Harmonic thermal response of thermally interacting geothermal boreholes. (English) Zbl 1429.86014
Summary: The thermal interaction between adjacent boreholes plays a fundamental role in the long-term thermal response of geothermal heat exchangers. When approximating the long-term behavior by a time-periodic one, that thermal interaction has to be taken into account in each of the harmonic terms that form the Fourier series expansion of the problem. Therefore, the aim of the present work is to analyze the thermal response of multiple thermally interacting boreholes to subannual harmonic excitations using asymptotic expansion techniques. These methods exploit the large disparity in time and length scales of the problem and allow the derivation of explicit expressions for the sought thermal response. Comparisons with the state of the art show that the attained accuracy and flexibility are on par with the best performing models available today.
MSC:
| 86A60 | Geological problems |
| 86A70 | Vulcanology; magma and lava flow |
| 34E05 | Asymptotic expansions of solutions to ordinary differential equations |
| 35C20 | Asymptotic expansions of solutions to PDEs |
| 35K05 | Heat equation |
| 35Q79 | PDEs in connection with classical thermodynamics and heat transfer |
| 45A05 | Linear integral equations |
Keywords:
geothermal heat exchangers; geothermal boreholes; heat equation; harmonic excitation; asymptotic matching; singular expansionReferences:
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