Mechanistic Studies of H₂ Adsorption and Diffusion in Low-Rank Coals: A Discussion on Geologic Hydrogen Storage

Abstract

An in-depth investigation of the adsorption and diffusion mechanism of hydrogen in low-rank coals is of great significance for optimizing the technical path of geological hydrogen storage and improving the efficiency of hydrogen storage. Two kinds of coal samples with a low metamorphic degree from Foran Coal Mine and Sihe Coal Mine were used as adsorbents, and the metamorphic degree and molecular structure of the coal samples were determined experimentally, and the adsorption and diffusion mechanism of H₂ molecules in the structure of low metamorphic coal was analyzed from the atomic level based on numerical simulation. It was found that the aliphatic carbon in the low-rank coal mainly links the aromatic ring in the form of a branched chain and exists as an aliphatic ring, side chain, or bridging carbon, and the lower the deterioration degree of the coal, the longer the length of the alkane side chain in the molecular structure. The branched structure present in the aliphatic carbon and the polybenzene ring structure present in the aromatic carbon can provide more effective adsorption sites and enhance the adsorption of H₂ by the low-rank coal structure. High specific surface area and porosity will enhance the adsorption of H₂ from coal samples, while the presence of oxygen-containing functional groups in low-rank coals will strengthen the interaction between the microporous structure and H₂. These findings provide theoretical support for the application of low-rank coals in geological hydrogen storage.

1. Introduction

Due to the combustion of fossil fuels, the emission of greenhouse gases into the atmosphere has had an adverse impact on global climate. With the increasing global demand for green, low-carbon energy, hydrogen has attracted significant attention as an alternative to fossil fuels [1,2,3]. This important clean energy source has a calorific value far exceeding that of coal, oil, and other fossil fuels and has the potential to fundamentally transform the existing energy supply chain. It can decarbonize fuel consumption, help reduce carbon dioxide emissions, and mitigate the “greenhouse effect” [4,5]. Storing hydrogen in geological structures such as underground coal seams, deep aquifers [6], salt caverns [7], and oil and gas fields [8] and releasing it when needed holds great promise and practical significance [9].

Under different geological conditions, coal seams, as widely distributed strata, primarily rely on adsorption to store gases within the pore spaces of coal rocks [10]. Tellez et al. [11] experimentally prepared 20 types of activated carbon from four coals of different coal ranks and studied the effect of oxygen content on hydrogen storage performance. The study found an inverse relationship between the specific surface area of the coal and hydrogen adsorption capacity. The highest hydrogen adsorption of 6.8 wt.% was obtained under experimental conditions of 4 MPa and 196 °C. Iglauer et al. [12] demonstrated the hydrogen adsorption capacity of sub-bituminous coal through hydrogen adsorption experiments, obtaining maximum hydrogen adsorption of 0.6 mols H₂/kg at 14.3 MPa and 318 K and observed that the adsorption capacity increased initially and then stabilized with increasing adsorption pressure. Kumar et al. [13] investigated the gas adsorption capacities of the Karanpura coalfield and explored the reasons for hydrogen loss during coal seam hydrogen storage. They found that the introduction of methane and carbon dioxide reduced the loss of hydrogen adsorption in coal seams, while the pore and fracture system in coal affected the migration and adsorption of coal seam gas within the coal reservoir.

