Modelling porous media is essential in many engineering and scientific fields, for example soil mechanics, seismology and biomechanics. The complex interactions between multiple phases can be described in a thermodynamically consistent framework by the theory of porous media. Numerical simulations of high-fidelity dynamic poroelastic systems require significant computational costs to resolve the multi-physics coupling with fine temporal and spatial resolution, posing a major challenge, especially when repeated solutions over large parameter space are required. Existing simplifications of such systems often rely on assumptions and fail to systematically bridge the gap between quasi-static and fully dynamic regimes. Model-order reduction techniques such as asymptotic analysis, provides for an effective framework to overcome this challenge. To this end, the high-fidelity dynamic poroelastic model is first non-dimenionalized and a key dimensionless parameter, based on material and geometric properties, is identified. A systematic decomposition of the model using asymptotic expansion leads to a hierarchical reduced model that balances accuracy and computational efficiency. This reduced model comprises two sub-models: namely a limit model, which is computationally efficient quasi-static model that captures the averaged system behavior; and a corrector model, which reintroduces the dynamic behavior. Using a finite-element based multigrid-in-time algorithm, the limit model is first solved over a coarse temporal grid, followed by the corrector model on a fine temporal grid to capture the higher frequency dynamics. Numerical simulations of a one-dimensional dynamic consolidation problem verify the performance and accuracy of the reduced model. The results confirm that the derived approach adequately captures the dynamics of the high-fidelity system when the key dimensionless parameter satisfies certain conditions.