Molecular Simulation Study on the Competitive Adsorption and Diffusion of CH₄ and CO₂ in Coal Nanopores with Different Pore Sizes

Abstract

Coalbed methane (CBM), mainly composed of methane (CH₄) and carbon dioxide (CO₂), has attracted increasing attention due to its dual significance as a clean energy resource and its role in greenhouse gas management. This research systematically examines the adsorption, desorption, diffusion, and bubble evolution dynamics of methane (CH₄) and carbon dioxide (CO₂) in graphene nanopores with diameters of 4 nm, 6 nm, and 8 nm by molecular dynamics simulations. Radial distribution function (RDF) analyses reveal strong solvation of both gases by water, with CO₂ exhibiting slightly stronger interactions. Adsorption and desorption dynamics indicate that CO₂ molecules display shorter residence times on the graphene surface (0.044–0.057 ns) compared with CH₄ (0.055–0.062 ns), reflecting faster surface exchange. Gas-phase molecular number analysis demonstrates that CH₄ accumulates more significantly in the vapor phase, while CO₂ is more prone to adsorption and re-dissolution. Mean square displacement (MSD) results confirm enhanced molecular mobility in larger pores, with CH₄ showing greater overall diffusivity. Structural evolution of the 8 nm system highlights asymmetric bubble dynamics, where large bubbles merge with the upper adsorption layer to form a thicker layer, while smaller bubbles contribute to a thinner layer near the lower surface. CH₄ and CO₂ follow similar pathways, though CO₂ diffuses farther post-desorption due to its weaker surface retention. These results provide fundamental insights into confinement-dependent gas behavior in graphene systems, offering guidance for gas separation and storage applications.

1. Introduction

Coalbed methane (CBM) is an unconventional natural gas, primarily composed of methane (CH₄), which is hosted within the porous matrix of coal seams [1,2]. Unlike conventional reservoirs where gas primarily accumulates in free form, CBM is dominantly adsorbed onto the internal surfaces of coal pores, which makes its exploitation more challenging but also offers unique opportunities for recovery [3,4]. Simultaneously, carbon dioxide (CO₂) has garnered growing interest for enhanced coalbed methane recovery (ECBM) due to its dual role as a major greenhouse gas and a potential agent for displacing methane [5,6,7]. The injection of CO₂ into coal seams enhances CH₄ recovery via competitive adsorption while simultaneously enabling long-term geological CO₂ sequestration [3,8]. Thus, understanding the adsorption and diffusion behaviors of CH₄ and CO₂ within coal pores is crucial for enhancing energy recovery efficiency and advancing carbon reduction efforts [9].

Recent developments in molecular simulation techniques have provided valuable insights into the competitive adsorption and diffusion behaviors of gases within coal matrices [10,11]. Computational approaches such as Grand Canonical Monte Carlo (GCMC) and Molecular Dynamics (MD) simulations have been extensively employed to investigate gas adsorption capacities, transport behaviors, and intermolecular interactions within coal matrices [4,12,13]. Previous studies have demonstrated that CO₂ generally exhibits a stronger affinity to coal surfaces than CH₄, which underpins its capability to displace methane [14]. Moreover, the significance of pore structure has been highlighted, with micropores recognized as the primary contributors to governing gas storage and diffusion behavior [15]. For example, researchers have shown that pore size distribution directly controls adsorption selectivity and transport efficiency of different gases, yet most analyses still focus on simplified or uniform pore structures [16,17].

Recent advances in molecular simulations have significantly deepened the understanding of gas adsorption and transport within coal pores. For instance, Pan et al. employed Grand Canonical Monte Carlo (GCMC) simulations to investigate CO₂ adsorption in coal molecular models, revealing that CO₂ exhibits a stronger binding affinity compared to CH₄ under identical conditions [18]. Building on this, Wang et al. demonstrated that decreasing coal particle size enhances gas adsorption capacity by increasing micropore volume and surface area, confirming micropores as the dominant space for gas adsorption [19]. Similarly, Liu et al. compared adsorption behaviors across different coal ranks, including lignite and bituminous coal, and reported that coal structure significantly influences both CH₄ uptake and CO₂ selectivity, although their studies were restricted to dry systems under ambient conditions [20].

