Earthquakes are one of the primary geological hazards, mainly attributed to tectonic plate motion or induced by anthropogenic processes, which pose the threat of casualties and property damage. Fluids play an important role in the seismic cycle alongside the tectonic deformations. Reservoir induced seismicity (RIS), associated with the impoundment of artificial reservoirs and fluctuations in their water levels, typically exhibits higher magnitudes than other natural and anthropogenic fluid-induced seismic events. However, despite extensive high-resolution in-situ monitoring of water levels and seismic activities, as well as their statistical analyses, there is still no comprehensive understanding of the underlying mechanism of RIS. This study introduces a fully coupled dynamic poroelastic model to simulate RIS sequences in a faulted reservoir. The model undergoes numerous verifications, including quasi-static Terzaghi consolidation, dynamic compressive poroelastic wave propagation and other benchmark. These verifications convincingly agree with analytical predictions, reinforcing the model reliability. Simulated seismic sequences, incorporating rate-dependent frictional contact under extensional conditions and adaptive time-stepping, demonstrate characteristics typical for induced seismicity. The model captures fluid flow within the rock and along the fault, intensified reservoir impoundment. The approach provides insights into the spatiotemporal characteristics and triggering mechanisms of RIS. It may contribute to earthquake prediction and mitigation policy, especially in regions with significant water level variations.