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. 2024 Feb 16;9(8):9170–9184. doi: 10.1021/acsomega.3c08091

Characterization of Coal Particle Methane Desorption and Optimization of Desorption Model Based on Desorption Damage

Xiang Fu 1, Xuan Liu 1,*, Qixuan Wu 1, Teng Chang 1, Yifan Wang 1
PMCID: PMC10905690  PMID: 38434877

Abstract

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In view of the current situation where most studies on gas desorption characteristics are limited to the atmospheric pressure desorption environment, we have independently developed a coal methane desorption instrument to test the nonatmospheric pressure desorption characteristics for coal particle gas beneath the condition of desorption damage. The instrument can arbitrarily adjust the gas pressure in the range of measurement while controlling the instantaneous release of excess gas to keep the desorption environment pressure constant. We measured the methane desorption amount of coal samples with different desorption times within 3 h and calculated the desorption velocity. The results show that the final desorption amount and desorption velocity of gas scale up with the increase of times, and the final desorption amount of coal sample W-01 increases the most, which is 18.5%. With the passage of time, the diffusion coefficient decreases gradually, and the number of desorption times is directly proportional to the diffusion coefficient. Its relative deviation of diffusion coefficient between different desorption times of the same coal sample can reach up to 40%, and the desorption time in the range of 5 to 30 min is the area with high relative deviation. A quantitative index Ki of a double-parameter damage model based on desorption conditions and adsorption pressure is proposed, and the damage extent of each sample is evaluated. The damage quantitative index of coal sample W-01 is the highest, which is 0.87. The methane desorption model of coal under the condition of desorption damage is constructed, and more than 30 groups of experiments are verified.

1. Introduction

A significant outburst of coal and gas accidents will be accompanied by energy release, which produces strong power in the period of underground mining.1−3 Gas outburst produces a large amount of pulverized coal, and the desorption gas of pulverized coal will further facilitate the outburst.4−6 Therefore, gas significantly influences the gestation and occurrence of gas outbursts.7−9 As coal mining depths increase, the amount and intensity of gas emissions also increase, which will induce more gas calamities.10−13 In addition to the high-intensity mining stage of deep coal seams, the coal has been strongly damaged many times during the coal-forming process, leading to the gas migration in the coal body and the circumstance of gas desorption–pulverization–desorption.14,15 Consequently, studying the law of gas desorption in coal under damage conditions is crucial for understanding gas emission laws and gas flow mechanisms and predicting coal and gas outbursts.16−18

The diversification law of gas desorption in coal particles is crucial for predicting coal and gas outbursts and is mainly used to determine the coal seam gas concentration and drill cutting desorption index. Scholars consider that the diffusion process in coal particles follows Fick’s law, propelled by a concentration gradient, resulting in a simplified model.19−23 The coal releases a significant amount of gas during coal seam pressure relief, including free gas in the fracture and instantaneously desorbed adsorbed gas, which, in turn, causes a series of chain reactions, such as aggravating coal damage and causing a mutation in the effective stress. In the study of the desorption law of adsorbed gas, scholars have researched the change law of gas desorption by using unlike experimental circumstances and established a large number of models with different applicabilities. In view of the theory of gas migration in porous media, Liu et al. conducted a study on the influence of particle size on the velocity and diffusion coefficient of gas desorption.24 Nie et al. indicated that gas desorption performance is substantially reduced in the presence of applied moisture.25 Yan et al. researched the effect of temperature on the gas desorption characteristics of anthracite, finding that higher temperatures led to increased desorption amount and diffusion coefficient.26 Neelu et al. described the gas desorption equation and explained the desorption effect of diffusion rate and time.27 Liu et al. conducted gas adsorption and desorption tests under various pressure boundary circumstances, proposing a new desorption model.28 Yang et al. artificially changed the microstructure of coal by adding surfactants, improved the efficiency of gas extraction, and avoided the abrupt emission of mass gas.29 Wei et al. showed that stress effects directly affect the desorption capacity of gas-containing coals.30 Wang et al. researched the multifractal features of coal pores and discussed the influence on gas desorption. The tectonism and metamorphism can promote gas desorption capacity.31 Xiao et al. built a simulation test device for the impact of water injection on the gas desorption characteristics of coal under the action of overburden pressure in the laboratory. The results revealed that the overburden pressure increased the summation desorption amount of coal samples, and the desorption amount slowly reduced with the intervention of water.32 Li et al. found that the fractal dimension can describe the microstructure diversity of coal and image its impact on gas adsorption capacity.33

In fact, after an outburst, coal samples collected were damaged by desorption, releasing most of the coal gas. The collection of critical records related to gas desorption amount and desorption speed as evidence is challenging, and this study can offer technical support for the material evidence analysis of accident investigation. In addition, in the process of mining, gas desorption will take place in the gas migration propelled by the pressure difference in coal, and the resulting desorption damage could change the parameters, such as gas desorption amount. However, this factor is hardly considered in the current research on gas migration. Therefore, the study conclusions can offer fundamental data to support research in this field.

