Molecular simulation of C₂H₄/CO₂/N₂/O₂ adsorption characteristics in lignite and anthracite

In the global energy system, fossil fuels account for 85% of the total energy supply, and coal is an important part of the consumption of them.¹ A current mining challenge is the spontaneous combustion of coal in goafs. The residual coal exposed during the mining process will oxidize and accumulate heat due to air leakage from the working face, and eventually, spontaneous combustion may occur in the goaf^2–4 and affect productivity. The toxic and harmful gases it produces will endanger the health of workers. Therefore, the early prediction and forecast is desirable to assist coal fire prevention and control.

In China, most mines use CO as an index gas to predict and forecast the spontaneous combustion in the goaf.^5–7 However, with the improvement of mining technology, more vehicles in the intake tunnel exhaust fumes to the mine ventilation, causing the CO concentration to rise and making CO prediction inaccurate.^8–10 Therefore, hydrocarbon gases have advantages and have been adopted by some coal mines to replace CO. During the oxidation of coal, the aliphatic side chains of molecules are broken to form alkanes, alkenes, and alkynes.^11–13 Among them, the detection temperature range of C₂H₄ is narrow, and the initial generation temperature of C₂H₄ only needs to be determined through experiments. When C₂H₄ is produced and monitored by a duct monitoring system, it is determined that there is an area in the goaf that has reached the initial temperature, and then the corresponding treatment measures are employed.^14–16 

However, the residual coal in the goaf will adsorb some gases, including C₂H₄, which will inevitably reduce the accuracy of evaluation. Therefore, it is necessary to evaluate the adsorption and diffusion behavior of C₂H₄ on coal molecules compared to other common gases to determine the adsorption capacity of C₂H₄ at different temperatures and pressures.

Coal is a porous material with a large specific surface area and pore volume, which provides porous cavities for gas adsorption. Gases present within coal are retained through physical adsorption. The adsorption capacity of gases in coal is mainly affected by rank,¹⁷ moisture content,¹⁸ pore structure,^19,20 pressure, temperature,²¹ and functional groups.²² Many scholars have made detailed studies on coal pyrolysis or spontaneous combustion to generate C₂H₄ and coal adsorption of CH₄ and CO₂. Wu and Wu²³ studied the generation rules of various index gases by using the temperature-programmed approach and obtained the prediction standard for the spontaneous combustion of the goaf with CO as the main component and a combination of multiple index gases; the initial generation temperature of each index gas corresponds to the increasing coal temperature within the goaf. Guo et al.²⁴ improved the accuracy by using the ratio of different index gases. In addition, Deng et al.²⁵ analyzed the relationship between the ratio of different index gases and temperature. As for the study of gas adsorption on the coal surface, Guan et al.²⁶ verified that CO₂ reached the adsorption limit capacity faster than CH₄ by a volumetric adsorption apparatus and verified the adaptability of the Langmuir formula to the adsorption isotherm fitting. Mastalerz et al.²⁷ analyzed the adsorption of N₂ and CO₂ on coal samples in different particle sizes and found that the optimal particle size for N₂ and CO₂ adsorption is 60 mesh. Busch et al.²⁸ found that in the numerical modeling of CH₄ and CO₂, for moist coals, adsorption rates of both gases were reduced by a factor of more than 2 with respect to dry coals. Fitzgerald et al.²⁹ studied the adsorption of CH₄, N₂, and CO₂ mixed gas on coal and summarized the relationship between the molar ratio and uncertainty. Vandamme et al.³⁰ provided a comprehensive framework to calculate the macroscopic strains induced by CO₂ adsorption in a porous medium from the molecular level. Tang and Ripepi³¹ researched adsorption of supercritical CO₂ on coal samples and found that the isosteric heat depends on both temperature and adsorption uptake.

Most of the literature studies of gas adsorption on coal focused on CH₄, N₂, H₂O, and CO₂, and the relationship of competitive adsorption was obtained by the experimental and molecular simulation methods.^32–35 In addition, the adsorption characteristics of C₂H₄ on other materials have also been explored.^36–38 As for the adsorption characteristics of C₂H₄ and other hydrocarbon index gases on coal, related studies are scarce.

Here, the adsorption capacity of C₂H₄ on coal molecules is calculated based on molecular mechanics and molecular dynamics, and the adsorption capacity of other common gases in coal mines is compared. The microscopic adsorption is linked with the macroscopic situation to provide theoretical support of adjustment for judging the temperature of the goaf through the coal mine index gas monitoring system. To compare the adsorption characteristics and adsorption capacity of C₂H₄ and other gases of coal, this paper establishes lignite and anthracite supercell models and uses Materials Studio software to achieve it. This research has the potential to impact the monitoring of spontaneous combustion.

