Analytical and Numerical Solutions of Radially Symmetric Aquifer Thermal Energy Storage Problems

Abstract

Abstract. The paper discusses analytical and numerical radial solutions of the differential equations for heat transport in water-saturated porous media. In particular, a similarity solution is obtained for a 2D-horizontal confined aquifer with constant radial flow. Numerical solutions are derived using a high-resolution Lagrangian approach suppressing spurious oscillations and artificial dispersion. There is a good correspondence between numerical and analytical solutions. The primary purpose of the investigation has been to calculate the recovery factor of an Aquifer Thermal Energy Storage (ATES) system with a cyclic repetition of injection and pumping. Solutions covering both instantaneous and delayed heat transfer between fluid and solid, as well as time varying water flow, are derived and applied to a one-well test case. In hydrological terms, these solutions are relevant for a wide range of problems where groundwater reservoirs are utilized for extraction and storage (viz. irrigation; water supply; geothermal extraction).