The study examines the desorption law of coalbed methane under desorption damage conditions using a self-developed coal particle gas desorption experimental device. A quantitative index of desorption damage is proposed, and a gas desorption model of coal particles considering desorption damage is established.

2. Coal Particle Gas Desorption Damage Experiment

2.1. Collection of Coal Samples

The research aims to explore the impact of gas desorption damage on various types of coal. Four samples are selected from Weijiadi Coal Mine (coal sample W-01, coal sample W-02), Shanxi Jinshengsongyu Coal Mine (coal sample JS), and Guizhou Gaoyuan Coal Mine (coal sample GY). According to the measured volatile matter (Vad) and other parameters of coal samples, coal samples W-01 and W-02 are bituminous coal, coal sample JS is lignite, and coal sample GY is fat coal. The lump coal gathered from the underground coal mine was mashed and sieved out in the laboratory to obtain coal particles with a particle size of 0.2 mm, and each coal sample was 30 g. The sampling site is shown in Figure 1. Figure 2 displays the particle size distribution curve of the coal samples. Obviously, the coal sample W-01 primarily has a particle size distribution of 0.2–0.25 mm after crushing. The distribution of coal sample W-02 and coal sample JS is comparatively uniform, and the particle size is distributed between 0.25 and 0.5 mm, while the particle size of the coal sample GS is mainly distributed around 4 mm.

Figure 1.

Figure 1

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Collection locations of the experimental coal samples.

Figure 2.

Figure 2

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Particle size distribution curve of coal samples: (a) coal sample W-01; (b) coal sample W-02; (c) coal sample JS; (d) coal sample GY.

2.2. Experimental Equipment and Methods

The coal gas desorption instrument determines the methane desorption amount based on the critical outburst pressure adsorption under different desorption damage degrees. The physical and schematic diagrams are shown in Figure 3.

Figure 3.

Figure 3

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Coal particle gas desorption test instrument: (a) actual diagram; (b) sketch diagram.

The following are the phases of testing and the test method: (1) the experimental instrument is attached and verified whether the test instrument is airtight. (2) The coal sample tank is filled with the screened coal sample and allowed to degas for 3 h. (3) The gas is added and let it sit until optimum for gas adsorption. (4) The exhaust valve is rapidly opened to expel the gases that remain in the coal sample tank following the adsorption equilibrium. Once the exhaust port has been linked to the gas desorption device for a predetermined amount of time, the time and water level height in the desorption device are recorded until the water level height in the device does not change for 30 min.

2.3. Experimental Data Processing

Utilizing the subsequent translation equation, the amount that was determined of gas desorption was translated to the desorption amount under standard circumstances

2.3. 1

where Qt is the gas desorption amount under standard circumstances (mL/g); Qt′ is the actual amount of gas desorption (mL/g); tw is the temperature of the water in the cylinder that is being measured (°C); Pr is the test ambient pressure (kPa); hw is the water surface height of the cylinder (mm); Pw is the pressure of saturated water vapor (kPa).

3. Discussion of Experimental Results

3.1. Experimental Results

Figure 4 depicts the cyclic desorption trends of gas in samples that have been measured at the adsorption equilibrium pressure. Figure 5 illustrates the converted gas desorption velocity.

Figure 4.

Figure 4

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Coal particles gas desorption curve: (a) coal sample W-01; (b) coal sample W-02; (c) coal sample JS; (d) coal sample GY.

Figure 5.

Figure 5

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Coal particle gas desorption velocity curve: (a) coal sample W-01; (b) coal sample W-02; (c) coal sample JS; (d) coal sample GY.

Due to the short burst time, the initial law of gas desorption is of major meaning to the accurate determination of methane content and the inference of outbursts. By analyzing the viewpoint of methane desorption release internal energy, the methane desorption change of the coal seam in the first 300 s will be the key to determining the outburst.34−36 Consequently, the discussion of methane desorption amount and desorption velocity in this experiment will focus on the first 5 min.

