On the quasi-steady limit of the enhanced multipole method for the thermal response of geothermal boreholes

The correct assessment of the maximum and minimum temperatures in a geothermal HVAC system requires the thermal inertia of the grout filling up the boreholes and of the ground located close to the boreholes to be taken into account. The classical multipole method, due to Bennet, Claesson, and Hellstrom, does not consider it, reason why the enhanced multipole method was recently proposed by the authors. Its development, though, took place without seeking any particular relationship with the classical multipole method. Hence, a term-by -term convergence was not sought and, consequently, not expected in the limit of vanishing thermal inertia. Nonetheless, the existence of that term-by-term convergence is mathematically proven in the present work. This positions the enhanced multipole method as the seamless extension of the classical multipole method towards problems with relevant thermal inertia in grout and ground.

Automated summary

The correct assessment of maximum and minimum temperatures in a geothermal HVAC system requires considering the thermal inertia of the grout and ground. The classical multipole method does not consider this, which led to the development of the enhanced multipole method. The present work mathematically proves the existence of term-by-term convergence, positioning the enhanced multipole method as an extension of the classical method for problems with relevant thermal inertia.