Optimal discretization of geothermal boreholes for the calculation of g-functions

Abstract

The effect of the discretization of geothermal boreholes on the accuracy of g-function evaluations is studied. A data set of 557,056 bore field configurations covering a large range of geometrical parameters is generated using pygfunction. A nonuniform discretization of borehole segments geometrically expanding in length toward the middle of the borehole is proposed. A nonuniform discretization is shown to achieve better accuracy than a uniform discretization. The nonuniform discretization is optimized to minimize the maximum absolute percentage error over the entire data set. The discretization is optimized for each bore field configuration, and an artificial neural network (ANN) is trained to predict the optimal discretization given only geometrical and thermal parameters of the boreholes, excluding the borehole positions. Thermal parameters that quantify the bore field temperature distribution are introduced as inputs to the ANN. The maximum absolute percentage error using a uniform discretization is 99.0% in the worst studied case of a dense rectangular field of Nb = 1116 boreholes with lengths of 418.8 m and spacings of 3.14 m and 3.18 m along rows and columns, while only 1% of the cases feature an error above 26.7%. The error is reduced to 3.6% using the global optimal discretization and 3.3% using the ANN.