IDEAS home Printed from https://ideas.repec.org/a/eee/energy/v98y2016icp50-63.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0360544215017740
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.energy.2015.12.129?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. Li, Min & Li, Ping & Chan, Vincent & Lai, Alvin C.K., 2014. "Full-scale temperature response function (G-function) for heat transfer by borehole ground heat exchangers (GHEs) from sub-hour to decades," Applied Energy, Elsevier, vol. 136(C), pages 197-205.
    2. Hähnlein, Stefanie & Bayer, Peter & Ferguson, Grant & Blum, Philipp, 2013. "Sustainability and policy for the thermal use of shallow geothermal energy," Energy Policy, Elsevier, vol. 59(C), pages 914-925.
    3. Claesson, Johan & Eskilson, Per, 1988. "Conductive heat extraction to a deep borehole: Thermal analyses and dimensioning rules," Energy, Elsevier, vol. 13(6), pages 509-527.
    4. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(1), pages 151-159, February.
    5. Zhang, Wenke & Yang, Hongxing & Lu, Lin & Fang, Zhaohong, 2013. "The analysis on solid cylindrical heat source model of foundation pile ground heat exchangers with groundwater flow," Energy, Elsevier, vol. 55(C), pages 417-425.
    6. Bandos, Tatyana V. & Campos-Celador, Álvaro & López-González, Luis M. & Sala-Lizarraga, José M., 2014. "Finite cylinder-source model for energy pile heat exchangers: Effects of thermal storage and vertical temperature variations," Energy, Elsevier, vol. 78(C), pages 639-648.
    7. 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.
    8. 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.
    9. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(5), pages 687-698, October.
    10. 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.
    11. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(3), pages 381-386, June.
    12. 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.
    13. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(4), pages 525-537, August.
    14. Bayer, Peter & de Paly, Michael & Beck, Markus, 2014. "Strategic optimization of borehole heat exchanger field for seasonal geothermal heating and cooling," Applied Energy, Elsevier, vol. 136(C), pages 445-453.
    15. Li, Min & Lai, Alvin C.K., 2013. "Analytical model for short-time responses of ground heat exchangers with U-shaped tubes: Model development and validation," Applied Energy, Elsevier, vol. 104(C), pages 510-516.
    16. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(2), pages 285-292, April.
    17. Lazzarotto, Alberto, 2014. "A network-based methodology for the simulation of borehole heat storage systems," Renewable Energy, Elsevier, vol. 62(C), pages 265-275.
    18. Beck, Markus & Bayer, Peter & de Paly, Michael & Hecht-Méndez, Jozsef & Zell, Andreas, 2013. "Geometric arrangement and operation mode adjustment in low-enthalpy geothermal borehole fields for heating," Energy, Elsevier, vol. 49(C), pages 434-443.
    19. Tye-Gingras, Maxime & Gosselin, Louis, 2014. "Generic ground response functions for ground exchangers in the presence of groundwater flow," Renewable Energy, Elsevier, vol. 72(C), pages 354-366.
    20. 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.
    21. Marcotte, D. & Pasquier, P. & Sheriff, F. & Bernier, M., 2010. "The importance of axial effects for borehole design of geothermal heat-pump systems," Renewable Energy, Elsevier, vol. 35(4), pages 763-770.
    22. Zarrella, Angelo & De Carli, Michele, 2013. "Heat transfer analysis of short helical borehole heat exchangers," Applied Energy, Elsevier, vol. 102(C), pages 1477-1491.
    23. Loveridge, Fleur & Powrie, William, 2013. "Temperature response functions (G-functions) for single pile heat exchangers," Energy, Elsevier, vol. 57(C), pages 554-564.
    24. 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.
    25. Rivera, Jaime A. & Blum, Philipp & Bayer, Peter, 2015. "Analytical simulation of groundwater flow and land surface effects on thermal plumes of borehole heat exchangers," Applied Energy, Elsevier, vol. 146(C), pages 421-433.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Fascì, Maria Letizia & Mazzotti Pallard, Willem & Lazzarotto, Alberto & Claesson, Joachim, 2023. "Temperature of energy boreholes accounting for climate change and the built environment – A new model for its estimation," Renewable Energy, Elsevier, vol. 202(C), pages 1479-1496.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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).
