In this study, the coal sample was collected from the Mesozoic Lower Jurassic in the Junggar Basin (ZG-1), China. Table 1 lists the analytical results. Ultimate analysis of the ash-free sample was conducted using the Elementar UNICUBE (German EA Company) in CHNS mode. By establishing two sets of parallel samples, the average values of carbon, hydrogen, nitrogen, and sulfur contents in the coal sample were determined. Maceral components of sample were observed and quantitatively analyzed using a Leica DM4500P polarized light microscope, and counts were statistically analyzed based on the total percentages of vitrinite, inertinite, and liptinite groups adding up to 100%. The reflectance of vitrinite in the coal samples was measured using the same microscope and an MSP-II microphotometer.

Table 1 shows the average mean vitrinite reflectance (R_{o, m}) of the samples is 0.41% and the volatile matter content is 46.42%, which is a low-rank lignite. (O’Keefe et al., 2013; Schobert, 2017). The vitrinite group has a higher content of 87.36%. It is characterized by a higher oxygen content and slightly lower carbon content, with aliphatic formations often located on the side chains of aromatic rings (Niekerk and Mathews, 2010). These experimental results provide a solid data foundation for establishing a molecular model of coal.

¹³C-NMR enables quantitative analysis of different types of carbon structures within the carbon skeleton, providing information on the relationship between carbon and hydrogen, conformation and conformation in the molecule. Measurements were made using a Bruker 400 M NMR spectrometer. The spectrometer was equipped with a 4 mm rotor, with a MAS spin rate of 10 kHz, a recovery time of 4 s, and a collection pulse program set to “cp” with a desired scan delay of 6.5 μs. Initial models were established and calculated using ACD/C Predictors, allowing for continuous adjustments and optimizations compared to the experimental ¹³C-NMR spectra (Liu et al., 2021). By adjusting the method in this way, an average molecular model was finally obtained representing the ZG-1 tested. The structural formula and comparison spectra are shown in Figures 1a,b.

The initial configurations are constructed using the PACKMOL package (Martínez et al., 2009). All the MD simulations are conducted with the GROMACS package (version 2021.5) due to its high efficiency in parallel computing, which is suitable for simulating complex systems such as coal nanopores (Berendsen et al., 1995; Van Der Spoel et al., 2005). Visualize all MD trajectories and configurations, the VMD package was utilized in this study.

The annealing of the coal molecules was first conducted to build a coal matrix for the subsequent simulations of gas adsorption. One hundred coal molecules were placed in a cubic box (L _x = L _y = 10 nm and L _z = 10 nm) and the boundary conditions with periodicity were imposed in all directions. Then the steepest descent algorithm was applied to achieve energy minimization tasks and eliminate nonphysical contacts. It has to be noticed that the maximum of the force within any pair of atomic was set up as 1,000 kJ/(mol × nm). Subsequently, the system was relaxed for 2 ns, employing a timestep of 0.5 fs, within a canonical ensemble (NVT). To build a model of low-rank coal, a 10 ns annealing cycle was conducted from 1000 K to 298.15 K using an isothermal-isobaric (NPT) ensemble under 10 MPa with a time step of 1 fs. These optimization conditions ensure the low-rank coal model is physically accurate (Dang et al., 2017; Zheng et al., 2013). Figure 1c shows the structure of the obtained low-rank coal with sizes L _x = L _y = 8 nm and L _z = 3.5 nm and chemical formula C₇₉₀₀H₈₆₀₀O₆₀₀.

Three different types of models were established to study the effects of temperature, pressure, pore size, water content, and gas mixing conditions on the H2 adsorption and diffusion behavior. Two layers of the low-rank coal model were placed parallel to mimic a coal nanopore Figure 2a. Figure 2b shows a series of anhydrous coal pore models with different pore sizes; A total of 11 sets of pore size parameters of 1, 2, 3, 4, 5, 7.5, 10, 12.5, 15, 17.5, and 20 nm were set in this work, and only the initial models of 2 nm and 20 nm are given for the convenience of display. Figure 2c shows a coal pore model with different water content at 298.15 K and 20 MPa with a pore size of 10 nm. Here, the density of water is expressed through the following Equation 1 (Li et al., 2024a): ρ w = N N A × m A A × 10 3 (1) where ρ w denotes the density of water, g/m²; N represents the number of water molecules introduced, N A refers to Avogadro’s constant, mol^-1; m A is the relative molecular mass of water, g/mol; and A corresponds to the surface area of the upper and lower boundaries of the coal pore, m².