In China, lignite and anthracite are representative. Lignite and sulfur-containing anthracite have risk of spontaneous combustion and conditions for producing C₂H₄. Here, by comparing the adsorption characteristics of C₂H₄ and other gases in lignite and anthracite, we discussed the governing factors for using C₂H₄ as an index gas. The basic unit models of lignite (C₂₀₆H₂₀₆N₂O₄₄) and anthracite (C₂₅₈H₁₇₂N₄O₁₂S) were quoted from the literature of Zhu et al.³⁹ and Liu et al.⁴⁰ Their models are reasonable and have a relatively close carbon content, so they were chosen for the simulation. The Amorphous Cell Tools, a module of Materials Studio, were used to generate unit supercells containing four molecules, fixed angle (α: 90°, β: 90°, and γ: 90°). Here, we adopted a regular supercell arrangement, which was helpful to observe the adsorption sites, because the molecular structure of coal has been optimized, and the adsorption sites of gases on the coal molecules will not change significantly. The regular supercell arrangement makes the law of different gases adsorption sites more obvious. The Forcite module of Materials Studio software was used to optimize and anneal the supercells, and the charge equilibration (QEq) was used to calculate the charge distribution. A CO₂ probe with a radius of 1.6 Å was used to determine the difference in the pore structure, and the Connolly free volume and the surface area were obtained.

The adsorption of C₂H₄ and other gases on lignite and anthracite models is simulated at the temperatures of 288.15, 298.15, 308.15, and 318.15 K. The parameters of molar mass, critical temperature, critical pressure, and acentric factor are shown in Table I,⁴¹ and the conversion of pressure and fugacity is realized by the Peng–Robinson formula.^42,43

The “fixed pressure” module in Sorption of Materials Studio was used to simulate the adsorption capacity of gases on the coal molecular supercells. Based on the GCMC (Grand Canonical Monte Carlo) method,^44–46 the adsorption isotherm of each component gas under different temperature conditions was obtained by the Langmuir formula.^47,48 The Langmuir fitting formula is

where a is the limit adsorption capacity when the pressure tends to infinity (mmol/g) and b is the adsorption constant (MPa⁻¹).

This approach determines the adsorption position based on the annealing principle in which the Metropolis algorithm is selected.

The specific setting details in the “fixed pressure” module are shown in Table II.

The unit of adsorption capacity obtained from the simulation results is (average molecules/cell), which should be converted to (mmol/g) by the following equation:⁴¹ 

where M_rcell is the relative molecular mass of the adsorbent in the supercell.

The “locate” module in Sorption of Materials Studio was used to locate the adsorption positions and show them on graphs. The specific setting details in the “locate” module are shown in Table III.

The basic unit models of lignite (C₂₀₆H₂₀₆N₂O₄₄) and anthracite (C₂₅₈H₁₇₂N₄O₁₂S) are shown in Fig. 1.

As shown in Fig. 2, the lignite supercell size was a = 22.47 Å, b = 22.47 Å, and c = 44.93 Å; and the anthracite supercell size was a = 21.88 Å, b = 20.24 Å, and c = 49.19 Å. The Connolly free volume of a supercell with the best structure of lignite is 5755 ų and the surface area is 5023 Ų. The Connolly free volume of a supercell with the best structure of anthracite is 4155 ų and the surface area is 4456 Ų.

The relationship between the fugacity and pressure of each gas is shown in Fig. 3, and the fugacity coefficient is the ratio of fugacity to pressure (the lines in the figures are drawn as guides to the eye). The fugacity of each gas is mainly affected by temperature and pressure. Under the same temperature condition, the fugacity coefficient decreases with the increase in pressure, while under the same pressure condition, the fugacity coefficient increases with the increase in temperature. In the pressure range of 0–10 MPa and the temperature range of 288.15–298.15 K, the fugacity coefficients of O₂ and N₂ change relatively small, basically between 0.9 and 1.0, while the fugacity coefficients of C₂H₄ and CO₂ change greatly, between 0.4 and 1.0. The main reason is that the critical temperatures of C₂H₄ and CO₂ are higher, which are 282.65 and 304.13 K, respectively, and the critical pressures are 5.1 and 7.4 MPa, respectively. Therefore, under the simulated temperature gradient, C₂H₄ enters a supercritical state when the pressure exceeds 5.1 MPa, which makes the fugacity coefficient decline faster. At 288.15 and 298.15 K, when the pressure exceeds 7.4 MPa, CO₂ changes from gaseous to liquid, and the fugacity coefficient declines slower. At 308.15 and 318.15 K, when the pressure exceeds 7.4 MPa, CO₂ enters the supercritical state, and the fugacity coefficient declines faster. The order of the fugacity coefficient of various gases affected by temperature and pressure is CO₂ > C₂H₄ > N₂ > O₂.

