Retracted Article: Research on CO₂/CH₄/N₂ competitive adsorption characteristics of anthracite coal from Shanxi Sihe coal mine

Abstract

This study aims to solve the problem of unsatisfactory development and utilization of coalbed methane and CO₂ storage efficiency. It is focused on the adsorption behavior of CO₂, CH₄, and N₂ in the macromolecular structure model of Shanxi Sihe coal mine anthracite, as well as the competitive adsorption behavior of CO₂/CH₄ and CH₄/N₂ binary gas mixtures with different ratios. Experimental analysis such as elemental analysis, solid ¹³C nuclear magnetic resonance (¹³C NMR), Fourier transform infrared (FT-IR) spectroscopy, X-ray photoelectron spectroscopy (XPS) and X-ray diffraction (XRD) analysis were used to construct the Shanxi Sihe coal mine model of the macromolecular structure of anthracite coal. The Grand Canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulation methods were used to study the adsorption capacity and heat characteristics of CO₂, CH₄, and N₂ at different temperatures using a molecular model of anthracite coal from Shanxi Sihe coal mine, as well as the competitive adsorption characteristics of CO₂/CH₄ and CH₄/N₂ binary mixtures. The mechanism of the influence of temperature and gas properties on the adsorption capacity and heat of adsorption was revealed from a microscopic perspective. The results indicated that the aromatic carbon content of anthracite in the Sihe coal mine, Shanxi is 81.19%, and the ratio X_bp of aromatic bridgehead carbon to surrounding carbon is 0.489. The aromatic structure is mainly composed of pyrene and anthracene. The molecular formula of the macromolecular structure model of anthracite in Shanxi Sihe coal mine is C₂₃₃H₁₅₇O₁₃N₂. The adsorption capacity and equivalent adsorption heat of the macromolecular model for adsorbing single-component gas CO₂/CH₄/N₂ decrease with the increase in temperature. The temperature has the greatest impact on CO₂ adsorption capacity and adsorption heat, followed by CH₄ and N₂. Under the competitive adsorption conditions of CO₂/CH₄ and CH₄/N₂ binary mixtures, the higher the partial pressure of a single-component gas in the mixture, the greater the adsorption capacity of the gas. The difference in the adsorption heat of CH₄ and N₂ is smaller than that of CH₄ and CO₂. The conclusions obtained from the study can provide technical and theoretical support for formulating reasonable drainage methods for coalbed methane wells.

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1 Introduction

Anthracite coal seams have excellent ability for coalbed methane adsorption. Understanding the adsorption mechanism and revealing the adsorption laws of anthracite coalbed methane is conducive to formulating a reasonable system for the discharge and extraction of anthracite coalbed methane wells, thereby achieving the goal of maximizing the production capacity of anthracite coalbed methane wells, reducing gas disasters, promoting resource utilization, and improving economic benefits.^1–5 Therefore, establishing a reasonable macromolecular structure model of anthracite and conducting gas adsorption molecular simulation research on anthracite provide critical theoretical guidance significant for the efficient utilization of underground coalbed methane in different environments. Shen et al.⁶ studied the adsorption and diffusion behaviors of deep coal samples and conducted high-pressure adsorption experiments on CH₄ in coalbed methane using the volumetric method. The study found that the adsorption rate of CH₄ showed a complex nonlinear functional relationship with the change in coal rank, while the adsorption amount of CH₄ showed a linear relationship with coal rank. Meng et al.⁷ established a macromolecular structure model of lignite based on the experimental results of Fourier transform infrared (FT-IR) spectroscopy and X-ray photoelectron spectroscopy (XPS), and studied the low-temperature oxidation reaction of lignite. The results indicated that in addition to active aliphatic chains, the low-temperature oxidation reactants of lignite also include α carbon atoms, hydroxyl groups, and aromatic ring ethers, and the main active structures are carbonyl and carboxyl groups. The accuracy of the model was verified by analyzing the content of each functional group in lignite through infrared spectroscopy. Krooss et al.⁸ conducted high-pressure adsorption experiments of CH₄ and CO₂ gases in dry and water-containing coal samples, and explored the effects of coal rank and moisture content on gas adsorption. The results indicated that coal rank and moisture had less effects on CH₄ adsorption. The adsorption amount of CO₂ and CH₄ has obvious inhibitory effects. Zhang et al.⁹ used a self-constructed coal macromolecular model to study the competitive adsorption behavior of CH₄ and CO₂. The results indicated that the adsorption selectivity of CH₄/CO₂ depends on the CO₂ concentration. Kurniawan et al.¹⁰ conducted isothermal adsorption experiments on CO₂/CH₄ mixtures of different components in 1.5 nm graphite slit holes, and the results indicated that the adsorption capacity of CO₂ significantly increased with the increase in CO₂ concentration.

