# Investigation of the Velocities of Coals of Diverse Rank under Water- or Gas-Saturated Conditions for Application in Coalbed Methane Recovery

Authors: Jizhao Xu; Cheng Zhai; Pathegama Gamage Ranjith; Yong Sun; Jisheng Guo; Zheng Ma; Huiteng Ma; Lei Qin
Journal: Geofluids
 (2019)

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## Abstract

Coalbed methane recovery enhanced by hydraulic or nonaqueous fracturing methods has been studied for decades, and it is of significance to evaluate fracturing results and scope for field applications. Monitoring variation in velocity is one way to explain fracturing effects. However, the existence of residual water or gas within cracks or pores may affect velocity measurements, and the correlation between velocity and inherent coal attributes (such as density and porosity) has not been studied comprehensively. In this paper, coal of different ranks (lignite, bituminite, and anthracite) was prepared under water and gas saturation to approximately simulate the residual water and gas in cracks under field applications. Correlations between the velocity and coal attributes were studied. For both water- and gas-saturated cores, the diverse velocity distributions were highly correlated to rank and saturation media. The longitudinal ultrasonic pulse velocity (UPVp) and transverse ultrasonic pulse velocity (UPVs) of different cores were distributed differently. For coal saturated with water or gas, the UPVp values of lignite, bituminite, and anthracite had positive linear correlations with the corresponding UPVs values. The discrete velocity ratio data were fit as negative linear correlations with UPVs, and different coals had different declining degrees, the difference of which might be attributed to the characteristics of structural cracks and the inherent properties of the coal, such as grain size and pore shape, which result in decreasing coal integrity and strength. Moreover, the difference in acoustic resistance between coal and fluids might have an inverse impact on the acoustic energy, and a larger difference might cause a large amount of energy to dissipate and finally cause the velocity to decrease. Under water and gas saturation conditions, the UPVp showed a positive linear correlation with density and a negative linear correlation with porosity. Finally, a potential field application was designed on the relations between the velocity and the elastic parameters to estimate fracturing effects by monitoring the petrophysical parameters of coal lithologies.


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## Body

## 1. Introduction

Effective coalbed methane (CBM) drainage is a topical research issue around the world. CBM also occupies an increasing proportion of the resource structure in China, and its efficient use is likely to ease the pressure on other diminishing fossil fuel reserves [1–4]. CBM reserves in China typically have properties that constrain their extractability, such as great depth, great density, or low permeability [5–7]. Some technologies, such as hydraulic and nonaqueous fracturing, have been proposed to improve fracture connection and thus enhance the permeability of the CBM reserves [8–11]. Meanwhile, the inherent properties of coal also play an important role in controlling fracturing [12–14]. For example, bulk density and strength (bulk modulus and shear modulus) provide information about integrity under different pressure-temperature states, as well as mineral constituents and their distribution influence homogeneity. Coal rank correlates with the degree of anisotropy in some respects, such as anisotropic ultrasonic velocity, porosity, and fracture orientation. It is of significance to evaluate fracturing results and scope for field applications. The ultrasonic pulse velocity (UPV) method is commonly used to obtain various information on material properties and rock quality because it is convenient, nondestructive, and highly efficient [15, 16]. The UPV method can be used to detect microscopic cracks within the matrix [17, 18] and to evaluate the efficacy of consolidation in concrete [19, 20].The UPV testing method in a laboratory setting uses a pair of transducers (one transducer as a signal emitter and another transducer as a receiver) to quantify ultrasonic pulse transmission through a sample using an oscilloscope. There are two main parameters of interest: longitudinal ultrasonic pulse velocity (UPVp) and transverse ultrasonic pulse velocity (UPVs), as shown in Figure1. The velocity is calculated as follows [21]:
(1)V=Lt2−t1,where L is the length of the sample, t1 and t2 are the docking time of the transducers and the first arrival time of the wave signal by the receiver sensor, respectively, and t2−t1 is the travel time.Figure 1
Schematic diagram of the UPV device used in this study.Vilhelm et al. [22] studied velocity dispersion in fractured rocks over a wide frequency range (~1 kHz, ~40 kHz, and ~1 MHz) and successfully used a displacement discontinuity approach in a theoretical model to conclude that the first arrivals of seismic waves can be used to evaluate P-wave velocity. Nakahata et al. [23] proposed a time domain simulation tool based on finite integration and an image-based modeling approach to better understand the characteristics of ultrasonic wave propagation in concrete. Pulse wave velocities are thought to reflect the mechanical properties of rocks [24–27], which were evaluated using the UPV method by Vasanelli et al. [28], in terms of the physical and mechanical properties of a highly porous building limestone. Statistical information on the correlation between compressional and shear wave velocities and the corresponding Poisson’s ratios of different lithologies at different pressure-temperature conditions has also been found [29–33]. Lokajíček et al. [34] studied the influence of thermal heating on elastic wave velocity within granulite samples under different stress levels using a three-dimensional P-wave elastic anisotropy method.UPV testing has also been used to evaluate coal properties and various influencing factors such as confining stress, temperature, moisture content, and porosity. The ultrasonic wave velocity of coal under lower confining stress increases with rank because of fracture closure [35, 36]. Liu et al. [37] divided the effects of water saturation on P-wave propagation in fractured coal into three types. Pulse wave velocity and anisotropy of tectonically deformed coal have been used to show that the Vp/Vs ratio, Poisson’s ratio, and anisotropy are all sensitive to deformation type and extent [21]. Additionally, structural fractures were found to have a significant impact on the elastic properties of coal samples from different deformation environments [21]. Lwin [38] studied the effect of different gases (He, N2, CH4, and CO2) on the ultrasonic response of coal and revealed a significant difference in density, P-wave modulus, and impedance for CO2 saturation compared with CH4 saturation. Yu et al. [39] studied pore variations and changes in P-wave velocity of coal affected by ultrasonic excitation and found that the P-wave velocity decreased with increasingly affected cycles.The velocity monitoring method has been applied to fracturing estimation; however, residual water or gas occupies pores and cracks after fracturing. The impact of residual water or gas on the accurate evaluation of velocity and the correlations between inherent attributes (porosity, density, and rank) have not been studied comprehensively. In this paper, three different ranks of coals, including 24 lignites, 26 bituminites, and 26 anthracites, are tested (UPVp and UPVs) under both water and gas (air) saturation. The correlations among velocity, density, and porosity are described, and the statistical results can provide reference parameters for further field monitoring in coal physics in terms of CBM reservoir fracturing processes.


