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A finite line source model with Cauchy-type top boundary conditions for simulating near surface effects on borehole heat exchangers

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  • Rivera, Jaime A.
  • Blum, Philipp
  • Bayer, Peter

Abstract

BHEs (borehole heat exchangers) are the most common shallow geothermal applications. By approximating the BHE as a line source, semi-analytical models can describe the heat exchange within the ground. These models though always assume prescribed temperature at the ground surface. This work presents a formulation which expands existing finite line source models by implementing a more general Cauchy-type top boundary condition and in this way, a better estimation of the heat fluxes at the ground surface. The new formulation is numerically verified and examined in a dimensionless analysis. It is demonstrated that the discrepancy to prescribed temperature settings is significant near to the ground surface, and it propagates deeper when groundwater flow is absent and when strong decoupling between the thermal regimes interacting at the land surface is assumed. The new approach shows to be suited especially for short BHEs, both for more flexible and accurate prediction of the ground thermal regime as well as for long-term analysis of technological performance.

Suggested Citation

  • Rivera, Jaime A. & Blum, Philipp & Bayer, Peter, 2016. "A finite line source model with Cauchy-type top boundary conditions for simulating near surface effects on borehole heat exchangers," Energy, Elsevier, vol. 98(C), pages 50-63.
    • Handle: RePEc:eee:energy:v:98:y:2016:i:c:p:50-63
    DOI: 10.1016/j.energy.2015.12.129
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    Cited by:

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    3. Rivera, Jaime A. & Blum, Philipp & Bayer, Peter, 2016. "Influence of spatially variable ground heat flux on closed-loop geothermal systems: Line source model with nonhomogeneous Cauchy-type top boundary conditions," Applied Energy, Elsevier, vol. 180(C), pages 572-585.
    4. Kordas, Olga & Nikiforovich, Eugene, 2019. "A phenomenological theory of steady-state vertical geothermal systems: A novel approach," Energy, Elsevier, vol. 175(C), pages 23-35.
    5. Zhang, Xueping & Han, Zongwei & Meng, Xinwei & Li, Gui & Ji, Qiang & Li, Xiuming & Yang, Lingyan, 2021. "Study on high-precision identification method of ground thermal properties based on neural network model," Renewable Energy, Elsevier, vol. 163(C), pages 1838-1848.
    6. Myungkwan Lim & Kyoungbin Lim & Changhee Lee, 2020. "A Study on Improving the Coefficient of Performance by Comparing Balancing Well and Standing Column Well Heat Exchange Systems," Sustainability, MDPI, vol. 12(24), pages 1-28, December.
    7. Gan, Guohui, 2018. "Dynamic thermal performance of horizontal ground source heat pumps – The impact of coupled heat and moisture transfer," Energy, Elsevier, vol. 152(C), pages 877-887.
    8. Luka Boban & Dino Miše & Stjepan Herceg & Vladimir Soldo, 2021. "Application and Design Aspects of Ground Heat Exchangers," Energies, MDPI, vol. 14(8), pages 1-31, April.
    9. Zhou, Yang & Zheng, Zhi-xiang & Zhao, Guang-si, 2022. "Analytical models for heat transfer around a single ground heat exchanger in the presence of both horizontal and vertical groundwater flow considering a convective boundary condition," Energy, Elsevier, vol. 245(C).
    10. R.V., Rohit & R., Vipin Raj & Kiplangat, Dennis C. & R., Veena & Jose, Rajan & Pradeepkumar, A.P. & Kumar, K. Satheesh, 2023. "Tracing the evolution and charting the future of geothermal energy research and development," Renewable and Sustainable Energy Reviews, Elsevier, vol. 184(C).
    11. Serianz, Luka & Rman, Nina & Golobič, Iztok & Brenčič, Mihael, 2022. "Groundwater heat transfer and thermal outflow plume modelling in the Alps," Renewable Energy, Elsevier, vol. 182(C), pages 751-763.
    12. Maragna, Charles & Loveridge, Fleur, 2019. "A resistive-capacitive model of pile heat exchangers with an application to thermal response tests interpretation," Renewable Energy, Elsevier, vol. 138(C), pages 891-910.
    13. Zhou, Yang & Wu, Zi-han & Wang, Kang, 2021. "An analytical model for heat transfer outside a single borehole heat exchanger considering convection at ground surface and advection of vertical water flow," Renewable Energy, Elsevier, vol. 172(C), pages 1046-1062.
    14. Bi, Yuehong & Lyu, Tianli & Wang, Hongyan & Sun, Ruirui & Yu, Meize, 2019. "Parameter analysis of single U-tube GHE and dynamic simulation of underground temperature field round one year for GSHP," Energy, Elsevier, vol. 174(C), pages 138-147.

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