# Moisture Content on Methane Desorption Characteristics in Coal and Its Effect on Outburst Prediction

Authors: Peng Li; Yaolin Cao; Xuelong Li; Fakai Wang; Zhongguang Sun; Qinke Huang; Deyou Chen
Journal: Advances in Civil Engineering
 (2021)

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## Abstract

Facts have proved that coal and gas outbursts require rapid desorption in a short period of time. Due to the limitation of experimental conditions, the methane desorption characteristics in the first few seconds (0–60 s) in coals with different moisture contents have not been fully studied at present. In this article, the initial desorption characteristics of methane in coals with different moisture contents were investigated using a self-developed experimental setup. In order to collect enough methane pressure data for analysis and calculation, a self-developed real-time data acquisition system with a time interval of about 10 ms was used in the experiment to calculate the initial gas desorption amount and the initial gas velocity diffusion index (ΔP). Experiments show that coal with low water content and methane outburst is more dangerous than coal with high water content and outburst; and the degree of outburst of coal and methane decreases exponentially with the increase of moisture content.


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## Body

## 1. Introduction

Gas is a by-product of coal formation [1]. Coal seam gas exists in coal seams in several forms such as adsorption on the surface of micropores and macropores; adsorption on the molecular structure of coal; free gas in fissures and macropores; and dissolving in coal fissure water [2–4]. Outburst is a dynamic phenomenon in which coal and gas are violently ejected from the face coal seam, causing certain economic losses and casualties. It gets worse as mining goes deeper in the coal seam [5, 6]. Outburst accidents frequently occur during deep coal mining. Based on the statistical research on a large number of experimental data of gas adsorption and desorption characteristics in coal, scholars have established coal seam outburst prediction indicators, for example, the index value KV of prominent risk prediction using gas emissions [7]. The V-index of gas emission is the gas desorption amount of coal in the interval of 35∼70 s under atmospheric pressure [8–10]. The gas desorption indices (K1 and Δh2) of coal cuttings have been widely used in China. K1 is the gas desorption amount in 1 min, Δh2 is the gas desorption amount in the interval of 3∼5 min under atmospheric pressure [11]. Moreover, the ∆p index has been widely adopted worldwide. In addition, Norbert proposed that the time constant T reflects the rate of pressure drop in front of briquette work [12].Therefore, it is of great significance to study the desorption characteristics of water to gas in coal for the prevention and control of outbursts. A large number of existing experimental studies have shown that the diffusion rate of anthracite decreases with the increase of water content, while the diffusion rate of asphalt shows a U-shaped distribution that first decreases and then increases with the increase of water content [13]. The desorption and diffusion experiments of methane and carbon dioxide show that the moisture content in the coal matrix has a more significant effect on the gas desorption rate, and the effect of moisture content on the methane diffusion rate is greater than that on carbon dioxide diffusion rate [14]. The results show that the initial desorption rate, diffusion capacity, and gas desorption capacity of coal after pulsating water injection are higher than static pressure, and the gas desorption diffusion effect is better than that of static pressure water injection [15]. Both the gas desorption and desorption rates of the coal samples decreased with the increase of the moisture content of the coal samples [16]. Adsorption-water-desorption experiments were carried out and it was concluded that the desorption rate decreased with decreasing critical pore size [17]. The analysis of the outburst prevention effect of coal seam water injection shows that the higher the water content of the coal seam, the smaller the outburst risk [18]. Research [19] shows that the cumulative degassing rate of dry and wet coal samples is similar to the Langmuir adsorption isotherm, adding water inhibits the desorption rate of coal, and the desorption rate of dry coal is greater than that of water.In this paper, the self-developed test equipment was used to study the methane desorption characteristics in the first tens of seconds (0–60 s) under different water contents from three aspects: gas pressure, initial desorption gas amount, and initial gas diffusion rate. High-purity methane was used in the experiments. The influence of different moisture content on outburst risk is analyzed. Experimental studies have shown that coal and methane bursts with low moisture content are more dangerous than high moisture content.


