A global model for fast calculation of the thermal response factor of large-scale boreholes heat exchangers combining the FLS model, the 2D heat equation and a three-points method

In order to progress towards more energy efficient buildings, vertical ground coupled heat pumps are a promising solution. Optimisation of both the design and operation of boreholes heat exchangers is a key factor to reduce energy consumption of such systems. This requires a fast evaluation of the thermal response factor of the ground heat exchanger, particularly if it contains numerous boreholes and operates for multiple years. To overcome this challenge, this article reports a new global model combining the finite line source (FLS) model, the two-dimensional (2D) heat conduction equation, and a newly devel-oped three-points method. The borehole field is sorted in increasing distance categories, each being sim-ulated with varying timesteps. The 2D heat conduction equation is used to determine: 1) when the detailed calculation needs to be performed; and 2) the growth of the timestep. A three-points method avoiding double integration of the temperature profiles is proposed to evaluate the borehole wall temper-ature. The global model calculation time and accuracy were evaluated. The thermal response factor cal-culation for a square field of 26 x 26 boreholes for one simulated year took 4 s, showing a calculation time reduction factor of around 1,000,000, and relative errors smaller than 2 % compared to the original FLS model with superposition principle. For 20 simulated years, the proposed model took only 1 min. It is appropriate for various boreholes configurations. Its features such as accuracy, speed and load -independency are essential for its integration into building energy simulation tools.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This article introduces a new global model for evaluating the thermal response factor of vertical ground coupled heat pumps. The model combines the finite line source model, the two-dimensional heat conduction equation, and a newly developed three-points method. It enables fast and accurate calculation of the thermal response factor for different borehole configurations, with high efficiency and accuracy.