Table 2 shows the parameters of the different water content models.

Figure 2d shows a mixed adsorption model of H₂, CH4 calculated under the corresponding simulation conditions using the modified Peng-Robinson equation of state, and CO₂ with a pore size of 10 nm. The number of gas molecules was calculated under the corresponding simulation conditions using the modified Peng-Robinson equation of state (Leachman et al., 2009; Mosher et al., 2013; Robinson et al., 1997; Span, 1994). In this study, pressure is indirectly controlled by adjusting the bulk phase chemical potential. The Peng-Robinson equation of state calculates the densities of gases and mixtures at specified pressures, ensuring adsorption occurs under controlled conditions.

The topologies of all the coal, H₂ and CH₄ molecules were expressed by the OPLS-AA force field (Jorgensen et al., 1996). The forcefield parameters were sourced from the LigParGen server (Dodda et al., 2017). Moreover, the OPLS-AA force field has been confirmed in earlier research, demonstrating alignment with experimental results and the NIST standard database (Fan et al., 2020; Zhan et al., 2020). The CO₂ molecules were modeled using the potential parameters of the Elementary Physical Model (EPM2) (Harris and Yung, 1995).

As shown in the Equation 2, the non-bonding interaction equations for this system are both expressed in terms of the Lennard-Jones (LJ) potential, as well as the Coulomb electrostatic interactions: u r i j = 4 ε i j σ i j r i j 12 − σ i j r i j 6 + q i q j 4 π ε 0 r i j (2) Where r i j , σ i j , ε i j , denote the distance between atoms, size parameters, and L–J energy, separately; the partial atomic charge q is used to calculate the Coulomb interaction, while ε 0 stands for the dielectric constant.

The Lennard-Jones potential parameters for distinct particles were determined using the Lorentz-Berthelot combination rules as below Equations 3, 4: σ i j = 1 2 σ i + σ j (3) ε i j = ε i ε j (4) where σ and ε represent the standard L-J parameters for size and energy, between atomic sites i and j.

After the construction of the adsorption system was completed, energy minimization was then performed using the steepest descent algorithm, reducing the maximum force between any atom pair to less than 1,000 kJ/(mol × nm). The next step involved relaxing the system for 2 ns with short timesteps of 0.5 fs. The system was then equilibrated for 40 ns over a longer time span of 1 fs in a typical ensemble of set simulation temperatures (Berendsen et al., 1984; Bussi et al., 2007). Finally, an additional 10 ns simulation in a canonical ensemble was used as the production phase. During the production phase, a velocity-rescale thermostat, and a Parrinello-Rahman barostat were utilized to regulate temperature and pressure. The particle mesh Ewald (PME) method was used to evaluate the pair of Coulomb interactions, with a Fourier spacing set at 0.12 nm and a cut-off radius of 1.2 nm. The van der Waals interactions were calculated using a standard cut-off approach, with the same cut-off radius of 1.2 nm (Darden et al., 1993).

The mean square displacement (MSD) and self-diffusivity are crucial indicators for analyzing the motion of gas molecules within coal nanopores. MSD is often utilized to assess the extent of a particle’s positional deviation from a reference point over time. According to the Einstein relation, the slope of the MSD as a function of time is directly linked to self-diffusivity. Both MSD and self-diffusivity are determined using the parameters outlined in Equations 5, 6: MSD = 1 N ∑ i = 1 N r i t − r i 0 2 (5) D = 1 6 N lim t → ∞ d d t ∑ i = 1 N r i t − r i 0 2 (6) where D represents the self-diffusion coefficient, N denotes the number of adsorbate molecules, t refers to the simulation time, and r i t and r i 0 are the position vectors at time t and the initial time, respectively.

