Transient Thermal Resistance of Borehole Heat Exchangers for Hourly Simulations of Geothermal Heat Pumps Systems

The correct design of borehole fields requires the correct evaluation of the transient ground thermal response in time, but also the accurate estimation of the borehole (BHE) thermal resistance, expecially the grout contribution. Generally, the borehole thermal resistance is considered as steady-state; however, when considering the borefield hourly response to the building variable thermal loads, also the transient behavior of the grout thermal resistance plays an important role, which is quite often neglected. This study analyzes, with a dimensionless approach, the transient grout thermal resistance, with particular attention devoted to the effect of the boundary condition imposed to the internal tubes, namely imposed heat flux, imposed temperature and imposed convective coefficient, the last being the real operating conditions. In addition, the effects of grout to ground thermophysical properties and of shank spacing are analysed. The steady state numerical results are also compared with literature correlations. Finally, numerical evidences are given to demonstrate that the usual approach of calculating the overall BHE resistance just summing the grout resistance, numerical obtained by imposing a temperature on the tube surface, to the convective one can lead to meaningful errors at low Biot numbers.