For coals of different metamorphic degrees, low-rank coals, such as high-carbon, low-energy coals, exhibit unique structural characteristics that result in hydrogen adsorption properties distinct from those of other coal types [14]. The structure of low-rank coal contains abundant micropores and mesopores, with a highly active surface that enables effective adsorption of gas molecules [15]. Zhang et al. [16] investigated the pore characteristics and adsorption capacity of low-rank coal by selecting four low-metamorphism coals and combining low-temperature gas adsorption experiments with micropore filling theory. They found that 94.71% of methane in low-rank coal was adsorbed in the micropore system (0.38–1.50 nm), and the moisture, volatile matter, and ash content in low-rank coal inhibited methane adsorption. Meng et al. [17], through isothermal adsorption experiments and the construction of an adsorption-desorption-permeation experimental platform, explored the pore structure of low-rank and high-rank coals and the deformation behavior of coal samples during methane adsorption. They found that, under the same experimental stress, low-rank coal exhibited higher permeability than high-rank coal. During the simulation study of hydrogen adsorption by coal, Wang et al. [18] investigated the relationship between coal rank and H₂ adsorption through the constructed microporous model of coal with different coal ranks and found a positive correlation between the coal rank and the absolute adsorption amount of H₂, concluding that anthracite coal seams have a high hydrogen storage capacity. Mirzaei et al. [19] introduced heteroatoms into the carbon skeleton and investigated the adsorption capacity of the coal-based adsorbent modified with heteroatom functional groups for H₂ and CH₄ by means of numerical simulations and found that the maximum hydrogen adsorption, 0.6 mmol/g, could be obtained at 20 bar and 298 K. Han et al. [20] investigated the adsorption capacity of different coal ranks for H₂ by a combination of experiments and numerical simulations and found that the organic pores and micropores in the coal pore structure provided the most effective hydrogen adsorption sites, proving that hydrogen adsorption hardly occurs at low pressure and that there exists a higher adsorption capacity at high pressure and that higher pore connectivity leads to higher efficiency of hydrogen entry into the pores and adsorption.

Therefore, to conduct a detailed analysis of the adsorption and diffusion behavior of hydrogen in low-rank coal and explore its potential in geological hydrogen storage, coal samples from the Foran and Sihe coal mines with low metamorphic degrees were selected as adsorbents. The degree of metamorphism and molecular structure of the coal samples were determined through elemental analysis, vitrinite reflectance measurement, XPS, and ¹³C NMR spectroscopy. Based on DFT calculations and dynamics simulation, the adsorption and diffusion mechanisms of H₂ molecules in the low-rank coal structure were analyzed at the atomic level. This study will contribute to advancing hydrogen storage technology, improving hydrogen extraction efficiency, and providing theoretical support for the application of low-rank coal in geological hydrogen storage.

2. Materials, Experimental and Simulation Setting

2.1. Coal Sample

In order to investigate the structural characteristics and construct the molecular structure of low-rank coal, two coal samples from the Foran and Sihe coal mines were selected for the experiment, labeled LR@1 and LR@2, with detailed information provided in Figure 1. The coal samples were processed according to the GB 474-2008 standard and were crushed and sieved to produce samples with particle sizes smaller than 0.154 mm. To construct the molecular structure of LR@1 and LR@2, characterization analysis was performed using elemental analysis, vitrinite reflectance measurement, XPS, and nuclear magnetic resonance (¹³C NMR) spectroscopy. The apparent relative density of coal was measured according to the GB/T 6949-2010 standard. The results of the elemental analysis and maximum vitrinite reflectance of the coal samples are shown in

Table 1. Elemental analysis, density, and degree of deterioration of coal samples.

Coal Sample	Elemental Content (%)					Density (g/cm3)	Maximum Vitrinite Reflectance (R0,max, %)
	C	H	O	N	S
LR@1	79.96	7.35	10.84	0.87	0.98	1.16	0.43
LR@2	80.06	6.25	12.03	0.51	1.15	1.18	0.56

. From Table 1, it can be observed that both LR@1 and LR@2 are lignite coals (R_0,max < 0.60%) [21].

2.2. Experimental Methods

The elemental analysis was performed using a German-made Elementar Unicube instrument, measuring the LR@1 and LR@2 coal samples in CHNS/O mode. X-ray Photoelectron Spectroscopy (XPS) analysis was conducted with an ES-CALAB 250Xi XPS spectrometer from the United States (Thermo Fisher Scientific, Agawam, MA, USA), following the GB/T 34326-2017 standard. The experimental conditions included a monochromatic Al Kα radiation source (hv = 1486.6 eV), a beam size of 400 μm, a power of 200 W, and scanning with a fixed analyzer energy (CAE). The vacuum in the analysis chamber during operation was maintained at 3 × 10⁻⁷ mbar. Energy calibration was carried out using the C1s peak (284.80 eV) as a reference, allowing for the determination of the chemical states of C, O, N, and S atoms in the coal samples. Nuclear Magnetic Resonance (NMR) spectroscopy was performed using a Bruker AVANCE III 600 MHz (Bruker, Fällanden, Switzerland) fully digitalized superconducting NMR spectrometer from Switzerland, following the SY/T 5777-1995 “NMR Hydrogen and Carbon Spectroscopy Analysis Methods for Soluble Organic Matter and Crude Oil in Rocks” standard. The experimental setup included a high-resolution 4.0 mm double-resonance MAS probe with a rotor speed of 10 kHz, a pulse width of 4 μs, a pulse delay time of 1 s, a contact time of 2 ms, and 10,000 scans. This allowed for the acquisition of carbon atomic structural information from the coal samples.

