Effects of Pore Parameters and Functional Groups in Coal on CO2/CH4 Adsorption.

The mechanisms of CO2/CH4 adsorption in coal are the theoretical foundation for CO2 sequestration in coal seams targeted for enhanced coalbed methane recovery. Herein, by changing the model (low rank coal: WMC, middle rank coal: XM and high rank coal: CZ) with plenty of side aliphatic chains and functional groups established in the literature, the influence and mechanism of pore parameters and functional groups(-CH3, -OH, -C2O, -C=O) on the adsorption of CO2 and CH4 in different rank coals are systematically studied. Using the Connolly surface algorithm to calculate the pore volume (V F) and the specific surface area (S SA) of coal with different functional groups, it can be seen that the influence of the functional group change on the pore structure is related to the coal rank. Changing the various functional groups in the original coal structure to a unified functional group (-CH3, -OH, -C2O, or -C=O) will increase the accessible pore volume (V F) and the specific surface area (S SA), except in low-rank and middle-rank coal, where the ordered arrangement of -C=O will decrease V F and S SA. The adsorption capacities of different pore parameters and functional groups were calculated by Grand Canonical Monte Carlo simulation and density functional theory. On pure adsorption, the pore parameters exert greater influence than the functional groups. By comparing the adsorption energy of the original pore structure containing functional groups and that of modified pores without functional groups, the contributions of the pore structure and original functional groups on CO2/CH4 adsorption are 71 and 29% and 83 and 17%, respectively. Small-diameter pores and -C2O have a strong adsorption capacity. In terms of competitive adsorption, the -C=O functional groups and pore diameters ranging from 1.0 to 2.0 nm can significantly enhance the selectivity of CO2 over CH4. The CH4 and CO2 adsorption does not occur via rigorous monolayer adsorption; multilayer adsorption can occur for CH4 and CO2 with pore diameters of 1.0-2.0 and 1.0-2.2 nm, respectively, thus causing micropore filling. These quantitative results establish a foundation for the development of adsorption theory for CO2/CH4 in coal.

Introduction

Coalbed methane (CBM) is a gas that accumulates via adsorptive or free state into pores in the coal matrix, and the adsorbed gas constitutes 80 to 90% of the total gas content in coalbeds.[1] Hydraulic fracturing using CO2 is a primary technique with promising results for enhancing CBM recovery.[2,3] Pore systems of coal contain many micropores (<2 nm), mesopores (2–50 nm), and macropores (>50 nm),[4] in which micropores occupy a large percentage and substantially influence gas adsorption.[5,6]

Therefore, studying the adsorption mechanisms of CO2 and CH4 in the micropore of coal is beneficial for understanding CO2 sequestration with enhanced CBM recovery and for preventing mine gas disasters.

Numerous experiment studies have investigated CO2/CH4 adsorption of coal; the majority of these studies used CO2/CH4 isothermal adsorption, low-temperature nitrogen adsorption, or scanning electron microscopy experiments to measure the influence of various factors on the gas adsorption capacity. These factors include temperature, pressure, rank, pore structure, and functional groups.[7−17,27] In earlier findings, MIP, LP–N2–Ad, LP–CO2–Ad, and Fourier-transform infrared (FT-IR) were used to study the effect of coal pore on the CO2/CH4 adsorption capacity.[11,12] In recent years, scanning electron microscopy and high-resolution transmission electron microscopy (HRTEM) have been used to more accurately describe the effect of the coal pore on CO2/CH4 adsorption.[13,14] The main conclusions of these studies were the adsorption capacity increases with increasing rank and the amount of adsorbate decreases with increased temperature and decreased pressure. Micropores possess the largest specific area and are the main controllers of gas adsorption; in addition, the micropore content is positively correlated with the adsorption capacity. High carbon contents and numerous oxygen- and nitrogen-containing functional groups result in sorbents possessing a high adsorbate capacity.[15−17] The documented experimental methods used to analyze the CO2/CH4 adsorption mechanisms have only been qualitative, and the specific effects of functional groups on adsorption cannot be quantitatively analyzed experimentally but can be evaluated by simulation.

The Langmuir monolayer,[24] the Brunauer–Emmett–Teller multilayer,[25] the Freundlich isotherm,[26] the micropore filling theories,[27] and the gas adsorption potential[28] have been used to quantitatively characterize CO2/CH4 adsorption in coal in previous literature, but the different adsorption theories do not match well with gas isothermal adsorption.[29] This is due to the different basic assumptions of these models; the adsorption mechanism reflected by the theories is also different, and the interaction potential of gas adsorption in coal is still unclear.

