Research on the Microscopic Adsorption Characteristics of Methane by Coals with Different Pore Sizes Based on Monte Carlo Simulation

Abstract

In order to explore the influence of different pore sizes of anthracite on the methane adsorption characteristics, a low-temperature liquid nitrogen adsorption experiment was carried out. Six types of anthracite with pore sizes ranging from 10 Å to 60 Å were selected as simulation objects. By means of molecular simulation technology and using the Materials Studio 2020 software, a macromolecular model of anthracite was established, and a grand canonical Monte Carlo (GCMC) simulation comparative study was conducted. The variation laws of the interaction energy and diffusion during the process of coal adsorbing CH₄ under different pore size conditions were obtained. The results show that affected by the pore size, under the same temperature condition, the peak value of the interaction energy distribution between coal and CH₄ shows a downward trend with the increase in the pore size under the action of pressure, and the energy gradually decreases. The isothermal adsorption curves all conform to the Langmuir isothermal adsorption model. The Langmuir adsorption constant a shows an obvious upward trend with the increase in the pore size, with an average increase of 16.43%. Moreover, under the same pressure, when the pore size is 60 Å, the adsorption amount of CH₄ is the largest, and as the pore size decreases, the adsorption amount also gradually decreases. The size of the pore size is directly proportional to the diffusion coefficient of CH₄. When the pore size increases to 50 Å, the migration state of CH₄ reaches the critical point of transformation, and the diffusion coefficient rapidly increases to 2.3 times the original value.

1. Introduction

Coal, as a porous medium, possesses a complex pore structure, and pores are the main sites where gas is stored. Coalbed gas mainly consists of methane (CH₄) and its homologous alkanes, CO, H₂S, H₂, etc. A total of 80–90% of the gas in coal seams and surrounding rocks exists in an adsorbed state. The pore size distribution of coal not only affects the storage state of gas in pores but also significantly influences the interaction between pores and gas or liquid molecules [1]. The pore structure of coal is an important indicator of coal’s ability to adsorb gas and the mobility of gas [2]. A systematic study of the pore structure of coal and its adsorption law for gas is of great significance for in-depth research on the occurrence of coalbed methane and the mechanism of coal and gas outburst.

At present, scholars at home and abroad have already achieved some important results in the research on the pore structure of coal. According to the classification of the International Union of Pure and Applied Chemistry (IUPAC), the pore sizes in a coal matrix and other porous materials are divided into micropores (diameter ≤ 2 nm), mesopores (diameter 2–50 nm), and macropores (≥50 nm) [3]. Cheng et al. [4] proposed a new pore classification method. Based on the occurrence and migration characteristics of methane in coal, the research results show that this new pore classification method can describe the pore structure of coal more accurately, thus providing more effective theoretical guidance for coal gas drainage. Wang et al. [5] conducted in-depth research on the pore structure of tectonic coal, and the results show that the pore structure characteristics of tectonic coal are important factors affecting the effect of gas drainage. Li et al. [6] used N₂ and CO₂ as probe molecules in experiments. Through isothermal adsorption experiments, they found that CO₂ adsorption can characterize the microstructure of coal more accurately. In 2022, Zhongbei et al. [7] Adopted the high-pressure isothermal gas adsorption method to study the adsorption performance of three fractal dimensions, characterized the differences in the microstructure of coal, reflected the influence of the microstructure of coal on the gas adsorption ability, and provided a valuable basis for the adsorption evaluation of different coal rank coal seams for gas. From a microscopic perspective, Qing et al. [8] adopted the molecular dynamics method and studied the adsorption characteristics of methane in pores with a diameter of 4 nm based on the grand canonical ensemble Monte Carlo simulation (GCMC). They studied the influence and mechanism of isothermal adsorption curves, concentration distribution, and diffusion coefficients on the methane adsorption behavior under different conditions, providing a theoretical basis for revealing the interaction mechanism between methane and coal with different metamorphic degrees. In 2018, Hong et al. [9] used the Materials Studio 2018 molecular simulation software to study the adsorption characteristics of methane by carbon materials with different pore sizes. Through the interpolation method, they obtained the optimal pore sizes of single-layer and double-layer carbon materials for methane adsorption. Han et al. [10] constructed coal pore structure models with pore diameters of 1, 2, and 4 nm by using graphene sheets and simulated the adsorption behavior of methane in pores of different sizes. They concluded that the adsorption amount is positively correlated with the pore size of pure gas adsorption, and the adsorption amount increases with the increase in pressure and pore size. Hao et al. [11] constructed different slit pore models of coal and carried out a series of molecular simulations. They proposed that the absolute adsorption amount increases with the increase in slit pores, and the increased slit pores can promote the self-diffusion and transport diffusion of methane molecules, providing a theoretical basis for studying the interaction between coal and methane.

