IDEAS home Printed from https://ideas.repec.org/a/eee/renene/v121y2018icp249-260.html
   My bibliography  Save this article

A block matrix formulation for efficient g-function construction

Author

Listed:
  • Dusseault, Bernard
  • Pasquier, Philippe
  • Marcotte, Denis

Abstract

A compact block matrix formulation allowing fast construction of the g-function of a ground heat exchanger is presented. This new formulation is nor sequential nor iterative, doesn't require use of Laplace or Fourier transform and provides a g-function by solving a single system of linear equations assembled in a block matrix system. A method to accelerate the integration of the finite-line source model based on Chebyshev polynomials is also introduced. Although it suffers from a fixed cost in terms of computational time, this approach allows to speed up the g-function assessment even further when used jointly with the block matrix formulation on large fields. By using both strategies, constructing the g-function of a ground heat exchanger composed of 50 regularly spaced boreholes can be achieved in less than half-second while committing only a small relative error. The speed and compactness of the block matrix formulation could be useful to design ground heat exchangers with optimization-based algorithms, which can require the assessment of several thousand g-functions.

Suggested Citation

  • Dusseault, Bernard & Pasquier, Philippe & Marcotte, Denis, 2018. "A block matrix formulation for efficient g-function construction," Renewable Energy, Elsevier, vol. 121(C), pages 249-260.
    • Handle: RePEc:eee:renene:v:121:y:2018:i:c:p:249-260
    DOI: 10.1016/j.renene.2017.12.092
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096014811731296X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.renene.2017.12.092?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. Lazzarotto, Alberto & Björk, Folke, 2016. "A methodology for the calculation of response functions for geothermal fields with arbitrarily oriented boreholes – Part 2," Renewable Energy, Elsevier, vol. 86(C), pages 1353-1361.
    2. Retkowski, Waldemar & Thöming, Jorg, 2014. "Thermoeconomic optimization of vertical ground-source heat pump systems through nonlinear integer programming," Applied Energy, Elsevier, vol. 114(C), pages 492-503.
    3. Lazzarotto, Alberto, 2016. "A methodology for the calculation of response functions for geothermal fields with arbitrarily oriented boreholes – Part 1," Renewable Energy, Elsevier, vol. 86(C), pages 1380-1393.
    4. Lamarche, Louis, 2009. "A fast algorithm for the hourly simulations of ground-source heat pumps using arbitrary response factors," Renewable Energy, Elsevier, vol. 34(10), pages 2252-2258.
    5. Marcotte, D. & Pasquier, P., 2014. "Unit-response function for ground heat exchanger with parallel, series or mixed borehole arrangement," Renewable Energy, Elsevier, vol. 68(C), pages 14-24.
    6. Lazzarotto, Alberto, 2014. "A network-based methodology for the simulation of borehole heat storage systems," Renewable Energy, Elsevier, vol. 62(C), pages 265-275.
    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. Anjan Rao Puttige & Staffan Andersson & Ronny Östin & Thomas Olofsson, 2020. "A Novel Analytical-ANN Hybrid Model for Borehole Heat Exchanger," Energies, MDPI, vol. 13(23), pages 1-19, November.
    2. Nguyen, A. & Pasquier, P., 2021. "A successive flux estimation method for rapid g-function construction of small to large-scale ground heat exchanger," Renewable Energy, Elsevier, vol. 165(P1), pages 359-368.
    3. 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).

    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. 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.
    2. 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.
    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. Marcotte, D. & Pasquier, P., 2014. "Unit-response function for ground heat exchanger with parallel, series or mixed borehole arrangement," Renewable Energy, Elsevier, vol. 68(C), pages 14-24.
    5. Anjan Rao Puttige & Staffan Andersson & Ronny Östin & Thomas Olofsson, 2020. "A Novel Analytical-ANN Hybrid Model for Borehole Heat Exchanger," Energies, MDPI, vol. 13(23), pages 1-19, November.
    6. Nguyen, A. & Pasquier, P., 2021. "A successive flux estimation method for rapid g-function construction of small to large-scale ground heat exchanger," Renewable Energy, Elsevier, vol. 165(P1), pages 359-368.
    7. 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.
    8. 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.
    9. Guo, Y. & Huang, G. & Liu, W.V., 2023. "A new semi-analytical solution addressing varying heat transfer rates for U-shaped vertical borehole heat exchangers in multilayered ground," Energy, Elsevier, vol. 274(C).
    10. 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.
    11. 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.
    12. Fossa, Marco & Priarone, Antonella, 2019. "Constant temperature response factors for fast calculation of sparse BHE field g-functions," Renewable Energy, Elsevier, vol. 131(C), pages 1236-1246.
    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. Paludetto, Delphine & Lorente, Sylvie, 2016. "Modeling the heat exchanges between a datacenter and neighboring buildings through an underground loop," Renewable Energy, Elsevier, vol. 93(C), pages 502-509.
    15. Başer, Tuğçe & McCartney, John S., 2020. "Transient evaluation of a soil-borehole thermal energy storage system," Renewable Energy, Elsevier, vol. 147(P2), pages 2582-2598.
    16. Dusseault, Bernard & Pasquier, Philippe, 2021. "Usage of the net present value-at-risk to design ground-coupled heat pump systems under uncertain scenarios," Renewable Energy, Elsevier, vol. 173(C), pages 953-971.
    17. 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.
    18. Parrales, Arianna & Colorado, Dario & Huicochea, Armando & Díaz, Juan & Alfredo Hernández, J., 2014. "Void fraction correlations analysis and their influence on heat transfer of helical double-pipe vertical evaporator," Applied Energy, Elsevier, vol. 127(C), pages 156-165.
    19. Sebarchievici, Calin & Sarbu, Ioan, 2015. "Performance of an experimental ground-coupled heat pump system for heating, cooling and domestic hot-water operation," Renewable Energy, Elsevier, vol. 76(C), pages 148-159.
    20. Yong Li & Shibin Geng & Xu Han & Hua Zhang & Fusheng Peng, 2017. "Performance Evaluation of Borehole Heat Exchanger in Multilayered Subsurface," Sustainability, MDPI, vol. 9(3), pages 1-16, March.

    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:121:y:2018:i:c:p:249-260. 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.