# Experimental Study on the Effect of Gas Pressure on Ultrasonic Velocity and Anisotropy of Anthracite

Authors: Bo Wang; Jialin Hao; Shengdong Liu; Fubao Zhou; Zhendong Zhang; Heng Zhang; Huachao Sun
Journal: Geofluids
 (2019)

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## Abstract

To research the elasticity of gas-bearing coal fluid-solid two-phase medium with seismic exploration method is critical to the prevention of gas disasters. To investigate the elasticity, the ultrasonic elastic test of anthracite samples under different gas pressures was carried out and the ultrasonic velocity and anisotropy of the samples were analyzed in this study. The results show that the velocities (P- and S-waves) decrease in turn in the strike, dip, and vertical directions. However, a negative linear correlation is proved to exist between ultrasonic velocity and gas pressure. With the increase of gas pressure, the anisotropy degree of both the P-wave and the S-wave of the samples decreases but the declining degree of the P-wave is greater than that of the S-wave. In addition, the decrease in velocity and the anisotropy degree of the P-wave is greater than that of the S-wave, indicating that the P-wave is more sensitive to gas pressure changes in terms of velocity and its anisotropy degree.


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## Body

## 1. Introduction

The condition of complex multiphase medium, which is composed of the material composition and structure of coal and fluid gas, is the bottleneck for the mechanism study of coal and the prevention of gas disasters [1]. So far, the information of material composition and structure of coal is obtained mainly through in situ coal seam drilling. However, drilling is costly, laborious, and time-consuming, and thus, it is urgent to analyze the composition and structure characteristics of coal from small-scale laboratory physical experiments. The coal ultrasonic testing technology, thanks to its good orientation, strong directivity, and outstanding penetration ability [2], is used to measure the elastic parameters of coal samples [3]. Although there is a great difference between the ultrasonic wave and the actual seismic frequency band, ultrasonic measurement is significant for actual low-frequency seismic exploration [4].In China, when the gas pressure in a coal seam reaches or exceeds 0.74 MPa, the coal seam can be defined as an outburst coal seam and corresponding outburst prevention measures should be taken [5]. For this reason, many scholars have carried out in situ seismic wave tests in coal mines in order to provide guidance for the prevention and control of gas disasters. Their research results showed that the presence of gas would reduce the strength of coal and cause coal seam fracture, which is prone to trigger coal and gas outburst accidents [6–8], and that there is a negative linear correlation between coal seam gas content and single-component seismic wave parameters. Specifically, as the gas pressure increases, the velocities (P- and S-waves) decrease gradually, the inherent dominant frequency of the coal seam decreases, the attenuation coefficient increases, and the quality factor decreases [9–11]. As instructive as the above occurrence rules are, it is still difficult to reveal the mechanism scientifically in that the current researches only focus on single-component seismic data on the single direction. Besides, the complex underground site conditions and various influence factors also increase the complexity of the issue under discussion. Therefore, many scholars have conducted long-term researches on the physical and mechanical properties of coal samples [12–16] and gained some important insights on elasticity. For example, the greater the density of the coal samples is, the larger the velocities (P- and S-waves) become [17]. Under normal temperature and atmospheric pressure conditions, the ultrasonic velocity decreases in turn in the strike direction x, the dip direction y, and the vertical direction z. That is to say, the velocities (P- and S-waves) display azimuthal anisotropy [17, 18]. Moreover, the attenuation of the P-wave is remarkably greater than that of the S-wave with the change of fracture orientation [19, 20].In summary, many researches have been conducted on the variation law of seismic wave parameters of outburst coal through in situ seismic wave test of coal seam but it is difficult to reveal the mechanism scientifically due to the limitation of site conditions and complex influence factors. Some scholars have studied the ultrasonic elastic parameters and anisotropic characteristics of coal samples such as velocity anisotropy, Poisson’s ratio, and attenuation with different degrees of metamorphism under normal temperature and atmospheric pressure conditions through laboratory coal physical experiments. However, the ultrasonic experiments of coal samples are mainly aimed at single-phase solid coal. Considering that gas-bearing coal is a fluid-solid two-phase medium and the limitations of test equipment and conditions, the current related research only focuses on single-phase solid coal and the results are lacking of representativeness and persuasion.The purpose of this paper is to study the influence of fluid gas on the ultrasonic velocity and anisotropy of coal samples. Therefore, the ultrasonic velocity response characteristics of coal samples under different gas pressures are tested and the effect of gas pressure on the ultrasonic anisotropy of coal samples is analyzed. The research results of this paper may provide some guidance for coal and gas disaster prediction.