In summary, relevant scholars have conducted relatively systematic research on the adsorption characteristics, evolution laws, and permeability enhancement mechanisms of different coal ranks and their pore structures through macroscopic experiments and have achieved fruitful results. They have obtained the microscopic adsorption variation laws of coal bodies with different pore size dimensions and methane. However, the evolution laws of the interaction mechanism at the molecular scale among pores with different sizes still need further discussion. Therefore, this paper uses the low-temperature liquid nitrogen adsorption experiment to determine the pore size distribution of anthracite in a certain Yangmei coal mine. Through Materials Studio 2020 and by using the grand canonical ensemble Monte Carlo method, it analyzes the variation laws of the adsorption characteristics during the process of anthracite with different pore size dimensions adsorbing gas, studies the influence of pore size changes on gas adsorption, and obtains the variation laws of the interaction mechanism between coal and methane molecules under different pore size dimensions.

2. Low-Temperature Liquid Nitrogen Adsorption Experiment

2.1. Preparation of Coal Samples and Experiment

Through on-site investigations, coal samples of anthracite from a certain Yangmei coal mine were collected. The collected lump coal was then ground, sieved, and dried. A standard sieve with a mesh size of 60–80 was used. Due to the relatively large particle size, screening for 15 min at a time was sufficient to obtain the corresponding amount of coal particles. Coal particles with a particle size below 3 mm were screened out and dried at 60 °C for 10 h before being subjected to testing. Under the condition of 77 K, nitrogen molecules filled the pores of the coal body through micropore filling, physical adsorption, and capillary condensation, and the pore volume was equal to the volume filled by the nitrogen molecules. In this experiment, an Autosorb iQ Station 1 specific surface area and pore size analyzer was used to conduct the low-temperature liquid nitrogen adsorption experiment.

2.2. Experimental Results

Based on the results of the low-temperature liquid nitrogen adsorption experiment, calculations were carried out using the Brunauer–Emmett–Teller (BET) and Barrett–Joyner–Halenda (BJH) theoretical models. The specific surface area and pore volume distribution of the coal samples are shown in

Table 1. Specific surface area and pore volume distribution of coal samples.

Pore Size/nm	0~0.2	0.2~1	1~2	2~3	3~4	4~5	5~6	6~10
Specific surface area (m2·g−1)	1.126	3.402	0.558	0.491	0.324	0.468	0.265	0.096
Pore volume/(cm3·g−1)	0.00158	0.00247	0.00156	0.00096	0.00077	0.00082	0.00069	0.00349

. According to the data in Table 1, it can be seen that the pores of the coal are widely distributed among micropores, mesopores, and macropores, but the distribution is the most concentrated on the scale of mesopores (with a diameter of 2–50 nm). It is thus evident that the adsorption of methane by coal on the mesopore scale is the most representative. In order to explore the changes in the microscopic adsorption mechanism and adsorption situation of coal for methane as the pore size changes, six pore size dimensions of 10 Å, 20 Å, 30 Å, 40 Å, 50 Å, and 60 Å were selected for simulation studies in this paper. The main focus was to investigate the microscopic adsorption characteristics of coal pores for methane at different pore size dimensions.

