Analysis of the long-term thermal response of geothermal heat exchangers by means of asymptotic expansion techniques

Most theoretical models for the thermal response of geothermal heat exchangers assume the mean azimuthal borehole wall temperature to be uniform along the boreholes. This simplifying assumption, closely related to the g-functions introduced by Eskilson in 1987, has dominated the research field for the past 30 years, allowing the analysis of large geothermal heat exchangers in reasonable amounts of time. The assumption, however, is not physically correct, which hinders the attainable accuracy. By using matched asymptotic expansion techniques, analytical models for the thermal response of geothermal heat exchangers have been derived in recent times, which do not require the aforementioned simplification. The resulting expressions, applicable to geothermal heat exchangers with irregularly placed heterogeneous boreholes, show accuracy and flexibility levels comparable to those of the Superposition Borehole Model, but with a computational cost more in line with the use of g-functions. The present article gives an overview of the models developed so far and focusses then on the long-term thermal response of geothermal heat exchangers, which can be approximated by a time-periodic response.