Modeling and simulation of the input–output behavior of a geothermal energy storage

Abstract

This paper investigates mathematical modeling and numerical methods for simulations of the input–output behavior of a geothermal energy storage. Such simulations are needed for the optimal control and management of residential heating systems equipped with an underground thermal storage. There, a given volume under or aside of a building is filled with soil and insulated to the surrounding ground. The thermal energy is stored by raising the temperature of the soil inside the storage. It is charged and discharged via pipe heat exchangers filled with a moving fluid. Simulations of geothermal energy storages aim to determine how much energy can be stored in or taken from the storage within a given period of time. The latter depends on the dynamics of the spatial temperature distribution in the storage, which is governed by a linear heat equation with convection and appropriate boundary and interface conditions. We consider semidiscretization and full discretization of that PDE using finite difference schemes and study associated stability problems. Finally, we present numerical results.