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

Abstract

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 developed three-points method. The borehole field is sorted in increasing distance categories, each being simulated 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 temperature. The global model calculation time and accuracy were evaluated. The thermal response factor calculation for a square field of 26×26 boreholes for one simulated year took 4s, 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 1min. 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.