IDEAS home Printed from https://ideas.repec.org/a/eee/renene/v96y2016ipap137-147.html
   My bibliography  Save this article

Fluid and borehole wall temperature profiles in vertical geothermal boreholes with multiple U-tubes

Author

Listed:
  • Cimmino, Massimo

Abstract

An analytical model for the calculation of fluid temperature profiles in geothermal boreholes with multiple U-tubes is presented. A linear system of first order differential equations is built based on a steady-state thermal resistances approach to the heat transfer between the U-tube pipes and the borehole wall. Analytical expressions for fluid temperature profiles are provided for boreholes with arbitrary borehole wall temperature profiles as well as piece-wise uniform and uniform borehole wall temperature for different U-tube configurations: independent, parallel and series. The analytical model is coupled to a finite line source model of the heat transfer between the borehole and the ground. Fluid and borehole wall temperature profiles are solved simultaneously using numerical Laplace transforms to consider the time variation of the temperatures and heat extraction rates. Results are verified against a finite difference model of the borehole. Differences between the fluid temperatures calculated with the numerical and analytical models are smaller than 0.003 °C.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:renene:v:96:y:2016:i:pa:p:137-147
    DOI: 10.1016/j.renene.2016.04.067
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096014811630369X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.renene.2016.04.067?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. 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. 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.
    3. 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.
    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. 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.
    6. Eslami-Nejad, Parham & Ouzzane, Mohamed & Aidoun, Zine, 2014. "Modeling of a two-phase CO2-filled vertical borehole for geothermal heat pump applications," Applied Energy, Elsevier, vol. 114(C), pages 611-620.
    7. Yang, Weibo & Shi, Mingheng & Liu, Guangyuan & Chen, Zhenqian, 2009. "A two-region simulation model of vertical U-tube ground heat exchanger and its experimental verification," Applied Energy, Elsevier, vol. 86(10), pages 2005-2012, October.
    8. Beier, Richard A., 2011. "Vertical temperature profile in ground heat exchanger during in-situ test," Renewable Energy, Elsevier, vol. 36(5), pages 1578-1587.
    9. Acuña, José & Palm, Björn, 2013. "Distributed thermal response tests on pipe-in-pipe borehole heat exchangers," Applied Energy, Elsevier, vol. 109(C), pages 312-320.
    10. Marcotte, D. & Pasquier, P., 2008. "On the estimation of thermal resistance in borehole thermal conductivity test," Renewable Energy, Elsevier, vol. 33(11), pages 2407-2415.
    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. Angelo Zarrella & Giuseppe Emmi & Samantha Graci & Michele De Carli & Matteo Cultrera & Giorgia Dalla Santa & Antonio Galgaro & David Bertermann & Johannes Müller & Luc Pockelé & Giulia Mezzasalma & D, 2017. "Thermal Response Testing Results of Different Types of Borehole Heat Exchangers: An Analysis and Comparison of Interpretation Methods," Energies, MDPI, vol. 10(6), pages 1-18, June.

    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. Zhang, Linfeng & Zhang, Quan & Huang, Gongsheng, 2016. "A transient quasi-3D entire time scale line source model for the fluid and ground temperature prediction of vertical ground heat exchangers (GHEs)," Applied Energy, Elsevier, vol. 170(C), pages 65-75.
    2. 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.
    3. 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.
    4. 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).
    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. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Nian, Yong-Le & Wang, Xiang-Yang & Xie, Kun & Cheng, Wen-Long, 2020. "Estimation of ground thermal properties for coaxial BHE through distributed thermal response test," Renewable Energy, Elsevier, vol. 152(C), pages 1209-1219.
    13. Matt S. Mitchell & Jeffrey D. Spitler, 2020. "An Enhanced Vertical Ground Heat Exchanger Model for Whole-Building Energy Simulation," Energies, MDPI, vol. 13(16), pages 1-27, August.
    14. 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.
    15. Bansal, Vikas & Misra, Rohit & Agarwal, Ghanshyam Das & Mathur, Jyotirmay, 2013. "‘Derating Factor’ new concept for evaluating thermal performance of earth air tunnel heat exchanger: A transient CFD analysis," Applied Energy, Elsevier, vol. 102(C), pages 418-426.
    16. Raymond, Jasmin & Lamarche, Louis & Malo, Michel, 2015. "Field demonstration of a first thermal response test with a low power source," Applied Energy, Elsevier, vol. 147(C), pages 30-39.
    17. Nguyen, A. & Elsami-Nejad, P., 2019. "A transient coupled model of a variable speed transcritical CO2 direct expansion ground source heat pump for space heating and cooling," Renewable Energy, Elsevier, vol. 140(C), pages 1012-1021.
    18. Biglarian, Hassan & Abbaspour, Madjid & Saidi, Mohammad Hassan, 2018. "Evaluation of a transient borehole heat exchanger model in dynamic simulation of a ground source heat pump system," Energy, Elsevier, vol. 147(C), pages 81-93.
    19. 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).
    20. Extremera-Jiménez, Alejandro J. & Gutiérrez-Montes, Cándido & Casanova-Peláez, Pedro J. & Cruz-Peragón, Fernando, 2022. "Vertical ground heat exchanger parameter characterization through a compound design of experiments," Renewable Energy, Elsevier, vol. 199(C), pages 1361-1371.

    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:96:y:2016:i:pa:p:137-147. 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.