2.3. Simulation Details

The DFT calculations were performed using the Dmol3 module in the Material Studio software (Material Studio 2024). All spin calculations were conducted using the Generalized-Gradient-Approximation (GGA) level with the Perdew–Burke–Ernzerhof (PBE) functional and the double numerical plus polarization (DNP) basis set [22]. The adsorption and diffusion of H₂ in the microporous structure were calculated using the Monte Carlo method, specifically through isothermal adsorption simulations under the Sorption module, with Fix pressure and Adsorption isotherm tasks. The force field used was COMPASS, and according to the studies of Arif et al. [23] and Wang et al. [18], the maximum adsorption pressure was set to 10 MPa, the temperature to 293.15 K, with 10,000 equilibrium steps and 100,000 production steps. Electrostatic interactions were handled using the Ewald and Group method, while van der Waals interactions were modeled using the atom-based method. To obtain the low-energy stable state of the coal microporous structure, geometry optimization, annealing, and dynamic relaxation were carried out in the Forcite module. The geometry optimization had a maximum iteration number of 50,000 steps, with energy convergence set to 4.184 J/mol. For annealing simulations, the initial temperature was 300 K, the temperature increase step was set to 5, and 10,000 cycles were run for 10 loops, using the Nose–Hoover thermostat for temperature control.

2.4. Calculation Methods

The information about the aromatic carbon skeleton in coal can be determined by the ratio of bridge carbons to surrounding carbons (X_BP). The bridge-to-surrounding carbon ratio (X_BP) can be calculated using the formula [24], as shown in Equation (1).

$$X_{BP}={\displaystyle \frac{f_a^B}{f_a^H+f_a^P+f_a^S}}$$

(1)

where $f_a^B$, $f_a^H$, $f_a^P$, and $f_a^S$ represent the fractional contributions of bridge aromatic carbons, protonated aromatic carbons, oxygen-substituted aromatic carbons, and hydrocarbon-substituted aromatic carbons, respectively, to the total number of carbon atoms in the coal structure.

To analyze the diffusion capability of H₂ on the surface of lignite, the diffusion coefficient D is calculated. The specific calculation methods [25,26] are given in Equations (2) and (3).

$$MSD={\displaystyle \frac{1}{N}}\sum _{i=1}^N{[r_i\left(t\right)-r_i\left(0\right)]}^2$$

(2)

$$D=\underset{t\to \infty }{\lim }\left({\displaystyle \frac{MSD}{6t}}\right)={\displaystyle \frac{1}{6}}{K}_{MSD}$$

(3)

where MSD denotes mean square displacement; N denotes the total number of diffusing molecules; $r_i\left(t\right)$ and $r_i\left(0\right)$ are the position vectors of the ith molecule at time t at time t = 0, respectively; and $K_{MSD}$ denotes the slope of the MSD curve.

3. Results and Discussions

3.1. XPS Analysis

The assignment patterns of carbon, oxygen, nitrogen, and sulfur and their corresponding chemical environments in LR@1 and LR@2 at room temperature were obtained by X-ray photoelectron spectroscopy, and the results and data analysis are shown in Figure 2 and

Table 2. Analysis of C 1s, O 1s, N 1s, and S 2p in two lignite coals, LR@1 and LR@2.

