Analytical and numerical solutions of radially symmetric aquifer thermal energy storage problems

Aquifer thermal energy storage (ATES) systems offer reduced energy costs, lower carbon emissions, and increased energy resilience. The feasibility, however, depends on several factors and require usually optimization. We study an ATES system with injection and extraction wells (cf. graphical abstract). The purpose of the investigation was to calculate the recovery factor of an ATES system with a cyclic repetition of injection and pumping. In the paper, we discuss analytical and numerical radial solutions of differential equations for heat transport in water-saturated porous media. A similar solution was obtained for a 2-D-horizontal confined aquifer with a constant radial flow. Numerical solutions were derived by using a high-resolution Lagrangian approach suppressing spurious oscillations and artificial dispersion. The numerical solution and the analytical solutions give consistent results and match each other well. The solutions describe instantaneous and delayed heat transfer between fluid and solid, as well as time-varying water flow. In hydrological terms, these solutions are relevant for a wide range of problems where groundwater reservoirs are utilized for extraction and storage (namely, irrigation; water supply; geothermal extraction).