The 3D porous carbon-based structures called Schwarzites have been recently a subject of renewed interest due to the possibility of being synthesized in the near future. These structures exhibit negatively curvature topologies with tuneable porous sizes and shapes, which make them natural candidates for applications such as CO2 capture, gas storage and separation. Nevertheless, the adsorption properties of these materials have not been fully investigated. Following this motivation, we have carried out Grand-Canonical Monte Carlo simulations to study the adsorption of small molecules such as CO2, CO, CH4, N2 and H2, in a series of Schwarzites structures. Here, we present our preliminary results on natural gas adsorptive capacity in association with analyses of the guest-host interaction strengths. Our results show that Schwarzites P7par, P8bal and IWPg are the most promising structures with very high CO2 and CH4 adsorption capacity and low saturation pressure (<1bar) at ambient temperature. The P688 is interesting for H2 storage due to its exceptional high H2 adsorption enthalpy value of -19kJ/mol.