The temperature penalty approach to the design of borehole heat exchangers for heat pump applications

Borehole heat exchangers (BHEs) are the most frequently adopted solution for ground coupled heat pump applications. In most installations, BHEs also represent the most important cost item, and a careful design analysis is needed to either assure long time performance or reduce the payback period, both parameters related to overall BHE length. The most efficient way, from a computational point of view, to predict the temperature evolution in time and space of a ground volume in contact with a system of BHE, is the recursive calculation of a basic thermal response factor, evaluated at different time steps and for given different heat pulses representing the building energy demand. Among the literature models, the Ashrae standard is the most simple method based on the above approach and it does not require, in principle, a dedicated computer code to solve the BHE sizing problem. In this paper a review of the existing response factor models for BHE analysis is performed and a new description of the Ashrae method is provided. In particular the real meaning of the temperature penalty parameter, fundamental in the Ashrae standard calculation, is clearly explained and a direct method for calculating the long-term effective ground resistance is given. The method is also able to take into account the geometrical disposition of multiple BHE at given overall length.