Then, cutting. in the First, the nozzles process The water of are water jet fixed slotting jet slotting, to the in a drill the coal nozzles bit seam with is rotate different their along axes with from perpendicular the conventional drill pipe, to and moving the water drill jets water bit generated axis. jet cutting. Then, by the in First, the the process nozzles of impact water are fixed jet coal slotting, with to the a rotating drill the nozzles bit trajectory. with rotate their Finally, along axes a disc-shaped perpendicular with the drill slotpipe, is to formed. the and drill Therefore, water bit axis. jets the generated Then, effects in the by process the nozzle of the of rotation water impact jet speed coal slotting, with and slotting a the rotating nozzles timetrajectory. onrotate the slotting along Finally, depth with a are the disc-shaped essentially drill pipe, the slot and effects is water formed. of the jets translation Therefore, generated the by the effects nozzle of the impact rotation coal speed with a and rotating slotting trajectory. time on Finally, the slotting a disc-shaped depth are slot essentially is formed. the Therefore, effects of the effects translation of the speed rotation and speed cutting and times slotting on the time cutting on the depth, slotting respectively. depth are The essentially relationship the effects between of the translation rotation speed speed and and the cutting translation times speed on the is cutting expressed depth, as follows: respectively. The relationship between the rotation speed and the translation speed is expressed as follows: 30v n = T (9)

7 Appl. Sci. 2019, 9, of 15 Appl. Sci. 2019, 9, x FOR PEER REVIEW 7 of 15 where n and speed t are andthe cutting rotation times on speed the cutting of the depth, drill respectively. pipe and The slotting relationship time, between respectively; the rotation speed vt and J are the and the translation speed is expressed as follows: translation speed and cutting times of the water jet, respectively; and r is the initial standoff distance of the water jet; that is r = ( D 2 n = 30v T 0 d0 )/, where D0 and d0 are the borehole diameter (9) and outer πr diameter of the slotting device, respectively. In the cutting experiments at different translation t = J n, speeds, the nozzle diameter, jet (10) pressure, and standoff distance were 3 mm, 15 MPa, and 165 mm, respectively. The experimental results are presented in Figure 6. The cutting depth decreased as a power function with the increase of the jet translation speed. Additionally, the decrease became progressively smaller. When the translation speed was 60 mm/s, the sample was completely cut through and the cutting depth was more than 200 mm, as shown in Figure 7. This is attributed to the fact that the initial damage of the rock sample occurred in a very short period of a few milliseconds, when the water jet impacted the rock. Subsequently, the impact depth gradually increased. However, when the impact time was excessively long, the high-pressure water accumulated in the slot and formed a water cushion, which weakened the jet impacting capacity. Hence, the cutting depth growth rate decreased as the impact time increased. Equation (11) describes the relationship between the cutting depth and the jet translation speed, as follows: where n and t are the rotation speed of the drill pipe and slotting time, respectively; v T and J are the translation speed and cutting times of the water jet, respectively; and r is the initial standoff distance of the water jet; that is r = (D 0 d 0 )/2, where D 0 and d 0 are the borehole diameter and outer diameter of the slotting device, respectively. In the cutting experiments at different translation speeds, the nozzle diameter, jet pressure, and standoff distance were 3 mm, 15 MPa, and 165 mm, respectively. The experimental results are presented in Figure 6. The cutting depth decreased as a power function with the increase of the jet translation speed. Additionally, the decrease became progressively smaller. When the translation speed was 60 mm/s, the sample was completely cut through and the cutting depth was more than 200 mm, as shown in Figure 7. This is attributed to the fact that the initial damage of the rock sample occurred in a very short period of a few milliseconds, when the water jet impacted the rock. Subsequently, the impact depth gradually increased. However, when the impact time was excessively long, the high-pressure water accumulated in the slot and formed a water cushion, which weakened the jet impacting capacity. Hence, the cutting depth growth rate decreased as the impact time increased. Equation (11) describes the relationship between the cutting depth and the jet translation speed, as follows: h v T 1 = k v α, (11) 2 T α h vt = k 2 v 1 T, (11) where hvt is the cutting depth at different translation speeds; k2 is the proportionality coefficient; α1 is the index. where h vt is the cutting depth at different translation speeds; k 2 is the proportionality coefficient; α 1 is the index. Figure Figure 6. The 6. effect The effect of of translation speed on cutting on cutting depth. depth.