Therefore, for quantitative analyses, systematic molecular simulations are used to investigate the adsorption capacity of CO2 and CH4.[18,19,42] Previous research has proposed some microscopic models to simulate adsorption, including carbon nanotube, kerogen, and macromolecular structure models. Dang et al.[20] employed Grand Canonical Monte Carlo (GCMC) simulation and density functional theory (DFT) to investigate the effects of oxygen-, nitrogen-, and sulfur-containing functional groups on CO2/CH4 adsorption in brown coal and discovered that the favorability sequence for CO2 adsorption is −C2O > pyridine-N > −C=O > −OH > thiophene-S > −COOH; in contrast, these functional groups had less influence on CH4 adsorption. Dong et al.[21] demonstrated that in middle-rank coal, the CO2 and CH4 adsorption sequences are thiophene-S > C2O > −OH > pyridine-N and thiophene-S > pyridine-N > C2O > −OH, respectively. Merkel et al.[22] hypothesized that because functional groups containing oxygen have preferential sorption for CO2, selectivity (SCO2/CH4) is higher in subbituminous coal, and −COOH and −OH exhibit weak affinity for CH4 in low-rank coals, whereas −CH3 and aromatic structure in middle- and high-rank coals significantly influence CH4 adsorption. Some researchers quantitatively analyze the influence of functional groups on adsorption by changing the functional groups in the coal structure. Song et al.[23] modified the functional groups of a vitrinite coal structure by simulation to analyze the CO2/CH4 adsorption mechanism and identified adsorption sequences of −OH > −COOH > original (Ori) > −C2O > −CO > −C and −OH > −CO > −C2O > Ori > −C > −COOH for CO2 and CH4, respectively.

The adsorption capacity of coal to gas is determined by pore parameters and functional groups, and the change of the functional group will cause a change of the pore structure. However, previous literature only considered the effect of pore parameters or functional groups on adsorption, and the contribution of pore parameters and functional groups to coal adsorption capacity was not discussed. Thus, previous reports present obvious contradictory conclusions. They were lacking the elucidation for the adsorption mechanism. Therefore, to establish the quantitative relationship between macroscopic CO2/CH4 adsorption capacity and microscopic structure parameters (pore parameters and functional groups), we explored the CO2/CH4 adsorption occurrence (monolayer or multilayer) and the essential factors controlling its adsorption capacity in coal.

The main work prepared a series of macromolecular models constructed in previous literature to construct pore structure and functional group structure models that has inherent microporosity. Molecular simulation methods were used to understand the contribution of pore parameters and functional groups and occurrence of CO2/CH4 adsorption in coal. Macromolecular models of low-rank coal (low rank, Coal Bed No. 11 of Wumuchang Coal Mine in Yimin Mining Area), middle-rank (XM coal, Coal Bed No. 8 of Ximin Coal Mine in Xishan Mining Area) and high-rank coal (CZ, Coal Bed No. 3 of Chengzhuang Coal Mine in Jincheng Mining Area) are altering from various functional groups to given one functional groups, then to construct pore structure models and functional group structure models. The structure of the given functional group is used to calculate the relationship of functional groups and pore parameters by the Connolly surface algorithm. The controlling effects of pore structure and functional groups of pure CO2/CH4 and competitive adsorption of the binary mixtures (CO2 + CH4) are analyzed quantitatively by GCMC. Using the interaction potential field theory, the interaction potential and density distributions between CO2/CH4 and the pore structures were simulated. According to the pore parameters and the main force of CO2/CH4 molecules, the micropore filling adsorption region is subdivided. The adsorption capacity of the pore structures and functional groups in the macromolecular models for methane and carbon dioxide was simulated using Materials Studio 2018 software.

Simulation Details

Models

Ori and VFG Macromolecular Models

The low-rank (WMC: C122H104N2O18; Ro, max = 0.51%),[30] middle-rank (XM: C203H130N2O8S2; Ro, max = 1.80%),[21] and high-rank (CZ: C199H148N2O9; Ro, max = 3.20%)[31] macromolecular models were built using ACD/NMR Predictor. FT-IR spectroscopy data provided information on oxygen functional groups, HRTEM provided information on the aromatic structure, and carbon-13 nuclear magnetic resonance (13C NMR) spectra provided the two-dimensional chemical structure. The plane macromolecular models for various original structures (Oris) are shown in Figure .

Figure 1

Plane models: (a) original models of low-rank coal (WMC), middle-rank coal (XM), and high-rank coal (CZ); (b) VFG model of WMC; (c) VFG model of XM; and (d) VFG model of CZ (gray is C atom, red is O atom, blue is N atom, and yellow is S atom).