Researchers have carried out a large number of theoretical, experimental and simulation studies on the gas adsorption and molecular model construction of coal at the macro and micro levels.^11–15 However, there is relatively little research on the construction of coal macromolecular models for anthracite and the micro mechanisms of adsorption and competitive adsorption at the molecular level. According to relevant studies, the estimated reserves of smokeless coal in China are 4.74 × 10⁸ t,¹⁶ accounting for one tenth of the total coal reserves in China, have the characteristics of low volatile matter and high degree of metamorphism. Coal mines with high content of anthracite are more suitable for the research of carbon sequestration technology. Therefore, Shanxi Sihe anthracite coal was chosen as the research object. In this study, through microscopic characterization experiments such as FT-IR spectroscopy, XPS, XRD and ¹³C NMR, parameters such as functional group distribution, aromatic structure, aliphatic structure, and element occurrence state of anthracite coal from the Sihe coal mine in Shanxi province were obtained. A macromolecular structure model of Shanxi Sihe coal mine anthracite coal was constructed, and its macromolecular structure model was used as the starting point. Based on the molecular dynamics (MD) and Grand Canonical Monte Carlo (GCMC) simulation methods, the characteristic laws of adsorption behavior and mixed gas competitive adsorption behavior of the macromolecular structure model of anthracite coal from Shanxi Sihe coal mine were explored. The research results contribute to a deeper understanding of the CH₄, CO₂, and N₂ adsorption characteristics of anthracite coal, aiming to reveal the mechanism of the influence of adsorption pressure, temperature, and other factors on the gas molecule adsorption behavior at the molecular level. The conclusions obtained from this study can provide vital theoretical support and technical optimization guidance for the efficient extraction and CO₂ storage of coal seam CH₄.

2 Materials and methods

2.1 Coal sample preparation

The experiment selected anthracite coal from the Sihe coal mine in Shanxi, China as the research object. Coal sample preparation was carried out in strict compliance with the instructions of the “Preparation method of coal samples” (GB474-2008). The pulverized coal sample in the air-drying state was used as the raw material, which was repeatedly crushed and screened using a crusher and vibrating screen machine. The coal sample was separated by passing through a 200 mesh sieve and sealed for storage. The Elementar Unicube elemental analyzer was used to determine the C, H, O, N, and S contents in coal samples. The elemental analysis results are shown in Table 1.

Table 1 Elemental analysis of anthracite

Coal sample	Element distribution, wdaf/%
	C	H	O	N	S
Anthracite coal	91.11	0.64	6.99	0.76	0.50

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2.2 Solid-state nuclear magnetic resonance (¹³C NMR) spectroscopy analysis

The Bruker Avance NEO 400WB high-resolution solid-state nuclear magnetic resonance spectrometer was used for ¹³C NMR spectrum measurement. The rotor was made of zirconia, with a working speed of 10 kHz and a pulse width of 4 μs. The cycle delay time was 0.5 s.

2.3 Fourier transform infrared (FT-IR) spectroscopy analysis

The FT-IR spectra of pulverized coal samples were recorded using a Fourier transform infrared spectrometer model, Thermo Scientific Nicolet iS20. In a dry environment, 200 mesh pulverized coal samples and potassium bromide powder were taken and added to the mortar at a mass ratio of 1/200. They are thoroughly ground multiple times and then placed on a tablet press to make transparent sheets with a thickness of 0.2–0.5 mm. The test wavenumber range was 400–4000 cm⁻¹, with 32 scans, a moving mirror speed of 0.475, and a resolution of 4 cm⁻¹.

2.4 X-ray photoelectron spectroscopy (XPS)

A Thermo Fisher ESCALAB 250Xi X-ray photoelectron spectrometer was used for testing, and the total acquisition time was 2 minutes and 16 seconds. The excitation source used Al Kα rays, and the spot size was 500 μm. The pass energy was set to 100.0 eV, energy step size was 1.0 eV, and the number of energy steps was 1361.

2.5 X-ray diffraction (XRD) analysis

A Rigaku Ultima IV X-ray diffractometer was selected, with a voltage of 40 kV, a current of 40 mA, a test range of 5–90°, a wavelength of 1.5418, and a scanning speed of 2° min⁻¹, and the light source was Cu-Kα rays.

2.6 Construction and optimization of macromolecular models

Based on the analytical data of the aromatic structure, aliphatic carbon structure and heteroatom structure of the anthracite coal from Shanxi Sihe coal mine, its molecular formula was deduced. The KingDraw software was used to build the Shanxi Sihe coal mine anthracite macromolecular model, which was then imported into the MestReNova software. By adjusting the positions and connection methods of different functional groups in the macromolecular structure model of anthracite from Shanxi Sihe coal mine, the ¹³C NMR spectrum of the constructed model was compared with the experimental ¹³C NMR test spectrum to verify its accuracy.

3 Results and discussion

3.1 ¹³C NMR analysis

The experimental results of −50–200 ppm chemical shift ¹³C NMR characterization of anthracite from Shanxi Sihe coal mine were processed by peak splitting (see Fig. 1). The ¹³C NMR peak positions and chemical shift assignments refer to the research results reported in the literature.^17–19 As can be seen from Fig. 1, the ¹³C NMR peak fitting curve of anthracite is divided into 11 peaks, corresponding to the type and content of carbon functional groups. The peak surface of the pulverized coal sample is mainly composed of two peak groups: aliphatic carbon (f_al) and aromatic carbon .

Fig. 1 ¹³C NMR peak splitting fitted spectra of anthracite.

The chemical shift attribution properties of different types of carbon in ¹³C NMR are shown in Tables 2 and 3.