Coal Sample	Elements
	N			S
	Peak Value	Elemental Structure	Relative Content (%)	Peak Value	Elemental Structure	Relative Content (%)
LR@1	399.38	Pyridine	64.37	164.62	Thiophene	47.63
	402.58	Pyrrole	35.63	168.37	Sulfone	23.42
				169.57	Sulfoxide	28.95
LR@2	398.87	Pyridine	32.99	164.08	Thiophene	51.01
	400.88	Pyrrole	42.12	168.42	Sulfone	48.99
	403.20	Oxidized nitrogen	24.89

. From Figure 2, it can be observed that the carbon structures in both LR@1 and LR@2 lignite coals are mainly composed of aliphatic carbon and aromatic carbon (C–C, C–H) at binding energies of 284.80 eV, 284.20 eV, and 284.11 eV, respectively. Oxygenated carbon (C–OH, C–O–H) is also present at 286.44 eV and 286.13 eV. The oxygen in coal is mainly organic oxygen and inorganic oxygen. Inorganic oxygen in coal mainly originates from minerals, such as kaolinite, montmorillonite, quartz, carbonate, and sulfate, which are mainly formed through the crushed minerals mixed in the coal formation process or minerals precipitated in the later geological action. Organic oxygen in coal is the oxygen directly involved in the structure of coal organic macromolecules and exists in oxygen-containing functional groups. Due to the small amount of nitrogen and sulfur structures in the coal and the complex forms of their existence, in order to accurately determine the distribution and relative proportions of nitrogen and sulfur structures in the two lignite coals, the results of the X-ray photoelectron spectroscopy (XPS) peaks analysis of the experimentally obtained nitrogen and sulfur structures are summarized in Table 2 and compared with the experiments of JIA et al. [27] and XIA et al. [28]. It can be found that the nitrogen and sulfur structures in the two lignites are mainly dominated by pyridine, pyrrole, and thiophene. The nitrogen structure of LR@1 and LR@2 lignite is mainly pyridine-type nitrogen (399.38 eV and 398.87 eV, N–6) and pyrrole-type nitrogen (402.58 eV and 400.88 eV, N–5). The sulfur structures are primarily thiophene-type sulfur and sulfone/sulfoxide-type sulfur. In both lignites, thiophene-type sulfur constitutes the highest relative content of sulfur at 47.63% and 51.01%, respectively.

3.2. ¹³C NMR Spectra Analysis

Through the ¹³C NMR spectra, the chemical environments of carbon atoms in coal molecules can be understood [29]. Different carbon atoms in coal may exist in various environments, such as aromatic rings, alkyl chains, or oxides. ¹³C NMR helps to distinguish these different chemical environments and enables the quantitative analysis of the relative proportions of different types of carbon. To fully understand the carbon structures in LR@1 and LR@2 lignites, PEAK-FIT software (PeakFit v4.12) was used to perform detailed peak fitting on the ¹³C NMR spectra of the coal samples, with the fitting results shown in Figure 3. The peak-fitting spectra of the coal samples reveal two distinct carbon peaks: one is the aliphatic carbon peak located at 0–80 ppm, and the other is the aromatic carbon peak located at 100–165 ppm [30]. This indicates that the carbon structures of both lignites are primarily composed of aliphatic and aromatic carbon. Moreover, there are no noticeable peaks corresponding to carbonyl or carboxyl groups (175–200 ppm [31]), suggesting that the carbon–oxygen structures in LR@1 and LR@2 are primarily linked by single bonds.

Based on the ¹³C NMR structural parameters of the coal samples, the forms and contents of aliphatic and aromatic carbons in LR@1 and LR@2 lignites can be quantitatively analyzed.

Table 3. Structural parameters of LR@1 and LR@2 coal samples.