Beyond adsorption, competitive displacement between CH₄ and CO₂ has also been extensively studied. Sun et al. provided a comprehensive review of molecular simulation approaches, including GCMC, MD, and DFT, for investigating CO₂/CH₄ competitive adsorption in shale organic–inorganic composite models. Their work systematically examined the impacts of temperature, pressure, moisture, and pore structure on adsorption behaviors, while also emphasizing current challenges such as multi-scale model integration and the incorporation of machine learning techniques. This review offers valuable theoretical insights for advancing shale gas exploitation and CO₂ [21]. Wang et al., employing COMSOL v.6.3 simulations coupled with a phase-field method, demonstrated that capillary number, viscosity ratio, and coal wettability are critical factors governing CH₄–water displacement patterns in hydraulically fractured coal seams. Their results revealed that elevated capillary numbers and viscosity ratios enhance gas recovery efficiency, particularly within low-permeability regions [22]. In addition, Yao et al. focused on coal swelling behavior under supercritical CO₂, and suggested that structural changes in coal pores further enhance CO₂ storage potential [23]. These findings collectively underscore the potential of CO₂ injection as a promising strategy for enhanced coalbed methane (ECBM) recovery, while also revealing a critical gap in the systematic evaluation of pore size effects on competitive adsorption and diffusion.

In terms of diffusion behavior, Zhou et al. using GCMC and MD simulations, the authors investigated CO₂/CH₄ diffusion mechanisms in organic and inorganic shale nanopores, revealing that higher temperatures and lower pressures enhance CH₄ diffusion efficiency while competitive adsorption weakens CH₄ surface diffusion, with pore size expansion further favoring CH₄ mobility over CO₂ [24]. Cai et al.reveals that temperature and pressure differentially affect gas adsorption and transport in Chinese coals of varying ranks, with lower-rank coals exhibiting higher methane adsorption capacity but greater thermal sensitivity, while CO₂ shows superior diffusivity, providing key insights for designing enhanced CBM recovery and carbon sequestration operations [25]. Meanwhile, Long et al. Using GCMC and MD simulations, this study revealed that CO₂ exhibits the strongest adsorption affinity (CO₂ > CH₄ > N₂) and slowest diffusion in coal nanopores, while larger pores enhance gas mobility but reduce adsorption density, providing molecular insights for gas injection strategies in CBM recovery [26]. Despite these advances, most studies adopt single pore sizes or oversimplified coal structures, which limit their ability to reflect realistic coal reservoir heterogeneity.

From the above literature, it is evident that significant progress has been made in understanding CH₄ and CO₂ adsorption and diffusion in coal pores. However, three major gaps remain. First, most prior work focuses on adsorption under ambient or low-pressure conditions, with insufficient consideration of real subsurface environments where high pressure and strong confinement dominate. Second, although both adsorption and diffusion processes have been studied, few works integrate them into a unified framework of competitive adsorption–diffusion coupling. Third, the impact of pore size diversity has yet to be systematically explored, despite being a fundamental characteristic governing gas storage and transport in coal reservoirs.

To address these research gaps, this study utilizes Molecular Dynamics (MD) simulations to systematically explore the competitive adsorption and diffusion behaviors of CH₄ and CO₂ within coal pores of varying sizes. By integrating adsorption thermodynamics with diffusion kinetics, the work aims to reveal how pore size regulates gas selectivity, transport efficiency, and displacement mechanisms. Unlike previous studies that primarily addressed single pore sizes or simplified conditions, this work establishes a unified microscopic framework to investigate CH₄—CO₂ competition across heterogeneous coal pores, offering novel theoretical insights for enhanced coalbed methane recovery and long-term CO₂ sequestration.

2. Simulation Methods and Models

2.1. Simulation Models

In this study, molecular dynamics simulations were performed using Gromacs v5.0.7, and a model was constructed to investigate gas adsorption and diffusion on coal seam surfaces (Figure 1). We simulate the microscopic surface characteristics of coal bodies by replacing the coal seam structure with parallel arranged double-layer graphene sheets. There is sufficient space between the two layers of graphene to accommodate the target molecules. Then adjust the porosity to 4 nm, 6 nm and 8 nm, respectively. Three components were introduced into the simulation system: water molecules, carbon dioxide (CO₂), and methane (CH₄). Among them, there are 1500 carbon dioxide and 1500 methane molecules, and water molecules are filled in the remaining parts according to the density at normal temperature and pressure. These molecules are uniformly and randomly distributed between two layers of graphene, forming a multi-component mixed system. The coal matrix exhibits considerable chemical and structural heterogeneity, including oxygen-containing functional groups and surface roughness, which may enhance the adsorption of polar molecules such as CO₂ [27]. In this study, a double-layer graphene model was used as a simplified representation of the coal pore walls. While this approach captures the essential confinement effects of the aromatic domains, it does not fully reflect the complexity of real coal. Future work will incorporate functional group diversity to improve model realism.

