IDEAS home Printed from https://ideas.repec.org/a/eee/appene/v231y2018icp320-330.html
   My bibliography  Save this article

Simple equations to evaluate the mean fluid temperature of double-U-tube borehole heat exchangers

Author

Listed:
  • Zanchini, Enzo
  • Jahanbin, Aminhossein

Abstract

The design of ground-coupled heat pump systems requires the knowledge of the mean temperature Tfm of the working fluid in borehole heat exchangers. This quantity is usually approximated by the arithmetic mean of inlet and outlet temperature. The approximation yields an overestimation of the thermal resistance of the heat exchanger in thermal response tests, as well as errors in the estimation of the outlet fluid temperature in the dynamic simulation of ground-coupled heat pumps. Recently (Applied Energy 206, 2017, 1406–1415), Zanchini and Jahanbin determined, by finite element simulations, correlations that allow an immediate evaluation of Tfm in any working condition, with reference to double U-tube boreholes with length 100 m and shank spacing 85 mm. In this paper, the analysis presented there is extended to double U-tube boreholes with any length, between 50 and 200 m, and any shank spacing, between 65 and 105 mm. The results hold for every thermal conductivity of the sealing grout between 0.9 and 1.6 W/(m K), every volume flow rate between 12 and 24 L per minute, every diameter of the BHE and every working condition (heating, cooling, thermal response test), both in quasi-stationary and in transient regime.

Suggested Citation

  • Zanchini, Enzo & Jahanbin, Aminhossein, 2018. "Simple equations to evaluate the mean fluid temperature of double-U-tube borehole heat exchangers," Applied Energy, Elsevier, vol. 231(C), pages 320-330.
    • Handle: RePEc:eee:appene:v:231:y:2018:i:c:p:320-330
    DOI: 10.1016/j.apenergy.2018.09.094
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0306261918314053
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.apenergy.2018.09.094?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. 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.
    2. Zanchini, E. & Lazzari, S., 2013. "Temperature distribution in a field of long Borehole Heat Exchangers (BHEs) subjected to a monthly averaged heat flux," Energy, Elsevier, vol. 59(C), pages 570-580.
    3. Ruiz-Calvo, F. & De Rosa, M. & Acuña, J. & Corberán, J.M. & Montagud, C., 2015. "Experimental validation of a short-term Borehole-to-Ground (B2G) dynamic model," Applied Energy, Elsevier, vol. 140(C), pages 210-223.
    4. 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.
    5. Zanchini, E. & Lazzari, S., 2014. "New g-functions for the hourly simulation of double U-tube borehole heat exchanger fields," Energy, Elsevier, vol. 70(C), pages 444-455.
    6. 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.
    7. Beier, Richard A., 2011. "Vertical temperature profile in ground heat exchanger during in-situ test," Renewable Energy, Elsevier, vol. 36(5), pages 1578-1587.
    8. 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. Zhang, Changxing & Wang, Xinjie & Sun, Pengkun & Kong, Xiangqiang & Sun, Shicai, 2020. "Effect of depth and fluid flow rate on estimate for borehole thermal resistance of single U-pipe borehole heat exchanger," Renewable Energy, Elsevier, vol. 147(P1), pages 2399-2408.
    2. Ding Ding & Wenjing He & Chunlu Liu, 2021. "Mathematical Modeling and Optimization of Vanadium-Titanium Black Ceramic Solar Collectors," Energies, MDPI, vol. 14(3), pages 1-20, January.
    3. 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.
    4. Aminhossein Jahanbin & Giovanni Semprini & Andrea Natale Impiombato & Cesare Biserni & Eugenia Rossi di Schio, 2020. "Effects of the Circuit Arrangement on the Thermal Performance of Double U-Tube Ground Heat Exchangers," Energies, MDPI, vol. 13(12), pages 1-19, June.
    5. 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.
    6. Christopher Vella & Simon Paul Borg & Daniel Micallef, 2020. "The Effect of Shank-Space on the Thermal Performance of Shallow Vertical U-Tube Ground Heat Exchangers," Energies, MDPI, vol. 13(3), pages 1-16, January.

    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. 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.
    2. Zhang, Changxing & Wang, Xinjie & Sun, Pengkun & Kong, Xiangqiang & Sun, Shicai, 2020. "Effect of depth and fluid flow rate on estimate for borehole thermal resistance of single U-pipe borehole heat exchanger," Renewable Energy, Elsevier, vol. 147(P1), pages 2399-2408.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Spitler, Jeffrey D. & Gehlin, Signhild E.A., 2015. "Thermal response testing for ground source heat pump systems—An historical review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 50(C), pages 1125-1137.
    13. 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.
    14. 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.
    15. Nian, Yong-Le & Cheng, Wen-Long, 2018. "Insights into geothermal utilization of abandoned oil and gas wells," Renewable and Sustainable Energy Reviews, Elsevier, vol. 87(C), pages 44-60.
    16. 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.
    17. 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).
    18. Tsubaki, Koutaro & Mitsutake, Yuichi, 2016. "Performance of ground-source heat exchangers using short residential foundation piles," Energy, Elsevier, vol. 104(C), pages 229-236.
    19. Claudia Naldi & Enzo Zanchini, 2019. "Full-Time-Scale Fluid-to-Ground Thermal Response of a Borefield with Uniform Fluid Temperature," Energies, MDPI, vol. 12(19), pages 1-18, September.
    20. Xuedan Zhang & Tiantian Zhang & Bingxi Li & Yiqiang Jiang, 2019. "Comparison of Four Methods for Borehole Heat Exchanger Sizing Subject to Thermal Response Test Parameter Estimation," Energies, MDPI, vol. 12(21), pages 1-30, October.

    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:appene:v:231:y:2018:i:c:p:320-330. 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.elsevier.com/wps/find/journaldescription.cws_home/405891/description#description .

    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.