Fluid–Solid Coupling Characteristics of Gas-Bearing Coal Subjected

Jan 9, 2018 - †State Key Laboratory of Coal Mine Disaster Dynamics and Control and ‡College of Resources and Environmental Science, Chongqing Univ...
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Fluid-Solid Coupling Characteristics of Gas-Bearing Coal Subject to Hydraulic Slotting: An Experimental Investigation Quanle Zou, and Baiquan Lin Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b02358 • Publication Date (Web): 09 Jan 2018 Downloaded from http://pubs.acs.org on January 10, 2018

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Energy & Fuels

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Fluid-Solid Coupling Characteristics of Gas-Bearing Coal Subject to Hydraulic Slotting: An Experimental Investigation

3

Quanle Zou1,2*, Baiquan Lin3

4

1

State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, China

5

2

College of Resources and Environmental Science, Chongqing University, Chongqing 400044, China

6

3

School of Safety Engineering, China University of Mining & Technology, Xuzhou 221116, China

1

7 8

ABSTRACT: Chinese coal seams are characterized by high gas content and low permeability. The permeability of coal

9

seams should be improved to achieve maximum extraction of coalbed methane. This study explores how coal and gas

10

behave when subjected to hydraulic slotting. A fluid–solid coupling experimental system of gas-bearing coal subjected to

11

hydraulic slotting was first established. Then, the fluid–solid coupling property of gas-bearing coal subjected to hydraulic

12

slotting was revealed using the established experimental system. Meanwhile, indicators used to describe the process of

13

hydraulic slotting were derived, and the influencing factors affecting the process of hydraulic slotting were analyzed

14

using the aforementioned indicators. The research achievements indicate that the gas pressure response of the monitoring

15

points in the coal sample shows different characteristics at different stages. Corresponding to the change trend of the gas

16

pressure, the vertical and parallel strains demonstrate the five-stage change characteristics. With the increase of gas

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pressure, the final deformation amount before slotting gradually increases, and the gas diffusion parameter increases

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exponentially. With the increase of the slot radius, the gas diffusion parameter shows a similar change tendency with the

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ultimate deformation amount, i.e., it tends to become flat after a rapid increase. The research achievements can provide

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certain theoretical and practical references for the reveal of the enhanced coalbed methane recovery mechanism through

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hydraulic slotting and the rational selection of the key parameters in the field test, respectively.

22

23

1. INTRODUCTION

24

Coalbed gas, whose main component is methane, is generated from organic matter during the process of coalification1-4.

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Its calorific value is more than 8000 kilocalories per cubic meter, which is almost equivalent to that of conventional

26

natural gas5-6. Thus, the exploitation and utilization of coalbed gas can not only make up for the lack of conventional

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natural gas but also effectively reduce the greenhouse gas effect and the occurrence of coal mine gas disasters7-11.

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Coalbed gas is mainly in an adsorbed state in coal mass, whose exploitation involves a complicated

29

desorption–diffusion–seepage process. As the coal mining depth extends, most coal seams are characterized by low

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permeability, so permeability-enhancing measures are needed to achieve better recovery efficiency. One of the core ideas

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of enhanced coalbed methane recovery methods is to perform artificial disturbance and positive stimulation on the

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physical and chemical properties of the coal seam12-15. At present, several stimulated measures have been developed for

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the abovementioned purpose, such as hydraulic slotting, hydraulic fracturing, liquid nitrogen fracturing and microwave

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irradiation stimulation16-20.

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Hydraulic slotting has proved to be an effective measure to achieve better enhanced coalbed methane (ECBM)

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recovery efficiency through the impact of the high-pressure waterjet on the borehole wall to generate numerous artificial

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fractures.

Currently,

hydraulic

slotting

has

achieved

rapid

development

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including

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permeability-enhancing mechanism exploration, technology and equipment development, and field investigation21-25. In

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regards to permeability-enhancing mechanism exploration, the theory of “pressure relief and permeability enhancement”

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has been proposed, and a relatively broad consensus has been reached regarding this theory. As shown in Figure 1, the

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stress concentration exists near the borehole, which blocks the flow of the gas into the borehole. After the implementation

42

of hydraulic slotting, the stress concentration is broken, pressure relief is achieved, and plenty of gas flows into the

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borehole through the fracture network and slots. Concerning the technology and equipment development, as shown in

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Figure 2(a), most of the hydraulic slotting systems include emulsion pump, water pressure controller, rotator, drilling rig,

45

drill pipe, drill and nozzle. The emulation pump is used to generate high-pressure water. The water pressure controller is

46

used to adjust the flow of the water according to the actual condition. The rotator is used to connect the high-pressure

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water pipe and the drill pipe. The drilling rig rotates the drill pipe and the drill to break the rock or coal. The nozzle is

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used to generate the high-pressure waterjet. Figure 2(b) displays the procedures of the hydraulic slotting, which can be

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summarized as follows: a borehole is drilled, the drill pipe is rotated, and the high-pressure water impacts the borehole

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wall to generate slots inside the coal seam. Numerous field tests have been conducted, and they have indicated that the

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gas drainage efficiency significantly improves after the implementation of hydraulic slotting. Above all, although

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numerous achievements have been made, the basic theoretical research of hydraulic slotting is still weak, which is

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embodied in the lack of systemic and in-depth studies on the coal rupture and gas seepage property under multifield

54

conditions. These shortcomings result in the irrational choice of the key parameters and relatively low ECBM efficiency. a

b Stress concentration Borehole

Borehole

Pressure relief

Slot

55 c Borehole

Pressure relief

Slot Fracture network

56 57

Figure 1. Permeability-enhancing mechanism of hydraulic slotting. (a) Stress concentration around the borehole. (b) Pressure relief around the borehole

58

after hydraulic slotting. (c) A fracture network forms around the borehole, and plenty of gas flows into the borehole. a

Rotator 抗高压密封水辫

Drill pipe 抗高压密封钻杆

Drill and nozzle 水射流割缝器

b Drill bit

Slot 乳化液泵站 Emulsion pump

Borehole Drilling 钻机 rig

59 60

Fractures

Waterjet

Drill pipe

水压控制器 Water pressure controller

Figure 2. Hydraulic slotting system and its procedures. (a) Hydraulic slotting system. (b) The procedures of hydraulic slotting.

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In this work, a fluid–solid coupling experimental system of gas-bearing coal subjected to hydraulic slotting was first

62

established. Second, the fluid–solid coupling property of gas-bearing coal subjected to hydraulic slotting was revealed

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using the established experimental system. Meanwhile, the indicators used to describe the process of hydraulic slotting

64

were derived, and the influencing factors affecting the process of hydraulic slotting were analyzed using the derived

65

indicators. The research achievements can provide certain theoretical and practical references for the reveal of the

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hydraulic slotting ECBM (HS-ECBM) mechanism and the rational selection of the key parameters in the field test,

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respectively.

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2. EXPERIMENTAL

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2.1. Experimental System. The purpose of this paper is (a) to simulate the entire process of HS-ECBM and

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summarize its characteristics; (b) to reveal the effect of initial gas pressure on the dynamic response characteristics of

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coal during HS-ECBM; and (c) to reveal the effect of the slot radius on the dynamic response characteristics of coal

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during HS-ECBM. Based on these objectives, the corresponding experimental system was established. As shown in

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Figure 3(a~b), the experimental system mainly includes six subsystems, i.e., the triaxial loading subsystem, temperature

74

control subsystem, adsorption–desorption subsystem, waterjet generation subsystem, experimental chamber, and

75

data-acquisition subsystem. (a)

(b)

4

4

2

1

5

5

6

3

2

6

7

3

8

9

10 11

11 13

1

13

0 20 40

12

10

9

60 80 100

620

12

7

640 660 680 700

8

(c)

(d) 17-1 14

15

16

21-2 21-3

21-1

17

21 21-1

17 16 14

21-2

20-1

14 15

76

18

19

21-3

20

22

19

18 23

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Figure 3. Experimental system. (a) The entire experimental system: 1. Computer; 2. Gas pressure acquisition device; 3. Strain acquisition device; 4.

