Adsorption properties of CH₄ and CO₂ in quartz nanopores studied by molecular simulation

Abstract

In this work, grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulation methods were used to study the adsorption properties of CH₄ and CO₂ as single components and binary mixtures in modeled quartz nanopores (d ∼ 2 nm), of which the surface was hydroxylated to different degrees. The variation of the adsorption and molecular diffusion characteristics of CH₄ and CO₂ as a function of temperature and pressure were determined, and the competitive adsorption of CH₄ and CO₂ was investigated. As single components, both the adsorption of CH₄ and CO₂ in the nanopore is described well by the Langmuir model, and the diffusion capacities of the gas molecules in a non-supercritical state are much larger than that in a supercritical state. It was found that there is a tight adsorption layer of CH₄ with a thickness of 3–5 Å in the nanopore, while CO₂ molecules adsorb tightly as a whole phase, especially in the supercritical fluid state. In the binary mixed system, CO₂ preferentially adsorbs to the nanopore surface compared to CH₄ due to the strong interactions between the CO₂ molecule and the hydrophilic groups on the pore surface. An obvious competitive adsorption of CO₂ and CH₄ occurs at certain temperature ranges (313–353 K) with increasing pressure. And the degree of surface hydroxylation has significant contributions to the adsorption selectivity of CO₂ over CH₄. This work provides microscopic information about adsorption properties of CH₄ and CO₂ in nanopores at the molecular level for the purpose of guidance towards the application of shale gas extraction by flowing CO₂.

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1. Introduction

CH₄ is a kind of typical clean fossil fuel with the advantages of high energy efficiency and large reserves, which is the main component of emerging unconventional resources for shale gas.^1–4 Much research has confirmed that CO₂ is adsorbed preferentially over CH₄ onto the organic/mineral surface in gas shale and could displace methane. Enhanced gas recovery (EGR) using CO₂ (CO₂-EGR) is recognized as one remarkable technique for a combined carbon sequestration and shale gas production strategy.^5–9

According to the references in the literature, nano-scale pores constitute up to 80% of the total effective porosity in gas shale, they are classified into three types by the pore diameter, micropore (d < 2 nm), mesopore (d = 2–50 nm) and macropore (d > 50 nm).^2,10,11 The adsorption properties of CH₄ in nanopores have significant contributions to shale gas extraction. The competitive adsorption of CH₄ and CO₂ in nanopores is a key factor in elucidating CO₂-EGR processes that play a considerable role in not only the displacement of CH₄ with CO₂ injection, but also storage of CO₂ trapped inside the gas shale pore, which would both be undoubtedly influenced by wettability and capillary effects. Many conventional experimental methods, including mercury injection, low-pressure gas adsorption, and nuclear magnetic resonance have been used to yield information about shale pores and the adsorption capacity of gases in shale.^12–14 It has to be stated that the complicated composition and pore structures of real shale makes finding the specific micro adsorption characteristics of the gases in shale difficult, let alone definitively revealing the microscopic mechanism. Investigations of the properties of gas molecules in the nanopores at the molecular level, particularly the effect of pore size and composition on the adsorption and desorption behavior of gases, is significant while still unclear.

Preferable adsorption of the injected gas onto the organic matter is considered to be the primary mechanism for the displacement of methane and CO₂ trapping. Actually, the organic carbon content in gas shale ranges from less than 1% to as high as 25% (in some organic-rich beds).^15–18 While the inorganic mineral portion of the shale, such as quartz, calcite, clay minerals, and muscovite mica account for a large proportion,^2,4,19 according to literature reports, the content of quartz could be as high as 87% in shale from the Qaidam Basin in China;² hence, studies about the adsorption of CO₂ and CH₄ in a quartz nanopore is meaningful.

In the last decade, studies about the adsorption and diffusion capacities of CH₄ and CO₂ in nanoporous materials like zeolites and metal organic frameworks (MOFs) have been extensively reported.^20–22 Molecular simulation approach were shown to be capable of describing the adsorption capacities of various gases in different nanoporous materials and had provided guidance on the design and application of nanoporous materials for zeolites and MOFs.^23–29

In this study, models of quartz nanopores that imitate the layer condition with different hydroxylation surfaces were constructed. The adsorption and motion behavior of pure, and binary mixed, CH₄ and CO₂ were investigated by the grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulation methods (GCMC/MD). Adsorption capacities of pure CH₄ and CO₂ along with the competitive adsorption of binary mixed CH₄/CO₂ were studied. How the adsorption capacity can be affected by the hydrophilic/hydrophobic properties of the nanopore surface was also discussed.

