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A fast convolution-based method to simulate time-varying flow rates in closed-loop and standing column well ground heat exchangers

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  • Beaudry, Gabrielle
  • Pasquier, Philippe
  • Marcotte, Denis

Abstract

The superposition principle is widely used to accelerate the computation of hourly fluid temperatures in ground heat exchangers. This work presents a first attempt at adapting this technique to non-stationary situations of ground-source heat pump operations that involve time-variant parameters, such as flow rates. An advanced response model is first employed to evaluate the outlet temperature signals corresponding to different sets of constant operating conditions. The transitions are then considered by combining the functions linearly and by using a scaled correction function. Eight synthetic validation studies were conducted, representing the dynamic operation of a closed-loop and a standing column well with time-variant circulation, pumping, and discharge rates, and groundwater velocities. It is shown that the developed method reproduces reference numerical results with mean absolute and relative errors that are lower than 0.04°C and 0.68%, respectively, and achieves a 30-day simulation with a 5-min time step in a few hundredths of a second. This represents a reduction of five to seven orders of magnitude in computing times and demonstrates the potential of the proposed method to accelerate the simulation of ground heat exchangers that operate with time-variant flow rates.

Suggested Citation

  • Beaudry, Gabrielle & Pasquier, Philippe & Marcotte, Denis, 2021. "A fast convolution-based method to simulate time-varying flow rates in closed-loop and standing column well ground heat exchangers," Renewable Energy, Elsevier, vol. 174(C), pages 55-72.
    • Handle: RePEc:eee:renene:v:174:y:2021:i:c:p:55-72
    DOI: 10.1016/j.renene.2021.04.045
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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).
    4. Nguyen, A. & Pasquier, P. & Marcotte, D., 2015. "Thermal resistance and capacity model for standing column wells operating under a bleed control," Renewable Energy, Elsevier, vol. 76(C), pages 743-756.
    5. De Carli, Michele & Tonon, Massimo & Zarrella, Angelo & Zecchin, Roberto, 2010. "A computational capacity resistance model (CaRM) for vertical ground-coupled heat exchangers," Renewable Energy, Elsevier, vol. 35(7), pages 1537-1550.
    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. Beaudry, Gabrielle & Pasquier, Philippe & Marcotte, Denis & Zarrella, Angelo, 2022. "Flow rate control in standing column wells: A flexible solution for reducing the energy use and peak power demand of the built environment," Applied Energy, Elsevier, vol. 313(C).
    2. Li, Yahui & Sun, Yuanyuan & Wang, Qingyan & Sun, Kaiqi & Li, Ke-Jun & Zhang, Yan, 2023. "Probabilistic harmonic forecasting of the distribution system considering time-varying uncertainties of the distributed energy resources and electrical loads," Applied Energy, Elsevier, vol. 329(C).
    3. Cimmino, Massimo, 2024. "g-Functions for fields of series- and parallel-connected boreholes with variable fluid mass flow rate and reversible flow direction," Renewable Energy, Elsevier, vol. 228(C).

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