As shown in Figure 4, under the conditions of the test, the trend of the gas desorption curve of four samples is essentially identical, but the amount of methane desorption Qt increases with the scale-up of desorption times. Among them, the gas desorption amount in coal sample W-01 is the highest, while in coal sample JS, it is the lowest. During a specific time frame, the proportion of methane desorption in the initial stage of desorption of the identical sample in various desorption times is similar to that of the total desorption. For instance, in the four desorption results of sample W-01, the desorption amount of methane in the first 5 min accounted for 14.9, 14.3, 15.8, and 17.1% of the total desorption amount, respectively. In sample W-02, the desorption amount of methane in the first 5 min accounted for 10.1, 12.8, 13.3, and 13.6% of the total desorption amount, respectively. In sample JS, the desorption amount of methane in the first 5 min accounted for 8.8, 10.2, 10.5, and 11.8% of the total desorption amount, respectively. In sample GY, the desorption amount of methane in the first 5 min accounted for 7.9, 10.8, 11.1, and 12.6% of the total desorption amount, respectively.

The gas desorption velocity is a crucial index that accurately represents the characteristics of gas desorption. Figure 5 illustrates the gas desorption velocity Vt rising with increasing desorption durations, which is similar to the changing rule of the gas desorption amount Qt in Figure 4. In the initial stage, the desorption velocity of gas is extremely quick and then steadily slackens off. Taking the instantaneous time of pressure relief as an example, the first desorption velocity of coal sample M-01 was 3.29 mL/g·min, accounting for 96.1% of the whole transversion of desorption. The second desorption velocity was 3.38 mL/g·min, accounting for 96.3% of the whole desorption process. The third desorption velocity was 3.73 mL/g·min, accounting for 96.7% of the whole desorption process. The fourth desorption velocity was 4.33 mL/g·min, accounting for 98.9% of the whole process. In coal sample JS, the first desorption velocity was 0.75 mL/g ·min, accounting for 91.1% of the whole process. The second desorption velocity was 1.05 mL/g·min, accounting for 92.5% of the whole process. The third desorption velocity was 1.41 mL/(g · min), accounting for 93.4% of the whole process. The fourth desorption velocity was 1.98 mL/g·min, accounting for 94.8% of the whole process. From the above analysis, the initial desorption velocity of methane accounts for a larger proportion of the whole process. Simultaneously, the change law of rapid desorption of methane in a brief time during an outburst is verified.

Scholars generally consider that the varying gas desorption rate with time is a mathematical form of a power function19,25,37

3.1. 2

where Vt and Vε are the gas desorption velocities at times t and tε (mL/g·min) and kε is the decay coefficient.

3.2. Influence of Desorption Damage on the Methane Diffusion Coefficient

For the purpose of obtaining the effect of desorption damage on methane diffusion from the mechanism level, the methane desorption data are analyzed using the traditional diffusion model. According to the actual measured gas emission at different times, the association between the diffusion velocity and time is fitted. Finally, the methane diffusion coefficient is calculated.38 Its expression is as shown in eq 3(39)

3.2. 3

where Mt is the methane diffusion mass of coal particles at time t (g); M∞ is the sum mass of gas diffusion (g); Di is the diffusion coefficient (m2/s); r is the average particle size (m).

Equation 3 could be further expressed by gas desorption amount, as illustrated in eq 4(38,40)

3.2. 4

where Qt is the cumulative desorption amount of methane (mL/g); Q∞ is the limit diffusion amount (mL/g).

From eq 4, the methane diffusion coefficient of each sample under the test can be obtained. The diffusion coefficient distribution of samples at each time is illustrated in Figure 6. The diffusion coefficient decreases with time but is not a constant. The test consequences show that with the increase in time, the variation rate of the diffusion coefficient slows and steadily is inclined to be stable, and the diffusion coefficient of different sample types is quite different. The methane diffusion coefficient of the samples decreased significantly in the first 30 min, and the downward trend gradually slowed down within 30–120 min and tended to be stable after 120 min. This conclusion is consonant with the study consequences of Li,41 Jian,42 and Yang.43

Figure 6.

Figure 6

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Diffusion coefficient of each coal: (a) coal sample W-01; (b) coal sample W-02; (c) coal sample JS; (d) coal sample GY.

The diffusion coefficient Di decreases with the increase of time (Figure 6), and its expression is as follows

3.2. 5

where ζ is the methane diffusion coefficient (m2/s); τ is the decay coefficient.

