Abstract
Large diameter borehole drilling in fractured soft coal seam may lead to problems such as drilling blockage, perforation, and hole collapse. The protective screen pipe in the drilling hole can support the damaged coal, prevent the drilling blockage, and improve the coal permeability. The mathematical model of gas drainage by large diameter borehole in fractured soft coal seam was established. Taking the 3205 working face in Shanxi Fenxi Zhongxing Coal Mine as the background, the numerical simulation was carried out by importing the mathematical model into COMSOL Multi-physics software to study the gas migration law around large boreholes with protective screen pipe in fractured soft coal seam. The results show that the gas flow velocity in section A of the borehole and pipe is between 0 and 0.25 m/s, and the gas flow velocity in the borehole is smaller than that in the pipe and screen hole. The gas velocity in the borehole is lower than that in the protective screen pipe. In the large diameter borehole, the protective screen pipe can support the collapsed coal and prevent the borehole blockage. The free gas in the borehole can be quickly extracted out through the screen holes, which ensures the gas extraction efficiency. The results provide a guidance for promotion and application of the technology of large diameter borehole with protective screen pipe in field.
1. Introduction
The main component of coal mine gas is methane (CH4). As an unconventional natural gas, methane is a kind of clean energy. Coal mine gas also causes gas accidents such as coal and gas outbursts and gas explosion.1 The coal and gas outburst can destroy the roadway facilities, destroy the mine ventilation system, and may even cause serious accidents such as gas explosion. There are 22 accidents with more than 100 deaths in China’s coal mines, and 20 times are gas accidents. In China, 95% of coal mines are underground mining, while high gas mines and coal and gas outburst mines account for 48%. The outburst disasters of China are the most serious in the world. Carrying out gas extraction is the key technology to prevent and control mine gas accidents.2 Several gas extraction enhancing methods have been proposed to improve the gas flow rate and reduce the gas pressure in coal seam, such as CO2 or gas mixture injection enhanced CH4 recovery,3,4 acid injection for permeability improvement,5 hydraulic flushing,6 hydraulic fracturing,7−9 etc,. The large-diameter drilling expands the contact area between the negative pressure of gas extraction and the coal seam.10 At the same time, there will be areas of increased permeability caused by crack development around the drilling hole. These all contribute to improve the gas extraction. However, large-diameter drilling in soft coal seams is very difficult and prone to problems such as hole collapse and perforation.
Fractured soft coal seams are often developed in coal and gas outburst mines or high gas mines in China. Under the condition of soft coal seams, coal mass is easy to fall off the borehole wall, and even problems such as borehole blockage and hole collapse occur. The drilling technology of borehole construction for gas extraction in soft coal seam was developed to provide technical support for mine safety production.11 The air-operated drilling technology and equipment of directional borehole along the layer were developed for the requirement of gas extraction in the mining or excavation face in soft coal seams.12 After that, the air composite directional drilling technology and equipment are proposed to achieve the advanced regional pre-extraction for gas control in soft coal seams, which plays an obvious guiding role in field application.13 By using composite directional and slag discharge technology, a technical scheme of directional drilling in soft coal seams was proposed, which provides a new technical means for progressive gas extraction.14 The advantages of the hydraulic fracturing technology and directional drilling technology were combined to form the roof comb-hole hydraulic fracturing technology, which proves good applicability in the field of gas enhanced extraction in soft coal seams.15 Numerical simulation on the stability of borehole wall was carried out to estimate the mechanical parameters of soft coal seams by Hoek–Brown criterion, and reveal the stress and displacement distribution around the borehole wall.16 A directional drilling technology with gas dynamic screw drill was developed and applied in soft coal seams.17,18 The grouting technology can enhance the strength of soft coal and prevent borehole col-lapse by detecting the strength and structure of coal rock mass, which may promote the development of gas drainage in soft coal seams.19,20 In addition, numerous scholars have conducted research on parameters of the stress, deformation, damage in coal seams after drilling. The influence of large diameter borehole on the strength of surrounding rock was analyzed by numerical simulation, and the strength of surrounding rock after drilling the pressure relief borehole was obtained.21,22 Gas extraction using large diameter borehole was also carried out to control spontaneous combustion of residual coal in goaf.23 The above research studies are mainly focused on the change in coal strength and gas migration in coal seams under the condition of large diameter boreholes, but fail to research the whole process of gas migration from coal seam to borehole under the condition of protective screen pipe.
