Introduction

Technologies for infusing CO2 or CO2–N2 mixtures into coal seams to replace CH4 have gradually matured in recent years, improving CH4 extraction rates and enabling the sequestration of large amounts of CO21,2,3,4. These technologies primarily utilize the different adsorption abilities of CO2, CH4, and N2 on coal to improve the CH4 extraction rate.

Gases in coal are mainly adsorbed physically. N2 and CO2 have a wide range of sources, where N2 accounts for approximately 78% of the atmosphere while CO2 is mainly generated through coal oxidation and combustion5. Scholars around the world have conducted multiple gas adsorption experiments6,7,8 and Monte Carlo simulation studies9,10,11 to investigate the adsorption characteristics of different gases on coal. The impact of temperature on gas adsorption has been investigated using the high-pressure volumetric method, which showed that low temperatures hinder gas adsorption on coal12,13. Li et al.14 proposed the theory of the competitive adsorption of multiple gases using the low-temperature nitrogen adsorption method. Zhu et al.15 experimentally verified that the maximum adsorption capacities of CO2, CH4, and N2 on anthracite exceed those on bituminous coal at different temperatures. Xiao et al.16,17 established the relationship between the coal adsorption capacity and temperature for CO2, CH4, and N2. Cheng et al.18,19 applied the grand canonical ensemble Monte Carlo method to investigate the adsorption properties of CO2/N2 on coal. Similarly, Wu et al.20,21 investigated the microscopic mechanism of the competitive adsorption of coal-fired flue gas on coal. The research revealed the competitive adsorption behavior during the gas adsorption. Qu et al.22 developed a macromolecular model of coal and used the grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) molecular simulations to reveal the microscopic mechanisms of CO2, O2, and CH4 adsorption and diffusion on coal molecules at different temperatures, pressures, and molar fractions. Gao et al.23 analyzed the adsorption capacity of CO2/CH4/N2/H2O on different molecular models of brown coal using molecular simulation. Wang et al.24 used molecular simulation to examine the adsorption behavior of CH4/CO2 on oxidized coal deposits. Yu et al.25 conducted experiments and simulations to examine the competitive adsorption mechanism of CO2 and CH4 on low-rank coal mirror groups. Bai et al.26 performed a molecular simulation to investigate the kinetic mechanism of CO2 and N2 replacement of CH4. The results showed that CO2 and N2 mainly replaced CH4 gas by occupying the adsorption site. Liu et al.27 performed CO2-ECBM tests on rectangular coal specimens and monitored the change patterns of pore pressure, gas flow, and outlet concentration with the amount of CO2 injected; they found that infusing CO2 into the coal body can effectively increase the CH4 recovery. Li et al.28 proposed a dynamic evolution model of coal permeability, which responded to the ECBM mining process and confirmed the technical feasibility of N2-BCEM injection.

Other international scholars have also studied the adsorption properties of gases consisting of single components and multiple components. Using computer molecular simulations, Laurent et al.29 investigated the absorbent behaviors of CO2 and CH4 in micropores. Perera et al.30 investigated the adsorption capacity of two gases at three temperatures. Abunowara et al.31 analyzed the characteristics of four coal sample adsorption gases in Malaysia using BET, XRD, FESEM, and other techniques, and the coal specimens exhibited a greater adsorption affinity for CO2 than for CH4 and N2. Busch et al.32 studied the gas adsorption of binary mixtures at a specific pressure using Langmuir’s method, which provides an essential idea for this current study on the adsorption of ternary gas mixtures.

The studies highlighted above mainly focused on the adsorption characteristics of binary gas systems, confirming the advantage of CO2 adsorption but ignoring the adsorption characteristics of ternary gas systems. In this article, we quantitatively analyzed the adsorption behavior of CO2, CH4, and N2 on coal and the main influencing factors. The injection of different ratios of CO2, CH4, and N2 into coal seams was simulated for the study.

Methodology

Molecular modeling of anthracite

The anthracite molecule (C208H162O12N4)33 (illustrated in Fig. 1) was selected to study the adsorption properties of anthracite for CO2, CH4, and N2. Geometry optimization, energy optimization, and simulated annealing were performed on the structure using the Forcite module in Materials Studio, and the optimized energy parameters are shown in Table 1 to obtain the lowest energy conformation, as shown in Fig. 2. The Amorphous cell module was used to put the two optimized anthracite molecular models into the computational cell (a = 18.607 Å, b = 18.607 Å, c = 18.607 Å), as shown in Fig. 3.

