First-principles calculation of adsorption of shale gas on CaCO3 (100) surfaces

Computational methods

Based on the first-principle method of DFT (28, 29), the ground state geometries and electronic properties of CH₄, C₂H₆, CO₂ and N₂ molecules adsorbed on CaCO₃ (100) were calculated using the Cambridge Sequential Total Energy Package (CASTEP) module in Materials Studio. Within the generalized gradient approximation (GGA), Perdew-Burke-Ernzerhof (PBE) (30) exchange correlation functionals combined with ultrasoft pseudopotentials were used in the calculations. The value of plane wave cutoff energy was 300 eV. The K point grid (31) size was 3 × 1 × 1. Self-consistent field calculations were performed with a convergence criterion of 2.0 × 10^-6 eV on single atom energy. The convergence of parameters was tested for each supercell. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) optimization algorithm proposed by Broyden, was used in the structure optimization (32-33-34-35).

Structural models

In this paper, the P (1 × 1) periodic supercell is used as the initial surface. Under the coverage of 1 monolayer (ML), the adsorption of CH₄, C₂H₆, CO₂ and N₂ on the surface was theoretically studied for each. First, an optimized CaCO₃ unit cell (Fig. 1) was cleaved for a (100) surface. Then a vacuum layer of 2-nm thickness was constructed to simulate the CaCO₃ (100) surface (Fig. 2). Finally, the CaCO₃ (100) structure was optimized. We focused on shale gas molecule adsorption on CaCO₃ (100) surfaces. Therefore, in the structural optimization computation, the position of oxygen atoms was kept on the surface layer, and the number of adsorbed of shale gas molecules was variable, whereas the atoms of the non–surface layer were immobilized. We adopted such a setting to simulate the adsorption of CaCO₃ on shale gas molecules in order to reduce the number of calculations and to exclude the effect of substrate thickness. The initial lattice constant of calcium carbonate was an experimental value for, a = 0.499 nm, c = 1.7061 nm (36). After optimization, the lattice constant was a = 0.499 nm, c = 1.7060 nm. The gas molecules were added on the CaCO₃ (100) surface to a height of 0.5 nm.

In the structural model of CaCO₃ (100) surface supercell, there were 3 possible high-symmetry adsorption sites, the top (T), the bridge (B) and the hollow (H) part, in a parallelogram consisting of 4 oxygen atoms of surface (Fig. 3). The bridges included the short-side bridge (B1) and the long-side bridge (B2).

Due to the nature of parallelogram geometry, each gas molecule had 4 types of adsorption forms in the CaCO₃ (100) surface H site. As shown in Figure 4 H1 was parallel to the short edge of the parallelogram, H2 was parallel to the short diagonal, H3 was parallel to the long diagonal and H4 was parallel to the long edge. Similarly, T-type sites were denoted by T1, T2, T3 and T4, and B-type sites were mainly related to the situation in which the adsorption of gas molecules was parallel to the short edge or long edge, and were designated as B11, B14, B21 and B24. Therefore, taking all of the possibilities into account, each gas species of CH₄, C₂H₆, CO₂ and N₂ had 12 adsorption modes on the CaCO₃ (100) surface.

To analyze the adsorption stability of shale gas molecules on CaCO₃ (100) surfaces, the adsorption energy of gas molecules on CaCO₃ (100) surfaces was calculated. The total energy of the system before adsorption was obtained by calculating the energy of CaCO₃ (100) surfaces and gas molecules. Then in the same way, the total energy of the system was calculated after adsorption. The equation to calculate the adsorption energy is given by

where E_gas+CaCO3 is the total energy of the system after gas adsorption, E_CaCO3 is the energy of pure CaCO₃ without the gas molecule, and E_gas is the energy of the isolated shale gas molecule. The value of ∆E_ad reflects the stability of the adsorption system. ∆E_ad < 0 means that the energy of the system decreases after adsorption, and the gas molecules are adsorbed. The adsorption process is exothermic. ∆E_ad > 0 means that the energy of the system increases, and the gas molecules cannot be adsorbed (37). A smaller value of ∆E_ad indicates better stability of the adsorption system.

Analysis of adsorption energy

Table I lists the adsorption energy of CH₄, C₂H₆, CO₂ and N₂ molecules on CaCO₃ (100) surfaces in the 12 adsorption modes. CH₄, C₂H₆ and N₂ molecules had negative ∆E_ad, and the lowest adsorption energy was -0.4160 eV, -0.7388 eV and -0.1567 eV, respectively. The adsorption capacity of 3 kinds of gases on the surface of calcium carbonate follows the order of C₂H₆ > CH₄ > N₂. However, the ∆E_ad of CO₂ was positive, which means that CO₂ molecule cannot be adsorbed on the surface of calcium carbonate. Therefore, the adsorption of CO₂ is not discussed in the following.

Since the percentage of CH₄ is dominant in shale gas, the adsorption energy of CH₄ molecular was compared for different adsorption sites to analyze the stability of shale gas molecules adsorbed on CaCO₃ (100) surfaces, as shown in Figure 5. It can be seen that CH₄ molecules had the lowest ∆E_ad at the H3 site.

