Molecular Dynamics Simulation of CH₄ Displacement through Different Sequential Injections of CO₂/N₂

Abstract

As a clean energy source, coalbed methane (CBM) produces almost no exhaust gas after combustion, and its extraction and efficient utilization play a key role in supporting sustainable development. Therefore, molecular dynamics simulations were used to research the diffusion of CH₄ in coal after injecting CO₂/N₂ in different sequences and to clarify the efficiency of CBM extraction under different injection sequences, so as to contribute to sustainable development. The results show that the adsorption amounts of CO₂ and N₂ in different injection sequences are obviously different. To narrow the gap between the two injection amounts, the injection pressure of N₂ can be appropriately increased and that of CO₂ can be reduced, or N₂ can be injected preferentially instead of CO₂. When CO₂ is injected first, the interaction energy between CH₄ and coal is stronger and increases slightly with displacement time as a whole. The interaction energy curve of the N₂ injection decreases, and the displacement effect becomes worse and worse. From the diffusion and relative concentration distribution of CH₄, it can be seen that the diffusion of CH₄ molecules outside the grain cell is more obvious when N₂ is injected first. In terms of the number of CH₄ molecules diffusing outside the crystal cell, it is less when CO₂ is injected first than when N₂ is injected first. The average value of the velocity distribution of CH₄ increases slightly when CO₂ is injected first and decreases significantly when N₂ is injected first, but the average value is overall higher for N₂ injection first. From the difference in diffusion coefficients before and after the gas injection, it can be seen that the decrease in permeability due to the expansion of the coal matrix by CO₂ is more obvious than the increase in permeability due to the contraction of the coal matrix by N₂.

1. Introduction

Climate and energy issues have always been international hot spots. In the context of sustainable development and bicarbon, the balance between energy demand growth and climate deterioration is constantly breaking down, and countries around the world are striving to address this issue. As a reliable source of clean, high-quality energy and chemical raw material, coalbed methane is an excellent fuel for industry, chemical industry, power generation and residential life and produces virtually no emissions after combustion, which is an important support for sustainable development around the world. In September 2020, China clearly put forward the goals of “carbon peak” by 2030 and “carbon neutral” by 2060, in which CCUS plays a crucial role [1]. As one of the important means of CCUS, CO₂-ECBM can not only sequester CO₂ in deep coal seams to achieve the purpose of CO₂ emission reduction but can also displace CH₄ in coal seams to increase the production of coalbed methane, which can be utilized as a supplementary energy source in China [2,3,4]. Therefore, the research on CO₂-ECBM is of great strategic significance for China to realize the bicarbon target and energy replenishment.

In the process of coalbed methane extraction, the recovery rate through pressure reduction is low, usually less than 50%. However, gas injection into the reservoir not only maintains the pressure easily but also achieves the purpose of continuous extraction [5]. In this regard, domestic and foreign personnel have conducted pilot tests in the United States, Canada and China. In these experiments, low, medium and high coal reservoirs were involved, and the types of gas injection included CO₂ and N₂, which had different effects on the permeability of coal reservoirs [6,7,8,9,10,11,12,13,14]. Dai et al. explored the capacity characteristics of coalbed methane reservoirs with double-pore structures, which is important for guiding the efficient development of coalbed methane [15].

The feasibility of CO₂-ECBM lies in the fact that CO₂ dominates competitive adsorption with CH₄, displacing CH₄ adsorption sites on the coal surface and allowing CH₄ to desorb and diffuse from the coal surface, thus increasing CBM production. Unlike conventional adsorbents, coal rock has strong inhomogeneity and a complex pore structure, which leads to the complexity of CH₄/CO₂ adsorption by coal rock, and different coal matrixes, especially microporous surface structure, component characteristics, etc., play a strong controlling role on CH₄/CO₂. Therefore, it may be more reasonable to analyze the adsorption of CH₄/CO₂ from a microscopic molecular point of view [16,17,18,19]. Li et al. researched the effect of coal rank and moisture on the competitive adsorption of CH₄ and CO₂ through molecular simulations [20,21,22,23]. Lu et al. found that supercritical CO₂ can change the nature of coal’s pore structures to affect the adsorption of CH₄ [24]. Li et al. discussed the effect of moisture, salinity, and other effects on gas adsorption [25].