Table 2 Chemical shifts assigned for different structural carbons in ¹³C NMR spectra

Carbon classification	Chemical shift (ppm)	Functional group category	Symbol
Aliphatic carbon	12–16	Aliphatic methyl carbon
	19–22	Aromatic methyl carbon
	26–37	Secondary carbon	f^Hal
	37–50	Methylene carbon	f^Hal
	50–90	Oxygenated aliphatic carbon	f^Oal
Aromatic carbon	100–129	Protonated aromatic carbon	f^Ha
	129–137	Bridging aromatic carbon	f^Ba
	137–148	Alkylated aromatic carbon	f^Sa
	148–165	Oxygen aromatic carbon	f^Oa
Carbonyl carbon	165–190	Carboxyl	f^Ca
	190–220	Carbonyl	f^Ca

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Table 3 Structural parameters of ¹³C NMR of anthracite

Coal sample		f^Hal	f^Oal	f^Ha	f^Ba	f^Sa	f^Pa	f^Na	f^Ca	fal	fa
Anthracite	5.63	3.49	6.33	47.18	26.70	4.089	3.23	34.02	3.34	15.45	84.54	81.19

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The aromatic size and type can be calculated from the ratio of bridge carbon to pericyclic carbon (X_bp) in the anthracite macromolecular structure, and the degree of condensation of the aromatic structure can be characterized. The calculation formula is shown in eqn (1).²⁰ Through calculation, it can be concluded that the structural parameters of the anthracite coal from Shanxi Sihe coal mine are non-protonated aromatic carbon (f^N_a) accounting for 34.02%, carboxyl carbon and carbonyl carbon (f^C_a) accounting for 3.34%, protonated aromatic carbon (f^H_a) accounting for 47.18%, bridged aromatic carbon (f^B_a) accounting for 26.70%, side-branched aromatic carbon (f^S_a) accounting for 4.089%, oxygen-substituted aromatic carbon (f^P_a) accounting for 3.23%, aliphatic carbon (f_al) accounting for 15.45%, and total aromatic carbon (f_a) accounting for 84.54%. The aromatic carbon ratio is 81.19%, and the condensation degree of the aromatic structure is 0.489.

The above-mentioned parameters can provide vital basis for constructing a macromolecular structure model of anthracite from Shanxi Sihe coal mine.

3.2 FT-IR analysis

The peak fitting was performed on the spectrum in the 400–4000 cm⁻¹ band area of anthracite coal from Shanxi Sihe coal mine.²¹ The fitting results are shown in Fig. 2 and 3. On the basis of peak splitting fitting, the peak splitting parameters of the four-band absorption peaks of anthracite coal from Shanxi Sihe coal mine were calculated and analyzed.

Fig. 2 FT-IR spectrogram of anthracite.

Fig. 3 FT-IR fitting spectrogram of anthracite.

The fitting results indicated that the benzene ring in the macromolecular structure of anthracite from Shanxi Sihe coal mine is mainly substituted with benzene ring disubstituted (relative area: 42.33%) and benzene ring pentasubstituted (relative area: 35.63%), with benzene ring tetrasubstituted as auxiliary (relative area: 16.33%). The relative area ratio of the absorption peaks caused by C–O vibrations of phenols, alcohols, ethers, and esters in the 1000–1800 cm⁻¹ band is 62.26%. The absorption peaks at 1393.20 cm⁻¹ and 1552.14 cm⁻¹ represent CH₃-, CH₂-deformation vibration and aromatic hydrocarbon C=C skeleton vibration respectively, with relative area ratios of 21.42% and 10.65% respectively. The interval with a wave number of 2800–3000 cm⁻¹ belongs to the absorption range of –CH_x in aliphatic chains and aliphatic rings. It is dominated by the asymmetric CH₃ stretching vibration (relative area: 38.68%), supplemented by the CH stretching vibration (relative area: 33.17%). It is demonstrated that the aliphatic chain in the molecular structure of anthracite is dominated by short-chain structures. The total hydroxyl groups are mainly provided by OH–OH hydrogen bonds (relative area 63.18%) and OH–π hydrogen bonds (27.11%), followed by cyclic hydrogen bonds (7.11%); OH–N hydrogen bonds (2.61%) have the least content.

The basic parameters required to construct the anthracite macromolecular structure model are shown in Table 4, and the calculation formula is shown in eqn (2).²² The length of the aliphatic hydrocarbon chain can reveal the length of the aliphatic chain and the degree of branching in the anthracite coal from Shanxi Sihe coal mine, expressed by the ratio of –CH₃ to –CH₂. The larger the parameter, the longer the aliphatic chain of the anthracite.

where A₁ is the fitting area of the wave peak in the corresponding interval, dimensionless.

Table 4 Results of FT-IR structural parameters of anthracite

Coal sample	Fat chain length	Aromaticity	Degree of condensation of aromatic rings	Aromatization index	Aromatic carbon ratio
Anthracite	1.068	0.68	0.486	4.01	0.66

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The aromaticity can represent the richness of aromatic functional groups to aliphatic functional groups in the anthracite coal, which is expressed by formula (3):

The degree of condensation (DOC) of aromatic rings can characterize the degree of condensation of aromatic rings in the anthracite structure of Shanxi Sihe coal mine. It is the ratio of the out-of-plane deformation vibration of aromatic ring CH in the peak position 700–900 cm⁻¹ area to the aromatic C=C skeleton vibration in the peak position 1600 cm⁻¹ area, which can be expressed as follows:

The aromatization index (H_ar/H_al) is the ratio of the C=C vibration of aromatic hydrocarbons at peak positions 1520–1650 cm⁻¹ and the vibration of aliphatic hydrocarbons at peak positions 2800–3000 cm⁻¹ in the anthracite coal of Shanxi Sihe coal mine. It can be represented by eqn (5):

The aromatic carbon ratio (f^C_ar) refers to the ratio of the number of carbon atoms in the molecular structure of anthracite coal in Shanxi Sihe coal mine to the total number of carbon atoms. The aromatic carbon ratio of anthracite coal can be calculated using formula (6):

where H_al/C_al is the ratio of H and C in the aliphatic group, which is 1.8.