2. Models and methodology

2.1 Modeling of quartz nanopores and surfaces

The model of a quartz nanopore with a diameter of ∼2 nm and a depth of 2.16 nm was constructed in a similar manner to previous publications,^30–32 digging a cylindrical hole in an α-quartz block (51.1 × 49.1 × 21.6 Å), all the atoms lying along the z axis with the diameter of ∼2 nm were removed (Fig. 1a). Nanopores with different active surfaces were obtained by adjusting the amount of hydroxyl and methyl groups added to unsaturated Si bond on the pore surface (Fig. 1b). The nanopore surface, which was fully hydroxylated with silanol groups with a coverage fraction of 8–9 hydroxyls per nm², and the surface hydrophobicity were adjusted by replacing the hydroxyl groups with methyl groups. The whole sorbent, including the quartz block and the pore surface groups, were regarded as rigid during the entire simulation. The charges of atoms were calculated by the electrostatic potential (ESP) fitting method.²⁵ For the SiOH group, the charges of Si, O and H atoms were q_Si–SiOH = 0.8025e, q_O–SiOH = −0.4725e and q_H–SiOH = 0.25e, respectively. For SiCH₃ group, the charge of the Si atom is the same as q_Si–SiOH. Charges of C and H atoms were q_C–SiCH3 = −0.294e and q_H–SiCH3 = 0.053e, respectively. For the sorbate, CO₂ (ref. 33) was present as a three-site rigid molecule with the charges of C and O atoms at q_C = 0.576e and q_O = −0.288e, respectively, the bond length of C–O was 1.18 Å and the bond angle ∠OCO was 180°. The CH₄ (ref. 34) molecule was present as a five-site rigid model with the charges of C and H atoms at q_C = −0.66e and q_H = 0.165e, respectively, and the C–H bond length was 1.09 Å.

Fig. 1 Models of a quartz nanopore with a three dimensional structure and surface landscape (in blue) (a) and the detailed structures of the hydrophilic–hydrophobic surface (b). Atoms: O in red, C in grey, H in white and Si in yellow.

2.2 Computer simulation details

According to literature, Dreiding³⁵ and UFF³⁶ force fields, as well as the COMPASS force field,^38–42 are often used in simulation studies related to gas adsorption in nanoporous zeolites and MOFs to produce mechanism verification of adsorption.^{23,25–27,37} No unique method or force field is assigned to definitely determine the parameters used in computer simulations. In consideration of the actual complex layer condition, which is different from gas adsorption in specific crystal structures, the whole simulation was presented by the general COMPASS force field to produce the CH₄ and CO₂ adsorption properties and the Materials Studio (MS) software package was used. The Lennard-Jones 9-6 potential was introduced to describe the van der Waals (vdW) term, the coulombic function was used to demonstrate the electrostatic interactions.

The adsorption processes of CH₄ and CO₂ in nanopores were performed by the grand canonical Monte Carlo (GCMC) method using the sorption module of MS. The vdW interactions were performed by the atom based summation method, while the electrostatic interactions based on coulombic function were summed by the Ewald method with an accuracy of 10⁻⁴ kcal mol⁻¹. Performances of adsorption simulations were obtained after an equilibration process of 5 × 10⁶ steps and a calculation process of 5 × 10⁶ steps at a certain pressure ranging from 10 kPa to 20 MPa at different temperatures.

The motion and diffusion properties of the adsorbed gases in nanopores were carried out by molecular dynamics (MD) simulations. The NPT (isothermal and isobaric) ensemble was used to perform the MD simulation with a time step of 1 fs in a run time of 5.0 ns. The Nose and Berendsen algorithm was selected for the temperature thermostat and pressure barostat, respectively. The mean square displacement (MSD) method was introduced to describe the motion properties of gas molecules in the nanopores.