In addition, the CH₄ desorption rate and CO₂ adsorption rate in the CO₂-ECBM process are fundamental to the diffusive behavior of gases, and this bidirectional diffusion determines the effectiveness of CO₂-ECBM [26]. Ciembroniewicz and Marecka found through experiments on the adsorption kinetics of CO₂ that even with the same coal rank, the adsorption rates of different coal samples were still very different [27]. Charrière et al. concluded that the smaller molecular diameter of CO₂ and the ability of CO₂ to dissolve in the macromolecular structure of coal resulted in stronger CO₂ adsorption than CH₄ [28]. Busch et al. researched and found that the rate of gas diffusion decreased with an increase in the coal rock particle size and moisture content and increased with an increase in temperature [29,30]. Paul et al. estimated the diffusion coefficients of CH₄ and CO₂ in coal through a combination of theory and experiment and found that the diffusion coefficients were significantly affected by the pore size distribution [31].

However, in practical applications, the effect of CO₂-ECBM is affected by multiple factors, and sometimes the expected effect cannot be achieved. The primary factor causing changes in the dynamic permeability of coal reservoirs during gas-phase displacement is the adsorption expansion of the matrix. Shi et al. researched and found that the adsorption of CO₂ causes coal to expand, which reduces its permeability and affects the effectiveness of its displacement [32,33,34,35]. Coal adsorption and the desorption of CO₂ result in irreversible expansion and contraction [36,37,38] and are susceptible to hydrogen bonding with CO₂, or charge transfer [39], and the structural reorganization of the coal causes it to undergo swelling [40,41]. Compared with CO₂-ECBM, N₂-ECBM has many advantages, such as a small change in porosity after the adsorption of N₂ in coal beds [42], a low swelling strain [42,43,44], small permeability loss [42], a high CH₄ recovery rate [45], and a high CH₄ concentration in the recovered gas [4]. N₂ has almost no chemical reaction with coal and formation fluids, and it only physically adsorbs on the inner surfaces of the coal pores and cracks [46,47]. The shrinkage and deformation of coal seams after the N₂ displacement of CH₄ results in higher permeability [48]. Zhang et al. experimentally verified that the injection of N₂ had a significant effect on the increase in coalbed methane production and that the injection of N₂ could produce more CH₄ after a CO₂ injection reached equilibrium [49,50,51]. YU et al. compared the effects of an injection of CO₂ and N₂ on coal samples containing CH₄, and the results showed that the injection of N₂ increased the permeability of the coal, while the injection of CO₂ significantly reduced the permeability of the coal [52,53,54]. Chen et al. investigated the solubilization effect in the competitive adsorption systems of CH₄/CO₂ and CH₄/N₂ and found that an increase in the CO₂ molar ratio exacerbated the solubilization of the coal matrix, while an increase in the N₂ molar ratio decreased the solubilization of the coal matrix [55].

Therefore, in order to improve the low CH₄ replacement efficiency due to the permeability attenuation caused by the CO₂ injection into the coal seam during CO₂-ECBM, N₂-ECBM is combined with it to fully utilize the effect of N₂ permeability enhancement and improve the recovery of CH₄. At present, most of the scholars in the research about CO₂/N₂ co-driving in coal seams only start with the competitive adsorption situation of the mixed gases, while there are fewer studies on the diffusion situation of CH₄ after the actual injections of CO₂ and N₂, which determines the final recovery rate. In the implementation of CO₂/N₂ co-driving CH₄, the first thing that needs to be determined is the gas injection sequence. Therefore, it is important to research the effect of the CO₂/N₂ injection sequence on CH₄ displacement, and after clarifying the injection sequence, we can continue to research the deformation effect or equilibrium pressure when CO₂ and N₂ are injected into the coal seam. In this paper, by establishing a molecular model of coal containing initial CH₄, injecting CO₂/N₂ gases successively and performing molecular dynamics simulation, we research the diffusion of CH₄ after different sequences of gas injections and evaluate the effect of displacement.