Defined as probability functions, radial distribution functions (RDFs) describe the spatial distribution of specific particles in relation to their coordinates, revealing details about particle aggregation and ordering behavior. It can be understood as the ratio of the local density to the average bulk density of the system. Consequently, RDF serves as a valuable tool for evaluating particle interactions. Notably, the intensity of particle interactions is reflected by the height of the RDF peak, with a higher peak signifying stronger interaction. The corresponding calculation formula is provided as Equation 7: g a b   r = d N 4 π ρ b r 2 d r (7) where d N is the number of particles b of atom a between the r and r + d r shell layers, and ρ b is the density of particle b.

The influence of temperature and pressure on the microscopic behavior of H₂ was focused on by setting the temperature variation range from 273.15 to 348.15 K and the pressure variation range from 5 to 20 MPa for the model of anhydrous coal pores with a pore size of 10 nm. Figure 3 shows the number density distribution of H₂ at various temperatures and pressures. H₂ forms a single adsorption layer on both coal surfaces, with the bulk density remaining stable within a specific interval. This phenomenon is consistent with the findings of previous studies (Li et al., 2024a). At the same pressure, the density peak of H₂ in both the adsorbed phase and the bulk phase diminishes as the temperature rises. This indicates that low temperature are more favorable for H₂ storage in coal. At constant temperature, the maximum density in the adsorption layer and the surrounding bulk medium increases significantly as pressure increases. Consequently, the H₂ storage capacity of coal also increases with higher pressure. This phenomenon is consistent with the results of Shang et al. (2024) in their study of the effect of temperature-pressure on UHS in kaolinite slits.

To better describe the H₂ characteristics in coal pores, Figure 4 depicts the diffusion features of H₂ in 10 nm coal pores under different temperature and pressure conditions. Overall, the diffusion coefficient of H₂ in coal is proportional to temperature and inversely proportional to pressure. As temperature increases and pressure decreases, the diffusion coefficient of H₂ gradually rises. This is because the increase in temperature enhances the kinetic energy of H₂, which in turn accelerates the mobility of H₂, prompting it to overcome the energy barriers and facilitating the desorption and diffusion of the gas. As the pressure decreases, the amount of H₂ in the coal pores decreases, and the collision frequency between H₂ decreases, which results in an increase in the mean free range of H₂, thus improving H₂ migration and diffusion. This finding is consistent with the results obtained in the previous study (Liu et al., 2022).

The adsorption and desorption behaviors of H₂ in anhydrous coal pores of 1–20 nm pore sizes were investigated at 298.15 K, 20 MPa. As shown in Figure 5, the number density distribution of H₂ at equilibrium varies with different pore sizes. In Figure 5a, for pore sizes smaller than 7.5 nm, the peak density of H₂ adsorption and the bulk phase density increase as the pore size enlarges. However, this trend becomes less evident for pore sizes greater than 7.5 nm, as depicted in Figure 5b. Such a trend is consistent with the results of H₂ in carbonate minerals and clay minerals with different pore sizes (Li et al., 2024a; Liu et al., 2022).

Figure 6 shows the mean square displacement (MSD) and the self-diffusion coefficient of H₂ under changing pore size conditions. From Figure 6a, in the 1–7.5 nm pore size range, the MSD increases as the pore size grows. In the pore size range of 7.5–20 nm, the MSD hardly varies with pore size but fluctuates within a range. Figure 6b similarly demonstrates such a trend. As the pore size grows, the diffusion coefficient increases rapidly for pore sizes smaller than 7.5 nm. However, when the pore size exceeds 7.5 nm, the diffusion coefficient shows only slight fluctuations with further increases in pore size. We consider that the reason for this phenomenon is the result of gas-solid interaction. At the same temperature and pressure, the interactions between H₂ and coal are more potent in smaller pore sizes. As the pore size increases up to several tens of nanometers, the effect of the solid phase surface on the gas keeps decreasing or even can be neglected. Therefore, in pore sizes smaller than 7.5 nm, the interaction between H₂ and coal surface is stronger. Meanwhile, for pore size conditions larger than 7.5 nm, the H₂ gas mainly exists in the bulk phase, and the migration ability gradually increases. This is consistent with the previous explanation (Shang et al., 2024). For UHS, a small pore size results in most of the H₂ being trapped in the adsorbed phase, causing substantial adsorption losses. On the other hand, when the pore size exceeds 7.5 nm, the impact of pore size on the H₂ diffusion coefficient diminishes, allowing for sufficient storage space within the pores, which makes this range more ideal for UHS.