8 Appl. Sci. 2019, 9, of 15 Figure 6. The effect of translation speed on cutting depth. Appl. Sci. 2019, 9, x FOR PEER REVIEW 8 of 15 The deep slot resulted from multiple high-pressure water jet cuts. Therefore, it was necessary to investigate Figure the effect 7. Figure Cutting of 7. Cutting cutting depths depths times from from a on a high-pressure the total cutting water jet jet with depth. with different With translation regard translation speeds. to the speeds. cutting times, previous studies have found that the first few cuttings play a major role in jet cutting, and the number The deep slot resulted from multiple high-pressure water jet cuts. Therefore, it was necessary of cuttings to investigate has a significant the effect of impact cuttingon times the ontotal the total depth cutting [31]. depth. When With the regard number to the of cutting cuts increases, times, the cutting depth previous slowly studies increases, have foundbut thatthe first increment few cuttings is small. play a major When role the in jet cutting, number and the number reaches ofa certain value, the cuttings hasdepth a significant is no impact longer affected. the total depth The [31]. relationship When the number between of cuts the increases, total cutting the cutting depth and depth slowly increases, but the increment is small. When the cutting number reaches a certain value, the cutting times is given in Figure 8. Thus, the relationship between the total cutting depth and the the cutting depth is no longer affected. The relationship between the total cutting depth and the cutting first cutting depth can be expressed as follows: times is given in Figure 8. Thus, the relationship between the total cutting depth and the first cutting depth can be expressed as follows: 2 hj n h h 1 J n = nj α =, h 1 n J α 2 (12), (12) where hj n where is the h J n total is thecutting total cutting depth depth at different at cutting times; h J 1 hj 1 is is the the cutting cutting depth depth when the when water the water jet cuts the jet cuts sample the sample once; once; α2 is αthe 2 is index. the index. Figure Figure 8. The 8. The effect effect of of cutting times on on cutting depth depth [31]. [31]. 4. Model for Calculating Water Jet Slotting Depth By comprehensively considering the influence of the jet pressure, translation speed, and cutting times on the total cutting depth, the cutting depth can be expressed as follows: α1 α2 h = kv J ( P P ), (13) T c

9 Appl. Sci. 2019, 9, of Model for Calculating Water Jet Slotting Depth By comprehensively considering the influence of the jet pressure, translation speed, and cutting times on the total cutting depth, the cutting depth can be expressed as follows: h = kv T α 1 J α 2 (P P c ), (13) where h is the total cutting depth and k is the proportionality coefficient. By combining Equations (9) and (10), the model for calculating the slotting depth caused by a high-pressure water jet in a coal seam is expressed as follows: h = k( nπr 30 )α 1 (nt) α 2 (p p c ). (14) As expressed in Equation (14), the rotation speed has a significant effect on the slotting depth under fixed slotting time. As the rotation speed increases, the slotting depth becomes smaller each time but increases with the slotting repetition. Therefore, there exists an optimal rotation speed for the water jet slotting. This study conducted rotary slotting experiments to determine the relevant parameters in Equation (14) and obtain the optimal rotation speed. As shown in Figure 9, the experimental system mainly was comprised of a high-pressure pump, hydraulic drilling rig, and the sample. The drilling rig, with a rated torque of 1250 N m, was used to control the rotation speed in the water jet slotting. The slotting sample was shaped coal with a ratio of coal particle:cement:water = 1:0.5:1, size of m, f coefficient of 0.21, and tensile strength of approximately 0.08 MPa. Appl. Sci. 2019, 9, x FOR PEER REVIEW 9 of 15 Figure 9. System used in experiment of rotary slotting by water jet. The experimental procedures are are as follows: as follows: first, first, the nozzle the nozzle diameter diameter and initial and standoff initial standoff distance distance were set were to 3 and set to and mm, 12.5 andmm, the jet and pressure the jet pressure was controlled was controlled at 10 MPa. at 10 Then, MPa. the Then, rotation the rotation speeds speeds were set were to 30, set 40, to 50, 30, and 40, 50, 60 and r/min, 60 respectively. r/min, respectively. Additionally, Additionally, the shaped the shaped coal sample coal sample rotary slotted rotary slotted by a high-pressure by a high-pressure water jet water and the jet and slotting the slotting time was time 0.5 was min 0.5 every min time. every Subsequently, time. Subsequently, the slotting the slotting depth was depth measured was measured and a slot and samplea slot sample was taken was again taken under again under the same the same slotting slotting conditions conditions until until the slotting the slotting depth did depth not change. did not