2. Parameters for Simulation of CO₂/N₂ Displacement of CH₄

2.1. Displacement Modeling

Materials Studio 2019 software was used to model the initial coal molecule containing CH₄. The macromolecular structure of Maran 8 coal was chosen for the simulation in order to minimize errors and be more suitable for molecular simulations [56], and the lowest energy configuration of the coal molecule is shown in Figure 1. Malan No. 8 coal has a maximum glassy reflectance of 1.205%, and it is a high-quality fertilizer coal in China and a major coal type for coking coal preparation. The macromolecular structure model of Malan No. 8 coal used in this paper has aromatic functional groups as its main skeleton. From the type of aromatic hydrocarbons, which include polycyclic aromatic hydrocarbons, which are more abundant in coal, the constructed structure is very representative of Malan No. 8 coal, which can be compared with the macromolecular structures of various coal grades to explore the mechanism of coalification.

Firstly, the periodic structure is created with an AC module, and a large number of coal molecules are added, with a cell size of 32 × 32 × 32 Å and a density of 1.3 g/cm³. After that, geometry optimization and annealing are performed to find the most stable coal molecule structure. After the annealing, the configuration with the lowest energy is selected as the final coal molecule configuration for this simulation. In order to simulate the real situation of the coal bed, 1 Mpa CH₄ is adsorbed into the coal molecule as the initial CH₄ of the coal bed, the fixed pressure task of the Sorption module is selected and the force field is COMPASS. After the adsorption of CH₄, the geometry optimization is carried out, and the optimized model is a model of the coal molecule containing the initial gas. The gas injection and displacement simulation requires the injection of 2 MPa of CO₂/N₂ successively, and a molecular dynamics simulation is carried out to observe the desorption and diffusion behavior of CH₄. The simulation flow chart is shown in Figure 2.

2.2. CH₄ Displacement Parameters

There are two schemes for the setting of displacement parameters. The first scheme is to inject 2 MPa CO₂ into the coal molecular model containing the initial gas and then perform the molecular dynamics simulation using the COMPASS force field, the NVT system, a temperature of 298 K, the temperature control method Nose, the pressure control method Berendsen, and a total simulation time of 100 ps. After that, 2 MPa N₂ was injected, and the molecular dynamics simulation was carried out with the same parameter settings as above. The parameters of the CO₂ and N₂ injections are shown in

Table 1. CO₂ and N₂ injection parameters when CO₂ is injected first.

Gas Molecule	Temperature/K	Number of Adsorbed Molecules/(Moleculars/u.c)	Adsorption Heat/(kcal/mol)
CO2	298 K	81	9.49
N2	298 K	8	4.99

.

The second scheme is to inject 2 MPa N₂ into the coal molecular model containing the initial gas, perform the molecular dynamics simulation, and then inject 2 MPa CO₂ and perform the molecular dynamics simulation with the same parameter settings as in the first scheme. The parameters of the CO₂ and N₂ injections are shown in

Table 2. CO₂ and N₂ injection parameters when N₂ is injected first.

Gas Molecule	Temperature/K	Number of Adsorbed Molecules/(Moleculars/u.c)	Adsorption Heat/(kcal/mol)
CO2	298 K	43	9.19
N2	298 K	41	6.09

. The diffusion of CH₄ in the coal can be analyzed at the end of the simulation.

Compared to the physical experiments [57,58], the simulated values of the adsorption heats of CO₂ and N₂ are slightly higher, which may be caused by the presence of ash in the coal or by the limitations of the coal macromolecule characterization for the analysis of ash correlation. It is also possible that the experimental tests include action within macropores, mesopores and micropores, whereas the simulations are calculated only at the micro- and nanoscales.