Figure 1
figure 1

Molecular structure of anthracite.

Full size image
Table 1 Energy parameters of optimized coal molecular structure.
Full size table
Figure 2
figure 2

Molecular structural model of anthracite.

Full size image
Figure 3
figure 3

Pore structure model of anthracite.

Full size image

Simulation parameter setting

To simulate the adsorption of CO2, CH4, and N2 on anthracite coal, we used a giant regular ensemble Monte Carlo simulation, selecting the Dreiding force field customized for computational accuracy, Charges selects QEq, the Ewald summation method for electrostatic interactions, and the atom-based method for van der Waals interactions. The temperatures used for the Fixed Pressure Task were 263.15 K, 273.15 K, 283.15 K, 293.15 K, 303.15 K, and 313.15 K, and the pressure ranged from 0.01 to 2 MPa.

Results and discussion

Single-component gas adsorption system

Figure 4 illustrates the adsorption isotherms of N2, CO2, and CH4, as single-component gases under varying pressures and temperatures. As observed from the figure, at temperatures of 263.15 K, 273.15 K, 283.15 K, 293.15 K, 303.15 K, and 313.15 K and at pressures ranging from 0.01 to 2 MPa, the adsorption sites on the surface of the anthracite coal become more active with increasing temperature. Consequently, CO2, CH4, and N2 are more readily detached from the coal surface, reducing the adsorption capacity. Similarly, Fig. 5 illustrates the variation of the CO2, CH4, and N2 adsorption with temperature at a pressure of 0.1 MPa. At 263.15 K, a considerably larger number of adsorbed CO2 molecules are in the anthracite molecular model than the number of CH4 and N2 molecules. With the increase of pressure from 0.01 MPa to 2 MPa in the system, the adsorption amount of CO2, CH4 and N2 showed an upward trend, indicating that the elevated pressure can promote the adsorption of CO2, CH4 and N2 by anthracite. The magnitude of adsorption at the same pressure is in the following order: CO2 > CH4 > N2. This result can be explained as follows: first, the molecules of the three gases have different equivalent diameters, where the molecular diameter of CO2 is 0.33 nm, that of N2 is 0.368 nm, and that of CH4 is 0.382 nm. Because the diameter of CO2 molecule is small, the critical temperature and critical pressure of CO2 are larger, which makes the competitive adsorption advantage of CO2 stronger than that of CH4 and N2 in the ternary gas system of CO2, CH4, and N2, and therefore the anthracite molecules preferentially adsorb CO2, so it leads to the adsorption amount of CO2 is larger than that of CH4 and N2. Owing to the small difference between the molecular diameters of CH4 and N2, both have different polarization volume, where that of CH4 is 4.48 × 10–30 m3 and that of N2 is 1.53 × 10–30 m3. The molecules with a higher polarization volume are adsorbed more easily; thus, the amount of CH4 adsorbed is larger than that of N2. Secondly, the critical temperatures are different, the critical temperatures of CO2, CH4 and N2 are 304 K, 191 K and 126 K. The size of the critical temperatures is CO2 > CH4 > N2. As the critical temperature increases, the gas adsorption on the surface of the coal becomes faster and adsorbs more easily. Third, van der Waals forces also play a role: an increase in the pressure of the system is accompanied by an increase in the van der Waals energy, and the stronger the effect of the van der Waals force, the faster the adsorption. Take a temperature of 263.15 K as an example, the van der Waals energy data released by anthracite adsorption of CO2, CH4, and N2 are shown in Table 2.

Figure 4
figure 4

Isothermal adsorption curves for single-component: (a) CO2, (b) CH4 and (c) N2.

Full size image
Figure 5
figure 5

Variation of single-component gas adsorption with temperature at 0.1 MPa.

Full size image
Table 2 Van der Waals energy released by adsorption of CO2, CH4 and N2 from anthracite coal at pressures of 0.01 MPa and 2 MPa.
Full size table

The isothermal adsorption curves of CO2, CH4, and N2 at different pressure ranges have the form of Langmuir curves. Hence, the Langmuir formula was used to fit the isothermal adsorption curves of CO2, CH4, and N2 for anthracite. The fitting results are presented in Table 3.