## 2. Sampling and Experiment

### 2.1. Sample Preparation

The samples in this study were collected at the tunneling face of the Xinjing Coal Mine in the Yangquan coalfield (Figure1). The Yangquan coalfield is one of the most important anthracite coal bases in China. Its annual gas emission accounts for about one-sixth of China’s total gas emission, and most of its coal seams are outburst seams. All the coal samples used in this paper were taken from #8 coal samples, larger than 300 mm in diameter, at the newly exposed tunneling face. They were wrapped and sealed in paper and black plastic bags and then transported to the ground. According to the standards of coal experiments [21], the coal block was processed into cubic coal samples of 50∗50∗50mm3. Then each surface was sanded and leveled with the abrasive paper to avoid secondary damage as much as possible, until the requirements for samples were met. Next, samples were ground, until the nonparallelism of the surfaces on both ends was less than 0.05 mm. Finally, five standard #8 coal samples were processed, as shown in Figure 2.Figure 1
Study area location and detailed stratigraphic column of coal-bearing strata in the Yangquan coalfield.Figure 2
Schematic diagram of coal sample acquisition.In Figure1, x and y denote the two directions parallel to the coal seam and z refers to the direction vertical to the coal seam.The size of coal samples is measured by a vernier caliper, and the density is measured by the drainage method [22]. Ash, moisture, and volatile matter of coal samples could be obtained by industrial analysis of coal [23]. Adsorption constants (a and b) of #8 coal samples were obtained by isothermal adsorption experiment [24]. The basic parameters of coal samples are shown in Table 1.Table 1
Basic parameters of coal samples.
Sample ID
Size (x∗y∗z) (mm3)
ρ (g/mm3)
Mad
Aad
Vdnf
a
b
#8-A
50.02∗50.00∗50.04
1.62
2.00
10.32
10.29
33.73
1.42
#8-B
49.96∗50.04∗50.01
1.60
1.98
10.37
10.25
33.69
1.41
#8-C
49.99∗50.02∗50.02
1.61
1.99
10.37
10.18
33.71
1.42
#8-D
50.05∗49.99∗50.01
1.63
2.01
10.25
10.35
33.77
1.45
#8-E
50.02∗50.03∗49.97
1.59
1.98
10.41
10.20
33.67
1.40


### 2.2. Experimental Apparatus and Experimental Error Analysis

The ultrasound pulse transmission method is used in the experiment [25, 26]. The acoustic signals of coal samples are collected by DB16A multichannel ultrasonic instrument. The sampling frequency is 100 kHz. The velocities (P- and S-waves) of coal samples can be calculated as follows [27, 28]:
(1)VP=LtP−t0,VS=LtS−t0,where VP and VS are the velocities (P- and S-waves), in m/s; L denotes the length of samples, in m; tP, tS are the first arrival time of signals, in s; t0 is the docking time of transducers, in s.Test errors are inevitable due to the experimental method and human factors [16], which may influence the test results. The error calculation is shown as equations 2 and 3:
(2)ΔV=ΔLt−t0+LΔtt−t02+LΔt0t−t02,(3)E=ΔVV×100%,where ΔV denotes the error of velocity, in m/s; t−t0 is the travel time of signals, in s; Δt is the picking error, in s; Δt0 is the error of docking time, in s; L and ΔL are the length and length error of coal samples, in m; E stands for the velocity error.Δt and Δt0 of the ultrasonic speed experiment are set at the value of 0.1 μs based on the sampling interval (0.1 μs). ΔL is the length error, being less than 0.05 mm. For example, the first arrival time of the signals of the coal samples is about 30 μs. The errors in actual measurement also include calibration errors and data reading errors. Therefore, according to equation (3), the velocity errors may change but only by E≤1.2%.


