We study numerically the adsorption of a mixture of CO$_2$ and CH$_4$ on a graphite substrate covered by graphene nanoribbons (NRs). The NRs are flat and parallel to the graphite surface, at a variable distance ranging from 6 r{A} to 14 r{A}. We show that the NRs-graphite substrate acts as an effective filter for CO$_2$. Our study is based on Molecular Dynamics (MD) simulations. Methane is considered a spherical molecule, and carbon dioxide is represented as a linear rigid body. Graphite is modeled as a continuous material, while the NRs are approached atomistically. We observe that when the NRs are placed 6 r{A} above the graphite surface, methane is blocked out, while CO$_2$ molecules can diffuse and be collected in between the NRs and the graphite surface. Consequently, the selectivity of CO$_2$ is extremely high. We also observe that the initial rate of adsorption of CO$_2$ is much higher than CH$_4$. Overall we show that the filter can be optimized by controlling the gap between NRs and the NRs-graphite separation.
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