The functional groups in the coal structures include hydroxy (−OH), carboxyl (−COOH), ether oxygen (−C2O: contain open ether and closed ether shown in Figure S1), carbonyl (−C=O), and methyl (−CH3) groups. We have excluded carboxyl (−COOH) because it does not form when the carbon content exceeds 87%.[32] To obtain a more reasonable model and a better understanding of the above-listed functional groups’ roles in displacement mechanisms, various functional group structures (VFGs: low rank-CH3, low rank-OH, low rank-C2O, and low rank-C=O; middle rank-CH3, middle rank-OH, middle rank-C2O, and middle rank-C=O; high rank-CH3, high rank-OH, high rank-C2O, and high rank-C=O) were generated through substitutions in the substrate of various original coal structures (Oris). There are 15 molecular models in this work, and the plane macromolecular models of Oris and VFGs are shown in Figure . The amount of functional groups in Oris and VFGs are shown in Table S1, and Oris and VFGs have the same number of functional groups.

Three-Dimensional Models

All Ori and VFG models (15 molecular models: 3 Oris and 12 VFGs) were thoroughly relaxed via the following two steps. (1) Geometry optimization: In this step, the parameters during energetic optimizations are set using the conjugate gradient method in the Materials Studio 2018 Forcite module. The energy and force of convergence criteria were set as 2.0 × 10–5 kcal/mol and 0.001 kcal/mol/Å, respectively. The displacement convergence criterion was set as 2.0 × 10–5 Å, with a maximum iteration of 50,000. A smart algorithm was adopted, and the Dreiding force field was used. The electrostatic and van der Waals interactions were evaluated using the atom-based method. (2) Annealing simulation: In this step, to overcome the energy barrier, the macromolecular model was equilibrated using the Anneal Task in the Materials Studio Forcite module. The initial and intermediate temperatures were 300 and 600 K, respectively, with 10 annealing cycles in the Dreiding force field.[33] Then, the amorphous cell module was used to obtain three-dimensional (3D) models of energetically optimized configurations.[34] The final energetically optimized configurations for Oris and VFGs are shown, respectively, in Figure and Figure S2. The cell parameters of different molecular models are shown in Table S2.

Figure 2

Optimal configurations for (a) low rank-Ori, (b) middle rank-Ori, and (c) high rank-Ori after adding PBCs.

Pore Structure Models

Micropores are the main site of adsorption. When the spacing is less than 0.61 nm, the methane molecule cannot enter the adsorption site, so the methane molecules cannot be adsorbed.[35] Hence, pores of different diameters (0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, and 2.4 nm) from the macromolecular models were selected to eliminate the influence of anisotropy and heterogeneity in the coal. Pores with different configurations at each diameter were selected, and the final result calculation used average values. For example, the different pore structure configurations at 1.2 nm are shown in Figure .

Figure 3

Different pore structure configurations at a diameter of 1.2 nm.

To separate the contribution of the pore structure and functional groups and quantitatively analyze the effects of different functional groups on the adsorption capacity, we simulated the adsorption energy of CO2/CH4 in pure pores and in different pore functional groups (P-VFGs). The pore without a functional group (None) condition excludes all functional groups shown in Figure c. The P-VFGs modified the original functional groups of molecular models by substituting the functional groups with −CH3, −C2O, −OH, and −C=O. Figure shows the steps for modifying the functional groups of a 1.2 nm pore to −C=O. First, a 1.2 nm pore in the coal structure (Figure a) was chosen, and then, the functional group was replaced with −C=O (Figure b).

Figure 4

Steps to modify the varied functional groups of a 1.2 nm pore to −C=O and a pore without functional groups. (a) −Ori pore, (b) −C=O pore, and (c) None.

Implementation of the Simulation

Isothermal Adsorption of Gas

The GCMC simulation method is used herein. The GCMC calculations were conducted in the Sorption module in Materials Studio 2018 using the optimal configurations of periodic boundary cells (PBCs), as shown in Figures and S2, as adsorbents and the gaseous species as adsorbates. The adsorption isotherms and the optimal adsorption configurations for the pure gas species (CO2, CH4) and the binary mixtures onto the structures were obtained using the adsorption isotherm and fix pressure, respectively. The maximum numbers of iterations and equilibration steps were set as 50 000 and 10 000, respectively. The convergence criteria for energy and the fugacity step were 5 × 10–4 kcal/mol and 20, respectively. The Ewald sum method was used for electrostatic action with a precision of 1.03 × 10–3 kJ/mol. The Van der Waals force was calculated via the atom-based method with cubic spline truncation. The cut-off distances for electrostatic action and the Van der Waals force were both set as 12.5 Å. To ensure balance in the system, 2 × 107 GCMC steps were adopted. The first 107 steps were used to reach the balanced state, and the second 107 steps were used to calculate the system adsorption isotherms and thermodynamic factors. The force field we used was COMPASS.[16]

The ideal adsorbed solution (IAS) theory was used to predict binary adsorption isotherms from the adsorption isotherms of the pure components.[36]

For the binary adsorption of A and B, the IAS theory requireswhere x and y denote the molar fraction of small molecules in the adsorbed phase and the molar fraction of small molecules in the gas phase, respectively.