### 2.3. Experimental Procedure

As shown in Figure3, the test is carried out by using the gas-bearing coal ultrasonic test system in the State Key Laboratory of Coal Resources and Safe Mining of China University of Mining and Technology (CUMT). The system can be used to test the ultrasonic velocity of coal under different gas pressure conditions. Then the ultrasonic elastic response and anisotropic characteristics of coal samples under different gas pressure conditions are revealed. In the test, the gas pressure is loaded in an isogradient manner. The specific test procedure is shown as follows.
(1)
The experiment is conducted under normal temperature and atmospheric pressure (298 K, 1 atm)
(2)
To ensure the coupling between the probe and the sample surface, the Shear Gel is applied on the probe surface after the prepared sample is put into the coal clamp and then covered with the top lid
(3)
To check the air tightness of the system, it is observed whether the piezometer reading is changed or not. A vacuum pump is used to vacuum the sealed cylinder block. When the negative pressure in the chamber is stabilized at -0.1 MPa, the vacuum should be stopped. The acoustic signals in thex and y directions and in the z direction under the negative pressure condition are collected by three ultrasonic transducers
(4)
When the vacuum test is finished, the cylinder body is filled slowly with the high-pressure mixture gas (CO260%+N2 40%) instead of CH4 gas in an isogradient manner through the pressure relief valve to a predetermined pressure value (-0.1-1.4 MPa) [29]. This operation can be justified by the fact that according to laboratory safety regulations, the use of CH4 gas is prohibited during the experiment and that the abovementioned mixed gas has similar adsorption effect with CH4 gas [30]. Then the air tightness of the system is checked again. After the gas reaches the adsorption equilibrium and the preset pressure value is maintained for 24 hours, the acoustic signals of the samples under different gas pressures are finally collected. Based on Langmuir isothermal adsorption equation (4) [24], the gas adsorption capacity of coal samples under different pressure equilibrium conditions can be estimated, as shown in Table 2 and Figure 4. It should be mentioned that the pure component isotherm is empirically used to describe an actual binary system, thus neglecting any competitive adsorption of CO2 and N2
(4)Q=a⋅b⋅P1+b⋅P,where Q denotes the gas adsorption capacity of the coal sample, in ml/g; P is the pressure of gas, in MPa; a and b are the adsorption constants of the coal sample.
As can be seen from Figure4, with the increase of gas pressure, the gas adsorption capacity of five coal samples is also increasing gradually, but the rising trend becomes milder in the later phase
(5)
The signals collected are calculated, processed, and analyzed (refer to Section2.2)Figure 3
Ultrasound anisotropy testing system of coal samples (simplified).Table 2
Gas adsorption capacity of coal samples under different gas pressure conditions.
P (MPa)
Q (ml/g)
#8-A
#8-B
#8-C
#8-D
#8-E
-0.1
0
0
0
0
0
0.2
7.46
7.41
7.46
7.59
7.37
0.4
12.22
12.15
12.21
12.40
12.09
0.6
15.52
15.44
15.51
15.71
15.37
0.8
17.94
17.86
17.93
18.14
17.79
1.0
19.79
19.71
19.78
19.99
19.64
1.2
21.26
21.18
21.24
21.45
21.11
1.4
22.44
22.36
22.43
22.62
22.30Figure 4
Deformation curves of isogradient pressurized adsorption and gas adsorption capacity of the coal samples.


## 2.1. Sample Preparation

The samples in this study were collected at the tunneling face of the Xinjing Coal Mine in the Yangquan coalfield (Figure1). The Yangquan coalfield is one of the most important anthracite coal bases in China. Its annual gas emission accounts for about one-sixth of China’s total gas emission, and most of its coal seams are outburst seams. All the coal samples used in this paper were taken from #8 coal samples, larger than 300 mm in diameter, at the newly exposed tunneling face. They were wrapped and sealed in paper and black plastic bags and then transported to the ground. According to the standards of coal experiments [21], the coal block was processed into cubic coal samples of 50∗50∗50mm3. Then each surface was sanded and leveled with the abrasive paper to avoid secondary damage as much as possible, until the requirements for samples were met. Next, samples were ground, until the nonparallelism of the surfaces on both ends was less than 0.05 mm. Finally, five standard #8 coal samples were processed, as shown in Figure 2.Figure 1
Study area location and detailed stratigraphic column of coal-bearing strata in the Yangquan coalfield.Figure 2
Schematic diagram of coal sample acquisition.In Figure1, x and y denote the two directions parallel to the coal seam and z refers to the direction vertical to the coal seam.The size of coal samples is measured by a vernier caliper, and the density is measured by the drainage method [22]. Ash, moisture, and volatile matter of coal samples could be obtained by industrial analysis of coal [23]. Adsorption constants (a and b) of #8 coal samples were obtained by isothermal adsorption experiment [24]. The basic parameters of coal samples are shown in Table 1.Table 1
Basic parameters of coal samples.
Sample ID
Size (x∗y∗z) (mm3)
ρ (g/mm3)
Mad
Aad
Vdnf
a
b
#8-A
50.02∗50.00∗50.04
1.62
2.00
10.32
10.29
33.73
1.42
#8-B
49.96∗50.04∗50.01
1.60
1.98
10.37
10.25
33.69
1.41
#8-C
49.99∗50.02∗50.02
1.61
1.99
10.37
10.18
33.71
1.42
#8-D
50.05∗49.99∗50.01
1.63
2.01
10.25
10.35
33.77
1.45
#8-E
50.02∗50.03∗49.97
1.59
1.98
10.41
10.20
33.67
1.40


## 2.2. Experimental Apparatus and Experimental Error Analysis

The ultrasound pulse transmission method is used in the experiment [25, 26]. The acoustic signals of coal samples are collected by DB16A multichannel ultrasonic instrument. The sampling frequency is 100 kHz. The velocities (P- and S-waves) of coal samples can be calculated as follows [27, 28]:
(1)VP=LtP−t0,VS=LtS−t0,where VP and VS are the velocities (P- and S-waves), in m/s; L denotes the length of samples, in m; tP, tS are the first arrival time of signals, in s; t0 is the docking time of transducers, in s.Test errors are inevitable due to the experimental method and human factors [16], which may influence the test results. The error calculation is shown as equations 2 and 3:
(2)ΔV=ΔLt−t0+LΔtt−t02+LΔt0t−t02,(3)E=ΔVV×100%,where ΔV denotes the error of velocity, in m/s; t−t0 is the travel time of signals, in s; Δt is the picking error, in s; Δt0 is the error of docking time, in s; L and ΔL are the length and length error of coal samples, in m; E stands for the velocity error.Δt and Δt0 of the ultrasonic speed experiment are set at the value of 0.1 μs based on the sampling interval (0.1 μs). ΔL is the length error, being less than 0.05 mm. For example, the first arrival time of the signals of the coal samples is about 30 μs. The errors in actual measurement also include calibration errors and data reading errors. Therefore, according to equation (3), the velocity errors may change but only by E≤1.2%.


