# Laboratory Study on Changes in Gas Desorption Properties of Anthracite after Cyclic Loading

Authors: Tie Li; Dong Wang; Mei-Hua Liu; Liang Chen; Hao Liu
Journal: Advances in Civil Engineering
 (2021)

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## Abstract

Coal mass is subjected to cyclic loading during pulsating hydraulic fracturing (PHF), and changes in its gas desorption properties affect gas drainage. Therefore, it is of great importance to correctly understand the influences of cyclic loading on the gas desorption properties of coal mass. Firstly, loading tests with different frequencies and amplitudes were performed on anthracite from Qinshui Basin (Shanxi Province, China) using a fatigue testing machine. Secondly, gas desorption tests were performed to determine the associated curves for each test group at different equilibrium pressures, and the initial desorption capacity and diffusion coefficient of the gas were calculated. Finally, the influence of different loading conditions on the gas desorption laws were analyzed. The test results demonstrate that a greater loading frequency increases the ratio of the initial desorption capacity so that the desorption rate of coal samples is higher, and the gas desorption properties become increasingly better in the initial stage. However, variations in the amplitude have minimal impact on the ratio of the initial desorption capacity. When the amplitude is too large in the initial stage, the diffusion coefficient decreases and the gas desorption properties worsen. In addition, the above test results are used to discuss the selection of the amplitude and frequency in the PHF process from a macroperspective. The contained research results provide an important theoretical basis for the field application of PHF technologies in coal mines.


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## Body

## 1. Introduction

Coal and gas outburst are one of the major disasters that significantly threatens safe production in coal mines, with China being one of the countries with the most serious coal and gas outburst disasters in the world [1–3]. To date, with increased mining depths and intensities in coal mines, hazard factors such as high in situ stresses, gas pressures, and gas contents readily induce rock and gas dynamic disasters, which further affects safe production in coal mines and threatens the lives of underground workers [4–7]. After many field practices, it has been proven that gas drainage is an effective means to prevent and control gas disasters in coal mines and to develop and utilize gas in coal seams [8–10].The permeability of coal seams is a key parameter that influences gas drainage effects [11, 12]. However, the permeability of coal seams in China is generally low, which mostly ranges from 10−4 to 10−3 mD at 3 to 4 orders of magnitude lower than those in the United States and Australia [13–15]. Existing studies show that technologies such as hydraulic slotting, fracturing, and flushing can effectively increase the permeability of coal seams, which improves the gas drainage effects [16–22]. Nevertheless, in recent years, it has been found that the engineering application of traditional hydraulic technologies requires the consumption of significant water resources to achieve the desired effects [19, 23]. Moreover, it is difficult to apply such technologies in areas with water shortages [24, 25]. To solve this problem, Li et al. [26] proposed the pulsating hydraulic fracturing (PHF) approach based on traditional hydraulic fracturing technologies. This method continuously injects pulsating water with a certain frequency into coal seams and produces a cyclic loading, unloading, and loading effect by controlling the pulsating water pressure. With an increasing number of cycles, fatigue failure gradually occurs in coal mass and some new pores and fractures are formed. These coalesce with preexisting pores to form an interconnected fracture network, which provides channels for gas migration and greatly improves the permeability of coal seams [27]. Xu et al. [28] and Ni et al. [29] separately performed PHF tests in Daxing Coal Mine in Tiefa coalfield, Liaoning Province, and in Changping Coal Mine in Qinshui coalfield, Shanxi Province, China. The field test results showed that the technology can safely and reliably improve gas drainage effects.During gas drainage from coal seams, gas is first desorbed from the coal matrix and diffused into fractures before flowing into drainage boreholes under seepage effects [30, 31]. Gas desorption is another important factor that impacts drainage effects. If coal mass has a strong gas desorption capacity, coalbed methane (CBM) adsorbed at the inner surface of pores in the coal matrix changes from an adsorbed state to a free state as much as possible, and the ability of CBM diffusion from the matrix and micropores to the fractures is improved [32]. Su et al. [33] demonstrated that pore structures in the coal mass significantly influence gas desorption properties. In the PHF process, pore structures in the coal matrix are likely to change to some extent under cyclic loading. Xie et al. [34] also proved such a perspective as they compared and analyzed pore structures in coal mass before and after PHF using a scanning electron microscope and found the preexisting pores after PHF, which change from small to large. However, the effects of cyclic loading on gas desorption properties have been rarely investigated to date. Therefore, to further understand the dynamics of gas migration in PHF processes, it is of great scientific importance to study the change laws of the desorption properties in coal mass under cyclic loading.Based on the above research status, loading tests with different frequencies and amplitudes were performed on anthracite from Qinshui Basin, Shanxi Province, China, by utilizing a fatigue testing machine. Furthermore, gas desorption curves for each test group at different equilibrium pressures were obtained through gas desorption tests, and the initial desorption capacity and diffusion coefficient of the gas were calculated. Finally, this study analyzed the effects of different loading conditions on gas desorption laws and provides a discussion of the selection of the amplitude and frequency in the PHF process from a macroperspective. Therefore, the research results offer an important theoretical basis for field applications of PHF technologies in coal mines.