## 2. Experimental Setup and Procedure

Experimental setup is shown in Figure1. It is mainly composed of a pressure container (5), a constant temperature water bath (11), a vacuum system (1), an inflation system (7–10), and a self-developed real-time data acquisition system (4). The container (5) is connected to the diffusion space (3) through the electromagnetic valve (6). The charging system of the test platform is equipped with a pressure regulating valve (8) to adjust the charging pressure to reach the set test adsorption gas pressure.Figure 1
Experimental setup. Denoted elements are as follows: 1, vacuum pump; 2, 6, 7, electromagnetic valves; 3, diffusion space; 4, pressure transducer and real-time data acquisition system (DAS); 5, coal sample container; 8, pressure regulating valve; 9, gas piping; 10, gas cylinder; 11, constant temperature water bath; 12, computer.The experimental platform adopts a real-time dynamic data acquisition system. In order to obtain enough gas pressure data during the initial desorption process, the data acquisition time interval is set to be about 10 ms. The ultimate pressure of the test device is almost absolute vacuum level (less than 10 mm Hg). For an isobarometer, we degas the diffusion space to a pressure below 10 mm Hg when the sample is not loaded. After stopping the vacuum pump and vacuuming for 5 minutes, the increase of space pressure should be less than 1 mm Hg. Otherwise, the experimental equipment should be overhauled until the air tightness meets the requirements.Coal material was sampled from Quanlun coal mine of Shandong energy group Guizhou Co., Ltd., in Guizhou province of China. The geographical location of the Quanlun coal mine is shown in Figure2. The coal mine is rich in coal seams to be mined, and the geological occurrence is simple (Figure 3). The coal lumps are ground and screened to reach an ideal particle size of 0.20 mm–0.25 mm. The coal sample weighs 3.5 g. The approximate analysis of coal samples was as follows: moisture content Mad = 1.50%, volatile content Vdaf = 7.06%, ash content Aad = 16.92%, total sulfur content St,d = 0.56%, porosity n = 10.49%, and average porosity size r = 9.3 nm.Figure 2
The geographical location of the Quanlun coal mine.Figure 3
Coal seam histogram.We placed the test coal sample in container (5). After 1.5 h evacuation, we turned off the vacuum pump (1) while injecting high-purity methane into the vessel. The coal sample was adsorbed for 1.5 h. When the pressure remains constant, the electromagnetic valve (2) opens and the electromagnetic valves (6, 7) close. The vacuum pump (1) was opened to degassing the diffusion space (including the instrument gas piping). Then, we stopped the vacuum pump, closed the electromagnetic valve (2), opened the electromagnetic valve (6), so that the coal sample container and diffusion space are connected, and started the data acquisition. At 10 s, we closed the electromagnetic valve (6) and recorded the diffusion space real-time pressure data. At 45 s, we connected the coal sample container and diffusion space and once again read the diffusion space real-time pressure data.When the coal sample container is filled with coal samples, we injected high-purity methane with a certain pressure. The experiments were carried out under the equilibrium methane pressure of 0.100 MPa and the pretreatment contents of 0.5%, 1%, 2%, 4%, 6%, 8%, and 10% of the water balance. The pressure regulating valve (8) is used to regulate the set methane pressure.Steps of moisture balance pretreatment of coal samples are as follows (as shown in Figure4): Firstly, we weighted a certain amount of air-dried coal sample (with a precision of 0.1 mg). Second, we placed the coal sample in a container and evenly added appropriate amount of distilled water. Third, we placed the container containing the quantitative sample in a moisture-proof sealed container (25°C, relative humidity in a humidified environment of 97%), filled it with a sufficient amount of potassium sulfate supersaturated solution, and weighed every 24 hours. Until two consecutive weighing, the weight change does not exceed 2% of the sample weight. Formula is as follows:(1)M0=1−G2−G1G2×Mad+G2−G1G2×100,where M0 is the moisture balance content, %; G1 is the sample mass after adding water to balance, g; G2 is the sample mass after adding water for equilibrium, g; Mad is the original sample moisture content, %.Figure 4
Preparation of coal samples and its moisture balance.In order to eliminate the influence of the coal sample’s own volume on the diffusion space, the mass of the coal sample was measured by an analytical balance, and the density was measured by the paraffin dipping method.Since the gas adsorption/desorption properties of coal are extremely temperature-sensitive, the entire vessel was placed in a constant temperature water bath (11) with a water temperature of 25°C (298.15 K) throughout the experiment.In order to ensure the reliability of the experimental device, the air tightness of the instrument was tested. The pressure change of the diffusion space in the experimental device was less than 10 Pa, which met the test pressure requirements of the methane diffusion process.


