This article presents a comprehensive study on the streamer propagation and electric field distribution within a two-dimensional fluid model of a packed bed reactor (PBR) filled with carbon dioxide, utilizing the PASSKEy simulation platform. The research delves into the spatiotemporal evolution of electron density, electric fields and key plasma species in the discharge process. The model simulates a PBR with layered dielectric spheres, indicates that the inner sides of the first and second layers of dielectric spheres are not the primary regions for reactions such as CO₂ dissociation; instead, the main regions are along the streamer propagation path and the outer side of the first layer of dielectric spheres. The study by examining the propagation of streamers in the presence of an electric field, highlighting the influence of anode voltage rise and dielectric polarization on local electric field enhancement. This enhancement leads to increased electron density and temperature, facilitating streamer propagation and the formation of filamentary microdischarges and surface ionization waves. The article provides a detailed analysis of the local electric field evolution at specific points within the PBR. The research further investigates the spatiotemporal dynamics of spatial and surface charges, revealing that negative charges concentrate within the streamer and on the dielectric surface, with densities significantly higher than positive charges. The positive charges' distribution is closely related to the streamer's path, and over time, they come to dominate the charge distribution in the discharge space. The study also explores the surface charge deposition on the dielectric spheres, discusses the evolution trends of the distribution. Additionally, the article discusses the temporal and spatial evolution of key plasma species, including ions and radicals, and their contribution to the overall discharge characteristics. The production mechanisms of carbon monoxide particles, carbon dioxide ions, and oxygen ions are analyzed, with a focus on their spatial distribution and correlation with electron density. The study concludes with an examination of the energy deposition within the PBR, integrating the spatial energy deposition of electrons and major positive ions. The results indicate a total energy deposition value of approximately 1.428 mJ/m, with carbon dioxide ions accounting for 8.8% of this value.