## 2. Materials and Methods

### 2.1. Coal Sample Preparation

Anthracite from the Qinshui Basin, Shanxi Province, China, was used for the coal samples in the tests. The coal samples were collected from a freshly exposed working face underground before being sealed and packed immediately and sent to the laboratory as fast as possible to prevent oxidization. The basic properties of the coal samples are shown in Table1.Table 1
Basic properties of the coal samples.
PropertyTypeProximate analysis (wt.%)MadAadVdafValueAnthracite coal1.898.599.41Mad, moisture content; Aad, ash yield; Vdaf, volatile matter.This study performed cyclic loading and methane desorption tests after processing the crushed coal samples into briquettes because the anisotropy of the coal sample could affect the test results. The briquettes were processed according to the following two primary steps:(1)
Preparation of pulverized coal: The coal blocks were ground into small powder particles using a crusher and a grinder and were screened repeatedly with standard sieves of 0.2 and 0.25 mm. Thus, pulverized coal particles with particle sizes of 0.2–0.25 mm were obtained.(2)
Compression molding: Pulverized coal of 200 g was placed into a mold with a diameter of 50 mm and pressed for 20 min to shape the sample with a material testing machine at 200 t under a molding pressure of 100 MPa. The pressure was increased to a preset value within 10 min at a loading speed of 20 kN/min. The deviation in pressures caused the final molding pressure to be 197 kN.


### 2.2. Cyclic Loading Tests

To study the influences of cyclic loading with different frequencies and amplitudes on the gas desorption properties in anthracite, this research designed seven groups of loading conditions, as shown in Table2.Table 2
Loading conditions for cyclic loading tests.
Test numberTest conditionLoading time (h)Loading frequency (Hz)Amplitude of loading pressure (MPa)11012–18627344710–20514–166—157———Notes: Group Nos. 1–5 are the test groups that change the frequency or amplitude alone; group No. 6 is the control group with a constant frequency and amplitude; group No. 7 represents the blank control group without cyclic fatigue loading.During cyclic loading, the specimens were molded under pressure for 20 min together with the mold and were placed on the fatigue testing machine (Figure1). Sine waves were applied on the coal samples for 6 h in total following the loading conditions in Table 2. After loading, the mold and specimen were removed, and the mold was opened with a wrench to retrieve the final specimen.Figure 1
Fatigue testing machine.This paper mainly analyzes the effect of loading frequency and loading amplitude on the coal desorption performance. The loading frequencies were set to 4, 7, and 10 Hz, and the loading amplitudes were set to 10–20, 12–18, and 14–16 MPa. For each experimental condition, three desorption tests were performed at different equilibrium pressures (0.5, 1, 0, and 1.5 MPa).


### 2.3. Gas Desorption Tests

In accordance with the Determination Method of Methane Adsorption Capacity in Coal (MT/T752-2004), the steps for the desorption tests are shown as follows:(1)
Loading samples: The coal samples that were subjected to cyclic loading were crushed with a hammer to obtain particles sized at 1–3 mm after screening. Coal samples of 100 g in each test group were placed into numbered coal sample tanks.(2)
Gas filling and leakage detection: High-purity methane was filled to the three preset pressures of 0.5, 1.0, and 1.5 MPa (pressure for adsorption equilibrium in the stable state) for each coal sample tank. The coal sample tanks were then placed into water to check for leakage. If there were no bubbles, the tank was qualified; otherwise, the tank was tightened or its sealing rings were replaced.(3)
Equilibrium adsorption: The qualified coal sample tanks after leak detection were placed in a constant temperature water bath at 30°C for adsorption equilibrium for more than 24 h. The measured gas pressures, room temperatures, and atmospheric pressures of the correspondingly numbered coal sample tanks were recorded.(4)
Desorption tests: The coal sample tank valve was opened rapidly. When the pressure gauge dropped to zero, the tank was rapidly connected to an electronic flowmeter interfaced with a computer to constantly record the gas desorption capacities at different moments within 2 h. After 2 h of desorption, the valve of the coal sample tank was quickly tightened.(5)
Laboratory test results under the pressure of adsorption equilibrium were obtained by repeating steps (1)–(4).After completing the desorption tests, the final obtained desorption capacity was converted into a volume under standard conditions as(1)Qt=273.15101325273.15+tw∗Patm−9.81hw−P0∗Qt′,where Qt, Qt′, and tw represent the volume (mL) in the standard state converted from the total gas desorption capacity, total gas desorption capacity (mL) measured during the tests, and room temperature (°C) in the test, respectively; and Patm, hw, and P0 indicate the atmospheric pressure (Pa) in the laboratory, height (mm) of a liquid column in the apparatus for desorption when reading data, and the saturated steam pressure (Pa) at the temperature tw, respectively.