## 2. Materials and Methods

### 2.1. Coal Preparation

Lignite, bituminite, and anthracite samples were collected from the Shengli Coal Mine, Inner Mongolia; the Datong Coal Mine, Shanxi; and the Yangzhuang Coal Mine, Huaibei; respectively. The large coal blocks were wrapped with preservative film and transferred to the State Key Laboratory of Coal Resources and Safe Mining in Xuzhou, Jiangsu, before being cored to produce 5 cm diameter cylinders with 10 cm height (Figures2(a) and 2(b)). To conveniently measure the pulse velocity of the cores, the tops and bottoms of the cylinders were ground flat to ensure a parallelism error of ≤0.005 mm [40]. The detailed properties of the 24 lignite cores (Ro,max of 0.32), 26 bituminite cores (Ro,max of 1.13), and 26 anthracite cores (Ro,max of 3.05) [41] are listed in Table 1. The density of the lignite, bituminite, and anthracite cores was measured to be 1.28 g/cm3 to 1.55 g/cm3, 1.23 g/cm3 to 1.42 g/cm3, and 1.29 g/cm3 to 1.61 g/cm3, respectively. The porosity of the cores was measured to be in the ranges of 1.07% to 3.17%, 0.3% to 4.0% and 0.3% to 2.9%, respectively. The core samples were preserved in a curing box to maintain their original structure and moisture content.Figure 2
Images of 76 coals with different ranks. (a) Overall view of the 76 coal cores, (b) lateral display of lignite cores, and (c) sketch image of UPV test method.
(a)
(b)
(c)Table 1
Detail properties of the coals with different ranks.
Type
Density (g/cm3)
Porosity (%)
Proximate analysis (%)
Ro,max (%)
Maceral analysis (%)
Mad
Aad
Vdaf
FCad
V
I
E
M
Lignite
1.28-1.55
1.07-3.17
11.37
14.63
53.41
20.59
0.32
79.5
15.5
3.6
1.4
Bituminite
1.23-1.42
0.3-4.0
8.83
3.30
29.64
58.23
1.13
58.7
32.6
3.4
5.3
Anthracite
1.29-1.61
0.3- 2.9
2.10
7.73
6.48
83.69
3.05
86.4
10.5
1.5
1.6
Mad: water content; Aad: ash content; Vdaf: volatile component; FCad: fixed carbon content; V: vitrinite; I: inertinite; E: exinite; M: mineral content; Ro,max: the maximum reflectance of vitrinite.


### 2.2. Experimental Equipment and Procedures

The UPV test equipment used to record the UPVp and UPVs values of the cores under water and gas saturation (the gas during the experiment and referred to in the paper is air) was an HS-YS4A Sonic wave parameter tester (Tianhong Electronics, Xiangtan, China). This apparatus operates with a high signal-to-noise ratio and has low temperature excursions and high repeatability with low failure rate. The instrument has two emitter options, 160 V or 1000 V, and the amplifier can be regulated with multistage attenuation processes.Gas saturation was carried out in an autoclave with a pressure of 1.5 MPa to ensure that air occupied the internal pores or cracks in the cores, and water saturation was undertaken using a vacuum pump (ZN-BSJ, Suzhou Niumag Analytical Instrument Corporation, Suzhou, China) by depressurizing the cores to approximately -1.0 MPa, thus allowing water ingress into the pore spaces of the core.The ambient temperature during the experiments was 25°C, and to eliminate the high-frequency effect on fluid-saturated samples when measuring velocity, the 160 V emitter was chosen with a frequency of 50 kHz. The experimental procedure was carried out in the following steps:(i)
All the cores were placed in a vacuum drying oven at 60°C for 72 h to remove the original gas and water from the cores, and their masses were tested using an electronic balance and were recorded asMpre
(ii)
The cores were placed in the autoclave at a pressure of 1.5 MPa for 72 h to achieve gas saturation, the velocity parameters were tested using the velocity apparatus by connecting the core surface and the transducers, and the values were recorded as UPVp-gas and UPVs-gas
(iii)
The cores were then immersed in the water saturator, and all the air was exhausted to ensure that water occupied the pores, at a pressure of -0.95 MPa for 72 h. The mass of water-saturated cores was recorded asMwater; then, the velocities were measured as UPVp-water and UPVs-water


## 2.1. Coal Preparation

Lignite, bituminite, and anthracite samples were collected from the Shengli Coal Mine, Inner Mongolia; the Datong Coal Mine, Shanxi; and the Yangzhuang Coal Mine, Huaibei; respectively. The large coal blocks were wrapped with preservative film and transferred to the State Key Laboratory of Coal Resources and Safe Mining in Xuzhou, Jiangsu, before being cored to produce 5 cm diameter cylinders with 10 cm height (Figures2(a) and 2(b)). To conveniently measure the pulse velocity of the cores, the tops and bottoms of the cylinders were ground flat to ensure a parallelism error of ≤0.005 mm [40]. The detailed properties of the 24 lignite cores (Ro,max of 0.32), 26 bituminite cores (Ro,max of 1.13), and 26 anthracite cores (Ro,max of 3.05) [41] are listed in Table 1. The density of the lignite, bituminite, and anthracite cores was measured to be 1.28 g/cm3 to 1.55 g/cm3, 1.23 g/cm3 to 1.42 g/cm3, and 1.29 g/cm3 to 1.61 g/cm3, respectively. The porosity of the cores was measured to be in the ranges of 1.07% to 3.17%, 0.3% to 4.0% and 0.3% to 2.9%, respectively. The core samples were preserved in a curing box to maintain their original structure and moisture content.Figure 2
Images of 76 coals with different ranks. (a) Overall view of the 76 coal cores, (b) lateral display of lignite cores, and (c) sketch image of UPV test method.
(a)
(b)
(c)Table 1
Detail properties of the coals with different ranks.
Type
Density (g/cm3)
Porosity (%)
Proximate analysis (%)
Ro,max (%)
Maceral analysis (%)
Mad
Aad
Vdaf
FCad
V
I
E
M
Lignite
1.28-1.55
1.07-3.17
11.37
14.63
53.41
20.59
0.32
79.5
15.5
3.6
1.4
Bituminite
1.23-1.42
0.3-4.0
8.83
3.30
29.64
58.23
1.13
58.7
32.6
3.4
5.3
Anthracite
1.29-1.61
0.3- 2.9
2.10
7.73
6.48
83.69
3.05
86.4
10.5
1.5
1.6
Mad: water content; Aad: ash content; Vdaf: volatile component; FCad: fixed carbon content; V: vitrinite; I: inertinite; E: exinite; M: mineral content; Ro,max: the maximum reflectance of vitrinite.


