## 3 Results and Discussion
As we can see from the H\({}_{2}\)S permeance, hydrogen sulfide is slightly favored to pass compared to CO\({}_{2}\) and CH\({}_{4}\). The higher permeance of H\({}_{2}\)S, however, is not sufficiently supported by considerations on the height of barrier required to cross the pore P3. In fact, both CH\({}_{4}\) and CO\({}_{2}\) have a very low barrier of 0.08 eV while the filtration of H\({}_{2}\)S proceeds barrier-less. Even though one of the dimensions of pore P3 is smaller than the dimensions of pore P1, CH\({}_{4}\) can easily cross it when slightly tilted since the pore H-H diagonal distance is large enough to allow its passage. The higher permeance of H\({}_{2}\)S can be understood in terms of number of attempts to cross the pore per unit of time. From an analysis of the MD trajectories it can be noticed that H\({}_{2}\)S concentration is higher closer to the membrane compared to CO\({}_{2}\) and CH\({}_{4}\). Hydrogen sulfide has, indeed, stronger Van der Waals interactions with the graphene membrane compared to the other two molecules, meaning that it is more likely to stick on the membrane surface and diffuse toward the pore. Since there is no crossing barrier, H\({}_{2}\)S drops down in the pore easily even if it has lost most of its translational velocity toward the membrane. A similar phenomenon is also reported for the filtration of N\({}_{2}\)/H\({}_{2}\) mixtures by means of graphene membranes where the larger interactions of N\({}_{2}\) with the membrane surface favor its permeation [21]. We stress that in our calculations the feed initially contains an equal amount of CH\({}_{4}\) and H\({}_{2}\)S. As a result, the number of pore crossing attempts of H\({}_{2}\)S is overestimated. We expect the CH\({}_{4}\) permeance to be higher in real separation processes because of its larger concentration occurring in natural gas. With pore P3 we proved that gas-membrane interactions play a role in the separation performance. We then designed a pore, P3 OH, which could enhance these interactions at the edges of the pore. The pore P3 OH is obtained by substituting half of the hydrogens saturating the carbon atoms of the pore with hydroxyl groups. Hydroxyl groups were chosen for their affinity with CO\({}_{2}\) and H\({}_{2}\)S, given that all of them are characterized by more polar bonds compared to CH\({}_{4}\). The pore P3 OH confirmed the importance of gas-pore interactions, showing not only a permeance increase (3.25 \(\times\) 10\({}^{5}\) of P3 OH with respect to 2.39 \(\times\) 10\({}^{5}\) of P3 for CO\({}_{2}\)/CH\({}_{4}\) case, and 11.91 \(\times\) 10\({}^{5}\) of P3 OH with respect to 5.79 \(\times\) 10\({}^{5}\) of P3 for H\({}_{2}\)S/CH\({}_{4}\) case), but also an improvement of the selectivity (5.9 of P3 OH with respect to 1 of P3 for CO\({}_{2}\)/CH\({}_{4}\) case, and 5.7 of P3 OH with respect to 2.8 of P3 for H\({}_{2}\)S/CH\({}_{4}\) case). We had tested also pore P2 OH and, since OH functionalization decreases the overall area of the pores, we found that no gas molecule can pass through P2 OH. A detailed analysis of the MD trajectories during gas separation simulations of pore P3 OH shows that the electrostatic interaction between hydroxyl groups and CO\({}_{2}\) or H\({}_{2}\)S, ensures that the molecules take the most favorable orientation to cross the pores. This finding is in accordance with the literature suggestion that a charged graphene membrane is able to enhance CO\({}_{2}\) fluxes through the pores. CO\({}_{2}\) molecules, unlike CH\({}_{4}\), are indeed reported to stick more easily to the graphene membrane and to access the pores [32]. Pore P3 OH showed that the functionalization is also a key factor to have good separation performance in membrane technology. On the basis of our results we can distinguish between two regimes.