To reveal the gas migration from coal seam to borehole under the condition of protective screen pipe, a mathematical model for gas extraction in soft coal seams will be established assuming that the coal seam is a dual pore structure with matrix and fractures. Taking the 3205 working face of Zhongxing Coal Mine as the background, the whole process of gas migration from coal seam to borehole wall, then to borehole space through the protective screen pipe will be simulated by using COMSOL Multiphysics software. This will provide reference for improving the efficiency of gas extraction along coal seam in broken soft coal seams.
2. Mathematical Model of Borehole Gas Extraction in Broken Soft Coal Seams
Gas is initially in a dynamic equilibrium state of adsorption and desorption. The pore gas pressure in the matrix is equal to the fracture gas pressure. When the equilibrium state is broken due to extraction, the adsorbed gas is desorbed and transported to the fracture system under the action of the concentration gradient. The mass conservation equation of gas in the coal matrix is24
 |
1 |
where pfg is the gas pressure in the fracture, MPa; τ is the gas desorption time, s; φm is the matrix porosity; ρg is the density of gas, kg/m3; Vsg is the adsorbed gas content, m3/kg; ρs is the density of the coal skeleton, kg/m3; ρgs is the density of gas in the standard state, kg/m3; Mg is the gas molar mass, kg/mol; R is the gas molar constant, J/(mol·K); and Tt is the temperature of coal seam, K.
The volume of adsorbed gas in the coal matrix can be expressed by the Langmuir equation25
 |
2 |
where VL is Langmuir volume constant, m3/kg; PL is the Langmuir pressure constant, Pa; and pm is the matrix gas pressure, MPa.
Bringing eq 2 into eq 1, the gas migration equation in the coal matrix can be obtained
 |
3 |
The coal matrix provides a mass source for the fracture, and the gas phase mass conservation equation of the fracture system is26
 |
4 |
where φf is the fracture porosity; k is the fracture permeability, m2; μg is the gas phase dynamic viscosity, Pa·s; and b1 is the slippage factor, Pa.
Coal is a dual porosity medium, and its mechanical properties are affected by pores and fractures. The total strain of coal is the sum of the strain caused by the stress and the gas pressure and the strain caused by gas adsorption and desorption. The modified Navier equation considering pore pressure, temperature variation, and adsorption is derived, the stress field governing equation27
 |
5 |
where αm and αf are the Biot’s effective stress coefficients corresponding to pores and fractures, respectively; εa is the strain of skeleton adsorption gas; and pf is the fluid pressure in fracture, MPa.
Based on the theory of damage mechanics, the elastic modulus of coal decreases with the occurrence of damage. The elastic modulus of coal can be expressed as28
 |
6 |
where E and E0 are the elastic modulus of post-damage and pre-damage coal, GPa; and D is the damage variable.
The maximum tensile stress criterion and Mohr–Coulombic criterion are used to determine whether tensile and shear damage occurs after the coal is subjected to force, which can be expressed as26
 |
7 |
where σ1 is the maximum principal stress, MPa; σ3 is the minimum principal stress, MPa; σt and σc are uniaxial tensile and uniaxial compressive strength of coal respectively, MPa; θ is the internal friction angle of coal, °; and F1 and F2 are the threshold functions of tensile and shear damage, respectively.
During the process of damage calculation, the maximum tensile stress criterion is first used to judge whether the coal is damaged under tensile stress. If no damage occurs, the Mohr–Coulombic criterion is then used to judge whether the coal is damaged under shear stress.