## 2.1. Coal Sample Preparation

Anthracite from the Qinshui Basin, Shanxi Province, China, was used for the coal samples in the tests. The coal samples were collected from a freshly exposed working face underground before being sealed and packed immediately and sent to the laboratory as fast as possible to prevent oxidization. The basic properties of the coal samples are shown in Table1.Table 1
Basic properties of the coal samples.
PropertyTypeProximate analysis (wt.%)MadAadVdafValueAnthracite coal1.898.599.41Mad, moisture content; Aad, ash yield; Vdaf, volatile matter.This study performed cyclic loading and methane desorption tests after processing the crushed coal samples into briquettes because the anisotropy of the coal sample could affect the test results. The briquettes were processed according to the following two primary steps:(1)
Preparation of pulverized coal: The coal blocks were ground into small powder particles using a crusher and a grinder and were screened repeatedly with standard sieves of 0.2 and 0.25 mm. Thus, pulverized coal particles with particle sizes of 0.2–0.25 mm were obtained.(2)
Compression molding: Pulverized coal of 200 g was placed into a mold with a diameter of 50 mm and pressed for 20 min to shape the sample with a material testing machine at 200 t under a molding pressure of 100 MPa. The pressure was increased to a preset value within 10 min at a loading speed of 20 kN/min. The deviation in pressures caused the final molding pressure to be 197 kN.


## 2.2. Cyclic Loading Tests

To study the influences of cyclic loading with different frequencies and amplitudes on the gas desorption properties in anthracite, this research designed seven groups of loading conditions, as shown in Table2.Table 2
Loading conditions for cyclic loading tests.
Test numberTest conditionLoading time (h)Loading frequency (Hz)Amplitude of loading pressure (MPa)11012–18627344710–20514–166—157———Notes: Group Nos. 1–5 are the test groups that change the frequency or amplitude alone; group No. 6 is the control group with a constant frequency and amplitude; group No. 7 represents the blank control group without cyclic fatigue loading.During cyclic loading, the specimens were molded under pressure for 20 min together with the mold and were placed on the fatigue testing machine (Figure1). Sine waves were applied on the coal samples for 6 h in total following the loading conditions in Table 2. After loading, the mold and specimen were removed, and the mold was opened with a wrench to retrieve the final specimen.Figure 1
Fatigue testing machine.This paper mainly analyzes the effect of loading frequency and loading amplitude on the coal desorption performance. The loading frequencies were set to 4, 7, and 10 Hz, and the loading amplitudes were set to 10–20, 12–18, and 14–16 MPa. For each experimental condition, three desorption tests were performed at different equilibrium pressures (0.5, 1, 0, and 1.5 MPa).


## 2.3. Gas Desorption Tests

In accordance with the Determination Method of Methane Adsorption Capacity in Coal (MT/T752-2004), the steps for the desorption tests are shown as follows:(1)
Loading samples: The coal samples that were subjected to cyclic loading were crushed with a hammer to obtain particles sized at 1–3 mm after screening. Coal samples of 100 g in each test group were placed into numbered coal sample tanks.(2)
Gas filling and leakage detection: High-purity methane was filled to the three preset pressures of 0.5, 1.0, and 1.5 MPa (pressure for adsorption equilibrium in the stable state) for each coal sample tank. The coal sample tanks were then placed into water to check for leakage. If there were no bubbles, the tank was qualified; otherwise, the tank was tightened or its sealing rings were replaced.(3)
Equilibrium adsorption: The qualified coal sample tanks after leak detection were placed in a constant temperature water bath at 30°C for adsorption equilibrium for more than 24 h. The measured gas pressures, room temperatures, and atmospheric pressures of the correspondingly numbered coal sample tanks were recorded.(4)
Desorption tests: The coal sample tank valve was opened rapidly. When the pressure gauge dropped to zero, the tank was rapidly connected to an electronic flowmeter interfaced with a computer to constantly record the gas desorption capacities at different moments within 2 h. After 2 h of desorption, the valve of the coal sample tank was quickly tightened.(5)
Laboratory test results under the pressure of adsorption equilibrium were obtained by repeating steps (1)–(4).After completing the desorption tests, the final obtained desorption capacity was converted into a volume under standard conditions as(1)Qt=273.15101325273.15+tw∗Patm−9.81hw−P0∗Qt′,where Qt, Qt′, and tw represent the volume (mL) in the standard state converted from the total gas desorption capacity, total gas desorption capacity (mL) measured during the tests, and room temperature (°C) in the test, respectively; and Patm, hw, and P0 indicate the atmospheric pressure (Pa) in the laboratory, height (mm) of a liquid column in the apparatus for desorption when reading data, and the saturated steam pressure (Pa) at the temperature tw, respectively.


