A novel three-dimensional implicit numerical model of a borehole field heat exchanger that accounts for seasonal fluctuations of the soil temperature

This study proposes a new three-dimensional implicit numerical model to simulate a borehole field heat exchanger that accounts for seasonal fluctuations of the soil temperature. The model uses an alternatingdirection implicit finite difference approach to perform the simulation. The effect of seasonal changes in the soil temperature is considered using an internal heat source term in the governing equations. The model is validated against several published in-situ tests as well as a laboratory experimental study and the results obtained from a TRNSYS version of the duct storage (DST) model, demonstrating an average error of less than 3%. The validated model is then applied to analyse the impact of accounting for seasonal soil temperature fluctuations at various borehole lengths and climate zones. This analysis compares the results obtained from a model that uses constant temperature boundary conditions against those from a model that contains the internal heat source term and uses adiabatic boundary conditions. A significant discrepancy between the outputs of the two models has been observed for shallow borehole heat exchangers (H 60 m) and at locations with a high annual amplitude of the surface temperature variations (Delta Ta 5 degrees C). Thus, the assumption of constant temperature at the ground surface is only appropriate for deep boreholes (H > 60 m) or at locations with a relatively low annual amplitude of the surface temperature variations (Delta Ta < 5 degrees C).