3. Results and Discussion

3.1. CO₂/N₂ Adsorption and Density Distribution

In terms of the adsorption amount in Figure 3, the number of adsorbed molecules can reach 81 when CO₂ is injected first. When N₂ is injected first, the number of adsorbed molecules is only 41. The fundamental reason for this is the different physicochemical properties of the two molecules. There are more oxygen-containing functional groups in the molecular model of Maran; Li et al. found that the electrophilicity of CO₂/CH₄/N₂ gases was ranked as CO₂ > N₂ > CH₄ and the nucleophilicity was ranked as CO₂ > CH₄ > N₂ through an electrostatic potential analysis, which indicated that CO₂ had stronger attraction with the surface of coal molecules, and the presence of oxygen-containing functional groups was more favorable for the adsorption of CO₂ [59]. Moreover, compared with N₂, the kinetic diameter of CO₂ molecules is smaller, 0.33 nm, so they can enter into smaller pores. In addition, CO₂ molecules have a stronger interaction with coal due to the existence of lone electron pairs, and the probability of adsorption is also larger. When N₂ is injected later, the adsorption amount is only eight. The kinetic diameter of N₂ is 0.364 nm; the larger the kinetic diameter of molecules, the larger the obstacle to diffusion, and at this time, due to the poor flow and diffusion of CO₂ molecules, the molecular diffusion channels are blocked, leading to difficulties in the subsequent N₂ injection. When CO₂ is injected later, the adsorption amount is 43, even more than that from the priority injection of N₂. One reason for this is because the kinetic diameter of CO₂ is smaller, and it can enter the micropores that N₂ cannot, and another is because CO₂ and N₂ produce competitive adsorption, which leads to N₂ desorption. Moreover, due to the high mobility and good diffusion effect of N₂ itself, it can effectively unblock the transportation channel without causing a channel blockage, and it is relatively easy to inject CO₂ molecules in the follow-up. In addition, the adsorption heats of CO₂ and N₂ were consistent with the law presented by the adsorption amount: the larger the adsorption amount, the stronger the force between the gas molecules, and the larger the adsorption heat. It is worth noting that when N₂ was injected first, the difference between the adsorption amounts of CO₂ and N₂ was very small, but the difference in the adsorption heat was obvious, which indicated that the interaction between the CO₂ molecules and the coal was more obvious, and the adsorption heat generated by the interaction between the gas molecules and the coal was larger than that generated by the interaction between the gas molecules themselves.

From the density distribution in Figure 4, the CO₂ adsorption showed a cluster shape, and N₂ showed a band shape. When N₂ is injected first, the density distributions of CO₂ and N₂ are close to each other, while when CO₂ is injected first, the density distributions of CO₂ and N₂ are obviously different. Based on the adsorption alone, it is impossible to directly judge the effect of an increase in CBM production, so an analysis of CH₄ diffusion is carried out next. However, it is clear that if the gap between the two injections is to be narrowed, it is appropriate to increase the injection pressure of N₂ and decrease the injection pressure of CO₂, or to prioritize the injection of N₂ instead of CO₂.

3.2. Interaction Energy

Analyzing the interaction energy between gas molecules and coal is more conducive to revealing its microscopic mechanism of action and determining the adsorption of CH₄ on the coal surface after a CO₂/N₂ injection from an energy point of view. The interaction energy is obtained from the following equation:

$$\begin{array}{c}{E}_{\mathit{interaction}}{=E}_{{\mathit{CH}}_4-\mathit{Coal}}-\left(E_{{\mathit{CH}}_4}{+E}_{\mathit{Coal}}\right)\end{array}$$

(1)

where E_interaction is the interaction energy between CH₄ and coal, E_CH4-Coal is the total energy of the CH₄-Coal system and E_CH4 and E_Coal are the single-point energies of CH₄ and coal (all units are eV/Ų).

Figure 5 shows the interaction energy curves of CH₄ with coal molecules during the displacement of CH₄ by different sequential injections of CO₂/N₂.