## 3. Results and Discussion

### 3.1. Analysis on Characteristics of Desorption Curves at Different Equilibrium Pressures

Figures2 and 3 show the desorption curves of the briquette samples at the select equilibrium pressures (0.5, 1.0, and 1.5 MPa) under different loading conditions. Because the production process of briquettes is different from that of common briquettes, the adsorption curves have certain differences from those of most coal mass analyses, but the general laws that govern this process are similar. The trends of the desorption curves for briquettes under different loading conditions are consistent. With an increasing desorption time, the desorption capacity from the briquette samples continuously increases and the initial desorption rate is rapid. After passing the early growth stage, the desorption rate drops sharply after 10 min and then becomes gentler. A faster initial gas desorption rate gives a quicker desorption rate attenuation. This is because when a coal sample tank is opened, the gas equilibrium state with a high concentration in the coal sample tank is broken instantly, and gas is desorbed from the adsorbed state. A higher equilibrium pressure gives a larger gas desorption capacity. However, due to the samples used in the tests, the curves are nearly flat in the later stage and the desorption capacities within 60 min are not significantly different at various equilibrium pressures.Figure 2
Desorption curves of the samples under different loading frequencies. (a) Equilibrium pressure of 0.5 MPa. (b) Equilibrium pressure of 1.0 MPa. (c) Equilibrium pressure of 1.5 MPa.
(a)(b)(c)Figure 3
Desorption curves of the samples under different loading amplitudes. (a) Equilibrium pressure of 0.5 MPa. (b) Equilibrium pressure of 1.0 MPa. (c) Equilibrium pressure of 1.5 MPa.
(a)(b)(c)Comparing the curves in Figures2 and 3 indicates that the desorption capacities of the samples within 60 min are different for the various loading frequencies and amplitudes. As the frequency increases, the desorption capacity within 60 min rises slightly with an obvious difference. However, the amplitude has little influence and the desorption capacity shows a small difference under various amplitudes (except for the test group under the amplitude of 10–20 MPa). After desorption on the pore surface, the adsorbed gas in the coal needs to enter the pore and fissure system of the coal body through diffusion, which then flows to the drainage hole via seepage. Therefore, the gas desorption characteristics significantly impact the gas drainage effect of the coal seam, which is discussed in Section 3.4.


### 3.2. Analysis on the Effects of Loading Frequency for Gas Desorption Parameters

The gas desorption curves in Section3.1 indicate that the associated process in coal mass has a fast initial gas desorption that then attenuates quickly. Therefore, it is important to study the initial desorption capacity and diffusion coefficient. Combining pore volumes in each stage with the initial gas desorption capacity and diffusion coefficient allows studying the influences of a changing loading frequency on the gas desorption parameters. Taking the desorption capacity within 1 min in the early stage in the test as the initial desorption capacity allows investigating the relationship between the initial desorption rate and the characteristics of pores in the coal mass. The statistical results of the desorption capacities at different equilibrium pressures in each test group are given in Table 3.Table 3
Cumulative desorption capacity from the briquettes under different loading frequencies.
Loading conditionsEquilibrium pressure (MPa)Desorption capacity within 1 min (Q1/mL·g−1)Desorption capacity within 60 min (Q60/mL·g−1)Q1/Q60 (%)Frequency (Hz)Amplitude (MPa)412–180.52.625.2350.0773.836.6257.90104.167.0958.70—152.224.7047.18412–181.02.795.4051.6574.186.6962.48104.277.1859.48—152.134.8743.77412–181.53.025.8052.1074.246.7562.78104.507.2262.27—152.414.9748.56Table3 indicates that changes in the loading conditions influence the Q1/Q60 value. With a greater loading frequency, the ratio of the cumulative desorption capacity within 1 min to that within 60 min increases. The Q1/Q60 values in the test groups under the frequencies of 4 and 7 Hz are 50.07–52.1% and 57.90–65.78%, respectively. The Q1/Q60 value for the test group under 10 Hz is slightly different from that for the test group under 7 Hz, which ranges from 58.7 to 62.27%. However, the Q1/Q60 value is in the range of 43.7–48.56% in the control group. Loading sine waves with different frequencies increases the gas desorption capacity by 16–34% in the early stage. The greater loading frequency (namely, the greater volume and specific surface area of pores) increases the ratio of the initial desorption capacity so that the desorption rate of the samples is larger. In addition, a greater equilibrium pressure causes a larger Q1/Q60 value. The increased ratio of the initial desorption capacity indicates that, in the initial stage, the desorption capacity is large and the desorption rate is greater.The initial gas desorption capacity is calculated based on the relational expression between the initial gas diffusion coefficient and the square root of time proposed by Barrer [35] as(2)Qi=At,where Qi, A, and t represent the initial gas desorption capacity, initial gas diffusion coefficient, and desorption time, respectively. In the test, gas desorption data within 2.64 min were used as the initial gas desorption capacity and the square root of time was regarded as the abscissa. Thus, the adsorption-desorption fit curves of the briquette samples at the selected equilibrium pressures (0.5, 1.0, and 1.5 MPa) under different loading frequencies are drawn, as shown in Figure 4. The fitting results are summarized in Table 4.Figure 4
Fit curves for the diffusion coefficient of the samples in the early stage under different loading frequencies. (a) Equilibrium pressure of 0.5 MPa. (b) Equilibrium pressure of 1.0 MPa. (c) Equilibrium pressure of 1.5 MPa.
(a)(b)(c)Table 4
Fit results for the relationship between the desorption capacity of the briquette samples within 2.64 min and the square root of time under different loading frequencies.
Loading conditions0.5 MPa1.0 MPa1.5 MPaFrequency (Hz)Amplitude (MPa)A1R2A2R2A3R2412–182.76350.99692.61600.99843.08280.995173.60110.99463.67420.99453.71560.9939103.98550.99384.05100.99084.01280.9938—152.47680.99622.15880.99652.63010.9875The fitting results indicate the curves have high fitting correlations with anR2 coefficient that reaches 0.98. The gas diffusion coefficient in the early stage is correlated with the pore characteristics in the coal samples, equilibrium pressure, and final gas desorption capacity. With a greater loading frequency, the gas diffusion coefficient gradually increases in the early stage. The diffusion coefficients in the test groups at frequencies of 4, 7, and 10 Hz are 2.6160–3.0828, 3.6011–3.7156, and 3.9855–4.0510, respectively, in the early stage, in which the maximum value is found in the test group under a frequency of 10 Hz. In the control group under loading with a stable pressure, the diffusion coefficient ranges from 2.1588 to 2.6301. Applying sine waves with different frequencies increases the diffusion coefficient by 12–60% in the early stage, indicating that, with a larger loading frequency, the gas desorption properties become increasingly better in the early stage.