## 2.2. Experimental Equipment and Procedures

The UPV test equipment used to record the UPVp and UPVs values of the cores under water and gas saturation (the gas during the experiment and referred to in the paper is air) was an HS-YS4A Sonic wave parameter tester (Tianhong Electronics, Xiangtan, China). This apparatus operates with a high signal-to-noise ratio and has low temperature excursions and high repeatability with low failure rate. The instrument has two emitter options, 160 V or 1000 V, and the amplifier can be regulated with multistage attenuation processes.Gas saturation was carried out in an autoclave with a pressure of 1.5 MPa to ensure that air occupied the internal pores or cracks in the cores, and water saturation was undertaken using a vacuum pump (ZN-BSJ, Suzhou Niumag Analytical Instrument Corporation, Suzhou, China) by depressurizing the cores to approximately -1.0 MPa, thus allowing water ingress into the pore spaces of the core.The ambient temperature during the experiments was 25°C, and to eliminate the high-frequency effect on fluid-saturated samples when measuring velocity, the 160 V emitter was chosen with a frequency of 50 kHz. The experimental procedure was carried out in the following steps:(i)
All the cores were placed in a vacuum drying oven at 60°C for 72 h to remove the original gas and water from the cores, and their masses were tested using an electronic balance and were recorded asMpre
(ii)
The cores were placed in the autoclave at a pressure of 1.5 MPa for 72 h to achieve gas saturation, the velocity parameters were tested using the velocity apparatus by connecting the core surface and the transducers, and the values were recorded as UPVp-gas and UPVs-gas
(iii)
The cores were then immersed in the water saturator, and all the air was exhausted to ensure that water occupied the pores, at a pressure of -0.95 MPa for 72 h. The mass of water-saturated cores was recorded asMwater; then, the velocities were measured as UPVp-water and UPVs-water


## 3. Results

Figure3 shows box plots of velocity recorded in different cores. There are significant differences in terms of velocity distribution and discrete degree according to coal rank and saturation media. For example, the box plot ranges (from lower to upper quartile) of UPVp are larger than those of UPVs for both water-saturated and gas-saturated cores. The UPVp(s) box plot ranges of water-saturated cores exceed those of gas-saturated cores. Water saturation in microcracks improves the continuity of wave propagation with less discrete velocity than gas saturation conditions. Statistically, the width of the UPVp box plots is smaller than the corresponding UPVs box plots under water saturation conditions, which indicates that UPVp has less data dispersion than UPVs. Thus, UPVp is more accurate or reliable for characterizing the existence of micro- or macrocracks with the assistance of adsorbed water. Anthracite cores have a smaller UPVp box plot width than the other plots, which means that the greater rank has less porosity and higher homogeneity, resulting in greater velocity concentration.Figure 3
Box plots of different coal rank samples at (a) water saturation and (b) gas saturation condition.
(a)
(b)UPVp and UPVs velocity ranges and mean values for the three types of coal are listed in Table2. The largest values in the velocity ranges were recorded in anthracite cores (UPVp-water 1.63 km/s to 2.25 km/s, UPVs-water 1.26 km/s to 1.87 km/s, UPVp-gas 1.12 km/s to 1.94 km/s, and UPVs-gas 0.74 km/s to 1.69 km/s). The lowest velocity ranges were recorded in lignite cores, with intermediate values recorded in bituminite cores. In addition, the anthracite cores had the largest UPVpmean value of 1.93 km/s and UPVsmean value of 1.58 km/s under water saturation, with UPVpmean and UPVsmean values of 1.61 km/s and 1.21 km/s, respectively, under gas saturation. The mean velocity values of other sample types followed a trend similar to the measured velocities, and it is posited that coal rank is largely responsible for the variation in recorded ultrasonic velocity.Table 2
UPVp and UPVs velocity ranges and the mean values of three ranks of coals.
Water saturation condition (km/s)
Gas saturation condition (km/s)
UPVp
UPVpmean
UPVs
UPVsmean
UPVp
UPVpmean
UPVs
UPVsmean
Lignite
[1.18, 2.17]
1.86
[1.13, 1.87]
1.57
[0.61, 1.67]
1.22
[0.44, 1.23]
0.90
Bituminite
[1.61, 2.17]
1.95
[1.04, 1.89]
1.59
[0.71, 1.85]
1.34
[0.64, 1.72]
1.07
Anthracite
[1.63, 2.25]
1.93
[1.26, 1.87]
1.58
[1.12, 1.94]
1.61
[0.74, 1.69]
1.21