The variation of diffusion coefficient with time is associated with the diffusion of gas in coal. According to the pore size (d) and the mean free path (λ) of gas molecules, the gas diffusion modes in coal could be separated into the next patterns: Fick diffusion (d > 10λ), interim diffusion (0.1λ < d < 10λ), and Knudsen diffusion (d < 0.1λ).44−46 The diffusion coefficient under a single mechanism in the above diffusion mode decreases in turn. Initial desorption period, Fick diffusion, and interim diffusion may predominate, so the corresponding variation ratio of the diffusion coefficient is larger. As the desorption continues, the methane content decreases and the Fick diffusion is limited. The interim diffusion and Knudsen diffusion become the primary diffusions, resulting in a decrease in the diffusion coefficient and a small variation ratio of the corresponding diffusion coefficient. During the final period of desorption, the gas diffusion steadily stabilizes, resulting in a stable diffusion coefficient.

In addition, for further research on the effect of desorption damage on the diffusion coefficient, the relative deviation Si between the diffusion coefficients under different damage conditions for each sample is counted. The larger the relative deviation, the stronger the effect of desorption damage on the methane diffusion coefficient. The specific expression of relative deviation Si is shown in eq 6

3.2. 6

where Si is the relative deviation; i is the number of repeated tests of desorption damage; Di is the diffusion coefficient of the i time desorption damage test (m2/s); Di+1 is the diffusion coefficient of the i+1 time desorption damage test (m2/s).

According to eq 6, the relative deviation Si of the methane diffusion coefficient is calculated. Figure 7 demonstrates that the relative deviation of the diffusion coefficient varies under different desorption damage conditions for the same coal.

Figure 7.

Figure 7

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Relative deviation of the diffusion coefficient of samples under different desorption damage circumstances: (a)–(c) coal sample W-01; (d)–(f) coal sample W-02; (g)–(i) coal sample JS; (j)–(l) coal sample GY.

Taking coal sample W-01 as an example, in Figure 7a, the relative deviation of the diffusion coefficient under the second desorption damage and the first desorption damage shows a complex polynomial function relationship. In the first 30 min, the relative deviation increases first and then decreases, up to 40%. With the passage of desorption time, the relative deviation decreases as a whole, and the 5–30 min interval is the area with a high relative deviation. The relative deviation changes in Figure 7b,c also show similar rules. Furthermore, the relative deviation of the methane diffusion coefficient of the other three samples is quite dissimilar, but the change rule is as if it is that of the sample W-01. Consequently, the desorption damage has a significant influence on the gas diffusion coefficient of coal particles, which cannot be ignored.

Based on the methane diffusion coefficient at t0, it is found that the desorption times of four samples have a linear relationship with the diffusion coefficient (Figure 8). The effect trend of desorption times on the diffusion coefficient may be due to the fact that some micropores in the coal body are opened due to damage and destruction after desorption, resulting in variations in the pores and diffusion routes of micropores and an increase in the diffusion coefficient.47,48 In order to verify the above judgment, pore analysis of coal samples was carried out by a low-temperature liquid nitrogen adsorption experiment. Figure 9 indicates a significant increase in pore volume peak area in coal samples after desorption, indicating the opening of micropores and pore channels during the desorption process, resulting in larger pore volume and adsorption capacity.

Figure 8.

Figure 8

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Relationship between the methane diffusion coefficient and desorption times at time t0.

Figure 9.

Figure 9

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Pore size distribution of four samples: (a) coal sample W-01; (b) coal sample W-02; (c) coal sample JS; (d) coal sample GY.

4. Quantitative Index of Desorption Damage

4.1. Double-Parameter Damage Model Diagram

According to the quantification of the double-parameter damage model of coal particle gas desorption conditions and adsorption pressure, the final damage of the samples in the test is created by the combined action of the two. Suppose the coal particles are globular (with the center of them as the origin), any plane passing through the center of the ball is taken, and its two-dimensional boundary has a critical failure curve K (x, y), where x and y are not less than 0. Any point on the curve represents that the coal particles are completely damaged (K = 1), and any point on the center side of the curve (nonorigin) represents that the coal particles are at a certain level of damage (0 < K < 1). The origin K (0,0) represents that the coal particles are in a nondestructive state. Figure 10 is a graphical interpretation of the double-parameter damage model of coal particles, in which the X-axis and Y-axis represent the desorption damage conditions and the contribution of adsorption pressure to the damage, respectively. When the coal particles under different paths reach the failure state, the contributions of desorption damage conditions and adsorption pressure to the damage level of coal particles are different.

Figure 10.

Figure 10

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Graphical explanation of the double-parameter damage model.

