Seasonal energy extraction and storage by deep coaxial borehole heat exchangers in a layered ground

Geothermal energy extraction and storage through boreholes have garnered significant attention, particularly regarding deep coaxial borehole heat exchangers. They can be modeled as linear systems if the water flow rate remains constant. The amplitude and phase shift of the transfer functions between the energy output of the exchanger and the thermal changes in the flowing water can be established analytically, provided that the operating regime is periodic over time. We begin by presenting a theoretical framework for a borehole situated in a homogeneous layer and subsequently extend the theory to a layered ground model using a matrix method. The applicability of our approach is demonstrated over operational periods of up to one year for typical exchangers with a radius of 0.2 m, reaching depths from several hundred meters to 1 km. Temperature variations of several degrees Kelvin in the inflowing water are associated with storage and extraction power amplitudes of several kilowatts for a 1 km deep borehole. We illustrate how the ratio between power and temperature amplitudes varies with changes in borehole radius and depth. Furthermore, we show that for very deep boreholes extending to a depth of 4 km, the borehole heat exchangers reach their maximum storage capacity.