## 4. Discussion

### 4.1. Correlation between UPVp and UPVs

Given the different velocity distributions of the three ranks of coal, it is necessary to analyze correlations between the UPVp and UPVs under the two different conditions. The scatter of velocity data and correlations of fit are shown in Figure4. The UPVp and UPVs values of the cores differed for both conditions, and they might depend on the coal rank and components within the coal matrix. Velocity values of cores from the same coal blocks were not consistent, because of the various orientations and distributions of microcracks. When an elastic wave transfers to existing defects, such as cleats, cracks, or pores, some reflection, refraction, and diffraction of waves and friction at the crack surface and the grain boundaries might be generated, causing amplitude attenuation and energy decrease [21, 40, 42]. The crack number and distribution might be the main factors influencing velocity decrease. The larger the number of existing cracks is, the greater the energy decrease, and the smaller the velocity is. Under water and gas saturation, the UPVp values generally exceed the UPVs values, and the UPVp and UPVs values of the same cores under water saturation exceed those under gas saturation, indicating that the discrete degree of velocity might occur more frequently under gas saturation due to the large dispersion of air molecules. The scatter in velocity data values is well fit and listed in Table 3.Figure 4
Scatterplot of velocity data and goodness-of-fit correlations between UPVs and UPVp of lignite, bituminite, and anthracite cores under water and gas saturation.
(a)
(b)
(c)
(d)
(e)
(f)Table 3
Correlations between UPVp and UPVs for lignite, bituminite, and anthracite under water or gas saturation.
Condition
Equation
R2
Lignite
Water saturation
UPVp−water=1.06∗UPVs−water+0.159
0.681
Gas saturation
UPVp−gas=1.31∗UPVs−gas+0.049
0.853
Bituminite
Water saturation
UPVp−water=0.521∗UPVs−water+1.12
0.659
Gas saturation
UPVp−gas=1.07∗UPVs−gas+0.193
0.775
Anthracite
Water saturation
UPVp−water=0.877∗UPVs−water+0.539
0.801
Gas saturation
UPVp−gas=0.791∗UPVs−gas+0.646
0.809Dependent on Figure4, the UPVp values of lignite, bituminite, and anthracite coal showed positive linear correlations with their corresponding UPVs values, under water and gas saturation, similar to the results reported by Kahraman [16], Sayed et al. [43], and Kassab and Weller [44] that UPVp scatter had a strong linear correlation with the corresponding UPVs scatter of dry rock or wet rock samples. When the UPVs-water value was 2.0 km/s, the potential UPVp-water values of lignite, bituminite, and anthracite were 2.279 km/s, 2.162 km/s, and 2.293 km/s, respectively. This difference appears to be dependent on porosity and moisture content, given that the lower the porosity and the higher the moisture content is, the larger the UPVp value is [45].


### 4.2. Analysis of Velocity Ratio vs. UPVs

Because the different cores have various UPVp and UPVs values, a parameterVr, namely, velocity ratio, is introduced to eliminate the impact of coal volume and density [21, 37] (seen in equation (2)) and to explore potential correlations between the ratio and the corresponding UPVs values for lignite, bituminite, and anthracite.
(2)Vr‐water=UPVp‐wateriUPVs‐wateri,Vr‐gas=UPVp‐gasiUPVs‐gasi,where Vr−water and Vr−gas are the velocity ratios of coal under water and gas saturation, respectively, and i is the number of one kind of coal; specifically, i equals to 24 for lignite and 26 for bituminite and anthracite. As seen in Figure 5, Vr correlates linearly with the corresponding UPVs values. The linear fitting equations are listed in Table 4. These discrete Vr data are fitted as negative linear relationships with UPVs, and different coals have different declining degrees. The difference in the velocity ratio might be attributed to the characteristics of structural cracks and inherent properties of the coal, such as grain size and pore shape, which result in the decrease of the coal integrity and strength.Figure 5
Correlations between Vr-water and UPVs-water and between Vr-gas and UPVs-gas for (a, b) lignite, (c, d) bituminite, and (e, f) anthracite.
(a)
(b)
(c)
(d)
(e)
(f)Table 4
Linear fit equations ofVr for lignite, bituminite, and anthracite under water and gas saturation.
Condition
Equation
R2
Lignite
Water saturation
Vr−water=−0.475∗UPVs−water+1.95
0.459
Gas saturation
Vr−gas=−0.492∗UPVs−gas+1.91
0.515
Bituminite
Water saturation
Vr−water=−0.511∗UPVs−water+2.05
0.837
Gas saturation
Vr−gas=−0.171∗UPVs−gas+1.41
0.456
Anthracite
Water saturation
Vr−water=−0.222∗UPVs−water+1.57
0.399
Gas saturation
Vr−gas=−0.447∗UPVs−gas+1.89
0.684For one particular coal with certain porosity, elastic waves show different responses to different fluids occupying the cracks; for example, the UPVp has higher sensitivity with a small amount of gas compared to the UPVs, and the UPVp value might decrease by a larger degree than the UPVs value [46, 47]. As shown in Figure 5, the declining tendency of the correlations between Vr and UPVs indicates that the degree of increase in the UPVp is smaller than that in the UPVs, when the elastic wave propagates via cracks occupied by fluids. According to Kuster and Toksoz [40], different media had different acoustic resistance (AR) values; for example, the AR value of gas was 0.0043×104g/(m2∗s), whereas that of water was 0.29−0.66×104g/(m2∗s), and coal had a smaller AR difference with water. It seemed that the difference in declining tendency might be attributed to coal rank, and the coal with a lower rank had a large amount of fissures. When the fissures were filled with water or gas, the larger AR difference between the coal and gas caused a large amount of energy to dissipate by means of wave reflection or refraction, and the Vr value changes were greater. Thus, the existence of cracks or pores had a significant inverse effect on wave velocity, considering the occupying fluids and coal rank.Moreover, under water saturation conditions, theVr scatter of lignite, bituminite, and anthracite had good linear fits with the corresponding UPVs, whereas the velocity ratio scatter of lignite and bituminite was more discrete under gas saturation, and those of anthracite had good linear correlation with the UPVs gas. The difference was expected that the adsorbed water improved the matrix homogeneity, given that the density of water exceeds that of air used in the experiments. Lignite had a mean Vr value of 1.19 when water-saturated and 1.36 when gas-saturated. Bituminite and anthracite had mean Vr values of 1.24 and 1.22, respectively, when they were under water saturation, and they had mean values of 1.26 and 1.34, respectively, under gas saturation. According to the linear fitting, when the UPVs-water value was 1.4 km/s, the potential Vr-water values of lignite, bituminite, and anthracite were 1.285, 1.335, and 1.259, respectively, and when the UPVs-gas value was 1.0 km/s, the potential Vr-gas values of lignite, bituminite, and anthracite were 1.418, 1.239, and 1.443, respectively. The parameter Vr value of coal might provide evidence to locate the cracks after fracturing by measuring the velocity ratio using the measure media.


