Molecular Simulation of CH₄ Adsorption Characteristics under the Coupling of Different Temperature and Water Content

Abstract

The adsorption characteristics of CH₄ have an important influence on gas content prediction, gas extraction, and hazard prevention. Therefore, we explored the mechanism of CH₄ adsorption under the action of water and temperature to grasp the influence of water and temperature on the adsorption characteristics of CH₄. In this paper, a giant, regular-system Monte Carlo method is used to simulate the CH₄ adsorption behavior at the molecular level under different temperatures, water contents, and the coupling of both. The results indicate that an empirical formula for the coupling effect of temperature and water content on CH₄ adsorption was obtained. The impact of different effects on CH₄ adsorption is as follows: coupling effect > single temperature effect > single water content effect. The optimal combination is at a temperature of 363 K and a water content of 8.31%. Compared with the CH₄ adsorption capacity without water at room temperature, the CH₄ adsorption capacity is reduced by 68.04% under the coupling effect of the optimal combination. Temperature has a negative effect on the adsorption of CH₄, and temperature changes the adsorption capacity by changing the average molecular kinetic energy of CH₄. The reason why the increase in H₂O reduces the adsorption capacity of CH₄ is that the interaction between H₂O and the oxygen-containing functional groups of coal is stronger than that of CH₄. As the water content increases, the adsorption heat decreases, thereby inhibiting the adsorption of CH₄. In addition, H₂O has a smaller molecular dynamics radius as compared to CH₄; the larger the free volume and surface area in the pore structure, the more adsorption pores it occupies, resulting in a more significant reduction in the adsorption of CH₄.

1. Introduction

CH₄ is a high-quality, efficient energy source and is also the second-largest greenhouse gas after carbon dioxide [1,2]. CH₄ emissions account for about 18% of the global emissions of greenhouse gases, and their development and utilization are of great significance for clean energy and carbon emission reduction [3]. CH₄ is mainly stored in coal seams in adsorbed and free states, of which more than 80–90% is stored in adsorbed states. Research on the adsorption capacity of coal for methane is an important basis for the calculation and exploitation of coalbed methane reserves [4].

In recent years, numerous scholars have carried out a lot of research on the characterization of CH₄ adsorption by coal. Li Shugang et al. quantitatively characterized the methane adsorption characteristics using microporous filling and monolayer adsorption theory and clarified the mechanism of methane adsorption in adsorption pores [5]. Feng Zengzhao et al. investigated the effect of water on the adsorption characteristics of coal and found a linear relationship between the CH₄ adsorption content of coal and the water content [6]. Qin Lei et al. studied the adsorption characteristics of gas after the addition of low-temperature liquid nitrogen, utilizing a low-temperature liquid nitrogen adsorption instrument, and concluded that the temperature decreases the content of oxygen-containing functional groups [7]. Li Xijian studied the adsorption of methane by coal through molecular simulation and concluded that the porosity, temperature, water, and ash content of coal affected the adsorption of methane by coal [8]. Zheng Chao et al. investigated the effect of water on the desorption/adsorption of CBM and found that the effect of water on adsorption in coal reservoirs is limited by the pore structure and that the mode of coal–water interaction in micropores is the core of CBM adsorption [9]. Li Bobo et al. concluded that the adsorption amount of the coal body is inversely proportional to the water content by conducting coal rock adsorption experiments [10]. Li et al. investigated the change in the adsorption energy of coal bodies under different temperature and pressure conditions and concluded that the physical properties and internal chemical structure of coal bodies would affect the change in gas adsorption energy [11]. Zhang et al. investigated the adsorption of CH₄ by nanopores using molecular simulation and concluded that the change in CH₄ adsorption was related to temperature, pressure, and burial depth, and was consistent with the reasons for the change in adsorption amount and adsorption heat [12]. Yan et al. investigated the relationship between the pore structure of the coal body and the adsorption of the gas at different temperatures. Researchers used low-temperature nitrogen adsorption and isothermal adsorption experiments to study the free energy of adsorption and entropy of adsorption of coal samples, concluding that both decreased gradually with an increase in temperature [13]. Cai et al. found that initial free gas pressure affects the heat of adsorption of the coal body, and the larger the initial gas pressure is, the smaller the heat of adsorption is [14].