### 3.3. Analysis on Influences of Loading Amplitude on Gas Desorption Parameters

The data for the cumulative desorption capacities within 1 and 60 min when changing the loading amplitude are shown in Table5.Table 5
Cumulative desorption capacities of briquettes under different loading amplitudes.
Loading conditionsAmplitude (MPa)Equilibrium pressure (MPa)Desorption capacity within 1 min (Q1/mL·g−1)Desorption capacity within 60 minQ60/mL·g−1)Q1/Q60 (%)Frequency (Hz)710–200.52.134.6046.3712–183.836.6257.9014–163.246.3251.19—152.224.7047.18710–201.01.884.7839.2712–184.186.6962.4814–163.466.6052.43—152.134.8743.77710–201.52.224.9145.1612–184.246.7562.7814–164.376.6066.17—152.414.9748.56Amplitude changes have minimal influence on the ratio of the initial desorption capacity. TheQ1/Q60 value is maximized and reaches 57.90–62.78% in the test group under an amplitude of 12–18 MPa, while that in the test group under an amplitude of 14–16 MPa is approximately 52% at the equilibrium pressures of 0.5 and 1.0 MPa. However, the Q1/Q60 value reaches 66.17% at the equilibrium pressure of 1.5 MPa. Compared with the control group (43.77–48.56%), the Q1/Q60 value increases by approximately 32%. The Q1/Q60 value is the minimum in the test group under an amplitude of 10–20 MPa, which is the only test group with a value smaller than the control group at around 93% of the control group. The adsorption-desorption fitting curves of the briquette samples at the selected equilibrium pressures (0.5, 1.0, and 1.5 MPa) under different loading amplitudes are shown in Figure 5. A statistical analysis of fitting results is demonstrated in Table 6. The fitting results for each curve are highly linearly correlated and with an R2 coefficient above 0.97.Figure 5
Fitting curves of the diffusion coefficients of the samples in the early stage under different loading amplitudes. (a) Equilibrium pressure of 0.5 MPa. (b) Equilibrium pressure of 1.0 MPa. (c) Equilibrium pressure of 1.5 MPa.
(a)(b)(c)Table 6
Fitting results for the relationship between the desorption capacity of the briquette samples within 2.5 min and the square root of time under different loading conditions.
Loading conditions0.5 MPa1.0 MPa1.5 MPaFrequency (Hz)Amplitude (MPa)A1R2A2R2A3R2710–201.98080.99932.00100.98842.55110.989412–183.60110.99463.67420.99453.71560.993914–163.36550.97213.24290.99564.01320.9915—152.47680.99622.15880.99652.63010.9875With a decreasing loading amplitude, the gas diffusion coefficient gradually increases in the early stage. The diffusion coefficients in the test groups under the amplitudes of 14–16, 12–18, and 10–20 MPa are 3.2429–4.0132, 3.6011–3.7156, and 1.9808–2.5511 MPa, respectively. Compared with the effects of the loading frequency, changes in the loading amplitude lead to small changes in the diffusion coefficient. Compared with the diffusion coefficient in the control group, those in the test groups with amplitudes of 12–18 and 14–16 MPa increase by 36–45%, while that in the test group under an amplitude of 10–20 MPa is only approximately 0.8% of the control group. Applying sine waves with certain amplitudes can increase the gas diffusion coefficient in the early stage. However, when the amplitude is too large in the early stage, the diffusion coefficient is reduced and the gas desorption properties worsen.