The damage variable of the coal is expressed as follows29
 |
8 |
where εt is the maximum principal strain of coal; εc is the minimum principal strain of coal; εt0 represents the ultimate tensile strain of coal when tensile damage occurs in coal; and εc0 represents the ultimate compressive strain of coal when shear damage occurs in coal.
Considering the pore pressure and damage evolution, the permeability model of coal in damage stage can be obtained30,31
 |
9 |
By combining eqs 3–5 and 9, the fluid–solid coupling equation of gas migration in coal seams is obtained.
The gas in the borehole is in a free space flow state, and the gas migration in the borehole satisfies the Navier–Stokes equation
 |
10 |
where u is the gas flow velocity in the free flow state, m/s; p is the gas pressure in borehole, Pa; T is the transpose symbol; μ is the gas dynamic viscosity, Pa·s; and f is the gas volume force, Pa/m.
3. Simulation of Large Diameter Borehole with Protective Screen Pipe in Soft Coal Seams
3.1. Engineering Background
Shanxi Fenxi Zhongxing Coal Mine is located in Jiaocheng County, Shanxi Province. It currently mines no. 2 and no. 4 + 5 coal seams with a production capacity of 3.0 Mt/a. It was identified as an outburst mine by the Chongqing Research Institute of China Coal Science and Industry Group in 2019, and no. 2 and no. 4 + 5 coal seams are outburst coal seams. In the 3205 working face of no. 2 coal seam, the test is located in the north wing of the third mining area. The east is 3203 working face, the south is the main return air roadway, the main track roadway and belt roadway are present in the third mining area, and the west is 3207 working face. The designed length of the roadway is 1625 m, the length that can be mined is 1597 m, and the inclined length is 180 m. The coal thickness is 1.8–2.3 m, with an average of 2.1 m. The no. 2 coal seam is a medium-thick coal seam. The coal seam structure is simple, and the coal seam dip angle is 2–10°, with an average of 6°. In order to improve the efficiency of gas extraction, large diameter boreholes were used to extract coal seam gas. A high-strength hollow spiral drill pipe with a diameter of 300 mm was developed. The diameter of the inner hole was set to 110 mm, which ensures that the protective screen pipe with large diameter can be smoothly placed to the bottom of the borehole in the inner hole, as shown in Figure 1.
Figure 1.
Schematic diagram for large-diameter drilling with full-length screen pipe.
The “one-word” type discarding drill bit was developed, and the center of the traditional drill bit was made into a “one-word” style detachable small drill bit, which can realize the pipe jacking detachable drill bit and the screen pipe while drilling. The sealing process was optimized, using two plugging and one injection pressure grouting sealing technology. Through theoretical calculation and field measurements, the sealing length of large diameter boreholes was determined, and the grouting holes around the boreholes were used to strengthen the sealing of the fracture belt around the large diameter boreholes, which effectively ensured the sealing quality.
The main materials used for the two plugging and one injection sealing technology are mainly composed of sealing sleeves, screen pipes, grouting pipes, exhaust pipes, Malisan, and so forth. After the drilling construction is completed and the drill pipe is withdrawn, 2–3 packages of Malisan are fixed at a certain position in the front section of the sealing casing. After the Malisan is unpacked and evenly mixed, the sealing casing is immediately inserted into the expected position of the hole according to the required sealing length. At this time, grouting pipes and exhaust pipes are inserted between the sealing casing and the hole wall at the end of the hole. At this time, 2–3 packages of Malisan are inserted at the end of the hole to prevent Malisan from expanding and overflowing outside the hole. After inserting Malisan, a woven bag or cotton yarn can be used to block the hole opening. After Malisan expands, foams, and solidifies, the slurry mixed evenly with water, cement, and special sealing agent can be injected into the hole in proportion until the exhaust pipe returns slurry, indicating that the hole is fully filled. At this time, grouting can be stopped, and the sieve tube connection can be sequentially sent into the sealing sleeve until the bottom of the hole. After the cement slurry solidifies, the hole can be connected to the gas extraction system for gas extraction.
