Both known and unmapped plugged and abandoned wells are potential leakage pathways for CO2 from geologic carbon sequestration (GCS) sites. Although many abandoned wells have cement bridge plugs installed to prevent leakage, the seal between the cement and the inner casing wall is subject to failure. In this study, we carried out detailed T2Well simulations of cases of sudden non-Darcy flow of CO2 and brine leakage up the gap between a cement plug and the inner steel casing wall that becomes a fully connected flow path during the post-injection period. The goal of our study was two-fold: (1) to understand the dynamics, rates, and the characteristic temporal signals associated with the onset of leakage through various gap-aperture sizes, and (2) to suggest potential monitoring strategies based on the findings. Simulation results show that the leakage of CO2 and brine upward is transient with interesting phase interference behavior. Time-dependent oscillatory flows with varying pressure, temperature, and flow rates of CO2 and brine show strong dependence on gap aperture. Phase-change and decompression lead to very low temperatures at the top of the well for gap apertures larger than 4 mm suggesting that remote thermal monitoring at the ground surface may be an effective way of monitoring even if well locations are not known a priori. Pressure in the well is also indicative of CO2 leakage. The temporal patterns of changing temperature and pressure may be useful diagnostic signals for leakage detection. Finally, these transient leakage signals may provide information on the cause of leakage and/or characteristics of the flow path that could inform effective remediation design and execution approaches.