    12. 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).
    13. 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.
    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.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    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. Shibin Geng & Yong Li & Xu Han & Huiliang Lian & Hua Zhang, 2016. "Evaluation of Thermal Anomalies in Multi-Boreholes Field Considering the Effects of Groundwater Flow," Sustainability, MDPI, vol. 8(6), pages 1-19, June.
    7. Bayer, Peter & de Paly, Michael & Beck, Markus, 2014. "Strategic optimization of borehole heat exchanger field for seasonal geothermal heating and cooling," Applied Energy, Elsevier, vol. 136(C), pages 445-453.
    8. Rivera, Jaime A. & Blum, Philipp & Bayer, Peter, 2017. "Increased ground temperatures in urban areas: Estimation of the technical geothermal potential," Renewable Energy, Elsevier, vol. 103(C), pages 388-400.
    9. 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.
    10. Dolf Talman & Zaifu Yang, 2012. "On a Parameterized System of Nonlinear Equations with Economic Applications," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 644-671, August.
    11. Zhiqiang Zheng & Balaji Padmanabhan & Steven O. Kimbrough, 2003. "On the Existence and Significance of Data Preprocessing Biases in Web-Usage Mining," INFORMS Journal on Computing, INFORMS, vol. 15(2), pages 148-170, May.
    12. Herings, P.J.J. & Talman, A.J.J. & Yang, Z.F., 1999. "Variational Inequality Problems With a Continuum of Solutions : Existence and Computation," Other publications TiSEM 73e2f01b-ad4d-4447-95ba-a, Tilburg University, School of Economics and Management.
    13. Carlos R. Handy & Daniel Vrinceanu & Carl B. Marth & Harold A. Brooks, 2015. "Pointwise Reconstruction of Wave Functions from Their Moments through Weighted Polynomial Expansions: An Alternative Global-Local Quantization Procedure," Mathematics, MDPI, vol. 3(4), pages 1-24, November.
    14. Allen C. Goodman & Miron Stano, 2000. "Hmos and Health Externalities: A Local Public Good Perspective," Public Finance Review, , vol. 28(3), pages 247-269, May.
    15. Bode, Sven & Michaelowa, Axel, 2003. "Avoiding perverse effects of baseline and investment additionality determination in the case of renewable energy projects," Energy Policy, Elsevier, vol. 31(6), pages 505-517, May.
    16. Ala, Guido & Fasshauer, Gregory E. & Francomano, Elisa & Ganci, Salvatore & McCourt, Michael J., 2017. "An augmented MFS approach for brain activity reconstruction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 141(C), pages 3-15.
    17. Bettina Campedelli & Andrea Guerrina & Giulia Romano & Chiara Leardini, 2014. "La performance della rete ospedaliera pubblica della regione Veneto. L?impatto delle variabili ambientali e operative sull?efficienza," MECOSAN, FrancoAngeli Editore, vol. 2014(92), pages 119-142.
    18. Haider A. Khan, 2004. "General Conclusions: From Crisis to a Global Political Economy of Freedom," Palgrave Macmillan Books, in: Global Markets and Financial Crises in Asia, chapter 9, pages 193-211, Palgrave Macmillan.
    19. Penn Loh & Zoë Ackerman & Joceline Fidalgo & Rebecca Tumposky, 2022. "Co-Education/Co-Research Partnership: A Critical Approach to Co-Learning between Dudley Street Neighborhood Initiative and Tufts University," Social Sciences, MDPI, vol. 11(2), pages 1-17, February.
    20. Broekhuis, Manda & Vos, Janita F.J., 2003. "Improving organizational sustainability using a quality perspective," Research Report 03A43, University of Groningen, Research Institute SOM (Systems, Organisations and Management).

    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:98:y:2016:i:c:p:50-63. 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.