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Triaxial loading device; 5. Triaxial stress loading control device; 6. Experimental chamber; 7. Temperature control device; 8. Vacuum pump; 9. Gas

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cylinder; 10. Pressure-reducing valve; 11. Gas volume measurement instrument; 12. Hydrochloric acid solution; 13. Metering pump. (b) The physical

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map of the entire experimental system. (c) Design scheme of the experimental chamber: 14. Press plate A; 15. Pushrod A; 16. Press plate B; 17.

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Pushrod B; 17-1. Inlet channel; 18. Upper cover; 19. Chamber; 20. Bottom cover; 20-1. Outlet channel; 21. Space diagram; 21-1. Through-holes for

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pressure sensors; 21-2. Through-hole for enameled wire bundle; 21-3. Through-hole for temperature sensor; 22. The physical map of the chamber and

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the bottom cover; 23. The physical map of the upper cover.

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(a) Triaxial loading subsystem. The triaxial loading subsystem mainly includes the triaxial loading platform,

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hydraulic pump station, and control panel. This subsystem can realize the separate loading of the vertical and horizontal

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directions. The maximum loading force is 2000 KN. The size of the loading platform is 720 mm × 800 mm. Flexible

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loading of the multiscale samples can be realized through the effective cooperation of the loading platform and square

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thin iron block. Automatic control of the loading can be achieved through the PLC program.

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(b) Temperature control subsystem. Electrical heating is adopted. This subsystem is made up of a temperature

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sensor, electrically heated wire, and control device. The temperature sensor and electrically heated wire are fixed on the

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upper cover of the experimental chamber. When the temperature in the chamber is below the setting temperature, the

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electrically heated wire begins to work until the preset temperature is reached. The temperature control precision is 0.1℃,

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and the temperature variation range is 0~100℃.

94 95

(c) Adsorption–desorption subsystem. This subsystem consists of the vacuum pump, pressure-reducing valve, and gas volume measurement instrument. The maximum vacuum degree of the vacuum pump is –101.325 KPa.

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(d) Waterjet generation subsystem. This subsystem mainly includes the metering pump, connecting lines, and

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waterjet generation device. The rated flow of the metering pump is 8 L/min. The connecting lines are corrosion-resistant.

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The waterjet generation device is made of a stainless steel tube with a closed front end and symmetrical through-holes on

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the sidewall.

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(e) Experimental chamber. This chamber is made up of the pushrod, press plate, chamber, upper board, and bottom

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board. Its design scheme is displayed in Figure 3(c~d). Pushrod A and pushrod B connect with press plate A and press

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plate B through the bolts, respectively. Two vertical through-holes are set in pushrod B, which are used to convey the

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liquid. Several through-holes are set in press plate B, which are used to provide the channels for gas pressure

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measurement. The upper board and bottom board connect with the chamber through fourteen bolts, and there are two

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sealing rings between them. The gas outlet channels are arranged in the bottom board. A schematic diagram of the

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assembly of the experimental chamber is displayed in Figure 3(c). It can be seen from Figure 3(c) that there are

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through-holes in the front wall of the chamber, which are used to connect the gas pressure sensor and enameled wire

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bundle. There are also through-holes in the back wall of the chamber, which are used to connect the gas inlet control

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valve, liquid inlet control valve, vacuum pumping valve, and gas outlet control valve. The flow path of the gas is as

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follows: gas cylinder→gas inlet control valve→experimental chamber→coal sample→outlet channel→gas outlet control

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valve→gas volume measurement instrument. The flow path of the liquid is as follows: metering pump→liquid inlet

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control valve→inlet chamber→coal sample→outlet channel→gas outlet control valve→gas volume measurement

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instrument. The size of the chamber is 360 mm × 260 mm × 320 mm, and its design pressure is 6 MPa.

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(f) Data-acquisition subsystem. Two types of data are collected in this paper, i.e., the strain and gas pressure. The

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strain measurement is realized through the strain indicators developed by Jiangsu Donghua Measuring Technology

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Limited Liability Company. The measurement of the gas pressure inside the coal sample is realized through the CY200

117

digital pressure sensor.

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2.2. Coal Specimen Preparation. In our experiment, physical simulation of hydraulic slotting is realized

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through the formation of the pressure relief space, which is achieved by removing partial coal inside the loaded coal

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sample. The coal removal method involved arranging sodium hydroxide powder (whose volume is slightly larger than

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that of the pressure relief space) inside the coal sample and then dissolving it using 10% hydrochloric acid. One of the

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purposes of the experiments is the real-time monitoring of the strain and gas pressure inside the coal sample during

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hydraulic slotting. It is necessary to insert the strain gauge and gas channel in the coal sample to achieve this purpose.

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The arrangement of the strain gauge is realized as follows. The coal samples are arranged layer by layer to form a total of

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five layers. The coal in every layer is prepressed to guarantee surface smoothness, and then the strain gauge is placed at

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the preset position. At layer three, a PVC tube is used to dig out and form a cylindrical space at the center of the coal

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sample. Subsequently, sodium hydroxide is poured into the cylindrical space and allowed to compact. The arrangement

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of the gas channel is realized as follows. After the coal samples are arranged as noted previously, an electric portable drill

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is used to drill cylindrical channels at the preset position on the coal samples. A rubber hose is then inserted into the end

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of the channel, and a flexible glue is used to seal the gap between the channel and the rubber hose. The coal samples and

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the arrangement of the strain gauge and gas pressure measuring tube are depicted in Figure 4. 3 测压管

1 应变片 2

4 进液管

出6 液 管

N a5O H Mould

(a)

(b)

(c)

132 133

Figure 4. Coal samples and the arrangement of the strain gauge and tubes. (a) Coal sample molding; (b) Coal samples; (c) The arrangement of the

134

vertical strain gauge (1), parallel strain gauge (2) gas pressure measuring tube (3), liquid inlet tube (4), sodium hydroxide (5) and liquid outlet tube (6).

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2.3. Experimental Design. The experimental design is displayed in Table 1. The variables considered in the

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experiments are slot radius and gas pressure. All of the variables have four levels. The vertical stress, maximum

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horizontal stress, minimum horizontal stress and gas pressure are determined in accordance with References [26-27],

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which have taken the similarity ratio and the burial depth into account.

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Table 1. Experimental Design Vertical stress

Maximum horizontal stress

Minimum horizontal stress

Temperature

Slot radius

Gas pressure

σ1/MPa

σ2/MPa

σ3/MPa

/℃

/mm

/MPa

No. 1

0.5

2

1 10

3

1.5

4

2 1.38

1.87

1.06

30

5

5

6

7.5

7

10

8

12.5

2

140

2.4. Experimental Procedures. The experimental procedures involve the following steps. (a) Preparation. The

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coal specimen is dried in a drying oven (temperature of 60℃) to eliminate the influence of moisture as much as possible.

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The gauze is used to polish the surface of the coal samples to avoid the partial stress concentration. After drying, the

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samples are placed inside the experimental chamber. The strain monitoring subsystem, temperature control subsystem,

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and gas pressure monitoring system are connected to the chamber, and the upper board of the experimental chamber is

145

installed. Finally, all the valves are closed. (b) Vacuum pumping. The valve of the vacuum pump is opened to conduct

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vacuum pumping for two hours. Meanwhile, the strain and gas pressure monitoring subsystems are turned on to record

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the strain and gas pressure, respectively, inside the coal sample. (c) Gas adsorption. The valve of the vacuum pump is

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now closed. The gas cylinder and the gas input valves are used to conduct gas adsorption for 48 h. (d) Triaxial loading.

