Thermal interactions in large irregular fields of geothermal boreholes: the method of equivalent boreholes

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.