### 3.4. Implications When Selecting Frequency and Amplitude during PHF

During PHF in underground coal mines, the ultimate goal is to improve the gas drainage [36, 37]. Research shows that, at larger frequencies, the gas desorption properties of the coal samples are increasingly enhanced. Therefore, after PHF, more adsorbed methane is converted into free molecules and diffuses into fractures. When there is more free methane in the fractures, the pressure gradient increases. According to Darcy’s law, a larger pressure gradient inevitably increases the gas flow per unit time [38]. Therefore, more methane flows into the drainage boreholes. In addition, the results from Section 3.3 demonstrate that a greater loading amplitude can improve the gas desorption properties to a certain extent, but there is an optimum. In sum, in field construction, the PHF effects can be enhanced by increasing the frequency and adopting an optimal amplitude.


## 3.1. Analysis on Characteristics of Desorption Curves at Different Equilibrium Pressures

Figures2 and 3 show the desorption curves of the briquette samples at the select equilibrium pressures (0.5, 1.0, and 1.5 MPa) under different loading conditions. Because the production process of briquettes is different from that of common briquettes, the adsorption curves have certain differences from those of most coal mass analyses, but the general laws that govern this process are similar. The trends of the desorption curves for briquettes under different loading conditions are consistent. With an increasing desorption time, the desorption capacity from the briquette samples continuously increases and the initial desorption rate is rapid. After passing the early growth stage, the desorption rate drops sharply after 10 min and then becomes gentler. A faster initial gas desorption rate gives a quicker desorption rate attenuation. This is because when a coal sample tank is opened, the gas equilibrium state with a high concentration in the coal sample tank is broken instantly, and gas is desorbed from the adsorbed state. A higher equilibrium pressure gives a larger gas desorption capacity. However, due to the samples used in the tests, the curves are nearly flat in the later stage and the desorption capacities within 60 min are not significantly different at various equilibrium pressures.Figure 2
Desorption curves of the samples under different loading frequencies. (a) Equilibrium pressure of 0.5 MPa. (b) Equilibrium pressure of 1.0 MPa. (c) Equilibrium pressure of 1.5 MPa.
(a)(b)(c)Figure 3
Desorption curves of the samples under different loading amplitudes. (a) Equilibrium pressure of 0.5 MPa. (b) Equilibrium pressure of 1.0 MPa. (c) Equilibrium pressure of 1.5 MPa.
(a)(b)(c)Comparing the curves in Figures2 and 3 indicates that the desorption capacities of the samples within 60 min are different for the various loading frequencies and amplitudes. As the frequency increases, the desorption capacity within 60 min rises slightly with an obvious difference. However, the amplitude has little influence and the desorption capacity shows a small difference under various amplitudes (except for the test group under the amplitude of 10–20 MPa). After desorption on the pore surface, the adsorbed gas in the coal needs to enter the pore and fissure system of the coal body through diffusion, which then flows to the drainage hole via seepage. Therefore, the gas desorption characteristics significantly impact the gas drainage effect of the coal seam, which is discussed in Section 3.4.