## 2.3. Experimental Procedure

As shown in Figure3, the test is carried out by using the gas-bearing coal ultrasonic test system in the State Key Laboratory of Coal Resources and Safe Mining of China University of Mining and Technology (CUMT). The system can be used to test the ultrasonic velocity of coal under different gas pressure conditions. Then the ultrasonic elastic response and anisotropic characteristics of coal samples under different gas pressure conditions are revealed. In the test, the gas pressure is loaded in an isogradient manner. The specific test procedure is shown as follows.
(1)
The experiment is conducted under normal temperature and atmospheric pressure (298 K, 1 atm)
(2)
To ensure the coupling between the probe and the sample surface, the Shear Gel is applied on the probe surface after the prepared sample is put into the coal clamp and then covered with the top lid
(3)
To check the air tightness of the system, it is observed whether the piezometer reading is changed or not. A vacuum pump is used to vacuum the sealed cylinder block. When the negative pressure in the chamber is stabilized at -0.1 MPa, the vacuum should be stopped. The acoustic signals in thex and y directions and in the z direction under the negative pressure condition are collected by three ultrasonic transducers
(4)
When the vacuum test is finished, the cylinder body is filled slowly with the high-pressure mixture gas (CO260%+N2 40%) instead of CH4 gas in an isogradient manner through the pressure relief valve to a predetermined pressure value (-0.1-1.4 MPa) [29]. This operation can be justified by the fact that according to laboratory safety regulations, the use of CH4 gas is prohibited during the experiment and that the abovementioned mixed gas has similar adsorption effect with CH4 gas [30]. Then the air tightness of the system is checked again. After the gas reaches the adsorption equilibrium and the preset pressure value is maintained for 24 hours, the acoustic signals of the samples under different gas pressures are finally collected. Based on Langmuir isothermal adsorption equation (4) [24], the gas adsorption capacity of coal samples under different pressure equilibrium conditions can be estimated, as shown in Table 2 and Figure 4. It should be mentioned that the pure component isotherm is empirically used to describe an actual binary system, thus neglecting any competitive adsorption of CO2 and N2
(4)Q=a⋅b⋅P1+b⋅P,where Q denotes the gas adsorption capacity of the coal sample, in ml/g; P is the pressure of gas, in MPa; a and b are the adsorption constants of the coal sample.
As can be seen from Figure4, with the increase of gas pressure, the gas adsorption capacity of five coal samples is also increasing gradually, but the rising trend becomes milder in the later phase
(5)
The signals collected are calculated, processed, and analyzed (refer to Section2.2)Figure 3
Ultrasound anisotropy testing system of coal samples (simplified).Table 2
Gas adsorption capacity of coal samples under different gas pressure conditions.
P (MPa)
Q (ml/g)
#8-A
#8-B
#8-C
#8-D
#8-E
-0.1
0
0
0
0
0
0.2
7.46
7.41
7.46
7.59
7.37
0.4
12.22
12.15
12.21
12.40
12.09
0.6
15.52
15.44
15.51
15.71
15.37
0.8
17.94
17.86
17.93
18.14
17.79
1.0
19.79
19.71
19.78
19.99
19.64
1.2
21.26
21.18
21.24
21.45
21.11
1.4
22.44
22.36
22.43
22.62
22.30Figure 4
Deformation curves of isogradient pressurized adsorption and gas adsorption capacity of the coal samples.