## 3. Results and Discussion

### 3.1. Initial Gas Pressure of Desorbed Gas

According to the measurement range of the pressure sensor (0–0.100 MPa), the real-time test methane pressure data collected by the pressure sensor and the real-time data acquisition system include the following: high range 45 s pressure data ⟶ 60 s pressure dataP2, and low range of 0 s pressure data ⟶ 10 s pressure data Pl. In order to simplify the analysis of the test data, the methane pressure data of the coal sample container for 10 s–45 s do not need to be collected or directly eliminated during the experimental. The intermediate time (the 10 s–45 s diffusion space’ pressure is constant) and the coal sample methane pressure data collected by pressure transducer and real-time data acquisition system (0 s pressure data ⟶ 10 s pressure data; 45 s pressure data ⟶ 60 s pressure data) are combined and analyzed. Figure 5 shows an example of pressure changes.Figure 5
An example of pressure variation.Figure5 shows that the gas pressure increases sharply at the initial time and then slowly rises. Changes in methane pressure at different times are different. The pressure rise rate of the diffusion space pressure from 45 s to 60 s is lower than that of the diffusion space pressure of 0 s to 10 s. The reason is that the methane adsorbed on the microporous surface of the coal matrix is rapidly desorbed into free methane under the action of pressure gradient and concentration gradient [16–19].Figure6 shows the change curve of methane desorption pressure when the coal sample container is filled with coal particles with different moisture contents. It can be seen from the figure that the desorption pressure curve of methane with low water content is always higher than that of high water content, indicating that the diffusion space pressure of methane in coal increases at a higher rate than that with low water content. That is, the methane content in the coal with lower moisture pressure will remain higher for a longer period of time. Therefore, a large amount of methane is desorbed into free gas after coal exposure, contributing to the generation of sufficient outburst energy. The results of this paper are consistent with the actual outstanding situation and many laboratory research results [13, 14].Figure 6
Methane desorption pressure curves of coal samples.


### 3.2. Initial Desorbed Methane Amount of Coal Sample

The amount of methane diffusing (n) through the electronic valve (6) is mainly composed of two components: the gas flux from the pore volume (n1) and the gas flux from the coal particles (n2).The gas mass flow rate (m) at the electronic valve (6) is calculated using the collected gas desorption pressure data using the following formula [18]:(2)m=Pσ∗T2γγ−1P2P2/γ−P2Pγ+1/γ,where P and T are the absolute pressure and temperature, respectively; γ is the adiabatic exponent; σ∗ is the cross-sectional area; and R is the gas constant. The amount of methane flowing through the electronic valve (6) can be calculated:(3)n=1M∫0t0mdt=PV298.15ZR,where M is the methane molar mass; R is the methane molar constant; V is the container diffusion space; and Z is the methane compressibility.The results of the experimental data analysis are shown in Figure7. It can be seen from the figure that the total amount of desorbed methane increases with time at an extremely fast rate at the initial time. Then, their growth rates are decreasing over time.Figure 7
The relationship between the total amount of methane desorbed.From a microscopic point of view, the adsorption of water and methane by coal is due to the interaction of water and methane molecules with coal-based molecules. The maximum adsorption potential of methane on the coal surface is −2.704 kJ/mol, and the maximum adsorption potential of water on the coal surface is −24.0 kJ/mol. The larger the adsorption potential is, the more the adsorbable molecules are adsorbed [20–23]. Therefore, the presence of moisture in coal can significantly affect the adsorption capacity of coal for methane. Moisture mainly affects the adsorption of methane by coal in three aspects [24–27]: First, part of the free water combined with the coal surface occupies a certain space on the coal surface, thereby reducing the adsorption space of methane molecules and reducing the coal surface. Adsorption capacity. Methane adsorption. Secondly, due to the certain vapor pressure of water, there is a small amount of gaseous water molecules in the coal micropores, which hinders the adsorption of methane molecules on the surface of coal, thereby reducing the amount of methane adsorption by coal. Third, water prevents methane molecules from entering the micropores. Since the specific surface area of pores is the main surface for coal adsorption [28], water will form capillary resistance in the micropores of coal [29, 30]. Especially when the pressure pores between the internal and external environments are not enough to overcome the capillary resistance, the methane molecules are prevented from entering the pores, thereby reducing the amount of methane adsorbed in the coal. In general, water will reduce the amount of adsorbed gas in the coal sample, thereby reducing the initial desorption pressure of methane.The gas flux (n1) from the container volume is equal to the gas increase in the diffusion space volume and can be calculated:(4)Δn=V298.15RP2Z2−P1Z1,where P1 and P2 are the coal-methane absolute pressure; V is the container diffusion space; and Z is the compressibility factor. The velocity of gas desorbed from coal particles (υ) in unit time Δt is calculated as(5)υ=ΔnΔt.The experimental data analysis is shown in Figure8. As can be seen from the figure, the methane desorption rate decreases very rapidly with time from the initial time. Then, the desorption rate decline rate keeps decreasing. The trend line has an unstable wave curve in the time period of 0.4–1.2 s, and at the same moisture content, they are similar in time of 45–49 s. For the experimental data with a water content of 10%, the desorption gas velocity is slightly larger than that after the unstable fluctuation curve. Then, the total amount of desorbed methane is still increasing rapidly. The total desorbed methane gap between the 0–10 s and 45–60 s time periods increased with time. They have similar trends in the moisture content of other coal samples.Figure 8
The relationship between desorption velocity and time of methane in coal. (a) Time range 0 s–10 s; (b) time range 45 s–60 s.
(a)(b)