To examine the effect of pore size on the competitive adsorption and diffusion of gases, three slit-shaped coal pore models with widths of 4 nm, 6 nm, and 8 nm were constructed. The simulations were conducted at a temperature of 298 K to mimic typical coal reservoir conditions. By varying the pore dimensions while keeping the thermodynamic state constant, CH₄ and CO₂ molecules were allowed to interact with the coal pore walls under different degrees of confinement, thereby revealing the regulatory effect of pore size on adsorption selectivity and transport dynamics. Periodic boundary conditions were implemented in all simulations to allow continuous molecular migration within the pore system, thereby more accurately representing the heterogeneous pore structure of real coal seams.

2.2. Simulation Methods

In this study, the graphene structure was modeled using the OPLS-AA force field [28]. Water molecules were represented by the TIP4P model [29], which employs virtual sites and applies the SETTLE algorithm to maintain molecular rigidity. Methane was described with the OPLS-UA model [30], in which the parameters of CH₄ are mapped onto the central carbon atom. Carbon dioxide molecules were treated using the EPM2 force field [31]. Non-bonded interactions between different molecular species were computed using the Lorentz–Berthelot combination rule, a standard approach in molecular dynamics for deriving Lennard–Jones parameters for dissimilar atom pairs. Specifically, for particles i and j, the Lennard–Jones distance parameter (σ) was calculated using Equation (1):

$${\sigma }_{ij}={\displaystyle \frac{{\sigma }_i+{\sigma }_j}{2}}$$

(1)

The energy parameter (ε) of the Lennard–Jones potential is determined according to Equation (2):

$$\begin{array}{c}{\epsilon }_{ij}=\sqrt{{\epsilon }_i\cdot {\epsilon }_j}\end{array}$$

(2)

The cutoff distance for short-range van der Waals interactions was set to 1.20 nm, while long-range electrostatic interactions were computed using the Particle Mesh Ewald (PME) method. In this approach, the total electrostatic energy is separated into three components, as expressed in Equation (3):

$$\begin{array}{c}{E}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}=E_{\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{l}}+E_{\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{a}\mathrm{l}}+E_{\mathrm{s}\mathrm{e}\mathrm{l}\mathrm{f}}\end{array}$$

(3)

The real-space contribution is given in Equation (4):

$$E_{real}={\displaystyle \frac{1}{2}}\sum _{i\ne j}{q}_i{q}_j{\displaystyle \frac{erfc\left(\kappa r_{ij}\right)}{r_{ij}}}$$

(4)

The reciprocal-space contribution is represented by Equation (5):

$$\begin{array}{c}{E}_{\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{a}\mathrm{l}}={\displaystyle \frac{1}{2V}}{\displaystyle \sum _{\mathit{k}\ne 0}}{\displaystyle \frac{4\pi }{k^2}}{e}^{-k^2/4{\kappa }^2}{\left|{\displaystyle \sum _j}{q}_j{e}^{i\mathbf{k}\cdot {\mathbf{r}}_j}\right|}^2\end{array}$$

(5)

The self-interaction correction is expressed in Equation (6):

$$\begin{array}{c}{E}_{\mathrm{s}\mathrm{e}\mathrm{l}\mathrm{f}}=-{\displaystyle \frac{\kappa }{\sqrt{\pi }}}{\displaystyle \sum _i}{q}_i^2\end{array}$$

(6)

In these equations, q_i denotes the charge of particle i, r_ij represents the distance between particles i and j, and κ is the Ewald parameter used to separate real-space and reciprocal-space contributions. Subsequently, the system was equilibrated under isothermal (NVT) conditions at 298 K for 2 ns using the V-rescale thermostat, with a coupling constant of 0.1 ps, to ensure temperature stabilization. After the pre-equilibration stage, production simulations of at least 20 ns were carried out under the same temperature conditions, during which the Nosé–Hoover thermostat was applied with a coupling time of 2 ps to ensure proper sampling of the canonical ensemble.

3. Results and Discussion

3.1. Structural Evolution Under Different Pore Sizes

The initial systems were constructed with 1500 CO₂ and 1500 CH₄ molecules, while the remaining pore volume was filled with water at ambient density. The structural evolution of the confined fluids exhibits significant dependence on pore size (Figure 2). For the 4 nm slit pore, strong confinement leads to the compression of water into the pore center. At 5 ns, water is squeezed into two separate domains, forming distinct water clusters. These domains gradually coalesce, with nearly half of the interface merged by 10 ns. By 20 ns, a single, continuous water domain is observed at the pore center, encapsulated by surrounding CO₂ and CH₄ molecules. This behavior can be attributed to the limited pore volume, which enforces strong competition between gas adsorption on the graphene walls and water structuring in the confined space, ultimately driving water molecules to aggregate in the middle of the pore.