Sample	faB	faH	faP	faS	faN	fal*	falH	falO	fal	fa	fa′	XBP
LR@1	13.16	28.60	9.26	6.68	29.09	3.78	27.95	0.88	42.31	57.69	57.69	0.295
LR@2	12.75	27.91	7.69	12.34	32.77	3.72	20.04	3.85	39.32	60.68	60.68	0.266

presents the macromolecular structural parameters of the coals. From Table 3, it can be observed that aromatic carbon (fa′) is the dominant component in both LR@1 and LR@2 lignites, with the highest relative content, accounting for 57.69% and 60.68%, respectively. The aliphatic carbon in the coal molecules primarily exists as methyl groups (f_al*, –CH₃), methylene groups (f_al^H, –CH₂–, –C–, –CH–), and oxygenated aliphatic carbons (f_al^O, O―C). Among these, the highest proportion of aliphatic carbon in both coal molecules is in the form of methylene groups, with relative contents of 27.95% and 20.04%, respectively. This suggests that the aliphatic carbon in the structures of both LR@1 and LR@2 mainly exists as long-side chains. In the coal molecular structure, aromatic carbons mainly include protonated aromatic carbons (f_a^H, Ar–H), bridge aromatic carbons (f_a^B, C–C), side-chain aromatic carbons (f_a^S, Ar–C), oxygen-substituted aromatic carbons (_fa^P, Ar–O), and non-protonated aromatic carbons (f_a^N). The aromatic carbon structures in both LR@1 and LR@2 lignites are predominantly protonated aromatic carbons, with relative contents of 28.60% and 27.91%, respectively. The bridge-to-surrounding carbon ratio (X_BP) reflects the average degree of condensation of aromatic rings. The calculated values for the aromatic bridge carbon to surrounding carbon ratio are 0.295 for LR@1 and 0.266 for LR@2, indicating the degree of aromatic condensation in the two lignites.

3.3. Molecular Structure Construction of Low-Rank Coal

Aromatic, aliphatic, and heteroatomic functional groups are present in the molecular structures of the two coals, LR@1 and LR@2, respectively, where the aromatic carbon structures can be determined based on the bridge-to-surrounding carbon ratio (X_BP), which is known to be 0 for the benzene ring, 0.25 for the naphthalene, 0.4 for the anthracene, 0.5 for the pyrene, and 0.6 for the pyrene isomers. The X_BP values for the aromatic carbon structures in LR@1 and LR@2 were calculated and found to be 0.289 and 0.273, respectively, as shown in

Table 4. Aromatic hydrocarbon structures in LR@1 and LR@2.

Typology	Amount		Typology	Amount
	LR@1	LR@2		LR@1	LR@2
	4	5		1	1
	1	1		2	2
	2	1		1	0
	1	1		1	1

. The relative errors were 2.281% and 2.559%, indicating that the determined aromatic carbon structures are consistent with the actual aromatic carbon structures in LR@1 and LR@2. Based on the calculated data, the number of aromatic carbons in the two coal structures was determined to be 125 and 112, respectively. The aliphatic carbons in the coal are primarily linked to aromatic rings in the form of branched chains and exist as fatty rings, side chains, or bridge carbons. The lower the coal rank, the longer the alkyl side chains in the molecular structure. From the number of aromatic carbons and the aromatic carbon ratio, the total number of carbons in the two coal structures was calculated to be 217 and 186, respectively. The number of aliphatic carbons was determined to be 92 and 74, respectively. Additionally, based on the elemental analysis data, the number of hydrogen atoms in the two coal structures was found to be 238 and 173, respectively.