3.3 XPS analysis

The composition of heteroatoms in coal molecules, as well as the presence and relative content of different elements, can be determined through XPS.²³ C 1s (284.8 eV) is used as the standard for calibration. Fig. 4 and 5 respectively represent the XPS spectra and peak fitting spectra of nitrogen and sulfur elements in the anthracite of Shanxi Sihe coal mine. The peak fitting results of the existing forms and contents of nitrogen and sulfur elements are obtained, further clarifying the occurrence characteristics of nitrogen and sulfur in the anthracite.

Fig. 4 XPS spectrum of anthracite.

Fig. 5 Peak fitting map of nitrogen and sulfur in anthracite.

The fitting results indicated that the main forms of nitrogen in the anthracite of Shanxi Sihe coal mine are pyridine nitrogen C₅H₅N and pyrrole nitrogen C₄H₅N, accounting for approximately 32.59% and 41.26% of the total nitrogen elements, respectively. Since pyridine nitrogen and pyrrole nitrogen have stable aromatic conjugated structures, they are largely preserved during the evolution of anthracite. Quaternary nitrogen accounts for approximately 15.01% of the total nitrogen element. The proportion of nitrogen oxides (N_xO_y) is relatively small, and they are mainly nitrogen oxides generated by the oxidation of C₅H₅N and C₄H₅N, accounting for approximately 11.15% of the total nitrogen element. The main occurrence form of sulfur in anthracite is thiophenes, which account for about 35.01% of the total sulfur element. In anthracite, thiophenes have the characteristic of aromatic structure and are one of the products of unstable side chain sulfur after aromatization. Therefore, thiophenes have gradually become the main organic sulfur structure in the anthracite. Sulfoxides account for approximately 27.74% of the total sulfur content, while mercaptans/thioethers and inorganic sulfur contents are relatively low, accounting for 14.23% and 23.01% of the total sulfur content, respectively.

3.4 XRD analysis

X-ray diffraction analysis is a technical means to study the structural characteristics of microcrystals, revealing the arrangement rules of carbon atoms, and to characterize the coal aggregation structure.^24–26 As shown in Fig. 6, the XRD pattern of anthracite coal has two broad peaks in the range of diffraction angles 2θ 20°–30° and 40°–50°, which respectively represent the 002 peak and 100 peak of the anthracite coal microcrystalline structure. The 002 peak is formed by the superposition of the γ band and the 002 band (as shown in Fig. 7), which represents the spatial arrangement of aromatic ring carbons in anthracite and the distance between the aromatic ring carbons and the aromatic ring layer. The γ band indicated the aliphatic carbon structure in anthracite. The value 2θ = 40°–50° is the 100 peak of the microcrystalline structure, which represents the degree of aromatic ring condensation of anthracite.

Fig. 6 XRD spectrum of anthracite.

Fig. 7 XRD-002 peak fitting spectra of anthracite.

Formula (7) can be used to calculate the layer spacing (d), stacking degree (L_c), extensibility of aromatic lamellae (L_a), number of aromatic lamella stacking layers (N_ave) and aromaticity (f_a) of the anthracite coal. The calculation results of the microcrystalline structure parameters of anthracite coal from Shanxi Sihe coal mine are shown in Table 5. The above-mentioned parameters are all key parameters for constructing the anthracite macromolecule model.²⁷

Table 5 Microcrystalline structure parameters of anthracite

Coal sample	θ002/°	θ100/°	d002/nm	La/nm	Lc/nm	fa	Nave
Anthracite	12.73	21.78	0.35	2.99	2.25	0.841	6.426

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3.5 Construction and optimization of the macromolecular structure model of anthracite coal in Shanxi Sihe coal mine

The ratio of bridgehead carbon to surrounding carbon in the anthracite from the Sihe coal mine in Shanxi is 0.489, indicating that the aromatic structures in the model are mainly pyrene and anthracene, supplemented by naphthalene. Through the MATLAB programming calculations, the type and number of aromatic structures closest to the bridge-circumference ratio of the anthracite macromolecular structure of Shanxi Sihe coal mine were obtained, as shown in Table 6. The total number of aromatic carbons in the anthracite coal molecules is 189. According to ¹³C NMR analysis, aromatic carbon accounts for 81.19%. Therefore, the total number of carbons in the macromolecular structure of anthracite coal in Shanxi Sihe coal mine is 233. According to the elemental analysis results, the carbon content in the anthracite sample is 91.11%, the oxygen content is 6.99%, the nitrogen content is 0.76%, and the sulfur content is 0.50%. From the above-mentioned values, it can be calculated that there are 13 oxygen atoms and 2 nitrogen atoms in the macromolecular structure of anthracite coal. Due to the low sulfur content, the quantity is less than one. Therefore, the macromolecular structure of Shanxi Sihe coal mine constructed in this article does not contain sulfur. According to XPS analysis, it can be concluded that the main forms of N element in anthracite from the Sihe coal mine in Shanxi province are pyridine nitrogen and pyrrole nitrogen, with a quantity ratio of approximately 1/1. Therefore, there is one pyridine nitrogen and one pyrrole nitrogen.