DFT Simulation

The adsorption energy and low-energy structures are calculated using the DFT-D3 correction method.[37,38] The local density approximation of Perdew and Wang[39,40] was used to describe the exchange and correlation functions. All electron double-numerical atomic orbitals augmented by d-polarization functions were chosen as the basis set with a basis file of 3.5, and the orbital cut-off quality was set at “fine”. The adsorption energy (ΔE) is defined as follows for single adsorption systems[41]where Eadsorbent+adsorbate is the total energy of the adsorption system, Eadsorbent is the molecular energy of the VFG molecule, and Eadsorbate is the energy of CO2 or CH4.

Interaction Potential

The potential energy of fluid–fluid interactions is calculated using the Lennard–Jones (L–J) potential[42,43]where rij is the separation distance between the two molecules i and j, σff is the fluid collision diameter, and εff is the depth of the interaction potential well. The parameter values are listed in Table .

Table 1

L–J 12–6 Parameters[44]

	σff (Å)	εff (K)
CH4	3.73	148
CO2	3.99	190

The potential energy of interaction between a fluid molecule and a carbon atom is calculated using the L–J potential and Coulomb terms as follows[45]where rij is the distance between two molecules i and j, σij and εij are the interaction energy parameters, and qi is the charge of the atomic species.

Local Density Distribution

The local density distribution shows, in a 3D plot, the distribution of fluids with respect to the pore wall, which helps us to understand how molecules are structured in the adsorbed layers.[46] It is defined aswhere v is the local volume of the ith fluid molecule within a distance between r and r + dr away from a molecule and Nr is the number of fluid molecules in the pore.

Langmuir–Freundlich Equation

To further understand the contribution of functional groups, the adsorption isotherms were fitted using the Langmuir–Freundlich (LF) equation,[47] which is used to indicate whether the adsorption process is homogeneous or heterogeneous.

The LF equation is given aswhere θis the amount of adsorbates, θm is the total number of binding sites, a is related to the median binding affinity constant K0 (K0 = a1/), and P is the equilibrium pressure; n is the heterogeneity index (0 < n < 1), in which 1 indicates homogeneity and 0 indicates heterogeneity.

Results and Discussion

Correlation between Functional Groups and Pore Parameters

Chemical composition is important for pore parameters.[48] To indicate the changes in the pore structure caused by functional groups, we used the Connolly surface algorithm to calculate the molecular surface and volume of coals using the Atom Volumes and Surfaces tool in Materials Studio 2018.[49] The parameters of vdWScaling, ConnollyRadius, and Max Solvent Radius in the Atom Volumes and Surfaces tool were set as 1.7, 1.65, and 2.0 Å, respectively. The inaccessible pore volume (VO), the accessible pore volume (VF), and the specific surface area (S) were calculated. Physical characterization of the microporous topology and morphology is provided in Table , and the Atom Volume Fields are shown in Figure .

Table 2

Microporous Structural Parameters Derived From the Atom Volumes and Surfaces Method for VFGs

sample	structural parameters	–Ori	–CH3	–C=O	–OH	–C2O
	VO/Å3	15237	21917	18825	15237	18094
low rank	VF/Å3	19917	28953	5928	28953	31973
	SSA/Å2	10332	12928	7930	10332	11850
	VO/Å3	18529	28946	26773	27397	27587
middle rank	VF/Å3	18200	21795	9964	29891	49191
	SSA/Å2	10846	17290	7727	12058	19183
	VO/Å3	17425	26426	26287	28329	27626
high rank	VF/Å3	20602	22515	44701	44099	45362
	SSA/Å2	9550	14099	18771	17234	20134

Figure 5

Atom Volume Fields for (a) low rank, (b) middle rank, and (c) high rank.

Overall, microporous structural distributions indicated that the sequences of VF and S are low rank < middle rank < high rank. The pore volume increases with the increasing coal rank. This is consistent with experimental results.[50] For low rank and middle rank, −C2O groups exhibit the highest VF and S, followed by −OH, −CH3, and −Ori; the VF and S of −OH and −CH3 are close to each other, and −C=O has the lowest VF and S. For high rank, functional groups more significantly influence the pore structural parameters than for low rank and middle rank: −C2O, −C=O and −OH exhibit the highest VF and S values followed by −CH3, and −Ori has the lowest. All values of VO are similar in the different functional groups and slightly higher than those of the −Ori values, demonstrating that the functional groups in coal can change the development of accessible micropores.

