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Weighted average of inlet and outlet temperatures in borehole heat exchangers

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  • Beier, Richard A.
  • Spitler, Jeffrey D.

Abstract

Vertical borehole heat exchangers are used to couple heat pumps to the ground, which serves as a source or sink of heat. These ground source heat pump systems heat and cool buildings efficiently with low maintenance costs. Many heat transfer models use the mean of the inlet and outlet circulating fluid temperatures as an average temperature along the entire borehole length. In this paper a weighting factor for the inlet and outlet temperatures has been developed that can be combined with 1D radial models in order to account for the variations in temperature with depth. The proposed method gives more accurate results than the mean temperature approximation without requiring computationally intensive 3D models. The method has been verified with measured data from thermal response tests on boreholes with single and double U-tubes, as well pipe-in-pipe (coaxial) boreholes. On the other hand, the usual mean temperature approximation sometimes leads to significant errors and unphysical temperatures.

Suggested Citation

  • Beier, Richard A. & Spitler, Jeffrey D., 2016. "Weighted average of inlet and outlet temperatures in borehole heat exchangers," Applied Energy, Elsevier, vol. 174(C), pages 118-129.
    • Handle: RePEc:eee:appene:v:174:y:2016:i:c:p:118-129
    DOI: 10.1016/j.apenergy.2016.04.077
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    References listed on IDEAS

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    6. Zhang, Linfeng & Zhang, Quan & Huang, Gongsheng & Du, Yaxing, 2014. "A p(t)-linear average method to estimate the thermal parameters of the borehole heat exchangers for in situ thermal response test," Applied Energy, Elsevier, vol. 131(C), pages 211-221.
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    Cited by:

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    3. Yu, Xiaohui & Li, Hongwei & Yao, Sheng & Nielsen, Vilhjalmur & Heller, Alfred, 2020. "Development of an efficient numerical model and analysis of heat transfer performance for borehole heat exchanger," Renewable Energy, Elsevier, vol. 152(C), pages 189-197.
    4. Dehghan B, Babak, 2018. "Thermal conductivity determination of ground by new modified two dimensional analytical models: Study cases," Renewable Energy, Elsevier, vol. 118(C), pages 393-401.
    5. Louis Lamarche & Jasmin Raymond & Claude Hugo Koubikana Pambou, 2017. "Evaluation of the Internal and Borehole Resistances during Thermal Response Tests and Impact on Ground Heat Exchanger Design," Energies, MDPI, vol. 11(1), pages 1-17, December.
    6. Aminhossein Jahanbin & Claudia Naldi & Enzo Zanchini, 2020. "Relation Between Mean Fluid Temperature and Outlet Temperature for Single U-Tube Boreholes," Energies, MDPI, vol. 13(4), pages 1-23, February.
    7. Zanchini, Enzo & Jahanbin, Aminhossein, 2017. "Correlations to determine the mean fluid temperature of double U-tube borehole heat exchangers with a typical geometry," Applied Energy, Elsevier, vol. 206(C), pages 1406-1415.
    8. Pasquier, Philippe & Marcotte, Denis, 2020. "Robust identification of volumetric heat capacity and analysis of thermal response tests by Bayesian inference with correlated residuals," Applied Energy, Elsevier, vol. 261(C).
    9. Beaudry, Gabrielle & Pasquier, Philippe & Marcotte, Denis, 2021. "A fast convolution-based method to simulate time-varying flow rates in closed-loop and standing column well ground heat exchangers," Renewable Energy, Elsevier, vol. 174(C), pages 55-72.
    10. Javed, Saqib & Spitler, Jeffrey, 2017. "Accuracy of borehole thermal resistance calculation methods for grouted single U-tube ground heat exchangers," Applied Energy, Elsevier, vol. 187(C), pages 790-806.
    11. Zhang, Changxing & Xu, Hang & Fan, Jianhua & Sun, Pengkun & Sun, Shicai & Kong, Xiangqiang, 2020. "The coupled two-step parameter estimation procedure for borehole thermal resistance in thermal response test," Renewable Energy, Elsevier, vol. 154(C), pages 672-683.
    12. Pasquier, Philippe, 2018. "Interpretation of the first hours of a thermal response test using the time derivative of the temperature," Applied Energy, Elsevier, vol. 213(C), pages 56-75.
    13. Changlong Wang & Han Fang & Xin Wang & Jinli Lu & Yanhong Sun, 2022. "Study on the Influence of Borehole Heat Capacity on Deep Coaxial Borehole Heat Exchanger," Sustainability, MDPI, vol. 14(4), pages 1-11, February.

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