### 3.3. Initial Velocity Diffusion of Coal-Methane

The index (∆P) of initial velocity diffusion of coal gas (abbreviated as IVDCG) is an index widely used worldwide to judge the outburst danger. It has been proved that with the increase of the IVDCG value, the outburst accidents probability increases significantly, and the critical value is 10 mmHg.Yang and Liu [31] showed that when the coal particle size is smaller than the limit size, the coal particles are basically composed of pores. The limit particle size of coal samples varies with the degree of coal metamorphism, and the particle size ranges from about 0.5 to 10 mm [32]. Therefore, the mass flow of methane at the initial velocity measurement will be proportional to its concentration gradient, which follows Fick’s law.(6)J=−D∂C∂X,where J is the methane diffusion velocity, m3/(m2·s); D is the methane diffusion coefficient, m2/s; C is the methane concentration, m3/t; and X is the distance from the center of the particle, m.The experimental research results of many scholars show the adsorption isotherm when coal-methane conforms to the Langmuir adsorbs equation [33, 34]:(7)W=abP1+bP×11+0.31M0,where W is at a certain temperature, mL/g; P is the gas adsorption equilibrium pressure, MPa; a is an adsorption constant, mL/g; b is an adsorption constant, MPa−1; and M0 is the moisture balance content, %.To further analyze the experimental data, it is assumed that (1) the coal is composed of spherical particles with an average radiusR of 0.125 mm; (2) the coal particles are uniform; and (3) the methane flow conforms to the law of mass conservation and the principle of continuity.The approximate solution of desorption of coalbed methane by coal particles under the first-order boundary condition can be calculated [35]:(8)C−CPC0−CP=−2R−1nπrnsinnπrRexp−n2π2DtR2.According to the determination method of the outburst hazard identification index ΔP, the following formula can be obtained:(9)ΔP=3.527ρ4/3πR3∫060∫∫∫C0−CPdVdt,where ρ is the particle density and CP is the methane concentration.The approximate solution of the outburst risk discrimination index ΔP is obtained by formulas (7) and (8):(10)ΔP=3.527ρabP1+bP×11+0.31M0−CP∑n=1∞6π2n2exp−π2n260DR2−expπ2n210DR2.It can be seen from formula (9) that the moisture content has a great influence on the determination of the outstanding risk judgment index. Without considering the influence of adsorption temperature and adsorption pressure, the methane diffusion coefficient D of coal is constant, so the index value of different coal samples will be significantly affected by moisture content. The greater the amount of methane adsorbed, the greater the effect of moisture content on IVDCG. Under the condition of constant equilibrium gas adsorption pressure and the same coal sample, the lower the water content, the larger the index ΔP; the higher the water content, the smaller the index ΔP. In addition, IVDCG has a certain relationship with the adsorption constant of coal. According to the outburst risk judgment index IVDCG, the final adsorption capacity of coal can be estimated.Table1 indicates that the moisture content has a significant effect on the measurement of IVDCG. The higher the moisture content, the lower the IVDCG. In order to study the change of IVDCG with moisture content, regression analysis was carried out on the measured IVDCG of methane in coal samples with different moisture contents.Table 1
Index ∆P measurement results.
CH4Mad (%)0.51246810∆P (mmHg)17.915.813.810.07.35.44.1The regression analysis results of the test data are shown in Table2. The regression analysis showed that the R-square of the exponential function in the fitting curve of the test data was the largest, so it could be concluded that the measured data of IVDCG decreased exponentially, while the moisture content of the coal samples increased. It can be seen from Figure 9 that when the equilibrium moisture content is reduced by 9.5%, the reduction rate of the outburst risk judgment index ΔP is 34.9%. So, we know that IVDCG is significantly affected by moisture content. With the increase of equilibrium moisture content in coal samples, the decrease of IVDCG decreases. It can be concluded that the experimental data show that IVDCG is greatly affected by the equilibrium moisture content.Table 2
The regression analysis results.
ModelFitting formulaAdj.R-squareLinearΔP = 17.07–1.43 ∗ Mad0.9464ExponentialΔP = 18.07 ∗ exp (−Mad/5.6) + 1.080.9978LogarithmicΔP = 15.66–4.68 ∗ Ln (Mad)0.9735PowerΔP = 15.59 ∗ Mad−0.470.8953Figure 9
The relationship between IVDCG and equilibrium moisture content.The relationship between outburst risk judgment index IVDCG and the equilibrium moisture content of coal samples is shown in Figure9. References [28–30] have demonstrated that IVDCG directly varies significantly with the humidity of coal samples, but there is no experimental data and description for coals with different moisture contents. It can be seen from Figure 9 that this relationship can be fully described by the exponential function equation of ΔP = k exp(−A ∗ Mad) + B (k is the moisture influence coefficient, its value indicates the degree of moisture affecting IVDCG; A is the attenuation of IVDCG, whose value represents the effect of moisture on the rate of decline; B is a constant).According to the outburst critical value of IVDCG (as shown in Table3) [11], when the moisture content of the experimental coal sample in the adsorption of methane is higher than 4%, the coal seam should be identified as nonoutburst coal seam. Under methane adsorption pressure of 0.1 MPa, it is confirmed that the outburst risk in low moisture content is much greater than that in high moisture content.Table 3
Indicator thresholds.
Coal seam∆P (mmHg)∆P (mmHg)The critical value≥10<10Outburst riskDangerSafeIn addition, studies have shown that the outburst risk judgment index IVDCG (ΔP) has a certain relationship with the adsorption constants (a and b) [36]. Therefore, the initial rate of methane diffusion can be used to approximate the final coal adsorption capacity.The outburst risk judging index ΔP is an index of the coal ability to absorb gas under standard atmospheric pressure (0.1 MPa) and the gas desorption rate when it is suddenly exposed to air. The diffusion performance of coal to gas is the result of the combined effect of coal’s physical and mechanical properties and impurities in coal. Under the condition of the same moisture content, the greater the IVDCG, the greater the outburst risk [13].Index ΔP is one of the outburst prediction indicators, and the critical value is 10 mmHg. When ΔP ≥ 10 mmHg, the coal seam has outburst risk; when ΔP < 10 mmHg, the coal seam has no outburst risk and is relatively safe.According to the exponential function equation obtained from the test, it can be seen that with the increase of the moisture content of the coal sample, the index ΔP of IVDCG decreases exponentially. Especially when the moisture content of coal samples increases to more than 4%, the index ΔP of IVDCG will decrease below the critical value of 10 mmHg. It can be seen that in the coal samples using water injection measures to measure IVDCG, with the increase of coal sample moisture, the index ΔP of IVDCG decreases, thus covering the outburst risk information, which will lead to inconsistent actual results [37–40].Due to the small amount of data in this experiment, the correction of the experimental data will continue to be carried out in future research.