In the 6 nm pore, the degree of confinement is reduced, and the system exhibits a relatively stable morphology. At 5 ns, water organizes into a planar rectangular slab located in the pore center, while undissolved CO₂ and CH₄ are preferentially adsorbed onto the upper and lower graphene surfaces. This configuration remains stable throughout the simulation. The observed structural stability arises from a balance between capillary forces driving water accumulation in the midplane and sufficient pore volume that allows gases to fully adsorb at the solid surfaces without significantly disrupting the water domain.

In the 8 nm pore, weak confinement produces more complex dynamics. At 5 ns, fewer gas molecules are adsorbed at the graphene walls, and two mixed gas bubbles of different sizes appear within the water region. By 10 ns, these internal cavities vanish as gases diffuse and merge into the interfacial layer, leading to increased gas adsorption on the upper surface. At 20 ns, the morphology remains similar to that at 10 ns, suggesting the system has reached a quasi-equilibrium state. The presence and subsequent dissolution of internal bubbles are attributed to the enlarged free volume, which weakens confinement effects and allows gases to initially nucleate inside the water phase before stabilizing at the solid–liquid interface.

Overall, the results demonstrate that pore size strongly regulates the phase distribution and evolution pathways of the CO₂—CH₄—H₂O system: narrow pores favor central water aggregation and symmetric gas adsorption, intermediate pores stabilize a water slab with bilayer gas layers, while wide pores facilitate transient gas bubble formation within water before interfacial adsorption dominates.

3.2. The Number Density Distributions of CH₄, CO₂, and Water at Different Pore Size

The 2D density contour maps provide insight into the equilibrium spatial distribution of CH₄, CO₂, and H₂O within slit pores of varying widths. In the 4 nm pore (Figure 3a–c), water is predominantly concentrated at the central region, forming a continuous band across the midplane, while CH₄ and CO₂ are mainly localized near the upper and lower graphene surfaces. CO₂ exhibits broader and more uniform coverage along the surfaces compared with CH₄, reflecting its stronger adsorption affinity under confinement.

For the 6 nm pore (Figure 3d–f), water occupies a well-defined planar slab at the pore center, as indicated by a pronounced central density region. CH₄ and CO₂ are again adsorbed near the solid interfaces, but the distribution is more diffuse compared with the 4 nm pore, consistent with weaker confinement. CO₂ maintains a wider interfacial spread than CH₄, highlighting its competitive advantage in occupying adsorption sites.

In the 8 nm pore (Figure 3g–i), the central water region is broader and more uniform, indicating reduced confinement effects. CH₄ and CO₂ are partially adsorbed on the graphene surfaces, with CO₂ showing noticeably larger coverage than CH₄. The remaining free volume in the pore allows for some mixing of gas molecules within the water layer, producing regions of moderate gas density inside the central water region.

Overall, the 2D density maps demonstrate that pore size strongly influences the spatial arrangement of confined fluids: narrow pores favor central water accumulation and well-separated interfacial gases, intermediate pores stabilize a planar water slab with moderately diffuse gas layers, and wide pores allow partial gas penetration into the liquid region while maintaining dominant interfacial adsorption. Across all pore sizes, CO₂ consistently occupies larger interfacial areas than CH₄, illustrating its stronger adsorption affinity and competitive advantage in confined environments.

3.3. The Radial Distribution Function and MSD Among Different Components

Radial distribution function (RDF) analysis was performed to investigate the microscopic distribution and interaction of molecules within nanopores of varying diameters (4 nm, 6 nm, and 8 nm). The RDFs of water—CH₄, water—CO₂, water—GRA, GRA—CH₄, GRA—CO₂, and CH₄—CO₂ exhibit distinct features depending on pore size, reflecting changes in molecular arrangement and adsorption behavior (Figure 4).

For water—CH₄ and water—CO₂, the primary peaks are located around 2.0–2.5 Å. With the increase in pore size from 4 nm to 8 nm, the RDF peak heights progressively rise, suggesting stronger local ordering and coordination of water molecules around the gas molecules. This suggests that larger pores promote closer packing and higher local density of water-gas interactions. The water—GRA RDF shows a main peak at approximately 3.0–4.0 Å, slightly shifting outward with increasing pore size, which indicates that water molecules adsorbed on graphene surfaces form a relatively stable but slightly more diffuse layer in larger pores.