Finally, change. thefinally, rotation the speed rotation was changed speed and was the changed abovementioned and the abovementioned process was repeated. process was repeated. The results are presented in Figure 10. At the same rotation speed, the slotting depth increased with the slotting time, but the growth rate gradually decreased, then tended to be stable, and finally reached a certain limit value. As the rotation speed increased, the slotting depth became greater at the initial period and the limit depth was reached faster. Hence, the slotting depth was the combined result of rotation speed and slotting frequency. Although the relative moving speedwas was higher at at a higher rotation speed, the slotting frequency per time increased, which resulted in deeper slotting depth at the initial period. Moreover, in the process of rotary slotting by the high-pressure water jet, the action mode of the water jet on the coal body changed. Similar to the oscillation effect of the pulsed water jet, the coal body is influenced by the water hammer pressure with periodic frequency, and thus the rock-breaking efficiency improves. In contrast, at lower rotation speed, the impact time

10 Appl. Sci. 2019, 9, of 15 a higher rotation speed, the slotting frequency per time increased, which resulted in deeper slotting depth at the initial period. Moreover, in the process of rotary slotting by the high-pressure water jet, the action mode of the water jet on the coal body changed. Similar to the oscillation effect of the pulsed water jet, the coal body is influenced by the water hammer pressure with periodic frequency, and thus the rock-breaking efficiency improves. In contrast, at lower rotation speed, the impact time of the single slotting coal becomes longer, and the hindrance of the water cushion becomes more severe. Therefore, in the early stages of slotting, the influence of slotting repetitions on the slotting depth is greater than that of a single impact. Increasing the rotation speed contributes to the improvement of the slotting efficiency and slotting depth. However, as the rotation speed increases, the limit slotting depth first increases and then decreases. This indicates that the influence of a single impact on the slotting depth is greater than that of numerous slotting repetitions at the later stages of jet slotting. This is attributed to the fact that the coal body is mainly destroyed by the quasi-static pressure of the Appl. Sci. 2019, water 9, x FOR jet. PEER REVIEW 10 of 15 Figure 10. Slotting depth at different rotation speeds. Figure 10. Slotting depth at different rotation speeds. To verify the proposed slotting depth model, the experimental data were fitted based on To verify Equation the (14). proposed The special slotting fitting parameters depth were model, giventhe in Equation experimental (15). The fitting data degree were reached fitted based on Equation (14). 86%, The which special indicatesfitting that theparameters model established were for calculating given in the Equation slotting depth (15). canthe be used fitting to describe degree reached the relationship between the parameters and the slotting depth. Based on the fitting parameters, 86%, which indicates that the model established for calculating the slotting depth can be used to the effects of the jet pressure, rotation speed, and slotting time on the slotting depth can be obtained. describe the relationship between the parameters and the slotting depth. Based on the fitting parameters, the effects of the jet pressure, h = (P rotation P c )n speed, t and ln(n) slotting. time on the slotting (15) depth can be obtained. Figure 11 shows the fitting curves between the slotting depths and slotting time under the different rotation speeds at the jet pressure of 10 MPa. Thus, ln( n ) h = ( P Pc ) n t to improve + the jet slotting depth, the rotation speed should be adopted according to the slotting time. Specifically,. when the slotting times are (15) 0 5, 5 10, and min, the optimized rotation speeds should be 60, 50, and 40 r/min, respectively. Moreover, as shown in Equation (15), the jet pressure and the threshold rock-breaking pressure of the coal are proportional to the slotting depth. In other words, the jet pressure and threshold pressure only affect the slotting depth magnitude, and have no effect on its changing trend. Therefore, when the jet Figure 11 shows the fitting curves between the slotting depths and slotting time under the different rotation speeds at the jet pressure of 10 MPa. Thus, to improve the jet slotting depth, the rotation speed should be adopted according to the slotting time. Specifically, when the slotting times are 0 5, 5 10, and min, the optimized rotation speeds should be 60, 50, and 40 r/min, respectively. Moreover, as shown in Equation (15), the jet pressure and the threshold rock-breaking pressure of the coal are proportional to the slotting depth. In other words, the jet pressure and threshold pressure only affect the slotting depth magnitude, and have no effect on its changing trend.