In addition to the primary carbon structures, both LR@1 and LR@2 coal structures contain heteroatom structures. Based on the XPS experimental data and elemental analysis results, the number of oxygen atoms in each coal structure is determined to be 22 and 21, respectively. The oxygen atoms in both coal structures mainly exist as oxygen-bound aliphatic carbons and oxygen-substituted aromatic carbons. In the LR@1 coal structure, the relative content of oxygen-bound aliphatic carbons and oxygen-substituted aromatic carbons is 0.88% and 9.26%, respectively. This gives a calculated number of C–O bonds as two and Ar–O bonds as twenty. In LR@2, the relative content of oxygen-bound aliphatic carbons and oxygen-substituted aromatic carbons is 3.85% and 7.69%, respectively. The calculated number of C–O bonds is seven, and the number of Ar–O bonds is fourteen. Based on the XPS analysis results, the nitrogen and sulfur atoms in both coal structures are mainly present in the forms of pyridine, pyrrole, and thiophene. Combining the elemental analysis data, it was determined that LR@1 contains two nitrogen atoms and one sulfur atom, present as one pyridine nitrogen, one pyrrole nitrogen, and one thiophene sulfur. LR@2 contains one nitrogen atom and one sulfur atom, present as one pyrrole nitrogen and one thiophene sulfur. Based on the experimental data and calculated results, the molecular formulas for LR@1 and LR@2 were determined to be C₂₁₇H₂₃₈N₂O₂₂S and C₁₈₆H₁₇₃NO₂₁S, respectively. The planar molecular structure models for LR@1 and LR@2 were constructed, as shown in Figure 4. To ensure the accuracy of the predictive model, the chemical shifts of carbon atoms in both coal structures were calculated using the MESTRENOVA software (MESTRENOVA 14.2.1), and their ¹³C NMR spectra were simulated. By comparing the simulated spectra with the experimental ¹³C NMR spectra and combining the XPS and ¹³C NMR structural parameters, the functional groups in the coal were optimized and adjusted. This allowed the model’s predicted ¹³C NMR spectrum to align well with the experimental spectrum. The two constructed coal molecular models were imported into ChemDraw software (ChemDraw 22.0.0 64-bit) after calculation to obtain the elemental contents in

Table 5. Comparison of experimental and calculated elemental contents.

Coal Sample	Actual Elemental Content (%)					Calculated Elemental Content (%)
	C	H	O	N	S	C	H	O	N	S
LR@1	79.96	7.35	10.84	0.87	0.98	78.39	8.26	11.51	0.86	0.98
LR@2	80.06	6.25	12.03	0.51	1.15	79.81	7.02	11.73	0.43	1.01

, and through comparison, it can be found that the error of each elemental content obtained from experiments and calculations is small, which verifies the reliability of the models, and the planar molecular structure models of LR@1 and LR@2 that are the most consistent with experimental situations were obtained.

3.4. DFT Calculations

To further explore the hydrogen adsorption ability of the molecular structures of LR@1 and LR@2, the electrostatic potential [32]] and frontier molecular orbitals (FMOs) [33] of the coal structures at the atomic level were analyzed. The electrostatic distribution can reveal the charge distribution on the coal molecular surface and its attraction to H₂. The FMOs can help predict the potential adsorption reaction sites and reactive groups. In FMOs, the Highest Occupied Molecular Orbital (HOMO) reflects the electron density distribution in the molecule and indicates the orbitals most likely to lose electrons. The HOMO energy level determines its electron-donating ability in reactions. The Lowest Unoccupied Molecular Orbital (LUMO) is the orbital in the coal molecule most likely to accept electrons, and the LUMO energy level determines the coal molecule’s ability to interact with electron acceptors [34]. DFT calculations were performed to obtain the electrostatic distribution of the two low-rank coal molecular structures and H₂, as shown in Figure 5. In Figure 5, the red regions represent high electron density areas, which are prone to nucleophilic reactions, while the blue regions represent low electron density areas, which are more likely to undergo electrophilic reactions. From the electrostatic distribution of the molecular structures in Figure 5, it can be seen that there is a smooth delocalized electron density distribution on the surfaces of both coal structures and the H₂ molecule. The head of the H₂ molecule exhibits nucleophilic behavior, while the middle region shows low electron density. Compared with functional groups such as pyridine and pyrrole, the positive electrostatic regions in the molecular structure of the two coals are concentrated in the branched H atoms, O–H groups, and part of the surface of the benzene ring, and the negative electrostatic regions are concentrated in the surface of the O–H groups and part of the benzene ring, which indicates that the head region of the H₂ molecule is susceptible to electrophilic and nucleophilic reactions with the oxygen-containing functional groups in the molecular structure of the two coals. This indicates that the head region of the H₂ molecule can easily have electrophilic and nucleophilic reactions with the oxygen-containing functional groups in the molecular structure of the two coals to form a stable adsorption structure. Additionally, the branched structure of the aliphatic carbon and the polyaromatic structure of the aromatic carbon provide more effective adsorption sites, enhancing the adsorption of H₂ by the low-rank coal structures. From the distribution of the FMOs in Figure 5, it can be seen that in LR@1, the HOMO and LUMO orbitals are concentrated on the polyaromatic carbon atoms and some protonated aromatic carbon atoms. In LR@2, the HOMO and LUMO orbitals are concentrated on the carbon atoms of anthracene, pyrene, and some benzene rings. This indicates that in the low-rank coal structures, the polyaromatic structures offer more regions for electron donation/acceptance, which can interact with H₂ molecules, promoting adsorption reactions.