Table 3 Fitting parameters of the Langmuir model.
Full size table

The fitting results show that the linear correlation coefficient R2 was greater than 0.94 in all cases, indicating good fitting and confirming the reliability of the simulated data. The adsorption constants k1, k2 decrease with increasing temperature; the adsorption amount also decreases, indicating that low temperatures are favorable for CH4 adsorption.

Figure 4 shows that the adsorption isotherm growth gradient of CO2, CH4, and N2 within the pressure range of 0.01–0.1 MPa is considerably larger than that within the pressure ranges of 0.1–1 MPa and 1–2 MPa. Therefore, CO2 was used as an example to calculate the adsorption isotherm growth gradients of the gases at different temperatures, as shown in Table 4.

Table 4 Growth gradient of CO2 adsorption isotherms at different temperatures.
Full size table

At different temperatures, the growth gradients of CO2 adsorption isotherms were 1.985–2.809 for pressures of 0.01–0.1 MPa, 1.468–1.892 for pressures of 0.1–1.0 MPa, and 0.975–1.035 for pressures of 1.1–2.0 MPa. These results show that the CO2 adsorption isotherm growth gradient is the largest and the adsorption rate is the fastest in the pressure range of 0.01–0.1 MPa. This phenomenon occurs because of the large number of adsorption sites on the anthracite surface. Initially, CO2, CH4, and N2 are easily adsorbed on these sites, resulting in a faster adsorption rate, but the gas concentration increases while the adsorption sites are gradually saturated, causing the adsorption rate to decelerate until it reaches equilibrium. Therefore, the larger the growth gradient of the adsorption isotherm, the faster the adsorption rate. This behavior occurs because the growth gradient represents the rate of gas adsorption; the faster the adsorption rate, the greater the number of adsorption sites on the anthracite surface.

Multi-component gas adsorption system

Adsorption amount

The single-component gas adsorption shows that CO2 has certain adsorption advantages over CH4 and N2. Different proportions of CO2, CH4, and N2 were added to the anthracite pore model. As the adsorption rate of the gases with pressure ranging from 0.01 to 0.1 MPa is the fastest in the single-component gas adsorption system, the adsorption characteristics of the three gases are discussed for a pressure of 0.1 MPa. The simulation results are shown in Fig. 6.

Figure 6
figure 6

Variation of multi-component gas adsorption amount with temperature at 0.1 MPa.

Full size image

A comparison of Fig. 6a–c shows that adding the same ratio of CH4 and different ratios of CO2 and N2 to the anthracite molecule with the temperature of 263.15 K, the relative CO2 adsorption increases from 0.20 to 0.42 mmol/g as the CO2 injection increases from 1 to 3%; The relative adsorption of the same proportion of CH4 decreases with the gradual increase in the CO2 injection. The relative adsorption of CH4 decreases from 0.25 to 0.10 mmol/g while that of N2 in different proportions decreases from 0.15 to 0.08 mmol/g. A comparison of the plots in Fig. 6a,d and e shows that at the temperature of 263.15 K, injecting the same proportion of N2 and different proportions of CO2 and CH4 increases the relative adsorption of CO2 with increasing amount of injected gas from 0.20 to 0.40 mmol/g. The relative adsorption of CH4 decreases from 0.25 to 0.11 mmol/g with decreasing CH4 injection, and the relative adsorption of equal proportions of N2 decreases from 0.15 to 0.09 mmol/g. These results show that the adsorption sensitivity of CO2 is very strong, and the relative CO2 adsorption increases rapidly when the CO2 injection increases from 1 to 3%, which far exceeds the relative adsorption of CH4 and N2. Second, the relative adsorption of CH4 decreases slowly as CO2 injection increases in the system, which is because CO2 has certain adsorption advantages and a stronger adsorption capacity than CH4. Hence, CO2 is preferentially adsorbed, decreasing the relative adsorption of CH4. Third, different proportions of N2 and equal proportions of N2 have less effect on changes in the adsorption amount of the system, indicating that N2 adsorption is more stable. The amount of gas adsorbed is affected not only by temperature and gas injections, but also by the adsorption potential. When a gas is adsorbed on the surface of the coal body, the adsorbent is also attracted to the adsorbate; the closer to the surface, the greater the gravitational force, which is the adsorption potential; thus, the adsorption amount is also related to the adsorption potential.