3.2. Physical Model and Definite Conditions
According to the geological conditions and coal seams, roofs and floors conditions of 3205 working face of Shanxi Fenxi Zhongxing Coal Mine, the gas extraction research area of large diameter borehole in soft coal seam is constructed by numerical simulation, as shown in Figure 2. The size of the research area is 5 m × 2 m × 1 m. The sliding boundary condition is adopted for the bottom plate boundary and the surrounding boundary of the model, and the gravity load of the overburden rock is 15 MPa applied on the top. The area is 5 m along the axis of the roadway and 2 m in the thickness direction of the coal seam. The boreholes and protective screen pipes are arranged in the central position of the research area. According to the scope of the research area, the geometric model of gas extraction law simulation of large diameter borehole in broken soft coal seam under the condition of protective screen pipe is shown in Figure 3. The diameter of the protective screen pipe is 90 mm, the wall thickness is 10 mm, the diameter of the screen hole on the protective screen pipe is 10 mm, the spacing of each row is 0.2 m, the length of the protective screen pipe is about 1.5 m, and the single PVC protective screen pipe requires more than 20 holes. The protective screen pipe is connected by plug or wire buckle and will be constructed underground.
Figure 2.
Studied area of gas extraction from soft coal seam using large borehole with the protective screen pipe.
Figure 3.
Physical geometry model of numerical simulation.
Because the row spacing of the screen hole is 0.2 m, according to the symmetry of the geometric model, the model thickness of the numerical simulation is set to 0.2 m to reduce the computer workload. The geometric model of the numerical simulation will ignore the protective screen pipe structure itself and focus on the spatial evolution process of the gas migration flow field after setting the protective screen pipe.
3.3. Simulation Results and Analysis
3.3.1. Stress Field Distribution
Through numerical simulation, the stress field distribution around the large diameter borehole in the broken soft coal seam under protective screen pipe condition is obtained, as shown in Figure 4. The supporting effect of the supporting pipe belongs to passive support, and it cannot cause the obvious redistribution of the stress field in the coal body, which further proves that the simulation results can be used to explain the basic law of coal seam methane extraction by large diameter boreholes in broken soft coal seam under the condition of the protective screen pipe.
Figure 4.
Stress field distribution around large bore holes in fractured soft coal seam.
3.3.2. Variation of Gas Pressure
The distribution law of gas pressure in the process of large diameter borehole extraction in broken soft coal seam under the condition of setting the protective screen pipe, as shown in Figure 5. After gas extraction for 5 days, the gas pressure in the coal around the borehole decreases rapidly, and the rapid decrease area of gas pressure is an irregular geometry. The decrease range in the horizontal direction is about 0.4–0.5 m, and the decrease range in the vertical direction is 0.2–0.35 m. The above law is mainly controlled by the range of damaged coal body with a sharp increase in permeability around the borehole, that is the stress reduction area in Figure 4. As the extraction time increases, the velocity of gas pressure reduction gradually slows down, mainly expanding outward along the rapid reduction area of gas pressure formed in the early stage.
Figure 5.
Pressure distribution of gas extraction from fractured soft coal seam with large borehole with the protective screen pipe.
To facilitate the analysis of gas migration in boreholes, pipes, and screen holes, different sections of the geometric model are intercepted in the model, as shown in Figure 6. Section A is located in the middle of the geometric model in Figure 3, and its normal direction is parallel to the y-axis, that is, y = 0.1 m plane, while section B is located at 1/4 of the geometric model in Figure 6, and its normal direction is parallel to the y-axis, that is, y = 0.05 m plane.
Figure 6.
Different cross section positions of large borehole with the protective screen pipe.