4.2. Double-Parameter Damage Model Based on Desorption Conditions and Adsorption Pressure Is Proposed

The interaction between desorption conditions and adsorption pressure was characterized by introducing a combination parameter ω, as shown in eq 7

4.2. 7

where KQ is the contribution of desorption conditions to the damage. Considering the influence of the methane desorption amount on the damage, the expression is shown in eq 8. KP is the contribution of the adsorption pressure to damage. Considering the effect of the pressure of gas and the pressure reaching the adsorption balance on the damage, the expression is shown in eq 9

4.2. 8

where Qmax,i is the maximum desorption amount of the i time desorption damage test (mL/g); Qmin,i is the minimum desorption amount of the i time desorption damage test (mL/g); QT is the cumulative desorption amount (mL/g).

4.2. 9

where Pm is the gas adsorption balance pressure (MPa); Pn is the pressure of the gas injected into the coal sample tank before the test (MPa).

The combined parameter ω can be calculated by eq 10

4.2. 10

Inserting eqs 8, 9, and 10 into eq 7, the modified double-parameter linear damage model according to desorption conditions and adsorption pressure is shown in eq 11. Ki represents the damage quantification index of coal particles after i repeated tests.

4.2. 11

The above-proposed coal particle gas desorption damage model has the following benefits: (1) considering the double-parameter damage condition of desorption condition and adsorption pressure. (2) Before the desorption damage test, the methane desorption amount was regarded as 0, and the gas adsorption balance pressure was 0, which had no effect on the coal particle damage. (3) When the coals were destroyed, the boundary condition of K = 1 was satisfied.

Coal particle methane desorption is a comprehensive course of methane desorption, diffusion in coal, and transfusion in fractures. With the increase in the number of desorption damage tests, the variation in the interior structure of coal is more intense, which will have different effects on the above three processes.49−51 Among them, the variation in gas diffusion ability created by the variation in coal damage is the significant reason for the change in methane desorption amount.

The desorption damage quantitative index of four samples under various desorption times could be calculated by eq 11, and the two have a good linear relationship (Figure 11). Additionally, the quantitative indexes of the desorption damage of different coal types are different. The quantitative indexes of desorption damage of bituminous coals are larger than those of lignite and fat coals, while the quantitative indexes of desorption damage of lignite and fat coal are close. The quantitative index of desorption damage of the same coal type will be modified with the initial state of the coals. For example, coal sample W-01 is a coal thrown after the outburst, and its initial state has been damaged by desorption. The coal sample W-02 is collected from the fresh coal wall; therefore, the quantitative index of damage to the coal sample W-01 is larger than that to W-02.

Figure 11.

Figure 11

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Relationship between desorption times of four samples and the quantitative index Ki of desorption damage: (a) coal sample W-01; (b) coal sample W-02; (c) coal sample JS; (d) coal sample GY.

5. Coal Particle Gas Desorption Damage Desorption Model

5.1. Determination of Desorption Model Form

According to different coal quality conditions and external conditions, researchers have created a quantity of coal particle methane desorption models with different adaptabilities. The representative models are mainly the Barrell formula, Sun Chongxu formula, Wenter formula, Exponential formula, Uskinov formula, Wang Youan formula, Bott formula, etc.19 (Table 1). The test consequences show that the desorption damage has an obvious influence on gas desorption. Nevertheless, there is no relevant study on the methane desorption law of coal particles under the condition of desorption damage. For this reason, it is essential to create a mathematical model of gas desorption of coal particles under the condition of desorption damage to characterize the characteristics of methane desorption.

Table 1. Mathematical Model and Experimental Fitting Results of Coal Particle Gas Desorption.

