Full-time-scale fluid-to-ground thermal response of a borefield with uniform fluid temperature

The most accurate method for the design and the simulation of a borehole heat exchanger (BHE) field is employing the fluid-to-ground thermal response of the field, namely the mean-fluid-temperature rise produced by a time-constant thermal power supplied to the fluid. Usually, a short-term and a long-term model are applied, with results matched at a selected time instant. In this paper we propose a method to determine the full-time-scale thermal response of a BHE field that employs one numerical model and yields accurate results with a reasonable computation time. Each BHE is modeled as a one-material cylinder with the same radius as the BHE, surrounded by the ground and containing a heat-generating cylindrical surface whose temperature represents that of the fluid. The condition of uniform fluid temperature and time-constant total power supplied to the fluid, necessary for the long-term accuracy, is obtained iteratively, by imposing at the generating surface uniform time-dependent temperatures that converge to the desired condition. A 2 × 2 square BHE field is employed as an example. The method is recommended to obtain the thermal response of a BHE field with uniform fluid temperature, with high accuracy both in the short and in the long term.