Table 6 Presence of aromatic carbon in the macromolecular configuration of anthracite

Existing form	Pyridine	Pyrrole	Pyrene	Anthracene	Naphthalene
Number	1	1	8	3	1

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According to the analysis results, the KingDraw software was used to build a macromolecular model of anthracite from Shanxi Sihe coal mine,^28–30 as shown in Fig. 8. Then, the Shanxi Sihe coal mine anthracite macromolecular model was imported into the MestReNova software, and the positions and connection methods of different functional groups in the anthracite macromolecular model were adjusted. Finally, the constructed model ¹³C NMR spectra were compared with the experimental ¹³C NMR spectra, as shown in Fig. 9. The results indicated that the ¹³C NMR spectra of the anthracite macromolecular model established in this study are in good agreement with the experimental spectra. The molecular formula of anthracite from Shanxi Sihe coal mine was ultimately determined to be C₂₃₃H₁₅₇O₁₃N₂.

Fig. 8 Planar model of the macromolecular structure of anthracite.

Fig. 9 Comparison of experimental ¹³C NMR spectra and model calculated spectra of anthracite.

The two-dimensional planar molecular model of anthracite was imported into the Materials Studio molecular simulation software, and the Forcite module and COMPASS force field were used to perform geometric optimization and molecular dynamics optimization on the anthracite macromolecular structure model of Shanxi Sihe coal mine. The iteration steps, calculation accuracy, charges term, dynamic ensemble, and time step are set to 3000, medium, forcefield assigned charge, NVT option, and 1.00 fs, respectively.²⁸ After multiple optimization processes, Shanxi Sihe coal mine anthracite was finally obtained. The lowest energy configuration of the macromolecule is shown in Fig. 10.

Fig. 10 Macromolecular structure model diagram of anthracite after optimization.

Fifteen macromolecular structural models of anthracite were selected using the amorphous cell module, with a calculation accuracy of fine and a force field of COMPASS. Fifteen single-molecule structures were placed into the crystal cells and subjected to three-dimensional periodic boundary conditions, with densities set at 1.32 g cm⁻³. The geometry optimization module was used to optimize the structure of the crystal cell model of anthracite. The COMPASS force field was used, with a calculation accuracy of fine and smart methods, and a maximum iteration step of 5000.²⁹ Further dynamic optimization processing was carried out using the Anne module and dynamics module, resulting in a structure model size of A = B = C = 3.89034 nm and a molecular formula of C₃₄₉₅H₂₃₅₅N₃₀O₁₉₅ for anthracite. The constructed molecular model is shown in Fig. 11.

Fig. 11 Optimized macromolecular structure model of Shanxi Sihe anthracite.

3.6 Adsorption capacity and adsorption heat of CO₂/CH₄/N₂ single-component gas in anthracite

The combined method of GCMC and MD simulation was used to simulate and analyze the adsorption characteristics of single-component gas molecules CO₂, CH₄, and N₂ in the macromolecular structure model of smokeless coal in Sihe coal mine, Shanxi. The competitive adsorption characteristics of smokeless coal on CO₂/CH₄ and CH₄/N₂ binary mixtures were studied. Gas adsorption simulation was performed using the fixed pressure task in the sorption module, with the customized calculation accuracy. The steps is set to 1 000 000, the calculation accuracy is set to customized, the COMPASS option is selected as the force field option, and the electrical and van der Waals are set to Ewald and atom based, respectively.^30–32

The molecular radius of the probe is the molecular dynamics radius of CO₂, CH₄ and N₂, which are 0.165 nm, 0.19 nm and 0.182 nm respectively. In the molecular structure of anthracite, the micropore volumes detected by CO₂, CH₄ and N₂ are 2967.13 ų, 2087.29 ų and 2389.81 ų respectively, and the specific surface areas are 3699.57 Ų, 2689.82 Ų and 3011.34 Ų respectively. The micropore volume and specific surface area detected by CO₂ molecules are higher than those of CH₄ and N₂, which indicate that some micropores in anthracite can be detected by CO₂ gas molecules, but not by CH₄ and N₂ gas molecules. Therefore, CO₂ gas is more easily adsorbed by anthracite than CH₄ and N₂ gas.

The adsorption kinetics curves of CO₂/CH₄/N₂ gas small molecules in the large molecule model of smokeless coal in Shanxi Sihe coal mine at different temperatures are shown in Fig. 12. By analyzing the adsorption capacity of smokeless coal in Shanxi Sihe coal mine at different temperatures (293.15 K, 303.15 K, 313.15 K, and 323.15 K), it can be concluded that at any temperature, the adsorption capacity of CO₂/CH₄/N₂ gas small molecules in the smokeless coal macromolecular model increases with the increase in adsorption pressure, while the gas adsorption increment of smokeless coal shows the opposite trend. The entire adsorption process can be divided into the initial adsorption stage (P < 3 MPa) and the gradual adsorption stage (P > 3 MPa). During the initial adsorption stage, gas molecules can fully enter the micropores of the coal molecular model, resulting in a rapid increase in adsorption capacity. In the macromolecular model of anthracite coal, the adsorption capacity of CO₂ gas molecules is the largest, followed by CH₄, and the adsorption capacity of N₂ is the smallest.

Fig. 12 Dynamic curve of CO₂/CH₄/N₂ single-component gas adsorption in anthracite at different temperatures. (a) Adsorption curve of the anthracite CO₂ system. (b) Adsorption increment curve of the anthracite CO₂ system. (c) Adsorption curve of the anthracite CH₄ system. (d) Adsorption increment curve of the anthracite CH₄ system. (e) Adsorption curve of the anthracite N₂ system. (f) Adsorption increment curve of the anthracite N₂ system.

