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Full-scale temperature response function (G-function) for heat transfer by borehole ground heat exchangers (GHEs) from sub-hour to decades

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  • Li, Min
  • Li, Ping
  • Chan, Vincent
  • Lai, Alvin C.K.

Abstract

Heat transfer by borehole ground heat exchangers involves diverse time–space scales and thus imposes a significant challenge to geothermal engineers. In order to overcome this challenge, this paper develops an analytical full-scale model from the idea of matched asymptotic expansion. The full-scale model is a composite expression consisting of a composite-medium line-source solution (inner solution), a finite line-source solution (outer solution), and an infinite line-source solution. The full-scale model is first verified by a frequency-decomposition method. Furthermore, the full-scale model is reformulated as a multi-stage model based on Duhamel’s theorem to reduce the computational cost. The multi-stage model combines the three separate solutions in a sequential way, i.e., the inner solution for the short-time scale, the conventional infinite line-source solution for the intermediate time scale, and the outer solution for the long-time scale. Finally, we perform a parametric study on a ground heat exchanger with single U-shaped tube, by which the spacing between U-tube legs, the length-to-radius ratio of borehole, the ratios of thermal diffusivities and conductivities of the ground and backfilling material are analyzed.

Suggested Citation

  • Li, Min & Li, Ping & Chan, Vincent & Lai, Alvin C.K., 2014. "Full-scale temperature response function (G-function) for heat transfer by borehole ground heat exchangers (GHEs) from sub-hour to decades," Applied Energy, Elsevier, vol. 136(C), pages 197-205.
    • Handle: RePEc:eee:appene:v:136:y:2014:i:c:p:197-205
    DOI: 10.1016/j.apenergy.2014.09.013
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    References listed on IDEAS

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    1. Claesson, Johan & Eskilson, Per, 1988. "Conductive heat extraction to a deep borehole: Thermal analyses and dimensioning rules," Energy, Elsevier, vol. 13(6), pages 509-527.
    2. Lee, C.K. & Lam, H.N., 2008. "Computer simulation of borehole ground heat exchangers for geothermal heat pump systems," Renewable Energy, Elsevier, vol. 33(6), pages 1286-1296.
    3. Li, Min & Lai, Alvin C.K., 2012. "Heat-source solutions to heat conduction in anisotropic media with application to pile and borehole ground heat exchangers," Applied Energy, Elsevier, vol. 96(C), pages 451-458.
    4. Li, Min & Lai, Alvin C.K., 2012. "New temperature response functions (G functions) for pile and borehole ground heat exchangers based on composite-medium line-source theory," Energy, Elsevier, vol. 38(1), pages 255-263.
    5. Li, Min & Lai, Alvin C.K., 2013. "Analytical model for short-time responses of ground heat exchangers with U-shaped tubes: Model development and validation," Applied Energy, Elsevier, vol. 104(C), pages 510-516.
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