Theoretical model for the thermal response of slender geothermal boreholes during short-term transient operating conditions
Many aspects of the operation of geothermal heating, ventilation, and air conditioning systems must be considered when designing and sizing geothermal heat exchangers. One of the most restrictive is the allowable temperature range of the heat carrying liquid, which limits the amount of heat that can be exchanged with the ground during short-term transient operating conditions. During such short-term events, thermal inertia of the heat carrying liquid, the grout within the borehole, and the surrounding ground plays an important role. Neglecting it during the design phase leads to overly conservative solutions for the geothermal heat exchanger, unnecessarily increasing the system’s initial investment costs. Numerous theoretical models in the literature already account for that thermal inertia. Most of them, however, rely on substantial simplifications in the borehole geometry and/or its thermal characteristics. Only a few models, such as the Enhanced Multipole Method recently developed by the lead author, retain the full geometric and thermal complexity of the problem, paving the way for a new generation of high-fidelity models. In this work, the Enhanced Multipole Method, which only addresses the heat transfer problem in a two-dimensional plane perpendicular to the borehole, is extended in the axial direction to also include the thermal inertia and convective transport of the heat carrying liquid. The resulting model is benchmarked against detailed numerical simulations of the transient thermal response of a complete geothermal borehole, demonstrating both its accuracy and potential.