A finite line source model with Cauchy-type top boundary conditions for simulating near surface effects on borehole heat exchangers

Abstract

BHEs (borehole heat exchangers) are the most common shallow geothermal applications. By approximating the BHE as a line source, semi-analytical models can describe the heat exchange within the ground. These models though always assume prescribed temperature at the ground surface. This work presents a formulation which expands existing finite line source models by implementing a more general Cauchy-type top boundary condition and in this way, a better estimation of the heat fluxes at the ground surface. The new formulation is numerically verified and examined in a dimensionless analysis. It is demonstrated that the discrepancy to prescribed temperature settings is significant near to the ground surface, and it propagates deeper when groundwater flow is absent and when strong decoupling between the thermal regimes interacting at the land surface is assumed. The new approach shows to be suited especially for short BHEs, both for more flexible and accurate prediction of the ground thermal regime as well as for long-term analysis of technological performance.