As shown in the figure, the interaction energy of CH₄ and the coal molecules exhibits a negative value, and the smaller its value, the stronger the interaction. There is a significant difference in the amount of CO₂ and N₂ injected between different injection sequences. When CO₂ is injected first, the number of molecules entering the cell can reach 81, while when CO₂ is injected later, the number of molecules is only 43. Similarly, there is a big difference in the injection amount of N₂. CO₂ displaces CH₄ mainly because the adsorption capacity of CO₂ on the coal surface is stronger than that of CH₄, which displaces the adsorption sites of CH₄ through competitive adsorption, but due to the swelling of the adsorbed CO₂ coal matrix, the permeability decreases, and the diffusion effect of CH₄ deteriorates. N₂ displaces CH₄ mainly because N₂ has almost no chemical interaction with coal, strong mobility and a fast diffusion speed, which can play a role in scouring CH₄ and taking CH₄ along with it. Therefore, from the perspective of the interaction energy, after injecting CO₂ first, there is a charge transfer between the CO₂ molecules and the coal molecules, and due to the high number of oxygen-containing functional groups in this model, the oxygen atoms show strong electronegativity near other oxygen atoms, which produces a larger amount of energy by interacting with CO₂ [22]. In addition, the coal body itself is rich in terms of its pore structure, and the interaction force between the adsorbed gas molecules exists and is gradually enhanced with an increase in the adsorption amount or coal surface coverage. The adsorbed gas molecules will form a strong potential energy field with the pores of the coal, and the pore surface is not only covered by a molecular layer but also filled with micropores, resulting in increased energy [58]. However, the swelling effect makes the transportation channel narrow, and then after injecting N₂, the injection of N₂ is very small, and the scouring effect is very weak. After injecting N₂ first, the high mobility of a large amount of N₂ preferentially takes away the free CH₄ and shrinks the coal matrix, and due to the pressure difference, CH₄ is desorbed from the coal surface and diffuses rapidly; therefore, when the pressures of the successive injections of CO₂ and N₂ are the same, the first injection of N₂ has a better effect on the displacement. The different injection sequences of the displacement mechanism are shown in Figure 6.

In addition, it can be seen from the fitted curves that the overall CH₄–coal interaction energy curves when CO₂ is injected first slightly increase with the change in the displacement time, indicating that the interaction between CH₄ and coal is becoming weaker and weaker, and the displacement effect is becoming better and better with the diffusion of CH₄ outward from the coal molecules. And the overall CH₄–coal interaction energy curve for the N₂ injection first keeps decreasing. This indicates that the effect of CH₄ expulsion is becoming worse and worse as time advances.

3.3. CH₄ Diffusion Distribution

Figure 7 shows the diffusion distribution of CH₄ with the change in exfoliation time after successive injections of CO₂ and N₂ and counts the number of CH₄ molecules diffused outside the crystal cell.

The figure can visually compare the advantages and disadvantages of CH₄ diffusion in two different gas injection sequences. Obviously, the displacement effect of injecting N₂ first and CO₂ later is better, and the diffusion of CH₄ molecules outside the cell is more obvious. From

Table 3. Number of CH₄ molecules diffusing out of the crystal cell.

Gas Injection Sequence	Number of CH4 Molecules Diffusing out of the Crystal Cell with Time/(Moleculars/u.c)
	10 ps	50 ps	100 ps	150 ps	200 ps
CO2 injection first	13	22	35	39	40
N2 injection first	12	35	41	45	48

, it can also be seen that, with the change in time, the injection of N₂ first, followed by the injection of CO₂, increases the number of CH₄ molecules diffused to the outside of the grain cell, and the diffusion speed is faster, especially in the first 100 ps. The main reason for this difference is the deformation of the coal matrix induced by the CO₂/N₂, and in order to reveal the change rule of the coal strain in the process of N₂/CO₂-ECBM, Wang et al. carried out a physical simulation experiment [60]. When N₂ is injected first, the pressure and concentration differences displace the adsorbed CH₄, and the high mobility flushes the free CH₄, but the smaller the micropores are, the smaller the pressure and concentration differences are. After injecting CO₂ again, the CH₄ in the remaining micropores is displaced and diffuses together with N₂. When CO₂ is injected first, it displaces the adsorption sites of CH₄, leading to CH₄ being in a free state, but the adsorption of CO₂ causes the coal matrix to swell, resulting in partial closure of the micropores, lower permeability, and slower diffusion. After the injection of N₂ molecules, the effect of the pressure difference and concentration difference cannot displace the CH₄ in the closed micropores, but only flush the CH₄ in the free state. Therefore, the displacements of the N₂ scheme are more effective.