The existing studies mainly focus on the CH₄ adsorption characteristics under the influence of single factors of temperature and water content, and there are a lack of studies on the influence of the coupling of the two. Therefore, in this paper, we use a coal sample from the Ping coal mine (PM) as the research object and utilize molecular simulation methods to study the effects of different temperatures, water contents, and the coupling of the two on the CH₄ adsorption characteristics.

2. Model Construction and Simulation Parameters

2.1. Coal Quality Analysis

The experimental coal samples were analyzed industrially according to GB/T 212-2008 “Methods of Industrial Analysis of Coal” [15]. Then, the maximum specular group reflectance of the coal sample was measured according to GB/T 8899-2013 “Coal microclassification and mineral determination methods” [16]. The experimental results are shown in

Table 1. Analysis of coal sample components.

Coal Sample	Maximum Vitrinite Reflectance/ %	Water/%	Ash/%	Volatiles/%	Fixed Carbon/%
PM	1.90	4.65	9.93	13.26	72.16

.

2.2. Coal Model Construction and Parameters

The model data from the literature [17] were used as a basis to construct the model in this paper, as shown in Figure 1a, with the following structural parameters: the molecular formula C₁₀₈H₇₁O₄N, a model molecular weight of 1445, an elemental content of C of 86.69%, an elemental content of H of 4.91%, an elemental content of O of 4.43%, and an elemental content of N of 0.97%.

The Forcite module in Materials Studio was selected for geometry optimization and annealed to obtain the lowest energy configuration of the coal model, as shown in Figure 1b. Specific parameter settings were as follows: Geometry optimization was selected for the task, COMPASS was selected for the force field, and charge equilibration (QEq) was used to calculate the charge. Specific parameter settings for the molecular dynamics optimization were the following: Anneal was selected for the task; the total number of annealing cycles was 10; the initial temperature was 300 K; the maximum temperature was 600 K; and the NVT system was used. The simulation time was 10 ps, the temperature control method was Nose, and the force field was set as described above.

The 15 optimized basic structural units were randomly placed into the empty box to establish the periodic boundary conditions of the structure of the coal model, and the optimized coal structure model cell parameters were obtained, in which the prism length was A = B = C = 2.8 nm, the inter-prism angle was α = β = γ = 90°, and the cell density was 1.1%. The optimized dry coal model of the E9-10 seam of the PINGDINGSHAN BAMINE is shown in Figure 1c.

2.3. Simulation Program

The Grand Canonical Ensemble Monte Carlo (GCMC) method was used to simulate the adsorption of CH₄ at different temperatures, water contents, and mutual coupling. The Sorption module of Materials Studio was used, with Adsorption Isotherm selected for the task item, COMPASS selected for the force field, and pressures ranging from 0.01 to 10 MPa.

(1) In the study of temperature effects, the simulation temperatures were set to 223 K, 243 K, 263 K, 303 K, 313 K, 343 K, and 363 K, and the adsorbent was a dry coal model with 0% water content.

(2) In the simulation of different water content, the temperature was fixed at 303 K, and the adsorbent was set as a coal structure model with water content of 1.10%, 4.27%, and 8.31%, respectively.

(3) In analyzing the coupling process adsorption, orthogonal tests were set up for different temperatures and water contents, and the primary and secondary order of the influencing factors were determined by polar analysis.

