Multipole method to calculate borehole thermal resistances in a borehole heat exchanger

Ground-source heat pump systems use borehole heat exchangers to transfer heat to and from the ground. An important feature is the local thermal resistances between the heat carrier flow channels in the borehole and the surrounding ground. The counter-flow heat exchange between the pipes is also important, particularly for the axial temperature variation. These resistances can be represented by a thermal network between the pipes and the ground. The borehole thermal resistance is readily obtained from the network. A fairly intricate mathematical algorithm, the multipole method, to compute the temperature fields and, in particular, the thermal resistances is presented. This article focuses on the application of the model, leaving the detailed mathematics to a background report. The formulas and methodology required for any particular case are presented in detail. The multipole method gives a solution with very high, and easily verified, accuracy for the steady-state heat conduction in a region perpendicular to the borehole axis. It is fairly straightforward to implement the algorithm in any design software. The computational time requirements are negligible.