Development and validation of a full-time-scale semi-analytical model for the short- and long-term simulation of vertical geothermal bore fields

This paper presents the development and validation of a full-time-scale semi-analytical bore field simulation model. The model allows for the simulation of bore fields comprised of arbitrarily positioned boreholes while accounting for both short-term transient thermal effects within the boreholes and long-term thermal interactions in the bore field. The g-function of the bore field, obtained from the finite line source solution, is corrected to account for the cylindrical geometry of the boreholes and coupled to a thermal resistances and capacitances model of the borehole interior, thereby extending the scope of g-functions to short time scales. Additionally, an improved load aggregation scheme for ground thermal response calculations allows the model to be used with variable simulation time steps. The complete model is validated using a combination of analytical, experimental and field monitored data to verify both its short-term and long-term behaviour. The model is implemented using the Modelica language as part of an implementation in the open-source buildings simulation library IBPSA.