The turbulent kinetic energy distribution of the gas in borehole and hole protective screen pipe is shown in Figure 7. It can be seen that the turbulent kinetic energy in the coal seam in the borehole is small (average about 5 × 10–4 m2/s2), while the turbulent kinetic energy of the gas in the protective screen pipe, especially in the screen hole, is large, and the maximum value is about 3.6 × 10–3 m2/s2. It shows that the gas flow kinetic energy of the protective screen pipe and the screen hole is larger due to the influence of the negative pressure of the extraction. The kinetic energy in the pipe will be transmitted to the borehole through the screen hole.
Figure 7.
Turbulent kinetic energy distribution of gas in borehole with the protective screen pipe.
The distribution of gas pressure in boreholes and protective screen pipes in sections A and B is shown in Figure 8. It can be found that the gas pressure in the borehole, the protective screen pipe, and the screen hole is close to the negative pressure of the extraction (absolute pressure is 0.09 MPa). In general, the gas pressure in the protective screen pipe is slightly lower than that in the borehole, and the screen hole plays a good transition role. Gas is turbulent in the free space of boreholes and protective screen pipes. Compared with gas migration in coal seams, its migration speed is faster, and the pressure drop potential energy required for movement is smaller.
Figure 8.
Gas pressure in boreholes and protective screen pipes.
3.3.3. Gas Migration Law
The streamline distribution of gas velocity field in boreholes and protective screen pipes in section A and section B is shown in Figure 9. In section A, there are four screen holes. The gas from the coal seam is collected in the free space of the borehole and then flows into the protective screen pipe through the screen hole. Finally, under the action of the negative pressure of the extraction, it enters the underground extraction system pipeline. The flow line of the gas velocity field in the borehole on section A points to four screen holes, collects to the center of the pipe through the flow line of the screen hole velocity field, and produces the eddy current phenomenon of convection. There is no screen holes in section B, and gas flows in the free space of borehole and the space of protective screen pipe, which has no direct influence on each other.
Figure 9.
Gas velocity field in borehole and protective screen pipe.
The gas flow velocity nephogram on the cross section A of the borehole and the protection pipe after different extraction time is shown in Figure 10a–d. It can be found that the gas flow velocity is between 0 and 0.25 m/s, and the gas velocity in the borehole is the smallest, the gas velocity in the protective screen pipe is the second, and the gas velocity in the screen hole is the biggest. With the increase of extraction time, the speed of gas migration gradually decreases. When the extraction is 5 days, the maximum gas flow velocity in the screen is 0.202 m/s, and when the extraction is 30 days, 60 days, and 120 days, the maximum flow velocity in the screen is 0.083, 0.054, and 0.034 m/s.
Figure 10.
Gas flow velocity in borehole and protective screen pipe (section A).
After different extraction time, the gas flow velocity on the cross section B of the borehole and the protective screen pipe is shown in Figure 11a–d. There is no screen hole distribution on section B, and the gas flow velocity is between 0 and 0.03 m/s. It can be intuitively seen that the gas flow velocity in the borehole is less than the gas flow velocity in the protective screen pipe. The gas velocity is the fastest near the center of the protective screen pipe, and the gas velocity decreases at the edge of the protective screen pipe. With the increase of extraction time, the speed of gas migration gradually decreases. When the extraction is 5 days, the maximum gas flow velocity in the center of the protective screen pipe is 0.00239 m/s, and when the extraction is 30, 60, and 120 days, the maximum flow velocity in the screen is 0.00216, 0.00139, and 0.00103 m/s.
Figure 11.
Gas flow velocity in borehole and protective screen pipe (section B).