## 3.2. Analysis on the Effects of Loading Frequency for Gas Desorption Parameters

The gas desorption curves in Section3.1 indicate that the associated process in coal mass has a fast initial gas desorption that then attenuates quickly. Therefore, it is important to study the initial desorption capacity and diffusion coefficient. Combining pore volumes in each stage with the initial gas desorption capacity and diffusion coefficient allows studying the influences of a changing loading frequency on the gas desorption parameters. Taking the desorption capacity within 1 min in the early stage in the test as the initial desorption capacity allows investigating the relationship between the initial desorption rate and the characteristics of pores in the coal mass. The statistical results of the desorption capacities at different equilibrium pressures in each test group are given in Table 3.Table 3
Cumulative desorption capacity from the briquettes under different loading frequencies.
Loading conditionsEquilibrium pressure (MPa)Desorption capacity within 1 min (Q1/mL·g−1)Desorption capacity within 60 min (Q60/mL·g−1)Q1/Q60 (%)Frequency (Hz)Amplitude (MPa)412–180.52.625.2350.0773.836.6257.90104.167.0958.70—152.224.7047.18412–181.02.795.4051.6574.186.6962.48104.277.1859.48—152.134.8743.77412–181.53.025.8052.1074.246.7562.78104.507.2262.27—152.414.9748.56Table3 indicates that changes in the loading conditions influence the Q1/Q60 value. With a greater loading frequency, the ratio of the cumulative desorption capacity within 1 min to that within 60 min increases. The Q1/Q60 values in the test groups under the frequencies of 4 and 7 Hz are 50.07–52.1% and 57.90–65.78%, respectively. The Q1/Q60 value for the test group under 10 Hz is slightly different from that for the test group under 7 Hz, which ranges from 58.7 to 62.27%. However, the Q1/Q60 value is in the range of 43.7–48.56% in the control group. Loading sine waves with different frequencies increases the gas desorption capacity by 16–34% in the early stage. The greater loading frequency (namely, the greater volume and specific surface area of pores) increases the ratio of the initial desorption capacity so that the desorption rate of the samples is larger. In addition, a greater equilibrium pressure causes a larger Q1/Q60 value. The increased ratio of the initial desorption capacity indicates that, in the initial stage, the desorption capacity is large and the desorption rate is greater.The initial gas desorption capacity is calculated based on the relational expression between the initial gas diffusion coefficient and the square root of time proposed by Barrer [35] as(2)Qi=At,where Qi, A, and t represent the initial gas desorption capacity, initial gas diffusion coefficient, and desorption time, respectively. In the test, gas desorption data within 2.64 min were used as the initial gas desorption capacity and the square root of time was regarded as the abscissa. Thus, the adsorption-desorption fit curves of the briquette samples at the selected equilibrium pressures (0.5, 1.0, and 1.5 MPa) under different loading frequencies are drawn, as shown in Figure 4. The fitting results are summarized in Table 4.Figure 4
Fit curves for the diffusion coefficient of the samples in the early stage under different loading frequencies. (a) Equilibrium pressure of 0.5 MPa. (b) Equilibrium pressure of 1.0 MPa. (c) Equilibrium pressure of 1.5 MPa.
(a)(b)(c)Table 4
Fit results for the relationship between the desorption capacity of the briquette samples within 2.64 min and the square root of time under different loading frequencies.
Loading conditions0.5 MPa1.0 MPa1.5 MPaFrequency (Hz)Amplitude (MPa)A1R2A2R2A3R2412–182.76350.99692.61600.99843.08280.995173.60110.99463.67420.99453.71560.9939103.98550.99384.05100.99084.01280.9938—152.47680.99622.15880.99652.63010.9875The fitting results indicate the curves have high fitting correlations with anR2 coefficient that reaches 0.98. The gas diffusion coefficient in the early stage is correlated with the pore characteristics in the coal samples, equilibrium pressure, and final gas desorption capacity. With a greater loading frequency, the gas diffusion coefficient gradually increases in the early stage. The diffusion coefficients in the test groups at frequencies of 4, 7, and 10 Hz are 2.6160–3.0828, 3.6011–3.7156, and 3.9855–4.0510, respectively, in the early stage, in which the maximum value is found in the test group under a frequency of 10 Hz. In the control group under loading with a stable pressure, the diffusion coefficient ranges from 2.1588 to 2.6301. Applying sine waves with different frequencies increases the diffusion coefficient by 12–60% in the early stage, indicating that, with a larger loading frequency, the gas desorption properties become increasingly better in the early stage.