## 3.1. Initial Gas Pressure of Desorbed Gas

According to the measurement range of the pressure sensor (0–0.100 MPa), the real-time test methane pressure data collected by the pressure sensor and the real-time data acquisition system include the following: high range 45 s pressure data ⟶ 60 s pressure dataP2, and low range of 0 s pressure data ⟶ 10 s pressure data Pl. In order to simplify the analysis of the test data, the methane pressure data of the coal sample container for 10 s–45 s do not need to be collected or directly eliminated during the experimental. The intermediate time (the 10 s–45 s diffusion space’ pressure is constant) and the coal sample methane pressure data collected by pressure transducer and real-time data acquisition system (0 s pressure data ⟶ 10 s pressure data; 45 s pressure data ⟶ 60 s pressure data) are combined and analyzed. Figure 5 shows an example of pressure changes.Figure 5
An example of pressure variation.Figure5 shows that the gas pressure increases sharply at the initial time and then slowly rises. Changes in methane pressure at different times are different. The pressure rise rate of the diffusion space pressure from 45 s to 60 s is lower than that of the diffusion space pressure of 0 s to 10 s. The reason is that the methane adsorbed on the microporous surface of the coal matrix is rapidly desorbed into free methane under the action of pressure gradient and concentration gradient [16–19].Figure6 shows the change curve of methane desorption pressure when the coal sample container is filled with coal particles with different moisture contents. It can be seen from the figure that the desorption pressure curve of methane with low water content is always higher than that of high water content, indicating that the diffusion space pressure of methane in coal increases at a higher rate than that with low water content. That is, the methane content in the coal with lower moisture pressure will remain higher for a longer period of time. Therefore, a large amount of methane is desorbed into free gas after coal exposure, contributing to the generation of sufficient outburst energy. The results of this paper are consistent with the actual outstanding situation and many laboratory research results [13, 14].Figure 6
Methane desorption pressure curves of coal samples.


## 3.2. Initial Desorbed Methane Amount of Coal Sample

The amount of methane diffusing (n) through the electronic valve (6) is mainly composed of two components: the gas flux from the pore volume (n1) and the gas flux from the coal particles (n2).The gas mass flow rate (m) at the electronic valve (6) is calculated using the collected gas desorption pressure data using the following formula [18]:(2)m=Pσ∗T2γγ−1P2P2/γ−P2Pγ+1/γ,where P and T are the absolute pressure and temperature, respectively; γ is the adiabatic exponent; σ∗ is the cross-sectional area; and R is the gas constant. The amount of methane flowing through the electronic valve (6) can be calculated:(3)n=1M∫0t0mdt=PV298.15ZR,where M is the methane molar mass; R is the methane molar constant; V is the container diffusion space; and Z is the methane compressibility.The results of the experimental data analysis are shown in Figure7. It can be seen from the figure that the total amount of desorbed methane increases with time at an extremely fast rate at the initial time. Then, their growth rates are decreasing over time.Figure 7
The relationship between the total amount of methane desorbed.From a microscopic point of view, the adsorption of water and methane by coal is due to the interaction of water and methane molecules with coal-based molecules. The maximum adsorption potential of methane on the coal surface is −2.704 kJ/mol, and the maximum adsorption potential of water on the coal surface is −24.0 kJ/mol. The larger the adsorption potential is, the more the adsorbable molecules are adsorbed [20–23]. Therefore, the presence of moisture in coal can significantly affect the adsorption capacity of coal for methane. Moisture mainly affects the adsorption of methane by coal in three aspects [24–27]: First, part of the free water combined with the coal surface occupies a certain space on the coal surface, thereby reducing the adsorption space of methane molecules and reducing the coal surface. Adsorption capacity. Methane adsorption. Secondly, due to the certain vapor pressure of water, there is a small amount of gaseous water molecules in the coal micropores, which hinders the adsorption of methane molecules on the surface of coal, thereby reducing the amount of methane adsorption by coal. Third, water prevents methane molecules from entering the micropores. Since the specific surface area of pores is the main surface for coal adsorption [28], water will form capillary resistance in the micropores of coal [29, 30]. Especially when the pressure pores between the internal and external environments are not enough to overcome the capillary resistance, the methane molecules are prevented from entering the pores, thereby reducing the amount of methane adsorbed in the coal. In general, water will reduce the amount of adsorbed gas in the coal sample, thereby reducing the initial desorption pressure of methane.The gas flux (n1) from the container volume is equal to the gas increase in the diffusion space volume and can be calculated:(4)Δn=V298.15RP2Z2−P1Z1,where P1 and P2 are the coal-methane absolute pressure; V is the container diffusion space; and Z is the compressibility factor. The velocity of gas desorbed from coal particles (υ) in unit time Δt is calculated as(5)υ=ΔnΔt.The experimental data analysis is shown in Figure8. As can be seen from the figure, the methane desorption rate decreases very rapidly with time from the initial time. Then, the desorption rate decline rate keeps decreasing. The trend line has an unstable wave curve in the time period of 0.4–1.2 s, and at the same moisture content, they are similar in time of 45–49 s. For the experimental data with a water content of 10%, the desorption gas velocity is slightly larger than that after the unstable fluctuation curve. Then, the total amount of desorbed methane is still increasing rapidly. The total desorbed methane gap between the 0–10 s and 45–60 s time periods increased with time. They have similar trends in the moisture content of other coal samples.Figure 8
The relationship between desorption velocity and time of methane in coal. (a) Time range 0 s–10 s; (b) time range 45 s–60 s.
(a)(b)