Adsorption potential

Polanyi34 and Dubinin35 proposed the adsorption potential theory. The theory posits that an adsorption potential field encircles a solid, and gas molecules are adsorbed within this field through the influence of attractive forces. Consequently, the connection between the adsorption potential and adsorption amount was used to analyze the adsorption features of three gases: CO2, CH4, and N2.

According to Polanyi, the relationship between adsorption potential and pressure is as follows:

$$\varepsilon =RT{\text{ln}}\frac{{P}_{0}}{P}.$$
(1)

In this context, ε represents the adsorption potential [J/mol]; R represents the ideal gas constant, taken as 8.3144 J/(mmol·K); T represents the absolute temperature [K]; P0 represents the vapor pressure at saturation of the gas corresponding to temperature T [MPa]; and P represents the pressure [MPa].

According to Dubinin, the formula for calculating P0 is,

$${P}_{0}={P}_{c}{\left(\frac{T}{{T}_{C}}\right)}^{2}.$$
(2)

In this context, Pc represents the critical pressure; the critical pressures of CO2, CH4, and N2 are taken as 7.38 MPa, 4.60 MPa, and 3.40 MPa, respectively. Tc represents the critical temperature, and the critical temperatures of CO2, CH4, and N2 are taken as 304.13 K, 190.56 K, and 126.20 K, respectively.

When we combine the simulation data and substitute Eq. (2) into Eq. (1), the relationship between the adsorption amount and adsorption potential energy of multi-component gases at different temperatures can be calculated, which is illustrated in Fig. 7.

Figure 7
figure 7

Curves of relationship between adsorption amount and adsorption potential energy of multi-component gases at different temperatures. (a) is injected in the ternary gas system with the same proportion of CH4, (b) is injected in the ternary gas system with the same proportion of N2.

Full size image

Figure 7a and b demonstrate that by injecting the same proportion of CH4 and N2 into the system, the CO2 adsorption increases rapidly at the temperature of 263.15 K. This phenomenon occurred because of the increased CO2 concentration in the system resulting from the increase in CO2 injection in the system from 1 to 3%. Because of the adsorption advantage of CO2 itself over CH4 and N2, the relative adsorption of CO2 rises rapidly. When the system temperature increases from 263.15 to 283.15 K, the CO2 adsorption rapidly decreases because CO2 is more temperature-sensitive than CH4 and N2. The adsorption levels off when the temperature increases from 283.15 to 313.15 K. This is because the adsorption decreases with increasing temperature, which is consistent with the conclusion of the single-component gas adsorption. The adsorption potential energy of CO2 increases from 8.78 to 11.35 kJ/mol, that of CH4 from 9.79 to 12.56 kJ/mol, and that of N2 from 10.93 to 13.91 kJ/mol, indicating that the adsorption potential energy of each gas component increases with increasing temperature, and the adsorption potential energy of the gas components follows the order: CO2 < CH4 < N2. As shown in Fig. 7a, CO2 adsorption decreases from 1.01 to 0.24 mmol/g, CH4 adsorption decreases from 0.48 to 0.16 mmol/g, and N2 adsorption drops from 0.31 to 0.13 mmol/g. As shown in Fig. 7b, CO2 adsorption decreases from 0.85 to 0.22 mmol/g, CH4 adsorption decreases from 0.47 to 0.13 mmol/g, N2 adsorption decreases from 0.31 to 0.13 mmol/g, and the adsorption amounts of the gas components are in the order of CO2 > CH4 > N2. Therefore, the adsorption amount has a negative correlation with the adsorption potential energy, i.e. the quantity of gas adsorbed reduces as the adsorption potential energy increases. From a thermodynamic perspective, anthracite adsorbs the most CO2, followed by CH4 and N2. This phenomenon occurs because a rise in temperature increases the thermal movement of the solid surface molecules, weakening the intermolecular interaction forces and, consequently, reducing the surface energy. Thus, the CO2, CH4, and N2 molecules are not easily adsorbed on the surface of the coal molecules, which reduces the adsorption amount.

Potential energy distribution

The potential energy distribution of the anthracite adsorption of CO2, CH4, and N2 was obtained through a simulation, and the relationship between the preferential adsorption potential and the amount of gas injected was analyzed. The results are illustrated in Fig. 8 for the pressure of 0.1 MPa and temperature of 263.15 K. The data on the initial potential energy distribution of the gases are shown in Table 5.