The increase in the number of small-molecular functional groups (C–CH3, C–OH, C–C2O, and C=O) or the increase in the diameter of aromatic cluster results in an increase in the total pore volume.[51] The number of functional groups in the VFG model is the same as the number of functional groups in the original structure, which indicates that the functional groups change the pore parameters by changing the size of the aromatic clusters. Figure shows the different values of VF and SA for VFGs and original structures. The VF and SA of C–CH3, C–OH, and C–C2O structure models increased, indicating that consistently and orderly arranged functional groups will increase the aromatic cluster diameter. However, C=O has the opposite influence on low rank, middle rank, and high rank. This is because the molecular structures of low-, middle-, and high-rank coals are different. In low- and middle-rank coals, the coal molecular structure contains more side chains, the open C=O groups are a cross-link and can impact the pore structure, and increased open C=O groups caused aromatic cluster structure compression and decreased diameter such that the pore volume decreased. However, in high-rank coals, the coal molecule is composed of aromatic structures, and an increased number of close C=O groups could increase the aromatic cluster diameters, so the pore volume increased.

Figure 6

Different values for (a) VF and (b) S of VFGs and Oris.

Contribution of Functional Groups to Adsorption

Functional groups can affect gas adsorption through changing pore parameters and their own polarity and acidity. The higher the micropore content, the stronger the adsorption capacity.[50] The C atom in CH4 is negatively charged, and CH4 is a nonpolar and neutral molecule; in contrast, CO2 is positively charged and has a greater quadrupole moment and acidity. Therefore, it can be inferred that CO2 is strongly adsorbed on basic and polar groups. The basicity (−C2O > C=O > −CH3 > −OH) and polarity (−OH > C=O > −C2O > −CH3) of functional groups determine the adsorption strength of CO2 and CH4.[52] To better explain the role of different functional groups on CO2/CH4 adsorption and selectivity, we used GCMC simulation to simulate the adsorption capacity in VFGs and V-Ori models.

Pure Adsorption

Figure a–f shows the adsorption amounts for pure CO2 and CH4 at 298 K. Different functional groups have significant influences on adsorption. The change trends of CO2 and CH4 are consistent, but the amplitude increases of CO2 are higher than those of CH4. Increasing the oxygen-containing functional group content will increase the chemical inertia of CH4 and increase the negative charge on the surface of coal; thus, oxygen-containing functional groups reduce the effective adsorption potential of CH4 molecules but increase the adsorption potential of CO2. Thus, oxygen-containing functional groups have a stronger adsorption capacity for CO2.

Figure 7

Adsorption amounts of pure gas (a,c,e) CH4 and (b,d,f) CO2 onto VFG and Ori models at 298 K.

The maximum adsorption amounts of CO2 and CH4 both follow the sequences of low-rank C2O > low-rank OH > low-rank Ori > low-rank CH3 > low-rank C=O; middle-rank C2O > middle-rank OH > middle-rank Ori > middle-rank CH3 >middle-rank C=O; high-rank C2O > high-rank C=O > high-rank OH > high-rank CH3 > high-rank Ori at the same pressure and temperature. The sequence of adsorption capacity is positively correlated with the micropore volume, as shown in section . Comparing adsorption with the VF and SA of the VFGs, low-rank and middle-rank −C2O and −OH, with higher VF and SA than −Ori, correspond to greater adsorption amounts of CO2/CH4. In contrast, the VF and SA of −C=O are smaller than those of −Ori and have an inhibiting effect on adsorption. For high rank, all functional groups improved the VF and SA; hence, the adsorption amounts of VFGs are all greater than those of high rank-Ori. The VF and SA of high rank-C2O, high rank-C=O, and high rank-OH are similar, but the adsorption capacity order is high rank-C2O > high rank-C=O > high rank-OH, corresponding to the basicity (−C2O > −C=O > −CH3 > −OH) of the functional groups. This suggests that the impact on CO2/CH4 adsorption capacity are pore diameter > basicity > polarity. When the pore diameters are similar, the basicity sequence is followed and the effect of polarity is weak.

This result is consistent with the results of the experiment. Liu et al.[53] showed that the narrow micropores can significantly and effectively increase the CO2 adsorption capacity, while the functional groups do not matter. Hao et al.[54] found a positive correlation between the methane-saturated adsorption capacity and the micropore volume of coals; when the microporosity parameters of two samples were similar, the CH4 adsorption capacity was determined by the coal surface chemistry.

The fitting process was conducted in Origin 2018 software using the LangmuirEXT1 method. The LF constants obtained are listed in Table S3. To ensure the positive parameters, R2 was higher than 0.95. When comparing the values of the parameters of LF sorption isotherms, the coefficients θm have the same order as the pure gas adsorption amounts, as shown in Figure . The values of θm for CO2 are larger than those for CH4, indicating that coal can provide more binding sites for CO2. However, the order of values for n is contrary to those of pure adsorption capacity, indicating that the adsorbed CO2 can increase coal heterogeneity.

