Conductive heat extraction to a deep borehole: Thermal analyses and dimensioning rules

The ground is a virtually unlimited, ubiquitously accessible heat source and sink for heat pumps. Deep boreholes may be used as heat exchangers in the ground. We present an extensive analysis of such a heat extraction (or injection) borehole. The effects of stratification of the ground, climatic variations, geothermal gradient, and groundwater filtration are dealt with. A basic tool for the analysis is the solution for a heat-extraction step. The thermal disturbance at and near the ground surface is shown to be negligible. Thermal recharge in order to improve the heat-extraction capacity a few months later is shown to be futile. The thermal processes in the borehole are, in good approximation, represented by a single borehole resistance. Formulae that relate the heat-extraction rate to the required extraction temperatures are given. They are based on superpositions of steady-state, periodic, and extraction-step solutions. A response-test method is proposed for the determination of three important parameters: average thermal conductivity in the ground, borehole thermal resistance, and average undisturbed ground temperature.