The Langmuir fitting curves of C₂H₄, CO₂, N₂, and O₂ on the lignite supercell of 288.15–318.15 K and the pressure of 0–10 MPa are shown in Figs. 4(a)–4(d), while the Langmuir fitting curves on the anthracite supercell are shown in Figs. 4(e)–4(h). By comparing the N₂/CO₂ adsorption capacity with that proposed by lignite model authors, the results are close. Therefore, the optimization of the model is reasonable, further, which means that the adsorption of C₂H₄ under the same simulation parameters is reasonable and credible; for the anthracite model, the scholars only established a coal molecular model without performing related simulations. We performed simulations and compared the adsorption capacity results with that of lignite and found that the simulations were reasonable.^39,40

As shown in Fig. 4, whether on lignite or anthracite, under the same pressure condition, as the temperature increases, the adsorption capacity of the gases decreases. This is because the increase in temperature inhibits the adsorption of gases and promotes desorption. During the adsorption process, the adsorption capacity increases rapidly at low pressure. As the pressure increases, the adsorption capacity increases slowly and the adsorption isotherm gradually tends to be flat. These trends of C₂H₄ and CO₂ are particularly obvious.

In the temperature and pressure range, comparing Figs. 4(a) and 4(e), it can be seen that the adsorption capacity of C₂H₄ in lignite is 0.418–2.121 mmol/g and that in anthracite is 0.779–1.786 mmol/g. Comparing Figs. 4(b) and 4(f), it can be seen that the adsorption capacity of CO₂ in lignite is 0.448–3.212 mmol/g and that in anthracite is 1.011–2.462 mmol/g. Comparing Figs. 4(c) and 4(g), it can be seen that the adsorption capacity of N₂ in lignite is 0.070–2.535 mmol/g and that in anthracite is 0.159–2.211 mmol/g. Comparing Figs. 4(d) and 4(h), it can be seen that the adsorption capacity of O₂ in lignite is 0.080–3.179 mmol/g and that in anthracite is 0.195–2.592 mmol/g. Langmuir fitting parameters of adsorption isotherms at different temperatures on lignite and anthracite are shown in Tables IV and V, respectively. Here, the parameters a and b come from Eq. (1), a is the limit adsorption capacity when the pressure tends to infinity, while b is the adsorption constant, related to adsorption energy. Comparing the adsorption limit capacities (parameter a) of various gases from lignite and anthracite, it can be seen that the adsorption limit capacity of each gas in lignite is greater than that in anthracite. This is because the supercell of lignite has a larger Connolly free volume and surface area than that of anthracite, which gives gas molecules more adsorption sites. The parameter b is related to adsorption energy, the larger the parameter b is, the easier the gas reaches the adsorption limit capacity. Obviously, gases on anthracite are easier to reach the limit adsorption capacity than that on lignite. On the same coal, the order of reaching the adsorption limit capacity from easy to difficult is C₂H₄ > CO₂ > N₂ > O₂.

The adsorbed gas molecules are all non-polar, so the adsorption capacity of each gas depends mainly on the critical temperature and critical pressure themselves. The pressure in the goaf is generally slightly higher than the atmospheric pressure. Therefore, this article focuses on the study of the adsorption laws and characteristics of C₂H₄ and other common gases of mine in the low-pressure stage. Taking the temperature condition of 288.15 K as an example, the adsorption capacity of each gas on lignite and anthracite is analyzed. In the lower pressure stage, it can be seen that the adsorption capacity of lignite (0–3 MPa) and anthracite (0–1.5 MPa) is positively related to the critical temperature. As shown in Table I, the higher the critical temperature, the greater the adsorption capacity. The order of adsorption capacity is CO₂ > C₂H₄ > O₂ > N₂. Among them, the critical temperatures of CO₂ and C₂H₄ are higher, which are closer to the simulated temperature, so they can reach the limit adsorption capacity faster, while the critical temperatures of N₂ and O₂ are lower and will not reach the limit adsorption capacity quickly like CO₂ and C₂H₄. In the fitting results of Langmuir adsorption isotherms of lignite, O₂ and N₂ exceed C₂H₄ at 3 and 5 MPa, respectively, while in the fitting results of Langmuir adsorption isotherms of anthracite, O₂ and N₂ exceed C₂H₄ at 1.5 and 2.5 MPa, respectively, and the adsorption capacity of O₂ gradually exceeds that of CO₂ after 5 MPa. This is because the molecular model of anthracite contains the sulfur-containing functional groups. The O₂ molecule has a relatively strong interaction with the C–S bond and the S–H bond. When O₂ molecules are adsorbed on the surface of coal, there is a large reduction in the vibration frequency of the C–S bond and S–H bond, which can adsorb more O₂ molecules.⁴⁹ Therefore, the coal molecules with sulfur-containing functional groups are easy to adsorb more O₂ molecules, and it is manifested as an increase in the limit adsorption capacity of O₂.