3. Construction and Simulation of Adsorption Models

3.1. Elemental Analysis and Construction of Coal Samples

In this study, the technical means of molecular simulation were employed. Taking the planar model of anthracite from a certain Yangmei coal mine constructed by relevant scholars using testing methods such as proximate analysis, elemental analysis, nuclear magnetic resonance (¹³C-NMR), and X-ray photoelectron spectroscopy (XPS) as the research object [12], the functional groups in the coal model mainly include carbonyl groups, carboxyl groups, hydroxyl groups, various aliphatic functional groups, and heteroatomic structures, and its molecular formula is C₂₀₇H₁₆₂O₁₂N₄. The corresponding planar diagram of the coal macromolecular structure was drawn using the KingDraw v3.0 chemical drawing software, and the model was imported into the Materials Studio 2020 software for hydrogenation saturation. Using the Forcite module, geometric optimization (Geometry Optimization) and simulated annealing (Anneal) were carried out on the obtained coal macromolecular model. Its bond lengths were stretched, bond angles were twisted, and an obvious parallelism was presented among the aromatic hydrocarbon structures. After optimization, the molecular structure with the minimum local energy was obtained [12,13], as shown in Figure 1. The Amorphous Cell module was utilized to add periodic conditions and construct unit cells. The final model size was 15.1 × 15.1 × 15.1 Å, and the density of the coal unit cell was 1.40 g/cm³. The actual density of anthracite is 1.40–1.80 g/cm³, which meets the density standard of actual anthracite. After optimization, the unit cell of anthracite was obtained.

3.2. Simulation Parameter Settings and Model Configurations

To explore the microscopic adsorption mechanism of anthracite under different pore conditions, the Sorption module was used in this adsorption simulation to simulate CH₄ adsorption under different pore diameters. The Analysis function in the Forcite module was employed to calculate the gas diffusion coefficient of the solid–gas saturated model. The specific steps are as follows [14,15,16]:

(1)

In the Sorption module, the task type was set as “Fixed pressure”, the method was “Metropolis”, the simulation accuracy was “Customized”, and the forcefield (Forcefield) was selected as the COMPASS II forcefield. For charges, the “Forcefield assigned” method was chosen. For the electrostatic interaction between atoms, the “Atom Based” method was selected, and for both van der Waals interaction and hydrogen bonding, the “Atom Based” method was also adopted. The number of equilibration steps was set to 1 × 10⁶, the number of production steps was set to 1 × 10⁶, and the number of escape steps was set to 20.

(2)

In the Sorption module, when the task type was selected as the “Locate” task, its corresponding parameter settings were the same as those of the “Fixed pressure” module.

(3)

In the Forcite module, the task type was set as “Dynamics”, the temperature was chosen as 298 K, the NVT ensemble was selected, the simulation time was set to 500 ps, the time step length was set to 1.0 fs, and the temperature control method was selected as “Nose”. The “Analysis” function was used to choose the diffusion coefficient (MSD).

The surface and pores of the coal seam provide space for gas adsorption. Determining the surface area and pore volume of coal with different pore diameters is a prerequisite for exploring the influence of coal pore size on the CH₄ adsorption characteristics. The Build Layer tool was used to construct anthracite pore models with six different vacuum layer thicknesses ranging from 10 Å to 60 Å. The porosity was calculated under models with different vacuum layer thicknesses and the adsorption process was simulated. By using the Connolly algorithm and taking CO₂ molecules with a kinetic diameter of 3.3 Å as molecular probes, the surface area, free volume, and occupied volume of the pore structures of coal with different pore diameters were determined, the porosity of coal samples with different pore diameters was calculated, and the influence of the change in porosity under different pore diameter conditions on the adsorption performance was discussed [17]. The calculation formula is as follows:

$$\varphi ={\displaystyle \frac{V_f}{V_t}}\times 100\%$$

In the formula, $\varphi$ represents the porosity, in percentage; $V_f$ represents the free volume, in ų; and $V_t$ represents the total volume, in ų.

In Figure 2, the surface and pores of the coal are distinguished by blue and gray curved surfaces. Among them, the area surrounded by blue represents the free volume, and the area surrounded by gray represents the occupied volume. It can be seen from Figure 2 that as the pore diameter increases, the pore area at the adsorption sites in the coal pore structure increases significantly. To determine the influence of the pore size, the porosities of the macropores of coal with different pore diameters were calculated. The results of the porosities of anthracite under different pore diameter conditions are shown in

Table 2. Percentage of each element in anthracite coal from a mine in Yang Blocs.

Sample Elements	C	H	O	N
Mass fraction/%	85.81	5.64	6.63	1.93

. As the pore diameter gradually increases, the porosities of anthracite with different pore diameters increase to varying degrees.

4. Simulation and Analysis of Coal’s Adsorption of Gas

4.1. Distribution of Interaction Energy

In the pore structures of coal with different pore diameters, energy changes occur when CH₄ comes into contact with the inner walls of the coal pores. To reveal the energy changes in the adsorption behavior of CH₄ under different pressures due to the change in pore diameter, the change in the energy peak of CH₄ adsorption was analyzed from the perspective of energy distribution. Fixed-pressure adsorption was carried out through the Sorption module in Materials Studio to obtain the distribution of the interaction energy between coal and methane. The peak represents the position where the energy is more concentrated [18], as shown in Figure 3.

