## 1 Introduction  
Natural gas is regarded as one of the most important fossil fuels for energy production in the modern economy. Unlike other fossil fuels, natural gas combustion in stoichiometric conditions does not produce any dangerous pollutant, like SO\({}_{2}\) and NO\({}_{x}\), but rather it gives rise to gas containing mainly CO\({}_{2}\) and H\({}_{2}\)O [1]. Furthermore, compared to other fossil fuels, natural gas produces a smaller amount of CO\({}_{2}\) molecules, reducing the risk of greenhouse effect. For these reasons and the lack of reliable renewable resources, natural gas is expected to be as important in the future as it is today [2]. Methane is the main component of the natural gas, although other contaminants, such as hydrogen sulfide and carbon dioxide, are present in its composition. A purification process must then be performed to remove these impurities before its use. Typically, the process consists in the absorption-desorption, also referred to as gas sweetening, of the impurities in aqueous amine solutions that allows for achieving the required gas purity [3]. However, the gas sweetening process has some technological disadvantages like the loss of amine solutions, the steam inclusion in the natural gas phase during the desorption step and the degradation of amine in corrosive byproducts [4]. The main concern is the elevated cost of the process as a consequence of the amine solution regeneration [4]. To overcome the inherent issues of the gas sweetening process, another approach has been proposed: gas filtration by nanoporous membranes [5]. Membrane gas separation relies on the ability of the membrane to allow the passage of specific molecules while rejecting others. Unlike the absorption process, the membrane mediated gas separation could in principle combine both low energy cost and low environmental impact [6]. The first membrane technology for gas separation was based on polymeric membranes, which performed poorly in terms of the permeability/selectivity tradeoff [5; 7]. Additionally, polymer membranes suffer from plasticization induced by the CO\({}_{2}\) gas that results in a strong loss in selectivity [8]. Polymeric membranes can also be coupled with ionic liquids which contribute to the adsorption of natural gas residuals such as CO\({}_{2}\). Nevertheless, their industrial application is prevented by the leak out of the ionic liquid through the largest pores of the supporting membrane or due to membrane compression during the filtration [9; 10; 11; 12]. Because of these drawbacks, polymeric membranes do not represent a reliable alternative to the absorption-desorption process. However, recently nanoporous graphene was suggested as a new promising material for gas filtration membranes thanks to its unique properties [13; 14; 15; 16]. Given that permeability scales inversely with the thickness of the membrane, the one-atom thick graphene is the perfect material to create highly permeable membranes [17]. Furthermore, the possibility to precisely control the pore dimensions [18] provides to nanoporous graphene a very high selectivity to numerous compounds. Another interesting property is its strength and chemical stability that make nanoporous graphene a very durable material [13], able to resist high pressures like the ones applied in the membrane gas separation processes [19]. The excellent performances of graphene as a gas filter are well documented in literature [20]. For instance, [PERSON] et al. showed by means of classical molecular dynamics simulations that H and N functionalized circular pores in graphene allow the passage of small gas molecules like N\({}_{2}\), CO\({}_{2}\) and H\({}_{2}\)S while blocking methane [15], demonstrating that graphene membranes are effective filters for gas purification. Ab initio molecular dynamics also confirmed the possibility to separate gas mixtures like H\({}_{2}\)/CH\({}_{4}\) with similar H and N-passivated pores predicting a very high selectivity [17]. [PERSON] et al.