Competitive Adsorption

Figure depicts the variations of competitive adsorption values (SCO2/CH4) for low rank, middle rank, and high rank at 298 K. Values of SCO2/CH4 are all apparently greater than 1.0, demonstrating the effectiveness of direct replacement of preadsorbed CH4 by injecting CO2. The values of SCO2/CH4 in different coal ranks range between 1.2 and 6.3. The calculated results agree with the experimental results.[55,56] These results show that the simulation methods used herein are reliable.

Figure 8

Adsorption selectivity of CO2 over CH4 for (a) low rank and low-rank VFGs, (b) middle rank and middle-rank VFGs, and (c) high rank and high-rank VFGs at 298 K.

Figure a gives the results of selectivity (SCO2/CH4) on low rank. When pressure is <4 MPa, the sequence is low-rank C=O > low rank-OH > low-rank C2O > low-rank Ori > low-rank CH3. When pressure is >4 MPa, the sequence is low-rank C=O > low-rank OH > low-rank Ori > low-rank C2O > low-rank CH3. Figure b gives the results of middle rank; at low pressure (<3 MPa), the sequence is middle-rank C=O > middle-rank OH > middle-rank CH3 > middle-rank C2O > middle-rank Ori; when the pressure >3 MPa, the sequence is middle-rank C=O > middle-rank CH3 > middle-rank C2O > middle-rank OH > middle-rank Ori. Figure c gives the results of the high rank; the sequence is high-rank C=O > high-rank OH > high-rank C2O > high-rank CH3 > high-rank Ori, and pressure has no effect on the order.

The principle of competitive adsorption is that CO2 occupies the adsorption position of CH4. The greater the difference in the total number of binding sites (θm) for CO2 and CH4, the stronger the competitive adsorption of CO2. The −C=O groups have a greater difference of θm as calculated in Section and listed in Table S1; therefore, the VFGs with −C=O have the largest values of S(CO2/CH4).

Overall, the competitive adsorption capacity is influenced by rank, pressure, binding site (θm) values, and pore diameter. Thus, conclusions about influencing factors for competitive adsorption are inconsistent. Du et al.[56] stated that SCO2/CH4 increased with increasing coal rank, and high-rank coal is conducive to the adsorption of CO2. This opinion is identical to that of Yu et al.,[57] and Liu et al.[58] found that the sequence of SCO2/CH4 is anthracite > bituminous > lignite. However, Merkel et al.[22] discovered that in the process of transforming subbituminous coal to anthracite, SCO2/CH4 declines. Therefore, the effects of pore diameter and functional groups on the competitive adsorption of CO2 and CH4 need to be further investigated.

Effects of Pore Structure and Functional Groups on Adsorption Energy and Adsorption Heat

Adsorption Energy

The ΔE of CO2/CH4 for the pure pore and P-VFGs was calculated using the DFT-D3 method using eq . For DFT calculations, the systems are studied by pores with different functional groups. The diameters of P-VFGs were divided into six categories: 0.6, 0.8, 1.0, 1.2, 1.4, and 2.0 nm. Figure shows the pore diameter of 1.2 nm with different functional groups. In order to calculate the contributions of the pore structure and the functional groups of CO2/CH4, only one CO2/CH4 molecule in DFT calculation systems was used. The ΔEs of CO2 and CH4 with pores without functional groups (None) and P-VFGs are shown in Tables and 4, respectively. For DFT calculations, the systems are studied by pore with different functional groups. Figure shows the pore diameter of 1.2 nm with different functional groups. In order to calculate the contributions of the pore structure and the functional groups of CO2/CH4, only a CO2/CH4 molecular in DFT calculation systems was used.

Table 3

Adsorption Energy of CO2 in P-VFGs (kJ)

pore size (nm)	ori	=O	–OH	–C2O	–CH3	none
0.6	–60.53	–69.48	–45.83	–74.43	–60.39	–43.64
0.8	–60.39	–73.32	–43.80	–72.52	–59.93	–42.15
1.0	–54.65	–65.58	–42.34	–67.45	–55.26	–38.91
1.2	–46.77	–50.38	–39.38	–60.75	–52.57	–32.83
1.4	–40.52	–47.12	–36.76	–50.94	–49.49	–29.13
2.0	–39.64	–45.92	–30.15	–42.28	–40.23	–27.66

