In this study, the effect of the O2 and N2 Penning ionization reactions on the evolution a capillary helium atmospheric pressure plasma jet (APPJ) with and without the presence of oxygen admixtures is investigated numerically using a two dimensional axi-symmetric model. In order to better understand potential applications of plasma surface interaction, the He and He+O2 (1000 ppm) APPJ is launched into a dielectric target. Moreover, the numerical model is compared with experimental measurements showing that the model captures the right physics and can elucidate the discharge dynamics. The comparison is realized for axial and radial measurements in order to have a complete picture of the plasma jet evolution. In this paper, the velocity and the shape of the plasma guided streamer were chosen as indicators of plasma jet evolution. In particular, the investigation is accomplished experimentally by tracking the spatio-temporal resolved emission of 706.5 nm (3s3S → 2p3P) line and numerically by calculating the reaction rate for the same transition. The O2 and N2 Penning reactions are then independently considered in the numerical model in order to isolate their contribution to the plasma evolution. It is shown that for the pure helium plasma, the N2 Penning reactions are more important to the plasma evolution. However, when oxygen admixtures are added to the plasma gas, the O2 Penning reactions become more important than the N2 ones.