    fitting parameters
coal sample W-01
 coal sample W-02
 coal sample JS
 coal sample GY
desorption model desorpted quantity Qt I II III IV I II III IV I II III IV I II III IV
Barrell formula k√t k = 0.6415 k = 0.7069 k = 0.7492 k = 0.7817 k = 0.5675 k = 0.6011 k = 0.6405 k = 0.6958 k = 0.5343 k = 0.5602 k = 0.5901 k = 0.6125 k = 0.5391 k = 0.5687 k = 0.5910 k = 0.6259
Sun Chongxu formula ati a = 3.8532 a = 4.0084 a = 4.6533 a = 5.7919 a = 2.1241 a = 3.2553 a = 3.6279 a = 3.7559 a = 1.8997 a = 2.2701 a = 2.5185 a = 2.8484 a = 1.4931 a = 2.4433 a = 2.5759 a = 3.1252
i = 0.1093 i = 0.1178 i = 0.1020 i = 0.0625 i = 0.2235 i = 0.1469 i = 0.1334 i = 0.1333 i = 0.2258 i = 0.1973 i = 0.1857 i = 0.1665 i = 0.2802 i = 0.1841 i = 0.1809 i = 0.1508
Wenter formula v1t1–kt/(1 – kt) v1 = 0.4213 v1 = 0.4725 v1 = 0.4750 v1 = 0.4762 v1 = 0.4747 v1 = 0.4781 v1 = 0.4795 v1 = 0.5008 v1 = 0.4289 v1 = 0.4473 v1 = 0.4678 v1 = 0.4744 v1 = 0.4183 v1 = 0.4301 v1 = 0.4660 v1 = 0.4714
kt = 0.8806 kt = 0.8821 kt = 0.8979 kt = 0.8992 kt = 0.7764 kt = 0.8531 kt = 0.8597 kt = 0.8667 kt = 0.7741 kt = 0.8028 kt = 0.8141 kt = 0.8334 kt = 0.7197 kt = 0.7522 kt = 0.8199 kt = 0.8491
exponential formula v0(1 – e–bt)/b v0 = 2.5673 v0 = 3.6657 v0 = 4.1125 v0 = 5.1889 v0 = 1.6334 v0 = 1.6574 v0 = 1.9286 v0 = 2.0941 v0 = 0.6368 v0 = 0.8844 v0 = 0.9892 v0 = 1.2827 v0 = 0.9874 v0 = 1.0173 v0 = 1.0715 v0 = 1.5778
b = 0.4162 b = 0.5523 b = 0.5922 b = 0.6858 b = 0.1070 b = 0.2659 b = 0.2951 b = 0.3111 b = 0.1191 b = 0.1598 b = 0.1695 b = 0.2144 b = 0.1755 b = 0.1818 b = 0.1846 b = 0.2588
Uskinov formula Inline graphic v0 = 3.8370 v0 = 4.8461 v0 = 6.0126 v0 = 9.2908 v0 = 1.9363 v0 = 3.1959 v0 = 4.1414 v0 = 4.3043 v0 = 1.8137 v0 = 2.2631 v0 = 2.5493 v0 = 2.9814 v0 = 1.2931 v0 = 2.1893 v0 = 2.6198 v0 = 3.4321
n = 1.6372 n = 1.6832 n = 1.7504 n = 1.8274 n = 1.1859 n = 1.4068 n = 1.5134 n = 1.5775 n = 1.2036 n = 1.2988 n = 1.3373 n = 1.4117 n = 1.0364 n = 1.2457 n = 1.3536 n = 1.4902
Wang Youan formula αβt/(1 + βt) α = 6.3847 α = 6.7541 α = 7.4715 α = 7.7379 α = 4.5277 α = 4.8924 α = 5.0211 α = 5.2294 α = 2.3846 α = 2.5677 α = 2.7514 α = 2.9871 α = 3.7811 α = 3.9715 α = 4.0122 α = 4.1788
β = 0.6915 β = 0.7122 β = 0.7352 β = 1.3642 β = 0.5149 β = 0.5329 β = 0.5517 β = 0.5698 β = 0.3155 β = 0.3379 β = 0.3611 β = 0.3828 β = 0.4289 β = 0.4356 β = 0.4510 β = 0.4722
Bott formula Q∞(1 – Ae–εt) A = 0.9077 A = 0.9155 A = 0.9332 A = 0.9750 A = 0.8238 A = 0.8307 A = 0.8511 A = 0.8647 A = 0.5610 A = 0.5887 A = 0.6011 A = 0.6228 A = 0.7929 A = 0.8106 A = 0.8311 A = 0.8492
ε = 0.3998 ε = 0.4578 ε = 0.4808 ε = 0.6867 ε = 0.1282 ε = 0.3132 ε = 0.3315 ε = 0.3455 ε = 0.0871 ε = 0.08922 ε = 0.0912 ε = 0.0932 ε = 0.1032 ε = 0.1184 ε = 0.1325 ε = 0.1549
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Although the above models have different adaptabilities, they all reflect the features and mechanism of coal methane desorption to a certain extent, which has a certain reference significance. It is feasible to modify the existing model reasonably by using the desorption features of coal under the condition of methane desorption damage. Therefore, the above desorption model is accustomed to fit the test consequences of coal methane desorption damage to obtain a mathematical model with high adaptability, and the correlation index R2 is used to evaluate the fitting results (Table 1). The adaptation of each desorption model is indicated in Table 2.