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The gas cylinder and the gas input valves are closed, and the triaxial loading system is started to impose the preset

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vertical and horizontal stresses on the coal sample. To avoid the rupture of the coal specimen due to the effect of

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concentration stress during confining pressure loading, the loading pattern of confining pressure in this paper is as

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follows: all the loading intervals are set to 0.25 MPa, and the pressures of all three directions are loaded at the same time.

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When one direction reaches the set pressure value, the pressure is kept constant. (e) Hydraulic slotting and desorption.

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When the gas pressure is stable, the metering pump and water input valve are opened to inject hydrochloric acid into the

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coal sample. The hydrochloric acid spurts from the though-holes in the stainless steel tube to react with sodium

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hydroxide, which realizes the simulation of hydraulic slotting. When sodium hydroxide comes into contact with the water

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output channel, the hydraulic slotting is stopped, and the water outlet is connected to the gas volume measurement

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instrument to measure the gas desorption volume. The data are recorded at 30-second intervals. Meanwhile, other

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parameters, such as the surrounding temperature, are recorded to transfer the gas volume in the surrounding area into the

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gas volume in the standard state. (f) Finally, all of the subsystems are put in order, and the next experiment is conducted.

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3. RESULTS

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Because all of the experiments produced similar results, in this section, experiment #1 (gas pressure of 0.5 MPa and

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slot radius of 10 mm) was chosen as an example to describe the time-varying response of gas-containing coal subjected

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to hydraulic slotting and then obtain the indices, which can characterize the gas–solid coupling property in the entire

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process of hydraulic slotting. 3.1. Variation in Gas Pressure Inside the Coal Specimen. The real-time variation in gas pressure inside the

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coal specimen of experiment #1 in the entire experimental process is displayed in Figure 5(a), where it can be seen that

168

the entire experimental process can be divided into five stages: vacuum pumping, gas filling, confining pressure loading,

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slotting, and desorption. Detailed description of the variation laws at every stage is presented in the following

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subsections.

2

3

4

5

0 0.00

-150 -0.15

-0.06 -0.08

2

4 6 4 时间×10 Time ×10/s4/s

8

3

0.56 0.54 0.52

∆= 0.0214 ∆= 0.0269

0.50 5.0

5.2

∆= 0.0133

5.4

∆= 0.0098

∆= 0.0089

∆= ∆= 0.0016 ∆= 0.0060 0.0024

100

0.0

0.1

0.2

0.3

0.4

0.5

5.8

6.0

6.2

6.4

0.6

0.7

1

0.4 0.2

t=0.74

0.0 0.72

2

0.75

0.78 0.81 Time×104/s

3

0.84

4

Time ×104/s

(b)

(c)

5

0.6 4

0.63

∆= 0.0292

0.62 0.61

2 0.6

Time ×103/s

∆=0.0492

0.60 6.74

0.59 5.6

150

0.64

Pressure/MPa

0.58

50 Time/s

(a) 0.60

0

-0.10 -0.12

0

171

172

-0.04

0.6 0.5 0.4 0.3 0.2 0.1 0.0 -0.1

1

Pressure/MPa

1

150 0.15

0.00 -0.02 -0.04 -0.06 -0.08 -0.10 -0.12

Pressure/MPa

0.00 -0.02

Pressure/MPa

450 0.45 300 0.30

6.48

6.54

6.60

6.66

6.72

6.78

Pressure/MPa

750 0.75 600 0.60

Pressure/MPa

Pressure/MPa 压力/M P a

166

Pressure/MPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.5 p=1.72exp(-x/2199.71)+106.94

0.4 0.3 0.2

Gas pressure decay curve Exponential fitting

∆= 0.5003

0.1

6.84

6.9

7.2

7.5

7.8

8.1

Time ×104/s

Time ×104/s

Time ×104/s

(d)

(e)

(f)

8.4

8.7

173

Figure 5. Variation in gas pressure at the monitoring point of the coal sample under a gas pressure of 0.5 MPa. (a) Variation in gas pressure in the

174

entire experiment; (b) Variation in gas pressure at the vacuum-pumping stage; (c) Variation in gas pressure at the gas-filling stage; (d) Variation in gas

175

pressure at the confining pressure loading stage; (e) Variation in gas pressure at the slotting stage; (f) Variation in gas pressure at the desorption stage.

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(a) Vacuum pumping: As shown in Figure 5(b), after opening the vacuum pump, the gas pressure inside the coal

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specimen rapidly decreases. After approximately 40 s, the internal gas pressure of the coal specimen decreases to the

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rated pressure of the vacuum pump (i.e., –0.1 MPa). Subsequently, the internal gas pressure of the coal specimen shows

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no significant change and presents small-range fluctuations.

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(b) Gas filling: After vacuum pumping for two hours, the valve of the gas cylinder is opened, and the experimental

181

chamber is filled with methane. The outlet pressure of the gas cylinder is set to 0.5 MPa throughout the process of gas

182

filling. As shown in Figure 5(c), at the initial stage of gas filling, the internal gas pressure of the coal sample exhibits a

183

rapid linear increasing trend. At 7400 s, the internal gas pressure of the coal sample reaches the maximum value of 0.58

184

MPa. Subsequently, the internal gas pressure of the coal sample gradually decays, and the attenuation amplitude is much

185

smaller than the increased amplitude. The final internal gas pressure of the coal sample is approximately 0.5 MPa.

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(c) Confining pressure loading: The period of gas filling is 12 hours. After gas filling, the valve of the gas cylinder

187

is closed, and no further gas is filled. As shown in Figure 5(d), the entire process of the confining pressure loading is

188

completed through eight loading steps, with the duration of each step being 1800 s. For each loading step, the gas

189

pressure inside the coal sample shows a similar trend, and the difference is the increase in amplitude. Figure 5(d) presents

190

the difference between the internal gas pressure at the end of each loading step and the pressure value at the beginning of

191

the loading step. It can be clearly observed that the variation magnitude of the internal gas pressure of the coal sample is

192

changed from 0.0269 MPa at the first step to 0.0016 MPa at the eighth step. The internal gas pressure at each step of the

193

loading process is significantly low, which is attributed to the fact that, for each loading step, the coal specimen is in a

194

state of expansion and is easily compressed due to the adsorption of methane. In addition, because of the relatively rapid

195

loading rate of the confining pressure, it is relatively impossible to adjust the gas inside the sample, which leads to the

196

increase in internal pressure of the coal sample. When the loading of the confining pressure is completed, the internal gas

197

pressure of the coal sample is larger than that of the experimental chamber. Subsequently, the gas inside the coal sample

198

will gradually enter the experimental chamber, leading to the gradual reduction of the internal pressure, i.e., for each

199

loading step, the internal gas pressure of the coal sample decreases slowly after the first jump28. With the increase of the

200

loading step, the gas inside the coal sample gradually decreases, and its ability to resist external pressure gradually

201

increases. The compression effect of the same confining pressure is gradually weakened, which leads to a decrease of the

202

compressed amplitude of the internal gas, i.e., with the increase of the loading step, the internal gas pressure of the coal

203

sample decreases.