## 3.3. Initial Velocity Diffusion of Coal-Methane

The index (∆P) of initial velocity diffusion of coal gas (abbreviated as IVDCG) is an index widely used worldwide to judge the outburst danger. It has been proved that with the increase of the IVDCG value, the outburst accidents probability increases significantly, and the critical value is 10 mmHg.Yang and Liu [31] showed that when the coal particle size is smaller than the limit size, the coal particles are basically composed of pores. The limit particle size of coal samples varies with the degree of coal metamorphism, and the particle size ranges from about 0.5 to 10 mm [32]. Therefore, the mass flow of methane at the initial velocity measurement will be proportional to its concentration gradient, which follows Fick’s law.(6)J=−D∂C∂X,where J is the methane diffusion velocity, m3/(m2·s); D is the methane diffusion coefficient, m2/s; C is the methane concentration, m3/t; and X is the distance from the center of the particle, m.The experimental research results of many scholars show the adsorption isotherm when coal-methane conforms to the Langmuir adsorbs equation [33, 34]:(7)W=abP1+bP×11+0.31M0,where W is at a certain temperature, mL/g; P is the gas adsorption equilibrium pressure, MPa; a is an adsorption constant, mL/g; b is an adsorption constant, MPa−1; and M0 is the moisture balance content, %.To further analyze the experimental data, it is assumed that (1) the coal is composed of spherical particles with an average radiusR of 0.125 mm; (2) the coal particles are uniform; and (3) the methane flow conforms to the law of mass conservation and the principle of continuity.The approximate solution of desorption of coalbed methane by coal particles under the first-order boundary condition can be calculated [35]:(8)C−CPC0−CP=−2R−1nπrnsinnπrRexp−n2π2DtR2.According to the determination method of the outburst hazard identification index ΔP, the following formula can be obtained:(9)ΔP=3.527ρ4/3πR3∫060∫∫∫C0−CPdVdt,where ρ is the particle density and CP is the methane concentration.The approximate solution of the outburst risk discrimination index ΔP is obtained by formulas (7) and (8):(10)ΔP=3.527ρabP1+bP×11+0.31M0−CP∑n=1∞6π2n2exp−π2n260DR2−expπ2n210DR2.It can be seen from formula (9) that the moisture content has a great influence on the determination of the outstanding risk judgment index. Without considering the influence of adsorption temperature and adsorption pressure, the methane diffusion coefficient D of coal is constant, so the index value of different coal samples will be significantly affected by moisture content. The greater the amount of methane adsorbed, the greater the effect of moisture content on IVDCG. Under the condition of constant equilibrium gas adsorption pressure and the same coal sample, the lower the water content, the larger the index ΔP; the higher the water content, the smaller the index ΔP. In addition, IVDCG has a certain relationship with the adsorption constant of coal. According to the outburst risk judgment index IVDCG, the final adsorption capacity of coal can be estimated.Table1 indicates that the moisture content has a significant effect on the measurement of IVDCG. The higher the moisture content, the lower the IVDCG. In order to study the change of IVDCG with moisture content, regression analysis was carried out on the measured IVDCG of methane in coal samples with different moisture contents.Table 1
Index ∆P measurement results.