With the increase in pore diameter or porosity, the energies at the interaction energy peaks of the pore diameters ranging from 10 Å to 60 Å are −10.15 kJ/mol, −9.85 kJ/mol, −9.65 kJ/mol, −9.35 kJ/mol, −8.55 kJ/mol, and −7.90 kJ/mol, respectively. The results indicate that the distribution of the interaction energy between coal and CH₄ molecules gradually shifts to the right, suggesting that the interaction between coal and CH₄ gradually weakens. This is caused by the reduction in van der Waals forces in the pore models with higher porosity, and the number of CH₄ molecules that can interact between coal and CH₄ decreases, resulting in a gradual decrease in the interaction energy [19].

According to the analysis in Figure 3, the energy distribution diagram of CH₄ shows a single-peak state, indicating that there is only one adsorption site. CH₄ molecules are randomly and evenly adsorbed in the pores, and the adsorption states are the same, without two or more adsorption sites with significant differences in adsorption. It can be seen from Figure 3a,b that the relative interaction energy distribution hardly changes in the pore models with pore diameters of 10 Å and 20 Å. The main reason is that the distance between the inner walls of the relatively opposite pore channels within the micropores is small, and the van der Waals force potential generated by the inner walls overlaps, exerting a stronger force on CH₄ molecules than that in mesopores and macropores, resulting in relatively insignificant changes in the adsorption energy of CH₄ in micropores under pressure compared to other larger pore diameters. From the analysis of Figure 3b–e, it can be obtained that at 1 MPa, the interaction energy distribution decreases at the peak with the increase in pore size, and the decline is relatively slow when the distribution reaches the peak. It can be seen from Figure 3d,f that as the pore diameter increases, there is a trend of a gradual decrease in the peak of the energy distribution within the range from 1 MPa to 3 MPa.

Based on the above analysis, it can be concluded that the larger the pore diameter of coal is, the weaker the van der Waals forces between the inner walls of the pores will be, and the smaller the interaction energy between CH₄ and the surface of the pores will be; so, CH₄ will not be adsorbed more strongly. When the pore diameter decreases, CH₄ molecules tend to gather at the pore entrances. Affected by the interaction forces at the narrow interface, the interaction energy becomes stronger, and the adsorption becomes more significant. In the models with a pore diameter of above 30 Å, the change in pressure is also one of the reasons for the distribution of the interaction energy between coal/CH₄ molecules.

4.2. Influence of Coal with Different Pore Diameters on the Isothermal Adsorption of CH₄

Based on the fact that methane in actual coal seams exists in the pores of anthracite with different pore diameters, under different pressures, methane gas molecules diffuse towards the surface of the coal seam. When they diffuse to the adsorption sites, they will be adsorbed at these sites. For coal samples with different pore diameters, isothermal adsorption simulations of methane gas under the same temperature and different pressure conditions were carried out for coal pore models with pore diameter sizes of 10 Å, 20 Å, 30 Å, 40 Å, 50 Å, and 60 Å, respectively. The linearized formula of the Langmuir model (Formula (1)) was used to process the adsorption equilibrium experimental data under different pressures for the description of the adsorption equilibrium process of CH₄ on the coal surface [18,19,20,21,22]:

$$Q={\displaystyle \frac{abp}{1+bp}}$$

(1)

In the formula, Q represents the adsorption amount of methane at the equilibrium state of the coal sample, in mmol/g; a represents the absolute adsorption amount of methane, in mmol/g; b represents the Langmuir adsorption equilibrium constant, in MPa⁻¹; and p represents the adsorption pressure, in MPa.

It can be seen from Figure 4 that the isothermal adsorption curves of CH₄ gas in the pore models of anthracite with different pore diameters conform to the characteristics of the isothermal lines of the Langmuir model. Therefore, the isothermal adsorption curves obtained from the simulation were fitted according to the linearized formula equation, and the volume constant a and pressure constant b in the Langmuir adsorption constants were obtained. The parameters are shown in

Table 3. Parameters of coal pore model with different pore sizes.