204

(d) Slotting: After the completion of the loading of the confining pressure, the valve is opened, and the metering

205

pump is opened to inject the hydrochloric acid with a certain concentration into the coal specimen. The hydrochloric acid

206

solution impacts the sodium hydroxide embedded in the coal sample. As shown in Figure 5(e), the internal gas pressure

207

of the coal sample rises first. When the experimental time is 6.74 × 104 s, the maximum value of 0.64 MPa is reached; a

208

rapid decline then occurs, and eventually a stable value is maintained. The pressure difference at the rising stage is

209

0.0492 MPa, and the pressure difference at the declining stage is 0.0292 MPa. This change trend can be explained as

210

follows: the impact of the hydrochloric acid solution on sodium hydroxide has a disturbance effect on the coal, which

211

leads to stress redistribution inside the coal sample. At the initial stage, the disturbance effect is weak, and its effect on

212

the internal gas pressure of the coal sample is relatively small. The monitoring points are located in the compressive

213

stress zone around the slot. Therefore, the monitored gas pressure slowly increases. With the passage of time, the slotted

214

radius continuously increases, and the disturbance of slotting on the surrounding coal correspondingly enlarges. The

215

stress concentration degree at the monitoring points constantly increases, and the gas is continuously compressed. When

216

the stress concentration reaches the fracture threshold value of the coal, the coal is broken, and the crack is generated,

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which is coalesced with other cracks. As a result, the compressed gas is released. Accordingly, the gas pressure at the

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monitoring points increases to the maximum and then suddenly drops.

219

(e) Desorption: When the slotting is completed, open the outlet valve and perform desorption. At this point, the gas

220

pressure inside the coal sample shows an obvious change, i.e., it first significantly decreases and then gradually

221

approaches a fixed value, which has the characteristics of the exponential function. In this paper, the exponential function

222

is used to fit the relationship curve between the internal gas pressure and time at the desorption stage, which is shown in

223

Figure 5(f). According to the fitted exponential function, the limit pressure of methane desorption is 0.1069 MPa, which

224

indicates that the desorption starting pressure of methane under the experimental condition is 0.1069 MPa. It can be seen

225

that the reduction rate of the internal gas pressure through the entire process of desorption is 0.5003 MPa, which

226

indicates that the weakening effect of desorption on the gas pressure inside the coal sample is very significant.

227

3.2. Variation in Deformation Inside the Coal Specimen. In this paper, the variations of the vertical strain

228

and parallel strain at the monitoring points in the entire process were also monitored, which are elaborated in the

229

following sections.

shown in Figure 6(a). Corresponding to the experimental process, the vertical strain at the internal monitoring points of

232

the coal sample also has five stages: contraction deformation due to vacuum pumping, swelling deformation due to

233

methane adsorption, compression deformation due to loading, relaxation due to slotting, and shrinkage deformation due

234

to desorption. The characteristics of the five stages are as follows. 8 6 4 1

2

2 0 2

4

5.0

5.2

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

∆= 1.344

-0.8 -1.2

1

2

3

Time ×104/s

(b)

(c)

1 ∆= ∆= 0.9007 1.0973

0.0

-0.4

(a)

3

0

8

0.1

2

0.0

Time ×104/s

2

-1

6

0.2

0.4

Time ×104/s

235 3

5

(3.78,0.36)

1

0.3

∆= 0.8018

5.4

∆= 0.6001

5.6

∆= ∆= -0.0707 ∆= -0.1110 ∆= -0.0474 0.4933

5.8

6.0

6.2

6.4

8 7 6 5 4 3 2

4

∆= 3.6644

∆= 5.4544

6.48

6.54

6.60

6.66

6.72

6.78

6.84

Time ×104/s

Time ×104/s

(d)

(e)

Vertical strain ×103/µε

0

4

Vertical strain ×103/µε

-2

3

0.4

Vertical strain ×103/µε

231

Vertical strain ×103/µε

3.2.1. Variation in Vertical Strain. The overall variation tendency of the vertical strain in the entire process is

Vertical strain ×103/µε

230

Vertical strain ×103/µε

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 21

5.6 5.4 5.2 5.0 4.8 4.6 4.4

4

5

5 ∆= 1.1076

6.9

7.2

7.5

7.8

8.1

Time ×104/s

8.4

8.7

(f)

236 237

Figure 6. Variation in vertical strain at the monitoring point of the coal sample under the gas pressure of 0.5 MPa. (a) Variation in vertical strain in the

238

entire experiment; (b) Variation in vertical strain at the vacuum-pumping stage; (c) Variation in vertical strain at the gas-filling stage; (d) Variation in

239

vertical strain at the confining pressure loading stage; (e) Variation in vertical strain at the slotting stage; (f) Variation in vertical strain at the desorption

240

stage.

241

(a) Contraction deformation due to vacuum pumping: There are many imperfections (pores, cracks, etc.) inside the

242

coal specimen, which are often filled with impurities, such as free gas and water. The purpose of vacuum pumping is to

243

eliminate the influence of the original impurities on the experimental results. When these impurities are drawn out, the

244

surface tension of the pores significantly decreases, which leads to shrinkage and deformation of the coal sample29-30. It

245

can be seen from Figure 6(b) that, when vacuum pumping is conducted for 3780 s, the vertical strain of the coal

246

specimen reaches a stable value of 0.36 × 103 µε.

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Energy & Fuels

247

(b) Swelling deformation due to methane adsorption: As shown in Figure 6(c), at the initial moment of gas filling,

248

the phenomenon of compression deformation that results from the sudden filling of 0.5-MPa methane cannot be

249

observed. During the entire process of gas filling, the vertical deformation of the coal sample shows a trend of gradual

250

decrease after a rapid decline. The rapid decline may result from the fact that the internal pressure of the coal specimen is

251

much lower than the external pressure, and the large pressure gradient is attributed to the high methane migration rate.

252

After adsorbing gas, the surface tension becomes larger, and then the expansion phenomenon occurs. The more the

253

adsorbed gas, the more obvious the expansion effect31-32. As the gas (methane) continues to enter the pores and cracks of

254

the coal sample, its internal pressure gradually increases, resulting in a decrease of the pressure gradient and capacity of

255

gas migration. Consequently, the increase amount of the expansion and deformation decreases. It can be seen from

256

Figure 6(c) that the amount of expansion deformation due to methane adsorption is approximately 1.344 × 103 µε, which

257

is 3.73 times larger than that caused by vacuum pumping.

258

(c) Compression deformation due to loading: According to the preset loading procedure, the entire loading process

259

is completed through eight loading steps. The duration of each step is 1800 s. For loading step one through step five, the

260

vertical strain inside the coal specimen shows a similar variation trend. The difference is the increase in magnitude. For

261

each step of loading, the vertical strain inside the coal specimen presents a slow increasing trend after a rapid increase.

262

The initial sudden rise results from the loading action, and the subsequent slow increase is due to the interaction between

263

methane and the coal specimen. In addition, the variation magnitude of the vertical strain in every step of the monitoring

264

point is presented in Figure 6(d). It can be observed that the variation magnitude of the vertical strain from loading step 1

265

through loading step 5 presents a tendency of significant decrease, which is due to the fact that, because the decrease of

266

gas results in the enhancement of the capacity to resist the outer pressure of the coal specimen with the increase in the

267

loading step, the deformation degree of the coal specimen gradually decreases under the same load. In contrast, the

268

vertical strain at the internal monitoring points of the coal specimen from loading step 6 and loading step 8 presents an

269

opposite variation, which indicates that the small-magnitude expansion occurs in the vertical direction of the coal

270

specimen. The total expansion degree is 0.2291 × 103 µε, which is far less than the compression degree. This may be

271

because, from loading step 6 through loading step 8, the coal specimen is subjected to unbalanced loading from two

272

directions (i.e., not the balanced loading from three directions) under the condition that one direction is fixed or

273

one-direction loading under the condition that the other two directions are fixed. Such complicated stress conditions lead

274

to the change of the vertical strain of the coal specimen.