Table 2. Correlation Index of Mathematical Models for Gas Desorption.

experimental group Barrell formula Sun Chongxu formula Wenter formula exponential formula Uskinov formula Wang Youan formula Bott formula
W-01 I 0.9011 0.9795 0.9488 0.8911 0.9520 0.8886 0.8959
II 0.9224 0.9741 0.9409 0.9156 0.9627 0.9422 0.8879
III 0.8905 0.9637 0.9054 0.9270 0.9822 0.9167 0.8703
IV 0.9112 0.9652 0.9347 0.9803 0.9525 0.9555 0.9011
W-02 I 0.8859 0.9799 0.9713 0.8912 0.9614 0.9122 0.9274
II 0.8957 0.9567 0.9208 0.9302 0.9832 0.9147 0.9008
III 0.9011 0.9566 0.9132 0.9327 0.9712 0.8955 0.9415
IV 0.9155 0.9715 0.9423 0.9095 0.9871 0.9257 0.9197
JS I 0.8772 0.9375 0.9141 0.9630 0.9647 0.9325 0.8815
II 0.8902 0.9391 0.9102 0.9633 0.9752 0.8841 0.9034
III 0.9144 0.9339 0.9025 0.9524 0.9544 0.9281 0.9537
IV 0.8995 0.9582 0.9303 0.9598 0.9657 0.9025 0.9401
GY I 0.9235 0.9704 0.9620 0.9322 0.9872 0.9114 0.9122
II 0.9115 0.9711 0.9098 0.9432 0.9847 0.9332 0.9266
III 0.8992 0.9535 0.9269 0.9487 0.9654 0.9187 0.9173
IV 0.8874 0.9464 0.9052 0.9393 0.9757 0.9042 0.9452
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According to the fitting results, the fitting degree of Sun Chongxu formula, Wenter formula, and Uskinov formula is higher, and the correlation index R2 is above 0.9. Among them, the fitting degree of the Uskinov formula is the highest, and its correlation index R2 is as high as 0.9872. For the test conditions, the mathematical form of the Uskinov formula is preferred to depict the methane desorption features of the test samples.

5.2. Optimization and Validation of the Desorption Model

The conclusion of the Uskinov formula has a substantial theoretical basis, and each parameter has a clear physical meaning, where v0 represents the methane desorption velocity at t = 0 (mL/g·min) and n is the attenuation coefficient of methane desorption velocity changing with time.52 In addition, according to Fick diffusion law, the methane desorption velocity of coal mainly depends on the maximum desorption amount of methane, and the v0 value should be proportional to the maximum desorption amount of gas.19,24,25

The above inference is proven by the fitting results of experimental data. The parameter n in the fitting formula of each sample rises with the improvement of desorption times (Figure 12). The linear relationship between the parameter v0 and the ultimate methane desorption amount under each coal sample test is good. In Figure 13, the linear relationship can be expressed as eq 12

5.2. 12

where v0 is the parameter in the Uskinov formula (mL/g·min); Qba is the gas adsorption capacity of coal particles with gas pressure from pa to pb (mL/g); a is the adsorption constant (m3/t); b is the adsorption constant (MPa–1); δ is a newly introduced parameter, which describes the linear relationship between v0 and adsorption capacity.

Figure 12.

Figure 12

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Variation law of Uskinov parameter n in samples with the desorption times: (a) coal sample W-01; (b) coal sample W-02; (c) coal sample JS; (d) coal sample GY.

Figure 13.

Figure 13

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Change law between the methane limit desorption amount of samples and Uskinov parameter v0: (a) coal sample W-01; (b) coal sample W-02; (c) coal sample JS; (d) coal sample GY.

According to the change rule of the above parameters, eq 12 is substituted into the Uskinov formula with a high fitting degree and optimized. The optimized desorption formula is shown in eq 13

5.2. 13

where pa is the desorption environmental pressure (MPa); pb is the adsorption balance pressure (MPa); i is the number of desorption; n is the decay coefficient.

The desorption velocity formula is the first derivative of the desorption amount formula to time t, as shown in eq 14

5.2. 14

where vt is the methane desorption rate of coal (mL/g·min).

Compared with the original Uskinov formula, the optimized formula increases the number of desorption times. By introducing adsorption equilibrium constants a and b, adsorption equilibrium pressure pb, and desorption environmental pressure pa, the effect of desorption pressure on methane desorption features of coal particles is reflected. The optimized model is more appropriate for the methane desorption law of coal under desorption damage conditions. The purpose of repeated desorption of samples in the laboratory is to determine this desorption law better. The data are the same as those of repeated desorption of coal samples damaged by the natural structure.

