  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.