Taking the adsorption of 288.15 K and 0.1 MPa as an example, the adsorption position of gas molecules on the lignite and anthracite was obtained. The regular arrangement of molecules in the supercell makes the comparison of the adsorption sites of different gases more obvious. Through the analysis and comparison of the adsorption sites of various gas molecules on lignite, it can be found from Fig. 5 that CO₂ and C₂H₄ have relatively close concentrated adsorption sites, located in the areas where oxygen-containing functional groups are concentrated, while O₂ and N₂ also have relatively close concentrated adsorption sites, located in the areas with higher local density, and the unique adsorption sites of O₂ and N₂ are not reflected in the adsorption of CO₂ and C₂H₄. Through the analysis and comparison of the adsorption sites of various gas molecules on anthracite, it can be found from Fig. 6 that CO₂ and C₂H₄ have relatively close concentrated adsorption sites, located in the areas where oxygen-containing functional groups are concentrated, while O₂ and N₂ also have relatively close concentrated adsorption sites, located in the areas where sulfur-containing functional groups are concentrated. It can be seen that the adsorption sites of O₂ and N₂ are fundamentally different from those of CO₂ and C₂H₄.

By using the Dreiding force field, there is only physical adsorption in the simulation. Through the observation of the simulation results, it is found that the isosteric heat is always less than 10 kcal/mol, further verifying that the form of adsorption of various gases is only physical adsorption.^39,41

In the low-pressure zone, the adsorption capacity of gas molecules is relatively low, and the adsorption sites of each gas molecules are more obvious. The order of gas molecule size is C₂H₄ > N₂ > O₂ > CO₂, and this is not reflected in the law of adsorption sites. Therefore, this phenomenon has nothing to do with the size of the molecular diameter and the size of the coal supercell voids. In fact, C₂H₄ and CO₂ exhibit the same characteristics and N₂ and O₂ exhibit another. N₂ and O₂ are non-polar diatomic molecules without electric charges on atoms. The physical adsorption mainly depends on the van der Waals forces, while the C₂H₄ and CO₂ have electric charges on atoms, and the physical adsorption is affected by electrostatic interactions and van der Waals forces. Part of the oxygen-containing functional groups of coal molecules have hydrogen bonds, such as –OH, and they are easier to adsorb CO₂ and C₂H₄. Therefore, the adsorption of CO₂ and C₂H₄ is relatively concentrated, which is the most obvious in lignite. It can be seen from Fig. 6 that CO₂ and C₂H₄ are mostly adsorbed near the oxygen-containing functional groups. In addition, the critical temperatures of CO₂ and C₂H₄ are higher, and they can maintain a higher density than N₂ and O₂, so their adsorption efficiency is higher, and more gas molecules can be adsorbed when the pressure is low.

The existence of these two different forms of adsorption sites makes the adsorption of CO₂ and C₂H₄ in coal easier to reach the limit adsorption capacities. Although O₂ and N₂ have lower adsorption efficiency in the low-pressure zone, there are more available adsorption sites for adsorption (such as the adsorption site on the left side of the lignite) in the high-pressure zone, causing their limit adsorption capacities to be larger than that of CO₂ and C₂H₄, that is, the adsorption sites of CO₂ and C₂H₄ are more selective than N₂ and O₂.

1. In the lignite and anthracite molecular models, within the low-pressure zone (lignite: 0–3 MPa and anthracite: 0–1.5 MPa), the order of adsorption capacity of C₂H₄ and other gases is CO₂ > C₂H₄ > O₂ > N₂. As the pressure increases, the adsorption capacity of O₂ and N₂ has exceeded that of C₂H₄ (lignite: 3 and 5 MPa, respectively, and anthracite: 1.5 and 2.5 MPa, respectively).

2. C₂H₄ and CO₂ have similar and concentrated adsorption sites, and it is easier to reach the limit adsorption capacity; O₂ and N₂ have similar adsorption sites, the number of sites is much more than that of C₂H₄ and CO₂, and their limit adsorption capacities are larger than those of C₂H₄ and CO₂. Gases on anthracite are easier to reach the limit adsorption capacity than lignite. On the same coal, the order of reaching the adsorption limit capacity from easy to difficult is C₂H₄ > CO₂ > N₂ > O₂.

3. The simulation results show that under a low-pressure zone, the adsorption capacity of C₂H₄ in lignite and anthracite is very strong. Therefore, in the spontaneous combustion monitoring of goaf, when C₂H₄ is monitored, its concentration is not quite accurate because of adsorption of residual coal, which is different from the detected temperature of C₂H₄ concentration obtained from the experiment. Therefore, further experiments and more on-site data statistics are required for correction.

This study was financially supported by the National Natural Science Foundation of China (Grant Nos. 51574143 and 51974149).

The data that support the findings of this study are available from the corresponding author upon reasonable request.