Application of matched asymptotic expansion techniques to the analysis of geothermal heat exchangers

Abstract

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 are derived, 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 SBM, but with a computational cost in line with the use of g-functions.