275

(d) Relaxation due to slotting: As shown in Figure 6(e), during the entire slotting process, the vertical strain shows

276

the variation characteristic of multiple rapid drops after a winding rise. The increase in the magnitude of the vertical

277

strain at the rising stage is 5.4544 × 103 µε. The decrease in the magnitude of the vertical strain at the declining stage is

278

3.6644 × 103 µε. This variation tendency can be interpreted as follows: during slotting, the disturbance range caused by

279

impact gradually increases. For the monitoring points, the change of stress around the slot with time experiences three

280

stages: original stress, concentrated stress, and residual stress. The process of stress concentration is the process of

281

loading at the monitoring points, which leads to the gradual increase of the deformation degree. The monitoring points

282

may be located in the compressive stress zone. Therefore, the deformation is characterized by compression. In addition,

283

the impact of the hydrochloric acid solution on the sodium hydroxide is very complex, which may be the reason for the

284

complexity of the strain at the increase stage. The loading causes the coal at the monitoring point to exhibit a “tight”

285

state. When the strain reaches a certain threshold value (which can be interpreted as the fracture threshold of the coal

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286

sample), the coal sample has a larger rupture, and then the relaxation phenomenon occurs, which is characterized by a

287

reversal of the curve of the vertical strain33-34. It can also be seen from Figure 6(e) that the relaxation is not done at one

288

particular time.

289

(e) Shrinkage deformation due to desorption: The desorption-induced deformation of the coal sample is the opposite

290

of the adsorption-induced deformation. The desorption of methane in the pores of the coal specimen leads to an increase

291

in surface energy, which induces the shrinkage of the surface layer. In contrast, the desorption of methane decreases the

292

widths of pores and cracks. The combined effects of these two aspects lead to the phenomenon of desorption-induced

293

shrinkage35-36. It can be seen from Figure 6(f) that the entire curve shows a trend of slow variation after a rapid increase,

294

which may result from the fact that, as time goes on, the great resistance causes a decrease of the desorption amount and

295

thus the deformation amount. This corresponds to the gas pressure variation at the internal monitoring points.

297

shown in Figure 7(a). Corresponding to the experimental process, the parallel strain at the internal monitoring points of

298

the coal sample also has five stages: contraction deformation due to vacuum pumping, swelling deformation due to

299

methane adsorption, compression deformation due to loading, relaxation due to slotting, and shrinkage deformation due

300

to desorption. The characteristics of the five stages are described in detail in the following sections . 3 2 1

2

0 3

4

5

-1

2

4

3

0.1

0.2

0.3

0.4

0.5

0.6

0.7

∆= 1.0981

-0.6 -0.8 0

1

2

3

4

(b)

(c)

∆= 0.5512

∆= 0.3122

∆= ∆= 0.0799 ∆= 0.3006 0.4002

0.6715 ∆= 0.7777

5.2

0.0

-0.4

(a)

∆=

5.0

0.0

2

0.0 -0.2

Time ×104/s

1 ∆= 0.9284

0.1

0.2

Time ×104/s

3

0

8

0.2

0.4

Time ×104/s

2

-1

6

(3.99,0.32)

1

5.4

5.6

5.8

6.0

6.2

6.4

3.5 3.0

4

∆= 0.6720

∆= 2.0570

2.5 2.0 1.5 1.0

6.48

6.54

6.60

6.66

6.72

6.78

6.84

Parallel strain ×103/µε

0

0.3

Parallel strain ×103/µε

1

301

302

Parallel strain ×103/µε

4

Parallel strain ×103/µε

3.2.2. Variation in Parallel Strain. The overall variation tendency of the parallel strain in the entire process is

Parallel strain ×103/µε

296

Parallel strain ×103/µε

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 21

3.0

5

2.9 2.8 2.7

5

∆= 0.5287

2.6 2.5 6.65

7.00

7.35

7.70

8.05

Time ×104/s

Time ×104/s

Time ×104/s

(d)

(e)

(f)

8.40

8.75

303

Figure 7. Variation in parallel strain at the monitoring point of the coal sample under the gas pressure of 0.5 MPa. (a) Variation in parallel strain in the

304

entire experiment; (b) Variation in parallel strain at the vacuum-pumping stage; (c) Variation in parallel strain at the gas-filling stage; (d) Variation in

305

parallel strain at the confining pressure loading stage; (e) Variation in parallel strain at the slotting stage; (f) Variation in parallel strain at the desorption

306

stage.

307

(a) Contraction deformation due to vacuum pumping: In this stage, the change trends of the parallel strain and the

308

vertical strain at the strain monitoring points are consistent. The difference is the change magnitude. From Figure 7(b), it

309

can be seen that when the vacuum pumping was conducted for 3990 s, the parallel strain reached a stable value of 0.32 ×

310

103 µε, which is slightly less than that of the vertical strain.

311

(b) Swelling deformation due to methane adsorption: As shown in Figure 7(c), in this stage, the parallel strain at the

312

internal monitoring point is similar to that of the vertical strain, i.e., it tends to be stable after a rapid decline. The

313

difference is the magnitude of the expansion. To clearly show the variation of the amplitude and the comparison between

314

the parallel strain and the vertical strain at the internal monitoring points in the gas-filling stage, Figure 8 was drawn. As

315

seen from Figure 8, the vertical strain of this stage is 1.2239 times larger than the parallel strain.

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1.5

Variation magnitude of vertical strain Variation magnitude of parallel strain Increase magnitude

Variation magnitude×103/µε

2.0

Variation magnitude

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

1.0

0.5

0.0

Gas-filling

Desorption

1.2

Variation magnitude of vertical strain Variation magnitude of parallel strain

1.0 0.8 0.6 0.4

Shrinkage

0.2 0.0

Swelling

-0.2 1

2

3

(a)

316

4

5

Loading step

6

7

8

(b)

317

Figure 8. Variation magnitude of vertical strain and parallel strain at the monitoring point of the coal sample under the gas pressure of 0.5 MPa. (a)

318

Variation magnitude of vertical strain and parallel strain at the gas-filling and desorption stages; (b) Variation magnitude of vertical strain and parallel

319

strain at the confining pressure loading stage.

320

(c) Compression deformation due to loading: As shown in Figure 7(d), different from the vertical strain, the parallel

321

strain shows a trend of contraction in the entire process. The change trend of each loading step is gentle after the rapid

322

increase. Similarly, the variation amplitude of the parallel strain is also measured (see Figure 8). It can be observed from

323

Figure 8 that a clear decreasing trend of the vertical strain change amplitude is presented from loading step 1 through

324

loading step 5, which is due to the fact that the enhancement of the deformation-resisting capacity of the coal specimen

325

through the decrease of the gas results in the gradual decrease in the deformation of the coal specimen under the same

326

load. , . In contrast, the vertical strain has a sudden jump at loading step 6 and then gradually decreases, which indicates

327

that a larger contraction occurs in the parallel direction, which may be due to the complex stress conditions at loading

328

steps 6~8. It can be seen from Figure 8 that, except for loading step 6, the absolute value of the vertical strain is greater

329

than that of the parallel strain, which shows that there is also a certain anisotropy characteristic of the coal sample37.

330

(d) Relaxation due to slotting: As shown in Figure 7(e), unlike the vertical strain, in the entire slotting process, the

331

vertical strain shows the characteristics of multiple increases after the tortuous decline. The parallel strain exhibits a

332

tendency of contraction after shrinkage. The decline magnitude of parallel strain at the decreasing stage is 2.057 × 103 µε,

333

and the increase magnitude of parallel strain at the increasing stage is 0.6720 × 103 µε. The two variation amplitudes are

334

significantly smaller than those of the vertical strain, which may be related to the lateral pressure. This trend can be

335

explained as follows: at the initial stage of slotting, the coal at the monitoring point is in the state of tension. As the

336

slotting process proceeds, the tension degree increases. When this type of state achieves the fracture threshold value of

337

the coal sample, the sample is broken, and the relaxation phenomenon occurs, which presents multiple reversals in the

338

variation direction of the parallel strain curve.