### 4.3. Correlations between UPVp and Density

Figure6 shows the distributions and relationships between UPVp and density for lignite, bituminite, and anthracite cores under water- and gas-saturated conditions, by considering the acoustic signal travel time along the coal sample. There were positive linear correlations between the UPVp and the density for lignite, bituminite, and anthracite under the two conditions, and as coal density increases, the UPVp velocity is different but generally trends upward. The values are listed in Table 5. The linear correlation coefficients for the anthracite UPVp values were 0.759 and 0.472, respectively, under water- and gas-saturated conditions, whereas the corresponding coefficients for bituminite coal were 0.689 and 0.430, respectively. For water-saturated lignite coal, the linear fitting coefficient was 0.406, and its UPVp-gas scatter had poor correlation with density (R2 less than 0.20), which might be attributed to the low rank and complex crack properties due to the large anisotropy, causing high possibility of discrete velocity distribution.Figure 6
Scatterplot and distribution of velocity data and the corresponding trends between UPVp and density for (a) lignite, (b) bituminite, and (c) anthracite at water/gas-saturated conditions.
(a)
(b)
(c)Table 5
Correlations between UPVp and porosity under water and gas saturation.
Condition
Equation
R2
Lignite
Water saturation
UPVp−water=2.49∗ρ−1.36
0.406
Gas saturation
\
\
Bituminite
Water saturation
UPVp−water=1.69∗ρ−0.46
0.689
Gas saturation
UPVp−gas=6.28∗ρ−7.62
0.430
Anthracite
Water saturation
UPVp−water=1.76∗ρ−0.49
0.759
Gas saturation
UPVp−gas=0.88∗ρ+0.49
0.472It should be noticed that there were several outliers of UPVp scatter for lignite and bituminite due to their high dispersion, and these outliers were labeled using the dotted cycles. The fitting difference might be explained from three aspects: (a) the presence of complex components, such as grains with different sizes, mineral distribution, or incomplete evolution of the plant material in the coal, leads to greater anisotropy in the lignite coal matrix, resulting in random distributions of density and wave velocity [24, 36]. (b) Fluids may occupy the void space, increasing the whole saturated coal density. Given that the water density is larger than gas density, the water-saturated coal had larger UPV values than the gas-saturated coal [37, 38]. Different coals have various UPVp values, which are mostly affected by physicochemical properties and coal rank. (c) Different coals have various pore structures and distributions. For example, anthracite has a large volume of micropores, whereas lignite and bituminite have numerous macropores or cracks [48]. The occupied water in the smaller volume pores is more likely to promote an increase in velocity with increasing density.


### 4.4. Correlations between the UPVp Values and Porosity

The presence of fissures always has a significant impact on pulse wave transmission, and wave velocity increases parallel to the bedding planes, but decreases in the perpendicular direction [49–51]. In this paper, coal porosity φ was calculated using a weighing method described as follows:
(3)φ=VcrackVcore=ΔMρwVcore=Mwater−MpreρwVcore=4Mwater−MpreρwπD2h,where Vcrack and Vcore are the volumes (cm3) of cracks and coal cores, respectively; ρw is the density of water and equals to 1.0 g/cm3; ΔM is the mass difference between Mwater and Mpre, (g); Mwater and Mpre are the coal mass at completely saturated and dry conditions, respectively (g); and D and h are the diameter and height of the coal cores, respectively, (cm).The porosity calculated in equation (3) only considers connected cracks, and closed pores are excluded for simplification. Figure 7 shows the scatterplot of data and the correlations between the UPVp and φ under water and gas saturation. The lignite cores had a mean φ value of 3.06, the bituminite cores had a mean φ value of 2.09, and the anthracite cores had a mean φ value of 1.21. This finding indicates that coal rank is inversely related to porosity; the coal with a lower rank had a larger porosity. For each kind of coal, the small porosity difference might be related to the number of connected cracks and the fact that some internal closed pores were not filled with water. However, the trend did not have disadvantageous impacts on the final results. The existence of fissures or cracks caused some reflection and refraction of waves at the crack surface, and some friction at grain boundaries, directly causing amplitude attenuation and a large energy decrease and delaying the first arrival time of the wave, finally resulting in a velocity decrease, which was coincident with the conclusion by Kohlhauser and Hellmich [51] and Li et al. [52].Figure 7
Scatterplot and linear correlations between UPVp and porosity under water and gas saturation for (a) lignite, (b) bituminite, and (c) anthracite (d) showing a sketch of wave transmission within the coal matrix.
(a)
(b)
(c)
(d)As shown in Figure7 and Table 6, the declining trends of lignite and bituminite under gas saturation were higher than under water saturation, whereas for anthracite, correlations between UPVp-water and φ had a larger decline compared to correlations between UPVp-gas and φ. The decline difference might be related to water sensitivity of the coals. That is, micropores within anthracite generally account for 50% of the total pores [53, 54], and water exhibits various modes of infiltration, such as seepage in macropores as well as diffusion and adsorption in micropores. Due to the larger adsorption capacity of anthracite, the adsorbed water molecules could squeeze into voids and increase the distance between grains, which might have some inverse impacts on the velocity. Meanwhile, the velocity of water-saturated cores decreased with increasing φ, which indicated that very large numbers of unconnected pores existed in addition to the pores filled with water. Crack properties such as surface physicochemistry, fracture roughness, and connectivity, should also be considered in the evaluation of velocity transmission.Table 6
Linear fit equations between UPVp and porosity at water and gas saturation.
Condition
Equation
R2
Lignite
Water saturation
UPVp−water=−0.092∗φ+2.16
0.433
Gas saturation
UPVp−gas=−0.272∗φ+2.07
0.564
Bituminite
Water saturation
UPVp−water=−0.218∗φ+2.37
0.533
Gas saturation
UPVp−gas=−0.527∗φ+2.39
0.526
Anthracite
Water saturation
UPVp−water=−0.256∗φ+2.24
0.706
Gas saturation
UPVp−gas=−0.237∗φ+2.01
0.769


