Short-Term Behavior of a Geothermal Energy Storage: Modeling and Theoretical Results

TL;DR

This paper models the short-term thermal behavior of geothermal energy storage systems using numerical methods for the heat equation, aiding in optimal control and management of residential heating.

Contribution

It introduces and analyzes finite difference discretization schemes for simulating the temperature dynamics in geothermal storage systems.

Findings

Stability conditions for the discretization schemes are derived.

Numerical simulations demonstrate the effectiveness of the proposed methods.

Abstract

This paper investigates numerical methods for simulations of the short-term 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 short 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 semi- and full discretization of that PDE using finite difference schemes and study associated stability problems. Numerical results based on the derived methods are presented in the companion paper [17].