## 3. Test Results and Discussion

### 3.1. Ultrasonic Velocity of Gas-Bearing Coal Samples

Since the five anthracite samples are all taken from large coal samples from the same coal seam, the measured ultrasonic velocity values can denote the comprehensive response values of various material components, pore structure, and bedding plane of coal. Therefore, the average value of the ultrasonic velocity data of the five anthracite samples is analyzed and the analysis results (shown in Table3) can reflect the general characteristics of #8 anthracite.Table 3
Test results of P- and S-wave ultrasonic velocities of the coal samples under different gas pressures.
P (MPa)
VP (m/s)
VS (m/s)
x
y
z
x
y
z
-0.1
1793
1733
1677
982
926
871
0.2
1733
1673
1650
959
911
863
0.4
1706
1653
1635
951
905
858
0.6
1691
1644
1627
947
901
851
0.8
1683
1635
1614
943
897
847
1.0
1675
1629
1607
937
893
845
1.2
1664
1621
1600
933
889
841
1.4
1652
1613
1596
927
886
841The ultrasonic elasticity test indicates that the ultrasonic velocity of coal samples shows similar downward trends with the increase of gas pressure. As shown in Figures5(a) and 5(b), the VP of anthracite coal samples is about 1600-1800 m/s while the VS is within the interval of 800-1000 m/s. Compared with the previous research results [14–19, 31–33], the ultrasonic velocity results of the coal samples in this study are within a reasonable range.Figure 5
Characteristic charts of ultrasonic velocity of coal samples at different gas pressures.
(a)
VP
(b)
VSAccording to the results of previous researches [14–19, 31–33], the VP and VS of the coal samples are the comprehensive response value of geological parameters such as material composition, pore structure, and environment of coal itself. The density, temperature, stress, and water of coal all influence the ultrasonic wave velocity of coal [17]. However, the five coal samples used in this experiment are all taken from the same position and the experiment is carried out under the same normal temperature and pressure. Therefore, it can be concluded that the density, temperature, stress, and moisture of coal samples cannot be the main factors leading to the above changes [34–36].The adsorption of gas leads to a decrease in the strength of coal samples [37], which can be reflected in the variation of the VP and VS.


### 3.2. Variation in Ultrasonic Velocity of Coal Samples under Different Gas Pressures

From Figure6, it can be seen that components of VP and VS of the coal samples are very different in the three directions, and meanwhile, their degree of decline varies from one another as the gas pressure increases.Figure 6
MeasuredVP and VS.
(a)
VP
(b)
VSSpecifically, as shown in Figures6(a) and 6(b), VP and VS of the coal samples decrease in turn in the strike direction x, the dip direction y, and the vertical direction z. However, in Figures 5(a) and 5(b), it can be seen that the correlation coefficient Rz2=0.95 between ultrasonic velocity and gas pressure in the vertical direction z is significantly higher than that in the strike direction x and the dip direction y. Therefore, the clay and pore fracture of coal may be the main cause for this phenomenon. Meanwhile, with the increase of gas pressure, VP and VS of the coal samples show a noticeable downward trend, in which VP decreases by 7.86%, 6.92%, and 4.83% in the strike direction x, the dip direction y, and the vertical direction z, respectively, while VS decreases by 5.6%, 4.53%, and 3.44%, respectively, in the corresponding three directions. The P-wave, especially high-frequency ultrasonic P-wave, is more sensitive to gas pressure changes, which may be justified by the strong absorption and attenuation of ultrasonic elastic waves by gas-bearing coal fluid-solid two-phase medium.Previous studies [37–40] have shown that the adsorption and desorption of coal samples are physical phenomena. When the coal samples absorb gas, they undergo expansion. On the contrary, compression deformation occurs after gas is desorbed. The deformation firstly weakens the strength of the coal samples and increases the brittleness of the coal samples, making the coal more prone to instability and damage. Then the instability and failure process of the coal samples are to be accelerated, leading to the decrease of coal sample strength and the increase of brittleness. In the meanwhile, along with the phenomena of gas adsorption and expansion deformation of the coal samples, there is a size effect on the coal samples—to be specific, the volume of the coal sample increases (adsorption expansion). Therefore, in the calculation of ultrasonic velocity of the coal samples, the proportion of the volume increase caused by the adsorption and expansion is analyzed below.According to the existing research, under the constant gradient pressure conditions, the adsorption expansion deformation of coal samples increases as time goes by but the cumulative deformation eventually tends to remain at a stable value. The isocratic pressure in the reference [40] is set to a value of 1.5 MPa. The microstrain of cumulative adsorption expansion is achieved under the condition of adsorption equilibrium. According to the reference [41], the maximum deformation of the coal sample used in the experiment can be calculated by the calculation formula of the coal adsorption deformation equation.
(5)ε=ABP1+BP,where ε denotes the adsorption deformation quantity of the coal sample, in ‰; P is the gas pressure, in MPa; A is the limit adsorption deformation constant of the coal sample when gas pressure tends to be infinite, in ‰; B is the adsorption deformation constant of the coal sample, in MPa-1.Table4 shows that the maximum adsorption deformation quantity of the gas-bearing coal sample in the calculation of coal ultrasonic velocities is only 2.99‰, so the effect of gas adsorption deformation on anthracite samples is small.Table 4
Adsorption deformation constant and quantity of coal samples.
Sample ID
A (‰)
B (MPa-1)
ε (‰)
#8-A
3.704
2.250
2.81
#8-B
3.563
2.198
2.69
#8-C
3.624
2.283
2.76
#8-D
3.926
2.277
2.99
#8-E
3.677
2.221
2.78The gas-bearing coal sample is a typical fluid-solid two-phase and two-porosity medium, and the sample is composed of solid skeleton, pore, fracture, and gas filled in the pore and fracture [42]. There exist three kinds of compressional wave (P-wave and two slow compressional waves P2 and P3) and S-wave. The velocity of the P-wave is the fastest, the S-wave ranks second, and P2 and P3 are the slowest [43]. The P-wave and S-wave propagate in the skeleton. Slow compressional wave P2 is produced by the interaction of the solid skeleton and gas in the pore, and slow compressional wave P3 is produced by the interaction of the solid skeleton and gas in the fracture.In this paper, only the P-wave and S-wave are studied. Accordingly, the influence factor of P-wave and S-wave velocity variations only includes the solid skeleton. On the one hand, the skeleton deformation is caused by gas adsorption. In the previous study, the effect of gas adsorption deformation on anthracite samples is small, so adsorption deformation has little effect on the wave velocity of anthracite samples. On the other hand, with the increase of gas pressure, adsorbed quantity of gas increases and adsorbed quantity of gas on the skeleton surface increases, which in turn leads to the decrease of solid skeleton strength. Ultimately, the velocities of the P- and S-wave decrease with the increase of gas pressure.