3. Results and discussion

3.1 Adsorption and diffusion properties of pure CH₄ in a quartz nanopore

The adsorption capacity of pure CH₄ in a nanopore over diverse temperatures is shown in Fig. 2, which is in good agreement with the Langmuir isotherm model of single components and is described by the follow equation:where V_L and b correspond to the Langmuir constants of the pure gas and P is the equilibrium pressure of the pure component. The Langmuir constants of pure CH₄ in a quartz nanopore are shown in Table S1,† of which all correlation coefficients (R²) are larger than 0.999. The extended Langmuir (EL) model and the ideal adsorbed solution (IAS) theory are commonly used to perform the predication of gas adsorption in mixtures. Recent studies showed that, in some cases, the adsorption of CH₄ in coal steam and nanoporous shale could be described by the Langmuir model, which is appropriate considering the nanopore size and the weak vdW interactions between the CH₄ molecules and the surface groups of the pore.^43,44

Fig. 2 Adsorption isotherms (solid line) and the fitted Langmuir isotherm model (open symbol) of pure CH₄ in a quartz nanopore with 100% surface hydroxylation at various temperatures.

The adsorption density distributions of pure CH₄ in a quartz nanopore under different pressures are shown in Fig. 3. We can clearly see that the CH₄ molecules adsorb to the surface of the nanopore preferentially. The thickness of the adsorption layer of CH₄ with increasing pressure at 323 K is shown in Fig. 4, the tightly adsorbed layer of CH₄ on the nanopore surface is approximately one molecule-layer thick (3–5 Å), and about 70–80% of the adsorbed CH₄ molecules are located in the tightly adsorbed layer, while the others located outside the layer were non-tightly adsorbed, which might be due to the limit of the nanopore size and the steric hindrance effect of the tightly adsorbed CH₄ molecules.

Fig. 3 Density distribution of pure CH₄ in a quartz nanopore with 100% surface hydroxylation at pressures of 4 MPa (a), 8 MPa (b), 15 MPa (c) and 20 MPa (d), T = 323 K.

Fig. 4 Images of the equilibration state of CH₄ molecules adsorbed in a quartz nanopore with 100% surface hydroxylation at pressures of 4 MPa (a), 10 MPa (b), 15 MPa (c) and 20 MPa (d), T = 323 K; CH₄ molecules in green refer to the tightly adsorbed portions.

The diffusion capacities of CH₄ molecules in the nanopore were calculated by MSD and diffusion coefficient (D) with the follow equations:

where N is the number of same type particles and r_i(t) is the particle position at time t. CH₄ molecules located at different positions inside the nanopore are marked to calculate the MSD. Fig. 5 shows that the diffusion capacity of CH₄ in a non-supercritical state (Fig. 5a) is much larger than that at a supercritical state (Fig. 5b), which indicates that CH₄ adsorbs more tightly in the nanopores in a supercritical state. The MSD of CH₄ molecules close to the pore surface is low compared with those located far away from the pore surface, either as a free gas or in a supercritical state. The tightly adsorbed layer formed by these CH₄ molecules close to the pore surface might have the isolation effect, thus explaining why the CH₄ molecules beyond the tightly adsorbed layer were not trapped tightly, and the adsorption amount would not constantly increase. These results match well with research on the adsorption tendency of CH₄ in silica nanoporous materials^45–47 and the motion properties of shorter train n-alkanes in a nanoporous silica medium.⁴⁸

Fig. 5 Variation of MSDs of CH₄ molecules adsorbed in various locations inside the nanopore versus simulation time at pressures of 4 MPa (a) and 10 MPa (b), T = 323 K.

3.2 Adsorption and diffusion properties of pure CO₂ in a quartz nanopore

The adsorption capacity of pure CO₂ in a nanopore at various temperatures is shown in Fig. 6, which matches well with the Langmuir model described by eqn (1). The Langmuir constants of pure CO₂ in a quartz nanopore are shown in Table S2† with all correlation coefficients (R²) larger than 0.99. This is consistent with the results of a recent experimental study about the adsorption properties of CO₂ in shale from Longmaxi Fm, China.⁴⁹ From Fig. 6, we can observe that the adsorbance of CO₂ inside the quartz nanopore rapidly attains saturation as the pressure increases to 7.4 MPa (approximately the critical pressure of CO₂) and then slightly increases with further pressure increase (7.4–20 MPa), indicating that the adsorption loading of CO₂ hardly increases as the pressure increases to a supercritical state.

Fig. 6 Adsorption isotherms (solid line) and the fitted Langmuir model isotherms (open symbol) of pure CO₂ in a quartz nanopore with 100% surface hydroxylation at various temperatures.