The curve of gas velocity with time at the position of large diameter borehole wall is shown in Figure 12. The gas flow velocity in the borehole is roughly divided into three stages: In the first stage, at the initial stage of extraction (0–7 days), the gas flow velocity is stable at 2.47 × 10–4 to 2.63 × 10–4 m/s, which is controlled by the rapid desorption and seepage of gas in the coal body around the borehole. After that, the change of flow velocity entered the second stage (7–30 days), the gas in the damaged area was gradually exhausted, and the gas migration speed decreased rapidly, from 2.47 × 10–4 m/s to 8.97 × 10–5 m/s, with a decrease of 63.6%. In the third stage (more than 30 days), the decrease of gas flow velocity slowed down and finally stabilized at about 3.5 × 10–5 m/s at 120 days.
Figure 12.
Gas velocity varies with time at the hole wall of large bore holes.
The curve of gas flow velocity at the center of the screen hole with time is shown in Figure 13. Similar to the position of the hole wall of the large diameter borehole, the gas flow velocity is also divided into three stages: in the first stage, in the initial stage of extraction (0–7 days), gas from the free space of the borehole gathers to the screen hole, and the gas flow velocity of the screen hole is between 0.192 m/s and 0.2 m/s. In the second stage (7–30 days), the gas migration velocity decreased rapidly from 0.192 to 0.083 m/s, with a decrease of 56.8%. In the third stage (more than 30 days), the decrease of gas flow velocity slowed down. At 120 days, the overall reduction was 83%.
Figure 13.
Variation of gas flow velocity in coal seam at borehole wall of large borehole.
According to the numerical simulation results, compared with the traditional 94 mm diameter extraction borehole, the extraction efficiency of 300 mm large diameter borehole will be increased by 2–3 times. Setting a protective screen pipe in a large diameter borehole can support the coal body that has fallen and destroyed and prevent borehole blockage. At the same time, due to the existence of a large number of screen holes in the pipe wall, the gas in the free space of the borehole can be quickly extracted, thereby ensuring the gas extraction efficiency of large diameter boreholes. Arranging large diameter boreholes with protective screen pipes in broken soft coal seams can greatly improve the extraction efficiency.
4. Field Application
The 3205 working face of no. 2 coal seam where the test is located is located in the north wing of the third mining area. The east is 3203 working face, the south is the main return air roadway, the main track roadway, and the belt roadway in the third mining area, and the west is 3207 working face. The test roadway is the transportation roadway of 3205 working face. According to the previous data and the actual investigation of the underground site, the borehole spacing is determined to be 6 m. According to the determined scheme, three groups of boreholes are successively constructed along the direction of the roadway to the mining face from the 3205 transportation roadway at 300 m away from the opening position. In the first group (1#–5#), five boreholes with a general aperture of 133 mm were constructed, and the screen pipes were set and sealed by an ordinary process. In the second group (6#–10#), five boreholes with large diameter of 300 mm were constructed, and the screen pipes were set and sealed by the ordinary process. In the third group (11#–15#), five boreholes with large diameter of 300 mm were constructed, and the full-length screen pipe was used to set and seal. The diameter of the screen pipe was 90 mm. The length of the first and second group using the ordinary process is generally below 30 m, while the third group of boreholes using the full-length screen pipe can be set to more than 100 m as needed, as shown in Figure 14. After the hole is sealed, the extraction pipeline is connected, and the calculation begins on the day when the hole is sealed. The monitoring data are recorded every 20 days for 120 days. The monitoring results are shown in Figure 15. The gas flow rate is the sum of each group boreholes.
Figure 14.
Field construction of large diameter boreholes.
Figure 15.
Monitored pure CH4 flow rate of gas extraction from boreholes.
Comparing the three groups of boreholes, the gas flow rate of the third group of boreholes is largest with fastest decreasing speed of the velocity, followed by that of the second group, while the gas flow rate of the first group is the lowest. The initial gas rate of the three groups is 0.0156, 0.0648, and 0.0839 m3/min, respectively. This implies that the gas flow rate of the large diameter borehole is larger, and the declining speed is faster than that of small diameter borehole. It indicates that the large diameter borehole can produce damage zone around the borehole resulting in greater permeability in the coal seam. The greater the permeability, the better the extraction effect. The protective screen pipes in large diameter boreholes can support the collapsed coal body and prevent borehole blockage. For boreholes with the same diameter, the gas flow rate and gas concentration of boreholes with full-length screen pipe have been significantly improved. Overall, the large diameter borehole with full-length screen pipe has the highest efficiency of gas extraction.