The increase in temperature is not conducive to the adsorption of CO₂/CH₄/N₂ gas molecules by the smokeless coal macromolecular model. The reason is that the increase in adsorption temperature can promote the increase in energy, activity, and kinetic energy of CO₂/CH₄/N₂ gas molecules, which is not conducive to the “capture” of CO₂/CH₄/N₂ gas molecules on the surface of smokeless coal molecules during the adsorption process. Moreover, high temperatures can inhibit the transformation of CO₂/CH₄/N₂ gas molecules from the free state to the adsorbed state. Some stable adsorbed gases will also desorb and transform into free gas due to high temperatures, and hence, the adsorption capacity of anthracite for CO₂/CH₄/N₂ gases will decrease with the increase in temperature. To sum up, in the anthracite molecular model of Shanxi Sihe coal mine, the increase in temperature has the greatest impact on the adsorption capacity of CO₂, followed by CH₄ and N₂.

In the study of the single-component gas adsorption behavior of anthracite coal from Shanxi Sihe coal mine, in addition to studying the amount of gas adsorption by anthracite, the isosteric heat of adsorption is also another key parameter characterizing the adsorption behavior of anthracite.³³ The isosteric heat of adsorption can indicate the heat in the system, and the change information is of great significance for explaining the adsorption law and adsorption mechanism. According to the energy particle fluctuation calculation in the giant canonical ensemble, the isosteric adsorption heat Q_st during the adsorption process of anthracite and gas can be obtained. The formula is as follows:

where U_total is the total interaction energy in the system, kJ mol⁻¹, and U_intra the internal energy of CO₂/CH₄/N₂ gas molecules, kJ mol⁻¹.

Within the range of simulation temperature, the isosteric adsorption heat of CO₂/CH₄/N₂ gas molecules adsorbed by the anthracite macromolecular model of Shanxi Sihe coal mine decreases with the increase in temperature, as shown in Fig. 13. In the macromolecular structure of anthracite, the average isobaric adsorption heat of CO₂ is the largest, followed by CH₄, and N₂ is the smallest, which is also consistent with the change in adsorption amount. The reason for the different adsorption heat of the three gases is that CO₂ not only has the highest polarizability, but also has the highest of four dipole moments and the smallest molecular dynamics diameter. Compared to CH₄ and N₂, there is a strong interaction force between CO₂ and the surface of smokeless coal in Shanxi Sihe coal mine, resulting in the maximum heat released by the adsorption of CO₂ by smokeless coal in Shanxi Sihe coal mine, followed by the polarization rate of CH₄, and the molecular dynamics diameter greater than CO₂. The isobaric adsorption capacity of CH₄ is less than that of CO₂, the polarizability of N₂ is smaller than that of CH₄, and although the molecular dynamic diameter is smaller than that of CH₄, the isobaric adsorption heat is the smallest. Therefore, the isobaric adsorption heat of CO₂/CH₄/N₂ is affected by the dynamic diameter, quadruple dipole moment and polarizability of the gas molecules. The increase in temperature has the greatest impact on the adsorption heat of CO₂, followed by CH₄, and N₂ is the smallest. That is, the greater the adsorption heat of the gas itself, the greater the impact of temperature increase on it. This is consistent with the sequence of the effects of temperature increase on the adsorption amount, indicating that the adsorption heat can be used to characterize the adsorption characteristics of anthracite coal in Shanxi Sihe coal mine.

Fig. 13 Equivalent adsorption heat of the CO₂/CH₄/N₂ single-component gas adsorbed by anthracite coal molecules at different temperatures.

3.7 Adsorption characteristics of the CO₂/CH₄ mixed gas and CH₄/N₂ mixed gas in anthracite coal

The competitive adsorption characteristics of CO₂/CH₄ and CH₄/N₂ binary mixtures in the macromolecular model of smokeless coal from the Sihe coal mine in Shanxi province were studied using molecular dynamics (MD) and Grand Canonical Monte Carlo (GCMC) simulation methods.³⁴ The ratios of CO₂/CH₄ and CH₄/N₂ binary mixtures are set to 0.8/0.2, 0.6/0.4, 0.4/0.6, and 0.2/0.8, and the temperature is set to 293.15 K. The isothermal adsorption curves of CO₂/CH₄ and CH₄/N₂ binary mixtures on the macromolecular structure model of smokeless coal from the Sihe coal mine, Shanxi province are shown in Fig. 14 and 15.

Fig. 14 Adsorption capacity curve of CO₂/CH₄ binary gas with different ratios in anthracite. (a) Anthracite: 20% CO₂ + 80% CH₄ system. (b) Anthracite: 40% CO₂ + 60% CH₄ system. (c) Anthracite: 60% CO₂ + 40% CH₄ system. (d) Anthracite: 80% CO₂ + 20% CH₄ system.

Fig. 15 Adsorption capacity curve of the CH₄/N₂ binary gas with different ratios in anthracite. (a) Anthracite: 20% N₂ + 80% CH₄ system. (b) Anthracite: 40% N₂ + 60% CH₄ system. (c) Anthracite: 60% N₂ + 20% CH₄ system. (d) Anthracite: 80% N₂ + 20% CH₄ system.

As shown in Fig. 14, the variation pattern of the total adsorption amount of CO₂/CH₄ mixed gas was similar to that of pure-component gas adsorption. As the pressure increased, the total adsorption amount also increased. The total adsorption amount of CO₂/CH₄ mixed gas was between that of CH₄ and pure CO₂ components, while the adsorption amount of single-component gas in the CO₂/CH₄ mixed gas was reduced compared to pure components. As the proportion of CO₂ in the CO₂/CH₄ mixture increased and the proportion of CH₄ decreased, the total adsorption amount of the CO₂/CH₄ mixture increased. The higher the proportion of CO₂, the higher the total adsorption amount. This indicated that in the CO₂/CH₄ mixture, the molecular surface of smokeless coal has a stronger adsorption capacity for CO₂ than CH₄, making it easier to adsorb CO₂ onto the surface of smokeless coal, thereby reducing the interaction between CH₄ and the surface of smokeless coal. It was also indicating from a microscopic perspective that CO₂ injection improves the extraction rate of coalbed methane, and the feasibility of sealing CO₂ in coal seams.