The density distribution of pure CO₂ inside the nanopore (Fig. 7) shows that CO₂ molecules also preferentially adsorb on the surface of the nanopore. In contrast to CH₄ molecules, which form a tightly adsorbed layer close to the pore surface, layered adsorbance of CO₂ in the quartz nanopore only occurs at pressures lower than 7 MPa, beyond that the CO₂ molecules fill in the quartz nanopore as a whole phase under supercritical conditions. This not only attributes to the strong interactions between the CO₂ molecules and the hydroxyl groups on the surface of the nanopore but also the interactions between CO₂ molecules (Fig. 8).

Fig. 7 Density distribution of pure CO₂ in a quartz nanopore with 100% surface hydroxylation at pressures of 3 MPa (a), 6 MPa (b), 14 MPa (c) and 20 MPa (d), T = 323 K.

Fig. 8 Images of the equilibration state of CO₂ molecules adsorbed in a quartz nanopore with 100% surface hydroxylation at pressures of 3 MPa (a), 6 MPa (b) and 10 MPa (c), T = 323 K.

The MSDs of the CO₂ molecules located in different positions inside the nanopore are calculated and shown in Fig. 9. It can be seen that the diffusion capacity of CO₂ in a quartz nanopore at non-supercritical state (Fig. 9a) is much larger than that at a supercritical state (Fig. 9b), and the adsorption of CO₂ as a supercritical fluid in the nanopore is very tight. Comparing with CH₄, the MSDs of CO₂ are lower, whether in a non-supercritical or supercritical state, which corresponds to the strong interactions between the CO₂ molecules and the hydroxyl groups on the nanopore surface. At pressures higher than the critical pressure, the MSDs of CO₂ molecules located at different positions in the nanopore are similar and small. This indicates that the CO₂ molecules at a supercritical state fill into the nanopore as a whole phase.

Fig. 9 Variation of MSDs of CO₂ molecules in various adsorbed locations inside the nanopore versus simulation time at pressures of 6 MPa (a) and 10 MPa (b), T = 323 K.

3.3 Adsorption properties of binary mixed CH₄ and CO₂ in a quartz nanopore

The adsorption isotherms of CH₄ and CO₂ in a mixture in a nanopore are shown in Fig. 10. In contrast to the adsorption isotherm of pure CH₄, two adsorption stages emerge for CH₄ in a mixture at temperature T < 353 K (Fig. 10a). At the beginning, the adsorption loading of CH₄ rapidly reaches a nearly saturated state at low pressures (10 kPa to 4.6 MPa), after that, the adsorption loading has a slight increase followed by decreases with further increases in pressure. Simultaneously, the adsorption loading of CO₂ (Fig. 10b) increases continuously, indicating that competitive adsorption is obviously occurring in the binary mixed CH₄/CO₂.

Fig. 10 Adsorption isotherms of binary mixed CH₄ (a) and CO₂ (b) in a quartz nanopore with 100% surface hydroxylation at various temperatures.

The selectivity parameter S is used to describe the competitive adsorption capacity of CH₄ and CO₂ in the mixture, which is defined by the following equation:

where x is the fraction of gas component in the adsorbed phase and y is the fraction of gas component in the bulk phase. As shown in Fig. 11, in the inspected temperature range (313–373 K) and pressure range (10–20 000 kPa), the S_CO2/CH4 is always larger than 4 and increases as the temperature decreases, which is mainly attributed to strong interactions between CO₂ molecules and hydroxyl groups on the surface of the pore when compared with CH₄. The diversity of the interactions between CO₂, CH₄ molecules and the sorbent atoms might recede at high temperatures.

Fig. 11 Selectivity of CO₂ over CH₄ in the nanopore with 100% surface hydroxylation at various temperatures.

