Numerical methods are proposed for the efficient evaluation of the g-functions of geothermal bore fields using the finite line source solution. The presented methods reduce the calculation time for the calculation of g-functions by reducing the number of numerical evaluations of the analytical finite line source solution. A similarity identification method is presented to identify pairs of boreholes for which the finite line source solution takes the same value. A load history reconstruction method is presented to evaluate the g-function at non-uniform time-steps. Using the proposed numerical methods, the calculation time for the g-function of a rectangular field of 12 × 12 boreholes is reduced by a factor 308. The numerical methods allow the evaluation of g-functions of bore fields with large amounts of boreholes in irregular configurations. The g-function of a field of 512 randomly positioned boreholes is calculated in 27 minutes.

A semi-analytical method for the calculation of g-functions of bore fields with mixed arrangements of series- and parallel-connected boreholes is presented. Borehole wall temperature variations are obtained from the temporal and spatial superposition of the finite line source (FLS) solution. The FLS solution is coupled to a quasi-steady-state solution of the fluid temperature profiles in the boreholes, considering the piping connections between the boreholes. The dimensionless borehole wall temperatures in the bore field and the inlet fluid temperature are obtained from the simultaneous solution of the heat transfer inside and outside the boreholes. The effective borehole wall temperature, i.e. the g-function, is defined based on the dimensionless inlet fluid temperature and a newly introduced effective bore field thermal resistance. The g-function evaluation method is validated against the DST model and its use is demonstrated in a sample simulation of a seasonal thermal energy storage system.

A model for the simulation of geothermal systems with parallel- and series-connected boreholes is presented. Mass and heat balance problems are formulated for each component in the system and are assembled into system-level problems. A third problem is formulated to account for heat transfer in the bore field, using the finite line source solution. This third problem is coupled to the system-level heat balance problem by an analytical solution of the heat transfer inside boreholes with multiple U-tubes. The simulation model allows for any number of independent fluid loops within the bore field or within individual boreholes and allows for combinations of specified inlet fluid temperatures and heat extraction rates in independent fluid loops. The model accounts for the axial variation of the fluid and borehole wall temperatures and heat extraction rates. The capabilities of the model are demonstrated through three example simulations.

Model Predictive Control (MPC) predictive’s nature makes it attractive for controlling high-capacity structures such as thermally activated building systems (TABS). Using weather predictions in the order of days, the system is able to react in advance to changes in the building heating and cooling needs. However, this prediction horizon window may be sub-optimal when hybrid geothermal systems are used, since the ground dynamics are in the order of months and even years. This paper proposes a methodology that includes a shadow-cost in the objective function to take into account the long-term effects that appear in the borefield. The shadow-cost is computed for a given long-term horizon that is discretized over time using predictions of the building heating and cooling needs. The methodology is applied to a case with only heating and active regeneration of the ground thermal balance. Results show that the formulation with the shadow cost is able to optimally use the active regeneration, reducing the overall operational costs at the expenses of an increased computational time. The effects of the shadow cost long-term horizon and the predictions accuracy are also investigated.

A new method is presented to evaluate thermal interactions between vertical geothermal boreholes. The finite line source (FLS) solution is extended to consider thermal interactions between groups of boreholes. Groups of boreholes that share similar temperatures and heat extraction rates are identified using hierarchical agglomerative clustering, and each group is represented in the model as a single equivalent borehole. Each equivalent borehole is split into segments, and temporal and spatial superposition of the FLS solution are employed to calculate the total temperature change along the length of the equivalent boreholes. The new method is shown to provide an accurate calculation of the g-function, with a mean absolute percentage error below 0.612% on the g-functions of regular borefields of up to 144 boreholes using only 3 to 5 equivalent boreholes. Calculation times are significantly reduced: the g-function of a borefield of 1024 randomly positioned boreholes is calculated in 3.65 s.