3.5. Adsorption and Diffusion of H₂ in a Microporous Model

To reveal the mechanisms of lignite structure on H₂ adsorption and diffusion and to investigate the interactions between H₂ molecules and the microporous structures of LR@1 and LR@2, Figure 6 summarizes the specific surface area, porosity, micropore structure, H₂ adsorption capacity, H₂ diffusion coefficient, and gas diffusion models for both microporous structures of LR@1 and LR@2. From Figure 6a, it can be seen that the microporous structure of LR@2 has a higher specific surface area and porosity compared with LR@1, with values of 2402.606 m²/g and 26.905%, respectively. This indicates that LR@2 contains more effective adsorption sites, which facilitate H₂ storage. The adsorption capacity of H₂ for both coal samples is shown in Figure 6b. The simulated adsorption capacities of the two coal samples are in good agreement with experimental results from related studies (Liu et al. [10] and Li et al. [35]), which confirms the reliability of the simulation. The H₂ adsorption capacity for LR@2 is higher than that for LR@1, with maximum adsorption of 0.474 mmol/g. This is attributed to LR@2 having a higher specific surface area and porosity compared with LR@1. Additionally, element analysis and coal molecular structure analysis confirm that LR@2 has a higher proportion of oxygen-containing functional groups than LR@1. Combined with electrostatic potential analysis, it is found that H₂ molecules are more likely to interact with these oxygen-containing functional groups in the coal structure. The MSD and diffusion coefficients of H₂ in the microporous structures of the two coal samples were calculated using Equations (2) and (3), as shown in Figure 6c. From Figure 6c, it can be observed that H₂ has a larger MSD and diffusion coefficient in the micropores of LR@1 compared with LR@2. This suggests that the presence of a higher proportion of oxygen-containing functional groups in LR@2 leads to stronger interactions between H₂ and the microporous structure, making the diffusion of H₂ more difficult.

4. Conclusions

An in-depth study of the adsorption and diffusion mechanism of hydrogen in low-rank coals is of great significance for optimizing the technological path of geological hydrogen storage and improving the efficiency of hydrogen storage. It was found that the high specific surface area and porosity in the coal structure will provide more effective adsorption sites, which is favorable for hydrogen storage. The presence of oxygen-containing functional groups will strengthen the adsorption of hydrogen in the coal structure, making it more difficult for hydrogen to diffuse. The specific conclusions are as follows:

(1) During the construction of the coal’s molecular structure, it was found that the aliphatic carbons in coal primarily exist as branched chains linked to aromatic rings in the form of alkyl groups, side chains, or bridge carbons. The lower the metamorphic degree of the coal, the longer the alkyl side chains in the molecular structure. The oxygen atoms in both coal structures mainly exist as oxygen-bound aliphatic carbons and oxygen-substituted aromatic carbons, with the C–O structures in LR@1 and LR@2 predominantly consisting of single bonds.

(2) Based on DFT calculations, it was determined that the head region of the H₂ molecule tends to undergo electrophilic and nucleophilic reactions with the oxygen-containing functional groups in the molecular structures of both coals, forming stable adsorption structures. Additionally, the branched structures of aliphatic carbons and the multi-aromatic ring structures of aromatic carbons provide more effective adsorption sites, thereby enhancing the adsorption capacity of low-rank coal structures for H₂₋.

(3) According to the simulation calculations of the micropore model, it was found that LR@2 has a higher specific surface area and porosity in its micropore structure compared with LR@1, with values of 2402.606 m²/g and 26.905%, respectively. The high specific surface area and porosity in the coal structure improve the coal’s ability to adsorb H₂. Additionally, the presence of oxygen-containing functional groups in low-rank coal strengthens the interaction between the micropore structure and H₂, making H₂ migration more difficult.