The radial distribution functions (RDFs) of GRA—CH₄ and GRA—CO₂ show prominent peaks in the 3.0–5.0 Å range. Notably, the peak intensity for GRA—CO₂ rises more markedly than that for GRA—CH₄ as pore size increases, indicating a stronger adsorption affinity of CO₂ molecules toward the graphene surface compared to CH₄. For CH₄—CO₂, a weak primary peak appears around 3.0–4.0 Å, and with larger pore size, secondary peaks emerge, indicating enhanced medium-range ordering and increased local clustering of gas molecules in wider pores.

In summary, as the pore diameter increases, the local coordination between water and gas molecules is strengthened, which in turn enhances the adsorption of gas molecules on the graphene surface, particularly favoring CO₂ over CH₄. Larger pores provide a more spacious environment, allowing molecules to arrange more orderly, resulting in enhanced local and medium-range molecular ordering. These RDF features highlight the significant role of pore size in modulating molecular distributions and interactions within confined environments.

RDF analysis reveals that CO₂ is more strongly solvated by water than CH₄, which increases its residence time near hydrated pore surfaces. This hydration-mediated solvation likely enhances the stability of CO₂ sequestration and promotes selective retention in competitive adsorption systems, providing mechanistic insight into both long-term storage and gas separation efficiency in mesoporous environments.

The mean square displacement (MSD) of CH₄, CO₂, and water molecules was analyzed in nanopores of different diameters to understand the effect of confinement on molecular mobility.

In the 4 nm pore (Figure 5a), molecular motion is relatively restricted due to strong confinement. CH₄ shows the highest diffusion, with its MSD increasing from 0 Ų at the beginning to 65.5 Ų at 20 ns. CO₂ exhibits slightly lower mobility, reaching 61.2 Ų at the same time, while water is the slowest species, with MSD rising to 37.4 Ų. These trends indicate that nonpolar gases can diffuse more easily even under confinement, whereas water’s movement is strongly hindered by hydrogen bonding and interactions with the pore walls.

When the pore size increases to 6 nm (Figure 5b), molecular diffusion is noticeably enhanced. CH₄ MSD rises sharply to 168.6 Ų at 20 ns, and CO₂ reaches 139.9 Ų. Water mobility also improves, with MSD increasing to 74.2 Ų. The larger pore volume reduces restrictions on molecular motion, and the hydrogen-bond network of water becomes less constrained, allowing all species to move more freely.

In the 8 nm pore (Figure 5c), the molecules experience minimal confinement, approaching near-bulk diffusion behavior. CH₄ reaches an MSD of 169.3 Ų, CO₂ 147.1 Ų, and water 79.7 Ų at 20 ns. The growth of MSD is smoother, reflecting the weaker influence of the pore walls. Water shows the largest relative increase compared to smaller pores, highlighting the significant effect of confinement on polar species.

Overall, MSD increases with pore diameter, reflecting reduced confinement effects. CH₄ consistently exhibits the highest mobility, followed by CO₂, with water being the slowest. The difference in MSD between pore sizes is most pronounced for water, which nearly doubles from the 4 nm to the 8 nm pore. These results demonstrate that pore size strongly influences molecular transport dynamics, particularly for polar molecules, whereas small nonpolar gases are less affected by confinement.

The diffusion behavior of CH₄, CO₂, and water in graphene nanopores exhibits a pronounced dependence on pore size, reflecting the confinement effect at the nanoscale (Figure 6). As the pore diameter increases from 4 to 8 nm, the mobility of all species is significantly enhanced, with CH₄ consistently showing the highest diffusivity, followed by CO₂ and water. This trend indicates that CH₄ experiences weaker surface interactions and less hindrance from confinement compared to CO₂, while water molecules remain the slowest due to strong hydrogen-bonding networks. The observed enhancement in molecular mobility with increasing pore size underscores the critical role of pore geometry in regulating competitive adsorption–desorption and transport processes, providing mechanistic insight into CH₄ migration and recovery in coalbed methane systems.

3.4. Adsorption and Desorption Behaviors of CH₄ and CO₂ on Graphene Surfaces

Analyzing the adsorption behavior of CH₄ and CO₂ on graphene surfaces across pore sizes of 4 nm, 6 nm, and 8 nm reveals several important trends.

For the 4 nm pore system (Figure 7a), methane adsorption starts rapidly, reaching around 373 molecules at 3 ns, after which it fluctuates and gradually decreases to 261 molecules by 20 ns. CO₂ shows a slightly different trend, increasing steadily to a peak of 368 molecules around 11 ns, then fluctuating and slightly decreasing to 323 molecules at the end of the simulation. Overall, CH₄ adsorption shows an early peak followed by a moderate decline, while CO₂ adsorption is more stable with a later peak.