3.4. Relative Concentration Distribution

Figure 8 shows the relative concentration distribution of CH₄ in coal after the injection of CO₂/N₂ in different sequences. The concentration profile is expressed as the ratio of the density of target particle A in a certain thickness interval normal to the surface to its total density in the system.

$$\begin{array}{c}{\rho }_r=\frac{{\rho }_i}{{\rho }_{\mathit{total}}}, i=\left(1 ,2, 3, \dots , n\right)\end{array}$$

(2)

where ${\rho }_r$ is the relative density of particle A at distance r, ${\rho }_i$ is the density of particle A in the thickness interval at distance r from the surface, $i$ is the number of partitions in the thickness interval and ${\rho }_{\mathit{total}}$ is the total density of particle A in the system.

As can be seen in the figure, when there is no gas injection, the concentration distribution of CH₄ is very concentrated, with obvious wave peaks, and the distribution of CH₄ can be roughly divided into three regions, with the coal molecules in the center region being more compact, and the volume of microporous area being smaller compared to the edge region. The pressure and concentration differences of N₂ are weaker in the smaller pores, while CO₂ can displace CH₄ in the micropores through competitive adsorption. Therefore, the displacement of CO₂ is stronger than that of N₂ at the center region, which indicates that the concentration distribution of CH₄ is smaller than that of N₂ when CO₂ is injected first. In addition, for the edge region, with a relatively poor texture density and larger microporous volume, the displacement effect of N₂ is more obvious, which is manifested by the larger concentration distribution of CH₄ when CO₂ is injected first than that of N₂. Compared with the initial CH₄ concentration distribution, the concentration degree of CH₄ is significantly reduced and more widely distributed after the CO₂/N₂ injection, which proves that the gas injection facilitates the diffusion of CH₄ and improves the displacement efficiency of CH₄.

3.5. CH₄ Velocity Distribution

Figure 9 shows the velocity distribution curve of CH₄ in the coal molecules along a certain direction after successive injections of CO₂ and N₂. As shown in Figure 9a, after injecting CO₂ first, the velocity distribution of the CH₄ molecules fluctuates uniformly above and below 0, which means that the CH₄ molecules diffuse in all directions, and the average value of the velocity distribution is 0.081 Å/ps. After the injection of N₂, the fluctuation amplitude increases slightly, and the average value of the velocity distribution is 0.095 Å/ps, which is slightly increased compared with the previous one, which effectively improves the diffusion efficiency of CH₄, but the improvement is limited. This is mainly because the amount of post-injected N₂ is very small under the same injection pressure, and the scouring effect is limited. As shown in Figure 9b, after the first injection of N₂, a large number of N₂ molecules diffuse together with CH₄, and the average value of the velocity distribution is 0.163 Å/ps, which is obviously larger than that of the first injection of CO₂. After the injection of CO₂, the average value of the velocity distribution was 0.102 Å/ps, which was significantly reduced because the injection of CO₂ caused a swelling of the coal matrix, which reduced the diffusion velocity of N₂ and weakened the scouring effect on CH₄.

3.6. Mean Square Displacement Curves and Diffusion Coefficients

The mean square displacement (MSD) is used to describe the degree of deviation of the spatial position of the target particle in the system at a certain moment relative to the initial position. Its expression is given by:

$$\begin{array}{c}\mathrm{MSD}=\underset{\mathrm{t}\to \infty }{\lim }\left\{\frac{1}{{\mathrm{N}}_{\mathrm{t}}}{\displaystyle {\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{N}}}{\left[{\mathrm{r}}_{\mathrm{i}}\left(\mathrm{t}\right)-{\mathrm{r}}_{\mathrm{i}}\left(0\right)\right]}^2\right\}\#\end{array}$$

(3)

where MSD denotes the mean square displacement, Å; r_i(t) and r_i(0) denote the position vectors of the ith particle at moment t and the initial moment and are dimensionless; t denotes the simulation time, in ps; N denotes the number of molecules of the adsorbent, and N_t denotes the number of statistically averaged molecular dynamics steps; and t₀ denotes the initial moment.

The diffusion coefficients were obtained using the MSD curves and Einstein’s method, which was calculated using the Einstein’s method equation [42]:

$$\begin{array}{c}\mathrm{D}=\frac{1}{6\mathrm{N}}\lim \frac{\mathrm{d}}{\mathrm{dt}}{\left\{{\displaystyle {\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{N}}}\left[{\mathrm{r}}_{\mathrm{i}}\left(\mathrm{t}\right)-{\mathrm{r}}_{\mathrm{i}}\left(0\right)\right]\right\}}^2\end{array}$$

(4)

where D denotes the diffusion coefficient, in nm²/ps.