339

(e) Shrinkage deformation due to desorption: As shown in Figure 7(f), the parallel strain at the internal monitoring

340

point of the coal sample is similar to that of the vertical strain, which rises quickly and then tends to be stable. The

341

difference is the growth magnitude. The variation of the amplitude and the comparison of the parallel strain and the

342

vertical strain at the internal monitoring points of the desorption stage are also clearly shown in Figure 8. It can be seen

343

from Figure 8 that the vertical strain of this stage is 2.0949 times larger than that of the parallel strain.

344

3.3. Desorption Property of Coal after Hydraulic Slotting. In the aforementioned desorption stage, the

345

natural desorption amount of methane after hydraulic slotting was determined through the gas volume measurement

346

instrument. The change trend of the desorption amount per mass with time is obtained. At the same time, the desorption

347

rate derived from the first-order differential of the time-varying desorption amount was obtained (Figure 9). It can be

348

seen from Figure 9 that the cumulative desorption amount after hydraulic slotting significantly increases and that the

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Energy & Fuels

3.0 2.5 2.0 Desorption amount Desorption rate

1.5 1.0 0.5 0.0

∆t=1.35×104s

6.75

350 351 352

7.20 7.65 8.10 8.55 Desorption time ×104/s

1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 -0.2

Desorption rate/(mL/(g·s))

corresponding desorption rate gradually decreases. The stable value is reached at 8.1 × 104 s. Desorption amount/(mL/g)

349

Figure 9. Desorption amount and desorption rate of the coal sample after hydraulic slotting.

4. DISCUSSION

353

4.1. Solid–Fluid Coupling Characteristics of Gas-Bearing Coal Subjected to Hydraulic Slotting. Four

354

time-varying curves of internal pressure, parallel strain, vertical strain, and desorption amount are plotted together

355

(Figure 10). The coal–gas interaction rules are obtained and described using the aforementioned curves; in brief, the

356

variation in internal gas pressure of the coal specimen is closely related to its deformation. For example, a good

357

consistency exists between the gas pressure and coal deformation during gas filling and desorption. There is sometimes

358

the hysteresis of coal deformation, such as the vacuum-pumping stage. When the external force (such as loading and

359

slotting) disturbance appears, this close relationship is broken, and the coal presents a disturbance-dominated

360

deformation law. Therefore, it is necessary to perform the appropriate disturbance, such as slotting, as accomplished in

361

this paper, to induce the development of coal deformation in the favorable direction.

2.0 1.5 1.0 0.5 0.0

Desorption amount

2

1

362 363

Gas pressure decrease; Coal shrinkage

Parallel strain

Vetical strain 8 7 6 5 4 3 2 1 0 -1 -2

Gas pressure increase; Coal swelling

4 Time ×104/s

6

10 8 6 4 2

Vetical strain×103/µε

2.5

Gas pressure 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 0

Parallel strain×103/µε

3.0

Gas pressure/MPa

Desorption amount/( mL/g)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 21

0 -2

8

2

3

4

Gas pressure increase; Coal shrinkage

Gas pressure increase before decrease; Coal shrinkage before swelling

5

Gas pressure decrease; Coal shrinkage

Figure 10. Coal-gas interaction characteristics in the entire experiment.

364

4.2. Descriptive Indictors of Solid–Fluid Coupling Characteristics of Gas-Bearing Coal Subjected to

365

Hydraulic Slotting. Using the aforementioned analysis, the main purpose of the three stages before slotting is to

366

construct the original state of the coal specimen. Stage 2, marked as 2 in Figure 10, can reflect the effect of gas on coal

367

without external disturbance. Stage 3, marked as 3 in Figure 10, mainly shows the effect of external force loading on coal,

368

but there is also gas desorption, and the change is complicated. Based on this, Langmuir fitting was conducted on the

369

expansion deformation of coal at stage 2, and the final deformation amount of the coal specimen after the loading was

370

used to describe the state of coal under different initial conditions. The deformation of the coal specimen during the

371

process of slotting is also complicated, but the deformation of the coal specimen at the desorption stage is relatively

372

regular. Therefore, the state of the coal specimen after the slotting is mainly described through the Langmuir fitting of the

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Page 13 of 21

373

desorption deformation section and the analysis of the desorption amount. The case with the gas pressure of 0.5 MPa is

374

taken as an example to describe in detail the method of obtaining these descriptive indictors. The specific results are

375

displayed as follows.

376 377

(a) Final deformation amount before slotting εbs: The final deformation amount before slotting, εbs, is defined as the sum of the vertical strain εv and the parallel strain εh at the monitoring points at the end of loading.

ε bs = ε v + ε h

378 379 380

(1)

It can be seen from the aforementioned analysis that, when the gas pressure is 0.5 MPa, the final deformation amount before slotting εbs is 5.903 × 103 µε.

381

(b) Ultimate deformation amount εmax and deformation rate vε: It can be found from the adsorption–deformation

382

curves that the change tendencies of vertical strain and parallel strain under the state of adsorption are consistent, that is,

383

they tend to be gentle after a rapid decrease, which is consistent with the characteristics of an exponential Langmuir

384

curve. The exponential Langmuir model can be expressed as follows:

ε=

385

ε max vε t1− c

(2)

1 + vε t 1−c

386

where εmax and vε represent the maximum amount of deformation and deformation rate of coal under the experimental

387

conditions, respectively.

388

Based on Formula 2, the fitting was performed on the deformation amount at the adsorption stage (shown in Figure

389

11a), where εs is the sum of the parallel strain εh and vertical strain εv. It should be noted that the horizontal axis is

390

relative time, so the beginning of the gas filling was labeled 0. The vertical axis represents the relative strain, i.e., the

391

strain at the adsorption stage minus the strain generated by the vacuum pumping. The same method was used to obtain

392

the fitting curves of coal deformation at the desorption stage, which are shown in Figure 11(b). 0.0

εv

Exponential Langmuir fitting of εv

εh

Exponential Langmuir fitting of εh

εs

Exponential Langmuir fitting of εs

Strain×103/µε

-0.5 Strain×103/µε

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

-1.0 -1.5 -2.0 -2.5 0

393 394

1

2 3 Relative time/s

4

1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

εv εh

Exponential Langmuir fitting of εv Exponential Langmuir fitting of εh

εs

0.0

0.4

Exponential Langmuir fitting of εs

0.8 1.2 1.6 Relative time/s

(a)

2.0

(b)

Figure 11. Deformation amount fitting at the adsorption stage (a) and desorption stage (b).

395

The key parameters of the ultimate deformation amount εmax and deformation rate vε of the fitting curves were

396

derived, and they are displayed in Table 2. It can be seen from Table 2 that the ultimate deformation amount εmax in the

397

parallel direction at the adsorption stage is much larger than that in the parallel direction at the desorption stage, and the

398

ultimate deformation amount εmax in the vertical direction at the adsorption section is almost equivalent to that in the

399

vertical direction at the desorption stage. Whether for the adsorption stage or desorption stage, the ultimate deformation

400

amount εmax is approximately the sum of the ultimate deformation amounts in the vertical and parallel directions. The

401

change of the deformation rate vε is not strong.