In the 6 nm pore system (Figure 7b), both CH₄ and CO₂ exhibit higher initial adsorption compared to the 4 nm system. Methane peaks at 406 molecules around 3 ns, followed by fluctuations between 375 and 402 molecules, indicating a dynamic equilibrium with minor desorption events. CO₂ adsorption is more moderate, peaking at 308 molecules around 15 ns and fluctuating between 272 and 308 molecules, showing a slower adsorption process and less dramatic variation compared to CH₄.

For the 8 nm pore system (Figure 7c), CH₄ adsorption peaks at 397 molecules at 12 ns and fluctuates around 360–377 molecules thereafter. CO₂ shows a steady increase, reaching 325 molecules at 19 ns, with relatively smaller fluctuations. Compared to the smaller pores, CH₄ adsorption in the 8 nm system is more stable after the peak, and CO₂ shows a smoother, more gradual adsorption trend.

Comparing the three pore sizes, several trends are evident. Smaller pores (4 nm) lead to faster initial CH₄ adsorption but earlier saturation and a more pronounced decline, indicating limited adsorption space and competitive desorption. Medium pores (6 nm) enhance CH₄ adsorption capacity, with fluctuations suggesting a more dynamic equilibrium, while CO₂ adsorption remains moderate. Larger pores (8 nm) support more stable CH₄ adsorption over time and allow CO₂ to gradually accumulate on the surface, likely due to more available adsorption sites and reduced steric hindrance. Overall, increasing pore size appears to stabilize CH₄ adsorption and moderately facilitates CO₂ accumulation, highlighting the pore-size-dependent adsorption/desorption behavior of gas molecules on graphene surfaces.

Based on the provided desorption data for CH₄ and CO₂ on graphene surfaces at different pore sizes, the following observations can be made: For the 4 nm pore (Figure 7d), the desorption of CH₄ starts at 161 molecules at 1 ns, rapidly increases to a peak of 274 molecules at 18 ns, and then slightly decreases to 252 molecules by 20 ns. CO₂ shows a similar trend, beginning at 178 molecules, peaking at 263 molecules at 4 ns, and gradually decreasing to 230 molecules at 20 ns. The data suggest that CH₄ exhibits a slower but steady increase, while CO₂ reaches its peak earlier and then fluctuates slightly, indicating that CO₂ may initially desorb faster than CH₄ but stabilizes sooner.

In the 6 nm pore (Figure 7e), CH₄ desorption begins at 133 molecules, fluctuates moderately, and reaches around 147 molecules at 20 ns. CO₂ starts at 148 molecules, increases with minor fluctuations, and reaches 171 molecules at 20 ns. Compared to the 4 nm pore, the desorption amounts are lower for CH₄, but CO₂ desorption remains significant. This suggests that increasing pore size slightly reduces CH₄ desorption efficiency while maintaining CO₂ desorption capacity.

For the 8 nm pore (Figure 7f), CH₄ desorption is minimal initially, starting at 47 molecules, gradually increasing to 116 molecules at 20 ns. CO₂ starts at 68 molecules, rises to 137 molecules by 20 ns. Both gases show a slower and steadier desorption process compared with smaller pores, indicating that larger pore sizes limit the immediate availability of adsorbed molecules for desorption, likely due to weaker confinement effects.

Overall, the desorption behavior reveals that pore size significantly influences the release of CH₄ and CO₂ from graphene surfaces. Smaller pores (4 nm) facilitate faster desorption and higher peak numbers, especially for CO₂, whereas larger pores (8 nm) exhibit more gradual desorption for both gases. This suggests that confinement within narrower pores enhances the desorption kinetics of both CH₄ and CO₂, with CO₂ generally desorbing more readily than CH₄ under the same conditions.

For the 4 nm pore, both CH₄ and CO₂ exhibit nearly identical residence times, with CH₄ at 0.05689 ns and CO₂ at 0.05663 ns. This indicates that, under strong confinement, the two gases have very similar interactions with the graphene surface, leading to comparable retention durations (Figure 8a).

In the 6 nm pore, CH₄ shows an increased residence time of 0.06201 ns, whereas CO₂ decreases to 0.04292 ns. This divergence suggests that as the pore becomes slightly larger, CH₄ interacts more strongly or remains trapped longer within the pore, while CO₂ desorbs more quickly, likely due to reduced confinement and weaker interactions with the surface.