The number of gas molecules adsorbed in a single crystal cell can be obtained by GCMC simulation. Formula (1) is replaced by the amount of adsorption commonly used in the experiment:

$$V=1000{\displaystyle \frac{N}{N_A·M}},$$

(1)

In the equation: V is the adsorption capacity, mmol/g; N is the number of gas molecules adsorbed in a single unit cell, moleculars/u.c; N_A is the Avogadro constant, 6.02 × 10²³; M is the unit cell mass, g.

The isothermal data were fitted by the Langmuir Equation (2):

$$V={\displaystyle \frac{abp}{1+bp}},$$

(2)

In the equation, V is the adsorption capacity, mmol/g; a is the saturated adsorption parameter, mmol/g; b is the adsorption equilibrium parameter, MPa⁻¹; p is pressure, MPa.

3. Simulation Results and Analysis

3.1. Effect of Temperature on Methane Adsorption Performance

Temperature is one of the important factors that affects CH₄ adsorption [18]. The isothermal adsorption data obtained from the simulation were fitted with the Langmuir equation, and the R² was 0.993~0.996, which was a good fit, indicating that the simulation results were reliable. Based on the values of adsorption constants a and b under different temperature conditions, the methane adsorption quantities X1~X10 at pressures ranging from 1 to 10 MPa were calculated, respectively, and the correction coefficient η_t of 303 K was taken as 1, which resulted in the curve of the average value of the correction coefficient η_t versus the temperature under different temperature conditions, as shown in Figure 2.

It can be seen from Figure 2 that the change in temperature correction coefficient η_t with temperature t satisfies Equation (3):

$${\eta }_t=1.27e^{-0.009t},$$

(3)

In the formula: η_t is the temperature correction coefficient; t is temperature, °C.

Adsorption of CH₄ at different temperatures were obtained by considering the temperature based on the Langmuir equation as shown in Figure 3. From the figure, it can be seen that the absolute adsorption amount of CH₄ decreases gradually with the increase in temperature, and the heat of adsorption decreases gradually under the same pressure. High-temperature environments inhibit the adsorption of CH₄ on coal because the increase in temperature increases the average kinetic energy of CH₄ molecules, weakening the van der Waals forces between CH₄ molecules. Low-temperature environments are just the opposite, where cooling reduces the kinetic energy of free CH₄ molecules, allowing the van der Waals forces between CH₄ molecules to increase.

3.2. Effect of Different Water Content on Methane Adsorption Performance

The actual coal seam contains a large amount of water, and the water content in the coal seam is also an important factor affecting CH₄ adsorption [19,20]. In order to clarify the effect of different water contents on CH₄ adsorption, different water molecules were added to the dry coal model, and the coal models with water content of 1.1%, 4.27%, and 8.31% were constructed, respectively. The number of water molecules were 23, 64, and 110, respectively. The molecular models with different water contents are shown in Figure 4, where the green ball-and-stick models represent the water molecules.

The isothermal adsorption data obtained from the simulation were fitted with the Langmuir equation. The fitting parameters of the Langmuir equation with different water content as shown in

Table 2. The fitting parameters of the Langmuir equation with different water content.

Water Content	a/(mmol/g)	b/MPa−1	R2
0%	3.88	0.10	0.995
1.1%	3.29	0.23	0.991
4.27%	2.79	0.22	0.994
8.31%	2.31	0.26	0.992

. Based on the adsorption constants a and b, with values under different water content conditions, the methane adsorption capacity X1~X10 at a pressure of 1~10 MPa was calculated, respectively. With the correction coefficient of 0% water content as 1, the curve of water content and 1/η_w under different water content conditions was obtained, as shown in Figure 5. From Figure 5, it can be seen that the temperature correction factor η_w and water content w satisfy Equation (4):

$${\eta }_w={\displaystyle \frac{1}{1.04+0.12w}},$$

(4)

In the formula, η_w is the correction coefficient of water content; w is temperature, %.