From the point of view of the quantity of adsorption energy, CH₄ molecules had a minimum adsorption energy of -0.4160 eV on H3, which was the most stable adsorption structure among the 12 high-symmetry sites (Fig. 6). Therefore, it is relatively easier for CH₄ molecules to be adsorbed on H3. When adsorbed on T2, CH₄ molecules had a maximum energy of -0.3625 eV, which means that it was most difficult for T2 to adsorb CH₄ molecules. Similarly, C₂H₆ molecules had their minimum adsorption energy and most stable adsorption structure at B14, which was the position for easiest adsorption. B24 had the maximum energy and the most unstable adsorption structure. At T2, N₂ molecules had their minimum adsorption energy, and could be easily adsorbed at T2. B21 was the most difficult position to adsorb N₂ molecules. The small absolute values of adsorption energy indicate very weak adsorption of CH₄, C₂H₆ and N₂ molecules on CaCO₃ (100) surfaces.

In terms of the range of adsorption energies, the adsorption energy of CH₄ at different sites ranged from -0.3625 eV to -0.4160 eV, with the largest difference being only 0.0535 eV. Besides, the largest differences of the adsorption energy ranges for C₂H₆ and N₂ molecules were only 0.1177 eV and 0.0762 eV, respectively. The range of adsorption energies was very small, which indicates that the adsorption of each gas molecule at the high-symmetry sites on CaCO₃ (100) surfaces was very similar, and the gas molecules tended to move on the calcium carbonate surfaces. By comparison, it is known that the mobility of CH₄ is the strongest.

Analysis of physical structure

In Table II we can see that after CH₄ molecules were adsorbed at H3 sites, the C-H bond length became 0.1097 nm, which is in good agreement with the experimentally spectroscopic data of 0.1086 ± 0.0001 nm (38). Compared with the value before adsorption, the bond length changed by 0.091%, and bond angle changed by 0.779%.

Similarly, the physical structure was analyzed for C₂H₆ and N₂ before and after adsorption. The relative changes were 1.422% and 1.400% for C=C bond length and H-C-H bond angle of C₂H₆, respectively. The N≡N bond length increased by 1.396% after N₂ was adsorbed. It was found that the structures of CH₄, C₂H₆ and N₂ molecules showed negligible changes, so the adsorption effect was weak on the CaCO₃ (100) surface.

Analysis of density of states

The CASTEP module can analyze the band structure, electronic density of states (DOS), optical properties, phonon dispersion relations, phonon DOS and stress before and after the optimization of the physical model. Here we mainly discuss the electronic DOS changes and their effect on adsorption. According to the analysis of the DOS changes for CH₄, C₂H₆, N₂ and CaCO₃ (100) surfaces before and after adsorption, the interactions between shale gas molecules and CaCO₃ (100) surface can be further understood.

In Figure 7 the DOS of CH₄ before and after adsorption at H3 and T2 is compared. The black curve represents the electronic DOS before adsorption, the red curve represents the electronic DOS after adsorption at H3, and the blue curve represents the electronic DOS after adsorption at T2. The vertical dashed line at 0 eV indicates the Fermi level. It can be seen that whether adsorbed at H3 or T2, the electron DOS curves of CH₄ molecules shifted to the left overall after adsorption. The adsorption energy decreased, and the electronic structure became more stable, which shows that the adsorption had a significant influence on the distribution of electron DOS of CH₄ molecules. Besides, the DOS curve of H3 has 2 peaks, at -12.77 eV and -5.18 eV, which move to the left about 0.3 eV compared with those of T2 at -12.47 eV and -4.88 eV. It is thus proven that the adsorption of CH₄ molecules on CaCO₃ (100) surface high-symmetry sites is basically from the point of view of electronic structure, and has better mobility on the surface of the calcium carbonate.

Figure 8 shows the partial density of states (PDOS) of oxygen atoms in CaCO₃ (100) surface before and after the adsorption of CH₄ molecules at H3 under the coverage of 1 ML. The contribution of s electronic states and p electronic states to the total density of states in energy regions is different. When the energy is greater than -10 eV, the p electronic states (red curve) play a major role in the total electron density. When the energy is less than -10 eV, the s electronic states (blue curve) play a major role in the total electron density. Before adsorption, the s electronic states energy is mainly continuously distributed in the ranges of 0 eV to -9 eV and -17 eV to -24 eV, and there are 7 peaks in the 2 intervals. While p electronic states energy is mainly continuously distributed in the ranges of 2 eV to -9 eV and -17 eV to -24 eV, and there are 9 peaks in the 2 intervals. After adsorption, the PDOS of s electronic state of oxygen atoms basically coincides with that of the state before adsorption, as does that of the p Electronic State. This suggests that there is no chemical bond formed between CH₄ molecules and the oxygen atoms on CaCO₃ (100) surfaces. This indicates that the adsorption of CH₄ on calcium carbonate surfaces is mainly affected by the Van Der Waals force, and it is physical adsorption. To better illustrate this point, we compared the DOS of CaCO₃ (100) surfaces with the different shale gas molecules adsorbed, as shown in Figure 9.

Figure 9 presents the DOS of CH₄, C₂H₆ and N₂ adsorbed on a CaCO₃ (100) surface. We can see that the adsorption of different gas molecules on the CaCO₃ (100) surface has similar effects on the electronic structure of the oxygen atom on the CaCO₃ (100) surface. After adsorption, the 3 DOS curves almost overlap, indicating that C₂H₆ and N₂ molecules have similar adsorption effects on oxygen atoms on the CaCO₃ (100) surface to those of the CH₄ molecule, and the adsorption of the 3 kinds of gas molecules on the CaCO₃ (100) surface are physical.