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A block matrix formulation for efficient g-function construction

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Lazzarotto, Alberto, 2014. "A network-based methodology for the simulation of borehole heat storage systems," Renewable Energy, Elsevier, vol. 62(C), pages 265-275.
    6. 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.
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    Cited by:

    1. 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.
    2. 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.
    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).

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