11 rotation speed should be adopted according to the slotting time. Specifically, when the slotting times are 0 5, 5 10, and min, the optimized rotation speeds should be 60, 50, and 40 r/min, respectively. Moreover, as shown in Equation (15), the jet pressure and the threshold rock-breaking pressure of Appl. the Sci. coal 2019, 9, are 5250 proportional to the slotting depth. In other words, the jet 11 ofpressure 15 and threshold pressure only affect the slotting depth magnitude, and have no effect on its changing trend. Therefore, when pressurethe changes, jet the pressure relationships changes, between the slotting relationships depth and the between rotation speed the and slotting slotting depth time and the rotation speed do not and change. slotting time do not change. Figure 11. Fitting Figure 11. curves Fitting between curves between slotting depth and slotting time time at different at different rotation speeds rotation underspeeds jet under pressure of 10 MPa. jet pressure of 10 MPa. Appl. Sci. 2019, 9, x FOR PEER REVIEW 11 of 15 According to the abovementioned analysis, the slotting depths under different jet pressures According and threshold to the abovementioned rock-breaking pressures analysis, can be the obtained. slotting Thedepths tensile strength under of different coal is typically tensile strength of 0.5 MPa. The other parameters were as follows: nozzle diameter of jet 3 mm pressures and initial and MPa [32]. Figure 12 shows the predicted slotting depths under the jet pressure of 25 MPa with standoff threshold distance rock-breaking pressures can be obtained. The tensile strength of coal is typically a tensileof strength 12.5 mm. of 0.5 MPa. Therefore, otherthe parameters optimized were asslotting follows: nozzle parameters diameter of were 3 mmobtained and initial as follows: when MPa [32]. the slotting Figure standoff12 distance time shows was of 12.5 the 0 5 mm. predicted min, Therefore, the optimized slotting the depths rotation slotting under parameters speed the was were jet 60 pressure obtained r/min; asof when follows: 25 MPa the slotting with a when the slotting time was 0 5 min, the optimized rotation speed was 60 r/min; when the slotting time was 5 10 min, the optimized rotation speed was 50 r/min; when the slotting time was min, time was 5 10 min, the optimized rotation speed was 50 r/min; when the slotting time was min, the optimized the optimized rotation rotation speed speed was was 40 r/min; 40 r/min; when when the the slotting slotting time time was was min, the min, optimized the optimized rotation speed rotation was speed 30 r/min was 30and r/minthe and slotting the depth reached m. m. Figure 12. Prediction Figure 12. Prediction curves curves of of slotting depth versus slotting time time at different at different rotation speeds rotation underspeeds jet under pressure of 25 MPa. jet pressure of 25 MPa. 5. Field Test 5.1. Test Background It is known that the slotting depth is more than 1 m when the jet pressure reaches 25 MPa.

12 Figure 12. Prediction curves of slotting depth versus slotting time at different rotation speeds under jet pressure of 25 MPa. 5. Field Test 5.1. Test Background Appl. Sci. 2019, 9, of Field Test It is known that the slotting depth is more than 1 m when the jet pressure reaches 25 MPa Test Background Therefore, the model for calculating the slotting depth cannot be verified by laboratory experiments when the jet pressure It is known is that high. thefield slotting tests depth were is more carried than 1out m when to further jet pressure investigate reacheswhether 25 MPa. the model Therefore, the model for calculating the slotting depth cannot be verified by laboratory experiments could be used in field applications. The high-pressure water jet slotting system was similar to the when the jet pressure is high. Field tests were carried out to further investigate whether the model laboratory slotting could be used experiments. in field applications. The field Thetest high-pressure site was water the Shoushan jet slotting system Number was similar 1 coal tomine the affiliated with Pingdingshan laboratory slotting Coal Group experiments. Co. Ltd., The field as test shown site was in the Figure Shoushan 13. The Number field 1 coal test mine for affiliated the slotting depth with Pingdingshan Coal Group Co. Ltd., as shown in Figure 13. The field test for the slotting depth investigation was conducted at the Number wind lane. The slotting target coal seam was investigation was conducted at the Number wind lane. The slotting target coal seam was the the Number Number 15 coal 15 coal seam, seam, and the hardness hardness coefficient coefficient f was , f was which , belongswhich to a soft belongs and crushedto a soft and crushed coal coal seam. The tensile strength was was MPa. MPa. Figure 13. Site of water jet slotting field test: Shoushan Number 1 coal mine affiliated with Pingdingshan Coal Group Co. Ltd Verification of Slotting Depth Model In the slotting experiments, the jet pressure, borehole diameter, outer slot diameter, and nozzle diameter were set as 25 MPa, 75 mm, 50 mm, and 3 mm, respectively. The slotting borehole depth was 15 m. As shown in Figure 14, the number 1, number 3, and number 5 inspection holes were arranged at the right of slotting borehole with a distance of 0.5 m, 1.5 m, and 2.5 m from the slotting borehole, respectively. On the left side, the number 2, number 4, and number 6 inspection holes were arranged at distances of 1, 2, and 3m, respectively. The depths and diameters of all inspection holes were 15 m and 42 mm, respectively. The inclination dip of all boreholes was 15. The slotting position of the high-pressure water jet was located 14 m away from the slotting borehole. Four groups of slotting tests were conducted. The rotation speed and slotting time in the high-pressure water jet slotting were n = 60 r/min and t = 5 min, n = 50 r/min and t = 10 min, n = 40 r/min and t = 15 min, and n = 30 r/min and t = 20 min, respectively.