3.4 Effect of the degree of quartz nanopore surface hydroxylation on the adsorption properties of CH₄ and CO₂

The adsorption isotherms of pure CH₄, CO₂ and the binary mixtures of CH₄ and CO₂ in nanopores with different degrees of surface hydroxylation at 323 K are shown in Fig. 12. It was found that the adsorption amount of CH₄ increases with increasing surface hydrophobicity while the adsorption amount of CO₂ is opposite. This indicates that the methyl groups on the surface significantly enhance the adsorption of CH₄ while adversely affecting CO₂ molecules. Because the hydroxyl groups have polar interactions with CO₂ molecules, the increase of the hydrophilicity of the sorbent surface promotes the preferable adsorption of CO₂ molecules compared with CH₄. So the selectivity of CO₂ over CH₄ decreases with increasing surface hydrophobicity and the competitive adsorption of CO₂/CH₄ is weakened with increasing nanopore surface hydrophobicity at 323 K, as shown in Table 1.

Fig. 12 Adsorption isotherms of pure CH₄ (a), CO₂ (b) and the binary mixtures of CH₄ (c) and CO₂ (d) in nanopores with different degrees of surface hydroxylation at 323 K.

Table 1 Selectivity of CO₂ over CH₄ versus the degree of surface hydroxylation at various pressures at 323 K

Pressure (kPa)	Selectivity of CO2 over CH4
	60% hydroxylation	30% hydroxylation	100% methylation
500	4.86	2.64	1.45
1200	4.37	2.46	1.59
3000	4.22	2.99	2.09
5000	4.58	3.15	2.37
8000	5.49	4.04	2.54
13 000	6.37	5.94	4.03
20 000	11.18	5.65	4.55

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The adsorption density distribution of binary mixed CH₄ and CO₂ in quartz nanopores with diverse hydroxylation surfaces are shown in Fig. 13. In order to show the adsorption position clearly for CH₄ and CO₂ separately, the orders of magnitudes of the CH₄ and CO₂ are different. It could be found that in Fig. 13a–c, CH₄ molecules preferentially adsorb onto the methyl sites while CO₂ molecules adsorb onto the hydroxyl sites preferentially, which is mainly attributed to the interaction strength between CO₂ and CH₄ molecules and the surface functional groups mentioned above. This demonstrates that the hydrophilicity of the nanopore surface has significant contributions to the adsorption of CO₂ while the increase of hydrophobicity benefits the adsorption of CH₄.

Fig. 13 Adsorption density distribution of a CH₄ and CO₂ mixture adsorbed in nanopores with 100% (a), 60% (b), 30% (c) surface hydroxylation and 100% surface methylation (d), at 323 K and 10 MPa. Color of density: green is CH₄; red is CO₂. Note that the densities in (a)–(d) are different orders of magnitude.

4. Conclusion

In this study, the adsorption properties of pure and binary mixed CH₄ and CO₂ in mimetic models of quartz shale nanopores with different hydrophilic/hydrophobic surface were investigated. For pure components, both the adsorption of CH₄ and CO₂ could be described using Langmuir isotherms and the diffusion capacities of the pure component at non-supercritical states is much larger than at supercritical states. A tightly adsorbed layer of CH₄ molecules with an approximate thickness of 3–5 Å is observed while CO₂ molecules are trapped inside the nanopore as a whole phase more tightly compared with CH₄ at supercritical states. This is attributed to the strong interactions between CO₂ molecules and also CO₂ molecules with nanopore surface hydroxyl groups.

For the binary mixed CH₄/CO₂ system, an obvious competitive adsorption occurs in the researched temperature range T < 373 K, and the S_CO2/CH4 increases when the pressure is larger than the critical pressure of CH₄ because the coulombic and hydrogen bonding interactions between CO₂ molecules and the hydroxyl groups on the pore surface are stronger than CH₄.

It was also found that the hydrophilic/hydrophobic properties of the nanopore surface has a significant effect on the adsorption of gases. The CO₂ molecules prefer to adsorb near hydroxyl groups due to polar interactions while CH₄ molecules adsorb near methyl sites preferentially. Hydrophilicity of the nanopore surface has significant contributions to the adsorption of CO₂ molecules and increases in hydrophobicity benefits the adsorption of CH₄.

According to the investigation results of the paper, the adsorption properties of CH₄ and CO₂ into a quartz nanopore in a certain temperature and pressure range are revealed. The competitive adsorption of CH₄/CO₂ was discovered by simulations at the molecular level. This can be very helpful for better understanding the microscopic adsorption states of gas component molecules in shale, and might provide guidance in shale gas extraction.

Conflict of interest

The authors declare no competing financial interests.

Acknowledgements

The funding of National Science Fund of China (No. 21473103 and 61575109) are gratefully acknowledged.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra05083b

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