The main target of UCG is usually deep water-bearing low-rank coal strata. Previous related studies have shown that the presence of water may affect gas diffusion (Gensterblum et al., 2013). As a result, this section investigates the influence of water content on the adsorption and desorption behavior of H₂ in coal pores using models with varying levels of water content. Figure 7 displays the morphology of water of different densities on the coal surface when the system is in equilibrium. Water forms clusters adsorbed on the coal surface and the size of the clusters increases with the increase in water density. Here, there is a difference in the morphology and size of water molecule clusters on the two coal surfaces due to different functional group compositions and properties on the coal A and B surfaces.

Figure 8a shows the number density distribution of H₂ under different water density conditions. H₂ adsorption exists on the coal surface when the water density is 0.05 × 10⁻³ g/m². In contrast, the coal surface is occupied by gradually increasing water molecule clusters as the water density increases, and most of the H₂ is in the bulk phase when the water density is 0.05 × 10⁻³ g/m². The strong affinity between water molecules and oxygen-containing functional groups in coal preferentially adsorbed water molecules on the coal surface. Moreover, due to H₂ bonding interactions, the water molecules adsorb each other and then form clusters, leading to the obstruction of H₂ adsorption. This is consistent with the findings of previous studies (Han et al., 2017). Figure 8b displays the diffusion coefficient of H₂ under different water densities. When the water density is low, the stronger interaction between water and coal surface allows H₂ to diffuse in the coal pores, which can explain the higher self-diffusion coefficient of H₂ at low water density. Expressed as the diffusion coefficient is 263.54 (±3.22) ×10⁻⁵ cm²/s for a water density of 0.23 × 10⁻³ g/m². With the increased water density, the water molecule clusters increase and continuously occupy the space in the coal pores. The diffusion of H₂ in the coal pores is hindered, reflected by the gradual decrease of the diffusion coefficient of H₂. The variation of water content can influence UHS tremendously. Water content conditions are feasible for UHS in post-burn UCG cavities.

Earlier research has demonstrated that the presence of other gases considerably influences the microscopic behavior of H₂ (Zhang et al., 2024; Zhou et al., 2019). The syngas also includes CO₂ and CH₄, among others, and will persist in the cavity, thereby influencing the adsorption and diffusion characteristics of H₂. For this reason, in this section, the gas mixture model (Figure 3d) is used to investigate the competitive adsorption law of mixed gases. Figure 9 shows the snapshots of adsorption of H₂, CH₄, and CO₂ adsorption in coal pores at different equilibrium times at 298.15 K, from 3 to 15 MPa. Figure 10 complements Figure 9 by showing the density distribution of the three gas molecules in the z-direction at equilibrium 10 ns under different pressure conditions. Both CH₄ and CO_2, like pure H₂, were observed to create a uniform adsorption layer across the coal matrix surface. Under the same temperature-pressure conditions, the CO₂ adsorption phase has the highest peak density with a sharp peak shape. This phenomenon is consistent with a denser surface distribution of CO₂ molecules, with most of the CO₂ molecules located in the adsorbed phase and a small amount in the bulk phase. The peak density of CH₄ in the adsorption phase is lower than that of CO₂, and most of the CH₄ molecules still exist in the bulk phase, denoting that the adsorption of CH₄ on the coal surface is weaker than that of CO₂. In contrast to CO₂ and CH₄, the adsorption phase density profile of H₂ only shows two tiny shoulders at 3 MPa, and almost all H₂ is in the bulk phase. This suggests that in the mixed presence of H₂, CH₄ and CO₂ in coal pores, the gas adsorption capacity is in the order of H₂<CH₄<CO₂. This is consistent with the phenomenon observed in shale casein by a previous author (Zhang et al., 2024). Regarding the reasons for the remarkable CO₂ adsorption effect, limited studies have attributed this phenomenon to the following (Mastalerz et al., 2004): (a) CO₂ is adsorbed not only in coal pores, but also in the organic structure of coal during gas-solid-phase-gas-phase interactions (Clarkson and Bustin, 1999); (b) CO₂ can be adsorbed in a larger range of coal pores (microporous-mesoporous) (Merkel et al., 2015); (c) CO₂ interacts more strongly with the surface of coal (Zhou et al., 2019).

