Fast calculation of the <i>g</i>-functions of geothermal borehole fields using similarities in the evaluation of the finite line source solution

Abstract

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.