402 403

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Energy & Fuels

404

Table 2 Statistics of εmax and vε at the adsorption and desorption stages Adsorption stage

Desorption stage

Key parameters

εmax vε/×10

405 406

-4

εh

εv

εs

εh

εv

εs

–1226.32

–1482.42

–2708.59

685.32

1435.93

2121.28

3.1255

2.0825

2.5024

3.1458

3.3153

3.2600

(c) Gas diffusion parameter KB: Yang38 obtained the time-varying rules of the ratio of the cumulative gas desorption amount Qt to the ultimate desorption amount Q∞ at t through theoretical derivation, namely   Q 2  ln 1 −  t   = KBt + C   Q∞  

407

(3)

408

According to this equation, the desorption amount under the condition of a gas pressure of 0.5 MPa was fitted, and

409

the result is displayed in Figure 12. It can be seen from Figure 12 that, when the gas pressure is 0.5 MPa, the gas

410

diffusion parameter KB equals 3.0447 × 10-4 s-1.

ln[1-(Qt/Q∞)2]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 21

411 412

0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 -3.0 -3.5 -4.0

ln[1-(Qt/Q∞)2]=-3.0447t+0.0276

0.0 0.2 0.4 0.6 0.8 1.0 1.2 Time/s

Figure 12. Gas diffusion constant after hydraulic slotting under a gas pressure of 0.5 MPa.

413

4.3. Effect of Gas Pressure on the Solid–Fluid Coupling Characteristics of Gas-Bearing Coal

414

Subjected to Hydraulic Slotting. Four key parameters were obtained from the detailed analysis of the entire

415

experiment: the final deformation amount before slotting εbs, ultimate deformation amount εmax, deformation rate vε, and

416

gas diffusion parameter KB, where the deformation rate vε represents the speed of deformation. The most direct

417

parameter representing the effect of slotting is the ultimate deformation amount εmax. Based on this, only the final

418

deformation amount before slotting εbs, ultimate deformation amount εmax, and gas diffusion parameter KB were

419

considered as the statistical indicators to reveal the change rules of the coal–gas interaction under different initial gas

420

pressures.

421

4.3.1. Effect of Gas Pressure on the Final Deformation Amount Before Slotting. The time-varying curves of

422

vertical strain and parallel strain under the gas pressures of 1 MPa, 1.5 MPa, and 2 MPa are analyzed. The final

423

deformation amount before slotting in the vertical and parallel directions at the aforementioned gas pressures was derived,

424

and then the final deformation amount εbs was obtained and plotted in Figure 13(a). It can be seen from Figure 13(a) that,

425

with the increase of gas pressure, the final deformation amount before slotting gradually increases. The quantitative

426

relationship between the final deformation amount and the gas pressure is obtained by fitting using the power function.

427

The final deformation amount before slotting is mainly composed of three parts: shrinkage deformation due to vacuum

428

pumping, adsorption-induced expansion deformation, and compression deformation due to loading. Shrinkage

429

deformation due to vacuum pumping is not affected by the gas pressure. With the increase of the gas pressure, both the

430

adsorption-induced expansion deformation and compression deformation due to loading increase. Compared with the

431

compression deformation due to loading, the adsorption-induced expansion deformation is relatively small. Therefore,

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432

the final deformation amount before slotting gradually increases.

433

4.3.2. Effect of Gas Pressure on the Ultimate Deformation Amount. The vertical strain and parallel strain at the

434

adsorption and desorption stages were extracted from the time-varying curves of the entire curves of vertical strain and

435

parallel strains under gas pressures of 1 MPa, 1.5 MPa, and 2 MPa. The scatter plot was drawn and fitted with the power

436

function. The results are shown in Figures 13(b-c). It can be seen from Figures 13(b-c) that, for both the adsorption and

437

desorption stages, the absolute value of the ultimate deformation amount in the vertical direction is larger than that in the

438

parallel direction, which indicates that the adsorption-induced expansion and desorption-induced shrinkage have a certain

439

anisotropy. In addition, the absolute values of the parallel and vertical ultimate deformation amounts at the desorption

440

stage are smaller than those at the adsorption stage, which may be because the irreversible property exists during

441

adsorption and desorption. Even if the coal is subjected to the desorption-enhancing measure, the ultimate deformation

442

amount cannot be fully recovered.

444

under the gas pressures of 1 MPa, 1.5 MPa, and 2 MPa were derived, linear fitting between ln[1-(Qt/Q∞)2] and t was

445

performed, and then the gas diffusion parameters under different gas pressures were obtained. The quantitative

446

relationship between the gas pressure and the gas diffusion parameter KB is obtained by fitting and shown in Figure

447

13(d). It can be seen from Figure 13(d) that, with the increase of gas pressure, the gas diffusion parameter increases

448

exponentially. This is mainly because, the greater the gas pressure, the greater the gas pressure gradient, the more

449

powerful the gas diffusion, and the faster the gas diffusion39-40.

max

bs

10.5 10.0 9.5 9.0 8.5 8.0 7.5 7.0 6.5 6.0 5.5

Ultimate deformation amount ε ×103/µε

4.3.3. Effect of Gas Pressure on the Gas Diffusion Parameter. The time-varying curves of gas desorption

Final deformation amount before slotting ε ×103/µε

443

ε =7791.73p0.36 bs

0.5

1.0 1.5 Gas pressure/MPa

2.0

-1

Parallel direction Vertical direction

-2

ε

Parallel direction Vertical direction

ε

2158.00p0.88

=

vmax

ε 0.5

hmax

-2274.29p0.92

-4 ε

vmax

=

-2707.74p1.02

-5 -6

0.5

1.0 1.5 Gas pressure/MPa

2.0

(b)

1098.39p0.92

=

1.0 1.5 Gas pressure/MPa

2.0

Gas diffusion parameter KB/s-1

max

450

4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5

=

hmax

-3

(a) Ultimate deformation amount ε ×103/µε

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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12 10

KB=5.74p1.03

8 6 4 2

0.5

1.0 1.5 Gas pressure/MPa

(c)

2.0

(d)

451

Figure 13. Effect of gas pressure on the coal-gas interaction property. (a) Effect of gas pressure on the final deformation amount

452

before slotting; (b) Effect of the gas pressure on the ultimate deformation amount at the gas-filling stage; (c) Effect of gas pressure on

453

the ultimate deformation amount at the desorption stage; (d) Effect of gas pressure on the gas diffusion parameter.

454

4.4. Effect of Slot Radius on the Solid–Fluid Coupling Characteristics of Gas-Bearing Coal

455

Subjected to Hydraulic Slotting. Another important parameter that affects the effect of slotting is the slot radius.

456

Compared with the entire coal sample, the slot radius is significantly small. Therefore, it has only a slight effect on the

457

final deformation amount before slotting. Based on this, only the effect of slot radius on the ultimate deformation amount

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Energy & Fuels

458

εmax and gas diffusion parameter KB was discussed in this paper.

