Analytical model for short-time responses of ground heat exchangers with U-shaped tubes: Model development and validation

Short-time responses of borehole ground heat exchangers (GHEs) are difficult to predict because they involve heat capacity effect and various arrangements of U-shaped tubes within boreholes. To meet this engineering challenge, this paper builds a composite-medium line-source model. The central idea of the new model is that the downward and upward channels of U-shaped tubes (not the borehole) are approximated as line sources or sinks of heat placed in a composite medium. This approach can account for not only the influence of the heat capacity of grouting material but also the difference between properties of soil and grout, whilst it is flexible enough to model various U-pipe configurations. The new composite-medium model is validated by using a reported laboratory experiment; it can yield predictions matching the experimental response profiles with acceptable accuracy for times as short as 5 min. Several uncertainties which may contribute to discrepancies between the model prediction and the laboratory data are analyzed, including heat input rate, thermal conductivities and heat capacities of the composite medium. The potential errors caused by these uncertainties are comparable to the observed discrepancies.