13 arranged at distances of 1, 2, and 3m, respectively. The depths and diameters of all inspection holes were 15 m and 42 mm, respectively. The inclination dip of all boreholes was 15. The slotting position of the high-pressure water jet was located 14 m away from the slotting borehole. Four groups of slotting tests were conducted. The rotation speed and slotting time in the high-pressure water jet slotting Appl. Sci. 2019, were 9, n 5250 = 60 r/min and t = 5 min, n = 50 r/min and t = 10 min, n = 40 r/min and t = 15 min, 13and of 15 n = 30 r/min and t = 20 min, respectively. Figure 14. Layout of slotting borehole and inspection holes. The slotting depth was estimated by observing whether water flowed out from the inspection hole. The results are presented in Table 1. Under the test conditions of n = 60 r/min and t = 5 min, water flowed out fromthe the number 1 and 1 and 2 2 inspection holes holes but but not not out of out the ofnumber the number 3 6 holes. 3 6 holes. This indicates This indicates that the thatslotting the slotting depth depth was more was more than than 1.0 m 1.0 but mless but than less than 1.5 m, 1.5which m, which is consistent consistent with with the depth the depth predicted predicted based based on Equation Equation (14). The (14). results The results of the of other three othertest three groups test groups were similar, were similar, which indicates which indicates that the that proposed the proposed model for model calculating for calculating the slotting the slotting depth is depth reliable is reliable and can and be used can be in used field applications. in field applications. Table 1. Results of water jet slotting in coal seam under different test conditions (rotation speed and slotting time). Whether ThereIs is Water Flowing Slotting Prediction Number Test Test Condition Flowing Out from Slotting Depth (m) Prediction Depth (m) Out Inspection from Inspection Hole or Not Hole or Not Depth (m) Depth (m) 60 r/min, t 1 1 n = 60 r/min, t = 5 min 1#~2#: Yes, Yes, 3#~6#: 3#~6#: No No 1.0~1.5 m1.0~1.5 m m m = 5 min 1#~2#: Yes, 4#~6#: No 2 n = 50 r/min, t = 10 min 1.0~1.5 m, close to 1.5 m 1.48 m = 50 r/min, t 1#~2#: 3#: a little Yes, water 4#~6#: No 1.0~1.5 m, 2 3 n = 40 r/min, t = 15 min 1#~3#: Yes, 4#~6#: No 1.5~2.0 m m m = 10 min 1#~3#: 3#: Yes, a little 5#~6#: water No close to 1.5 m 4 n = 30 r/min, t = 20 min 1.5~2.0 m, close to 2.0 m 1.91 m 4#: a little water 6. Conclusions This study investigated the effects of the nozzle diameter, jet pressure, rotation speed, and slotting time on the cutting depth. A model for calculating a slotting depth suitable for field application was established, and optimized slotting parameters were obtained. Based on water jet slotting field tests, the proposed calculation model was verified. The following conclusions were drawn from this study: (1) The attenuation coefficient of the jet axial dynamic pressure first decreased and then increased with the increase of the nozzle diameter. For a much higher jet impact velocity, there existed an optimal nozzle diameter. Additionally, the cutting depth linearly increased with the jet pressure and decreased as a power function with the increase of the jet translation speed. Moreover, the number of cuttings had a significant impact on the cutting depth, and the several previous cuttings played a major role in the jet cutting. With the further increase of cutting times, the cutting depth slowly increased, but the increment was small.