The methane desorption amount and desorption velocity of the four samples under different desorption circumstances are fitted by eqs 13 and 14. The results are indicated in Figures 14 and 15. For both the gas desorption amount and the desorption speed, the optimized formula fitting degree R2 is above 0.99, which proves that the formula can greatly depict the gas desorption features of coal under the condition of desorption damage within 3 h.

Figure 14.

Figure 14

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Comparison between the calculated value of the modified Uskinov formula and the experimental value of desorption amount: (a)–(d) coal sample W-01; (e)–(h) coal sample W-02; (i)–(l) coal sample JS; (m)–(p) coal sample GY.

Figure 15.

Figure 15

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Comparison between the calculated value of the modified Uskinov formula and the experimental value of desorption rate: (a)–(d) coal sample W-01; (e)–(h) coal sample W-02; (i)–(l) coal sample JS; (m)–(p) coal sample GY.

Based on the experimental data and the mathematical form of the Uskinov formula, the desorption times, adsorption equilibrium constants a and b, adsorption equilibrium pressure pb, and desorption environmental pressure pa were introduced to construct the desorption mathematical model of coal under the condition of desorption damage. The test data indicate that the optimized model has an excellent application influence on the samples repeatedly desorbed in the lab and the structurally damaged coal desorbed during the coal formation period. The research results can not only promote the theoretical research of the outburst mechanism but also provide a new way for the prediction of outburst risk and offer technical support for the prevention and control of outburst accidents.

6. Conclusions

This review focuses on the characteristics of coal methane desorption under the condition of desorption damage. The influence of key variables such as environmental pressure and coal damage degree on methane desorption in the desorption process is studied. These are the primary conclusions.

  • (1)

    Desorption damage significantly impacts coal desorption process dynamics, with methane desorption amount and velocity increasing with desorption times and the diffusion coefficient increasing linearly with desorption times.

  • (2)

    A double-parameter damage model based on desorption conditions and adsorption pressure was proposed, and the damage quantitative index Ki of coal particles after i repeated tests was calculated. The damage quantitative index could indicate the damage degree of coal during desorption.

  • (3)

    A methane desorption model of coal under desorption damage conditions was developed and verified in 32 groups, demonstrating an accurate description of methane desorption characteristics.

Acknowledgments

We appreciate the financial support of the Discipline Innovation Team of Liaoning Technical University (Grant No. LNTU20TD-30) and the Project of the Natural Science Foundation of Liaoning Province (Grant No. 2022-BS-328).

Glossary

Variable Annotation

variable

parameter variable unit

Qt

The amount of methane desorption under standard temperature and pressure conditions, mL/g

Qt′

The measured amount of methane desorption under the experimental conditions, mL/g

tw

Water temperature, °C

Pr

The atmospheric pressure of the experimental environment, kPa

hw

The height of the water column inside the measuring cylinder, mm

Pw

The saturated water vapor pressure at temperature tw, kPa

Vt

The rates of methane desorption at times t, mL/g·min

Vε

The rates of methane desorption at times tε, mL/g·min

kε

The attenuation coefficient of the methane desorption velocity

tε

Desorption time at ε time, s

t

Desorption time, s

Mt

The gas diffusion mass of coal particles at the time t, g

M∞

The total mass of gas diffusion, g

r

The average diameter of coal particles, m

Q∞

Limit diffusion amount, mL/g

ζ

The gas diffusion coefficient of coal particles at the time t0, m2/s

τ

The attenuation coefficient of gas diffusion coefficient

Si

Relative deviation

i

The number of repeated tests of desorption damage

Di

The diffusion coefficient under the condition of the i time desorption damage test, m2/s

Di+1

The diffusion coefficient under the condition of the i+1 time desorption damage test, m2/s

KQ

The contribution of desorption conditions to the damage

KP

The contribution of adsorption pressure to damage

Qmax,i

The maximum desorption amount of the i time desorption damage test, mL/g

Qmin,i

The minimum desorption amount of the i time desorption damage test, mL/g

QT

Cumulative desorption amount, mL/g

Pm

Gas adsorption equilibrium pressure, MPa

Pn

The pressure of methane injected into the coal sample tank, MPa

Ki

Damage quantification index

v0

Gas desorption velocity at t = 0, mL/g·min

Qba

The gas adsorption capacity of coal particles with gas pressure from pa to pb, mL/g

a

Adsorption constant, m3/t

b

Adsorption constant, MPa–1

δ

The linear relationship between v0 and adsorption capacity

pa

Desorption environmental pressure, MPa

pb

Adsorption equilibrium pressure, MPa

n

The attenuation coefficient of gas desorption rate changing with time

The authors declare no competing financial interest.

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