The isothermal adsorption curves and heat of adsorption of CH₄ after Langmuir’s equation and consideration of water content correction are shown in Figure 6. From Figure 6a, it can be seen that the adsorption of CH₄ decreases with increasing water content when the temperature and pressure are certain. According to the fitted data, the limiting adsorption amount of CH₄ decreased by 15.2%, 28.09%, and 40.46% with the increase in water content relative to the water content of 0%, respectively, and the increase in water content had an inhibitory effect on the adsorption of CH₄.

The magnitude of the heat of adsorption can be used to measure the strength of gas adsorption by the coal body [21]. From Figure 6b, it can be seen that the heat of adsorption of CH₄ by the coal body decreases gradually when the water content increases from 1.1% to 8.31%. The heat of adsorption decreases because the addition of H₂O competes with CH₄ for adsorption and H₂O is more readily adsorbed in the coal.

Figure 7 shows the adsorption sites occupied by water molecules and methane molecules at 303 K under different water content conditions. The linear structure in the figure is a coal model, the red dot is the density distribution of CH₄, and the green ball-and-stick structure is composed of H₂O molecules. From the figure, it can be seen that the density distribution of CH₄ in the crystalline cells is different under different water contents. With more water molecules, there is less CH₄ adsorption, the red dotted distribution decreases, the gas density distribution in some positions decreases, and the gas distribution is close to the position of water molecules. This is because the number of adsorption sites on the surface of the coal body is certain, but there is competitive adsorption behavior between molecules. The gas with strong adsorption capacity can replace the gas with weak adsorption capacity and occupy the adsorption site, while the gas with weak adsorption capacity is desorbed [22,23]. H₂O can better combine with the oxygen-containing functional groups in the coal, which is more conducive to the occupancy of the adsorption sites, and it has a repellent effect on CH₄. Therefore, with the increase in water content, the CH₄ adsorbed by the coal body gradually decreases.

In addition, during the coalification process, the short fat chains of coal molecules will be shed, and a large number of ultra-micro pores will be formed in the later stage. These pores provide a large specific surface area, which is the main space for the adsorption of gas molecules [24]. In order to better explore the effect of H₂O on CH₄ adsorption, H₂O and CH₄ were used as probe molecules to detect the pore structure of the unit cell. The molecular dynamics diameters of H₂O and CH₄ were 0.26 nm and 0.38 nm, respectively. Figure 8 shows the pores detected by probe molecules with different diameters, and the blue part represents the detected pores.

From the figure, it can be clearly seen that the pore distribution detected by the H₂O probe molecules is denser and the free volume of the pore structure is larger. A larger free volume in the coal pore structure means that gas molecules have more freedom in the pore structure. This improves the chances of contact between gas molecules and the coal surface, which promotes the adsorption of gas molecules by the coal [25]. For H₂O with smaller molecular dynamics diameters, it is easier to enter the pore structure of coal. The H₂O that enters the pore structure first will take priority during adsorption and first adsorb on the surface structure of coal, thereby reducing the probability of CH₄ adsorption.

3.3. Effect of Temperature and Water Content Coupling on Methane Adsorption Performance

3.3.1. Orthogonal Test Design

An orthogonal test was designed to simulate the effect of temperature and water content coupling on CH₄ adsorption. The experimental design was carried out as a two-factor, nine-level orthogonal test, and the determined levels of each factor are shown in

Table 3. Experimental factors and levels.

Numbering	Experiment Factor
	Temperature/K	Water Content/%
1	223	1.10
2	243	4.27
3	263	8.31
4	313	-
5	343	-
6	363	-

.

The two experimental factors, temperature and water content, and their corresponding levels were arranged sequentially without considering the interaction of individual factors. Based on the results of polar analysis, the effects on CH₄ adsorption under different factors were plotted and the experimental factors were ranked in order of significance. The orthogonal table is shown in

Table 4. Orthogonal table.

Numbering	Experiment Factor
	Factor 1 (Water Content)	Factor 2 (Temperature)
1	1	1
2	3	2
3	2	3
4	3	4
5	1	5
6	2	6
7	3	6
8	2	5
9	2	1
10	1	2
11	1	4
12	3	3
13	2	4
14	1	3
15	3	5
16	1	6
17	2	2
18	3	1

.