### 4.5. Potential Applications

Based on the above results and the reported results from Kahraman [16], Vasanelli et al. [28], and Liu et al. [37], it is evident that wave velocity has some correlations with the rock properties, such as density and porosity. According to Chen et al. [21], Sansalone and Streett [55], and Bogas et al. [56], the coal regarded as a homogenous material simply might have some relations between velocity and the related mechanical parameters, shown in the following equation:
(4)UPV=Edρ⋅1−υd1+υd⋅1−2υd,(5)υd=1/2UPVp/UPVs2−1UPVp/UPVs2−1,where υd is the dynamic Poisson’s ratio, Ed is the elastic modulus, and ρ is the density. Based on the above equation, the P-wave velocity is directly proportional to the square root of the dynamic modulus of elasticity and inversely proportional to the square root of its density, and the Poisson’s ratio υd is proportional to the square of velocity ratio. Based on equations (4) and (5), the determined UPVp and UPVs could approximately deduce the elastic parameters, and the relevant intensity region of specified coal layers could be plotted, from which the potential fracture-generating region could be drawn. The UPV test method has application in enhanced CBM recovery by hydraulic fracturing or aqueous fracturing methods (such as CO2 fracturing), as shown in Figure 8.Figure 8
Potential application of velocity measurements by hydraulic fracturing or CO2 fracturing during enhanced CBM recovery.A number of drill groups are advanced into a coal seam with each group containing a single fracturing fluid (water or LCO2) injection hole and eight monitoring holes (A1,A2,…,A8) around the injection hole (hole depth of J), as shown in parts (I) and (II) in Figure 8. Taking the example of monitoring holes A3 and A5, two transducers are initially placed at the bottom of the monitoring holes and simultaneously moved by the same distance (l) from the hole bottom in sequence to measure the velocity distributions of the region between hole A3 and hole A5, and velocity values are recorded as VA3−A5i (i=0,1,2,…,J/l). When the fracturing process is finished, the posttest velocity of the specific region is recorded as VA3−A5i′ (i=0,1,2,…,J/l). By comparing the pre- and posttest velocities, the relationship between velocity and cracks can be deduced:
(6)V′A3−A5i<VA3−A5i;somecracksaregenerated,V′A3−A5i=VA3−A5i;nocracksaregenerated.Thus, it is possible to locate petrological changes caused by the mechanical effects of water or CO2 injection, rapidly identify the effective fracture zone, and deduce fracture orientations. Depending on the collected velocity data, it is possible to forecast changes in physical parameters when subjected to crustal stress. This potential application could save a significant amount of core drilling work and help to obtain useful information about coal at depth in real time.Although correlations among velocity, density, and porosity of water and gas-saturated coal cores have been identified, there is still a need for further study. For example, velocities recorded in different cores with various fluid media and fluid contents should be further investigated and velocity anisotropy should be quantified in future research. Additionally, correlations between velocities of different coal types under fluid saturation and the relevant elastic properties should be tested.


## 4.1. Correlation between UPVp and UPVs

Given the different velocity distributions of the three ranks of coal, it is necessary to analyze correlations between the UPVp and UPVs under the two different conditions. The scatter of velocity data and correlations of fit are shown in Figure4. The UPVp and UPVs values of the cores differed for both conditions, and they might depend on the coal rank and components within the coal matrix. Velocity values of cores from the same coal blocks were not consistent, because of the various orientations and distributions of microcracks. When an elastic wave transfers to existing defects, such as cleats, cracks, or pores, some reflection, refraction, and diffraction of waves and friction at the crack surface and the grain boundaries might be generated, causing amplitude attenuation and energy decrease [21, 40, 42]. The crack number and distribution might be the main factors influencing velocity decrease. The larger the number of existing cracks is, the greater the energy decrease, and the smaller the velocity is. Under water and gas saturation, the UPVp values generally exceed the UPVs values, and the UPVp and UPVs values of the same cores under water saturation exceed those under gas saturation, indicating that the discrete degree of velocity might occur more frequently under gas saturation due to the large dispersion of air molecules. The scatter in velocity data values is well fit and listed in Table 3.Figure 4
Scatterplot of velocity data and goodness-of-fit correlations between UPVs and UPVp of lignite, bituminite, and anthracite cores under water and gas saturation.
(a)
(b)
(c)
(d)
(e)
(f)Table 3
Correlations between UPVp and UPVs for lignite, bituminite, and anthracite under water or gas saturation.
Condition
Equation
R2
Lignite
Water saturation
UPVp−water=1.06∗UPVs−water+0.159
0.681
Gas saturation
UPVp−gas=1.31∗UPVs−gas+0.049
0.853
Bituminite
Water saturation
UPVp−water=0.521∗UPVs−water+1.12
0.659
Gas saturation
UPVp−gas=1.07∗UPVs−gas+0.193
0.775
Anthracite
Water saturation
UPVp−water=0.877∗UPVs−water+0.539
0.801
Gas saturation
UPVp−gas=0.791∗UPVs−gas+0.646
0.809Dependent on Figure4, the UPVp values of lignite, bituminite, and anthracite coal showed positive linear correlations with their corresponding UPVs values, under water and gas saturation, similar to the results reported by Kahraman [16], Sayed et al. [43], and Kassab and Weller [44] that UPVp scatter had a strong linear correlation with the corresponding UPVs scatter of dry rock or wet rock samples. When the UPVs-water value was 2.0 km/s, the potential UPVp-water values of lignite, bituminite, and anthracite were 2.279 km/s, 2.162 km/s, and 2.293 km/s, respectively. This difference appears to be dependent on porosity and moisture content, given that the lower the porosity and the higher the moisture content is, the larger the UPVp value is [45].