### 3.3. Anisotropy Characteristics of Velocity

It is known that with the increase of gas pressure,VP and VS of the coal samples decrease. Meanwhile, the velocity (P- and S-waves) distribution of the coal samples exhibits different characteristics in the three directions. So, the influence of gas pressure on the ultrasonic velocity anisotropy of anthracite is analyzed in this section and the velocity anisotropy values of selected coal samples can be calculated with the following formulas [17].
(6)AVP=2VPmax−VPminVPmax+VPmin×100%,AVS=2VSmax−VSminVSmax+VSmin×100%,where AVP and AVS denote the anisotropy values of velocities (P-wave and S-wave, respectively). The results obtained are shown in Figure 7.Figure 7
Anisotropy ofVP and VS of coal samples.As can be seen from Figure7, when the coal samples are under vacuum (negative pressure), the anisotropy between x and z is greater than those between x and y and y and z. Through X-ray tomography of coal samples, the CT digital images of coal samples can be obtained in order to interpret the differences in the above directions [44, 45]. The test was carried out on Xradia 510 Versa high-resolution three-dimensional X-ray microimaging system (3D-XRM). The correlation between CT image thresholds from three views and three anisotropic values of P-wave velocity can be established; as shown in Figure 8, there is a negative correlation between them. It can be seen that there is a logarithmic negative correlation between them. The threshold of CT images from the x and z views shows that the average density of clays and pore fractures is the smallest, which leads to the maximum anisotropy between x and z. The main cause of the abovementioned directional differences may be the inconsistency between the clays and the pore fractures of the coal [14–19].Figure 8
The relation between CT image threshold and anisotropic value from different views.With the increase of gas pressure, the anisotropy of wave velocity of coal samples keeps the same difference as that of vacuum but decreases gradually on the whole and the decrease of P-wave velocity anisotropy is much larger than that of S-wave velocity anisotropy. Specifically, the decreases of P-wave velocity anisotropy in the strike directionx, the dip direction y, and the vertical direction z are 45.56%, 48.43%, and 53.91%, respectively, while the decreases of S-wave velocity anisotropy are only 7.66% (x and y), 18.8% (x and z), and 17.77% (y and z), respectively. It can be concluded that the anisotropy of P-wave velocity decreases much more than that of the S-wave, which indicates that the P-wave is more sensitive to gas pressure changes.Therefore, the most possible cause is that the coal samples undergo adsorption due to the existence of fluid gas [37, 46]. As a result, the strength of the coal samples is weakened and the strong ultrasonic anisotropy of the coal samples is also gradually weakened under the action of the high-pressure gas adsorption expansion.


## 3.1. Ultrasonic Velocity of Gas-Bearing Coal Samples

Since the five anthracite samples are all taken from large coal samples from the same coal seam, the measured ultrasonic velocity values can denote the comprehensive response values of various material components, pore structure, and bedding plane of coal. Therefore, the average value of the ultrasonic velocity data of the five anthracite samples is analyzed and the analysis results (shown in Table3) can reflect the general characteristics of #8 anthracite.Table 3
Test results of P- and S-wave ultrasonic velocities of the coal samples under different gas pressures.
P (MPa)
VP (m/s)
VS (m/s)
x
y
z
x
y
z
-0.1
1793
1733
1677
982
926
871
0.2
1733
1673
1650
959
911
863
0.4
1706
1653
1635
951
905
858
0.6
1691
1644
1627
947
901
851
0.8
1683
1635
1614
943
897
847
1.0
1675
1629
1607
937
893
845
1.2
1664
1621
1600
933
889
841
1.4
1652
1613
1596
927
886
841The ultrasonic elasticity test indicates that the ultrasonic velocity of coal samples shows similar downward trends with the increase of gas pressure. As shown in Figures5(a) and 5(b), the VP of anthracite coal samples is about 1600-1800 m/s while the VS is within the interval of 800-1000 m/s. Compared with the previous research results [14–19, 31–33], the ultrasonic velocity results of the coal samples in this study are within a reasonable range.Figure 5
Characteristic charts of ultrasonic velocity of coal samples at different gas pressures.
(a)
VP
(b)
VSAccording to the results of previous researches [14–19, 31–33], the VP and VS of the coal samples are the comprehensive response value of geological parameters such as material composition, pore structure, and environment of coal itself. The density, temperature, stress, and water of coal all influence the ultrasonic wave velocity of coal [17]. However, the five coal samples used in this experiment are all taken from the same position and the experiment is carried out under the same normal temperature and pressure. Therefore, it can be concluded that the density, temperature, stress, and moisture of coal samples cannot be the main factors leading to the above changes [34–36].The adsorption of gas leads to a decrease in the strength of coal samples [37], which can be reflected in the variation of the VP and VS.