The difference between the adsorption capacity of single-component CH₄ in a CO₂/CH₄ mixed gas and the adsorption capacity of a pure CH₄ component was the recovery capacity of gas injection and extraction. The higher the proportion of CO₂ injected, the greater the recovery capacity of CH₄. As for four different ratios of single-component gases in anthracite, the adsorption capacity gradually increases with the increase in pressure, and the increase in adsorption capacity was more significant in the low-pressure stage (0–3 MPa), while the increase in adsorption capacity in the high-pressure stage (3–10 MPa) gradually slowed down. When the proportion of CH₄ reached 80%, the adsorption capacity of CH₄ was greater than that of CO₂. This was because although the adsorption capacity of CO₂ in anthracite was greater than that of CH₄, the partial pressure of CH₄ was greater than that of CO₂. When the CO₂/CH₄ mixture gas competed for adsorption on the surface of anthracite, the adsorption capacity of anthracite for each single-component gas not only depends on the adsorption capacity of the gas itself, but also on the partial pressure of the single-component gas. Under these environmental conditions, the partial pressure of a single-component gas played a dominant role in the adsorption of CH₄ throughout the entire adsorption process. As the adsorption behavior progressed, the adsorption capacity of CH₄ in anthracite coal quickly approached saturation, while the adsorption capacity of CO₂ had not yet reached saturation. With the increase in pressure, the competitive adsorption advantage of CO₂ for CH₄ in CO₂/CH₄ mixed gas was fully reflected. Therefore, the adsorption capacity of CO₂ in the CO₂/CH₄ mixed gas gradually increased and exceeded that of CH₄.

As shown in Fig. 15, the adsorption capacity of both CH₄/N₂ mixed gas and pure-component gas increased with the increase in adsorption pressure, and the total adsorption capacity of CH₄/N₂ mixed gas was between that of pure CH₄ and N₂. The higher the proportion of CH₄ in the CH₄/N₂ mixture, the more the CH₄ molecules adsorbed, and the adsorption curve of the CH₄/N₂ mixture was closer to the pure CH₄ adsorption curve. The higher the N₂ ratio, the more the N₂ molecules adsorbed, and the adsorption curve of the CH₄/N₂ mixed gas was closer to the pure N₂ adsorption curve.

The difference in adsorption capacity between single-component CH₄ and pure-component CH₄ was the increased recovery of CH₄. The higher the proportion of injected N₂, the greater the recovery of CH₄. In addition, when the proportion of N₂ in the CH₄/N₂ mixture reached 60%, the adsorption capacity of N₂ was already close to that of CH₄. When the proportion of N₂ reaches 80%, the phenomenon of N₂ adsorption exceeding CH₄ adsorption occurs within the simulated pressure range. This is because when the proportion coefficient of N₂ in the CH₄/N₂ mixed gas was high, it can greatly promote the probability of collision between N₂ molecules and anthracite surface molecules during thermal motion, which will help N₂ molecules occupy more space on the anthracite surface. The adsorption sites fully compete with CH₄ molecules for adsorption, thus reducing the adsorption sites for CH₄ and the adsorption amount was less than the adsorption amount of N₂. This proved the feasibility of injecting N₂ to improve CH₄ recovery from the molecular level.

Overall, the adsorption capacity changes of CH₄/N₂ mixtures with different ratios on the molecular structure model of anthracite are similar to those of CO₂/CH₄ mixtures. However, due to the differences in molecular diameter, boiling point, pressure, and other factors of CO₂/CH₄/N₂ single-component gases in the mixed system, the total adsorption amount and adsorption capacity of each component of the two mixtures are different. In addition, the difference in total adsorption amount between single-component CH₄ and pure-component CH₄ after CO₂ injection is greater than the difference in total adsorption amount between single-component CH₄ and pure-component CH₄ after N₂ injection. This indicates that injecting CO₂ into anthracite coal seams can more effectively improve the extraction rate of CH₄ in anthracite coal seams than injecting N₂.

Fig. 16 shows the isometric adsorption heat of CO₂/CH₄ and CH₄/N₂ mixed gases on the macromolecular structure of anthracite coal in Shanxi Sihe coal mine. It can be seen from Fig. 16 that under competitive adsorption conditions, as the gas adsorption pressure continued to increase, the isobaric adsorption heat of single-component CO₂ and CH₄ gas molecules in the CO₂/CH₄ mixed gas slowly increased on the anthracite macromolecular structure model. Compared with CO₂, the isosteric adsorption heat of CH₄ on the anthracite macromolecular structure model was smaller, which indicated that the interaction force of anthracite on CO₂ gas was stronger than that of CH₄. In the high-pressure stage of CO₂/CH₄ mixed gas, the magnitude of the change in the equivalent adsorption heat of CO₂ and CH₄ was relatively small. This was due to the combined effect of the decrease in the active adsorption sites of anthracite molecules and the increase in gas adsorption capacity. As the proportion coefficient of CO₂ in the CO₂/CH₄ mixture gas increased, the adsorption heat of CO₂ and CH₄ gas in a single component decreased. In the CO₂/CH₄ mixture gas, the adsorption heat of CO₂ in an equal amount was greatly affected by the change in CH₄ proportion, while the adsorption heat of CH₄ in an equal amount was less affected by the change in CO₂ proportion.