## 4.2. Analysis of Velocity Ratio vs. UPVs

Because the different cores have various UPVp and UPVs values, a parameterVr, namely, velocity ratio, is introduced to eliminate the impact of coal volume and density [21, 37] (seen in equation (2)) and to explore potential correlations between the ratio and the corresponding UPVs values for lignite, bituminite, and anthracite.
(2)Vr‐water=UPVp‐wateriUPVs‐wateri,Vr‐gas=UPVp‐gasiUPVs‐gasi,where Vr−water and Vr−gas are the velocity ratios of coal under water and gas saturation, respectively, and i is the number of one kind of coal; specifically, i equals to 24 for lignite and 26 for bituminite and anthracite. As seen in Figure 5, Vr correlates linearly with the corresponding UPVs values. The linear fitting equations are listed in Table 4. These discrete Vr data are fitted as negative linear relationships with UPVs, and different coals have different declining degrees. The difference in the velocity ratio might be attributed to the characteristics of structural cracks and inherent properties of the coal, such as grain size and pore shape, which result in the decrease of the coal integrity and strength.Figure 5
Correlations between Vr-water and UPVs-water and between Vr-gas and UPVs-gas for (a, b) lignite, (c, d) bituminite, and (e, f) anthracite.
(a)
(b)
(c)
(d)
(e)
(f)Table 4
Linear fit equations ofVr for lignite, bituminite, and anthracite under water and gas saturation.
Condition
Equation
R2
Lignite
Water saturation
Vr−water=−0.475∗UPVs−water+1.95
0.459
Gas saturation
Vr−gas=−0.492∗UPVs−gas+1.91
0.515
Bituminite
Water saturation
Vr−water=−0.511∗UPVs−water+2.05
0.837
Gas saturation
Vr−gas=−0.171∗UPVs−gas+1.41
0.456
Anthracite
Water saturation
Vr−water=−0.222∗UPVs−water+1.57
0.399
Gas saturation
Vr−gas=−0.447∗UPVs−gas+1.89
0.684For one particular coal with certain porosity, elastic waves show different responses to different fluids occupying the cracks; for example, the UPVp has higher sensitivity with a small amount of gas compared to the UPVs, and the UPVp value might decrease by a larger degree than the UPVs value [46, 47]. As shown in Figure 5, the declining tendency of the correlations between Vr and UPVs indicates that the degree of increase in the UPVp is smaller than that in the UPVs, when the elastic wave propagates via cracks occupied by fluids. According to Kuster and Toksoz [40], different media had different acoustic resistance (AR) values; for example, the AR value of gas was 0.0043×104g/(m2∗s), whereas that of water was 0.29−0.66×104g/(m2∗s), and coal had a smaller AR difference with water. It seemed that the difference in declining tendency might be attributed to coal rank, and the coal with a lower rank had a large amount of fissures. When the fissures were filled with water or gas, the larger AR difference between the coal and gas caused a large amount of energy to dissipate by means of wave reflection or refraction, and the Vr value changes were greater. Thus, the existence of cracks or pores had a significant inverse effect on wave velocity, considering the occupying fluids and coal rank.Moreover, under water saturation conditions, theVr scatter of lignite, bituminite, and anthracite had good linear fits with the corresponding UPVs, whereas the velocity ratio scatter of lignite and bituminite was more discrete under gas saturation, and those of anthracite had good linear correlation with the UPVs gas. The difference was expected that the adsorbed water improved the matrix homogeneity, given that the density of water exceeds that of air used in the experiments. Lignite had a mean Vr value of 1.19 when water-saturated and 1.36 when gas-saturated. Bituminite and anthracite had mean Vr values of 1.24 and 1.22, respectively, when they were under water saturation, and they had mean values of 1.26 and 1.34, respectively, under gas saturation. According to the linear fitting, when the UPVs-water value was 1.4 km/s, the potential Vr-water values of lignite, bituminite, and anthracite were 1.285, 1.335, and 1.259, respectively, and when the UPVs-gas value was 1.0 km/s, the potential Vr-gas values of lignite, bituminite, and anthracite were 1.418, 1.239, and 1.443, respectively. The parameter Vr value of coal might provide evidence to locate the cracks after fracturing by measuring the velocity ratio using the measure media.


## 4.3. Correlations between UPVp and Density

Figure6 shows the distributions and relationships between UPVp and density for lignite, bituminite, and anthracite cores under water- and gas-saturated conditions, by considering the acoustic signal travel time along the coal sample. There were positive linear correlations between the UPVp and the density for lignite, bituminite, and anthracite under the two conditions, and as coal density increases, the UPVp velocity is different but generally trends upward. The values are listed in Table 5. The linear correlation coefficients for the anthracite UPVp values were 0.759 and 0.472, respectively, under water- and gas-saturated conditions, whereas the corresponding coefficients for bituminite coal were 0.689 and 0.430, respectively. For water-saturated lignite coal, the linear fitting coefficient was 0.406, and its UPVp-gas scatter had poor correlation with density (R2 less than 0.20), which might be attributed to the low rank and complex crack properties due to the large anisotropy, causing high possibility of discrete velocity distribution.Figure 6
Scatterplot and distribution of velocity data and the corresponding trends between UPVp and density for (a) lignite, (b) bituminite, and (c) anthracite at water/gas-saturated conditions.
(a)
(b)
(c)Table 5
Correlations between UPVp and porosity under water and gas saturation.
Condition
Equation
R2
Lignite
Water saturation
UPVp−water=2.49∗ρ−1.36
0.406
Gas saturation
\
\
Bituminite
Water saturation
UPVp−water=1.69∗ρ−0.46
0.689
Gas saturation
UPVp−gas=6.28∗ρ−7.62
0.430
Anthracite
Water saturation
UPVp−water=1.76∗ρ−0.49
0.759
Gas saturation
UPVp−gas=0.88∗ρ+0.49
0.472It should be noticed that there were several outliers of UPVp scatter for lignite and bituminite due to their high dispersion, and these outliers were labeled using the dotted cycles. The fitting difference might be explained from three aspects: (a) the presence of complex components, such as grains with different sizes, mineral distribution, or incomplete evolution of the plant material in the coal, leads to greater anisotropy in the lignite coal matrix, resulting in random distributions of density and wave velocity [24, 36]. (b) Fluids may occupy the void space, increasing the whole saturated coal density. Given that the water density is larger than gas density, the water-saturated coal had larger UPV values than the gas-saturated coal [37, 38]. Different coals have various UPVp values, which are mostly affected by physicochemical properties and coal rank. (c) Different coals have various pore structures and distributions. For example, anthracite has a large volume of micropores, whereas lignite and bituminite have numerous macropores or cracks [48]. The occupied water in the smaller volume pores is more likely to promote an increase in velocity with increasing density.