3.3.2. Analysis of Extreme Variance of Test Results

The polar analysis is shown in

Table 5. Range analysis.

Item	Level	Factor 1 (Water Content)	Factor 2 (Temperature)
K	1	8.52	5.57
	2	8.02	5.25
	3	7.10	4.54
	4	-	3.15
	5	-	2.65
	6	-	2.47
k	1	1.42	1.86
	2	1.34	1.75
	3	1.18	1.51
	4	-	1.05
	5	-	0.88
	6	-	0.82
R		0.24	1.03

, where K is the sum of the experimental results corresponding to the influencing factors, k is the mean value of K, and R is the polar deviation of the factors. From the table, it can be seen that the effect of temperature on CH₄ adsorption is more significant, and the best-optimized combination is a water content of 8.31% and a temperature of 363 K.

To consider the effect of combined water and temperature on CH₄ adsorption, Equations (3) and (4) are synthesized to obtain the empirical Equation (5) for the coupled effect of water and temperature:

$$X_O=X_{d}1.27e^{-0.009t}{\displaystyle \frac{1}{\left(1.05+0.12w\right)}}$$

(5)

In the equation, Xo is the adsorption amount of coupling, mmol/g; X_d is the adsorption capacity of dry coal at room temperature, mmol/g; t is the temperature, °C; w is the water content of coal, %.

To verify the accuracy of the empirical equation, the simulated data were fitted with Equation (5) and the Langmuir equation, and the fitting parameters are shown in

Table 6. Coupling effect Langmuir equation fitting parameters.

Temperature (K)	a/(mmol/g)				b/MPa−1
	0.00%(L/J) *	1.10% (L/J)	4.27%(L/J)	8.31% (L/J)	0.00% (L/J)	1.10% (L/J)	4.27% (L/J)	8.31% (L/J)
223.00	5.35/5.33	4.63/4.53	3.99/3.94	3.35/3.33	0.09/0.07	0.10/0.09	0.11/0.12	0.15/0.14
243.00	4.07/4.15	3.95/3.97	3.56/3.62	3.20/3.24	0.11/0.11	0.15/0.14	0.16/0.15	0.13/0.15
263.00	4.03/3.99	3.66/3.72	3.01/3.00	2.60/2.59	0.16/0.15	0.14/0.12	0.18/0.17	0.24/0.23
303.00	3.88/3.86	3.29/3.20	2.79/2.69	2.31/2.30	0.10/0.12	0.23/0.25	0.22/0.22	0.26/0.28
313.00	3.57/3.47	2.98/2.90	2.64/2.66	2.14/2.16	0.11/0.10	0.15/0.17	0.19/0.16	0.17/0.15
343.00	3.46/3.39	2.61/2.60	2.30/2.34	1.55/1.59	0.19/0.18	0.23/0.27	0.22/0.21	0.25/0.25
363.00	2.98/2.99	2.37/2.34	1.69/1.68	1.24/1.25	0.22/0.20	0.38/0.36	0.30/0.29	0.39/0.37

* L is the Langmuir equation fitting, and J is the value obtained by the empirical formula fitting.

. From the table, it can be seen that the difference between the empirical equation and the limit adsorption amount of CH₄ obtained by Langmuir is no more than 2.9%, and the empirical equations with the R² ranging from 0.989 to 0.996 have a good fitting degree, detailed information is shown in

Table 7. R² after fitting the Langmuir equation with coupled effects.