This paper adopts methods of numerical simulation and onsite testing to conduct research, and the results of these two methods are mutually verified, indicating that the large diameter borehole with full-length screen pipe technology has broad application prospects in soft coal seams. However, the influences of different pipe diameters and screen hole diameters on the gas extraction efficiency were not studied, which will limit the selection of the optimal screen pipe. In the future, attention should be paid to conduct research in this area.
5. Conclusions
The fluid–solid coupling mathematical model of gas extraction from large diameter boreholes in soft coal seam under the condition of protective screen pipe was constructed, which was used to simulate the gas extraction of large diameter boreholes with protective screen pipe in soft coal seam. Conclusions can be drawn:
-
(1)
The gas pressure in the protective screen pipe is slightly lower than that in the borehole. The gas is turbulent in the free space of borehole and protective screen pipe. Compared with gas migration in coal seam, its migration velocity is faster, and the pressure drop potential energy required for movement is smaller. The gas velocity in the borehole < the gas velocity in the protective screen pipe < the gas velocity in the screen hole.
-
(2)
The gas flow velocity in the borehole is roughly divided into three stages: the first stage, in the early stage of extraction (0–7 days), is controlled by the rapid desorption and seepage of gas in the coal mass in the damage area around the borehole. In the second stage (7–30 days), the gas in the damage area is gradually depleted, and the gas migration velocity decreases rapidly. In the third stage (>30 days), the decrease of gas flow velocity slowed down and finally stabilized at about 3.5 × 10–5 m/s at 120 days.
-
(3)
In the field test, the large diameter borehole can produce damage zone around the borehole resulting in greater permeability in the coal seam, as well as the better effect of the gas extraction. The protective screen pipes in large diameter boreholes can support the collapsed coal body and prevent borehole blockage. The gas extraction flow and concentration of boreholes using the full-length protective screen pipe technology have been significantly improved.
Acknowledgments
The author(s) would like to thank all editors and anonymous reviewers for their comments and suggestions. This research was funded by the National Science and Technology Major Project of China (grant no. 2016ZX05067-005-002).
Glossary
Nomenclature
- pfg
gas pressure in the fracture
- τ
gas desorption time
- φm
matrix porosity
- ρg
density of gas
- Vsg
adsorbed gas content
- ρs
density of coal skeleton
- ρgs
density of gas in the standard state
- Mg
gas molar mass
- R
gas molar constant
- Tt
temperature of coal seam
- VL
Langmuir volume constant
- PL
Langmuir pressure constant
- pm
matrix gas pressure
- φf
fracture porosity
- k
fracture permeability
- μg
as phase dynamic viscosity
- b1
slippage factor
- αm
Biot’s effective stress coefficients corresponding to pores
- αf
Biot’s effective stress coefficients corresponding to fractures
- εa
strain of skeleton adsorption gas
- pf
fluid pressure in fracture
- E
elastic modulus of post-damage coal
- E0
elastic modulus of pre-damage coal
- D
damage variable
- σ1
maximum principal stress
- σ3
minimum principal stress
- σt
uniaxial tensile strength of coal
- σc
uniaxial compressive strength of coal
- θ
internal friction angle of coal
- F1
threshold function of tensile damage
- F2
threshold function of shear damage
- εt
maximum principal strain of coal
- εc
minimum principal strain of coal
- εt0
ultimate tensile strain of coal
- εc0
ultimate compressive strain of coal
- u
gas flow velocity in the free flow state
- p
gas pressure in borehole
- T
transpose symbol
- μ
gas dynamic viscosity
- f
gas volume force
The authors declare no competing financial interest.
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