## 4.4. Correlations between the UPVp Values and Porosity

The presence of fissures always has a significant impact on pulse wave transmission, and wave velocity increases parallel to the bedding planes, but decreases in the perpendicular direction [49–51]. In this paper, coal porosity φ was calculated using a weighing method described as follows:
(3)φ=VcrackVcore=ΔMρwVcore=Mwater−MpreρwVcore=4Mwater−MpreρwπD2h,where Vcrack and Vcore are the volumes (cm3) of cracks and coal cores, respectively; ρw is the density of water and equals to 1.0 g/cm3; ΔM is the mass difference between Mwater and Mpre, (g); Mwater and Mpre are the coal mass at completely saturated and dry conditions, respectively (g); and D and h are the diameter and height of the coal cores, respectively, (cm).The porosity calculated in equation (3) only considers connected cracks, and closed pores are excluded for simplification. Figure 7 shows the scatterplot of data and the correlations between the UPVp and φ under water and gas saturation. The lignite cores had a mean φ value of 3.06, the bituminite cores had a mean φ value of 2.09, and the anthracite cores had a mean φ value of 1.21. This finding indicates that coal rank is inversely related to porosity; the coal with a lower rank had a larger porosity. For each kind of coal, the small porosity difference might be related to the number of connected cracks and the fact that some internal closed pores were not filled with water. However, the trend did not have disadvantageous impacts on the final results. The existence of fissures or cracks caused some reflection and refraction of waves at the crack surface, and some friction at grain boundaries, directly causing amplitude attenuation and a large energy decrease and delaying the first arrival time of the wave, finally resulting in a velocity decrease, which was coincident with the conclusion by Kohlhauser and Hellmich [51] and Li et al. [52].Figure 7
Scatterplot and linear correlations between UPVp and porosity under water and gas saturation for (a) lignite, (b) bituminite, and (c) anthracite (d) showing a sketch of wave transmission within the coal matrix.
(a)
(b)
(c)
(d)As shown in Figure7 and Table 6, the declining trends of lignite and bituminite under gas saturation were higher than under water saturation, whereas for anthracite, correlations between UPVp-water and φ had a larger decline compared to correlations between UPVp-gas and φ. The decline difference might be related to water sensitivity of the coals. That is, micropores within anthracite generally account for 50% of the total pores [53, 54], and water exhibits various modes of infiltration, such as seepage in macropores as well as diffusion and adsorption in micropores. Due to the larger adsorption capacity of anthracite, the adsorbed water molecules could squeeze into voids and increase the distance between grains, which might have some inverse impacts on the velocity. Meanwhile, the velocity of water-saturated cores decreased with increasing φ, which indicated that very large numbers of unconnected pores existed in addition to the pores filled with water. Crack properties such as surface physicochemistry, fracture roughness, and connectivity, should also be considered in the evaluation of velocity transmission.Table 6
Linear fit equations between UPVp and porosity at water and gas saturation.
Condition
Equation
R2
Lignite
Water saturation
UPVp−water=−0.092∗φ+2.16
0.433
Gas saturation
UPVp−gas=−0.272∗φ+2.07
0.564
Bituminite
Water saturation
UPVp−water=−0.218∗φ+2.37
0.533
Gas saturation
UPVp−gas=−0.527∗φ+2.39
0.526
Anthracite
Water saturation
UPVp−water=−0.256∗φ+2.24
0.706
Gas saturation
UPVp−gas=−0.237∗φ+2.01
0.769


## 4.5. Potential Applications

Based on the above results and the reported results from Kahraman [16], Vasanelli et al. [28], and Liu et al. [37], it is evident that wave velocity has some correlations with the rock properties, such as density and porosity. According to Chen et al. [21], Sansalone and Streett [55], and Bogas et al. [56], the coal regarded as a homogenous material simply might have some relations between velocity and the related mechanical parameters, shown in the following equation:
(4)UPV=Edρ⋅1−υd1+υd⋅1−2υd,(5)υd=1/2UPVp/UPVs2−1UPVp/UPVs2−1,where υd is the dynamic Poisson’s ratio, Ed is the elastic modulus, and ρ is the density. Based on the above equation, the P-wave velocity is directly proportional to the square root of the dynamic modulus of elasticity and inversely proportional to the square root of its density, and the Poisson’s ratio υd is proportional to the square of velocity ratio. Based on equations (4) and (5), the determined UPVp and UPVs could approximately deduce the elastic parameters, and the relevant intensity region of specified coal layers could be plotted, from which the potential fracture-generating region could be drawn. The UPV test method has application in enhanced CBM recovery by hydraulic fracturing or aqueous fracturing methods (such as CO2 fracturing), as shown in Figure 8.Figure 8
Potential application of velocity measurements by hydraulic fracturing or CO2 fracturing during enhanced CBM recovery.A number of drill groups are advanced into a coal seam with each group containing a single fracturing fluid (water or LCO2) injection hole and eight monitoring holes (A1,A2,…,A8) around the injection hole (hole depth of J), as shown in parts (I) and (II) in Figure 8. Taking the example of monitoring holes A3 and A5, two transducers are initially placed at the bottom of the monitoring holes and simultaneously moved by the same distance (l) from the hole bottom in sequence to measure the velocity distributions of the region between hole A3 and hole A5, and velocity values are recorded as VA3−A5i (i=0,1,2,…,J/l). When the fracturing process is finished, the posttest velocity of the specific region is recorded as VA3−A5i′ (i=0,1,2,…,J/l). By comparing the pre- and posttest velocities, the relationship between velocity and cracks can be deduced:
(6)V′A3−A5i<VA3−A5i;somecracksaregenerated,V′A3−A5i=VA3−A5i;nocracksaregenerated.Thus, it is possible to locate petrological changes caused by the mechanical effects of water or CO2 injection, rapidly identify the effective fracture zone, and deduce fracture orientations. Depending on the collected velocity data, it is possible to forecast changes in physical parameters when subjected to crustal stress. This potential application could save a significant amount of core drilling work and help to obtain useful information about coal at depth in real time.Although correlations among velocity, density, and porosity of water and gas-saturated coal cores have been identified, there is still a need for further study. For example, velocities recorded in different cores with various fluid media and fluid contents should be further investigated and velocity anisotropy should be quantified in future research. Additionally, correlations between velocities of different coal types under fluid saturation and the relevant elastic properties should be tested.


## 5. Conclusions

Based on this study, the following major conclusions can be drawn:(i)
The velocities recorded in the three different coal ranks displayed various distributions and discrete degrees, likely related to rank and saturation media. By comparing the range of the UPVp and UPVs box plots, it is evident that the UPVp is more accurate or reliable for characterizing the existence of micro- or macrocracks with the assistance of adsorbed water
(ii)
The UPVp values of lignite, bituminite, and anthracite coals showed positive linear correlations with their corresponding UPVs values, under water and gas saturation. The UPVp values correlated positively with the density of water/gas-saturated cores and correlated negatively with the porosity of both prepared cores
(iii)
The ratio of UPVp/UPVs had a negative linear correlation with the UPVs values for lignite, bituminite, and anthracite, and the different decline trends might be attributed to coal rank. The coals with lower rank had large amounts of fissures. The larger difference of acoustic resistance between coal and gas dissipated a large amount of energy by means of wave reflection or refraction



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*Source: 3729381-2019-05-02.xml*