Figure 8
figure 8

Potential energy distribution of multi-component gas. (a) and (b) are the potential energy distributions analyzed in the system of CH4 and N2 in the same proportions, with the initial ratio of CO2, CH4, and N2 all being 1:44:55.

Full size image
Table 5 Potential energy distribution of initial adsorbates injected with equal proportions of CH4 (a) and equal proportions of N2 (b) in a ternary gas system.
Full size table

Adsorption energy is the energy produced during adsorption. Molecules decelerate and eventually stop at the surface of the adsorption medium during adsorption, which releases some energy. Thus, the greater the absolute value of the adsorption energy, the greater the intermolecular interactions and preferential adsorption.

A comparison of (a) and (b) in Fig. 8 shows that for different injection ratios of CO2, CH4, and N2 into the system, the absolute magnitude of the potential energy peak of CO2 increases with the increasing quantity of gas injected the system. In the two gas systems with certain CH4 and N2 ratios, the potential energy peak of the optimal adsorption site of CO2 decreases from − 8.85 kcal/mol to − 9.65 and − 9.15 kcal/mol, respectively. The potential energy peak of the optimal adsorption site of CH4 decreased from − 3.95 kcal/mol to − 5.05 and − 6.95 kcal/mol, respectively. The potential energy peak of the optimal adsorption site of N2 decreased from − 3.65 kcal/mol to − 4.65 and − 3.95 kcal/mol, respectively. A comparison of (a) and (b) shows that the optimal adsorption site for injecting the same proportion of CH4 into the system is higher than that of N2; thus, the preferential adsorption potential of CO2 is greater than that of CH4, and that of CH4 is greater than that of N2. This result is consistent with the order of magnitude of the amount of the three gases adsorbed. The absolute values of the potential energy peaks for both CH4 and N2 showed a rising pattern with the increase in CO2 injection; hence, CO2 can promote the adsorption behavior of CH4 and N2 on anthracite.

Conclusions

  1. (1)

    The adsorption behavior of the single-component gas system is in accordance with Langmuir’s law of adsorption, and the values of adsorption constants k1, k2 are generally negatively correlated with temperature. From the perspective of the adsorption rate, CO2, CH4, and N2 attained the fastest adsorption rate in the single-component gas adsorption system at temperatures of 263.15 K, 273.15 K, 283.15 K, 293.15 K, 303.15 K, and 313.15 K, as well as pressures in the range of 0.01 to 2 MPa. In different pressure ranges, the adsorption rate of CO2 increased with increasing temperature because adsorption is typically exothermic, and when the adsorption process has not reached equilibrium, elevated temperatures accelerate the rate of adsorption. The adsorption amount was positively correlated with pressure and negatively correlated with temperature, and the adsorption amounts were in this order of magnitude: CO2 > CH4 > N2.

  2. (2)

    In the multi-component gas system, at the same pressure, the proportion of the relative adsorption amount of CO2 in the system increased from 1/3 to 2/3 with the increase in CO2 injection from 1 to 3%, whereas the relative adsorption of CH4 and N2 decreased. The relative CO2 adsorption was positively correlated with the amount of gas injected but negatively correlated with temperature. The relative adsorption amounts were in this order of magnitude: CO2 > CH4 > N2.

  3. (3)

    In the multi-component gas system, under identical pressures, the adsorption potential energy of CO2, CH4, and N2 at 263.15 K was 8.78 kJ/mol, 9.79 kJ/mol, and 10.93 kJ/mol, respectively, with the values increasing with increasing temperature. The adsorption potential energy of CO2, CH4, and N2 was positively correlated with temperature and negatively correlated with the adsorption amount. The adsorption potential energy of the three gases was in this order of magnitude: CO2 < CH4 < N2.

  4. (4)

    In the multi-component gas system, at the same temperature and pressure, the potential energy peaks of CO2, CH4, and N2 were − 8.85 kcal/mol, − 3.95 kcal/mol, and − 3.65 kcal/mol, respectively, and the absolute values at the optimal adsorption sites were in this order of magnitude: CO2 > CH4 > N2. The absolute values of the potential energy peaks of the optimal adsorption sites for CH4 and N2 increased as the injection of CO2 into the system increased. Furthermore, the preferential adsorption potentials followed the order of CO2 > CH4 > N2.