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A spectral model for transient heat flow in a double U-tube geothermal heat pump system

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  • Al-Khoury, Rafid
  • Focaccia, Sara

Abstract

This paper introduces a semi-analytical model based on the spectral analysis method for the simulation of transient conductive-convective heat flow in an axisymmetric shallow geothermal system consisting of a double U-tube borehole heat exchanger embedded in a soil mass. The proposed model combines the exactness of the analytical methods with an important extent of generality in describing the geometry and boundary conditions of the numerical methods. It calculates the temperature distribution in all involved borehole heat exchanger components and the surrounding soil mass using the fast Fourier transform, for the time domain; and the complex Fourier and Fourier-Bessel series, for the spatial domain. Numerical examples illustrating the model capability to reconstruct thermal response test data together with parametric analysis are given. The CPU time for calculating temperature distributions in all involved components, pipe-in, pipe-out, grout, and soil, using 16,384 FFT samples, for the time domain, and 100 Fourier-Bessel series samples, for the spatial domain, was in the order of 3 s in a normal PC. The model can be utilized for forward calculations of heat flow in a double U-tube geothermal heat pump system, and can be included in inverse calculations for parameter identification of shallow geothermal systems.

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  • Al-Khoury, Rafid & Focaccia, Sara, 2016. "A spectral model for transient heat flow in a double U-tube geothermal heat pump system," Renewable Energy, Elsevier, vol. 85(C), pages 195-205.
    • Handle: RePEc:eee:renene:v:85:y:2016:i:c:p:195-205
    DOI: 10.1016/j.renene.2015.06.031
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    References listed on IDEAS

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    1. Pasquier, Philippe & Marcotte, Denis, 2012. "Short-term simulation of ground heat exchanger with an improved TRCM," Renewable Energy, Elsevier, vol. 46(C), pages 92-99.
    2. Zarrella, Angelo & Scarpa, Massimiliano & De Carli, Michele, 2011. "Short time step analysis of vertical ground-coupled heat exchangers: The approach of CaRM," Renewable Energy, Elsevier, vol. 36(9), pages 2357-2367.
    3. De Carli, Michele & Tonon, Massimo & Zarrella, Angelo & Zecchin, Roberto, 2010. "A computational capacity resistance model (CaRM) for vertical ground-coupled heat exchangers," Renewable Energy, Elsevier, vol. 35(7), pages 1537-1550.
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    Cited by:

    1. Liu, Zhijian & Xu, Wei & Zhai, Xue & Qian, Cheng & Chen, Xi, 2017. "Feasibility and performance study of the hybrid ground-source heat pump system for one office building in Chinese heating dominated areas," Renewable Energy, Elsevier, vol. 101(C), pages 1131-1140.
    2. Javadi, Hossein & Mousavi Ajarostaghi, Seyed Soheil & Rosen, Marc A. & Pourfallah, Mohsen, 2019. "Performance of ground heat exchangers: A comprehensive review of recent advances," Energy, Elsevier, vol. 178(C), pages 207-233.
    3. Mao, Liangjie & Wei, Changjiang & Zeng, Song & Cai, Mingjie, 2023. "Heat transfer mechanism of cold-water pipe in ocean thermal energy conversion system," Energy, Elsevier, vol. 269(C).
    4. Cimmino, Massimo, 2016. "Fluid and borehole wall temperature profiles in vertical geothermal boreholes with multiple U-tubes," Renewable Energy, Elsevier, vol. 96(PA), pages 137-147.
    5. Zhou, Zhihua & Wu, Shengwei & Du, Tao & Chen, Guanyi & Zhang, Zhiming & Zuo, Jian & He, Qing, 2016. "The energy-saving effects of ground-coupled heat pump system integrated with borehole free cooling: A study in China," Applied Energy, Elsevier, vol. 182(C), pages 9-19.
    6. Cerfontaine, B. & Radioti, G. & Collin, F. & Charlier, R., 2016. "Formulation of a 1D finite element of heat exchanger for accurate modelling of the grouting behaviour: Application to cyclic thermal loading," Renewable Energy, Elsevier, vol. 96(PA), pages 65-79.

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