Pore Diameter/Å	Surface Area/Å2	Free Volume/Å3	Occupied Volume/Å3	Porosity%
10	2468.89	8355.84	8116.71	50.72
20	2460.12	10,631.16	8118.79	56.69
30	2470.55	12,920.03	8107.32	61.44
40	2463.97	15,189.34	8115.41	65.17
50	2459.37	17,461.22	8120.93	68.25
60	2468.89	19,744.05	8115.49	70.86

.

The absolute adsorption amount of CH₄ continuously increases with the increase in adsorption pressure. When it approaches the critical pressure of CH₄, the absolute adsorption amount increases slowly and tends to stabilize. In the range of 1–5 MPa, the adsorption amount of methane rises rapidly with the increase in adsorption pressure, which is in the rapid adsorption stage. When the adsorption pressure reaches 5–10 MPa, the adsorption amount of CH₄ increases slowly with the increase in adsorption pressure, which is in the slow adsorption stage. The results indicate that pressure can promote the ability of coal to adsorb CH₄, but the effect is not as obvious as that in the range of 1–5 MPa, and the influence gradually decreases in the slow adsorption stage. During the adsorption process, with the increase in pressure, the influence of pore diameter on the adsorption of CH₄ is relatively obvious. When the pore diameter increases from 10 Å to 60 Å, the absolute adsorption amount of CH₄ increases from 51.07 mmol/g to 108.97 mmol/g. The growth rates in the pores are basically the same. When the pressure is 10 MPa, with every 10 Å increase in pore diameter, the absolute adsorption amount increases by an average of 16.43%.

After Langmuir nonlinear fitting, the R² values are all greater than 0.95, indicating a good fitting effect. As can be seen from Table 3, under the pore diameters ranging from 10 Å to 60 Å, the Langmuir adsorption constants a of the coal samples are 51.55 mmol/g, 64.00 mmol/g, 78.97 mmol/g, 92.87 mmol/g, 106.80 mmol/g, and 124.60 mmol/g, respectively. The value of the adsorption constant a reflects the absolute adsorption amount of CH4 of the coal sample. It can be observed that the adsorption constant a shows an obvious upward trend with the increase in pore diameter, with an overall increase as high as 58.26%. The change in the adsorption constant b from 50 Å to 60 Å is only 0.27 MPa⁻¹, which is negligible compared to the change in the adsorption constant b from 10 Å to 20 Å. Combined with the analysis of the free volumes of anthracite with different pore diameters calculated by the Connolly algorithm, the adsorption amount of CH₄ is related to the porosity of coal. With the increase in porosity, more space is provided for the adsorption of CH₄, and the absolute adsorption amount of CH₄ keeps rising under the action of pressure and tends to reach a saturated state. This indicates that the pore diameter has a significant impact on the adsorption amount of methane, that is, the adsorption amount of CH₄ in anthracite increases with the increase in pore diameter.

4.3. Influence of Coal with Different Pore Diameters on the Diffusion of CH₄

Coal with different pore diameters can affect the kinetic behavior of CH₄ molecules [23]. Under the conditions of constant temperature and constant pressure, the diffusion coefficients of methane in the pore models of anthracite with pore diameters ranging from 10 Å to 60 Å were calculated, respectively. The mean square displacement and its diffusion coefficient D, which can describe the random motion of CH₄ molecules diffusing in different pore diameters, were calculated by selecting the diffusion coefficient (MSD) through the Analysis function of the Forcite module. The calculation formula is as follows [24]:

$$MSD={\displaystyle \frac{1}{N}}{\sum }_{i=1}^N\left[r_i\right(t)-r_i(0){]}^2$$

(2)

$$D={\displaystyle \frac{1}{6N}}\mathit{lim}{\displaystyle \frac{d}{dt}}{\sum }_{i=1}^N\left[r_i\right(t)-r_i(0){]}^2$$

(3)

$$D={\displaystyle \frac{1}{6}}\underset{t\to \infty }{\lim }({\displaystyle \frac{MSD}{t}})={\displaystyle \frac{1}{6}}{K}_{MSD}$$

(4)

In the formula, N represents the number of molecules and r(t) and r(0) are the position vectors of the center of mass of the diffusing molecules from time t to t = 0, respectively. K_MSD is the slope of the mean square displacement (MSD) curve, that is, the diffusion coefficient is one-sixth of the slope of the MSD curve. The integrated data of the mean square displacement of CH₄ in anthracite with different pore diameters are shown in Figure 5. The slope of the mean square displacement in the larger pore diameter models is greater than that in the smaller pore diameter models. This is because the larger pore diameters provide a larger area for the diffusion motion, giving CH₄ molecules more diffusion space. By calculating the slope of each point on the curve, the diffusion coefficients of CH₄ molecules in coal samples with different pore structures were finally obtained. The influence of different pore diameters on the diffusion ability of CH₄ is in the order of 60 Å > 50 Å > 40 Å > 30 Å > 20 Å > 10 Å.