For the 8 nm pore, CH₄ residence time slightly decreases to 0.05464 ns, while CO₂ increases modestly to 0.04418 ns compared with the 6 nm pore. This indicates that in the largest pore, CH₄ is slightly less confined than in the 6 nm case, whereas CO₂ finds slightly longer retention due to a more balanced interaction between confinement and surface adsorption.

Overall, the data show that CH₄ generally exhibits longer residence times in smaller pores, with a peak at 6 nm, while CO₂ retention decreases as pore size increases from 4 nm to 6 nm and then stabilizes at 8 nm. These trends highlight the sensitivity of gas-surface interactions to pore size, with CH₄ being more influenced by confinement and CO₂ being more sensitive to reduced adsorption strength in larger pores.

The dynamic desorption behavior of CH₄ and CO₂ on the graphene surface was further investigated by tracking individual molecular trajectories. As illustrated by the snapshots, although both gases initially adsorb on the graphene surface, CO₂ exhibits a slightly shorter residence time compared to CH₄ (e.g., 0.0566 ns vs. 0.0569 ns for the 4 nm pore). This indicates a relatively weaker interaction between CO₂ and the graphene surface, facilitating its faster desorption.

Structurally, at equivalent time points, CO₂ molecules are observed to migrate farther from the graphene surface after desorption, whereas a fraction of CH₄ molecules remains near the surface or slides along it. This difference can be attributed to molecular characteristics: CO₂, being a linear polar molecule, interacts with graphene primarily through weak dipole–π interactions, while CH₄, a nonpolar molecule, experiences stronger van der Waals interactions with the surface, resulting in longer retention.

Trajectory analysis further reveals that the post-desorption migration is not only influenced by molecular type but also by the local pore environment. In narrow or crowded regions, CH₄ diffusion is hindered, whereas CO₂, due to its faster desorption, can more readily access the pore center and propagate along the channel, covering a greater distance.

Overall, these observations demonstrate that CO₂ desorbs more rapidly yet migrates farther, while CH₄ exhibits a slightly longer residence time with slower migration. The combination of structural snapshots and molecular dynamics trajectories provides a clear microscopic insight into the desorption and subsequent migration mechanisms of these gases on graphene surfaces (Figure 8b,c).

3.5. The Variation in Molecular Weight of CH₄ and CO₂ in the Gas Phase over Time and the Evolution of Bubbles

The temporal evolution of gas-phase CH₄ and CO₂ molecules within graphene nanopores of varying sizes was systematically analyzed to elucidate their desorption behaviors and pore confinement effects.

For the 4 nm pore system (Figure 9a), the number of gas-phase CH₄ molecules rapidly increases from 322 at 0 ns to approximately 1167–1176 at 20 ns, while CO₂ rises from 205.6 to 648.2 over the same period. This indicates a relatively fast release and accumulation of CH₄ in the gas phase, with CO₂ showing slightly slower growth but eventually reaching a comparable plateau, reflecting competitive desorption dynamics under confined conditions.

In the 6 nm system (Figure 9b), CH₄ starts at 111 molecules and increases to 937, whereas CO₂ rises from 48.2 to 393.6. Here, both gases show a steady increase, but CH₄ dominates the gas phase more significantly than CO₂, suggesting that the larger pore favors CH₄ desorption due to weaker interactions with the graphene surface or less steric hindrance, while CO₂ desorption is somewhat slower and more dispersed.

For the 8 nm pores (Figure 9c), the initial gas-phase population is much smaller (43 for CH₄ and 14.8 for CO₂), but both gases increase substantially, reaching around 773–833 for CH₄ and 234–272 for CO₂. The larger pore allows more extensive diffusion and escape of CH₄, while CO₂, although also increasing, shows a lower number compared to CH₄, indicating that CH₄ benefits more from larger confinement, whereas CO₂ molecules may still interact with the surface or cluster slightly.

In conclusion, across the three pore sizes, CH₄ consistently exhibits higher gas-phase populations and faster accumulation than CO₂. This trend highlights that CH₄ desorption is more efficient, especially in larger pores, whereas CO₂ desorption is somewhat hindered, likely due to stronger adsorption on the graphene surface. The disparity in desorption behavior becomes more evident with increasing pore size, indicating that both pore confinement and surface interactions critically influence the relative desorption rates of CH₄ and CO₂. These observations can inform molecular-level understanding of selective gas release in nanoporous graphene systems.