CH4Mad (%)0.51246810∆P (mmHg)17.915.813.810.07.35.44.1The regression analysis results of the test data are shown in Table2. The regression analysis showed that the R-square of the exponential function in the fitting curve of the test data was the largest, so it could be concluded that the measured data of IVDCG decreased exponentially, while the moisture content of the coal samples increased. It can be seen from Figure 9 that when the equilibrium moisture content is reduced by 9.5%, the reduction rate of the outburst risk judgment index ΔP is 34.9%. So, we know that IVDCG is significantly affected by moisture content. With the increase of equilibrium moisture content in coal samples, the decrease of IVDCG decreases. It can be concluded that the experimental data show that IVDCG is greatly affected by the equilibrium moisture content.Table 2
The regression analysis results.
ModelFitting formulaAdj.R-squareLinearΔP = 17.07–1.43 ∗ Mad0.9464ExponentialΔP = 18.07 ∗ exp (−Mad/5.6) + 1.080.9978LogarithmicΔP = 15.66–4.68 ∗ Ln (Mad)0.9735PowerΔP = 15.59 ∗ Mad−0.470.8953Figure 9
The relationship between IVDCG and equilibrium moisture content.The relationship between outburst risk judgment index IVDCG and the equilibrium moisture content of coal samples is shown in Figure9. References [28–30] have demonstrated that IVDCG directly varies significantly with the humidity of coal samples, but there is no experimental data and description for coals with different moisture contents. It can be seen from Figure 9 that this relationship can be fully described by the exponential function equation of ΔP = k exp(−A ∗ Mad) + B (k is the moisture influence coefficient, its value indicates the degree of moisture affecting IVDCG; A is the attenuation of IVDCG, whose value represents the effect of moisture on the rate of decline; B is a constant).According to the outburst critical value of IVDCG (as shown in Table3) [11], when the moisture content of the experimental coal sample in the adsorption of methane is higher than 4%, the coal seam should be identified as nonoutburst coal seam. Under methane adsorption pressure of 0.1 MPa, it is confirmed that the outburst risk in low moisture content is much greater than that in high moisture content.Table 3
Indicator thresholds.
Coal seam∆P (mmHg)∆P (mmHg)The critical value≥10<10Outburst riskDangerSafeIn addition, studies have shown that the outburst risk judgment index IVDCG (ΔP) has a certain relationship with the adsorption constants (a and b) [36]. Therefore, the initial rate of methane diffusion can be used to approximate the final coal adsorption capacity.The outburst risk judging index ΔP is an index of the coal ability to absorb gas under standard atmospheric pressure (0.1 MPa) and the gas desorption rate when it is suddenly exposed to air. The diffusion performance of coal to gas is the result of the combined effect of coal’s physical and mechanical properties and impurities in coal. Under the condition of the same moisture content, the greater the IVDCG, the greater the outburst risk [13].Index ΔP is one of the outburst prediction indicators, and the critical value is 10 mmHg. When ΔP ≥ 10 mmHg, the coal seam has outburst risk; when ΔP < 10 mmHg, the coal seam has no outburst risk and is relatively safe.According to the exponential function equation obtained from the test, it can be seen that with the increase of the moisture content of the coal sample, the index ΔP of IVDCG decreases exponentially. Especially when the moisture content of coal samples increases to more than 4%, the index ΔP of IVDCG will decrease below the critical value of 10 mmHg. It can be seen that in the coal samples using water injection measures to measure IVDCG, with the increase of coal sample moisture, the index ΔP of IVDCG decreases, thus covering the outburst risk information, which will lead to inconsistent actual results [37–40].Due to the small amount of data in this experiment, the correction of the experimental data will continue to be carried out in future research.