It can be seen from

Table 4. Adsorption constants of different pore size pore coal with CH₄ Langmuir.

Adsorbate	Pore Diameter/Å	a/(mmol·g−1)	b/(MPa−1)	R2
CH4	10	51.55	6.40	0.9542
	20	64.00	2.73	0.9943
	30	78.97	1.50	0.9928
	40	92.87	1.29	0.9933
	50	106.80	1.13	0.9906
	60	124.60	0.86	0.9961

and

Table 5. Diffusion coefficients of CH₄ molecules in different coal pore sizes.

Pore Spacing/Å	Curve Slope	Diffusion Coefficient/Å·ps−1	R2
10	3.40	0.567	0.9996
20	4.56	0.760	0.9906
30	6.46	1.077	0.9976
40	7.83	1.305	0.9980
50	10.33	1.722	0.9951
60	23.35	3.892	0.9977

that among the six different pore diameters of anthracite, the diffusion coefficient of CH₄ is the smallest when the pore diameter is 10 Å, with a value of 0.567 Å/ps; when the pore diameter is 60 Å, the diffusion coefficient is the largest, with a value of 3.892 Å/ps. The diffusion coefficients of pore diameters from 10 Å to 50 Å increase relatively gently at an average rate of 32.25%. However, the increase in the diffusion coefficient from a pore diameter of 50 Å to 60 Å surges by approximately 126%. This is due to the limited pore volume and the relatively strong binding effect of van der Waals forces on CH₄ in smaller pores, which increases the diffusion resistance inside the coal pores. Most of the CH₄ remains in a free state and moves randomly and freely; so, the diffusion coefficient of CH₄ increases slowly. As the pore diameter increases, its pore volume also becomes larger, and the binding effect on CH₄ gradually weakens. When the migration state of CH₄ begins to change from being mainly in a free state to mainly in an adsorbed state under the action of pressure, the diffusion coefficient in the model will increase rapidly when the pore diameter is 50 Å.

Based on the above analysis, a larger pore volume provides more diffusion space for the diffusion of CH₄, enabling more methane to pour into the pore channels within the same period of time. The degree of CH₄ diffusion in the pores of coal is directly related to the porosity of the coal. That is to say, it is easier for CH₄ to diffuse in larger pores, with a relatively larger diffusion coefficient, while it is more difficult for CH₄ to diffuse in smaller pores, with a relatively smaller diffusion coefficient.

5. Conclusions

(1)

The size of the pore diameter in coal directly affects the interaction energy during the adsorption of CH₄. Due to the relatively stronger van der Waals force generated between the upper and lower layers of smaller pores, the force exerted on CH₄ is more significant than that in other larger pores. As the pore diameter increases, the van der Waals forces between the inner walls of the pores decrease, and the interaction energy between CH₄ and coal molecules gradually weakens.

(2)

The adsorption processes of anthracite with different pore diameters all conform to the Langmuir model. There is a positive correlation between the pore diameter size and the adsorption amount. Under the same temperature and pressure conditions, with every 10 Å increase in pore diameter, the absolute adsorption amount of CH₄ increases by an average of 16.43%. After reaching the critical pressure of CH₄, the absolute adsorption amount increases slowly and tends to reach a saturated state.

(3)

The diffusion coefficient of CH₄ in the pores of anthracite increases linearly with the change in diffusion time. When the pore diameter is less than 50 Å, the diffusion coefficient of CH₄ in the pores increases at a uniform rate of 32.25%. When the pore diameter reaches 50 Å, the diffusion of CH₄ changes from being mainly in a free state to being mainly in an adsorbed state, and the diffusion coefficient increases rapidly at a rate of 126% at 50 Å.

(4)

In this paper, the microscopic adsorption law of methane by coal with pore diameters ranging from 10 Å to 60 Å has been studied. However, there are still many factors that affect the adsorption of methane by coal, such as the influence of different specific surface areas of pores and changes in air pressure. For such issues, further in-depth research should be continued.