## 3.3. Analysis on Influences of Loading Amplitude on Gas Desorption Parameters

The data for the cumulative desorption capacities within 1 and 60 min when changing the loading amplitude are shown in Table5.Table 5
Cumulative desorption capacities of briquettes under different loading amplitudes.
Loading conditionsAmplitude (MPa)Equilibrium pressure (MPa)Desorption capacity within 1 min (Q1/mL·g−1)Desorption capacity within 60 minQ60/mL·g−1)Q1/Q60 (%)Frequency (Hz)710–200.52.134.6046.3712–183.836.6257.9014–163.246.3251.19—152.224.7047.18710–201.01.884.7839.2712–184.186.6962.4814–163.466.6052.43—152.134.8743.77710–201.52.224.9145.1612–184.246.7562.7814–164.376.6066.17—152.414.9748.56Amplitude changes have minimal influence on the ratio of the initial desorption capacity. TheQ1/Q60 value is maximized and reaches 57.90–62.78% in the test group under an amplitude of 12–18 MPa, while that in the test group under an amplitude of 14–16 MPa is approximately 52% at the equilibrium pressures of 0.5 and 1.0 MPa. However, the Q1/Q60 value reaches 66.17% at the equilibrium pressure of 1.5 MPa. Compared with the control group (43.77–48.56%), the Q1/Q60 value increases by approximately 32%. The Q1/Q60 value is the minimum in the test group under an amplitude of 10–20 MPa, which is the only test group with a value smaller than the control group at around 93% of the control group. The adsorption-desorption fitting curves of the briquette samples at the selected equilibrium pressures (0.5, 1.0, and 1.5 MPa) under different loading amplitudes are shown in Figure 5. A statistical analysis of fitting results is demonstrated in Table 6. The fitting results for each curve are highly linearly correlated and with an R2 coefficient above 0.97.Figure 5
Fitting curves of the diffusion coefficients of the samples in the early stage under different loading amplitudes. (a) Equilibrium pressure of 0.5 MPa. (b) Equilibrium pressure of 1.0 MPa. (c) Equilibrium pressure of 1.5 MPa.
(a)(b)(c)Table 6
Fitting results for the relationship between the desorption capacity of the briquette samples within 2.5 min and the square root of time under different loading conditions.
Loading conditions0.5 MPa1.0 MPa1.5 MPaFrequency (Hz)Amplitude (MPa)A1R2A2R2A3R2710–201.98080.99932.00100.98842.55110.989412–183.60110.99463.67420.99453.71560.993914–163.36550.97213.24290.99564.01320.9915—152.47680.99622.15880.99652.63010.9875With a decreasing loading amplitude, the gas diffusion coefficient gradually increases in the early stage. The diffusion coefficients in the test groups under the amplitudes of 14–16, 12–18, and 10–20 MPa are 3.2429–4.0132, 3.6011–3.7156, and 1.9808–2.5511 MPa, respectively. Compared with the effects of the loading frequency, changes in the loading amplitude lead to small changes in the diffusion coefficient. Compared with the diffusion coefficient in the control group, those in the test groups with amplitudes of 12–18 and 14–16 MPa increase by 36–45%, while that in the test group under an amplitude of 10–20 MPa is only approximately 0.8% of the control group. Applying sine waves with certain amplitudes can increase the gas diffusion coefficient in the early stage. However, when the amplitude is too large in the early stage, the diffusion coefficient is reduced and the gas desorption properties worsen.


## 3.4. Implications When Selecting Frequency and Amplitude during PHF

During PHF in underground coal mines, the ultimate goal is to improve the gas drainage [36, 37]. Research shows that, at larger frequencies, the gas desorption properties of the coal samples are increasingly enhanced. Therefore, after PHF, more adsorbed methane is converted into free molecules and diffuses into fractures. When there is more free methane in the fractures, the pressure gradient increases. According to Darcy’s law, a larger pressure gradient inevitably increases the gas flow per unit time [38]. Therefore, more methane flows into the drainage boreholes. In addition, the results from Section 3.3 demonstrate that a greater loading amplitude can improve the gas desorption properties to a certain extent, but there is an optimum. In sum, in field construction, the PHF effects can be enhanced by increasing the frequency and adopting an optimal amplitude.


## 4. Conclusions

This study performed loading tests with different frequencies and amplitudes on anthracite from Qinshui Basin, Shanxi Province, using a fatigue testing machine. This research developed gas desorption curves in each test group at different equilibrium pressures through gas desorption tests and calculated the initial gas desorption capacity and diffusion coefficient. Finally, the influences of different loading conditions on the gas desorption laws were analyzed. The conclusions are drawn as follows:(1)
Applying sine waves of different frequencies increases the gas desorption capacity by 16–34% in the early stage. A greater loading frequency increases the ratio of the initial desorption capacity so that the desorption rate of the samples is larger. The diffusion coefficient increases by 12–60% in the early stage, indicating the gas desorption properties become increasingly better with the loading frequency.(2)
The influence laws of the changing amplitude on the ratio of the initial desorption capacity are minimal. For the test groups under amplitudes of 12–18 and 14–16 MPa, a smaller frequency increases theQ1/Q60 value by about 32%, while the Q1/Q60 value in the test group under an amplitude of 10–20 MPa is only about 93% of the control group. Applying sine waves with certain amplitudes can increase the gas diffusion coefficient in the early stage. However, when the amplitude is too large, the diffusion coefficient reduces and the gas desorption properties worsen.(3)
In the PHF process for underground coal mines, the fracturing effects can be enhanced by increasing the frequency. However, economic costs need to be considered when selecting the proper frequency. In addition, when the amplitude is 12–18 MPa, the gas diffusion coefficient is the largest in the early stage. Therefore, the amplitudes in this range are selected for PHF. The research results provide an important theoretical basis for the field applications of PHF technologies in coal mines. This paper mainly analyzed the effects of the loading frequency and amplitude on the gas desorption characteristics. The relationship between the loading frequency and balance force is not considered and will be addressed in future studies.



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