  Streamer discharges can be used as a primary source of reactive species for
plasma-assisted combustion. In this research we investigate positive streamers
in a stoichiometric air-methane mixture at 1 bar and 300 K with a
three-dimensional particle-in-cell model for the electrons. We first discuss
suitable electron scattering cross sections and an extension of the
photoionization mechanism to air-methane mixtures. We discuss that the addition
of 9.5% methane leaves electron transport and reaction coefficients essentially
unchanged, but it largely suppresses photoionization and shortens the photon
mean free path. This leads to (1) accelerated streamer branching, (2) higher
electric field enhancement at the streamer head, (3) lower internal electric
fields, and (4) higher electron densities in the streamer channel. We also
calculate the time-integrated energy density deposited during the evolution of
positive streamers in background electric fields of 12.5 and 20 kV/cm. We find
typical values of the deposited energy density in the range of 0.5-2.5
kJ/m$^{3}$ within the ionized interior of streamers with a length of 5 mm; this
value is rather independent of the electric fields applied here. Finally we
find that the energy deposited in the inelastic electron scattering processes
mainly produces reactive nitrogen species: N$_2$ triplet states and N, but also
O and H radicals. The production of H$_2$ and O$_2$ singlet states also occurs
albeit less pronounced. Our calculation of the primary production of reactive
species can for example be used in global chemistry models.