14 Appl. Sci. 2019, 9, of 15 (2) Water jet slotting experiments were conducted with different rotation speeds and slotting times. The results revealed that the slotting depth increased with the slotting time, but the growth rate gradually decreased and tended to be stable. As the rotation speed increased, the slotting depth became greater at the initial period, and the limit depth was reached faster. At the early slotting stages, more slotting repetitions were helpful in increasing the slotting depth. At the later slotting stages, a longer single impact improved the slotting efficiency. (3) A model for calculating the water jet slotting depth was established according to the effects of key parameters on the cutting depth. This model was subsequently verified using the rotatory slotting experiment data, and the results revealed that the fitting was good. Based on the proposed model, the slotting depths under different jet pressures and the threshold rock-breaking pressures were calculated. (4) Water jet slotting field tests were carried out. The slotting depths at different rotation speeds with different slotting times were analyzed. Comparisons with the depths predicted by the calculation model were made, which revealed that the differences are acceptable. Author Contributions: J.Z., Y.W., Z.G., and S.X. contributed to conceiving and designing the experiments, analyzing the data, and writing the paper. H.Z. and X.H. performed the experiments. Funding: This research was funded by the National Natural Science Foundation of China, grant numbers , , and the National Science and Technology Major Projects of China, grant number 2016ZX Acknowledgments: We thank Liwen Bianji, Edanz Editing China ( for editing the English text of a draft of this manuscript. Conflicts of Interest: The authors declare no conflict of interest. References 1. Liu, T.; Lin, B.Q.; Yang, W.; Zou, Q.L.; Kong, J.; Yan, F.Z. Cracking process and stress field evolution in specimen containing combined flaw under uniaxial compression. Rock Mech. Rock Eng. 2016, 49, [CrossRef] 2. Liu, S.M.; Harpalani, S. Permeability prediction of coalbed methane reservoirs during primary depletion. Int. J. Coal Geol. 2013, 113, [CrossRef] 3. Lu, Y.Y.; Xiao, S.Q.; Ge, Z.L.; Zhou, Z.; Ling, Y.F.; Wang, L. Experimental study on rock-breaking performance of water jets generated by self-rotatory bit and rock failure mechanism. Powder Technol. 2019, 346, [CrossRef] 4. Xiao, S.Q.; Ge, Z.L.; Lu, Y.Y.; Zhou, Z.; Li, Q.; Wang, L. Investigation on coal fragmentation by high-velocity water jet in drilling: Size distributions and fractal characteristics. Appl. Sci. 2018, 8, [CrossRef] 5. Hu, S.S.; Cheng, Y.Q. Discussions on key development fields of China s coal science and technology at early stage of 21st century. J. China Coal Soc. 2005, 30, Ge, Z.L.; Mei, X.D.; Jia, Y.J.; Lu, Y.Y.; Xia, B.W. Influence radius of slotted borehole drainage by high pressure water jet. J. Min. Saf. Eng. 2014, 31, Lin, B.Q.; Lv, Y.C.; Li, B.Y.; Zhai, C. High-pressure abrasive hydraulic cutting seam technology and its application in outbursts prevention. J. China Coal Soc. 2007, 32, Shen, C.M.; Lin, B.Q.; Zhang, Q.Z. Induced drill-spray during hydraulic slotting of a coal seam and its influence on gas extraction. Int. J. Min. Sci. Technol. 2012, 22, [CrossRef] 9. Lin, B.Q.; Yan, F.Z.; Zhu, C.J.; Zhou, Y.; Zou, Q.L.; Guo, C.; Liu, T. Cross-borehole hydraulic slotting technique for preventing and controlling coal and gas outbursts during coal roadway excavation. J. Nat. Gas. Sci. Eng. 2015, 26, [CrossRef] 10. Yu, H.; Lu, T.K. Research on high pressure water jet cutting to improve gas drainage efficiency. Coal Sci. Technol. 2009, 37, Zhang, Q.Z.; Lin, B.Q.; Meng, F.W.; Shen, C.M. Research and application on disturbance influence law of seam slot cutting with high pressurized water jet. Coal Sci. Technol. 2011, 39, Shen, C.M.; Lin, B.Q.; Wu, H.J. High-pressure water jet slotting and influence on permeability of coal seams. J. China Coal Soc. 2011, 36,

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