Abstract
The interest of exploring deep geological resources for energy-related activities is rapidly increasing. Lowering the risks associated with these activities requires the development of fast and accurate in situ rock characterization methods. Monitoring and interpreting periodic signals, whether natural or man-induced, can provide valuable information about subsurface formations. This study focuses on improving the understanding of injection-induced pore pressure oscillations in confined formations and describes the use of periodic signals for characterizing hydraulic diffusivity. We revisit existing analytical solutions of cyclic pore pressure diffusion into geologic formations with one-dimensional or axisymmetric geometries and compare their performance with numerical simulations, including uncoupled hydraulic (H) and coupled hydro-mechanical (HM) models. We investigate the solutions in three main applications: (a) energy storage in porous rock, (b) CO₂-rich water injection into a caprock representative for CO(2) storage, and (c) stimulation of an enhanced geothermal system in crystalline rock. The wave propagation extends over kilometer scales for the first case. In the second case, the wave propagation is confined to tens of centimeters. For the last case, the wave propagation occurs on the order of tens of meters. Numerical and analytical solutions match under identical assumptions, with errors of less than 3% across all the considered cases. While numerical solutions account for multidimensional hydro-mechanical rock response, analytical solutions provide an immediate initial approximation of the problem, enabling rapid reactions. This study highlights how simplified tools can aid in real-time interpretation for diverse subsurface energy applications, bridging analytical and numerical approaches for practical subsurface monitoring and characterization.