In the 8 nm graphene nanopore system (Figure 9d,e), the temporal evolution of CH₄ and CO₂ gas bubbles reveals key insights into the adsorption and bubble coalescence mechanisms. Initially, gas molecules were uniformly dispersed within the system. Over time, a fraction of both CH₄ and CO₂ adsorbed onto the graphene surfaces, forming relatively thin adsorption layers. Simultaneously, two distinct gas bubbles emerged in the bulk phase—a larger bubble near the upper surface and a smaller bubble near the lower surface. The closer position of the larger bubble to the upper adsorption layer promoted its faster incorporation, resulting in a relatively thick upper layer, whereas the smaller bubble merged with the lower adsorption layer, leaving it comparatively thinner. This asymmetry in adsorption layer thickness suggests that bubble-surface interactions are strongly dependent on spatial proximity and local gas density. Moreover, the similar behavior observed for CH₄ and CO₂ indicates that, despite differences in molecular size and diffusivity, both gases follow comparable adsorption–coalescence dynamics under confinement. These observations highlight the importance of pore size and bubble positioning in regulating gas redistribution and surface coverage within nanoporous materials, providing mechanistic insights into selective adsorption and transport processes relevant to gas separation and storage applications. In addition, the adsorption and desorption data related to CH₄ and CO₂ are provided in

Table 1. Adsorption and desorption data.

Pore Size	Adsorption Capacities (Number)		Desorption Rate (Number/ns)
	CH4	CO2	CH4	CO2
4 nm	255	323	17.86	21.61
6 nm	394	276	46.85	51.68
8 nm	375	325	48.21	54.36

.

4. Conclusions

This work systematically investigated the adsorption, desorption, diffusion, and bubble evolution behaviors of CH₄ and CO₂ molecules within graphene nanopores of varying pore sizes (4 nm, 6 nm, and 8 nm) using molecular dynamics simulations. The radial distribution function (RDF) analyses revealed strong interactions between water molecules and both CH₄ and CO₂, with pronounced peaks at approximately 2.7–3.0 Å for water—CH₄ and 2.8–3.1 Å for water—CO₂, indicating preferential solvation of gas molecules in the aqueous environment. The gas–graphene RDF curves demonstrated clear adsorption layers forming at ~3.5 Å from the surface, consistent with the observed molecular adsorption behavior. Notably, the water—CO₂ interactions were slightly stronger than water—CH₄, as reflected in the RDF peak intensities, suggesting higher solubility and more dynamic exchange for CO₂ in the aqueous phase.

Mean square displacement (MSD) analyses highlighted the dependence of molecular mobility on pore size. For CH₄, the diffusion rate increased from 4 nm to 8 nm pores, with MSD values reaching ~1167 at 20 ns for 4 nm and ~169,310 for 8 nm systems, reflecting enhanced mobility in wider pores. CO₂ exhibited similar trends but with slightly lower overall MSD values, consistent with its higher interaction with water and stronger adsorption on graphene surfaces. These results were corroborated by gas-phase molecular number analyses, where CH₄ molecules in the gas phase increased more steadily than CO₂ in all pore sizes, reflecting slower desorption kinetics for CH₄. For example, in the 8 nm system, gas-phase CH₄ numbers rose to ~773 molecules at 20 ns, whereas CO₂ reached ~235 molecules, indicating a larger fraction of CH₄ remaining in the gas phase due to weaker adsorption relative to CO₂.

Adsorption and desorption analyses further quantified molecular retention on graphene surfaces. The average residence times of CH₄ were 0.0569 ns, 0.0620 ns, and 0.0546 ns for 4 nm, 6 nm, and 8 nm pores, respectively, while CO₂ residence times were slightly shorter, ranging from 0.0442 ns to 0.0566 ns, confirming faster surface exchange for CO₂. Dynamic structural analyses of the 8 nm system illustrated that gas molecules initially dispersed in the bulk gradually adsorbed onto the graphene surfaces, forming asymmetric adsorption layers. Large gas bubbles near the upper surface merged into the upper adsorption layer, producing a relatively thick layer, whereas smaller bubbles near the lower surface contributed to a thinner lower layer. CH₄ and CO₂ exhibited similar structural evolution patterns, although CO₂ tended to diffuse slightly farther from the surface post-desorption due to its shorter residence time.

Overall, this study demonstrates that both pore size and molecular type critically influence adsorption/desorption kinetics, gas-phase redistribution, and bubble dynamics within graphene nanopores. Larger pores facilitate higher mobility and more pronounced gas-phase accumulation, whereas CO₂ exhibits faster surface exchange and slightly stronger water interactions compared to CH₄. These results offer a mechanistic understanding of how pore confinement influences the transport and adsorption behavior of small gas molecules, providing critical guidance for the design of advanced graphene-based materials for gas separation, storage, and capture.