Coupling Effect	R2
223.00 K + 1.10%	0.96847
223.00 K + 4.27%	0.74753
223.00 K + 8.31%	0.97558
243.00 K + 1.10%	0.99894
243.00 K + 4.27%	0.95586
243.00 K + 8.31%	0.997
263.00 K + 1.10%	0.99463
263.00 K + 4.27%	0.99487
263.00 K + 8.31%	0.99952
313.00 K + 1.10%	0.96832
313.00 K + 4.27%	0.98273
313.00 K + 8.31%	0.99609
343.00 K + 1.10%	0.92212
343.00 K + 4.27%	0.99146
343.00 K + 8.31%	0.99261
363.00 K + 1.10%	0.93762
363.00 K + 4.27%	0.97839
363.00 K + 8.31%	0.99352

.

The isothermal adsorption curve of CH₄ under coupling is shown in Figure 9, from which it can be seen that the adsorption amount of CH₄ increases gradually with the increase in pressure under the condition of a specific temperature and water content, indicating that the coupling will not change the overall trend of CH₄ adsorption. When one of the variables of water content and temperature is fixed, the CH₄ adsorption gradually decreases with the increase in the other variable. According to the fitted data, compared with the limiting CH₄ adsorption amount at room temperature without water, the limiting CH₄ adsorption amount of the optimal combination of single conditions decreased by 23.2% and 40.46%, respectively, while it decreased by 67.61% under the coupling effect, which indicates that the coupling of temperature and water content inhibits the adsorption of CH₄ from the coal body more significantly.

3.4. Mechanism of Coupling Effect on CH₄ Adsorption

The effect of different actions on CH₄ adsorption can be obtained through analysis, as follows: coupling action > single temperature action > single water content action. First of all, the structure of the coal model is complex, containing a variety of functional groups. The structure of each functional group is different, with different intermolecular forces. The adsorption capacity of the gas is different, which will form adsorption sites with different adsorption capacities [26]. The interaction force between coal and H₂O is stronger than that between coal and CH₄, and H₂O is easier to combine with oxygen-containing functional groups in coal, thus occupying adsorption sites. When the water content increases, more CH₄ is displaced from the coal, which manifests as a decrease in adsorption. In addition, the molecular dynamics radius of H₂O is smaller than that of CH₄. H₂O enters the coal and can detect a richer specific surface area. Part of the pore surface will be covered by H₂O, resulting in the weakening of the adsorption of CH₄ by coal and preventing CH₄ from binding to the adsorption sites on the coal surface. Adsorption is an exothermic reaction, with increasing temperature inhibiting CH₄ adsorption and decreasing temperature, promoting CH₄ adsorption. When water content and temperature are coupled, the addition of temperature changes the average molecular kinetic energy of CH₄, and CH₄ is more susceptible to van der Waals forces, which increases the extent of CH₄ adsorption effects on coal. The mechanism of the effect of coupling on CH₄ adsorption is shown in Figure 10.

4. Conclusions

(1) The effect of coupled action on methane adsorption is significantly stronger than that of single action. The effect of different actions on CH₄ adsorption: coupling action > single temperature action > single water content action. The optimal combination of the effects on methane adsorption was temperature 363 K and water content 8.31%, and the CH₄ adsorption was reduced by 67.61% under the coupling effect compared with that of CH₄ adsorption without water at room temperature.

(2) Considering the effects of temperature and water content comprehensively, the empirical equations for the effects of the coupling of the two on CH₄ adsorption amount were obtained based on analyzing the correction coefficients of temperature and water content.

(3) Temperature has a negative effect on the adsorption of CH₄. The adsorption of CH₄ is an exothermic reaction. Temperature will change the average kinetic energy of CH₄ molecules, thereby changing the adsorption of CH₄. The absolute adsorption capacity of CH₄ at low temperatures is significantly greater than that at high temperatures.

(4) The increase in water content has an inhibitory effect on the adsorption of CH₄. An increase in H₂O decreases the heat of adsorption. Water molecules can more easily occupy the advantageous adsorption sites due to their small kinetic diameter and structure, which is more favorable for combining with the coal molecule structure and entering the coal molecule. This reduces the adsorption of CH₄ by coal.