Nanosecond pulsed discharges have attracted the attention of engine manufacturers due to the possibility of attaining distributed ignition sites that accelerate burn rates while resulting in very little electrode erosion. Multidimensional modeling tools currently capture the electrical structure of such discharges accurately, but resolving the chemical structure remains a challenging problem owing to the disparity of time-scales in streamer propagation (nanoseconds) and ignition phenomena (microseconds). The purpose of this study is to extend multidimensional results towards resolving the chemical structure in the wake of streamers (or the afterglow) by using a batch reactor model. This can afford the use of very detailed chemical kinetic information. The full non-equilibrium nature of the electrons is taken into account, along with fast gas heating, shock wave propagation, and thermal diffusion. The results shed light on ignition phenomena brought about by such discharges.