IDEAS home Printed from https://ideas.repec.org/a/eee/renene/v172y2021icp1046-1062.html
   My bibliography  Save this article

An analytical model for heat transfer outside a single borehole heat exchanger considering convection at ground surface and advection of vertical water flow

Author

Listed:
  • Zhou, Yang
  • Wu, Zi-han
  • Wang, Kang

Abstract

Borehole heat exchangers (BHEs) are widely used with ground source heat pump (GSHP) system for utilization of shallow geothermal energy. In this paper, heat transfer between a single BHE and the surrounding soil is investigated, in which convection at ground surface and advection of vertical water flow are considered in heat conduction process. The length of the borehole is much greater than its diameter, hence it is treated as a line source, and then an improved finite line source model is developed to describe the heat transfer process. The governing equations of the model are presented, and an analytical solution is established by introducing a new variable and using the Green’s function method. The analytical solution is compared with a numerical solution to confirm the derivation and programming process, and then computational examples of the analytical solution are presented. The effect of vertical water flow on the temperature response of the ground outside the borehole is demonstrated; the line source model under a convective boundary condition is compared with that under a prescribed surface temperature to show the error caused by neglecting the surface convection effect; the mean borehole wall temperature and the total heat flux at ground surface are computed, and their responses to variations of external factors are analyzed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:renene:v:172:y:2021:i:c:p:1046-1062
    DOI: 10.1016/j.renene.2021.03.102
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960148121004584
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.renene.2021.03.102?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zhou, Guoqing & Zhou, Yang & Zhang, Donghai, 2016. "Analytical solutions for two pile foundation heat exchanger models in a double-layered ground," Energy, Elsevier, vol. 112(C), pages 655-668.
    2. Mustafa Omer, Abdeen, 2008. "Ground-source heat pumps systems and applications," Renewable and Sustainable Energy Reviews, Elsevier, vol. 12(2), pages 344-371, February.
    3. 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.
    4. 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.
    5. Rivera, Jaime A. & Blum, Philipp & Bayer, Peter, 2015. "Ground energy balance for borehole heat exchangers: Vertical fluxes, groundwater and storage," Renewable Energy, Elsevier, vol. 83(C), pages 1341-1351.
    6. Eslami-nejad, Parham & Bernier, Michel, 2012. "Freezing of geothermal borehole surroundings: A numerical and experimental assessment with applications," Applied Energy, Elsevier, vol. 98(C), pages 333-345.
    7. Li, Min & Lai, Alvin C.K., 2015. "Review of analytical models for heat transfer by vertical ground heat exchangers (GHEs): A perspective of time and space scales," Applied Energy, Elsevier, vol. 151(C), pages 178-191.
    8. 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.
    9. Bayer, Peter & Saner, Dominik & Bolay, Stephan & Rybach, Ladislaus & Blum, Philipp, 2012. "Greenhouse gas emission savings of ground source heat pump systems in Europe: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 16(2), pages 1256-1267.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kong, Gangqiang & Dai, Guohao & Zhou, Yang & Yang, Qing, 2024. "Analytical solution model of heat transfer for energy soldier piles during excavation to backfilling," Renewable Energy, Elsevier, vol. 226(C).
    2. 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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. 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.
    3. 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.
    4. Cui, Yuanlong & Zhu, Jie & Twaha, Ssennoga & Riffat, Saffa, 2018. "A comprehensive review on 2D and 3D models of vertical ground heat exchangers," Renewable and Sustainable Energy Reviews, Elsevier, vol. 94(C), pages 84-114.
    5. Li, Min & Lai, Alvin C.K., 2015. "Review of analytical models for heat transfer by vertical ground heat exchangers (GHEs): A perspective of time and space scales," Applied Energy, Elsevier, vol. 151(C), pages 178-191.
    6. 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.
    7. Carotenuto, Alberto & Ciccolella, Michela & Massarotti, Nicola & Mauro, Alessandro, 2016. "Models for thermo-fluid dynamic phenomena in low enthalpy geothermal energy systems: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 60(C), pages 330-355.
    8. Zhou, Guoqing & Zhou, Yang & Zhang, Donghai, 2016. "Analytical solutions for two pile foundation heat exchanger models in a double-layered ground," Energy, Elsevier, vol. 112(C), pages 655-668.
    9. Somogyi, Viola & Sebestyén, Viktor & Nagy, Georgina, 2017. "Scientific achievements and regulation of shallow geothermal systems in six European countries – A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 68(P2), pages 934-952.
    10. Ma, WeiWu & Li, Min & Li, Ping & Lai, Alvin C.K., 2015. "New quasi-3D model for heat transfer in U-shaped GHEs (ground heat exchangers): Effective overall thermal resistance," Energy, Elsevier, vol. 90(P1), pages 578-587.
    11. 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.
    12. 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.
    13. Abbas, Zulkarnain & Yong, Li & Abbas, Saqlain & Chen, Dongwen & Li, Y. & Wang, R.Z., 2021. "Performance analysis of seasonal soil heat storage system based on numerical simulation and experimental investigation," Renewable Energy, Elsevier, vol. 178(C), pages 66-78.
    14. Zhang, Donghai & Gao, Penghui & Zhou, Yang & Wang, Yijiang & Zhou, Guoqing, 2020. "An experimental and numerical investigation on temperature profile of underground soil in the process of heat storage," Renewable Energy, Elsevier, vol. 148(C), pages 1-21.
    15. Fadejev, Jevgeni & Simson, Raimo & Kurnitski, Jarek & Haghighat, Fariborz, 2017. "A review on energy piles design, sizing and modelling," Energy, Elsevier, vol. 122(C), pages 390-407.
    16. Aneta Sapińska-Sliwa & Marc A. Rosen & Andrzej Gonet & Joanna Kowalczyk & Tomasz Sliwa, 2019. "A New Method Based on Thermal Response Tests for Determining Effective Thermal Conductivity and Borehole Resistivity for Borehole Heat Exchangers," Energies, MDPI, vol. 12(6), pages 1-22, March.
    17. Andrea Ferrantelli & Jevgeni Fadejev & Jarek Kurnitski, 2019. "Energy Pile Field Simulation in Large Buildings: Validation of Surface Boundary Assumptions," Energies, MDPI, vol. 12(5), pages 1-20, February.
    18. Go, Gyu-Hyun & Lee, Seung-Rae & Yoon, Seok & Kang, Han-byul, 2014. "Design of spiral coil PHC energy pile considering effective borehole thermal resistance and groundwater advection effects," Applied Energy, Elsevier, vol. 125(C), pages 165-178.
    19. Li, Min & Zhang, Liwen & Liu, Gang, 2020. "Step-wise algorithm for estimating multi-parameter of the ground and geothermal heat exchangers from thermal response tests," Renewable Energy, Elsevier, vol. 150(C), pages 435-442.
    20. Song, Xianzhi & Shi, Yu & Li, Gensheng & Shen, Zhonghou & Hu, Xiaodong & Lyu, Zehao & Zheng, Rui & Wang, Gaosheng, 2018. "Numerical analysis of the heat production performance of a closed loop geothermal system," Renewable Energy, Elsevier, vol. 120(C), pages 365-378.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:renene:v:172:y:2021:i:c:p:1046-1062. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/renewable-energy .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.