By linearly regressing the MSD curve to obtain the slope (k), the equation for calculating the diffusion coefficient (D) can be simplified to Equation (5).

$$\begin{array}{c}D=\frac{\mathrm{k}}{6}\end{array}$$

(5)

Figure 10 shows the MSD curves and the linear fitting of CH₄ after successive injections of CO₂ and N₂.

As can be seen from Figure 10, after injecting CO₂ first, the MSD curve of CH₄ is at the bottom; that is, the diffusivity of CH₄ is the worst, and the final transportation distance of CH₄ is the shortest. After injecting N₂, the curve shifts up slightly, which makes the final transportation distance of CH₄ longer and the diffusion effect better, but it is still lower than that of the MSD curve when injecting N₂ first. This is due to the high mobility of a large amount of N₂, which can carry CH₄ to be transported over a longer distance. In addition, after the injection of N₂ followed by CO₂, the curve shifted downward significantly, the diffusion ability of CH₄ was obviously weakened, the transportation distance became shorter, and the CO₂ significantly hindered the diffusion efficiency of CH₄. On the whole, under the same injection pressure, the displacement effect of injecting N₂ first is better.

The diffusion coefficients of CH₄ after the sequential injections of CO₂ and N₂ are shown in Figure 11. The difference in the diffusion coefficient of CH₄ when N₂ was injected first could reach 27.9%, while the difference in the diffusion coefficient of CH₄ when CO₂ was injected first was only 1.2%. It can be seen that the enhancement of CH₄ diffusion ability is limited when N₂ is injected afterward, while the diffusion ability of CH₄ is greatly affected when CO₂ is injected afterward, which indicates that the decrease in permeability due to the expansion of the coal matrix by CO₂ is more obvious than the increase in permeability due to the contraction of the coal matrix by N₂. It can be seen that although carrying out the CO₂ injection first can effectively replace CH₄, the slower diffusion efficiency affects the recovery efficiency, and the enhancement effect of the N₂ injection is very limited. On the other hand, injecting N₂ first can effectively improve the CH₄ recovery efficiency; even though the diffusion efficiency will decrease after injecting CO₂, it is still better than injecting CO₂ first, and because of the influence of CO₂ on the diffusion rate, it is more necessary to give priority to the role of N₂, so injecting N₂ first and then injecting CO₂ is a more preferable solution.

4. Conclusions

(1) Due to the different physicochemical properties of CO₂ and N₂ molecules, the adsorption amounts of CO₂ and N₂ are obviously different under the same injection pressure and different injection sequences. To narrow the gap in injection amount, the injection pressure of N₂ can be appropriately increased, the injection pressure of CO₂ can be reduced, or N₂ can be injected in preference to CO₂.

(2) Due to the microporous filling effect and the presence of a large number of oxygen-containing functional groups, there is a stronger interaction energy between CH₄ and coal when CO₂ is injected first, and the overall interaction energy curve increases slightly with the change in the displacement time. The interaction energy curve when N₂ was injected first decreases, and the displacement effect becomes worse and worse.

(3) The diffusion of CH₄ molecules outside the grain cell is more obvious when N₂ is injected first. In terms of the number of CH₄ molecules diffusing outside the crystal cell, this is less for the injection of CO₂ first than the injection of N₂ first.

(4) Compared with the initial CH₄ concentration distribution, the concentration of CH₄ was significantly reduced and more widely distributed after the CO₂/N₂ injection, which proved that the gas injection promoted the diffusion of CH₄ and could improve the displacement efficiency of CH₄.

(5) The mean value of the velocity distribution of CH₄ increases slightly when CO₂ is injected first. When N₂ is injected first, the average value of the velocity distribution of CH₄ decreases significantly, but it is higher than that of CO₂.

(6) The difference between the diffusion coefficients before and after the injection of N₂ shows that the decrease in permeability due to the expansion of the coal matrix by CO₂ is more obvious than the increase in permeability due to the contraction of the coal matrix by N₂.