## 3.2. Variation in Ultrasonic Velocity of Coal Samples under Different Gas Pressures

From Figure6, it can be seen that components of VP and VS of the coal samples are very different in the three directions, and meanwhile, their degree of decline varies from one another as the gas pressure increases.Figure 6
MeasuredVP and VS.
(a)
VP
(b)
VSSpecifically, as shown in Figures6(a) and 6(b), VP and VS of the coal samples decrease in turn in the strike direction x, the dip direction y, and the vertical direction z. However, in Figures 5(a) and 5(b), it can be seen that the correlation coefficient Rz2=0.95 between ultrasonic velocity and gas pressure in the vertical direction z is significantly higher than that in the strike direction x and the dip direction y. Therefore, the clay and pore fracture of coal may be the main cause for this phenomenon. Meanwhile, with the increase of gas pressure, VP and VS of the coal samples show a noticeable downward trend, in which VP decreases by 7.86%, 6.92%, and 4.83% in the strike direction x, the dip direction y, and the vertical direction z, respectively, while VS decreases by 5.6%, 4.53%, and 3.44%, respectively, in the corresponding three directions. The P-wave, especially high-frequency ultrasonic P-wave, is more sensitive to gas pressure changes, which may be justified by the strong absorption and attenuation of ultrasonic elastic waves by gas-bearing coal fluid-solid two-phase medium.Previous studies [37–40] have shown that the adsorption and desorption of coal samples are physical phenomena. When the coal samples absorb gas, they undergo expansion. On the contrary, compression deformation occurs after gas is desorbed. The deformation firstly weakens the strength of the coal samples and increases the brittleness of the coal samples, making the coal more prone to instability and damage. Then the instability and failure process of the coal samples are to be accelerated, leading to the decrease of coal sample strength and the increase of brittleness. In the meanwhile, along with the phenomena of gas adsorption and expansion deformation of the coal samples, there is a size effect on the coal samples—to be specific, the volume of the coal sample increases (adsorption expansion). Therefore, in the calculation of ultrasonic velocity of the coal samples, the proportion of the volume increase caused by the adsorption and expansion is analyzed below.According to the existing research, under the constant gradient pressure conditions, the adsorption expansion deformation of coal samples increases as time goes by but the cumulative deformation eventually tends to remain at a stable value. The isocratic pressure in the reference [40] is set to a value of 1.5 MPa. The microstrain of cumulative adsorption expansion is achieved under the condition of adsorption equilibrium. According to the reference [41], the maximum deformation of the coal sample used in the experiment can be calculated by the calculation formula of the coal adsorption deformation equation.
(5)ε=ABP1+BP,where ε denotes the adsorption deformation quantity of the coal sample, in ‰; P is the gas pressure, in MPa; A is the limit adsorption deformation constant of the coal sample when gas pressure tends to be infinite, in ‰; B is the adsorption deformation constant of the coal sample, in MPa-1.Table4 shows that the maximum adsorption deformation quantity of the gas-bearing coal sample in the calculation of coal ultrasonic velocities is only 2.99‰, so the effect of gas adsorption deformation on anthracite samples is small.Table 4
Adsorption deformation constant and quantity of coal samples.
Sample ID
A (‰)
B (MPa-1)
ε (‰)
#8-A
3.704
2.250
2.81
#8-B
3.563
2.198
2.69
#8-C
3.624
2.283
2.76
#8-D
3.926
2.277
2.99
#8-E
3.677
2.221
2.78The gas-bearing coal sample is a typical fluid-solid two-phase and two-porosity medium, and the sample is composed of solid skeleton, pore, fracture, and gas filled in the pore and fracture [42]. There exist three kinds of compressional wave (P-wave and two slow compressional waves P2 and P3) and S-wave. The velocity of the P-wave is the fastest, the S-wave ranks second, and P2 and P3 are the slowest [43]. The P-wave and S-wave propagate in the skeleton. Slow compressional wave P2 is produced by the interaction of the solid skeleton and gas in the pore, and slow compressional wave P3 is produced by the interaction of the solid skeleton and gas in the fracture.In this paper, only the P-wave and S-wave are studied. Accordingly, the influence factor of P-wave and S-wave velocity variations only includes the solid skeleton. On the one hand, the skeleton deformation is caused by gas adsorption. In the previous study, the effect of gas adsorption deformation on anthracite samples is small, so adsorption deformation has little effect on the wave velocity of anthracite samples. On the other hand, with the increase of gas pressure, adsorbed quantity of gas increases and adsorbed quantity of gas on the skeleton surface increases, which in turn leads to the decrease of solid skeleton strength. Ultimately, the velocities of the P- and S-wave decrease with the increase of gas pressure.