459

4.4.1. Effect of Slot Radius on the Ultimate Deformation Amount. The exponential Langmuir model was

460

adopted to fit the time-varying curves of vertical strain and parallel strain at the desorption stage under the slot radiuses

461

of 5 mm, 7.5 mm, 10 mm, and 12.5 mm, respectively, to obtain the ultimate deformation amount under different slot

462

radiuses. Subsequently, the SLogistic1 function was used to obtain the quantitative relationship between the slot radius

463

and ultimate deformation amount. The results are shown in Figure 14(a). The relationships between the slot radius and

464

the ultimate deformation amount in the vertical and parallel directions are as follows:

4360.16 1 + exp  −0.56 ( rs − 6.77 ) 

(4)

2390.82 1 + exp  −0.41( rs − 6.47 ) 

(5)

465

ε v max =

466

ε h max =

467

It can be seen from Figure 14(a) that, for both vertical and parallel directions, the ultimate deformation amount tends

468

to be flat after a rapid increase with the increase of the slot radius, which indicates that the slot radius has the optimal

469

value. When the slot radius is below the optimal value, the effect of the slot radius on the ultimate deformation amount is

470

significant. However, when the slot radius is above the optimal value, the change of the ultimate deformation amount is

471

small with the increase of the slot radius. 4.4.2. Effect of Slot Radius on the Gas Diffusion Parameter. The time-varying curves of gas desorption under

473

the slot radiuses of 5 mm, 7.5 mm, 10 mm and 12.5 mm were derived, linear fitting between ln[1-(Qt/Q∞)2] and t was

474

performed, and then the gas diffusion parameters under different slot radiuses were obtained. The quantitative

475

relationship between the slot radius and the gas diffusion parameter KB is obtained by the fitting using the SLogistic1

476

function, as shown in Figure 14(b). It can be seen from Figure 14(b) that, with the increase of the slot radius, the gas

477

diffusion parameter shows a similar change tendency with the ultimate deformation amount, which may result from the

478

fact that, with the enlargement of the slot radius, the disturbance action is weakened. Under the same gas pressure, the

479

gas pressure gradient decreases, and the diffusion power is weakened.

max

4.5 4.0

Parallel direction Vertical direction

3.5 3.0 2.5 2.0 1.5 1.0 5.0

7.5 10.0 Slot radius/mm

12.5

Gas diffusion parameter KB/s-1

472

Ultimate deformation amount ε ×103/µε

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 21

12 11 10 9 8 7 6 5 5.0

(a)

7.5 10.0 Slot radius/mm

12.5

(b)

480 481

Figure 14. Effect of slot radius on the coal-gas coupling property. (a) Effect of slot radius on the ultimate deformation amount; (b) Effect of slot radius

482

on the gas diffusion parameter.

483

4.5. Guiding Significance of the Investigation on the Gas Pressure and Slot Radius for the Field

484

Test. Gas pressure is a crucial external factor influencing the efficiency of HS-ECBM recovery. As shown in Figure 15,

485

with the increase in the burial depth, the permeability of the coal seam decreases, and the gas pressure increases41-42.

486

Enlightenment can be gained from the aforementioned variation rules that the hydraulic slotting is necessary for the

487

permeability enhancement of the deep coal seam to significantly improve the CBM recovery efficiency. Furthermore,

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488

deep coal seams are characterized by high gas content, which indicates that their exploitation value is relatively higher.

489

However, according to the analysis in Section 4.3, with the increase in the gas pressure, the deformation of the coal and

490

gas diffusion increase, which may result in two issues: the effect of hydraulic slotting becomes better, but the problem of

491

strong borehole spray may occur23. To solve the above problem, safety protection is necessary when hydraulic slotting is

492

used in the deep coal seams21. 100

8

10

Gas pressure/MPa

Permeability/10-15m2

1 0.1 0.01 0.001

Measured value of gas pressure Linear fitting

6 4 2 0

0

400

800

1200

1600

0

200

Burial depth/m

400

600

800

Burial depth/m

(a)

(b)

493 494

Figure 15. Variation in permeability of the coal seam and gas pressure with the burial depth. (a) Variation in permeability of the coal seam with the

495

burial depth; (b) Variation in gas pressure with the burial depth.

496

Slot radius is a crucial internal factor influencing the efficiency of HS-ECBM recovery. A larger slot radius can

497

produce a larger disturbance range, which can improve the effect of HS-ECBM recovery. However, the efficiency of the

498

construction of the slotted borehole may be the more reasonable indictor for evaluating the efficiency of HS-ECBM

499

recovery. Based on stress evolution of the coal around the slot under different slot radiuses, Yang43 obtained the variation

500

rules of an equivalent borehole radius with the borehole radius under various rates of stress drop (Figure 16). It can be

501

seen from Figure 16 that the slot radius has the optimal value, which is consistent with the conclusion obtained in Section

502

4.4. Enlightenment can be gained from the above conclusion that it is inadvisable to improve the efficiency of HS-ECBM

503

recovery by blindly enlarging the slot radius. A better choice is the formation of the fracture network by drilling

504

multi-boreholes44. 7 Equivalent borehole radius/m

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

5% 10% 20% 30% Rate of 40% stress drop 50% 60% 70%

6 5 4 3 2 1 0 0.1

0.2

0.3 0.4 0.5 Slot radius/m

0.6

0.7

505 506

Figure 16. Variation in the equivalent borehole radius with the borehole radius under various rates of stress drop43.

507

5. CONCLUSIONS

508

In this paper, a fluid–solid coupling experimental system of gas-bearing coal subjected to hydraulic slotting was

509

established. The fluid–solid coupling property of gas-bearing coal subjected to hydraulic slotting was revealed using the

510

established experimental system. Meanwhile, indicators used to describe the process of hydraulic slotting were derived,

511

and the influencing factors affecting the process of hydraulic slotting were analyzed using the aforementioned indicators.

512

During the experiment, the gas pressure response of the monitoring points in the coal sample shows different

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Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

513

characteristics at different stages: at the vacuum-pumping stage, the gas pressure rapidly decreases to the stable value. At

514

the gas-filling stage, the gas pressure tends to be flat after an approximatively linear increase. For every loading step at

515

the confining pressure-loading stage, the gas pressure slowly decreases after a sudden rise. With the increase of the

516

loading step, the change magnitude of the gas pressure decreases. At the slotting stage, the gas pressure tortuously

517

increases, rapidly drops, and then tends towards a stable value. At the desorption stage, the gas pressure tends to be stable

518

after the rapid decrease, and it presents the characteristics of the exponential function. Corresponding to the change trend

519

of the gas pressure, the vertical strain and parallel strain show the five-stage change characteristics, i.e., contraction

520

deformation due to vacuum pumping, swelling deformation due to methane adsorption, compression deformation due to

521

loading, relaxation due to slotting, and shrinkage deformation due to desorption.

522

The final deformation amount before slotting, ultimate deformation amount, and gas diffusion parameter were

523

adopted to describe the coal–gas coupling characteristics. With the increase of gas pressure, the final deformation amount

524

before slotting gradually increases. For both adsorption stage and desorption stage, the absolute value of the ultimate

525

deformation amount in the vertical direction is larger than that in the parallel direction. In addition, the absolute values of

526

the parallel and vertical ultimate deformation amounts at the desorption stage are smaller than those at the adsorption

527

stage. With the increase of gas pressure, the gas diffusion parameter increases exponentially. The ultimate deformation

528

amounts in both the vertical and parallel directions tend to be flat after a rapid increase with the increase of the slot radius,

529

which indicates that the slot radius has the optimal value. With the increase of the slot radius, the gas diffusion parameter

530

shows a similar change tendency with the ultimate deformation amount.

531

To solve the problem of strong borehole spray encountered in the process of hydraulic slotting in the deep coal

532

seams, safety protection measures should be adopted. Moreover, the efficiency of HS-ECBM recovery can be improved

533

through the formation of the fracture network by drilling multi-boreholes instead of blindly enlarging the slot radius.

534



535

Corresponding Author

536

*Tel: +8617783372719. E-mail: [email protected] (Q. Zou).

537

Notes

538

The authors declare no competing financial interest.

539



540

This work is financially supported by the State Key Research Development Program of China (Grant

541

No.2017YFC080206), the National Natural Science Foundation of China (Grant No. 51704046), and the Fundamental

542

Research Funds for the Central Universities (Project No.106112017CDJXY240001), which are gratefully acknowledged.

543

The authors thank K Anand Kumar for editing this paper.

544



545

(1) Moore, T.A. Coalbed methane: A review. Int J Coal Geol. 2012, 101, 36-81.

546

(2) Wang, L.; Liu, S.; Cheng, Y.; Yin, G.; Zhang, D.; Guo, P. Reservoir reconstruction technologies for coalbed methane

547 548 549

AUTHOR INFORMATION

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