## 4. Conclusions

(1)
The greater the methane adsorption capacity, the greater the effect of moisture content on IVDCG. Under the condition of constant equilibrium methane adsorption pressure, the lower the moisture content, the larger the index ΔP; the higher the moisture content, the smaller the index ΔP.(2)
The rate of desorption of methane decreases with time at a great rate at the initial time. Then, the desorption rate keeps decreasing. For the experimental data with a moisture content of 10%, the desorption gas velocity is slightly larger than that after the unstable fluctuation curve. However, the total amount of desorbed methane is still increasing rapidly. The total desorbed methane gap between the 0–10 s and 45–60 s time periods increases with time.(3)
Outburst judgment index IVDCG is greatly affected by moisture content. The relationship between IVDCG and equilibrium moisture content can be fully described by the exponential function equation of ΔP = ke − A Mad + B. As the equilibrium moisture content increases, the exponential ΔP decreases exponentially.(4)
When the moisture content increases to more than 4%, the index ΔP of IVDCG will decrease to below the critical value of 10 mmHg, so the coal seam should be identified as a nonoutburst.(5)
When determining the outburst judgment index ΔP, the moisture content should be consistent with the moisture content on-site. If the critical value (10 mmHg) is adopted, the critical value of the response index should be adjusted according to the actual moisture content after water injection.



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*Source: 6797786-2021-12-21.xml*