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 Hellström, 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. •Revised version of enhanced multipole method proposed.•Behavior of enhanced multipole method for vanishing thermal inertia analyzed.•Term-by-term convergence towards classical multipole method mathematically proven.•Simple, albeit approximate, formulas for thermal resistances derived and assessed.