IDEAS home Printed from https://ideas.repec.org/a/eee/energy/v59y2013icp570-580.html
   My bibliography  Save this article

Temperature distribution in a field of long Borehole Heat Exchangers (BHEs) subjected to a monthly averaged heat flux

Author

Listed:
  • Zanchini, E.
  • Lazzari, S.

Abstract

A method to evaluate the long-term temperature distribution in a field of long Borehole Heat Exchangers (BHEs) subjected to a monthly averaged heat flux is presented, under the assumption that the effects of the groundwater flow are negligible. Each BHE is considered as a cylindrical heat source with diameter D and length L. For each ratio L/D and dimensionless radial distance r/D, the g-function (time-dependent dimensionless temperature, averaged along the BHE length, due to a uniform and constant heat load) is determined by finite-element simulations and written in polynomial form through accurate interpolations, in a very broad range of values of the dimensionless time. Tables of the coefficients of the polynomial functions are provided. The g-functions are then used to determine the time evolution of the mean dimensionless temperature at the interface BHE-ground, averaged among BHEs, for some BHE fields subjected to a monthly averaged heat load.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:energy:v:59:y:2013:i:c:p:570-580
    DOI: 10.1016/j.energy.2013.06.040
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0360544213005380
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.energy.2013.06.040?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. Zanchini, Enzo & Lazzari, Stefano & Priarone, Antonella, 2012. "Long-term performance of large borehole heat exchanger fields with unbalanced seasonal loads and groundwater flow," Energy, Elsevier, vol. 38(1), pages 66-77.
    2. Zanchini, E. & Lazzari, S. & Priarone, A., 2010. "Effects of flow direction and thermal short-circuiting on the performance of small coaxial ground heat exchangers," Renewable Energy, Elsevier, vol. 35(6), pages 1255-1265.
    3. Lazzari, Stefano & Priarone, Antonella & Zanchini, Enzo, 2010. "Long-term performance of BHE (borehole heat exchanger) fields with negligible groundwater movement," Energy, Elsevier, vol. 35(12), pages 4966-4974.
    4. Bozzoli, F. & Pagliarini, G. & Rainieri, S. & Schiavi, L., 2011. "Estimation of soil and grout thermal properties through a TSPEP (two-step parameter estimation procedure) applied to TRT (thermal response test) data," Energy, Elsevier, vol. 36(2), pages 839-846.
    5. Zanchini, E. & Lazzari, S. & Priarone, A., 2010. "Improving the thermal performance of coaxial borehole heat exchangers," Energy, Elsevier, vol. 35(2), pages 657-666.
    6. 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. 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.
    2. 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.
    3. Longo, L. & Colantoni, A. & Castellucci, S. & Carlini, M. & Vecchione, L. & Savuto, E. & Pallozzi, V. & Di Carlo, A. & Bocci, E. & Moneti, M. & Cocchi, S. & Boubaker, K., 2015. "DEA (data envelopment analysis)-assisted supporting measures for ground coupled heat pumps implementing in Italy: A case study," Energy, Elsevier, vol. 90(P2), pages 1967-1972.
    4. 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.
    5. Gultekin, Ahmet & Aydin, Murat & Sisman, Altug, 2019. "Effects of arrangement geometry and number of boreholes on thermal interaction coefficient of multi-borehole heat exchangers," Applied Energy, Elsevier, vol. 237(C), pages 163-170.
    6. Alberdi-Pagola, Maria & Poulsen, Søren Erbs & Jensen, Rasmus Lund & Madsen, Søren, 2020. "A case study of the sizing and optimisation of an energy pile foundation (Rosborg, Denmark)," Renewable Energy, Elsevier, vol. 147(P2), pages 2724-2735.
    7. 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.
    8. 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.
    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.

    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, 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.
    2. 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.
    3. Zanchini, Enzo & Lazzari, Stefano & Priarone, Antonella, 2012. "Long-term performance of large borehole heat exchanger fields with unbalanced seasonal loads and groundwater flow," Energy, Elsevier, vol. 38(1), pages 66-77.
    4. Zhang, Xueping & Han, Zongwei & Ji, Qiang & Zhang, Hongzhi & Li, Xiuming, 2021. "Thermal response tests for the identification of soil thermal parameters: A review," Renewable Energy, Elsevier, vol. 173(C), pages 1123-1135.
    5. 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.
    6. Longo, L. & Colantoni, A. & Castellucci, S. & Carlini, M. & Vecchione, L. & Savuto, E. & Pallozzi, V. & Di Carlo, A. & Bocci, E. & Moneti, M. & Cocchi, S. & Boubaker, K., 2015. "DEA (data envelopment analysis)-assisted supporting measures for ground coupled heat pumps implementing in Italy: A case study," Energy, Elsevier, vol. 90(P2), pages 1967-1972.
    7. Davide Quaggiotto & Angelo Zarrella & Giuseppe Emmi & Michele De Carli & Luc Pockelé & Jacques Vercruysse & Mario Psyk & Davide Righini & Antonio Galgaro & Dimitrios Mendrinos & Adriana Bernardi, 2019. "Simulation-Based Comparison Between the Thermal Behavior of Coaxial and Double U-Tube Borehole Heat Exchangers," Energies, MDPI, vol. 12(12), pages 1-18, June.
    8. 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.
    9. 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.
    10. 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.
    11. Yoshitaka Sakata & Takao Katsura & Ahmed A. Serageldin & Katsunori Nagano & Motoaki Ooe, 2021. "Evaluating Variability of Ground Thermal Conductivity within a Steep Site by History Matching Underground Distributed Temperatures from Thermal Response Tests," Energies, MDPI, vol. 14(7), pages 1-17, March.
    12. 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.
    13. 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.
    14. Jin Luo & Joachim Rohn & Manfred Bayer & Anna Priess, 2013. "Thermal Efficiency Comparison of Borehole Heat Exchangers with Different Drillhole Diameters," Energies, MDPI, vol. 6(8), pages 1-20, August.
    15. Jensen-Page, Linden & Narsilio, Guillermo A. & Bidarmaghz, Asal & Johnston, Ian W., 2018. "Investigation of the effect of seasonal variation in ground temperature on thermal response tests," Renewable Energy, Elsevier, vol. 125(C), pages 609-619.
    16. Oh, Kwanggeun & Lee, Seokjae & Park, Sangwoo & Han, Shin-In & Choi, Hangseok, 2019. "Field experiment on heat exchange performance of various coaxial-type ground heat exchangers considering construction conditions," Renewable Energy, Elsevier, vol. 144(C), pages 84-96.
    17. Song, Xianzhi & Wang, Gaosheng & Shi, Yu & Li, Ruixia & Xu, Zhengming & Zheng, Rui & Wang, Yu & Li, Jiacheng, 2018. "Numerical analysis of heat extraction performance of a deep coaxial borehole heat exchanger geothermal system," Energy, Elsevier, vol. 164(C), pages 1298-1310.
    18. Peng Li & Peng Guan & Jun Zheng & Bin Dou & Hong Tian & Xinsheng Duan & Hejuan Liu, 2020. "Field Test and Numerical Simulation on Heat Transfer Performance of Coaxial Borehole Heat Exchanger," Energies, MDPI, vol. 13(20), pages 1-19, October.
    19. 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.
    20. Jia, Jie & Lee, W.L. & Cheng, Yuanda, 2019. "Field demonstration of a first constant-temperature thermal response test with both heat injection and extraction for ground source heat pump systems," Applied Energy, Elsevier, vol. 249(C), pages 79-86.

    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:energy:v:59:y:2013:i:c:p:570-580. 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/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.