Table 4

Adsorption Energy of CH4 in P-VFGs (kJ)

pore size (nm)	ori	=O	–OH	–C2O	–CH3	none
0.6	–44.76	–33.67	–45.17	–41.27	–45.51	–32.37
0.8	–46.25	–38.24	–49.29	–44.77	–48.12	–33.42
1.0	–41.49	–33.32	–43.87	–38.69	–40.08	–37.61
1.2	–38.54	–31.90	–39.75	–34.89	–35.45	–31.41
1.4	–23.23	–18.30	–23.88	–19.78	–19.61	–28.71
2.0	–20.56	–13.84	–17.23	–16.12	–18.20	–13.15

For the same None and P-VFG models, the ΔE values for CO2 (−30.15 to −74.43 kcal/mol) are higher than those for CH4 (−13.84 to −49.29 kcal/mol), indicating that CO2 interacts with pure pore and P-VFGs more strongly than CH4. For CO2, the sequence of ΔEs is 0.6 > 0.8 > 1.0 > 1.2 > 1.4 > 2.0 nm. For CH4, the sequence of ΔEs is 0.8 > 0.6 ≈ 1.0 > 1.2 > 1.4 > 2.0 nm. When the pore diameters are >1.0 nm, the ΔEs exhibited a declining trend. These results are consistent with experimental results, which have shown that CO2 tends to adsorb in 0.6 nm pores and CH4 tends to adsorb in 0.8 nm pores.[59]

For the same pore diameter, the sequences of functional group ΔE values for CO2 and CH4 are −C2O > −C=O > −CH3 > −Ori > −OH and −OH > −CH3 > −Ori> −C2O > −C=O, respectively. The variations of ΔE values for the same pore diameters of CO2 and CH4 are caused by their polarity and basicity. The electropositive C atoms of CO2 have a strong electrostatic attraction for the O atoms in the functional groups, and CO2 is an acidic molecule that can react with basic groups. In contrast, the C atom in CH4 is electronegative and CH4 is a neutral molecule, weakening its interactions with the P-VFGs.

Compared with the ΔEs of None and −Ori pores, note that the functional groups enhance the adsorption energy, which is attributed to the functional groups providing a stronger electrostatic interaction of the carbon surface with CO2/CH4 molecules. For instance, the CO2 ΔE of a pure pore is −43.64 kJ at 0.8 nm; however, the ΔE of −Ori is −60.39 kJ. By comparing the adsorption energy of the Ori-containing functional groups and modified pores None, we can roughly estimate that the contributions of the pore structure and the functional groups of CO2 are 71 and 29%, respectively. Similarly, the contributions of the pore structure and the functional groups of CH4 are 83 and 17%, respectively. The effect of functional groups on CO2 was greater than that on CH4.

In recent years, many researchers have used physical and chemical methods to treat porous materials to change their functional groups. Ma et al.[60] researched that the CO2 capture may depend on the functional groups in porous carbon materials, and the adsorption amount of CO2 is relative to the oxygen content. Fu et al.[61] found that reducing the total amount of primary oxygenic groups including C–O, C =O, and −COOH decreased the maximum CH4 adsorption capability on all coals by 2.50–18.18%. These studies show that the adsorption capacity of CO2/CH4 is relative to the enhanced oxygen functional groups. It is basically consistent with our conclusions.

Adsorption Heat

Table and Table show the adsorption heat of CO2/CH4. The variation characteristics of adsorption heat are similar to that of adsorption energy. The adsorption heat of the same amount conforms to CO2>CH4. The adsorption heat of CH4 is much less than 42 kJ/mol which belongs to physical adsorption. The adsorption heat of CO2 in 0.6/0.8 nm size with—=O/–C2O is higher than 42 kJ/mol. It shows that there may be chemical adsorption between CO2 and coal. So, the adsorption energy of 0.6/0.8 nm size with—=O/–C2O is greater.

Table 5

Adsorption Energy of CO2 in P-VFGs (kJ/mol)

pore size (nm)	ori	=O	–OH	–C2O	–CH3	none
0.6	–38.94	–50.51	–45.83	–52.26	–39.58	–30.46
0.8	–39.81	–46.75	–43.80	–47.04	–40.12	–32.98
1.0	–37.32	–40.11	–42.34	–41.92	–38.03	–31.32
1.2	–33.13	–38.84	–39.38	–35.34	–34.37	–28.64
1.4	–31.53	–34.72	–36.76	–33.61	–32.32	–22.56
2.0	–31.02	–34.19	–30.15	–33.36	–32.87	–22.45

Table 6

Adsorption Energy of CH4 in P-VFGs (kJ/mol)

pore size (nm)	ori	=O	–OH	–C2O	–CH3	none
0.6	22.25	20.57	24.72	21.53	24.54	16.22
0.8	23.68	19.24	29.19	20.84	28.65	19.31
1.0	19.97	18.48	24.34	18.62	23.84	16.12
1.2	17.12	16.35	22.13	17.58	21.73	13.25
1.4	16.31	13.81	19.32	14.71	19.11	11.98
2.0	16.08	13.33	19.46	14.23	19.09	11.21

Potential Field Distribution

To further quantitatively analyze the effect of pore diameter on adsorption and the number of adsorption layers on adsorption, the pore models of various diameters built in Section were used to simulate the density of CO2/CH4, interaction energy, and interaction potential distributions of coal and CO2/CH4.