## 3.3. Anisotropy Characteristics of Velocity

It is known that with the increase of gas pressure,VP and VS of the coal samples decrease. Meanwhile, the velocity (P- and S-waves) distribution of the coal samples exhibits different characteristics in the three directions. So, the influence of gas pressure on the ultrasonic velocity anisotropy of anthracite is analyzed in this section and the velocity anisotropy values of selected coal samples can be calculated with the following formulas [17].
(6)AVP=2VPmax−VPminVPmax+VPmin×100%,AVS=2VSmax−VSminVSmax+VSmin×100%,where AVP and AVS denote the anisotropy values of velocities (P-wave and S-wave, respectively). The results obtained are shown in Figure 7.Figure 7
Anisotropy ofVP and VS of coal samples.As can be seen from Figure7, when the coal samples are under vacuum (negative pressure), the anisotropy between x and z is greater than those between x and y and y and z. Through X-ray tomography of coal samples, the CT digital images of coal samples can be obtained in order to interpret the differences in the above directions [44, 45]. The test was carried out on Xradia 510 Versa high-resolution three-dimensional X-ray microimaging system (3D-XRM). The correlation between CT image thresholds from three views and three anisotropic values of P-wave velocity can be established; as shown in Figure 8, there is a negative correlation between them. It can be seen that there is a logarithmic negative correlation between them. The threshold of CT images from the x and z views shows that the average density of clays and pore fractures is the smallest, which leads to the maximum anisotropy between x and z. The main cause of the abovementioned directional differences may be the inconsistency between the clays and the pore fractures of the coal [14–19].Figure 8
The relation between CT image threshold and anisotropic value from different views.With the increase of gas pressure, the anisotropy of wave velocity of coal samples keeps the same difference as that of vacuum but decreases gradually on the whole and the decrease of P-wave velocity anisotropy is much larger than that of S-wave velocity anisotropy. Specifically, the decreases of P-wave velocity anisotropy in the strike directionx, the dip direction y, and the vertical direction z are 45.56%, 48.43%, and 53.91%, respectively, while the decreases of S-wave velocity anisotropy are only 7.66% (x and y), 18.8% (x and z), and 17.77% (y and z), respectively. It can be concluded that the anisotropy of P-wave velocity decreases much more than that of the S-wave, which indicates that the P-wave is more sensitive to gas pressure changes.Therefore, the most possible cause is that the coal samples undergo adsorption due to the existence of fluid gas [37, 46]. As a result, the strength of the coal samples is weakened and the strong ultrasonic anisotropy of the coal samples is also gradually weakened under the action of the high-pressure gas adsorption expansion.


## 4. Conclusions

Many achievements have been made in the ultrasonic elasticity test of single-phase solid coal seam. However, in the actual gas geological condition, coal seam is not a single solid medium but a two-phase and two-porosity. So, the ultrasonic velocity and anisotropy of gas-bearing coal two-phase and two-porosity are studied in this paper. Relevant results can be mainly applied in seismic exploration of a high-gas mine, which can provide theoretical guidance for the prediction and prevention of coal and gas disasters by identifying abnormal areas of gas enrichment in seismic exploration. Finally, the following conclusions can be drawn.(1)
In the strike, dip, and vertical directions, there is a negative linear relationship between the ultrasonic velocity and gas pressure. It is manifested by the fact that the ultrasonic velocity (P-wave and S-wave) decreases with the increase of gas pressure. As for the cause of this phenomenon, it can be concluded that the increase of gas pressure leads to the increase of gas adsorption quantity on the skeleton surface, causing the decrease of skeleton strength, and resulting in the decrease of P-wave and S-wave velocities propagating in the solid skeleton of gas-bearing coal samples. Moreover, the correlation coefficient between the ultrasonic velocity and the gas concentration in the vertical direction is significantly higher than that in the strike direction and the dip direction
(2)
The degree of S-wave anisotropy is greater than that of the P-wave. In addition,AVPx&z is greater than AVPx&y and AVPy&z; AVSx&z is greater than AVSx&y and AVSy&z. With the increase of gas pressure, the anisotropy of velocities (P- and S-waves) of coal samples decreases stepwise as a whole
(3)
The decrease in P-wave velocity and its anisotropy is greater than that in the S-wave, which indicates that P-wave velocity is more sensitive to gas pressure changesIn the actual seismic exploration, under the constraints of drilling and logging, the above laws of the ultrasonic anisotropy of the coal samples affected by gas may provide some theoretical guidance for the prevention of gas disasters.



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*Source: 3183816-2019-08-19.xml*