To further analyze the competitive adsorption properties of the gas mixtures, the interaction energy, including van der Waals and Coulomb forces, between H₂, CH₄, CO₂ and coal at 3, 9, and 15 MPa were calculated, as shown in Figure 11. Overall, the interaction energies between the three gas molecules and coal intensify as pressure increases. This indicates that the attraction of coal to gases is proportional to the pressure. van der Waals interactions are observed between H₂ and coal. Major van der Waals interactions are observed between CH₄ and coal, with weak Coulombic interactions. The interaction energy of CO₂ with coal is much larger than that of H₂ and CH₄, and there is a contribution from Coulomb interactions in particular. This phenomenon is due to the very low zeta potential of the coal surface. H₂ and CH₄ have no external dipole moments, so the weaker interactions between H₂, CH₄, and coal are mainly due to dispersive or induced forces. However, CO₂ has a large quadrupole moment (−4.3 × 10⁻²⁶ esu.cm²) (Buckingham et al., 1968), allowing for charge interactions between CO₂ and coal, which in turn interact strongly with the coal surface. This agrees with the understanding achieved by previous work (Iglauer et al., 2021).

To gain deeper insights into the distribution patterns of the gases on the coal matrix, the RDFs between the hydrogen atoms in H₂, the carbon atoms in CH₄ and CO₂, and the carbon atoms in coal were calculated respectively, as shown in Figure 12. H₂ has no significant peak. CH₄ had a broad peak at 0.514 nm only at 3 MP CO₂ was observed as a broad peak at 0.478 nm at 9 MPa, with a sharper peak at 0.448 nm at 3 MP. The RDF and mean distances indicate that the coal surface affects the distribution of the gas mixtures differently. CO₂ and CH₄ are more tightly distributed near the coal surface, while H₂ is distributed in the bulk phase. This is corroborated by the number density distribution (Figure 10) and the interaction energy perspective (Figure 11). For such reason, we suggest that CO₂ molecules have higher polarity and stronger affinity to the coal surface. This is the main reason why the adsorption of CO₂ is better than CH₄ and H₂. This is in agreement with Li et al. (2024b).

The MSDs and diffusion coefficients of H₂, CH₄, and CO₂ under different pressure conditions were calculated in Figure 13 The movement characteristics of the gas mixture in the coal nanopore can be represented. It is obvious that the movement of the three gases in the coal nanopore is significantly different. Figure 13a indicates that under the same temperature and pressure conditions, the MSD of H₂ is the highest, and the MSDs of CH₄ and CO₂ are lower than that of H₂, especially CO₂, which has the smallest MSD, indicating that H₂ is free to move and tends to be present in the bulk phase. In contrast, the movement of CH₄ and CO₂ molecules was inhibited, and CO₂ molecules had the highest diffusion resistance. From Figure 13b, the higher the pressure, the smaller the diffusion coefficients of the three gases, indicating that the resistance to diffusion of the gases is higher, while the attraction is stronger, a finding confirmed by analyzing the interaction energy (Figure 11).

Therefore, the syngas present in the UCG cavities with CO₂ and CH₄ as the main components will be preferentially adsorbed over H₂. Fundamentally, CO₂ and CH₄ will occupy the adsorption sites on the coal surface in preference to H₂, which in turn reduces the interaction between H₂ and coal (Figure 14). The presence of CO₂ and CH₄ as syngas provides the possibility to reduce H₂ adsorption losses and to increase the purity of H₂ in the cavities (Zhang et al., 2024).