Partial oxidation of methane in a unidirectional flow porous reactor is studied numerically. A number of partial oxidation mechanisms affecting H-2 and CO yields are comparatively analyzed using kinetic modeling for a range of rich and ultrarich equivalence ratios, residence times, and preset reactor temperatures. Temperature profiles, hydrogen yields, and methane conversion ratios are predicted for various equivalence ratios using two-temperature filtration combustion model with selected detailed chemical mechanism. The simulation results show that the hydrogen yield has two obvious sections: the ignition section and stream reforming section. The hydrogen yield increases with temperature and equivalence ratio increase. The two-temperature model results show a good qualitative agreement with the experimental results especially for the maximum solid temperature and hydrogen production. The wave starts to propagate downstream at phi > 1.5. The maximum solid temperature decreases from 1760 K to 1665 K as the equivalence ratio increases from 1.5 to 3.0. The H-2 yield is higher and methane conversion ratio is lower for high equivalence ratios, the thermal efficiency increases with the equivalence ratio increase. The H2 conversion ratio and H-2 energy efficiency reach their maximum values at phi = 2.25, while CO conversion ratio and syngas energy efficiency reach maximum values at phi = 2.0. The results obtained for a unidirectional flow reactor are important for model validation and predictive modeling of a reciprocal flow reactor.