Fig. 16 Heat curve of equivalent adsorption of CO₂/CH₄ and CH₄/N₂ mixed gas in anthracite. (a) Anthracite–CO₂/CH₄ mixed gas. (b) Anthracite–CH₄/N₂ mixed gas.

As the pressure increased, t, the adsorption heat of CH₄ molecules in the CH₄/N₂ mixture gas, slowly decreased, while the adsorption heat of N₂ gas molecules slowly increased. The trend of equal adsorption heat of CH₄ gas molecules in the CH₄/N₂ mixture gas was opposite to that in the CO₂/CH₄ mixture gas, indicating that the addition of different gases had different effects on the adsorption heat of CH₄. This was because the competitive adsorption behavior of mixed gases on the surface of anthracite was related to the properties and composition of each individual component gas in the system. The increasing in adsorption pressure had little effect on the adsorption heat of two single-component gases in the CH₄/N₂ mixture. Under competitive adsorption conditions, the equivalent adsorption heat of CH₄ was greater than that of N₂. This indicated that the interaction force between anthracite molecules and CH₄ was stronger, resulting in a greater adsorption capacity of CH₄ than that of N₂. As the CH₄ content in the mixture increased, the isosteric adsorption heat of CH₄ and N₂ gas molecules on the surface of anthracite decreased. The isosteric adsorption heat of CH₄ was greatly affected by changes in the N₂ component, indicating the presence of strong adsorbates in the competitive adsorption process of the mixture. The increase in proportion caused the isobaric adsorption heat of both strong adsorbates and weak adsorbates to decrease, and the increase in the proportion of weak adsorbates had a greater impact on the isobaric adsorption heat of strong adsorbates. The average isobaric adsorption heat of CH₄ in the CH₄/N₂ mixed gas was greater than the isobaric adsorption heat in the CO₂/CH₄ mixed gas, indicating that the inhibitory effect of CO₂ injection on CH₄ adsorption in anthracite coal seams was stronger than the inhibitory effect of N₂ injection. The difference in the isosteric heat of CH₄ and N₂ was smaller than the difference in the isosteric heat of CH₄ and CO₂.

4 Conclusions

This study constructed a three-dimensional macromolecular structure model of anthracite coal from the Sihe coal mine in Shanxi province through elemental analysis, nuclear magnetic resonance (¹³C NMR), Fourier transform infrared (FT-IR) spectroscopy, X-ray photoelectron spectroscopy (XPS), and X-ray diffraction (XRD) characterization experiments. On this basis, molecular simulation studies were conducted on the adsorption capacity, adsorption heat, and competitive adsorption of single-component and binary-component mixed gases by anthracite coal from Shanxi Sihe coal mine, revealing the micro mechanism of anthracite coal adsorption of gases in Shanxi Sihe coal mine. The following main conclusions were obtained:

(1) The main forms of nitrogen in the anthracite of Shanxi Sihe coal mine are pyridine nitrogen and pyrrole nitrogen. The ratio X_bp of aromatic bridgehead carbon to surrounding carbon is 0.489, the aromatic carbon rate is 81.19%, and the aromatic carbon structures are mainly pyrene and anthracene. The molecular formula of the anthracite molecular structure model of Shanxi Sihe coal mine is C₂₃₃H₁₅₇O₁₃N₂.

(2) In the macromolecular structure model of anthracite coal in Shanxi Sihe coal mine, the adsorption capacity of single-component gas molecules CO₂/CH₄/N₂ decreases with the increase in temperature. The increase in temperature has the greatest impact on the adsorption capacity of CO₂, followed by CH₄, and N₂ is the smallest. The isosteric adsorption heat of CO₂ adsorbed by anthracite molecules is the largest, followed by CH₄, and N₂ is the smallest. The isosteric adsorption heat decreases with the increase in temperature. The temperature increase has the greatest impact on the CO₂ adsorption heat, followed by CH₄, and N₂ is the smallest. The greater the heat and adsorption capacity of gas adsorption, the greater the effect of temperature increase on it.

(3) In the competitive adsorption process, when the proportion of CO₂ reaches 40%, the adsorption capacity of CO₂ is greater than the adsorption capacity of CH₄. When the proportion of N₂ reaches 60%, the adsorption capacity of N₂ is close to that of CH₄. When the proportion of N₂ reaches 80%, the adsorption capacity of N₂ is greater than the adsorption capacity of CH₄. Injecting CO₂ into anthracite coal in Shanxi Sihe coal mine is more conducive to increasing CH₄ recovery than injecting N₂.

(4) The isobaric adsorption heat of CO₂ and CH₄ in the CO₂/CH₄ mixture gas increases slowly with the increase in pressure in the anthracite macromolecular structure of Shanxi Sihe coal mine. The molecular structure decreases slowly as the pressure increases, and the N₂ adsorption heat increases slowly as the pressure increases. The difference in isosteric heat of CH₄ and N₂ is smaller than the difference in isosteric heat of CH₄ and CO₂.

Author contributions

Jia Jinzhang: formal analysis and contributed to the conception of the study and the data analysis. Xiao Lingyi: performed the experiment, manuscript preparation and writing original manuscript.

Conflicts of interest

The authors declare that they have no potential conflict of interests to influence the work reported in this paper.

Acknowledgements

This work was partly supported by the National Natural Science Foundation of China (grant number 52174183).

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