Figure shows the interaction energy between pores and CO2/CH4. The interaction energy increases first and then decreases, with increasing pore diameter. When the diameter is greater than 1.2 nm and less than 2.0 nm, the interaction potential field of CH4 shows obvious intersection with each other, which means that pores in this range may generate multilayer adsorption. The intersection diameters for CO2 range from 1.2 to 2.2 nm. Additionally, multilayer adsorption is caused by the van der Waals attraction exerted by the first layer of high-density gas. Multilayer adsorption is the foundation of micropore filling.[62−65]

Figure 9

Interaction energy between pores with various diameters and gas molecules for (a) CH4 and (b) CO2.

The potential well in the interaction potential distribution curve is where CO2/CH4 may be adsorbed, and the peak in the density profile indicates that CO2/CH4 may form an adsorption layer.[35] Based on these findings, the interaction potential distribution curves and the density profiles of CO2/CH4 in the micropore structures were compared, as shown in Figure . With increasing pore diameters, the depth of the potential well and the main density peak both decrease, implying that the interaction of the wall with CO2/CH4 decreases and confirming that CO2/CH4 is mainly adsorbed in pores with diameters <2 nm. Furthermore, two peaks emerged in the density profile. The primary peak indicates the first absorbed layer close to the pore wall; after the first layer of gas is adsorbed and equilibrated, a significant secondary peak appeared. Both the density peaks correspond well to the main peak of the interaction potential. Thus, when the diameter of micropores is 1.0–2.0 nm for CH4 and 1.0–2.2 nm for CO2, multilayer adsorption (micropore filling) occurs.

Figure 10

Comparison of interaction potential distribution curves and density profiles for (a) CH4 and (b) CO2.

Many researchers used a slit shape pore without functional groups to study the microscopic mechanism of gases adsorption. Li et al.[66] found that as the breadth of the slit increased, the amount of adsorption decreased. Liu and Hou[67] show that the density in the center of 1 nm pore is generally higher than that of the 3 nm pore. Multilayer adsorption comes into being in the 1 nm pore by CO2/CH4 molecules. Long et al.[68] found that the tight adsorption amounts and adsorption heats decreased with increasing pore size. This is similar to our results, and the adsorption capacity decreases with the increase of pore size.

The selectivity of CO2 over CH4 indicates that CO2 forms multiple layers more easily than CH4 because the adsorption energy of CH4 is weaker. Thus, the higher the distribution of 0.8–2.0 nm pores, the more favorable the competitive adsorption of CO2. Competitive adsorption is not only affected by the micropore volume but also affected by the micropore size distribution. Li et al.[69] discovered that the higher the proportion of the micropore (>1 nm), the higher the SCO2/CH4 values by experiment.

Conclusions

Herein, we combined the GCMC simulation, DFT, and interaction potential field to study the CO2/CH4 adsorption in coal pores and functional groups. The conclusions are as follows.

Correlations between functional groups and pore parameters are affected by the coal rank. The consistent and ordered arrangement of −CH3, −OH, −C2O, and −C=O will increase the accessible pore volume (VF) and the specific surface area (SA), except in low-rank and middle-rank coals, where the ordered arrangement of −C=O will decrease VF and S.

For pure adsorption, pore parameters exert greater influence on the adsorption of CO2 and CH4 than functional groups. By comparing the adsorption energy of the original pore structure containing functional groups and the modified pores without functional groups, the contributions of the pore structure and original functional groups are 71 and 29% and 83 and 17%, respectively, for CO2/CH4 adsorption. The greater the micropore volume, the stronger the adsorption capacity, and with increasing pore diameters, the adsorption capacity decreases.

For competitive adsorption, the −C=O functional groups and pore diameters ranging from 1.2 to 2.0 nm significantly enhance the selectivity of CO2 over CH4. Competitive adsorption is not only affected by the micropore volume but also by the micropore size distribution.

Monolayer adsorption is the main occurrence form of methane and carbon dioxide. Multilayer adsorption can occur for CH4 at diameters of 1.2–2.0 nm and for CO2 at diameters of 1.2–2.2 nm through the intersection of interaction energy. Multilayer adsorption is the foundation of micropore filling. The higher the distribution of 0.8–2.0 nm pores, the more favorable the competitive adsorption of CO2.